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Vehicle structural design strategies for enhanced safety in side impact collision Asadkarami, Ali 2007

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V E H I C L E STRUCTURAL DESIGN STRATEGIES FOR ENHANCED SAFETY IN SIDE IMPACT COLLISIONS by A L I A S A D K A R A M I B . S c , Iran University of Science and Technology, 2002 A T H E S I S S U B M I T T E D IN P A R T I A L F U L F I L L M E N T O F T H E R E Q U I R E M E N T S F O R T H E D E G R E E O F D O C T O R O F P H I L O S O P H Y in T H E F A C U L T Y O F G R A D U A T E S T U D I E S (Mechanical Engineering) T H E U N I V E R S I T Y O F B R I T I S H C O L U M B I A August 2007 © A l i Asadkarami, 2007 A B S T R A C T One of the major challenges for automotive engineers is to provide adequate protection to motor vehicle occupants involved in side impact collisions. Although, side impacts are less frequent than frontals, to both the occupant and vehicle designer they are as serious because the number and severity of injuries per accident is greater. The objective of the current research work is to develop an approach to optimize the vehicle structure for side impact collisions and provide recommendations to enhance vehicle structural design. To achieve the above objectives, this research study was broken into five phases: Phase 1) A side impact finite element simulation package was developed as an analysis tool for use in this research. As such, this phase discusses the development and verification of the finite element simulation package based on FMVSS-214 standard compliance test configuration utilizing the LS-DYNA software. This package consists of finite element model of a U.S. Moving Deformable Barrier (MDB), a US Side Impact Dummy (SID) , and a target vehicle ( 1990 Ford Taurus), Phase 2) The previously developed simulation package was utilized to investigate the effect of the collision parameters on the occupant injury likelihood within this phase, Phase 3) A new criterion was developed and verified which simplifies the numerical analyses such that they are computationally cost effective, Phase 4) The critical vehicle structural components in providing side impact crashworthiness were identified, and the effects of their stiffness on the occupant injury likelihood were investigated within this phase, and Phase 5) The results of the previous phases were utilized in this phase to develop a strategy for optimizing the stiffness of the side structure elements, thus minimizing the injury likelihood. The results of this study demonstrated a successful example of the developed state-of-the-art strategy to optimize the vehicle structure to improve side impact crashworthiness. This new strategy is a significant contribution of this research, and improves upon the current design strategy in two ways: 1) this new approach recognizes the effects of the collision parameters on the occupant injury likelihood and addresses their effect on the optimization of the vehicle structure for side impact collisions, and 2) the developed strategy improves the efficiency of the design analysis tools by utilizing a new developed criterion for assessing the vehicle structural side impact crashworthiness. The development and verification of this criterion is also a significant contribution of this research, which could substantially improve the efficiency of the design process and thus should be of benefit to vehicle designers especially early in the vehicle design process. This work also provides insight information for vehicle regulators by substantiating the relative effect of various key collision parameters on the risk of occupant injury in side impact collisions in North America. - i i i -Table of contents Abstract ii List of Tables viii List of Figures ix Abbreviations and Acronyms xiii Acknowledgements xvi Co-Authorship statement xvii Chapter 1. Introduction 1 Chapter 2. Literature review 8 2.1. Introduction 8 2.2. The side impact phenomena 10 2.3. Occupant loading in side impact collisions 11 2.4. Typical occupant injuries in side impact collisions 13 2.4.1. Head injuries IS 2.4.2. Thorax injuries 14 2.4.3. Abdomen injuries 15 2.4.4. Pelvis injuries 15 2.5. Current side impact standards and evaluation procedures 16 2.5.1. National Highway Traffic and Safety Administration (NHTSA) 16 2.5.2. Canadian Motor Vehicle Safety Standard (CMVSS) for side impacts 19 2.5.3. European Union Directive 20 2.6. Anthropomorphic Test Device ( A T D ) 21 2.6.1. The Side Impact Dummy (SID) 23 2.6.2. EUROSID-1 26 2.6.3. Biofidelic Side Impact Dummy (BIOSID) 28 2.6.4. WorldSID 28 2.7. Side impact performance improvement strategies 29 - iv -2.7.1. Vehicle side structure 30 2.7.2. Interior structure and padding system 38 2.7.3. Side impact air bags 39 2.8. Summary and conclusions 40 Chapter 3. Development and validation of the finite element models 42 3.1. Introduction 42 3.2. N H T S A Moving Deformable Barrier ( M D B ) 43 3.2.1. Development of the UBC Simplified NHTSA MDB model 45 3.2.2. Validation of the UBC Simplified NHTSA MDB model 46 3.3. U S Side Impact Dummy (SID) 48 3.3.1. Sled test of the US SID 49 3.3.2. SID standard calibration tests 56 3.4. Finite Element Vehicle Model 63 3.5. Summary and conclusions - Phase 1 64 Chapter 4. Collision parameter effects on occupant injury in side impact collisions 65 4.1. Introduction 65 4.2. Side impact simulations 66 4.2.1. Simulation procedures 66 4.2.2. Simulation results 68 4.3. Summary and conclusions - Phase 2 81 Chapter 5. Side structure performance criterion (SSPC) 84 5.1. Introduction 84 5.2. Proposed new index - side structure performance criterion (SSPC) 85 5.2.1. SSPC calculation 88 5.3. SSPC verification 93 5.3.1. The effect of MDB velocity variations on the SSPC 93 5.3.2. The effect of MDB vertical position variations on the SSPC 95 5.3.3. The effect of MDB horizontal position variations on the SSPC 97 5.3.4. The effect of MDB mass variations on the SSPC 99 5.4. Discussion 100 5.5. Summary and conclusions -Phase 3 103 - v -Chapter 6. Parametric study of the vehicle side structure 106 6.1. Introduction 106 6.2. Design of computer experiments 107 6.2.1. Grid-based Optimal Design Method 109 6.3. Structural parameters and numerical experiments setup 111 6.4. SSPC estimation 114 6.4.1. Artificial neural network estimation 115 6.4.2. Full quadratic response surface estimation 119 6.5. The effects of vehicle structural parameters on the sspc 121 6.6. SSPC Response as a function of structural and collision parameters 124 6.7. Summary and conclusions - Phase 4 126 Chapter 7. Calculation of injury risk and optimization of the vehicle side structure... 128 7.1. Introduction 128 7.2. Calculation of injury risk 130 7.3. Assessing the stochastic distribution of the collision parameters 133 7.4. Reliability analysis based on the acquired collision parameters 136 7.4.1. Monte Carlo method 138 7.4.2. Numerical experiment setup for P(Injp> 3%) 138 7.4.3. Estimation of the probability of injury likelihood exceeding 3% 139 7.5. Optimization of the vehicle side structure 141 7.6. Summary and conclusions- Phase 5 146 Chapter 8. Discussion, conclusions and potential future work 148 Chapter 9. References 168 Appendix A. Parametric study database - side structure thickness - SSPC database 179 Appendix B. Reliability analysis database - side structure thickness - probability of serious injury database 187 Appendix C. Target vehicle - 1990 Ford Taurus - specifics 195 Appendix D. Target vehicle - 1990 Ford Taurus - material properties (LS-DYNA version 970): 196 - v i -Appendix E. The SID material properties (LS-DYNA version 970): 224 Appendix F. The MDB material properties (LS-DYNA version 970): 229 - vn -L I S T O F T A B L E S Table 2-1: Occupants involved in single or multiple vehicle collisions 9 Table 2-2: NHTSA's dynamic performance requirements for side impact 19 Table 2-3: Abbreviated Injury Scale (AIS) 23 Table 3-1: Lateral impact thorax performance of L S - D Y N A US SID 60 Table 3-2: Pelvis response in the standard pelvis calibration test of L S - D Y N A US SID 62 Table 4-1: Range of simulation collision parameters and FMVSS-214 values 67 Table 5-1: Correlation between M D B velocity and injury measures with SSPC 94 Table 5-2: Correlation between M D B C G height and injury measures with SSPC 96 Table 5-3: Correlation between the M D B horizontal position and injury measures with the SSPC 97 Table 5-4: Correlation between the M D B mass and injury measures with the SSPC 99 Table 6-1: Important structural components of the target vehicle during a side impact 107 Table 6-2: Lower and upper bounds of the side structure components thickness variation 113 Table 6-3: A selected region of the side structure thickness - SSPC database 114 Table 7-1: A sample of the side structure thickness - probability of serious injury database 139 Table 7-2: verification of the optimization process with R E L A N results 143 Table 7-3: Comparison between the calculated optimum thicknesses based on FMVSS-214 test condition and with the effect of collision parameters considered 145 Table C - l : The target vehicle specifics 193 - v i i i -L I S T O F F I G U R E S Figure 2-1: Illustration of typical side impact crash 11 Figure 2-2: Door, torso and vehicle velocities in atypical side impact 12 Figure 2-3: Front view schematic of the human ribcage 14 Figure 2-4: FMVSS side impact test configuration 18 Figure 2-5: The correlation between the TTl and the probability of injury 25 Figure 2-6: Structural elements of a typical vehicle 31 Figure 2-7: Relative performance of "stiff' versus "compliant" vehicle side structure 31 Figure 2-8: Desired velocity profile of the vehicle side structure 37 Figure 3-1: Moving Deformable Barrier specification 44 Figure 3-2: M D B barrier face specifications 44 Figure 3-3: U B C Simplified FE model of the NHTSA moving deformable barrier (MDB) 45 Figure 3-4: Side view of the simplified M D B deformation 46 Figure 3-5: NHTSA M D B center of gravity velocity 47 Figure 3-6: NHTSA M D B center of gravity acceleration 48 Figure 3-7: a.) M A D Y M O US SID dummy at the start of the analysis (t = 0); b.) M A D Y M O U S SID dummy at t = 35 ms 50 Figure 3-8: a.) L S - D Y N A U S SID dummy at the beginning of the analysis (t = 0); b.) L S - D Y N A U S SID dummy at t = 35 ms into the analysis 52 Figure 3-9: SID Model verification results: Lower spine acceleration 53 Figure 3-10: SID Model verification results: Upper thorax acceleration 53 Figure 3-11: SID Model verification results: Lower thorax acceleration 54 Figure 3-12: SID Model verification results: Upper spine acceleration 54 Figure 3-13: SID Model verification results: Pelvic acceleration 55 Figure 3-14: Pendulum thorax test setup 57 - ix -Figure 3-15: position of pendulum test accelerometers and SID midsagittal plane 58 Figure 3-16: SID Thorax calibration test: Lower spine lateral acceleration 59 Figure 3-17: Thorax calibration test: Upper thorax lateral acceleration time history 59 Figure 3-18: Thorax calibration test: Lower spine lateral acceleration time history 60 Figure 3-19: L S - D Y N A SID Model: Pelvis pendulum test setup 61 Figure 3-20: L S - D Y N A SID Model: H-Point position in SID 62 Figure 3-21: Ford Taurus finite element model 63 Figure 4-1: M D B position variation with respect to the target vehicle : 68 Figure 4-2: The TT1 variation of US SID with M D B velocity 69 Figure 4-3: The Peak lateral pelvic acceleration variation of US SID with M D B velocity 69 Figure 4-4: Door deformation time history for impact velocities of 51.3 km/hr and 59.4 km/hr 70 Figure 4-5: The TTI variation of US SID with M D B bumper height 72 Figure 4-6: The Peak lateral pelvic acceleration variation of US SID with M D B bumper height 72 Figure 4-7: Door deformation time histories for M D B height of 480 mm and 600 mm above the pavement. 73 Figure 4-8: The TTI variation of US SID with horizontal position of side impact 76 Figure 4-9: The peak lateral pelvic acceleration variation of US SID with horizontal position of side impact 77 Figure 4-10: Door deformation time histories for M D B horizontal positions of 790 mm and 1090 mm from front wheelbase centreline : 77 Figure 4-11: The effect of M D B mass on the TTI level in side collisions 79 Figure 4-12: The effect of M D B mass on the peak lateral pelvic acceleration in side collisions 79 Figure 4-13: Deformation and contact duration of M D B and the door with the US SID for M D B mass = 1350 kg 80 Figure 4-14: Deformation and contact duration of M D B and the door with the US SID for M D B mass = 1890 kg 81 Figure 5-1: Schematic of the geometry elements utilized in defining the SSPC 86 Figure 5-2: The door nodes which are in contact with thorax area 89 - x -Figure 5-3: The door nodes which are in contact with pelvis area 89 Figure 5-4: Deformation of the nodes in contact with the thorax (FMVSS-214 test condition) 90 Figure 5-5: Velocity of the nodes in contact with the thorax (FMVSS-214 test condition) 90 Figure 5-6: Deformation of the nodes in contact with the pelvis (FM VSS-214 test condition) 91 Figure 5-7: Velocity of the nodes in contact with the pelvis (FMVSS-214 test condition) 92 Figure 5-8: Typical SSPC, history curve for one of the nodes (node # 918) - FMVSS-214 test condition 92 Figure 5-9: Correlation between SSPCmax and maximum normalized injury measure with varying M D B velocity 94 Figure 5-10: Correlation between SSPCmax and maximum normalized injury measure with varying M D B CG height 96 Figure 5-11: Correlation between the SSPCmax and the maximum normalized injury measure with varying M D B horizontal position 98 Figure 5-12: Correlation between SSPCmax and maximum normalized injury measure with varying M D B mass 100 Figure 5-13: Correlation between the SSPC and the TTI/85 101 Figure 6-1: A grid-based optimal design for two design variables 110 Figure 6-2: Door components as defined in this research 111 Figure 6-3: Vehicle side structural elements 111 Figure 6-4: A typical multilayer back propagation neural network 116 Figure 6-5: Estimated SSPC with Neural Network method versus 118 Figure 6-6: Estimated SSPC with full quadratic response surface versus actual SSPC calculated from FE analysis 121 Figure 6-7: SSPC versus normalized thickness of the structural components loaded in bending 122 Figure 7-1 TTI versus injury risk 131 Figure 7-2: Cumulative distribution of side impact collision velocity within U.S 135 Figure 7-3: Cumulative distribution of striking vehicle mass in side collisions within U.S 135 Figure 7-4: Cumulative distribution of striking vehicle's height in side collisions within U.S 136 - xi -ure 7-5: Estimated probability of injury likelihood exceeding 3% with full quadratic response surface versus actual P(Injp> 3%) calculated from R E L A N analysis 141 ure C - l : Target vehicle model (i.e. 1990 Ford Taurus) 194 - xii -A B B R E V I A T I O N S A N D A C R O N Y M S A A A M American Association for Automotive Medicine AIS Abbreviated Injury Scale A M A American Medical Association A P F Abdomen Performance Criterion A T D Anthropomorphic Test Device B C British Columbia, Canada BIOSID Biofidelic Side Impact Dummy C A E Computer Aided Engineering C A L 3 D General purpose transient dynamic finite element software program C F C Channel Frequency of Class C G Centre of Gravity C M V S S Canadian Motor Vehicle Safety Standard C P U Central Processing Unit D O E Design O f Experiments method E E V C European Enhanced Vehicle-safety Committee E C E Economic Commission for Europe E U European Union E U R O S I D European Side Impact Dummy F A R S Fatal Accident Reporting System database F E A Finite Element Analysis F M V S S U.S . Federal Motor Vehicle Safety Standard H P C Head Performance Criterion Hybrid II, III Standard crash test dummies as used by automotive testing I C B C Insurance Corporation of British Columbia Injp Occupant injury probability ISO International Organization for Standardization L S - D Y N A General purpose transient dynamic finite element software program developed by L S T C L S T C Livemore Software Technology Software M A D Y M O Mathematical Dynamic Models developed by T N O Automotive Mass std Standard mass M D B Moving Deformable Barrier - x i i i -N H T S A U.S . National Highway Traffic Administration N C A C U.S . National Crash Analysis Centre P v E L A N General purpose reliability software developed at the University of British Columbia R D C Rib Deflection Criteria R I B Y Maximum absolute value of acceleration of rib on struck side in lateral direction S A E Society of Automotive Engineers SID U S Side Impact Dummy SSPC Side Structure Performance Criterion S S P C t Thorax Side Structure Performance Criteria SSPCp Pelvic Side Structure Performance Criteria SSPCa Side Structure Performance Criterion value for the unaltered structure and So geometry of the target vehicle PSPF Pubic Symphysis Peak Force P y Peak lateral pelvic acceleration P(Injp> 3%) Probability of injury likelihood exceeding 3% TTI Thoracic Trauma Index T12 Maximum absolute value of acceleration of the twelfth thoracic vertebrae, in the lateral direction U B C University of British Columbia V * C Viscous Criteria WorldSID World Side Impact Dummy c Acceleration limit at each region of the intruding door (based on occupant body tolerance) 3D Three dimensions G Gravitational acceleration of bodies, Equal to 9.81 m/s H Normalized M D B horizontal position H M D B M D B height V MDB M D B velocity d0 Initial distance (lateral-component) between occupant and interior door structure dc Lateral displacement of the struck vehicle's centre of gravity (CG) M Normalized M D B mass ta Time when the initial contact between M D B and bullet vehicle starts B-pillar thickness - xiv -lUD Upper door thickness 1LD Lower door thickness 1 DR Door rail thickness 1 RP Rocker panel thickness h Floor pan thickness h Roof thickness R Performance function S Normalized M D B speed V Velocity (lateral-component) of the point on the interior structure V Normalized M D B C G height M Statistical mean value Statistical standard deviation - X V -A C K N O W L E D G E M E N T S The author would like to express his deepest gratitude to Dr. Douglas P. Romi l ly who not only served as his supervisor but also encouraged and challenged him throughout his academic program. The author is indebted to the faculty members, Dr. Ricardo Foschi, Dr. Reza Vaz i r i and Dr. Peter Cripton whom provided help, comments, and encouragement in the preparation of this dissertation. Appreciation and thanks are given to my father, Asad Asadkarami, mother, Ashraf Asadkarami, and my wife, Nafiseh Asadkarami for their immense support and encouragement. Among those who have contributed their time and energy to helping me during my program are Randal Clark, Chris Skipper, Pirooz Darabi, Al i reza Forghani, Bijan Azad i , N i m a and Navid Zobeiry, Mehdi Haghshenas, A m i n Karami, and A m i r Nejat. Thank you al l . - xvi -C o - A U T H O R S H I P S T A T E M E N T The research contained within this thesis draws on the expertise from the Injury biomechanics laboratory of Dr. Douglas P. Romilly. The doctoral candidate designed the computer experiments, their outcome measures and reliability analyses under the combined mentorship of Drs. Romilly and Foschi. The research was performed by the candidate. The candidate lead the preparation of the manuscripts with revisions from the senior co-author Dr. Romilly. - xvii -Chapter 1. I N T R O D U C T I O N Occupant protection and vehicle safety has become a widespread concern. As a result, occupant safety and injury reduction in collisions have become one of the primary factors influencing the design of the passenger vehicles. According to National Highway Traffic Safety Administration's (2004) database, 22 percent of accidents on the road are categorized as side impacts (as defined in the following paragraph) thus ranking this kind of collision as the second most frequent type of accident after frontal impacts [1]. There are approximately 10,000 fatalities per year resulting from side impact collisions in the U.S., which constitutes nearly 29% of all motor vehicle fatalities. Also, there are approximately 3000 incapacitating injuries per year in the US, comprising 24% of the total resulting from motor vehicle accidents. Canada follows a similar trend in both annual fatality and serious injury rate. Based on the Insurance Corporation of British Columbia (ICBC) 2004 database, 21 percent of accidents in British Columbia were categorized as side impacts causing 20% of all fatalities and 21% of all serious injuries on the road [2]. A side impact is defined as a collision in which the front or rear end of the striking vehicle contacts the struck vehicle in the area of one or more of the vehicle structural pillars. When a vehicle strikes a target vehicle, most of the kinetic energy of the vehicle is transferred into deforming the target vehicle and bullet vehicle. This primary collision is followed by a second collision between the occupant and the vehicle structure. The impact of the occupant with the vehicle interior causes a third collision between the occupant's internal organs and external support structure. The resulting injuries (possibly leading to fatality) can be categorized into three major areas according to the potentially injured regions of the body: 1. Head and neck region: The direct contact between the occupant's head and vehicle's interior structure during a side collision may result in following injuries: • Traumatic brain injury caused by the impact between occupant's brain and the interior of the skull. • Fracture in the vertebral column damaging the arteries that circulate through them. • Severe damage of the spinal cord causing fatal injuries or functional disabilities. 2. Thorax and abdominal region: High speed impact between occupant's thorax and abdominal region with the interior door panel during a side impact collision can cause the following injuries: • Puncture of the lungs or the liver or a rupture in the wall of the heart once these organs strike the ribcage. • Respiratory or circulatory complications due to damage to the chest. 3. Pelvic region: Direct contact between the pelvic area and the vehicle interior structure during a side collision may cause following injuries: • Pelvis bone fracture. • Leg bone fracture. • Hip joint damage. In order to ensure a minimum level of vehicle crashworthiness performance in side impact accidents, standards have been developed by governmental regulatory agencies which define the required level of performance for vehicle compliance. The predominant side impact protection standards which provide the basis for the majority of governmental vehicle regulations are: • FMVSS-214 (developed by National Highway Traffic Safety Administration (NHTSA) and the basis for the Canadian Motor Vehicle Safety Standard (CMVSS-214)) • ECE - R95 (developed by European Union (EU)) At present, vehicle manufacturers must demonstrate that their designs satisfy the appropriate standard in order to sell their vehicles in North America or Europe. Thus no car manufacturer can ignore side impact crashworthiness in the design of their vehicles. To satisfy the requirements of the above side impact standards, automotive manufacturers have adopted three primary approaches for enhancing their vehicles' crashworthiness in side impacts: • Improving the vehicle structure to absorb more side impact energy or redirect the impact energy away form the occupant. • Improving the vehicle interior side structure (e.g. better padding system). • Utilizing supplemental safety devices (e.g. side impact airbags). While optimum vehicle performance will be achieved by employing combinations of these three approaches into a single strategy for occupant safety enhancement, the scope of this research will be focussed only on the first approach as the vehicle structure is both the dominant and the first line of defence in side collisions as it must appropriately absorb and/or redirect most of the impact energy. The stiffness of the structural components loaded during a side impact collision is one of the main parameters affecting the distribution of the impact energy in the target vehicle's structure, while the portion of this energy which is available to be transferred to the occupant has a predominant effect on the occupant injury probability. Therefore, the objectives of the current research are: 1) To identify the vehicle structural components critical to providing occupant side impact protection. 2) To investigate and determine the relationship between the stiffness of these identified critical vehicle structural components and occupant injury probability in a range of side impact collision severities. 3) To provide a design strategy for developing recommendations to enhance vehicle structural design to minimize occupant injury risk in side impact type accidents in North America based on the research results. To reduce the scope of the program tasks and provide a platform to demonstrate that indeed the research objectives have been achieved, it was deemed necessary to select and focus the work on a representative side impact collision (i.e. typical vehicle and range of side impact collision parameters). It was also necessary to consider the form of crash analysis method to be used in this study. Since full-scale physical crash testing is very expensive and not generally suitable for parametric study of vehicle structural components, a numerical analysis and side impact accident simulation technique were selected as the analysis tool. A typical side impact collision was also required to be utilized as the modeling baseline. Since Canadian side impact standard (i.e. CMVSS-214) does not properly address the occupant injury likelihood in side impact collisions, the FMVSS-214 compliance test and its requirements were considered as the baseline for this work. It should be noted that while the CMVSS-214 was originally established based on the FMVSS-214, it did not follow the FMVSS-214 updates. As such, it only examines the side door strength and does not address the occupant injury likelihood in such collisions. To investigate and better understand the importance of vehicle structure to side impact crashworthiness, the overall approach to this research program was broken down into five phases deemed necessary to meet the defined objectives. These are as follows: Phase 1: Develop and validate a side impact simulation package based on the FMVSS-214 compliance test. Phase 2: Investigate the effects of side impact collision parameters (such as impact velocity, position, etc.) on the occupant injury likelihood. Phase 3: Develop and validate a new criterion which simplifies the numerical analyses such that they are computationally cost effective. Phase 4: Conduct parametric investigation with respect to the major components of a vehicle side structure and examine their stiffness effect on the occupant injury risk. Phase 5: Develop a relationship between occupant injury likelihood and structural design parameters in order to develop a strategy for optimizing the stiffness of the side structure elements, thus minimizing the injury likelihood. Subsequent chapters of this thesis outline the relevant background information and the steps that were taken to complete each of the above phases. A thorough understanding of the side impact phenomenon, past investigations of vehicle structure and its effect on injury likelihood as well as occupant injury mechanisms in side impacts is needed to pursue and complete the defined phases. Chapter 2 contains a critical literature review of relevant side impact injury biomechanics, current side impact crashworthiness strategies, and the history and basis for the current safety standards pertaining to vehicle side impact performance. Also since the US Side impact compliance test (i.e. FMSS-214) was utilized as a modeling baseline in this research, the procedure, requirements, and injury measures of this test were thoroughly discussed in this chapter. To complete Phase 1 of this investigation, numerical finite element models of the essential elements of FMVSS-214 compliance test were required, including the US Moving Deformable Barrier (MDB), the US Side Impact Dummy (SID), and the selected mid-size target vehicle (i.e. Ford Taurus). Chapter 3 outlines the sets and procedures employed for developing and validating each of these models based on FMVSS-214 compliance test requirements. The side impact simulation package developed in the previous phase was utilized to investigate the collision parameters effect including side impact velocity, position, and the mass of striking object on FMVSS-214 defined injury measures. Chapter 4 outlines the series of numerical analyses performed and discusses their results as used to complete Phase 2 of this research. Conclusions were drawn from results of this chapter indicating the effects of each collision parameter on occupant injury measures. To simplify the numerical analyses and minimize the computational cost of side impact simulation and pursue Phase 3 of this investigation, a new criterion entitled the Side Structure Performance Criterion (SSPC) was developed and validated. The development process for this criterion, its validation, and its effectiveness in reducing the numerical analysis time are discussed in Chapter 5. This chapter also describes the relationship between the SSPC and occupant injury measures as well as the relationship between SSPC and collision parameters in order to be utilized in optimization of the vehicle side structure stiffness. Using the developed models and new SSPC criterion, a parametric study of vehicle side structure was performed and the results are provided in Chapter 6. This study utilizes the FMVSS-214 compliance test setup as a typical side collision and describes the correlation between the stiffness of the vehicle side components and SSPC to complete Phase 4 of this research. In this analysis, the thicknesses of side structure components were considered as representatives of the vehicle's side structure stiffness and SSPC as an indicator of occupant injury risk. A Computer Design of Experiments method was utilized to establish the required numerical analyses and neural network as well as full quadratic response surface estimation methods were employed to represent the generated database correlating SSPC to the thicknesses of the vehicle side structure elements. The development of the relationship between actual serious injury probability and Side Structure Performance Criterion (SSPC) is described in Chapter 7. This relationship and the stochastic distribution of collision parameters in North America as well as Monte Carlo reliability analysis method were utilized to develop a database correlating the thicknesses of the vehicle side components to the probability of serious injury likelihood exceeding 3% (an injury level which was selected based on FMVSS-214 compliance requirements). A Computer Design of Experiments method and full quadratic response surface method were utilized to develop an exclusive function between the probability of serious injury risk exceeding 3% and vehicle side components thicknesses. This equation was then utilized in the optimization analysis of the vehicle side structure. This analysis demonstrates a strategy for calculating optimum thicknesses of the vehicle side structure components required to minimize occupant injury risk over a range of side impact collision parameters, thus completing the final Phase 5 of the proposed research. Conclusions regarding the contributions and the results of each completed phase of this research are provided in Chapter 8. This chapter summarizes and discusses the major findings, objectives achieved and contributions of the investigation, as well as the enhanced understanding attained during the course of the research study. Potential future works to extend this research beyond the initial research goals and further enhance side impact protection in vehicle design are also outlined at the end of Chapter 8. Chapter 2. L I T E R A T U R E R E V I E W 2.1. I N T R O D U C T I O N According to the 2004 Fatal Accident Reporting System (FARS) report, the societal cost of side impact collisions exceeds three billion dollars annually [1]. The FARS database contains the collection of collision cases collected by the National Highway Traffic Safety Administration (NHTSA) at data collection sites throughout the U.S. According to this database, 60 percent of motor vehicle collisions were recognized as frontal impacts, categorizing them as the most frequent collision on the road in the U.S. The next most frequent collision type is side impacts which constitute approximately 22 percent of all motor vehicle collisions. Table 2-1 shows the number of people injured or killed in the various types of vehicle collisions in 2004 in the U.S. The information presented in this table shows that about 29 percent of road vehicle collision fatalities result from side impact collisions. These collisions also cause 24 percent of the incapacitating injuries to the occupants, although they comprise only 22 percent of the total number of all vehicle collisions. As it can be seen, side impacts are less frequent than frontal impacts, however they result in more serious injuries per collision. The reason is that in a front-end collision, the vehicle occupants are, to a greater extent, protected by the presence of a larger structural crush zone, i.e. including the energy-absorbing bumper and front-end structure, the car's engine, the front suspension and wheels, the engine-mounting frame and integral firewall. Supplemental safety systems (i.e. seatbelts and airbags) are also available to reduce the potential for occupant injury. However, in the case of a side impact collision, the vehicle crush zone is comprised of only the side doors and the relatively light framework of the occupant cell, plus interior foams which offer some limited protection. Some vehicle types are now also equipped with supplemental side impact airbags which have increased the level of side impact protection available to the occupants, however the level of protection does not reach the level which currently exists for frontal collisions. Table 2-1: Occupants involved in single or multiple vehicle collisions (adapted from [1]) 2004 F A R S Data Impact location No injury Possible injury Non-incapacitating Evident Injury Incapacitating Injury Fatal Injury Injured, Severity Unknown Total Front 13289 5533 8351 8462 19966 170 55771 Left side 1639 748 1184 1422 5294 28 10315 Right side 1401 620 1209 1572 4730 24 9556 Rear 2474 922 867 754 1790 51 6858 Other 917 180 505 505 1953 62 4122 Total 19720 8003 12116 12715 33733 335 86624 The purpose of this literature review is to provide an understanding of previous work related to occupant injury mechanisms, current strategies for improving the vehicle crashworthiness in side impact collision, and impact analysis. The review also discusses current side impact standards around the world and provides an insight into the development of the injury indices of the North American side impact standard. The four main areas that will appear in this literature review are: 1) the occupant loading and typical injuries in side impact collision, 2) current side impact standards, 3) available side impact Anthropomorphic Test Devices (ATDs), and 4) side impact performance improvement strategies. 2.2. T H E S I D E I M P A C T P H E N O M E N A The general side impact collision orientation can be seen in Figure 2-1. The impact angle (45 < y < 135 ) is the angle between the forward direction of the struck or target vehicle and the forward direction of the impacting object. This object is usually a vehicle as is assumed in the current study, however it could also be a stationary object (barrier, pole, bridge post, etc. as well). Both the target vehicle and the impacting (or bullet) vehicle can have a velocity vector that is not coincident with the forward direction of the vehicle. This angle is called the side-slip angle, a . Note that the side-slip angle for the impact vehicle is denoted a, while for the target vehicle is denoted as a,. After the side impact occurs, both vehicles move off together before finally separating. The total energy initially in the system is the initial kinetic energy of the bullet and target vehicle, and the amount of energy left in the system when both the bullet and target vehicle have the same velocity is the kinetic energy of the two vehicles at that velocity. This residual amount of kinetic energy is far lower than the initial kinetic energy of the impacting object and the struck vehicle [3] indicating as the crash progresses, much of the striking vehicle's initial kinetic energy is dissipated through the deformation of both the bullet and target vehicle. - 10-OG-t Figure 2-1: Illustration of typical side impact crash On initial contact with the impacted vehicle, the striking vehicle loads and transfers momentum to the door and the side structure. It has been determined that, in many cases, the rapidly deforming door makes contact with the occupant and actually accelerates them to speeds above the impacted vehicle's velocity [4] (see Figure 2-2). This high occupant acceleration produces substantial dynamic loading of the occupant, thus resulting in a high risk of injury. 2.3. O C C U P A N T L O A D I N G I N S I D E I M P A C T C O L L I S I O N S Previous studies have shown that the greatest injuries occur in about the first 50 ms of the impact [5, 6] while intrusion is still increasing, and the tires of the impacted car have moved 80-130 mm. A typical sequence is illustrated below in Figure 2-2 with critical points identified as follows [6, 7]: D A: Door hit the occupant B: Max. Rib acceleration C: Max. Spinal acceleration D: Max pelvis injury TIME OF 1 100 T0R80 WPACT TIME (m.) Figure 2-2: Door, torso and vehicle velocities in a typical side impact (adapted from [7]) • Inner door contacts the occupant at 15-25 ms after the object contacts the door (see time line A) • Maximum rib acceleration at 25-30 ms (see time line B) • Maximum spinal acceleration at 30-35 ms (see time line C) • Maximum thoracic compression and pelvic injury by 50 ms (see time line D) The greatest loading on the near-side occupant comes from direct contact with the rapidly moving side ' structure. The typical sequence of such a loading on the occupant body is discussed as follows. Assuming the occupant is wearing a seatbelt, the motion of the impacted vehicle would be transferred to the pelvis. Thus, the restrained pelvis would be accelerated laterally, while the (laterally) unrestrained head/torso would hit the deforming side structure. Typically, the greatest intrusion of the side structure is lower down the body, so as the impacted car moves laterally, the unrestrained head (dependent on relative forward or back positioning) can hit the B-pillar, or exit the window and potentially strike the impacting object and cause a severe head injury. The spinal column is also one of - 12-the most vulnerable parts of the occupant's body as damage to the spine is responsible for the most disabling severe injuries. Typical load paths to the occupant's spine are from: 1) The door or B-pillar loading the shoulder. 2) The door loading the ribs, abdomen and pelvis, and then, in turn, these body parts loading the spine. 3) The deforming door may also strike the seat, which can then load the spine [8]. It should be noted that the far-side structure of the vehicle plays no significant part in loading the near-side occupant [3]. The discussed loading sequence of the occupant body in side impact collisions causes occupant injury in different regions of the human body which is outlined in the following section. 2.4. T Y P I C A L O C C U P A N T I N J U R I E S I N S I D E I M P A C T C O L L I S I O N S For the purposes of assessment, injuries resulting from side impacts can be broken into four major body areas, i.e.: 1. The head and neck region 2. The thorax region 3. The abdomen area 4. The pelvis area The injury mechanisms associated with these body regions in side impact collisions are discussed in the following sub-sections. 2.4.1. Head injuries Statistics show that the head and neck area have the highest injury risk (about 70%) due to a side impact collision [9]. Utilizing the Abbreviated Injury Scale (AIS) (i.e. see Section 2.6 and Table 2-3), - 13 -head injury due to the side impact collisions accounts for about 10 percent of the AIS >3 (serious-to-fatal) injuries [7]. The injury mechanisms typically include hyper-flexion due to overly strong and fast lateral inclination movements of the head, or by direct contact of the head against either the components penetrating from outside, or parts of the vehicle interior. 2.4.2. Thorax injuries In contrast, the thorax (or chest area) has about a 55% risk of injury due to a side impact collision [9]. Chest injury also accounts for between 23-31 percent of the AIS >3 injuries due to contact with the vehicle side interior during side collisions [10]. The human ribcage is composed of 12 separate ribs as shown in Figure 2-3. Figure 2-3: Front view schematic of the human ribcage Although the upper seven ribs are well supported at both the back and front, the bottom five ribs are increasingly less supported. Specifically, the last two ribs (ribs 11 and 12) do not have any front support and their front ends are only anchored in the abdominal muscles. Even with the better-anchored - 14-ribs, no single rib can carry a high load without the danger of fracturing and possibly puncturing a lung or other organ. In the case of a side collision, the high penetration velocity and concentrated loading on a few ribs are typically responsible for such injuries [9, 11]. 2.4.3. A b d o m e n in ju r i e s Injuries to the abdomen account for between 6-12 percent of the AIS >3 injuries in side impact collisions [10]. The abdomen is that part of the body below the diaphragm and above the pelvic inlet. This part of the body contains some vital organs such as the liver, spleen, pancreas and kidneys. Although some of these organs, like the spleen and liver, are mostly protected inside the ribcage, they move up and down as the diaphragm flexes. These organs particularly are easily injured by high velocity penetration, and thus abdomen injury is believed to be quite velocity sensitive. In other word, high velocity impact with low penetration can cause the same injury level as a low impact velocity with higher penetration [7]. Thus, high velocity side impact collisions can potentially cause severe abdominal injuries. 2.4.4. P e l v i s i n ju r i e s On the AIS scale, the pelvis accounts for about 6 percent of the serious-to-critical injuries in side impacts [10]. The pelvis and hips have two bony load points that transfer the side impact loading to the human body [7] defined as the: • Ilium or wing of the pelvis (which is at the upper extreme of the pelvis). • Greater trochanter of the femur which can transfer the loading from vehicle side structure to the acetabulum and finally to the pubic symphysis. In a side impact situation, load can be applied to the both upper and lower paths. However, the fracture of each of these parts can have quite different outcomes in terms of occupant disability. The fracture of the ilium tends to heal in time with resulting low disability, while the fracture of the trochanter and/or acetabulum and/or pubic symphysis can lead to a very serious disability. - 15 -2.5. C U R R E N T S I D E I M P A C T S T A N D A R D S A N D E V A L U A T I O N P R O C E D U R E S To ensure a minimum level of vehicle crashworthiness performance in side impact collisions, standards have been developed by the governmental regulatory bodies which certify vehicle compliance. The two predominant standards which provide the foundation for all side impact protection standards are: • FMVSS-214 (developed by National Highway Traffic Administration (NHTSA)). • ECE - R95 (developed by European Union (EU)). It is beneficial at this point to briefly review the critical elements and specific differences in procedures and criteria within these two standards to enhance our understanding of the vehicle compliance process and methods for ensuring occupant protection. Since the current research work was carried out in Canada, the Canadian Side impact standard (i.e. CMVSS-214) is also reviewed in the following subsections [89]. It should be noted that this standard was originally established based on FMVSS-214, however, it was not updated since it was adopted from FMVSS-214 in 1978. Therefore, the CMVSS-214 does not address the occupant injury likelihood in side impact collisions and it was deemed to be not suitable to be considered as the modeling baseline for this research. Clearly, if side impact protection is to be further enhanced in all vehicles, these standards must also be enhanced to ensure vehicle compliance - without undue costs to the automotive manufacturing sector and ultimately, the consumer. 2.5.1. N a t i o n a l H i g h w a y T r a f f i c a n d Safety A d m i n i s t r a t i o n ( N H T S A ) Vehicle-to-vehicle side impacts account for approximately 60 percent of all side impact collisions, thus NHTSA has focused its research primarily on impacts between vehicles. NHTSA's research in the 1970's ultimately lead to the adoption of the Federal Motor Vehicle Safety Standard (FMVSS) 214 in 1973. This first side impact standard involved a quasi-static door crush test on production vehicles. The door was crushed with a cylindrical impacter that was hydraulically pushed into the door until 305 mm of - 16-crush was obtained. The force-deflection characteristics of the door were then used to asses the strength of the door. Researchers and policy makers soon realized that the static crush test was not the most effective means of assessing side impact crashworthiness in actual collisions. This lead NHTSA to initiate research aimed at developing test and evaluation procedures and associated compliance requirements for a full-scale side impact crash test. Documentation related to these requirements and procedures were added to FMVSS-214 in 1990 via Subsections S5 and S6 [12]. These subsections include test procedures and evaluation criteria for a dynamic side impact crash test that includes a Moving Deformable Barrier (MDB) striking the side of a production vehicle at a velocity of 54 km/hr (i.e. 33.5 mph) [12]. A l l passenger vehicles manufactured after September 1, 1996 are to meet the requirements of S5.1, S5.2 and S5.3 when tested under the conditions defined in S6 of FMVSS-214. Trucks, buses and multi-purpose vehicles with masses less than 2725 kg are required to meet the new standards if manufactured after September 1, 1998. In the FMVSS 214 dynamic side impact crash test, the impacting M D B and the struck vehicle are perpendicular at the time of impact but the four wheels of the M D B are "crabbed "at 27° (angle ^ in Figure 2-1) such that the line of forward motion of the moving deformable barrier forms an angle of 63° with the centerline of the test vehicle. The vehicle is impacted such that a longitudinal plane tangent to the left forward edge of the moving barrier passes through the impact reference line within a tolerance of ± 50 mm (see Figure 2-4). The Anthropomorphic Test Device (ATD) employed in the test must conform to the requirements of subpart F of part 572 FMVSS 214, i.e. the so-called Side Impact Dummy (SID). - 17-IMPACT POINT ^ VEHICLE A / / VEHICLE B OlRECTlON OF TRAVEL @ 53.9 km* Figure 2-4: F M V S S side impact test configuration (adapted from [12]) The performance requirements for both the responses of the vehicle and the dummy are given in Table 2-2. The vehicle performance criteria specify that the door must remain attached to the vehicle and latched during the test. The dummy performance criteria requires that the Thoracic Trauma Index1 (TTI) be less than 85 g's for a four-door vehicle and less than 90 g's for a two-door vehicle and the peak lateral pelvic acceleration be less than 130 g's. The TTI and the pelvic acceleration are injury criteria associated exclusively with the Side Impact Dummy (SID). 1 TTI = 0.5 (T 1 2 + RIBY) Where : T i 2 - Maximum absolute value of acceleration of the twelfth thoracic vertebrae, in the lateral direction (in G's) RIBY - Maximum absolute value of acceleration of rib on stuck side in the lateral direction (in G's) - 18-Table 2-2: NHTSA's dynamic performance requirements for side impact. Vehicle response S3.3.1 Any door, which is struck by the moving deformable barrier shall not separate totally from the car S5.3.2 Any door which is not struck by moving deformable barrier shall meet the following requirements: • The door shall not disengage from the latched position. • The latch shall not separate from the striker and the hinge components shall not separate from each other or from their attachment to the vehicle. • Neither the latch nor the hinge systems of the door shall put out of their anchorages. Dummy response S5.2 The Thoracic Trauma Index TTI shall not exceed 85g for the passenger car with four doors, and shall not exceed 90g for passenger cars with two side doors. S5.2 The peak lateral acceleration of the pelvis shall not exceed 130g's. 2.5.2. Canadian Motor Vehicle Safety Standard (CMVSS) for side impacts As discussed earlier, the Canadian side impact standard was originally adopted from early FMVSS-214 quasi-static door crush test on production vehicles in 1978 [89]. The door was crushed with a cylindrical impacter that was hydraulically pushed into the door. The tested vehicle door, with the seats removed, has to show following strength in order to pass this standard: • The average force required to deform the door up to 152 mm must not exceed 10.01 kN. • The average force required to deform the door up to 305 mm must not exceed 15.57 kN. • The average force required to deform the door up to 457 mm must not exceed 31.14 kN. - 19-The above vehicle door strength specifications are the only requirements of the Canadian side impact standard. This standard does not have any dynamic test requirements (i.e. actual side impact collision test). Thus, it does not have any injury requirements similar to the updated FMVSS-214. As such, this standard and its requirements could be insufficient to protect the occupants in side impact collisions. 2.5.3. E u r o p e a n U n i o n D i r e c t i v e The European side impact directive (ECE-R95) was adopted by the European parliament and the Council of the European Union (EU) on May 20, 1996 [13]. The primary studies on the test procedure and its components, i.e. Moving Deformable Barrier and Anthropomorphic Test Device (ATD), were performed by European Enhanced Vehicle-safety Committee (EEVC) in 1980-1990 [14, 15]. While similar in goals, the E U side impact standard differs from the North American vehicle standard in both test procedures and performance criteria. In contrast to the FMVSS 214 side impact test, the European standard requires that the forward motion of the EU-defined M D B (i.e. more compliant, lower mass, reduced height) be oriented perpendicular to the longitudinal direction of the impacted vehicle (instead of crabbed) and shall strike the stationary test vehicle at the lower speed of 50 km/hr (i.e. 31 mph). In terms of performance criteria, the EU test specifies the use of the EUROSID, a different A T D with correspondingly different evaluation parameters. The five performance criteria to be met for vehicle compliance are: • The Head Performance Criteria (HPC) may not be greater than 1000, • The Rib Deflection Criteria (RDC) may not be more than 42 mm, • The Viscous Criteria (V*C) may not be more than 1.0 m/s, • The Pubic Symphysis Peak Force (PSPF) may not be more than 6 kN, and • The Abdomen Performance Criterion (APC) must be no more than 2.5 kN. - 2 0 -In addition to the dummy evaluation criteria, there are several other structural performance requirements for the vehicle, including: • The doors of the car must not open during the test, • The A T D must be capable of being removed from the test vehicle without the use of tools, • Interior devices or components must not become detached or damaged in such a way as to increase the risk of injury to a vehicle occupant. Several previous studies have attempted to compare the effectiveness of these two standards [14-18]. Dalmotas et al [17] showed that the difference in results was mostly attributed to the differences between the U.S. and European crash test M D B and procedures rather than due to the different crash dummy design employed. Deformation patterns produced by the U.S. M D B barrier showed much better agreement with North American mid-size vehicle crush response, however the European barrier element's stiffness correlated well with a typical mid-size European and Australian passenger vehicle [18]. Also, according to these studies, despite the lower mass and reduced stiffness the European barrier provides much more severe loading than its U.S. counterpart. This suggests that the design characteristics of the European barrier do not properly represent North American vehicle design and construction practices, particularly as they pertain to the front-end stiffness of passenger vehicles at the height of the bumper. One of the main components of the discussed standards is the specific A T D utilized in performing the standard test. These ATDs are utilized as a human surrogate to assess the occupant injury likelihood during the side impact collision. The development of such ATDs and their associate injury indices are discussed in the following section. 2.6. A N T H R O P O M O R P H I C T E S T D E V I C E (ATD) Anthropomorphic Test Devices, also called dummies, are mechanical devices used to mimic the human body in simulated collision conditions. Biofidelic dummies must be able to imitate the body's characteristics such as size, shape, stiffness and mass so that their mechanical responses simulate human -21 -responses of velocity, acceleration, deformation, etc. in case of a designed crash test [19]. The reliability of the ATD's injury assessment in comparison to human injuries is called the biofidelity of the ATD. The injury indices defined on an instrumented ATD gives a quantitative assessment of injury risk to a vehicle occupant in a similar real-world crash. These injury indices are usually developed based on their ability to correlate well with the injury scale defined based on the severity of injuries on the human body. Such an injury severity scale is necessary for the consistent collection of crash data and to allow comparison of data from different sources. The Abbreviated Injury Scale (AIS), developed by the American Association for Automotive Medicine (AAAM) is the most widely used anatomic injury severity scale in the world [20]. This injury scale was approved by a joint committee comprised of representatives of the American Medical Association (AMA), American Association for Automotive Medicine (AAAM) and Society of Automotive Engineers (SAE) in 1971. The Abbreviated Injury Scale (AIS) underwent major revisions in 1980-1990 and revised scales are referred to as the AIS-80, AIS-85 and AIS-90 [20, 21]. As shown in Table 2-3, a six point scale, based on a revision of the AIS is used to rank threat to life in all parts of the body. It should be noted that the AIS-80 does not recognise the location of the injury in its coding and only specifies the severity of the injuries (i.e. Table 2-3). However, AIS-85 and 90 combine the six point severity scale with numeric codes to designate specific injuries that include the injury location and type as well as its severity [20]. - 2 2 -Table 2-3: Abbreviated Injury Scale (AIS) [21] AIS Severity Code Examples 1 Minor Abrasion, throat lacerations, ear canal injury 2 Moderate Cornea laceration, minor compression fracture of spine or thorax 3 Serious Disc rupture with nerve root damage, eye avulsion, brain stem contusion 4 Severe Brain stem laceration, inhalation burns, chest puncture 5 Critical Aorta laceration, Bronchus rupture, lumbar spine cord laceration, brain stem compression or contusion 6 Maximum Brain stem crush, skull crush, decapitation 9 Injury severity unknown -Since most of the side impact ATD's injury indices were originally developed and validated based on the AIS-80 injury severity scale, the current study will refer to this injury scale as AIS injury scale through this document. Several ATDs were designed specifically for representing the vehicle occupant in the side impact collisions. The development and specifications of four of the most common ones are discussed in the following sub-sections. 2.6.1. The Side Impact D u m m y (SID) The Side Impact Dummy (SID) was adopted from the " A T D 572" which was originally a frontal impact dummy [19, 22]. A series of modifications were made to the thorax of the frontal impact dummy to improve its response to lateral impacts. The modifications were made by the University of Michigan Transportation Research Institute under contract with NHTSA between 1979 and 1982. These included alternations of the thoracic lateral dynamic stiffness, mass distribution and rib linkage [22]. -23 -For validation purposes, measurements of SID responses that are related to the potential injury concerns were compared to human cadaver responses in pendulum and sled tests. The ratio of the predicted SID-to-cadaver AIS was found to be within 5 percent [23]. However, several problems were found with the SID as the prototype and early production dummies were utilized in actual crash and sled test programs. The sources of these problems were: • Bending failures and a lack of repeatability of the shock absorber used to transfer load from the struck side ribs to the spine • Tearing failures on the struck side of the leather hinge connecting the ribs to the spine • Tearing failures of the urethane outer torso skin After some design changes, six SIDs were tested for repeatability and reproducibility in a series of seventy two pendulum impacts with the results indicating that the redesigned SID properly produces repeatable injury measures. Extensive testing was performed with the SID and the cadavers to determine the biofidelity of the SID [24, 25]. A study conducted by Eppinger et al [25], obtained data from 49 detailed experiments with cadaver specimens to develop an injury index that relates human thoracic and abdominal injury in the cadavers with the mechanical response of the surrogate occupant used in their studies, i.e. the SID. The tests were conducted at the University of Heidelberg, Highway Safety Research Institute, ONSER State University and Wayne State University. The injuries sustained by the specimens were identified through autopsy and rated on the AIS scale. After examining several possibilities for an injury index that had a monotonic increase with the AIS, the Thoracic Trauma Index (TTI) was developed: Mass ( 2 - 1 ) std where: Age: Age of the test subject (in years) - 2 4 -Tu: Maximum absolute value of acceleration of the twelfth thoracic vertebrae, in the lateral direction. RIBY: Maximum absolute value of acceleration of rib on struck side in lateral direction. Mass: Cadaver mass Mass std: Standard mass (165 lb) A cumulative probability relationship was then developed that could be used to predict the percentage of expected injury greater than or equal to AIS 3, 4 or 5 for a given value of TTI. This relationship is shown in Figure 2-5. Figure 2-5: The correlation between the T T I and the probability of injury (adapted from [25]) -25 -The TTI expression used in the Federal Motor Vehicle Safety Standard (FMVSS) regulation uses a standard mass of 165 lb (typical mass of the SID) and the age term is taken as zero for calculating TTI. TTI = 0.5(ri2 + RIBY) (2-2) This injury index is referred to in the FMVSS regulations as TTI (d), however, within this thesis it will be referred to merely as the TTI. 2 . 6 . 2 . E U R O S I D - 1 The European Enhanced Vehicle-safety Committee (EEVC) of the Economic Commission for Europe (ECE) sponsored the development of EUROSID, which was developed in the 1983-85 time frame. Further modification of EUROSID in 1987 lead to the new version of this A T D called EUROSID-1. This version of EUROSID was designed to have better side impact response biofidelity for the head, neck, shoulder, thorax and pelvis. The head of the Hybrid III dummy was selected as the head of the EUROSID-1 and the lower extremities of Hybrid II dummy were used to represent the lower body in this A T D . Hydraulic dampers and springs in the chest structure were designed to mimic human lateral force-deflection compliance, while a specially designed abdominal insert was used to provide human-like abdominal compliance. The pelvis was designed to measure pubic symphysis loads [26], however the current design (EUROSID-1) has been found to have the following limitiations: 1. The maximum rib-to-spine displacement is limited to 50 mm of travel. 2. The shoulder is unstable when loaded laterally. 3. The load distribution function of the humerus is not simulated in the arm structure. As was mentioned earlier, the EUROSID-1 is the dummy utilized in the European side impact standard. Therefore this dummy is instrumented to measure the Head Performance Criteria (HPC), two - 2 6 -thorax injury indices, plus the abdomen and pelvis injury indices [13]. The HPC is the maximum of the following expression and is calculated only when head contact occurs: HPC where: ( ' 2 " 0 > 2 . 5 \ (2-3) a = Resultant acceleration at the center of gravity of the head in m/s2 divided by 9.81 recorded versus time and filtered at channel frequency class 1000 Hz. t],t2 = Any two times between the initial contact and the last instant of contact The maximum allowable value of HPC is 1000. There are two thorax injury indices: 1. The chest deflection which is the maximum value of the deflection of any rib as determined by the thorax displacement transducers. This signal then must be filtered at Channel Frequency of Class (CFC) 180. The Thorax displacement should not exceed 42mm. 2. The Viscous Criteria (V*C) which is the maximum value of the relative thorax compression and the velocity of compression derived by differentiation of the compression, filtered at CFC 180: V * C = MAX ( D \ (dD\ 1,0.140 J K dt , (2-4) The pelvis injury index of EUROSID-1 called pubic symphysis peak force is the maximum force measured by a load cell at the pubic symphysis of the pelvis. Recorded signal from the load cell must be filtered at CFC 600 Hz and its maximum should not exceed 6 kN. The abdominal injury criterion is given by the maximum value of the sum of the three forces measured by the transducers mounted 39 mm below the surface on the crash side, filtered at CFC 600 Hz. The maximum allowable value of this index is 2.5 kN. - 2 7 -2.6.3. B i o f i d e l i c S i d e I m p a c t D u m m y ( B I O S I D ) Biofidelic Side Impact Dummy (BIOSID) is another lateral impact A T D which is representative of the 50% adult male in size, weight and impact response [27]. The dummy was developed under the direction of the SAE side impact dummy task force. The head and neck of the Hybrid III was chosen for this A T D . This design feature produces repeatable head accelerations in similar lateral impacts. The head is also instrumented to measure the triaxial acceleration of its center of gravity. The Hybrid III neck was chosen due to its human like response in side impacts [28]. The chest area is developed using a unique "far-side mounted" rib structure [29] which allows side deflections of 75 mm without exceeding the elastic limit of the rib steel and causing the permanent deformation of the rib structure. Only the upper half of the arm is simulated with BIOSID and provides a mechanism to mimic the load distribution between the arm and the thorax and shoulder ribs. The pelvic structure of this dummy is very similar to EUROSID-1 pelvis and is instrumented to measure sacrum, iliac wing, and pubic symphysis loads [27]. One of the design limitations of the BIOSID is the need to replace the foam block pelvis insert after each test. The crushable insert is required to meet the biofidelity impact requirement for the pelvis. The performance criteria for BIOSID are as same as that of EUROSID-1. 2.6.4. W o r l d S I D Aiming to obtain a new, globally harmonized 50 t h percentile male side impact dummy has been developed in the form of the World Side Impact Dummy (WorldSID) within a task group comprised of dummy and biomechanics experts from the automotive industry, government agencies and research institutes from around the world and under auspices of the International Organization for Standardization (ISO) [30]. The main objective of development of the WorldSID was to produce a harmonized midsized male side impact dummy with high biofidelity to be used in regulatory test procedures, including those defined by International Harmonized Research Activities (IHRA), and also for all other test procedures. The WorldSID head is a completely new design. The skull is fabricated from polyurethane and the skin is permanently attached to the skull. The neck and the arm of the WorldSID are adapted from EUROSID - 2 8 -dummies. The thorax and abdomen assembly is comprised of the rib units, individually attached to a rigid spine box [31, 32]. Each rib unit is constructed of a super-elastic alloy, Nitinol™ and has a maximum elastic deflection capacity of 75 mm which accommodate ribs high deflections without any permanent deformation. The pelvis consists of a conical shaped polyurethane pelvic bone that mimics human pelvic bone. Primary verification side impact tests including pendulum, sled and full-scale side impact tests have been performed on the WorldSID dummy [31, 32] however, final design documents have not yet been published in the public domain at the time this document was prepared. Furthermore, no injury indices have been yet defined for this A T D . As discussed earlier, all of the above ATDs were developed to investigate the occupant injury likelihood during side impact collisions. Furthermore, some of them were utilized as one of the main components of the side impact standard tests. Once such standards were established, the vehicle manufacturers were required to meet them. The next section discusses the strategies adopted by the vehicle manufacturers to enhance the crashworthiness of their products in order to meet the side impact standards and reduce the occupant injury likelihood in side impact collisions. 2.7. S I D E I M P A C T P E R F O R M A N C E I M P R O V E M E N T S T R A T E G I E S To satisfy the side impact performance requirements defined for vehicle compliance, it is recognized that automotive manufacturers have adopted three major approaches for enhancing occupant safety in such crashes: • Improving the vehicle door and frame side structure efficiency to absorb/redirect energy, • Providing more protective interior structures (e.g. padding) and optimizing occupant positioning, • Utilizing supplemental safety systems (e.g. side impact airbags). - 2 9 -While full scale testing is essential to vehicle compliance, the use of numerical modeling is rapidly gaining acceptance as an effective and more efficient means of investigating the performance of proposed new vehicle design concepts employing combinations of these three primary strategies to enhance occupant safety. 2.7.1. Vehicle side structure The following vehicle elements are those which primarily control the crashworthiness performance of the vehicle in a side impact collision (see Figure 2-6): • ' A ' , ' B ' and ' C pillars • Door structure • Seat • Rocker panel • Floor pan • Roof • Cant rails • Structural joints (e.g. the joint between ' B ' pillar and rocker panel) The behaviour of these elements during the crash directly affects the injury risk to the occupant. Upon initial consideration, a first approach for improving the sidewall efficiency in a side impact might be through altering the stiffness of the described elements in order to make the vehicle as stiff as possible laterally. For a stiffer structure, the impacted vehicle accelerates faster, as a greater resisting force is offered, but the relative door-to-occupant velocity is lowered. The lower contact velocity of the door with the occupant produces lower acceleration and velocity of the occupant's torso. However, as shown by Daniel [7], this will cause the occupant to make contact with the door structure before the peak door velocity, i.e. when the door is still accelerating as shown in Figure 2-7. - 3 0 -Figure 2-6: Structural elements of a typical vehicle Impact in weak -structure Figure 2-7: Relative performance of "stiff versus "compliant" vehicle side structure (adapted from [7]) Often designers seek to make the dummy contact the door after the peak velocity of the door reached, i.e. when the door velocity is falling. The reason for this is illustrated in Figure 2-7 and is follows. - 3 1 -For any given door velocity-time history, more energy is typically available for transfer from the door to the occupant if contact begins during the rise of the punch, and less energy is available for transfer to the occupant if contact begins while the door is already decelerating [4]. To investigate the effect of the vehicle structural components on the occupant injury likelihood, researchers and vehicle designers utilized one or both of the following approaches: 1) Experimental methods, and 2) Numerical methods. The following two sub-sections discuss some of these approaches and their result in vehicle side impact crashworthiness improvement. 2.7.1.1. Experimental approaches There are two major side impact experiment types for evaluation of the vehicle structural elements: • Sled type tests [33-37] This type of test can evaluate the performance of the door structure (including the inner door padding, side airbags, etc). • Full-scale side impact tests [6, 38-50] This type of test has been usually utilized to validate a design hypothesis or fully evaluate a vehicle performance in side impact collisions. Sled tests usually consist of a reinforced vehicle door (to simulate door pre-crush) and an A T D (i.e. US-SID, EUROS1D, etc) that is stabilized on a seat mounted on a "dolly" in vehicle design position. The dolly slides on the guide rails of the sled carriage. During the test the sled is accelerated to a desired speed and strikes the stationary honeycomb ram. The acceleration of the dolly is dependent on the impact velocity of sled and the mass of the dolly (which includes the ATD). The momentum exchange between the door and dummy in this method may not be accurately controlled, since there is a lack of precise control of the door velocity profile after dummy contact [36]. Aekbote et al [33] in 1999 improved this method by reproducing "double-peak" characteristics of the door velocity profile. The door velocity profile was simulated in four phases: In the first phase, a pre-crushed door mounted on a door sled (at - 3 2 -approximately the same distance from the dummy as in a car), is accelerated by a hydraulic power cylinder until it impacts the stationary dummy, to generate the first peak. In the second phase, from the onset of dummy contact, the door sled is decelerated by a honeycomb block (mounted on another 'Base sled'), simulating the first ride-down of the velocity profile. During this phase, the hydraulic cylinder is dormant. In the third phase, the hydraulic cylinder accelerates both the door and base sleds together to simulate the second peak. In the fourth phase, the door and base sleds are decelerated until door-dummy separation, thus simulating the entire door velocity profile from start of crash event until the door and dummy separate. Sled tests usually are utilized to evaluate the performance of door subsystems, trim panels and safety countermeasures i.e. airbags. Although sled tests are less expensive (in compare to full-scale side impact tests), they are unable to fully capture the door velocity profile history at all points. Also, they can not evaluate the vehicle side structure performance in such collisions. Thus, full-scale side impact tests are still required to fully evaluate a vehicle performance in side impact collisions and validate any new design hypothesis. Some of these design hypothesis and full-scale side impact tests, which were performed to evaluate them, are discussed as outlined below. One of the first attempts to investigate the vehicle side structure characteristics was done by Cesari in 1976 [39]. To minimize intrusion into the occupant compartment, a 6 mm steel plate was fitted to the length of side exterior of a small hatchback vehicle. The presence of the external steel plate virtually eliminated intrusion into the vehicle occupant cell, but produced limited improvement in the occupant injury assessment parameters. In subsequent tests, to examine the effects of padding alone (i.e. 6 mm plate not present), 100 mm of padding was fitted to the door adjacent to the dummy's thorax, abdomen and pelvis. Similarly in these tests, padding alone produced only marginal improvement based on the occupant injury assessment parameters. It was only when the two strategies were combined that significant benefits were seen in the full scale tests. -33 -The Volvo design team realized that the floor cross member between the rocker panels and over the propeller shaft initiated collapse in their 240 model and had to be redesigned [48]. To give a stable floor collapse while the B-pillar bends, five bulkheads added to the floor. The B-pillar was also redesigned to give greater bending stiffness, along with the roof/B-pillar joint. In the doors, beams were placed near the outer skin to allow the inner panel to crush under occupant contact. To avoid crush at chest height, the door beam, the B-pillar and the B-pillar joints with roof and rocker panel have matched stiffness properties. The door contained 100 mm thick constant stiffness padding at chest height, and 60 mm constant force padding at pelvis height. It was also pointed out that door locks and window mechanisms must be kept out of the way of the occupant. One novel feature was an enlarged lower B-pillar joint with foam blocks placed between the seat and the structure. The blocks were loaded by the B-pillar joint, which in turn load thick walled tubes in the front seats. These modifications reduced intrusion and lowered TTI from 115 to 80. It was noticed that the spinal acceleration at T ] 2 peaked when the pelvic padding bottomed out, and that spinal loading also came from the seat/chassis interaction, and not only from the door. Goetz et al [49] describes the safety features of the Mercedes Benz 190 model. Following factors were considered as design recommendations to increase the resistance of the side structure: high strength of locks and hinges, equally high strength of their fastenings points in doors and pillars, and highly stress-resistant doors and pillars. To increase the crashworthiness of the vehicle in lateral impact, the floor edges were wrapped around the rocker panel in this model. This type of joint provides form-locking connection and also changes the loads on the spot-welds from vertical tension to shearing stress which is more favourable. To increase the side structure integrity, the lower edge of the door was designed to hook into the rocker panel. It is also pointed out that unless door reinforcements are connected to the side frame, they only strengthen the door and not the side frame. This previous work highlights two important points: 1) the first two design strategies (i.e. vehicle structural enhancements and interior protection) offer potential benefits to occupant protection in side - 3 4 -impacts, and 2) the occupant safety benefits resulting from the various design strategies may be synergistic in nature, due to the fact that the injury criteria are acceleration-based- a key parameter in dynamic loading. This latter point suggests that solely utilizing full-scale vehicle testing to optimize proposed new vehicle designs may be impractical, although full scale tests will likely never lose their place as critical tools for validating the accuracy of numerical models and ensuring as-manufactured vehicle compliance. 2.7.1.2. Numerical approaches Although performing full-scale crash testing is the most direct method for evaluating new design concepts, it is very expensive. In addition to the initial cost of the physical components and test facilities required, collecting and analyzing the data is also costly [19]. These reasons in conjunction with the continuous improvement in computing speed and software tools have lead researchers to utilize numerical analysis techniques such as Finite Element Modeling (FEM) and dynamic modeling tools in order to investigate the side impact collision of the vehicles. One of the early approaches to model the side impact collisions was using lumped mass models [46, 51-54]. Kanianthra et al [46] characterized struck car by nine masses and twenty one nonlinear spring and damper units that interconnect the various masses representing the different components of the struck vehicle. The M D B was represented by a single mass and two nonlinear energy absorbing elements that include springs and dashpots. The SID was simulated by four masses and six set of springs and dampers. The major advantage of this type of modeling is its simplicity and low computational cost of the analysis, therefore this method is a good analysis tool in early stages of concept designing. Unfortunately however, it has low accuracy problem and it is difficult to predict deformation based injury criteria (i.e. rib deflection criteria) using this modeling method. By increasing the computational speed of the computers, researchers started using F E M and more sophisticated models to simulate side impact collisions [55, 56]. These researchers have included Gruber et al [57], that modeled the three major mobile barriers (i.e. NHTSA, E U , ISO) using L S - D Y N A and - 3 5 -subsequently utilized these barrier models and a simplified car model to simulate side impacts, and Sugimoto [58], who utilized an FE analysis to investigate the effects of varying the striking vehicle characteristics (i.e. weight, width, ground clearance, velocity) in a side impact collision (based on the NHTSA collision orientation protocol). According to this research, collision speed has the highest effect on the injury indices. Deng [59] developed a finite element model of a side impact collision using ' C A L 3 D ' finite element software. This model was then validated against the test data for the vehicle and the occupant kinematics. The parameter variation study indicated that for the modeled vehicle, a stiffer side structure and more spacing between the occupant and the door would reduce injury severity indices. Malkusson and Karlsson [60] tried to find the best door velocity profile to mitigate occupant injury in side impact collisions. Their model consisted of a dummy (SID and EUROSID) and an impacting plane. The velocity of the plane was controlled at three levels; one at the lower part of the pelvis, one at the upper part of the pelvis and one in the area of upper thorax. By varying the velocity characteristics of the plane and comparing injury levels, desirable velocity characteristics were found. Figure 2-8 shows the schematic of the optimum velocity profile based on the results obtained from their study. As can be seen in this figure, their results indicated that reducing the door velocity at the occupant's head and thorax level can substantially reduces the probability of the injury. - 3 6 -Figure 2-8: Desired velocity profile of the vehicle side structure (adapted from [60]) Nelson and Sparke [61] and Kim et al [62] also employed numerical modelling, this time in an attempt to optimize the vehicle side structure. Nelson and Sparke conducted a parametric study to optimize the side structure; specifically the vehicle door and its attached accessories. In this research, optimization variables were divided into three categories: 1) occupant variables (e.g. position, size, etc.), 2) crash variables (e.g. collision speed, bullet vehicle mass and stiffness, etc.), and 3) design variables (e.g. structural stiffness, presence of airbag, padding, etc.). Social harm (which is a measure of the cost to the community of injury caused by car crashes) was used for the objective function for comparison and evaluation. For each simulation (utilizing L S - D Y N A and M A D Y M O 3D), the EUROSID dummy injury responses were translated into injury risk via the use of injury assessment functions, and then from injury risk into social harm. While a very interesting approach, and one which would add greatly to the literature and highlight the benefits of numerical studies in the field of assessing side impacts, it is unfortunate that the authors did not report any substantive results from the research. This problem and -37-lack of information about the modelling process is very common in the literature which makes the most of the results irreproducible or vague. 2.7.2. Interior structure and padding system As illustrated experimentally early on by Cesari [39], compliant interior structures and/or padding, when utilized in conjunction with relatively stiffer side structure, can effectively reduce the risk of occupant injury i f placed appropriately. Later Transport Canada funded studies [16] have also verified the effectiveness of properly located padding to effectively enhance occupant safety. The three common locations for padding that can enhance side impact protection are [7]: • Inside the door, between outer and inner panels • Between the door and the occupant • In the seat Often it is difficult to make padding in the seat work effectively. " Wings ", as may be employed on a bucket seat, would protect a belted occupant's pelvis, but any forward motion would act to move the torso away from the seat thus reducing the padding's utility. To ensure effectiveness, padding located in or on an adjacent door must be positioned to protect the wide range of different sized occupants in their different seating positions. No matter how good the padding, i f a lock, or window mechanism contacts part of the thorax, injury will likely be sustained [49]. There are three primary types of automotive interior padding available in the market [7]; 1) constant strength, 2) constant stiffness and 3) viscous (i.e. speed sensitive). The advantage of constant strength padding is its high energy absorbing capability, however, with this type the same force is exerted on the occupant whether the contact occurs at low or high speed. Constant stiffness padding exerts a lower force at low contact speed, but typically bottoms out earlier at high speed due to its limited energy absorption capabilities. An "ideal" energy absorber is the viscous type, where the resisting force is matched with impact speed, and energy absorption at constant force is achieved. A form of this type of -38-padding, which is commercially called Dynapad [63], is composed of closed cells filled with air, each containing an orifice, or other restrictor, for the air to escape. The flow of air through the restrictor provides the required energy dissipation while the compression of the air provides a nonlinear spring characteristic [64]. Padding lowers the contact force on the occupant by crushing and absorbing energy. However, padding also takes up space between the occupant and door, closing the gap between the two, giving an earlier contact time. The longer contact time induced from the padding can increase the energy transfer to the occupant [4]. As the padding does not change the velocity profile of the door, this gives a higher contact velocity of the door to occupant [4, 6, 16, and 65]. 2.7.3. Side impact airbags Side impact airbags are similar to their front impact counterparts in terms of having a sensor, inflator and airbag [9]. However they have about half the time to inflate (e.g. Volvo's side impact airbag inflates in 12 ms [66]) and the bag can theoretically be in many locations, i.e. the seat cushion, seat back, door, roof rail, or B-pillar. Seat mounted airbags follow the position of the occupant as he/she moves the seat forward or back. However they do deploy slightly out of position, i.e. behind the occupant. The airbag usually gives head and chest protection, by spreading the load over the occupant and moving them away from the side of the vehicle, with the pelvis being protected typically with padding alone. Limiting the contact force on the occupant is also a key task for the airbag [67], absorbing energy as the intruding side structure deflates the airbag. However it is important that the force-deflection characteristics of the airbag be tailored to those of the occupant, with the bag remaining softer than the occupant to cushion the impact [66, 68]. - 3 9 -2.8. S U M M A R Y A N D C O N C L U S I O N S Side impacts have become the topic of many research studies since early 1970, due to the high injury rates and fatalities second only to frontal impacts. Vehicle designers and government regulatory agencies (e.g. NHTSA and Transport Canada) have tried to mitigate occupant injuries by improving design strategies and legislating side impact standards. However, the current published literature typically consists of mostly conference papers and technical reports. This fact and the confidentiality of results not provided in these documents causes two major problems: 1) The published results constitute a small fraction of actual work in this area by the vehicle manufacturers, meaning that finding and obtaining meaningful results in the published literature is both difficult and time consuming, and 2) most of the articles are not comprehensive and obtained results are irreproducible and sometimes vague. However, it is clear that continued research is required to address the existing limitations of the current vehicle design strategies for vehicle side impact protection. This literature review has attempted to provide an overview of common injuries and standards as well as injury reduction strategies in such collisions. This review has also shown that crash simulation and numerical analysis can offer a cost effective alternative to the physical test environment in the early stages of vehicle design. Improving the vehicle structure, optimizing the vehicle padding system and utilizing the side impact airbags currently are three major approaches to reduce the occupant injury risk. However, the scope of the current study is limited to investigating the first approach (i.e. improving the vehicle structure). As defined previously, the approach of this research study was broken into five phases in order to achieve the objectives of the current research study: Phase 1: To develop and validate a side impact simulation package based on the FMVSS-214 compliance test. Phase 2: To investigate the effects of side impact collision parameters (such as impact velocity, position, etc.) on the occupant injury likelihood. - 4 0 -Phase 3: To develop and validate a new criterion which simplifies the numerical analyses such that they are computationally cost effective. Phase 4: To conduct parametric investigation with respect to the major components of a vehicle side structure and examine their stiffness effect on the occupant injury risk. Phase 5: To develop a relationship between occupant injury likelihood and structural design parameters in order to develop a strategy for optimizing the stiffness of the side structure elements, thus minimizing the injury likelihood. The subsequent chapters of this document discuss each of the above phases respectively. - 4 1 -Chapter 3. D E V E L O P M E N T A N D V A L I D A T I O N O F T H E F I N I T E E L E M E N T M O D E L S 3.1. I N T R O D U C T I O N Numerical analysis and a collision simulation approach using L S - D Y N A [69] software was utilized in this study to investigate the potential effects of vehicle design modifications on vehicle crashworthiness and associated occupant safety with the hope of gaining insight into the most efficient way to enhance vehicle design. This chapter outlines the development and validation procedure of this side impact simulation package. To better understand side impact collisions and establish a baseline for improving the side impact performance of a vehicle, a numerical representation of this type of accident was required. Since this investigation was funded by the AUT021 - Canada Network of Centers of Excellence and it was performed in Canada, the North American side impact test procedure as specified in the FMVSS-214 standard was considered applicable. As described in the previous chapter (see Figure 2-4), three essential components of this test includes the NHTSA Moving Deformable Barrier (MDB), the US Side Impact Dummy (SID) and the target vehicle. To simulate the FMVSS-214 compliance test and pursue the objectives of Phase 1 of this research work, a finite element model of each component of this test needs to be obtained or developed and properly validated. These models are described below: • M D B model: A simplified model of NHTSA M D B was developed and validated by comparing the results obtained from the M D B simulation with the published results of a full-scale physical impact test under the same conditions [70]. The physical impact test involved towing a 26° crabbed NHTSA M D B into a fixed load cell barrier at a perpendicular angle at a velocity of 40.2 kph (25 mph). - 4 2 -• SID model: A model of the US SID was acquired from the NHTSA website [71] and was used in its unmodified form. The accuracy of the model was assessed through an independent validated M A D Y M O software-based SID model and NHTSA standard calibration test requirements. • Target vehicle: The target vehicle model (i.e. Ford Taurus) was also acquired from the National Crash Analysis Centre (NCAC) website [72]. This model was enhanced and validated in order to be used more effectively for side impact crash analysis [19]. Both the dummy and the target vehicle models are public-domain models, while the developed M D B model is reproducible based on the information provided in [12, 70], thus providing other researchers the means of reproducing the research results generated within this study. The following sections of this chapter discuss in more detail the development and validation procedures of these three components of FMVSS-214 test simulation tools. 3.2. N H T S A M O V I N G D E F O R M A B L E B A R R I E R (MDB) The NHTSA M D B represents an average North American passenger vehicle and is used to represent the bullet vehicle. The M D B (see Figures 3-1 and 3-2), including the impact surface, supporting structure, and carriage weighs 1,368 kg (3,015 lbs), has a track width of 1,880 mm (74 in.) and a wheelbase of 2,591 mm (102 in.). The barrier face assembly (as shown in Figure 3-2), which approximates the stiffness of a typical mid-sized North American passenger vehicle, is composed of two predominant aluminum honeycomb sections: 1) the front block (i.e. component A in Figure 3-2) and 2) the main block (i.e. component B in Figure 3-2). The front block is positioned 330 mm (13 in.) above the ground and is stiffer than the main block, which is positioned 729 mm (28.7 in.) above the ground. The front block is a sandwich structure of aluminum honeycomb fixed between two thin aluminum plates. A thin aluminum face covers the main block and connects to the M D B mounting plate (i.e. component D in Figure 3-1). The barrier face assembly is bolted to the mounting plate at the upper vertical location (i.e. point C in Figure 3-2).. -43 -143 74" 4 9 . 2 5 " — ' fit—3 •  i Q - s f -J I N S T R U M E N T A T I O N *--* B A L L A S T A R E A BARRIER FACE TOP VIEW =~Aa ft ^ RIGHT SIDE VIEW -n= * n . - i i r - i ^ f 162* Figure 3-1: Moving Deformable Barrier specification (adapted from [12]) B 1 - P i M * AlLm. Hansy-gomt Stack - - ^ p * _ M m Han*yegn* B jmpar, 2*S psi . 15 D«i enafi «trend , a . S p » o u * * M n g » - 7 | ^ M a . t a f l l F ^ a i a , - 5 K 2 . w 4 i—a.osa* M M , B « * / I / —~ A. ee* , P l l » , 2S kH M S * . / / F K 3 4 / /tr • Do MetSera i ;| :On% .-33" I HONEYCOMB 8" : :. SUMPER r 1 i r \ T FRONT VIEW n GROUND 13* SECTION A-A NHTSA BARRIER FACE 0,125" AJum. Facas; 50 ksi 2D24-T3 Figure 3-2: M D B barrier face specifications (adapted from [12]) Several researchers have previously created finite element (FE) models of this M D B [57, 70] for use in side impact analysis. However, these models were not suitable to be utilized in this research study due to the following problems: 1) They are not public and could not be acquired from a public domain database. 2) They are extensive and require considerable computational resources when used in side impact crash simulations [70]. Therefore, a simplified FE model of the NHTSA M D B has been developed - 4 4 -for use in this research program. The development and validation procedure for this model is discussed in the following sections. 3.2.1. Development of the U B C Simplif ied N H T S A M D B model A valid public domain model of the N H T S A M D B could not be identified during the course o f this research, thus a new and simplified finite element model o f N H T S A M D B was developed based on design information provided in [70, 73] utilizing L S - D Y N A [69]. The major simplification made in developing U B C simplified N H T S A M D B model was to represent the rear structure o f the M D B and its mass with a rigid block. This rigid block substantiated the inertial properties o f the M D B rear structure, while eliminating its structural stiffness properties. Since the vehicle's rear structural stiffness does not play a part in the first 50 ms o f the crash event, i.e. the period when the predominant injuries of interest occur, this assumption was deemed reasonable for simplifying the barrier model. The face o f this M D B model was developed in detail based on the actual M D B face utilizing the design information provided in [70, 73]. Figure 3-3: U B C Simplified F E model of the N H T S A moving deformable barrier (MDB) -45 -The simplification applied to this model, substantially reduced the model's complexity and its size in comparison to similar NHTSA M D B models (i.e. effectively 10 times smaller than the N C A C model [70]).This M D B finite element model is composed of six separate components and contains 858 shell and 2085 solid elements (see Figure 3-3). The validation of this model is presented in the following sub-section. 3.2.2. Val ida t ion of the U B C Simplified N H T S A M D B model To validate the simplified M D B model, simulation results using this model were compared to available full scale tests reported by Zaouk and Marzoughui [70]. In these full-scale tests, the M D B was towed into a fixed load cell barrier at a perpendicular angle. The impact speed used was 40.2 km/h (25 mph), with the M D B crabbed at a 26° angle. For comparison, the numerical simulation representing this physical test was run for 80 ms of impact (i.e. the period when the significant variations of M D B velocity and acceleration occur). It was noted that the CPU time required for the simulation was only 1.5 hours using a single Pentium 4 - 2.8 GHz processor (i.e. 1/100* of the required processing time for the N C A C model). The general deformation results of the barrier from the simulation are shown in Figure 3-4 and correlate well with post-test photos and measurements of the barrier deformation provided in [70] after the event. Figure 3-4: Side view of the simplified M D B deformation - 4 6 -Figure 3-4 shows the isometric view of the M D B at 10 ms, 20 ms, and 80 ms respectively (left-to-right). The next step in the validation was to compare the velocity and acceleration time histories at the M D B ' s center of gravity. Figures 3-5 and 3-6 show the comparison of the acceleration and velocity records respectively between FEA simulation and test measurements. 12.00 10.00 -2.00 20.00 40.00 60.00 t ime (msec) 80.00 - • — FEA results - i — Test Results 100.00 Figure 3-5: NHTSA MDB center of gravity velocity - 4 7 -5.00 T 60.00 70.00 80.00 90, 0 0 — • — Test results FEA results 35.00 time (msec) Figure 3-6: NHTSA MDB center of gravity acceleration It can be observed from the curves that the full scale test results are well followed by the simulation results. Comparing these results, the maximum error of predicted velocity history of M D B center of gravity utilizing numerical simulation is less than 8%, while the maximum error of acceleration history of M D B center of gravity is 1 6 % . Since the design aspects of NHTSA M D B and their effects on occupant injury level have not been investigated in this research, and the simulation results of developed M D B model are within a reasonable error bound, the developed model was deemed suitable and utilized in side impact crash simulation in the following phases of work. The US SID dummy has been specified for use in assessing the performance of vehicles in side impact crash tests according to the test procedures defined in FMVSS-214. The general procedure for obtaining occupant injury values in a full-scale crash test is to record the acceleration time histories inside the SID and calculate injury measures including: 3.3. US SIDE IMPACT D U M M Y (SID) peak lateral pelvis acceleration; and - 4 8 -• Thoracic Trauma Index (TTI) The finite element model of the US SID employed within this study was acquired from the NHTSA website [71], i.e. version 1.0, and was used in its unmodified form. To examine the accuracy of this model, the following steps were taken: 1) A validated US SID model developed in M A D Y M O software [74] and the acquired L S - D Y N A model were utilized to simulate two identical sled tests in which the dummy impacts a rigid wall with the perpendicular velocity of 6.2 m/s. The results of these simulations were compared to assess the accuracy of the acquired US SID model. 2) Two standard calibration tests (as defined by FMVSS-214 for the actual physical US SID) were simulated using L S - D Y N A to assess the accuracy of the numerical model based on the accepted physical model results. The details of the above analyses are discussed in the following two sections (i.e. Section 3.3.1, and Section 3.3.2). 3.3.1. Sled test of the US SID A previously validated M A D Y M O US SID model was utilized to verify the acquired L S - D Y N A US SID model by comparing the results of a sled test scenario simulated with both models. The simulation involved impacting the US SID dummy into a fixed rigid wall at a perpendicular angle. The speed of the impact was 6.2 m/s perpendicular to the rigid wall plate (see Figures 3-7, 3-8). For consistency, the gravity was set to " o f f for both the M A D Y M O and L S - D Y N A analyses. The duration of the simulation and dynamic analysis was set to 50 ms, i.e. the time required for most side impact injury measures to reach a maximum. 3.3.1.1. MADYMO US SID Dummy Model A major advantage of using M A D Y M O in predicting vehicle crashworthiness is its exclusive dummy and human models database, with all of the M A D Y M O models being previously validated using - 4 9 -component and full scale testing on the complete SID [74]. In most cases the M A D Y M O models can also be coupled with other FE software, however unfortunately, L S - D Y N A (i.e. the FE software used in this study) cannot be coupled with M A D Y M O in the MS Windows platform, so the M A D Y M O US SID dummy model was only utilized for verification purposes in this research. For mitigating the analysis time of the described sled test, the M A D Y M O 'ellipsoid' formulation of the US SID dummy model was used in this study. This type of model is based fully on M A D Y M O ' s rigid-body modeling features. In this formulation the inertial properties of the dummy hardware components are assigned to the ellipsoids and cylinders, which constitute the geometry of the dummy. Figure 3-7: a.) M A D Y M O US SID dummy at the start of the analysis (t = 0); b.) M A D Y M O US SID dummy at t = 35 ms. - 5 0 -In the rigid-body model formulation, the structural stiffness of the SID's flexible components is lumped into kinematic joints, while the contact stiffnesses of the soft materials (i.e. flesh and skin components of the dummy) are represented by force-based contact characteristics defined for the ellipsoids. These characteristics are used to describe both contact interactions within the models, and between the model and its environment. Injury measures for the SID (i.e. TTI, peak lateral pelvic acceleration) are calculated using M A D Y M O ' s predefined validated algorithms. Further details of this SID model are available in [74]. 3.3.1.2. LS-DYNA US SID Dummy Model As the current study is utilizing L S - D Y N A as the primary simulation software, a compatible software SID model was required. The acquired L S - D Y N A SID model contains 35 rigid materials, 2712 beam elements, 12,803 shell and 41,297 solid elements. Most of the soft material (except the neck and chest inner rubber layer) within the dummy is defined using FuChangfoam material [69]. The neck and chest inner rubber are defined using MoonyRivl inrubber material [69]. Injury measures such as peak lateral pelvis acceleration and TTI are calculated using the simulated dummy's nodal acceleration history as obtained from locations equivalent to the FMVSS specified full scale crash test dummy accelerometer positions. 3.3.1.3. Results In terms of injury assessment, the most important output parameter values for the US SID dummy are: • the lower spine acceleration • the upper and lower rib acceleration • the pelvis acceleration as these parameters relate directly to the FMVSS-214 requirements for TTI (i.e. Thoracic Trauma Index) and peak lateral pelvis acceleration levels. Acceleration results for both the L S - D Y N A and M A D Y M O -51 -ellipsoid US SID models up to the test time of t = 50 ms are compared in Figures 3-9 to Figure 3-13 below. Figure 3-8: a.) LS-DYNA US SID dummy at the beginning of the analysis (t = 0); b.) LS-DYNA US SID dummy at t = 35 ms into the analysis - 5 2 -Lower spine acceleration (3 u u - i q -499--80--60--40--20--0--40-LS DYN A results 00 0.00 10.00 20.00 -20 60.00 70 00 time (msec) Figure 3-9: SID Model verification results: Lower spine acceleration Upper thorax acceleration -450--100--+se-MADYMO results LS DYNA ts 60.00 70 00 time (msec) Figure 3-10: SID Model verification results: Upper thorax acceleration -53 -o u o - i a Lower thorax acceleration l 1 o n M A D Y M O results I UU 1 \ / \ L S D Y N A results OU - o . 0 0 0 . ) 0 1 0 . 0 0 20W 3 0 . 0 0 I 4o7od 5 0 . b u 6 0 . 0 0 7 0 - o u A r\r\ t ime (msec) 0 0 Figure 3-11: SID Model verification results: Lower thorax acceleration Upper spine acceleration u o TO - 7 6 -- 6 0 -- 5 0 -- 4 0 -- 3 0 -- 2 0 -- 1 0 -— 0 -L S D Y N A results - i q . 0 0 0 . 0 0 1 0 . 0 0 2 0 . 0 0 3 0 . 0 0 4 0 . 0 0 \ / 5 0 . 0 0 6 0 . 0 0 7 0 1 0 0 0 t ime (msec) Figure 3-12: SID Model verification results: Upper spine acceleration - 5 4 -o u u a -460--140--1-20--100-1fJ.OO -80--60--40--20--40-Pelvic acceleration LS DYNA results MADYMO results 00 10.00 20.00 0 / 40.00 50.00 60.00 70 00 time (msec) Figure 3-13: SID Model verification results: Pelvic acceleration The acceleration values in Figures 3-9 to 3-13 show that both the L S - D Y N A and M A D Y M O SID dummies predict similar maximum peak values within 4%. These peaks could be directly applied to calculate the TTI and peak lateral pelvis acceleration. However, secondary peaks in some of the signals (i.e., lower and upper thorax acceleration) are a bit different. These differences may be accounted for by the nature of the analyses, i.e. L S - D Y N A uses the finite element method and assigns stiffness and inertia of the components to the material property while M A D Y M O uses rigid body dynamics and assigns stiffness of the components to the joint properties with springs and dampers. As the critical injury parameters are based on the peak values, differences in these secondary peaks are certainly notable but of little consequence to the analysis. - 5 5 -3.3.2. S I D s t a n d a r d c a l i b r a t i o n tests According to the NHTSA guidelines [73], the SID measurement device must pass two specified calibration tests prior to being used in a FMVSS-21 Compliance test. These two calibration tests require that the SID be struck in the lateral direction at: 1) the thorax, and 2) the pelvis, with a 152 mm diameter, 23.35 kg cylindrical ballistic pendulum at 4.3 m/s [73]. These two calibration test procedures will be explained in detail in the following two sections. The NHTSA test procedures (see FMVSS-214) also specify how the accelerometer data obtained should be sampled and processed. Analog data is to be recorded in accordance with the SAE J-211 class 1000 specification [75]. The data is then to be processed through the Finite Impulse Response (FIR 100) filter program. The FIR 100 filter program filters the data with a 300HZ, SAE 180 filter, then sub-samples the data using a 1600 HZ sampling rate and removes bias. The FMVSS-214 dummy requirements establish a window for the peak response of the measured major accelerations of the SID. Once the tested dummy provides responses within these corridors, it would be considered as a representative SID. It is this criterion that will be used to validate the SID model used in this study. 3.3.2.1. Pendulum Thorax Test The pendulum thorax test is the first calibration test that any developed SID must pass in order to be recognized as a valid representative dummy in the FMVSS-214 compliance test. The details of this test as well as required measurement devices mounted on the SID are described in this section (see Figure 3-14, Figure 3-15). The SID has three accelerometers mounted in the thorax region for measurement of lateral accelerations. The primary axis of each accelerometer is aligned perpendicular to the midsagittal plane of the SID (see Figure 3-15). One accelerometer is aligned perpendicular to the lumbar adaptor, while the other two accelerometers are mounted on the impacted side of the rib bar, one at the top and the other at the bottom (see Figure 3-15). The accelerometer at the top measures the left upper rib lateral (Y) - 5 6 -acceleration (see Figure 3-15) while the accelerometer at the bottom measures the left lower rib lateral (Y) acceleration. Figure 3-14: Pendulum thorax test setup -57-accelerometer Figure 3-15: position of pendulum test accelerometers and SID midsagittal plane The dummy position for the thorax impact is shown in Figure 3-14 and Figure 3-15. The longitudinal centerline of the impacting pendulum is placed at the lateral side, at the intersection of the centerline of the third rib and the rib bar, and perpendicular to the midsagittal plane of the thorax (see Figure 3-15). For a properly calibrated SID subjected to a thorax impact of 4.3 m/s, the peak twelfth thoracic vertebrae (Tn ) acceleration must be between 15 and 22 G, the peak left upper rib acceleration must be between 37 and 46 G and the peak left lower rib acceleration must be between 37 and 46 G. The acceleration time histories for the L S - D Y N A finite element simulation of the calibration test were sampled and fdtered in exactly the same manner as the physical tests, with the time histories of the above signals (i.e., upper rib acceleration, etc.) shown in Figure 3-16 through Figure 3-18. The peak values extracted from these figures have been recorded in Table 3-1. - 5 8 --5.00 Lower torso acceleration time (sec) A c c e p t a b l e r ange 0.05 0.06 Figure 3-16: SID Thorax calibration test: Lower spine lateral acceleration Upper torso acceleration 50.00 40.00 30.00 > o u (0 20.00 10.00 0.00 -10.00 -20.00 A c c e p t a b l e 0.05 .06 time (sec) Figure 3-17: Thorax calibration test: Upper thorax lateral acceleration time history - 5 9 -Lower spine acceleration time (sec) Acceptable 0:D6 Figure 3-18: Thorax calibration test: Lower spine lateral acceleration time history Table 3-1: Lateral impact thorax performance of L S - D Y N A US SID Acceptable Range (G) Dummy response (G) T12 peak acceleration 15<Ti2<22 21 Upper rib peak acceleration 37 < upper rib acc. < 46 39 Lower rib peak acceleration 37 < lower rib acc. < 46 39 TTI 26 < TTI < 34 30.5 The dummy response results show that the L S - D Y N A SID peak responses of the lower spine and the thorax as well as the TTI value are within the acceptable range specified by N H T S A in FMVSS-214, indicating that the L S - D Y N A SID model predictions correlate well with those of the physical SID. - 6 0 -3.3.2.2. Pendulum pel vie test The pendulum pelvis calibration test is the second calibration test which any developed SID has to pass prior to be utilized in FMVSS-21 Compliance test. The details of this test and its configuration (see Figure 3-19) as well as the results of acquired SID model during this test are outlined in this section. The SID has an accelerometer mounted in the rear wall of the pelvis instrument cavity for measurement of lateral acceleration in the pelvic region. The primary axis of the accelerometer is aligned perpendicular to the midsagittal plane of the SID (see Figure 3-15). The dummy position for pelvic impact is shown in Figure 3-18. The longitudinal centerline of the pendulum is placed 99.1 mm above the seating surface and passes through the H-point (see Figure 3-20) of the SID. The results of the peak lateral pelvic acceleration test are listed in Table 3-2, and must fall between 40 and 60 G to meet the specified calibration test requirements. Figure 3-19: L S - D Y N A SID Model: Pelvis pendulum test setup - 6 1 -Figure 3-20: L S - D Y N A SID Model: H-Point position in SID Table 3-2: Pelvis response in the standard pelvis calibration test of L S - D Y N A US SID Acceptable Range (G) Dummy response (G) Peak lateral Pelvis Acceleration 4 0 < P y < 6 0 58 Since the L S - D Y N A US SID shows acceptable thorax and pelvis behaviour in all verification and calibration tests, it has been deemed validated and sufficiently accurate for the use in subsequent full-scale side impact analysis. - 6 2 -3.4. FINITE E L E M E N T V E H I C L E M O D E L While only a limited number exist, most of the public domain vehicle finite element models (FEM) currently available (developed either by independent researchers and/or the National Crash Analysis Center (NCAC)), are accessible from the N C A C website [72]. As expected, based on the focus of past work in the vehicle crashworthiness area, nearly all were developed for simulation of frontal impact testing. Fortunately, there also exists, through N C A C , a version of the Ford Taurus model that was enhanced specifically for use in simulating side impact collisions (see Figure 3-19). This model was developed by EASi Engineering using the P A T R A N pre-processor and LS D Y N A , and is derived from an earlier frontal impact model [76]. The side door structure and the driver-side interior are modeled in more detail in this enhanced F E M model than in the original model developed for frontal impact studies of the Taurus. This enhanced model provides better and more accurate simulation results of side-impact collisions as validated through a comparison with the results of two actual full-scale instrumented side impact crash tests sponsored by NHTSA [19]. Since the Ford Taurus can be considered fairly representative of a typical North American passenger vehicle, and the side-impact model was enhanced and validated specifically for side impact testing, this model was selected for use in this research study. Figure 3-21: Ford Taurus finite element model - 6 3 -3.5. S U M M A R Y A N D C O N C L U S I O N S - P H A S E 1 A complete side impact simulation package consisting of a new more efficient M D B FE model, a validated SID model, and a mid-size FE target vehicle model based on the Ford Taurus, has been assembled and marks the completion of Phase 1 of this research project. These models, have been outlined, examined, and verified (as appropriate) to develop confidence in their accuracy and suitability for future use in side impact simulation and analysis. In the case of the M D B model, development work has been performed to simplify the model while maintaining accuracy for the purpose of increasing computational efficiency. The synthesis of this simulation package is, in itself, an achievement, and can be made available to other researchers working in area of side impact vehicle crashworthiness. But more importantly for this study, it constitutes an essential tool which will first be utilized to investigate the relative effects on occupant injury measures related to variations in bullet vehicle parameters (i.e. bullet vehicle's mass, velocity, etc - i.e. Phase 3), and ultimately to achieve the objectives of this project. The result of this work is discussed in the following chapters. - 6 4 -Chapter 4. COLLISION P A R A M E T E R E F F E C T S ON OCCUPANT INJURY IN SIDE IMPACT COLLISIONS 4.1. I N T R O D U C T I O N The risk of injury to an occupant during side impacts is clearly dependent on a wide range of variables related to the specifics of the collision event and the vehicles involved, as well as the occupant themselves (i.e. age, health, position, etc.). When addressing optimization of the vehicle structural design, it is extremely difficult to consider this wide range of variables and design an optimum vehicle structure for all types of collisions and vehicle occupants. Therefore the scope of this study has been limited to addressing a range of collision types, but does not consider the effects of occupant parameter variations on the occupant injury likelihood. Thus the US SID (i.e. 50 t h percentile male side impact dummy) was selected as the occupant representation during this research and the occupant parameters such as its position and configuration were kept at the specified values as defined by the FMVSS-214 compliance. The other two major types of parameters that affect the occupant injury in side impact collisions are vehicle design and collision related parameters. Vehicle design related parameters (i.e. stiffness of the vehicle side structure, side-airbags, etc.) are the ones that can be modified by the designers to increase the crashworthiness performance of the vehicle in side impacts. However, collision parameters such as bullet vehicle's velocity, mass, etc. cannot be controlled by the vehicle designers since their values differ from collision to collision. These parameters usually have a stochastic nature with their distribution potentially changing between (or even within) different regional jurisdictions. Although collision parameters cannot be controlled by the vehicle designer, their effect on the potential for occupant injury needs to be well understood in order to identify the vehicle design features which can mitigate injury over the required range of these parameters. This chapter presents Phase 2 work for this research project: An investigation to better understand and quantify the sensitivity of occupant injury measures to a range of collision parameters (e.g. striking vehicle's velocity, mass, vertical - 6 5 -and horizontal position of the impact point, etc.). This phase of work will utilize numerical simulations of the FMVSS side impact test and a SID occupant as developed previously in Phase 1 of this research work. 4.2. SIDE IMPACT SIMULATIONS After acquiring and validating the three FE components required for a complete side impact simulation model as discussed in Chapter 3 (i.e. Phase 1), this developed software package was used to perform a series of numerical simulations to examine the effects of side impact collision parameters on occupant injury risk. These parameters included the: 1) bullet vehicle mass, 2) bullet vehicle bumper height, 3) bullet vehicle initial impact velocity, and 4) horizontal position of the impact on the target vehicle structure. For the purposes of reproducibility and acceptance as a representative collision, the FMVSS-214 side impact standard test procedure was chosen as a basis for performing these analyses, with the UBC simplified M D B model and the Ford Taurus midsize vehicle model representing the bullet vehicle and target vehicle respectively. The effect of varying these collision parameters were assessed using established NHTSA defined injury indices as calculated from the US SID model results. 4.2.1. Simulat ion procedures In total, four sets of simulations (i.e. a total of 28 numerical analyses) were performed in this phase of the research, with each simulation set varying one of the listed collision parameters over a selected range. Within each simulation set, the remaining parameters were kept at the specified values as defined by the FMVSS-214 test (see Table 4-1). Variation range of these parameters was selected to cover most of the broad range of side impact collisions as follows: • The bullet vehicle's mass range was selected to cover the mass range of a small vehicle to a typical truck. - 6 6 -• The vertical position of the impact was also selected based on the height difference between a pickup truck and small vehicle (i.e. Table 4-1, Figure 4-1). • The velocity of the striking vehicle was varied within ±30% of FMVSS-214 impact velocity (i.e. 54 km/hr). This range was considered the side impact collision A V range having the highest probability of occurrence. • The range of bullet vehicle's horizontal position in respect to the target vehicle was selected to cover the range of side impact collisions in which striking vehicle impacts target vehicle in driver region of occupant compartment (i.e. see Table 4-1, Figure 4-1). The reason for this selection was that the direct impact of the bullet vehicle to the occupant compartment in side impact is considered to be more severe than direct impact of the bullet vehicle to the front or rear end of the target vehicle. Table 4-1: Range of simulation collision parameters and FMVSS-214 values M D B Vertical position Horizontal position from M D B Impact of M D B C G front wheel base (mm) Mass (Kg) M D B velocity (km/hr) (mm) F M V S S - 2 1 4 value 54 500 940 1350 Range of simulation 38-70 420-650 790-1090 690-2120 parameters (±30%) - 6 7 -Figure 4-1: M D B position variation with respect to the target vehicle Once the range of selected collision parameters was established, four sets of side impact simulations were performed to investigate the effect of these parameters on FMVSS-214 defined injury measures (i.e. the TTI, and peak lateral pelvic acceleration). The following section outlines the details of each set of simulations and obtained results. 4.2.2. Simulation results The results of the side impact simulations with varying collision parameters are presented in this section. The values of these parameters were altered by varying the velocity, mass, and position of the M D B model representing the bullet vehicle in these simulations. 4.2.2.1. Impacting vehicle (MDB) velocity It is intuitive that the impacting vehicle's velocity would be one of the predominant parameters that would affect the degree of injury to occupants in a side impact crash, however the expected changes in potential type and severity of these injuries with impact speed changes are not well known. To quantify the relationship between the bullet vehicle impact velocity and occupant risk measures (i.e. the TTI and peak lateral pelvic acceleration), seven numerical simulations were conducted in which the MDB's speed was varied between 38 and 70 km/hr (i.e. ±30% of the standard test speed of 54 km/hr) while the rest of -68 -the crash parameters were kept at the FMVSS-214 specified levels (see Table 4-1). The results obtained from these numerical simulations are shown in Figures 4-1 and 4-2. Figure 4-2: The T T I variation of US SID with M D B velocity c o HO-"•5 2 ^O-<D 0) lOO1 Ivic acc (G) 80-Ivic acc (G) Ivic acc (G) 60-a. 40-"re 20 re o-(0 0) Q. 30 40 50 60 70 MDB velocity (km/hr) 80 Figure 4-3: The peak lateral pelvic acceleration variation of US SID with M D B velocity As would occur in a real collision, the simulation results indicate that the striking M D B energy and momentum both increase with higher M D B velocity, thus increasing the amount of kinetic energy available to be transferred to the occupant during the impact. Consequently, injury indices would - 6 9 -generally be expected to increase as M D B impact velocity increased in this set of simulations. This is reflected in the results shown in Figures 4-1 and 4-2. Specifically, the TTI showed a near uniform increase with increasing M D B velocity (see Figure 4-1), while the peak lateral pelvic acceleration levelled off above 50 km/hr (see Figure 4-2). This levelling off phenomenon can be explained by comparing the door deformation time histories of the target vehicle for two different M D B impact velocities as plotted in Figure 4-4. As can be seen in this figure, a higher impact velocity increases the door intrusion and intrusion rate at the door waistline, causing early contact between the thorax and the high velocity intruding structure, thus increasing the TTI value (see also Figure 4-2). However at pelvic height, the data shows that the door intrusion and its intrusion rate does not substantially change at higher impact velocities once above 50 km/hr, thus resulting in no significant changes in peak lateral pelvic acceleration values at high velocity impacts (see also Figure 4-3). -4400 -50 50 100 150 200 250 Door deformation (mm) • Door time= - • — D o o r time= -A—Door time= - • — Door time= Door time= - • — Door time= k -Door def- vel=59. =15 ms def- vel=59. =25 ms def- vel=59. =50 ms def- vel=51. =15 ms def-vel=51. =25 ms def- vel=51 =50 ms defatt=0 4 km/hr, 4 km/hr, 4 km/hr, 3 km/hr, 3 km/hr, 3 km/hr, Figure 4-4: Door deformation time history for impact velocities of 51.3 km/hr and 59.4 km/hr - 7 0 -Based on this set of simulation results, it can be seen that the TTI value increases significantly (i.e. 41%) beyond its acceptable level (i.e. 85G based on FMVSS-214 requirements) with only a 30% increase in impact velocity above the standard test velocity (i.e. 54 km/hr). This indicates the predominant effect of the impact velocity parameter on the resulting TTI value and likelihood of injury. In contrast, the peak lateral pelvic acceleration value does not even surpass the acceptance level (i.e. 130 G based on F M V S S -214 requirements) for the same range of impact velocity variation. To examine the significance of this effect on TTI, and to enable us to compare it with the effect of other collision parameters on the TTI level, a linear regression was performed to obtain the correlation of non-dimensionalized TTI (i.e. TTI over its FMVSS-214 standard limit) with non-dimensionalized impact velocity (i.e. V M D B over its value in FMVSS-214 test procedure). This analysis provided the following relationship between M D B velocity and resulting TTI, over the range of M D B velocities considered: TTI V l i i . = 2 . 0 7 - ^ 5 . - 1 . 2 7 (4-1) 85 54 where V MDB : M D B velocity The adjusted R 2 value for the TTI was found to be 0.98, indicating an excellent correlation between TTI and M D B velocity. 4.2.2.2. Impacting vehicle (MDB) Vertical Position The next series of numerical simulations were performed to determine the effect of the bullet vehicle height on occupant injury. The variation in the bullet vehicle height could range from a small car height to a larger truck height. The published literature indicates that the height difference between a small compact vehicle (e.g. Hyundai Accent) and a larger pick up truck (e.g. Ford F150) can range up to 250 mm [77]. As such, seven simulations were performed in which the M D B vertical position was varied between -80 mm below and +150 mm above the FMVSS-214 specified bumper height for the M D B (see -71 -Figure 4-1). This puts the M D B ' s centre of gravity height between 420 mm and 650 mm above the pavement. Other crash parameters (i.e., M D B velocity, mass, etc.) were kept at the FMVSS-214 specified level for the tests (see Table 4-1). The results of these tests are shown in Figure 4-5 and Figure 4-6. Figure 4-5: The T T I variation of US SD3 with M D B bumper height l a 2 -S <D TO (0 <D 120 100 80 60 (TJ Q S. 8 8 4 0 20 400 450 500 550 600 650 700 MDB C G height Figure 4-6: The Peak lateral pelvic acceleration variation of US SID with M D B bumper height - 7 2 -As can be seen in Figure 4-5, the TTI value increased uniformly with increasing height of the impact, while the peak lateral acceleration (i.e. Figure 4-6) value does not vary significantly with increasing M D B C G height. The door intrusion profile was found to be the reason for such behaviour of the TTI and the peak lateral pelvic acceleration during this set of simulations. In order to explain this behaviour, the door deformation profile histories for two sample simulations (of the total set of seven simulations performed), are plotted in Figure 4-7. • Door def- MDB height = 600mm, time=15 ms — • — D o o r def- MDB height = 600mm, time=25 ms — * — D o o r def- MDB height = 600mm, time=50 ms — • — Door def- MDB height = 480mm, time=15 ms —>K— Door def- MDB height = 480mm, time=25 ms — • — Door def- MDB height = 480mm, time=50 ms — m -Door def at t=0 -50. 0 50 100 150 200 250 300 D o o r d e f o r m a t i o n (mm) Figure 4-7: Door deformation time histories for MDB height of 480 mm and 600 mm above the pavement. As can be seen in this figure, the higher M D B vertical position increased the intrusion depth of the door in thorax region of the SID, causing earlier loading of the thorax, and thus increasing the TTI level. However in contrast, the intrusion depth of the door in the pelvic region of the SID did not change significantly with increasing height of the M D B C G (i.e. Figure 4-7). This is why the peak lateral pelvic acceleration value did not show any large variation or dependency on M D B height during this complete set of simulations (i.e. Figure 4-6). The difference in the door intrusion profile within this set of -73 -simulations results from the variation in stiffness of the involved structure as the M D B height is varied. At low M D B height, the high stiffness of the lower parts of the struck vehicle (i.e. floor pan, rocker panel, etc) play a more dominant role relative to the vehicle's middle structure (i.e. door, A and B-pillars), which decreases the intrusion depth. As the M D B ' s C G height increases, the M D B puts more loading on the middle structure of the vehicle causing sharper intrusion of the vehicle side structure. The door tilts inward above the rocker panel and causes earlier loading of the occupant thorax through increased tilt angle of the door (see Figure 4-7). This however, has little effect on the loading of the occupant pelvis as the door deformation in the pelvic region of the occupant does not show a significant change with height variation of the M D B CG. The simulation results also show that once the M D B height exceeds its standard defined height (i.e. 500 mm as specified in FMVSS-214, see Table 4-1), the TTI level increases 20% above its acceptable level (i.e. 85 G based on FMVSS-214 requirements), while the peak lateral pelvic acceleration never exceeds 110 G, i.e. 26% below its acceptable level (i.e. 130 G based on FMVSS-214 requirements) within the selected range. This highlights the predominant effect of the TTI index relative to the peak lateral pelvic acceleration index in assessing vehicle crashworthiness in this set of simulations. To compare the significance of the M D B height on the TTI value relative to the effect of other collision parameters on the TTI, a linear regression analysis was performed. This analysis generated the correlation between non-dimensionalized TTI values and the non-dimensionalized M D B vertical position as provided by the following equation: TTI = 0.97 H MDB - 0 . 0 9 85 500 (4-2) where: H MDB : M D B height - 7 4 -The adjusted R 2 value based on the TTI was found to be 0.98 indicating a high correlation between the TTI and the vertical position of the bullet vehicle. 4.2.2.3. MDB Horizontal Position The other collision parameter that could affect the occupant injury level in side impacts is the horizontal position of the bullet vehicle with respect to the target vehicle. Clearly, the horizontal position of a side impact collision could vary anywhere from the front to the rear fender of the target vehicle, however, the direct impact of the bullet vehicle's C G to a region of the target vehicle which is in direct contact with the occupant would likely be considered to be the most severe condition for this collision type. To investigate the effect of this parameter on occupant injury risk, seven numerical simulations were performed in which the horizontal position of the M D B centreline was varied from 790 mm to 1090 mm from the front wheelbase centreline (i.e. see Figure 4-1). The selected range constitutes a variation of ± 150 mm from the M D B standard horizontal position (as defined in the FMVSS-24 compliance test) to cover the range of side impact collisions in which striking vehicle impacts target vehicle in driver region of occupant compartment. The other collision parameters were kept as specified in FMVSS-214. The results of these simulated tests are shown in Figures 4-8 and 4-9, which relate the horizontal position of the M D B centre of gravity (CG) to the FMVSS-214 defined injury measures (i.e. the TTI, and peak lateral pelvic acceleration). - 7 5 -8 6 8 4 8 2 8 0 « • Configuration ]A in Figure 4 - 1 ^ * • * • • * • i i 7 8 \76 ' 7 4 7 2 7 0 6 8 7 7 0 8 2 0 8 7 0 9 2 0 9 7 0 1 0 2 0 1 0 7 0 1 1 2 0 MDB horizontal position from the frontal wheelbase (mm) Figure 4-8: The T T I variation of US SID with horizontal position of side impact As can be seen in these two figures, the injury measures did not vary considerably with variations in the M D B ' s horizontal position, except for the TTI value which showed a substantial jump in the simulation results when the horizontal position of the M D B CG was aligned with the B-pillar (i.e. configuration A in Figure 4-1). While a change was not unexpected when this region of high structural stiffness was aligned with the striking M D B CG, the actual reason and extent of the effect was not known. Upon analysing the simulation results, it was found that direct loading of the B-pillar by the M D B causes it to plastically collapse, thus significantly changing the target vehicle's door deformation profile and causing early loading on the occupant's thorax by the intruding structure. In other cases without direct contact of the M D B with the B-pillar, the intruding structure's profile did not change substantially as the impact zone of the M D B was varied horizontally, as in these cases the B-pillar did not reach a collapse condition. - 7 6 -c o 2 jQ> 0) O O re o > 0) a 140 120 oJ 100H 80 40 £ 20 ^ 0 re a> a 770 820 870 920 970 1020 1070 1120 MDB horizontal position from the frontal wheelbase (mm) ure 4-9: The peak lateral pelvic acceleration variation of US SID with horizontal position of side impact - 4 6 G & O O TJ 0) SI « ^ o c o "55 o a E E, TJ C 3 O k. O) E re P o ' € a> > -100 100 200 • Door mm, - •—Door mm, - A — D o o r mm, - » — Door mm, -XS— Door mm, - • — Door mm, -A. -Door def- Hon time=15 def- Hor-time=25 def- Hor-time=50 def- Hor-time=15 def- Hor-time=25 def- Hor-time=50 def at t -pos= 10901 ms •pos= 10901 ms -pos= 10901 ms pos= 790 ms -pos= 790 ms •pos= 790 ms :0 300 Door deformation (mm) Figure 4-10: Door deformation time histories for M D B horizontal positions of 790 mm and 1090 mm from front wheelbase centreline. - 7 7 -To illustrate this effect, the door deformation profde histories for two simulation cases are plotted in Figure 4-10: Case 1) the M D B C G does not hit the B-pillar directly (i.e. M D B horizontal position = 790 mm), and case 2) the M D B C G hits the B-pillar directly (i.e. M D B horizontal position = 1090 mm). As can be seen in this figure, the door intrusion at the thorax level of the SID increased substantially once the target vehicle's B-pillar was directly hit by the M D B . As a result, injury indices are relatively constant for the range of the horizontal positions examined until the B-pillar becomes directly aligned with the M D B centre of gravity (CG). 4.2.2.4. MDB Mass The striking vehicle's mass is another factor that could affect injury levels in a side impact crash. To investigate the effect of this collision parameter on occupant injury level in side collisions, seven simulations were performed in which the M D B ' s mass was varied from 690 kg to 2120 kg. This range is within ±50% of the M D B standard mass (defined in FMVSS-24 compliance test) and effectively covers the higher probability potential range in bullet vehicle mass (i.e. note the mass of a S M A R T FOR TWO vehicle is 730 kg and that of the Ford F-150 truck is 2200 kg). As with the previous numerical simulations, other simulation parameters were kept consistent with FMVSS-214 specifications (see Table 4-1). The results of these tests are shown in Figure 4-1 land Figure 4-12. -78 -Figure 4-11: The effect of M D B mass on the T T I level in side collisions Figure 4-12: The effect of M D B mass on the peak lateral pelvic acceleration in side collisions As expected, impact momentum and energy increases as the M D B mass increases. However, the energy and momentum transfer from an impacting object to the target vehicle relies on maintaining contact between them. Once the impacting object loses contact with the target vehicle's side structure, it can no longer transfer momentum and energy to the target vehicle. Figure 4-13 and Figure 4-14 shows deformation and contact duration of a section of the M D B and the door (which is in direct contact with - 7 9 -the US SID) for simulations in which the M D B mass was set to 1350 kg and 1890 kg respectively. As can be seen in these two figures, the 1350 kg M D B started losing its contact with the door 35 ms after initial impact, while the 1890 kg M D B lost contact with the door only 25 ms after initial impact, thus limiting the amount of momentum and energy that could be transferred from M D B to the door within first 50 ms of the impact (i.e. the time period in which injury indices maximize in side collisions) in the heavier M D B . This early separation of M D B from the target door occurred in the simulations in which the M D B ' s mass was over 1400 kg. When the M D B ' s mass was below 1400 kg, some portion of the increased impact energy transferred to a part of the door, which was in contact with the occupant, for a longer period of time causing higher injury risk (i.e. higher TTI and peak lateral pelvic acceleration). However, when MDB' s mass was increased over 1400kg, the door structure deformed in such a way that the M D B lost contact with the portion of the door which was close to the occupant, thus no longer being able to transfer additional impact energy after initial contact. This part of the door was thus limited in its ability to affect injury parameters once no longer in contact with the M D B . Therefore, both the TTI and peak lateral pelvic acceleration remained almost constant when the M D B mass reached or exceeded the 1400 kg level, and decreased for M D B mass values below this level (see Figure 4-11 and Figure 4-12). Figure 4-13: Deformation and contact duration of M D B and the door with the US SID for M D B mass - 1350 kg -80-Figure 4-14: Deformation and contact duration of MDB and the door with the US SID for MDB mass = 1890 kg Sugimoto et al [58] and Hobbs [6] reported a similar effect of increasing mass of the M D B on the injury indices, however, the effect of a mass reduction of the striking vehicle below the FMVSS-214 standard M D B mass was not examined in these analyses as small vehicles were not part their full-scale experiments [6, 58]. The target vehicle utilized in these previous analyses are different from the one utilized in the current study, and unfortunately the presented data in these articles is very limited. Thus, only the general trends of the results are compared here. 4.3. SUMMARY AND CONCLUSIONS - PHASE 2 The objective of this phase was to investigate the effect of four collision parameters (i.e. striking vehicle's velocity, mass, vertical and horizontal position of the impact point) on occupant injury measures. To accomplish this objective, numerical simulations were performed utilizing a previously developed side impact collision simulation package (i.e. Phase 1). The results of this phase have lead to the following conclusions (listed in order of decreasing significance): • The TTI was found to be the predominant injury index (when compared with the peak lateral pelvic acceleration) within the defined range of collision parameters in this study. -81 -As reported in the results section of this phase, the peak lateral pelvic acceleration value did not exceed the compliance acceptance level (i.e. 130G) as defined in FMVSS-214, while the TTI value exceeded its acceptable value (i.e. 85G) in several of the side impact simulation cases. • The initial velocity of the striking vehicle had the highest effect on the occupant injury measures, while the height, mass, and the horizontal position of the impacting vehicle were found to be the second, third and the fourth most significant collision parameters affecting the injury likelihood, respectively. The results of the linear regression analyses and comparison of the TTI variation (i.e. as the predominant injury measure) for each of the different collision parameters confirmed the above statement. • Increasing the impact velocity substantially increased the occupant injury measures. Higher impact velocity significantly increases the amount of energy available to be transferred to the occupant, and injury indices would generally be expected to increase. However it was found that once the impacting vehicle's velocity exceeds 50 km/hr, the door intrusion rate at pelvic level of the SID is significantly lower than its rate at thorax level of the SID. This causes an earlier contact of the SID's thorax with high velocity intruding structure, thus increasing the TTI value, while the peak lateral pelvic acceleration value does not show a significant variation. • Increasing the vertical position of the bullet vehicle increased the TTI value. Relatively higher C G of the bullet vehicle caused a sharper intrusion profile which concentrates the loading on the occupant's chest causing a higher thorax injury risk, and since door deformation in pelvic region of the occupant did not show a significant change with varying height of the M D B C G , this does not alter pelvis injury risk. - 8 2 -• Reducing the mass of the impacting vehicle below the 1400 kg decreased the occupant injury measures, while increasing the mass of the impacting vehicle above the 1400 kg did not cause a significant variation of the injury measures. The early separation of the impacting vehicle from target vehicle's door structure was found to be the main reason for small variations of injury measure values once the impacting vehicle's mass increased above 1400 kg. • The horizontal position of the impacting vehicle did not affect the injury measures until the CG of the impacting vehicle was aligned with the B-pillar of the target vehicle, thus resulting in a sudden jump in the TTI value. According to the analyses, the horizontal position of the impact does not affect the intrusion profile of target vehicle's side structure (within the range studied) until the impact position causes plastic failure of the B-pillar and increases the door intrusion and velocity at the door waistline. This causes earlier contact between the SID's thorax and the intruding structure, thus increasing the TTI level. During this phase of the work, the developed and utilized side impact simulation package was found to be effective in predicting the occupant injury risk in such collisions, however, completing each analysis was very time consuming (i.e. 48 hours for each analysis with 2.8 GHz CPU). As described earlier, one of the major goals of this study is to optimize the selected target vehicle structure for side impact collisions. Since computational time and cost are essential factors in the numerical analysis and optimization process, the developed simulation package appears to still be somewhat inefficient for performing the optimization process, which requires a large number of numerical simulations. The next chapter describes and verifies a new method to increase the efficiency of such a simulation package and reduce the analysis time. -83 -Chapter 5. SIDE STRUCTURE PERFORMANCE CRITERION (SSPC) 5.1. I N T R O D U C T I O N For the early stages of vehicle structural development, numerical modelling and simulation is rapidly becoming the accepted tool for investigating the crashworthiness performance of the newly designed structure. As vehicle compliance is the ultimate goal, these numerical methods typically employ one of the standard test procedures (FMVSS-214, ECE-R95, etc.) for this purpose. Currently, designers rely on indices based on specified measured responses of crash test dummies (i.e. TTI, maximum pelvis acceleration, etc.) to assess how a vehicle structure performs in the desired crash situation. This can be a very time consuming procedure since a typical vehicle FE model is usually very sophisticated, and thus adding an additional complicated dummy FE model to the analysis can dramatically increase the analysis time. This is not particularly appealing, especially at the beginning of the design process when many potential structural concepts are available, thus requiring many numerical simulations in order to narrow the field and begin to optimize the vehicle structural performance during a crash event. The objective of this phase, i.e. Phase 3, of this research program is to reduce the complexity of numerical modeling early in the vehicle design process. To achieve this, a new index - named the Side Structure Performance Criterion (SSPC) - has been conceived, developed and evaluated. This new dimensionless index acknowledges the variation in the occupant's vulnerability in different regions of the body, and using the FMVSS-214 injury measures and limits (i.e. specifically TTI and peak lateral pelvis acceleration), provides a new proposed assessment criterion for computer-based vehicle side impact simulations. This chapter introduces this new criterion and presents the procedure used to verify its utility for vehicle side impact performance assessment. - 84 -5.2. P R O P O S E D N E W I N D E X - SIDE S T R U C T U R E P E R F O R M A N C E C R I T E R I O N (SSPC) In the development of this new criterion, it was recognized that the force acting on the occupant during a side impact collision is proportional to the occupant's body acceleration which is a direct function of: • The door velocity at the contact point. A higher inner door velocity will result in a higher velocity difference between the intruding structure and the relatively stationary or low velocity occupant body at the beginning of the contact, thus increasing the potential for injury. • The amount of intrusion of the vehicle's side structure. The amount of side structure intrusion affects the contact duration between the occupant and the intruding structure. A greater intrusion will result in higher contact duration between the occupant and the side structure, thus increasing the amount of the transferred energy to the occupant, resulting in an increased injury potential for the occupant. • The relative door-occupant compliance. The relative door-occupant compliance determines the rate of energy transfer from the vehicle side structure to the occupant. A better vehicle design will reduce the energy transfer rate and peak impact force to the occupant, thus decreasing the risk of injury. (It should be note that accurately assessing this parameter for the vehicle side structure is quite complicated and is beyond the scope of this thesis. As such for simplicity, and because it is believed that these effects due to compliance variation are somewhat secondary, the varying effects of the door-occupant compliance are not dealt with in this research). Based on the described parameters and their effect on the occupant injury, the proposed relationship for the SSPC in side impact crashes was defined as follows: - 8 5 -d-dr V SSPC = max( ( - . ) d„ c(t-t0) (5-1) where: d '• Intrusion distance (lateral-component) of any point on the interior door structure at given time / (see Figure 5-1) d0 : Initial distance (lateral-component) between occupant and interior door structure at the point selected (see Figure 5-1) dG : Lateral displacement of the struck vehicle's centre of gravity (CG) y '• Velocity (lateral-component) of the point on the interior structure ° 'Time when the initial contact between M D B and bullet vehicle starts c • Acceleration limit at each region of the intruding door (based on occupant body tolerance) t = 23 ins Conditions at the begmning of the impact ^Velocity of contact nodes Door displacement (»•«?• d) nt t=23 ins profile Figure 5 -1 : Schematic of the geometry elements utilized in defining the SSPC - 8 6 -The first term in the above equation ( ) represents the intrusion weighting function. The d — dG term in the SSPC equation is the side structure deformation at each contact node, which is then normalized over the initial distance between the occupant and inner door structure - i.e. d0 (see Figure 5-1). The larger da becomes, the shorter the contact time between the occupant and the side structure, thus reducing the potential for injury. V The second term ( ) is a weighting function that accounts for the amount of momentum c(t-t0) going towards the occupant body during the side impact event. The V term in the SSPC equation is the velocity of each contact node (i.e. Figure 5-1) that is normalized by the parameter (c) multiplied by the impact time (i.e. t —10). The term (t —10) represents the time duration after initial impact of the bullet and m the target vehicle. The constant term in this equation has dimensions of acceleration (i.e. — ) and it is specified based on the injury measures utilized (i.e. FMVSS-214 maximum allowable TTI and peak lateral pelvis acceleration): m • c = 130 G (i.e. 1275 — ) for pelvis area (base on peak lateral pelvis acceleration criteria) s m • c = 85 G (i.e. 833 — ) for thorax and abdomen area (base on peak TTI) s The numerical modeling and side impact simulation results were used as inputs for calculating the SSPC. The following sub-section describes the SSPC calculation procedure as applied to the FMVSS-214 standard test condition. - 8 7 -5.2.1. S S P C calculation To calculate the developed criterion (i.e. SSPC), the earlier developed side impact simulation package (Phase 1) was utilized. Once the finite element simulation of FMVSS-214 test was completed, the displacement and velocity time histories for the two sets of nodes on the target vehicle's inner door elements were selected and subsequently used for the SSPC calculation. These nodes included: 1) The nodes that are in contact with the thorax area (as shown in Figure 5-2). 2) The nodes that are in contact with the pelvis area (as shown in Figure 5-3). Since the injury tolerance for the thorax and abdomen are different from those of the pelvic area, the SSPC value was calculated separately for each of these two regions. The following steps were pursued to calculate the SSPC in thorax region: 1) The deformation of each node in contact with the thorax was obtained (see Figure 5-4), and normalized using da =150 mm (see Figure 5-1). 2) The velocity of the contact nodes (see Figure 5-5) were normalized by the thorax constant (c = 85 G) and multiplied by the impact time (i.e. (t — t0)). 3) The following equation was calculated over the impact period for all contact nodes using the products of the first two steps: ( d — d, G V ) . The result of this calculation 150 8 5 ( r - / 0 ) for node number (918) and its time history is plotted in Figure 5-8 (see Figure 5-2 for the associated node position). 4) The maximum SSPC value (calculated based on the above equation) for all contact points was considered as the thorax SSPC: i.e. SSPC, = max( d-d, c, V •)• 150 8 5 ( / - / 0 ) -88-Figure 5-2: The door nodes which are in contact with thorax area Figure 5-3: The door nodes which are in contact with pelvis area - 8 9 -LS-DYNA USER INPUT 0.06 0.08 Time (sec) Figure 5-4: Deformation of the nodes in contact with the thorax (FMVSS-214 test condition) zn r H r -+ LU o > 2 0 -2 -4 -6 -8 -10 -12 14 LS-DYNA USER INPUT -V MR? m m WNMffl mm if I i i 0 0 .02 0 .08 0. 0 .04 0 .06 * Time (sec) • Figure 5-5: Velocity of the nodes in contact with the thorax (FMVSS-214 test condition) - 9 0 -A similar approach was utilized to calculate the maximum SSPC in the pelvis area. To calculate SSPC in this region, the nodes in contact with the pelvis region were identified (see Figure 5-3). The deformation and velocity of these nodes were obtained from the simulation package as shown in Figure 5-6 and Figure 5-7. Then the SSPCp was calculated using steps similar to those for calculating the previous SSPC, value with the major difference being the value assigned to the normalizing constant (i.e. c) in the calculation process (see Equation (5-2)). Since the human body has a higher injury tolerance in pelvis area, the c value was increased to 130 (based on peak lateral pelvis acceleration criteria). d — dr-SSPC, = max( 150 130( f - f 0 ) ) (5-2) Once both the SSPC, and the SSPC P were calculated, the final value of SSPC was specified as: SSPC = max(SSPC,, SSPC p ) (5-3) LS-DYNA USER INPUT 1<D o GL. •Jo l: >-100 150 -200 Node No - A . 929 - B _ 930 -C_931 _D_ 947 - E - 956 E 957 - G _ 958 -±L 959 983 _ J L 984 JK_ 985 _L_ 986 0.04 0.1 Or 06 0.08 Time (sec) Figure 5-6: Deformation of the nodes in contact with the pelvis (FMVSS-214 test condition) -91 -Ill L S r D Y N A U S E R I N P U T -6 -8 ,10 -12 -14 " 1 Hi » V KV JI ft ' 1 jWKf - A i f --0 0.02 008 0:1 0.04 0.06 Time(sec) Figure 5-7: Velocity of the nodes in contact with the pelvis (FMVSS-214 test condition) - 9 2 -Elimination of the SID model from the side impact simulation package and the introduction of the SSPC criterion to allow performance assessment were found to reduce the analysis time required for case evaluation by a factor of 10. However, verification of the ability of this criterion to be utilized as an injury severity measure in side impact performance assessment is still necessary to ensure confidence in the research results. The next section discusses the SSPC verification procedure and results. 5.3. SSPC V E R I F I C A T I O N To verify the SSPC, two types of numerical simulations with similar accident parameters (i.e. same M D B velocity, mass, etc.) were conducted. The first simulation type excluded the SID to calculate the SSPC while the second included the SID to calculate the injury measures (i.e. the TTI and peak lateral pelvis acceleration). Each simulation type included four sets of numerical analyses in which one of the accident parameters was varied over a reasonable range (see Table 4-1) while the remaining parameters were kept at the specified FMVSS-214 test values. These accident parameters included M D B velocity, CG height, horizontal position, and mass. The following sub-sections describe these sets of simulations. 5.3.1. The effect of M D B velocity variations on the S S P C As was determined in the previous chapter, the M D B velocity is one of the predominant accident parameters that affect occupant injury risk. To find the correlation between the SSPC and occupant injury measures with varying M D B velocity, seven sets of simulations were performed in which the M D B ' s speed was varied between 38 and 70 km/hr (i.e. ±30% of the standard test speed of 54 km/hr) while the remaining parameters were kept at the FMVSS-214 specified levels (see Table 4-1). For each set of accident parameters, two separate simulations were performed: the first included the SID to calculate the TTI and peak lateral pelvis acceleration while the second one was run without the SID to calculate the SSPC. The results of these analyses are summarized in Table 5-1, with the results plotted in Figure 5-9. -93 -Table 5-1: Correlation between M D B velocity and injury measures with SSPC M D B velocity (km/hr) T T I (G) 2 P y (G) TTI/85 P y /130 Max (SSPC p ,SSPC t) 37.8 15 27.9 0.1764 0.2146 0.138 43.2 24.8 45 0.2917 0.3461 0.2176 51.3 68.5 104.8 0.8058 0.8061 0.3897 54 71.45 109 0.8405 0.8384 0.4724 59.4 83.08 102.7 0.9774 0.79 0.5967 64.8 99.76 103.7 1.1736 0.7977 0.7198 70.2 120.1 124.5 1.4138 0.9576 0.889 R 2 = 0 9737 0 0.5 1 1.5 max(TTI/85,Py/130) Figure 5-9: Correlation between S S P C m a x and maximum normalized injury measure with varying M D B velocity 2 P y: Peak lateral pelvic acceleration - 9 4 -As expected, injury measures (i.e. TTI and peak lateral pelvis acceleration) as tabulated in Table 5-1 were increased with increasing M D B velocity, and as required, a similar trend can also be seen in SSPC variation with M D B velocity. This is because greater impact energy increases the rate and magnitude of the transferred energy to the struck vehicle structure and the occupant, which causes higher SSPC and injury potential respectively. The SSPC is a single dimensionless criterion that is defined to predict occupant injury severity in comparison to FMVSS-214 injury measures that are defined to predict the injury potential in different parts of the body and have units of acceleration. To make these two types of measures comparable, first both the TTI and peak lateral pelvis acceleration were normalized over their defined limits in FMVSS-214 (see Table 5-2) and then, the higher normalized injury measure compared with SSPC. Figure 5-9 shows a high linear correlation (i.e. R2=0.97) between SSPC and maximum normalized injury measures in this set of numerical simulations. 5.3.2. The effect of MDB vertical position variations on the SSPC The M D B vertical position was the next crash parameter varied to examine the correlation between the SSPC and injury measures. Similar to the previous crash parameter, seven sets of numerical simulations were performed in which the M D B vertical position was varied over a reasonable range (see Table 5-2) while the other collision parameters were kept at FMVSS-214 standard levels (as defined in Table 4-1). Two types of simulations were again carried out for each set of collision parameters, i.e. with and without the SID to calculate the injury measures and the SSPC respectively. The results of these simulations are summarized in Table 5-2 and Figure 5-10. As mentioned earlier, increasing the M D B C G height puts more loading on more compliant parts of the struck vehicle's side structure (particularly the centre region of the door) which increases the extent of door intrusion. As expected, this results in more concentrated loading on the occupant thorax and increases both the TTI and consequently the SSPC value. As can be seen in Table 5-2, however, the peak lateral pelvis acceleration did not change noticeably due to the less significant change in lateral intrusion of the door adjacent to the pelvis area. - 9 5 -Table 5-2: Correlation between MDB C G height and injury measures with SSPC MDB C G height (mm) TTI (G) P y(G) TTI/85 P y /130 Max (SSPCp,SSPCt) 420 63.08 83.96 0.7421 0.6458 0.2933 480 73.75 95.5 0.8676 0.7346 0.4148 500 71.45 109 0.8405 0.8384 0.4724 555 81.75 100 0.9617 0.7692 0.53093 600 92.45 111 1.0876 0.8538 0.6484 625 94.8 104.2 1.1152 0.8015 0.6865 650 101.2 100 1.1905 0.7692 0.771 max(TTI/85,Py/130) Figure 5-10: Correlation between SSPC m a x and maximum normalized injury measure with varying MDB C G height - 9 6 -Figure 5-10 shows a high correlation (i.e. R2=0.97) between the SSPC value and the maximum normalized injury measure. Due to the reasons described earlier, it was noted that both the TTI and the SSPC t were the two predominant parameters affecting the maximum normalized injury measure and the SSPC respectively. 5.3.3. The effect of M D B horizontal position variations on the SSPC The M D B horizontal position was another accident parameter that was altered to investigate the validity of the SSPC and its correlation with the SID injury measures. As listed in Table 5-3, six sets of simulations were performed in which the horizontal position of the M D B centreline was varied from 789 mm to 1089 mm from the front wheelbase centreline. The other accident parameters were kept as specified in FMVSS-214. Again, each set of simulations were preformed with and without the SID. Once the analyses were complete, SID injury measures (TTI, and peak lateral pelvis acceleration) and SSPC values were calculated and their correlations examined. The results of these analyses are summarized in Table 5-3 and Figure 5-11. Table 5-3: Correlation between the M D B horizontal position and injury measures with the SSPC M D B horizontal position from frontal wheel- base (mm) T T I (G) Py(G) TTI/85 P y /130 Max (SSPC p ,SSPC t) 789 70.3 100.8 0.827 0.775 0.445 859 69.7 95.2 0.820 0.732 0.457 889 72 102.1 0.847 0.785 0.459 939 71.4 109 0.840 0.838 0.472 989 71.7 115.8 0.843 0.89 0.476 1089 83.3 114.5 0.98 0.88 0.515 - 9 7 -The results of these simulations indicated that the M D B horizontal position does not notably change side intrusion profile unless the MDB directly hits the B-pillar and forces it to plastic collapse. In this case, the target vehicle deformation profde changes significantly causing an early loading on the occupant's thorax, and results in increases in both the TTI and the SSPC values. In the other simulations in which B-pillar did not collapse plastically, injury measures and SSPC did not vary considerably. 0.52 0.51 0.5 >< 0.49 TO E O 0.48 Q_ in to 0.47 0.46 0.45 0.44 0.8 F T = 0 . 9 0 2 4 P y = p e a k l a t e r a l p e l v i c . a c c e l e r a t i o n . 0.85 0.9 0.95 m a x ( T T I / 8 5 , P y / 1 3 0 ) Figure 5-11: Correlation between the S S P C m a x and the maximum normalized injury measure with varying M D B horizontal position Although injury measures showed some small variation (with the exception of one set of simulations) with changing MDB horizontal position, the maximum normalized value of these measures was very well correlated with the SSPC value. Figure 5-11 illustrates the high linear correlation (i.e. R2=0.90) achieved between the SSPC and maximum normalized injury measures in the described set of numerical simulations. - 9 8 -5.3.4. The effect of M D B mass variations on the SSPC The M D B ' s mass is another factor that was chosen to investigate the correlation between the SSPC and the SID injury measures. Similar to investigating the previous crash parameters, seven sets of simulations (see Table 5-4) with varying M D B mass was setup, while the other collision parameters were kept at the FMSSS-214 level (see Table 4-1). The SID injury measures and the SSPC were calculated utilizing the methods described earlier. The results are summarized in Table 5-4 and the correlation between the SSPC and the SID's maximum normalized injury measure is shown in Figure 5-12. Table 5-4: Correlation between the M D B mass and injury measures with the SSPC M D B mass (Kg) T T I (G) Py (G) TTI/85 P y /130 Max (SSPC p ,SSPC t) 675 17.3 28.4 0.204 0.218 0.301 810 33.5 53.3 0.394 0.410 0.338 1012 44.6 60.4 0.525 0.464 0.351 1375 71.3 109 0.838 0.838 0.472 1755 82.9 98.6 0.975 0.758 0.526 1890 80 110.8 0.941 0.852 0.538 2092 84.9 109.4 0.999 0.841 0.548 Similar to the results of the previous phase (i.e. Phase 3), when the M D B mass was below 1400 kg, both the TTI and the peak lateral pelvic acceleration were increased with increasing M D B mass, however, once the M D B mass was increased to higher than 1400 kg, both the TTI and the peak lateral pelvic - 9 9 -acceleration remained at the same level. A similar trend can also be seen in the SSPC variation with the M D B mass (see Table 5-4). 0 . 6 0 . 5 0.4 x (0 E O 0 . 3 CL CO W 0 . 2 0.1 — S 0.969 Py= peak lateral pelvic acceleration 0 . 2 0.4 0 . 6 0 . 8 max(TTI/85,Py/130) 1.2 Figure 5-12: Correlation between S S P C m a x and maximum normalized injury measure with varying M D B mass Similar to the results of the previous set of simulations, the SSPC and the maximum normalized injury criteria of the SID were found to be well correlated as is illustrated in Figure 5-12. A correlation coefficient R2=0.969 was found from the linear regression analysis performed between the SSPC and the maximum normalized injury measure. 5.4. DISCUSSION The results of the above sets of simulations are summarized and their significance is discussed in this section. These results consist of four sets of side impact crash simulations, in which accident parameters (i.e. M D B ' s mass, velocity, etc) were altered to verify the new developed injury criterion (i.e. the SSPC) and investigate the correlation between the SSPC and the SID's maximum injury measures. To accomplish this, both the TTI and the peak lateral pelvic acceleration were first normalized using the 100-FMVSS-214 defined limits, and then the maximum normalized values were correlated with the SSPC m a x . Figure 5-9 through Figure 5-12 show the correlation between the SSPC and the maximum normalized injury measures for the various simulation runs performed. As a result, the TTI was found to be the predominant injury measure relative to the peak lateral pelvic acceleration in most simulation cases. As for other few cases, the normalized TTI values were found to be very close to the normalized peak lateral pelvic acceleration values. These cases also occurred, when both the TTI and the peak lateral pelvic acceleration values were substantially lower than their acceptable level (i.e. 60-80% below FMVSS-214 acceptable limit). This was expected due to the higher injury risk of the thorax region in side impact collisions [9]. Therefore the TTI was considered as the main injury indicator of the SID within the selected range of the side collision parameters. To obtain the relationship between the TTI and the SSPC, a linear regression analysis was performed utilizing the results of all four sets of SSPC verification simulations, with the result provided below: — = 1.546 S S P C + 0.0983 (5-4) 85 R 2 = 0.8386 0 0.2 0.4 0.6 0.8 1 S S P C Figure 5-13: Correlation between the SSPC and the TTI/85 - 101 -As shown in Figure 5-13, high correlation was found between the normalized TTI and the SSPC (i.e. R2=0.838) indicating the accuracy of utilizing the SSPC instead of the TTI in side impact simulations. As described earlier, occupant injury is the function of both accident parameters and structural parameters. However in this chapter, the target vehicle's structure was not altered during the SSPC verification simulations and only the collision parameters (i.e. M D B velocity, mass, position, etc) were changed to monitor the SSPC and the injury measures correlation. A linear regression was performed to obtain the relation between the SSPC and the collision parameters including the M D B speed, vertical position, horizontal position, and mass. To make this relationship dimensionless, collision parameters were normalized over their standard value specified in FMVSS-214 compliance (see Table 4-1): SSPC, = -1.779 +1.258 S + 0.249 M + 0.54 V + 0.19 H 8 0 (5-5) a = 0.025 where: SSPCgg: SSPC value for the current (unaltered) structure and geometry of the target vehicle S: normalized M D B speed M: normalized M D B mass v: normalized M D B C G height H: normalized M D B horizontal position a : standard deviation of the regression analysis The above equation also confirmed the predominant effect of the collision velocity on the occupant injury likelihood relative to the other parameters. This was because the gradient of SSPCgo had the highest value in the direction of the M D B speed (i.e. S). The next most influential collision parameters on - 102-the SSPC were M D B height (i.e. V) , mass (i.e. M), and horizontal position (i.e. H) respectively as indicated below: dSSPC„ dSSPC, dSSPCe dSSPCe dS dv dM dH The developed equation in this section (i.e. Equation 5-5) will be utilized in the next two phases (i.e. Phase 4, 5) to develop a general equation which correlates the SSPC to both the collision parameters and the structural parameters. 5.5. SUMMARY AND CONCLUSIONS - P H A S E 3 To increase the efficiency of the numerical simulation work for evaluating vehicle structural side impact performance, a new criterion, i.e. SSPC has been introduced. As discussed earlier, SSPC is a criterion based solely on parameters related to the struck vehicle's side structure which has been proposed to quantify the severity of the side impact collision and occupant injury. Numerical simulation and a previously validated side impact simulation package were utilized in this phase of work to perform the SSPC calculation and verification process. Utilizing the new SSPC for assessment provides two predominant advantages with respect to computational efficiency: 1) Since the SSPC is evaluated based only on parameters from the target vehicle's side structure, it eliminates the need for a SID numerical model within the simulation package, thus reducing computational time and expense. 2) Since the severity of the impact punch affects the target vehicle's side structure earlier than the occupant, the SSPC maximizes earlier in the crash simulation than the SID injury measures (i.e. typically within the first 25 msec of the impact). As such, the required computational simulation period can be significantly reduced, again reducing computational time and expense. - 103 -Because of the reasons outlined above, utilizing the SSPC for crashworthiness assessment of the target vehicle reduced the simulation time by the factor of 14, increasing the efficiency of the analysis that is crucial in the optimization process of the vehicle structural performance during a side impact crash event. However the developed new index (i.e. SSPC) has the following limitations that need to be considered prior to the usage: 1) The SSPC does not consider the effect of the relative door-occupant compliance. Thus this index is unable to assess the effects of the vehicle interior structure (i.e. padding system) and supplementary safety devices such as side airbags on occupant injury likelihood in side collisions. 2) The SSPC has been verified based on FMVSS-214 compliance requirements. Further efforts are required to validate/verify this index based on other side impact compliances (i.e. ECE-R95 [13]) in order to increase the reliability of the SSPC in predicting the occupant injury likelihood. In spite of the above limitations of the SSPC, the high correlation between the SSPC and the TTI, as the predominant injury measure, built confidence in utilizing the SSPC as an index that can assess the performance of the selected target vehicle's structure within the above range of side impact collisions. Phases 2 and 3 of this research program have only investigated the effects of the collision parameters on occupant injury measures and the SSPC. This is because vehicle designers cannot change the above collision parameters of the striking vehicle as their values for any individual collision will be determined by a probabilistic distribution which will vary from one jurisdiction to another. However, designers can alter the target vehicle structural parameters (i.e. thickness and geometry of structural elements) to improve vehicle crashworthiness and thus improve occupant safety. The next chapter discusses Phase 4 of the research project - to utilize the new SSPC to assess potential enhancements in - 104-vehicle side impact protection through changes in the relative stiffness of various predominant components of the vehicle structure. This next phase of the research work is designed to identify and highlight potential vehicle structural design strategies to mitigate occupant injury in side impact collisions. - 105 -Chapter 6. P A R A M E T R I C STUDY O F T H E V E H I C L E SIDE STRUCTURE 6.1. I N T R O D U C T I O N Since automobile manufacturers and their design engineers do not have any control over accident parameters (i.e. accident velocity, position, etc.) which vary significantly due to regional, driver and environmental factors, their capabilities for reducing occupant injury risk during collisions are limited to improving the vehicle impact performance via vehicle structural design enhancements and the addition of supplemental safety systems which meet or exceed regulatory vehicle crashworthiness standards. As noted previously, the current research work focuses specifically on vehicle structural enhancements to reduce injury potential in side impact collisions. The objective of this phase of the research, i.e. Phase 4, is to first identify the vehicle structural elements which play a predominant role in providing vehicle crashworthiness during a side impact collision, and then develop a relationship between vehicle structural changes and their effect on vehicle side impact performance and the potential for occupant injury. This relationship also needs to be enhanced in order to consider the effects of collision parameters as well as vehicle structural parameters on the occupant injury likelihood. This is accomplished using a numerical modeling parametric analysis approach, investigating the effect of component thickness changes over a range of values on the calculated SSPC for the specific set of collision parameters selected. To reduce the simulations' analysis time and increase the efficiency of the numerical modeling process, the new SSPC has been utilized as the indicator of occupant injury risk in computer side collision simulations. Based upon a substantial review of previous side impact numerical modeling results using the mid-sized Ford Taurus and MDB collisions (i.e. Phases 2 and 3), the structural components (or elements) listed in Table 6-1 were identified as the predominant vehicle structural elements involved in providing vehicle crashworthiness performance, and thus most likely to affect occupant risk potential through design changes. As such, the parametric study has been limited to investigating design/stiffness changes - 106-to these identified elements. To maintain essentially the same vehicle structural design geometry, stiffness changes in these elements were achieved via changes to the specific element material thickness (i.e. varied within a reasonable range - typically -50%...+200%). Computer side impact simulations of the vehicle having the modified structure were then performed using the FMVSS-214 impact test conditions, and the corresponding SSPC values calculated to assess the potential for crashworthiness performance enhancement. Table 6-1: Important structural components of the target vehicle during a side impact Structural components Door structure Door rail B-pillar Roof Floor pan Rocker panel In order to reduce the computational effort and improve efficiency in this study, the researchers employed a "design of computer experiments" approach (as described in the following section) for the construction of a response database. This database was then represented with an artificial neural network, as well as a full-quadratic response surface to correlate the SSPC with the thickness of the selected structural components. Once this equation was established with a reasonable error bound, the effects of varying the thickness of each component on the SSPC level could be assessed and evaluated for the FMVSS-214 collision condition. The last section of this chapter presents and discusses the newly developed relationship between the SSPC and both the collision parameters and selected vehicle structural design parameters. 6.2. DESIGN OF COMPUTER EXPERIMENTS 'Design of experiments' is a systematic approach to investigate a system or a design concept. It maximizes the information gained while minimizing the resources required completing the investigation. In contrast to 'one change at a time' experimental methods, this method of setting up the experiments has - 107-the advantage of investigating the significance of the input variables acting in combination with one another, as well as alone. 'One change at a time' testing methods always have the risk of failing to discover the significance of input variable dependency or interaction. For example, an examiner may find one input variable has a significant effect on the output while failing to discover that changing another variable may alter the effect of the first one. In this study, 'design of computer experiments' was employed for response database construction in order to reduce the computational expense and analysis time to an acceptable level without sacrificing prediction accuracy. The method generates a set of representative input vectors that covers the entire design space but allows them to be spread as wide as possible in order to optimally capture the effects of the design variables on the output over the entire design space. For each set of input variable combinations (i.e. in the current study this would be the thicknesses of the vehicle side structure components), a side impact FE simulation was performed to calculate the SSPC value. The database thus comprises a set of structural component's thicknesses as input variable combinations and the resulting SSPC values (i.e. see Table 6-3). Several 'design of computer experiments' methods are available in the literature [78-80], however the Latin Hypercube Design [81] is the first approach introduced for computer experiments. It is a stratified Monte Carlo method, such that variables at different levels are sampled with the same chance. Because the samples generated by the Latin Hypercube Design are not uniformly distributed and may show congregations and voids elsewhere, other methods (e.g. Max-Min Latin Hypercube Design [82], Optimal Latin Hypercube Design [83], etc.) have since been proposed to overcome the problem. The 'Grid-based optimal design' method [80] has been utilized as a 'design of computer experiment' method in this research to improve uniformity of the designed database. This method is easy to implement and covers the entire design space with good uniformity. As this method has not typically been applied in automotive crashworthiness studies previously and is thus likely to be unfamiliar to the - 108-reader, the following section has been included for completeness to describe both the general approach and more specifically outline how it has been utilized in the current work. 6.2.1. Grid-based Optimal Design Method The overall goal of applying this method is to optimally design the computer experiments required to accurately estimate the correlation between the design variables (i.e. in the current study this would be the thicknesses o f the vehicle side structure components) and the output (i.e. S S P C in this phase of study). This method selects the design variables values so that they cover the design space as uniformly as possible. This is quantified by building a database which could consist o f several input and output variables. Prior to building the database, the number o f input variables (i.e. n) and number o f levels o f each variable must be specified as /, (/' = 1,...,«), so that the design space is divided into ]~~[ i=]/, sub-cubes. These sub-cubes help the uniform selection o f the data points within the design space that is essential in capturing the behavior of the output within al l regions of the design space. The number o f data points within each sub-cube must also be specified. It should be noted that each data point is a combination o f design variables values which specifies one o f the computer experiments needs to be performed in order to construct the database. To spread out the data points as far as possible from each other within each sub-cube, an algorithm is utilized to randomly select these data points within each sub-cube boundaries while maximizing the minimum distance between sample points. This method enables the user to define the optimal (i.e. minimum necessary) number o f sample points in each sub-cube as well as the number o f levels for each variable. Therefore, the user can assign more levels to more important variables increasing the number o f samples taken from these variables, and thus increasing the efficiency of the method. Figure 6-1 shows an example of such a design method for two design variables (i.e. X i and X 2 ) , each o f which has five levels, with one data point per sub-cube. The lower and the upper bound of both variables are 0 and 1 (i.e. 0 < (Xi and X 2 ) < 1). Both variables have the following five levels: - 109-• Level one: 0 < (X, and X 2 ) < 0.2 • Level two: 0.2 < (X, and X 2 ) < 0.4 • Level three: 0.4 < (X, and X 2 ) < 0.6 • Level four: 0.6 < (X, and X 2 ) < 0.8 • Level five: 0.8 < (X, and X 2 ) < 1 Therefore the whole design area consists of 25 sub-cubes (i.e. 5x5 squares in this case), and as can be seen in Figure 6-1, each sub-cube contains one random combination of the design variables. Figure 6-1: A grid-based optimal design for two design variables The following section describes how this method has been specifically applied in constructing the vehicle structural element stiffness-SSPC database used for creating a response model that can estimates the SSPC value based on a new set of the structural components thicknesses. - 110-6.3. STRUCTURAL PARAMETERS AND NUMERICAL EXPERIMENTS SETUP The predominant structural components of the target vehicle that can affect the occupant injury risk are listed in Table 6-1. The schematic of these components are also shown in Figure 6-2 and Figure 6-3. Figure 6-2: Door components as defined in this research Figure 6-3: Vehicle side structural elements - I l l -Some of these components, such as the door and part of the B-pillar, may come into direct contact with the occupant, while the others absorb and/or redirect the impact energy to the other structural components (i.e. rocker panel, B-pillar, etc.) during a side impact collision. The deformation and velocity of the former components affect the occupant injury risk directly, while the latter components affect the injury risk indirectly by altering the behavior of the former components. The stiffness properties of both types of side structural components have been investigated in this research project to assess their effect on occupant injury risk. There are three ways a designer can alter the stiffness of the vehicle structural components: 1) alter the position of the existing material, 2) change the material properties, or 3) add or subtract material. The first two approaches might be more desirable to designers due to manufacturing considerations of the vehicle structural components. However, utilizing the third approach and changing the thicknesses of the selected structural components is the most convenient and efficient method of varying the stiffness of these elements in the developed numerical model. Since the objective of this phase of the research study is to investigate the effect of the selected structural elements' stiffness on the SSPC rather than designing a new vehicle structure, the third approach (i.e. varying the thicknesses of structural components) was utilized to alter the stiffness of the selected structural components. A reasonable range, i.e. 50% and 200% of the original thickness of the selected components, were chosen as the lower and upper bounds for the parametric study. The original thicknesses and the range of thickness modification are summarized in Table 6-2. The door structure is clearly one of the most important structural components in side impacts due to its position and potential for direct contact with the occupant. Therefore, the door was divided in two parts (i.e. upper door and lower door) to investigate each door regions' influence on the vehicle's side impact crashworthiness. - 112-Table 6-2: Lower and upper bounds of the side structure components thickness variation Side structure components Original thickness (mm) Lower bound thickness (mm) Upper bound thickness (mm) B-pillar 1.69 0.78 3.64 Upper door 0.91 0.42 1.96 Lower door 0.91 0.42 1.96 Door rail 1.65 0.76 3.55 Rocker panel 0.95 0.44 2.04 Floor pan 1.3 0.60 2.8 Roof 1 0.464 2.15 The grid-based optimal design method was utilized to generate a sample of appropriate thicknesses of the vehicle side structure. A l l of the element thicknesses were altered in two levels with one combination per sub-cube, except for the thickness of the B-pillar and the upper door, which were altered in three levels with one combination per sub-cube due to their more predominant importance over the other components. To construct the response database, 321 computer side impact simulations (using LS-D Y N A ) were performed using the thickness combinations generated by the experimental design method. A selection of the created database is shown in Table 6-3, while the complete database is presented in Appendix A . - 113 -Table 6-3: A selected region of the side structure thickness - SSPC database Exp,. Number B- Pillar thickness (mm) Inner Door-up thickness (mm) Inner Do or-low thickness (mm) Door Rail thickness (mm) Rocker pannel thickness (mm) Floor Pan thickness (mm) Roof thickness (mm) SSPC max : Original ' 1.69 0 91 0.91 1.65 0.95 • '*' 1.3 Q-.4724. 1 2.01 E+00 7.22E-01 8:34E-01 1.55E+00 4.53E-01 0.5463 0.9887,1 0.4318 •2 T.27E+00 6.64E-01 8.00E-01 1.03E+O0 4:83 E-01 0.57745 1.8 0.4522 3 9.67E-01 6.99E-01 4.70E-01 1.74E+00 4.68 E-01 0.48005 0.96095 0.4589 4 1.62E+00 5.25E-01 •9.18E-01 2.16E+00 4.64E-01 0.48316 1.9749 0,4857 5 1 1 '1:04E+00 ; . 9.35E-01 • 6.11E-01 • 1.05E+00 5.98E-01 : ' 0.55137 0.52392 : 0.4439. 1 1 1 317 1.69 0:91 0.91 1.65 9.50E-01 2.4 1 0.489085 318 1,69 0.91 0.91 1.65 9:50E-01 2.5. 1 0.491019 319 1.69 0.91 0.91 1.65 9.50E-01 2.6: 1 0,494238 320 1.69 0.91 .0.91. 1.65 9.50E-01 2.7 1 0.490918 321 1.69 0.91 0.91 1,65 9:50E-01 •2,8 1 0.492723 Once the simulations were completed, the next step was to develop a response model to map the input thicknesses to the resulting SSPC value utilizing the created response database. The following sections describe two approaches that were used in this study to create such a response model, 1) the artificial neural network approach and 2) the full-quadratic response surface approach. 6.4. SSPC ESTIMATION To investigate the effects of the selected components on the SSPC (i.e. occupant injury likelihood indicator), the constructed side structure thickness - SSPC database needs to be represented by a response model. The developed response model maps the SSPC - component's thicknesses functional relationship which will also be used as a surrogate model to substantiate the SSPC value during reliability analysis in the next phase (i.e. Phase 5) of this research study. Artificial neural network and response surface approaches are the two usual types of methods employed to represent such functional dependencies. The advantage of the former method is its relatively high accuracy in representing the dependency. But since in this approach the relationship between inputs and outputs are very complicated, the explicit gradient function of this relationship would be complex and - 1 1 4 -inefficient to calculate. Thus the developed response model would inefficient and thus unsuitable for use in traditional optimization methods which require the derivatives of the objective function with respect to design variables. However in contrast, response surface approach methods represent the output vector with a less complicated explicit function of input variables, making the method suitable for traditional optimization methods and reliability analysis. In this research, the multilayer back-propagation neural network method and the full-quadratic response surface method were utilized to represent the structural thickness - SSPC relationship. To train the artificial neural network and calculate the coefficients of the full-quadratic response surface, the previously developed structure thickness - SSPC database were utilized. This process is described in the following sections.. 6.4.1. Artificial neural network estimation Artificial neural networks are computational devices composed of many highly interconnected processing units. Each processing unit keeps some information locally and is able to perform some simple calculations. The networks as a whole have the capability to respond to input stimuli and produce the corresponding response, and to adapt to the changing environment by learning from experience. There are several different artificial neural network approaches [84]. Among them, the back-propagation neural network approach is the most popular and widely used for general mapping. A back-propagation neural network (see Figure 6-4) includes the following layers: • An input layer that contains the components of the input vector. • One or several hidden layers • An output layer - 115-Figure 6-4: A typical multilayer back propagation neural network Each layer has its corresponding processing elements called neurons. As shown in Figure 6-4, neurons in each layer are linked to the neurons in neighbour layers by connections with associated weights. These weights are determined during the training of the network to the data generated by numerical experiments. During the operation of the network, each neuron calculates the weighted sum of the inputs from the preceding layer and applies the results to the nodal function. The nodal function then produces the neuron's output which becomes the input for the neurons of next layer, and so on until the output layer is reached. The neural network needs to be trained by the previously generated database prior to being used as a response model. ' R E L A N ' software [85], which was developed at the University of British Columbia, - 1 1 6 -was utilized to develop and train the single hidden layer neural network within this project such that a corresponding SSPC value could be predicted based on knowledge of a specific set of target vehicle structural elements' thicknesses. In the process of applying this software to the research task, part of the created database was used for training the network, while the remainder was utilized for verification. The number of neurons and the corresponding weights were adjusted so that the prediction error of the network is minimized. The selected data were divided into five equal groups, and each time, four groups of the data were utilized to perform the training, while the remaining group was utilized for verification of the trained network. The network with the minimum total error resulting during the training and the verification tasks was selected as the optimal. To increase the accuracy of the neural network, a final training was carried out, during which any combination in the verification dataset with a prediction error larger than a specified value was put into the training dataset, while the same numbers of samples in the training dataset with the smallest error were put into the verification dataset. This process was repeated until both the training error and the testing error were reduced below specified limit values, or a maximum numbers of iterations were reached. Once training was complete, the created network acts as an approximating function for the relationship between the inputs and the outputs. - 117-12-T Actual SSPG Figure 6-5: Estimated SSPC with Neural Network method versus actual SSPC calculated from FE analysis To assess the accuracy of the network, the actual values of SSPC calculated by FE modeling (i.e. using L S - D Y N A software) were compared to the predicted SSPC value utilizing the described neural network. This comparison is shown in Figure 6-5 and correlates quite well, with a maximum error on SSPC prediction of less than 3%. This result demonstrates the high accuracy of the neural network estimation and verifies the ability of this approach for use in SSPC prediction in future phases of this research work. In spite of the high accuracy of the utilized neural network, the gradient function of the SSPC is very inefficient to analytically calculate and use in this SSPC estimation method. Thus the artificial neural network estimation is not suitable for conventional optimization or reliability analyses. The next section describes the details of the full quadratic response surface method which has the advantage of representing the output variables with a simple and efficient explicit function of input variables, making the method suitable for most of the optimization and reliability analyses. - 118-6.4.2. Full quadratic response surface estimation The full quadratic response surface method is one of the commonly used response surface methods which can represent the relationship between an output (i.e. SSPC g) and input variables (i.e. side structure components thicknesses, i.e. tf, tj) with a full quadratic equation (i.e. Equation 6-1). 7 7 SSPCg =a0 +Ya,t, + X £ W ; & i * J t6"1) i=l j=l i=l 7=1 The subscript g in Equation (6-1) indicates the SSPC value when thicknesses of the target vehicle side components are varied and tested within the FMVSS-214 compliance condition, while the a, b and c parameters represent constants in the equations. The least square regression method was employed to determine the values of these constants. This method minimizes both the squared error sum (or residual of the predicted surface) and the actual output to fit the best surface through the data points, i.e.: minimize Where: SSPCg-SSPC g y it =1 V it k J (6-2) SSPCg : actual SSPC for each numerical simulation k SSPCg : estimated SSPC from response surface Using an implementation process similar to the previous method, part of the created database was used for the least square regression analysis, while the remainder was utilized for verification. The selected data were divided into five equal groups, and each time, four groups of the data were utilized to perform the least square regression and the calculation of constant terms in Equation 6-1, while the remaining group was utilized for verification of the developed SSPC-component thicknesses functional - 119-relationship. The relationship with the minimum total error resulting during the least square analysis and the verification tasks was selected as the optimal, i.e.: SSPCg = 0427 x (0.7998 - 0.0519tB + 0.0408f y D + 0.1154t ID + 0.05 tDR + 0.4107 V + 0.0877*V - 0 . 0 8 5 6 ^ + 0.0083/ 2 + 0.0272f*o - 0.0312/, 2 0 - 0 . 0 0 1 8 ^ - 0 . 0 1 4 5 ^ + 0 . 0 1 0 6 ^ + 0 . 0 0 4 5 ^ + 0 . 0 1 8 5 ^ + 0 . 0 0 0 4 ^ -0.0052tBtDR - 0 . 0 5 8 8 ^ + 0 . 0 2 1 5 ^ +0.0022tBtR+0.004tUDtLD -0.009tUDtDR (6-3) - 0 . 2 5 6 4 ^ V -0.07S6tUDtF -0.0232tUDtR -0.0\02tIDtDR-0A3l\tLDtRP + 0.0419/^^+0.0098^0^+0.0355^0, /^ -0.049 \ t D R t F + Q.QQ2tDRtR -0.0363tRPtF+0A272tRPtR+0.0\66tFtR) where: tB: B-pillar thickness tUD: Upper door thickness tw: Lower door thickness tDR : Door rail thickness tRI,: Rocker panel thickness tF : Floor pan thickness t„: Roof thickness To investigate the accuracy of the developed response surface, the actual values of the SSPC calculated by numerical simulation were compared to the predicted SSPC values utilizing the full quadratic response surface. Figure 6-6 shows this comparison, with a maximum error on the SSPC prediction of less than 10%, indicating good accuracy of the method. As described earlier, the developed mapping function is very efficient to differentiate with respect to the input variables (i.e. structural thickness values) making this method suitable for conventional optimization or reliability analyses. Since - 120-it has been shown here to provide good accuracy, the full quadratic response surface was chosen to represent the relationship between SSPC and the thickness values of the target vehicle's side structure components. 1.2 0.8 1 , , , , , , , , 1 0.8 0.85 0.9 0.95 1 1.05 1.1 1.15 1.2 1.25 Actual S S P C Figure 6-6: Estimated SSPC with full quadratic response surface versus actual SSPC calculated from F E analysis Once the relationship between the SSPC and the structural component thicknesses was established, the effects of each component's thickness on the SSPC could be investigated. The next section discusses and compares the relative effect of these components on the SSPC as the occupant injury likelihood indicator. 6.5. T H E E F F E C T S O F V E H I C L E S T R U C T U R A L P A R A M E T E R S O N T H E SSPC Seven components of the target vehicle's side structure (i.e. B-pillar, upper door, lower door, etc) were selected for investigation in this study. After establishing the explicit relationship between the thickness of these components and the SSPC, the thickness of these components was varied between the - 121 -defined upper bounds and lower bounds (as listed in Table 6-2) to investigate their influence on the SSPC. Figure 6-7 shows the effect of increasing thicknesses of the selected components on the SSPC level. To plot each curve, only one thickness value was altered at a time, while the others were kept at their original value. o Q_ CO CO 0.55 0.5 0.45 0.4 0.35 0.3 Lower Bounc Original values - • — B-pillar thickness - • — Upper door thickness Lower door thickness Door rail thickness Rocker panel thickness - • — Floor pan thickness — i — Roof thickness 1.5 2.5 Normalized thickness ^upperBound Figure 6-7: SSPC versus normalized thickness of the structural components loaded in bending A l l the thickness values were normalized by their original value to illustrate the relative effects of all components in one diagram. These results are shown in Figure 6-7. The curves shown in Figure 6-7 clearly indicate that of all the components evaluated, increasing the upper door thickness had the highest effect on the SSPC, and that increasing the door thickness (i.e. stiffness) substantially reduced the SSPC value. Further investigations using the side impact model simulations indicate that the reduction of the door intrusion (mainly around the thorax region) was the - 122-predominant reason for this SSPC reduction. Reduced door intrusion was also found to be the reasons for SSPC decreases when the thickness of the B-pillar and the lower door were individually increased. Increasing the thickness of the rocker panel, however, increased the SSPC value. Less deformation of the rocker panel and subsequently higher velocity and intrusion of the door structure were found to be the main reason for an increased SSPC value in this case. It was also noted that varying the thickness of the door rail did not significantly affect the velocity and intrusion of the door areas that come into contact with the occupant during a side impact collision. This was probably due to the fact that the door rail had a small contact area with the occupant compartment (i.e. see Figure 6-2) limiting its ability to transfer the impact energy from the door to the occupant compartment. Thus the SSPC value did not substantially change when the door rail thickness was varied over the designated range (i.e. Table 6-2) Decreasing the thickness of the floor pan and the roof reduced the SSPC level due to the higher energy absorption of these components, with the roof result being most significant. It should be noted that these parts are neither in direct contact with the intruding object or with the occupant throughout the impact, and thus the more energy that can be transferred and absorbed by theses components, the higher likelihood of enhancing vehicle crashworthiness. While decreasing the relative thickness of the roof and the floor pan reduces the stiffness of these parts, this change increases the extent of deformation and energy absorption in case of a side impact within the selected range of this research study. However, there must be a limit for decreasing the stiffness of these components as the stiffness reduction decreases the vehicle structural integrity and thus, reduces the overall energy absorption capability of the vehicle structure. This limit was not achieved within the selected range of this study, therefore the results of this phase of research show the SSPC reduction with decreasing thickness of the floor pan and the roof. In summary, theses analyses indicate that increasing the relative stiffness of the door structure and/or the B-pillar is beneficial to vehicle crashworthiness for the FMVSS-214 test condition as shown by the associated reduction in the SSPC level found in the simulation studies. However in contrast, increasing the relative stiffness of the rocker panel, roof, and the floor pan was found to increase the - 123 -SSPC values, thus indicating a design change that would be harmful to vehicle crashworthiness in side impact collisions. The thickness changes to the door rail was found to have little effect on the SSPC value, thus indicating that relative stiffness changes would not significantly affect the injury level for the FMVSS-214 side impact test condition. The analyses of this phase of the current research, i.e. Phase 4, were performed for the FMVSS-214 test condition to discover the relationship between the SSPC (i.e. injury likelihood indicator index) and the vehicle structural components thickness. Since this equation (i.e. Equation 6-3) does not contain the effect of the collision parameters, it cannot be utilized to optimize the vehicle structure for side impact collisions (i.e. the objective of this research study). The next section discusses the incorporation of the collision parameters (i.e. impact speed, position, etc) in the developed SSPC - structural components thicknesses (i.e. Equation 6-3) utilizing the results of the previous phase, i.e. Phase 3, of this project. 6.6. SSPC RESPONSE AS A FUNCTION OF STRUCTURAL AND COLLISION PARAMETERS To optimize the thicknesses of the selected structural components and achieve the objective of this research project, the relationship between the SSPC and both structural and collision parameters is required. The relationship between SSPC and collision parameters was established during Phase 3 of this research work (i.e. Equation 5-5), while the relationship between the SSPC and structural parameters was established during Phase 4 (i.e. Equation 6-3) and has been discussed previously in the current chapter. The former equation correlates the SSPC to the collision parameters such as the bullet vehicle's mass (i.e. M), speed (i.e. S), vertical position (i.e. v), and horizontal position (i.e. H), while the geometry and the structural components thicknesses are kept at their original level (i.e.SSPCgo = f{S,M,V,H,g0) ). The latter equation (i.e. Equation 6-3) correlates the SSPC to the selected structural components thicknesses, while the described collision parameters are kept at FMVSS-214 level (le.SSPCg=f(S0,M0,V0,H0,g)). - 124-To combine these two equations and develop an exclusive relationship between the SSPC and both the structural and collision parameters, the following steps were taken: 1) Equation 6-3 (i.e. SSPCg) was normalized using the SSPC0 (i.e. SSPC value for the FMVSS-214 compliance condition with the original structural thicknesses): 'SSPC0 = 0.472 0 SSPC„ SSPC„ ^>r = r= 0.472 SSPC0 2) The final SSPC equation was considered to be the product of the above factor (i.e. r) and the SSPCgo: SSPC = rxSSPCgo = rf(S,M,v,H,g0) The first term in the above equation (i.e. r) corresponds to the SSPC variation due to the structural components thickness variation, while the second term (i.e. SSPC go) corresponds to the SSPC variation due to the collision parameters variation. The following shows the final SSPC equation containing both structural and collision parameters: SSPC = (0.7998 — 0.0519tB + 0.040S7 y D +0.1154/ / 0 + 0 . 0 5 / ^ + 0 . 4 1 0 7 ^ + 0.0877/,, -0 .0856/ f l + 0.0083/ 2 +0.0272/^ -0.0312/ 7 2 D - 0.001 8/ 2 f i - 0 . 0 1 4 5 / ^ + 0.0106/ 2 + 0.0045/ 2 +0.01 S5tBtUD + 0 .0004/ B / / D -0 .0052/ f i / O f t - 0.0588/ B / R P + 0.021 StBtF + 0 . 0 0 2 2 / ^ + 0 . 0 0 4 / ^ / ^ - 0 . 0 0 9 / w / O f i - 0 . 2 5 6 4 / ^ / ^ - 0 . 0 7 8 6 / w / / r - 0 . 0 2 3 2 / w / x - 0 . 0 1 0 2 / / o / D f f -0.131 \tLDtRP + 0.0419/ / o / / r + 0.0098/ / D / / ? + 0 .0355/^r^ -0.049 \ t D R t F + 0 . 0 0 2 / ^ - 0 . 0 3 6 3 / ^ + 0 . 1 2 7 2 / ^ + 0 . 0 1 6 6 / ^ ) -(-1.779 + 1.2585 + 0.249 M + 0.54v +0.19/7) The above developed equation will be utilized in the optimization process of the vehicle structural components thickness. This process and its results are presented in the next chapter (i.e. Phase 5 of this research). - 125 -6.7. SUMMARY AND CONCLUSIONS - PHASE 4 The objective of this phase of the research, i.e. Phase 4, was to develop a relationship between the SSPC (i.e. injury likelihood indicator) and both vehicle structural and collision parameters, and then investigate the effects of the structural parameters on the vehicle side impact performance and the occupant injury likelihood. To accomplish this objective, first the vehicle structural elements which play a predominant role in providing vehicle crashworthiness during side impact collisions were identified, and then simulations were performed to vary the thickness of these components. The structural parameters were: the upper door and lower door thickness, the B-pillar thickness, the door rail thickness, the floor pan thickness, and the roof thickness. To establish the required numerical simulations, a 'Computer Design of Experiment' method was utilized. The results of these simulations were utilized to determine the relationship between the SSPC and the selected structural parameters. Artificial neural network and full-quadratic response surface methods were examined to determine such a relationship. Due to the discussed advantages and good accuracy of the full-quadratic response surface, this method was finally employed to develop the functional relationship between the SSPC and the structural parameters. Further investigation of this relationship provided the following findings: • Increasing the thickness of the B-pillar, upper door and lower door reduced the SSPC level, however in contrast increasing the thickness of the roof, floor pan and rocker panel increased the SSPC level. In other words, increasing the stiffness of the door and B-pillar and decreasing the stiffness of the roof, floor pan and rocker panel was beneficial to the reduction of injury likelihood in FMVSS-214 compliance condition. • While changing the thickness of the upper door had the highest effect, the door rail thickness hardly had any effect on SSPC level. • The door intrusion profile and its history were found to be the predominant reason for these effects on the SSPC. For example, increasing the thickness of the door and B-pillar reduced the intrusion of the door towards the occupant compartment, while increasing the thickness of the - 126-floor pan and the roof prevented them from absorbing enough impact energy, thus causing more deformation in the door and B-pillar leading to increased intrusion and subsequently a higher SSPC value. The door rail thickness however, did not affect the intrusion level and therefore did not substantially affect the SSPC level. To achieve the final objective of this research phase (i.e. Phase 4), the developed structural parameters - SSPC function was combined with the previously developed collision parameters - SSPC function developed in Phase 3. The resulting developed equation (i.e. Equation 6-4) thus correlates the SSPC to both the vehicle structural and collision parameters. This equation is employed in the next chapter to estimate the occupant injury risk and optimize the thickness of the selected side components utilizing reliability analysis techniques. - 127-Chapter 7. C A L C U L A T I O N OF INJURY RISK AND OPTIMIZATION OF T H E V E H I C L E SIDE STRUCTURE 7.1. INTRODUCTION Injury risk reduction in different types of collisions is one of the major concerns of vehicle designers, and thus any new design of a vehicle is required by regulation to be evaluated with respect to its performance in protecting the occupant. For side impact collisions, the injury indices specified in FMVSS-214 (i.e. TTI, and peak lateral pelvic acceleration) are regulated as the occupant injury level indicators for the vehicle compliance in North America. However, upon reviewing the mid-sized Ford Taurus collision simulation results obtained from Phase 3, it appears that within the range of collision parameters investigated, the TTI is the predominant index (i.e. thorax injuries are relatively more severe than pelvic injuries). Therefore, the TTI was deemed to be the injury measure that controls the current target vehicle (i.e. 1990 Ford Taurus) design acceptance for side impact collision crashworthiness. To define the probability of injury at a specific AIS level, the current research work proceeds by utilizing the work of Eppinger [25], which relates TTI to the risk of injury. For the vehicle compliance acceptable level of the TTI (i.e. 85G as defined by FMVSS-214) as outlined in Chapter 2, a specific probability of serious injury likelihood can be determined. The resulting value is used within the current research to demonstrate a strategy for optimizing the vehicle structure with enhanced side impact performance capability. The specific objectives of this next phase of work (Phase 5) are outlined below. The objectives of Phase 5 are based on the need to develop the necessary input components (i.e. relationships) to the risk and reliability analysis to be employed in this research, and then formulate and implement a new strategy for vehicle structural design optimization to enhance crashworthiness in side impact collisions. The first of these objectives is to develop a relationship between the occupant injury likelihood and the structural design parameters identified in the previous phase (i.e. Phase 4) that contribute significantly to the vehicle's crashworthiness during side impacts. Once established, this relationship can then be used to fulfill the second objective, which is to develop a strategy to optimize the - 128-thickness of selected vehicle structural components based on accepted vehicle compliance criteria, i.e. by minimizing the injury likelihood. To accomplish these objectives, the current chapter first reviews the correlation between TTI and occupant injury likelihood, and then develops a mathematical relationship between the thickness of the vehicle side structure components, collision parameters and injury probability utilizing the results from the previous phases (i.e. Phases 3 and 4). Since the collision parameters (i.e. collision velocity, bullet vehicle's mass, etc.) have a stochastic nature, a reliability analysis was used to incorporate their effect on the occupant injury likelihood. To perform the reliability analysis, the following items were required: 1) A statistical distribution of the collision parameters. Since a statistical distribution of the collision parameters for vehicle accidents in Canada could not be found in the literature, this data was extracted from the US Fatal Accident Reporting System (FARS) website [1]. The details of these statistical distributions are presented in Section 7.3. 2) A performance function which establishes a limit for the occupant injury likelihood at a specific AIS level. The selected AIS level is discussed in the next section of this Chapter (i.e. Section 7.2), while the established performance function, and the reliability analysis are presented in Section 7.4. The Grid-based optimal design (i.e. utilized Design of Experiment method) and Monte Carlo reliability method [86, 87] were utilized to evaluate the effects of the selected vehicle structural design parameters on the probability of occupant injury likelihood exceeding the selected limit. To setup an explicit relationship between structural design parameters and this probability, a full quadratic response surface was employed. This equation was minimized in the final step to discover the optimal values of the selected vehicle structural design parameters. The results of this analysis demonstrate a successful - 129-example of the developed design strategy for optimizing the vehicle crashworthiness performance in side impact collisions. 7.2. CALCULATION OF INJURY RISK The goal of this research is to develop a vehicle diesign strategy to minimize the occupant injury risk by optimizing the structure of the target vehicle. In previous chapters, the TTI was considered as the representative of occupant injury risk in side impact collisions and the performance of the target vehicle was examined by utilizing this index. However, the relationship between TTI and occupant injury probability needs to be established in order to quantify improvement in the vehicle's crashworthiness in side impacts. The independent development of this relationship is beyond the capabilities and scope of the current research project, however previous work available in the literature provides many of the necessary components for completing this task as outlined below. As discussed in Chapter 2 of this document, the TTI was developed and utilized as an injury index based on its monotonic increase with the AIS injury scale (see Section 2.6.1, and Table 2-3). The cumulative probability relationship between the TTI and the expected injuries levels greater than or equal to AIS 3, 4 and 5 is developed in the study conducted by Eppinger Et al [25]. This relationship is shown in Figure 7-1. Three curves are plotted in this figure: Curve 1) correlates the TTI to the injury probability of AIS > 3, Curve 2) correlates the TTI to the injury probability of AIS > 4, and Curve 3) correlates the TTI to the injury probability of AIS > 5. As discussed in Chapter 2, AIS 3 corresponds to serious injuries (see Table 2-3) which are very common in side impact collisions [1]. Since the first curve of the Figure 7-1 includes the serious injury probability (i.e. AIS > 3), this curve was selected to quantify the injury probability of the occupant in this study. To establish an explicit equation between the TTI and occupant injury likelihood based on this curve (i.e. Curve 1), a curve fitting method was employed. Due to the specific shape of this curve, an exponential function was found to be the best curve fitting function to estimate the TTI-occupant injury likelihood relationship. Thus, the following equation was utilized to establish such an equation between the TTI and occupant injury likelihood: - 130-( TTI-60 y Injp = 1 - m ' (for AIS > 3) (7-1) where: Inj : occupant injury probability. TTI: Thoracic Trauma Index. m: first constant of the equation. k: second constant of the equation. Figure 7-1 T T I versus injury risk (adapted from [25]) The above equation was rearranged as follows to find the constants (i.e. m, k): - 131 -ln(m - 60) = ln(m) + -(- ln(l - Inj p)) (7-2) A linear least squares method and the data points from curve 1 of Figure 7-1 were utilized to determine the m and k values listed below: Comparing the results of the above injury probability prediction function with the actual data points forming curve 1 of Figure 7-1, a maximum error of less than 2% in the predicted injury likelihood values was determined. This built confidence in utilizing Equation (7-3) to calculate the injury probability based on the known TTI value. Once this equation was established, the thicknesses of the vehicle side structure were correlated to the injury probability through Equations (5-4), (6-4), and (7-3) as follows: (7-3) (7-3) where, TTI = 85 • (l .546 SSPC + 0.0983) (5-4) and, - 132-SSPC = (0.7998- 0.05 l9tB + 0 . 0 4 0 8 ^ 0 + 0 . 1 1 5 4 ^ + 0 . 0 5 ^ + 0.4107/^ + 0.0877/ F -0 .0856r / ; + 0.0083/ 2 + 0 .0272/ 2 o -0.0312t 2 L D - 0 . 0 0 1 8 / ^ - 0 . 0 1 4 5 / ^ +0.0106/ 2 +0.0045/ 2 +0.0185/ f i / U D +0.0004/B/Lo - 0 . 0 0 5 2 / s / D « - 0 . 0 5 8 8 / ^ + 0.0215fBiV + 0 . 0 0 2 2 / ^ + 0.004tUDtw - 0.009tUDtDR - 0 . 2 5 6 4/ y oV -0.0H6tUDtF -0.0232tUDtR - 0.0102t L DtD R - 0 .1311/ / DV + 0 . 0 4 1 9 / i D ^ +0.0098/ / D / w +0.0355/o,^> - 0 . 0 4 9 1 r o « ^ + 0.002/ D /A - 0.0363/ f t F / F + 0 . 1 2 7 2 * ^ + 0 .0166 / F ^) -(-1.779 +1.258 S + 0.249 M + 0.54 v + 0.19 H) The above set of equations was subsequently utilized in the reliability analysis and optimization process as described in Sections 7.4 and 7.5. 7.3. A S S E S S I N G T H E S T O C H A S T I C D I S T R I B U T I O N O F T H E C O L L I S I O N P A R A M E T E R S Collision parameters have a stochastic nature and cannot be altered by an individual vehicle designer. These parameters have a substantial effect on occupant injury as can be explicitly seen by examining Equation 6-4 where collision speed, mass of striking object and its position directly affect the SSPC and consequently the injury probability. Thus, the distributions of these parameters are required in order to incorporate their effect into the optimization process of the selected target vehicle structure. This distribution may change from one jurisdiction to another. Since this study is performed in North America, the statistical distributions of these collision parameters were extracted from FARS [1] database as outlined below. As was seen in Chapter 3, the horizontal position of the impact has the lowest effect on the occupant injury in side collisions unless the striking object CG is nearly aligned with and results in plastic failure of the B-pillar. As horizontal position effects when not striking the object CG were small, and because including this low significance collision parameter as a variable would greatly increase the required reliability analyses (i.e. 288 more analyses required), it was decided to simplify the,set of equations (7-3) in this study by applying the worst case scenario of the horizontal position of impact to Equation (7-3) (i.e. H- 1089 mm). As such, this parameter as a variable was eliminated from the equation - 133 -and further analyses. The distributions of the other collision parameters were obtained from the FARS database and can be seen in Figure 7-2 through Figure 7-4. To utilize this data in further reliability analyses, lognormal distribution functions were assigned to these parameters. Distribution trends of the collision parameters are very well followed by lognormal distribution functions and the fact that the outputs of these functions are always positive makes them one of the best choices for representing collision parameters distributions. The following shows the statistical characteristics of theses parameters: for collision ve ju = 38.3 km/hr cr = 11.8 km/hr for bullet vehicle's mass: / i = 1447 kg cr = 600 kg for vertical position of collision: /u = 24 in er = 13.5 in where: ju : mean value, cr: standard deviation - 134-Cumulative distribution function 0.9 0.8 0.7 0.6 CO 0.5 - Q o Q . 0.4 0.3 0.2 0.1 0 V (km/h) Figure 7-2: Cumulative distribution of side impact collision velocity within U.S. (adapted from [1]) Cumulative distribution function 4500 Mass (kg) Figure 7-3: Cumulative distribution of striking vehicle mass in side collisions within U.S. (adapted from [1]) - 135 -Cumulative distribution function 1 0.9 0.8 0.7 0.6 i f la TO 0.5 O 4 0.4 0.3 0.2 0.1 0 0 10 20 30 40 50 60 Vehicle height (in) Figure 7-4: Cumulative distribution of striking vehicle's height in side collisions within U.S. (adapted from [1]) Once the above collision parameter distributions were established, the set of equations (7-3) were utilized to perform the reliability analysis on the target vehicle's side structure. 7.4. R E L I A B I L I T Y A N A L Y S I S B A S E D O N T H E A C Q U I R E D C O L L I S I O N P A R A M E T E R S To incorporate the effects of the collision parameters in the optimization process of the vehicle structure, a reliability analysis was needed. As discussed earlier, the reliability analysis requires the statistical distribution for the collision parameters as well as a performance function that specifies a limit for the occupant injury probability. To select such a limit, different organizations may have different viewpoints. For example, the safety rulemaking agencies (i.e. NHTSA, Transport Canada, etc) are primarily focussed on health of the vehicle occupant and the associated societal costs. In contrast, while the vehicle manufacturers are also concerned about safety (especially as it effects the likelihood of possible lawsuits against the company due to occupant injury or death.), they also desire to minimize their vehicle design and manufacturing costs. These different viewpoints may potentially lead to the different - 136-limits for the occupant injury probability. However, considering any of the discussed viewpoints to establish a limit for the occupant injury probability requires insight information from these organizations. As such information was not available to the author nor was the objective of the current study to establish such an injury probability limit, this limit was selected based on FMVSS-214 acceptable TTI value. Based on FMVSS-214, a 3% injury probability level, which corresponds to TTI = 85 (i.e. see the red bar denoting this point on Figure 7-1) was selected as the occupant injury limit in the reliability assessment, and the probability of exceeding this limit was calculated for different design options using the Monte Carlo reliability method. Thus the performance function was defined as following: R = 0.03 - Injp (7-4) Where: R: performance function, Inj: occupant injury probability The above performance function and set of equations (7-3) were utilized to setup the reliability analysis. The Monte Carlo reliability approach was utilized to calculate the probability of injury likelihood exceeding 3% (P(Injp> 3%)) for different thicknesses of the side structure elements. To minimize this injury likelihood, the relationship between thicknesses of the vehicle side components and P(Injp> 3%) was established. Thus similar to the process used in the last chapter, a grid based optimal design method was utilized to setup the necessary numerical experiments and the full quadratic response surface was employed to represent the dependency between P(Injp> 3%) and the thickness parameters of the selected structural components. The Monte Carlo method and details of the P(Injp> 3%) estimation procedure are discussed in the following sub-sections. - 137-7.4.1. M o n t e C a r l o m e t h o d The Monte Carlo method [86, 87] is one of the common methods of calculating the reliability performance function and probability of failure. The method was named after Monte Carlo, Monaco, where the primary attractions are casinos containing games of chance. The random behaviour in games of chance is similar to how the Monte Carlo method selects random variable values to simulate a model. For example when a player rolls a dice, he knows that either a 1, 2, 3, 4, 5, or 6 will come up, but he does not know which for any particular roll. It is the same with the variables that have a known range of values but an uncertain value for any particular time or event. To perform the Monte Carlo sampling, the ranges and distributions of the random variables need to be defined. Then, the method calculates multiple scenarios of the defined performance function by repeatedly sampling values from the probability distributions of the random variables. To acquire accurate results, a large number of scenarios must be produced and the relative portion of the successful trials examined. To achieve the convergence, the reliability problem has to be solved with different numbers of samples, thus final solution is achieved once the results of two subsequent solutions do not show significant changes from one to another. 7.4.2. N u m e r i c a l e x p e r i m e n t se tup fo r P ( I n j p > 3 % ) To discover the correlation between P(Injp> 3%) and the thicknesses of the vehicle side structure elements, a set of numerical experiments had to be performed to construct the response database. Similar to the development of the vehicle structure thicknesses/SSPC database, the grid based optimal design method was employed to produce a broad range of sample sets of appropriate component thicknesses of the vehicle structure. To construct the response database, 321 numerical experiments were performed utilizing R E L A N [85] and the Monte Carlo method. The thickness combinations generated by the experimental design method were then utilized to perform the reliability analysis. Each reliability analysis was performed with 106 samples as well as 105 samples of random variables drawn from the collision parameters distribution to ensure convergence of the solutions. This convergence (i.e. the coefficient of variation) was achieved once the difference between the results of two analyses was less than 10"9. Once - 138-the convergence was achieved, the failure probabilities (i.e. P(Injp> 3%)) were considered as the final solutions. A portion of the produced database is shown in Table 7-1 and the complete database is presented in Appendix B. Table 7-1: A sample of the side structure thickness - probability of serious injury database Exp. Number B- Pillar thickness (mm) Inner Dbor-up thickness, (mm) Inner Door-low thickness (mm) Door Rail thickness (mm) Rocker pannel thickness (mm) Floor.Pan thickness (mm) Roof thickness (mm) Injury probability (Piiij>0.03) (AIS>3) ^Original 1.69. 0.91 0:91. 1.65 0.95. , 1.3 "•'1 .0.2919 '1 :2.00640 0.72163 0.83371 1.54780 0.45268 0.54630 : 0.98871 0.27180 2 1.27390 0.66350 0.80049 1.03410 0.48298 .0.57745 1.80000 0.27840 3 0.96655 0.69927 0.46983 1.73530 0.46841 0.48005 0.96095 0.28290 4 1.61550 0.52525 0.91843 -.2:15880 0.46419 0.48316 1.97490 0.28420 5 1.04320 0.93497 0.61073 1.05430 0.59811 0.55137 0.52392 0.27930 6 1.78180 ' 0.70606 0.44025 1.08610 0.52739 0.58123 1.59070 0:27080 7 0.97204; 0.82811 0.71241 1,14550 0.56624 0.47780 1.26150 0:28240 8 1.38950 0.44841 0.67459 1.45560 0:56608 0.47869 2.05630 0.29600 9 1.04400 0.49197 0.51378 3:34290 0.48026 0.58453 0.69343 0.30100 10 1.05320 0.77485 0.64333 2.71650 0.48275 0.56871 1.61200 0.28800 i 1 1 1 314 1.69000 0:91000 0:91000 f65000 0.95000 2.10000 1:ooooo 0:29890 315 ' 1.69000 0.91000 0.91000 1.65000 0.95000 2.20000 .1.00000 0.30020 316 1.69000 0.91000 0:91000 1.65000 0.95000 2.30000 1.00000 0.30150 317 1.69000 0.91000 0:91000 •1.65000 0.95000 2.40000 1.00000 0.30270 318 . -1.69000 0.91000 0.91000 •1.65000. 0.95000 2.50000, 1.00000 , 0.30420 319 1:69000 0.91000 0.91000 1 \65000 0.95000 2:60000 1.00000 0.30590 ,320 1.69000 0.91000 0.91000 1.65000 0.95000 2:70000 1: ooooo 0.30730 321 1.69000 0.91000 0.91000 1.65000 0.95000 2.80000 1.00000 0.30880 The next step was to represent the produced database with a function, which maps the input thicknesses to P(Injp> 3%) value. This step is presented in the following sub-section. 7.4.3. E s t i m a t i o n o f the p r o b a b i l i t y o f i n j u r y l i k e l i h o o d exceed ing 3 % The Full quadratic response surface method was utilized to represent the vehicle structure thicknesses - P(Injp> 3%) database, thus providing the following equation: - 139-P(lnj p >3%) = a0 + Xa,t, + £b}t) + £ £ & i * J i=\ j=\ i=\ >=1 (7-5) where: /: thickness of the selected side components (i.e. B-pillar, upper door, etc) a, b, c: constants of the equation The Least-squares method was utilized to determine the constants of the above equation. The final form of Equation (7-6), with the determined constants and component thicknesses substituted in, is as following: P(lnjp > 3%) = (0.219 - 0.0142/B + 0.0158/^ + 0.0469/ / o + 0.0141/D f l + 0.14251^ + 0.037/ / r - 0.03286/R + 0.0029/ 2 + 0.009/ 2 D - 0 . 0 1 1 ^ - 0.0005/^ - 0.0039/2 R P + 0.003 \t\ + 0.0015/ 2 + 0.0059/ B / U D + 0.0003/ B / i D - 0 .0018/ B / M - 0.023 5 / s / ^ + 0.0044/ B / F + 0.0006/B/ f f (7-6) + 0 .0014/ U D / i D -0.09tUDtRP -0.0265tUDtF - 0 . 008 / W J / f f - 0 .0036/ / D / D f i - 0 . 0 5 0 8 / ^ / ^ + 0 . 0 0 7 8 / ^ + 0 . 0 0 2 9 / ^ + 0 . 0 1 4 / ^ / ^ - 0 . 0 1 4 3 / ^ + 0.007tDRtR - 0.0\4ltRIJF + 0 . 0 4 9 8 V / R + 0.008/ / r/ K) . s - 140-0.32 0.32 Actual - P(lnjp> 3%) Figure 7-5: Estimated probability of injury likelihood exceeding 3% with full quadratic response surface versus actual P(Injp> 3%) calculated from R E L A N analysis To assess the accuracy of the above equation, the actual values of the P(Injp> 3%) calculated by R E L A N were compared to the predicted P(Injp> 3%) value utilizing the full quadratic response surface as shown in Figure 7-5. The maximum error of the full-quadratic response surface estimation was less than 2% which verifies the high accuracy of the estimation method. Since the developed estimation function is differentiable with respect to the input variables (i.e. components thicknesses), it enables the use of traditional optimization techniques. This benefit of the full-quadratic response surface method simplified the process of optimizing the vehicle structure as discussed in the following section. 7.5. O P T I M I Z A T I O N O F T H E V E H I C L E SIDE S T R U C T U R E The ultimate goal of this research is to develop a design strategy to minimize the occupant injury risk by optimizing the stiffness of the target vehicle's side structure. To achieve this goal, Equation (7-6) which quantifies the dependency between the probability of injury likelihood exceeding 3% and thickness - 141 -of the vehicle components, was selected as the objective function to be minimized within the optimization process. Thickness parameters of the side structure components were considered as the design variables and their upper and lower bounds were considered as constraints as previously defined in Table 6-1. These constraints were imposed on the optimization problem due to the previous selection of the range of these component thicknesses (i.e. Phase 4 of this study) in developing the component thicknesses-SSPC relationship (i.e. Equation 6-4). It is important to note that these constraints are not real constraints (however a structural designer would define suitable restraints based on issues such as manufacturing capabilities and vehicle weight), but they are imposed here due to the assumptions of the current study in formulating the optimization problem. Thus, any solution determined will be optimized only within the range of the imposed constraints. This optimization problem can be summarized as following: minimize P(lnjp > 3%) where the design variables are: t B' t(JD ' ^ LD' t DR ' t RP ^ F R and the imposed constraints are: 078 mm < tB < 3.64mm, 0.42mm <tUD < 1.96mm, 0.42mm < tLD < 1.96mm, 0.16mm <tDR < 3.55mm, 0.44mm <tRI, < 2.04mm, 0.60mm < tF < 2.80mm, 0.464mm < tR < 2.15mm and - P ( l n j p > 3 % ) < 0 To solve the above optimization problem, functions within the M A T L A B [88] optimization toolbox and the Quasi-Newton line search method were utilized. An advantage of this line search method is that it - 142-is globally convergent and the vector of input variables generated by this approach in each iteration is always in the feasible region, thus increasing the performance of the optimization process. The optimization steps of this approach are also selected in a way to ensure the monotonic decrease of the objective function. Quadratic convergence, which accelerates the convergence of the optimization process, is another advantage of this method. Further details of this method are described in [86-88]. The thickness values resulting from this optimization process are as following: tB = 2.3 mm tuo =1.9 mm tw =1.7 mm - tDR = 1.5 mm tRP = 2 mm tF =1.7 mm tR = 0.5 mm Once the optimization process was completed and the above component thicknesses were utilized, the value of P(Injp> 3%) function' was reduced from its initial value of 0.28 (based on actual vehicle component thicknesses) to 0.0196 constituting 93% reduction in P(lnjp> 3%) value. To verify the results, the obtained thickness values were substituted in the R E L A N program and the P(lnjp> 3%) value was calculated by utilizing the Monte Carlo reliability method. The difference between two values of P(Injp> 3%) was less than 3% (i.e. Table 7-2). Table 7-2: verification of the optimization process with RELAN results Optimal Design verification Full-quadratic response surface estimation RELAN - Monte Carlo estimation P(Injp> 3%) 0.0196 0.02 - 143 -Comparing the above results with the original thicknesses of selected components (i.e. Table 6-1), suggests that decreasing the stiffness of the roof is beneficial and decreases the injury probability, while increasing the stiffness of the B-pillar, door, and rocker panel reduces the injury risk. The thickness of the floor pan and door rail in the optimal design is not very different from their original value, indicating the low effect of these components in occupant protection once all collision parameters are introduced into the analysis. Table 7-3 shows the enhanced vehicle structural design results comparison between this phase of study (i.e. Phase 5) which includes the effect of the collision parameters and the previous phase (i.e. Phase 4) in which the collision parameters were set to the FMVSS-214 test condition. As can be seen in this table, the calculated thicknesses of the door structure (i.e. lower and upper door) and the roof are similar in both conditions. This confirms the beneficial effect of increasing the door stiffness as well as reducing the roof stiffness in both conditions. However, the optimum thicknesses of the other components (i.e. B-pillar, door rail, rocker panel, and floor pan) are different from one vehicle structural design enhancement condition to another (i.e. see Table 7-3). While the design enhancement results based on the FMVSS-214 test condition (i.e. Case 1 in Table 7-3) recommend reducing the stiffness of the floor pan and the rocker panel, the results of this phase of study (i.e. Case 2 in Table 7-3) recommend increasing the stiffness of the rocker panel and keeping the original floor pan thickness. Both structural design enhancement case results suggest that increasing the stiffness of the B-pillar reduces the occupant injury level, however, Case 1 results recommend a higher increase in the B-pillar stiffness in comparison to the Case 2 results (i.e. 50% higher thickness). - 144-Table 7-3: Comparison between the calculated optimum thicknesses based on FMVSS-214 test condition and with the effect of collision parameters considered \ Thickness \ . (mm) Design enhancement\ cases B-pillar Upper door Lower door Door rail Rocker panel Floor pan Roof 1) Optimum values based on FMVSS-214 test condition 3.6 1.9 1.9 3.5 0.4 0.6 0.4 2) Optimum values considering the effects of the selected collision parameters 2.3 1.9 1.7 1.5 2 1.7 0.5 Original values 1.69 0.91 0.91 1.65 0.95 1.3 1 Although the Case 1 results recommend increasing the value of the door rail thickness, the results of the previous phase (i.e. see Figure 6-7) indicated a limited effect of such a thickness increase on the SSPC (as an occupant injury level indicator). The results of the Case 2 design enhancement also suggest a limited effect of the door rail thickness on the occupant injury likelihood as the recommended door rail thickness in this case is very close to the door rail original thickness. - 145 -7.6. S U M M A R Y A N D C O N C L U S I O N S - P H A S E 5 The global objective of this research study was to develop and demonstrate a new strategy for vehicle structural design optimization for enhancement of vehicle crashworthiness in side impact collisions. Based on this global objective, the objectives of this phase of study (i.e. Phase 5) were established to develop and demonstrate the essential aspects of the optimization procedure and can be summarized as follows: 1) To develop a relationship between the occupant injury likelihood and previously defined (i.e. in Phase 4) structural parameters, and 2) to develop a strategy to optimize the thickness of selected vehicle's structural components by minimizing the probability of occupant injury likelihood exceeding 3% (i.e. P(Injp> 3%)). To accomplish the first objective, a set of equations (i.e. Equation 7-3) was developed that correlates the occupant injury likelihood to the selected structural thicknesses. This set of equations, as well as a Design of Experiment methodology and available collision parameter distributions for North America side impacts were utilized to establish a set of reliability analyses that correlates the P(Injp> 3%) to the vehicle component structural thicknesses. The full-quadratic response surface was then utilized to represent the produced database. To achieve the second objective of this phase, the developed equation with the assumed constraints - including lower and upper bounds of thicknesses and the fact that the injury probability is always zero or positive - were utilized in optimization process of the target vehicle's structure. A M A T L A B optimization code was then employed to solve the optimization problem and minimize the P(Injp> 3%) within identified constraints. The result of this optimization process was verified using the established R E L A N reliability software. The results of the optimization process recommend the following trends for improving the selected vehicle's side impact crashworthiness based on the assumed North America collision parameters distributions: • Decreasing the stiffness of the roof reduces the probability of injury risk. This likely causes more energy absorption as well as energy transfer towards the roof and away from the occupant. - 146-• Increasing the stiffness of the door, B-pillar, and rocker panel decrease the injury risk probability and is beneficial in increasing the side impact crashworthiness of the vehicle. This is most likely due to more energy absorption of theses components once their stiffness is increased. The thickness increase of the door and B-pillar also reduces extent of intrusion into the occupant compartment, which decreases the contact time between the occupant and the intruding structure. • The stiffness of the door rail and floor pan did not considerably change in the optimal design results. This demonstrated that the original stiffness of these components are at their optimum level for side impact crashworthiness in the current design of the selected target vehicle. The above conclusions were drawn within the limitations of this study which include the following. First, the study uses one target vehicle model for all the numerical analyses, i.e. the Ford Taurus midsize vehicle model. In addition, the current study does not include the effect of any interior padded structure or supplementary safety devices (i.e. side airbags, etc.), or consider how they may affect the optimization results. Further analysis is required to assess the effect of these limitations on the occupant injury likelihood trends discussed here. In spite of the above limitations, the analyses performed in this phase of the study demonstrated a successful example of the developed strategy for optimizing the crashworthiness performance of a vehicle structure in side impact collisions. The next chapter summarizes the conclusions drawn from all phases of this research work. - 147-Chapter 8. D I S C U S S I O N , C O N C L U S I O N S A N D P O T E N T I A L F U T U R E W O R K As was highlighted in Chapter 1, side impact collisions are the second most frequent collisions on the road after frontal impacts [1], and thus should be a major focus of continuing research work in the fight to reduce societal cost from traffic collisions. According to the Fatal Accident Reporting System (FARS) [1], side impacts are the cause of 29% of all motor vehicle fatalities as well as 24% of all motor vehicle serious-to-critical injuries indicating the importance of enhancing occupant protection in new vehicle designs - i.e. the primary focus of the current research work. The governmental regulatory agencies (i.e. NHTSA, Transport Canada, etc.) recognize the need for improving the vehicle crashworthiness in side impacts, and as discussed in Chapter 2, have introduced side impact standards (i.e. FMVSS-214 and ECE-R95) to ensure a minimum level of vehicle crashworthiness performance in side impact collisions. It should be noted that these standards expect a certain level of vehicle crashworthiness for a single specific collision condition (i.e. one specific velocity, a single defined impacting object, etc.) which has been believed to provide some level of occupant protection in side impact collisions for the vehicle market region. At present, vehicle manufacturers must demonstrate that their designs satisfy the appropriate standard in order to sell their vehicles in U.S. or Europe. Although the Canadian vehicle users (i.e. people in the country that the current research was conducted) benefit from the fact that the manufactures usually design their vehicles to satisfy both aforementioned side impact standards, unfortunately the Canadian side impact standard does not impose any clear occupant protection level expectancy from the automobile manufacturers. As discussed in Chapter 1 and 2, the Canadian side impact standard (i.e. CMVSS-214) only requires certain side door strength without introducing any type of dynamic test or occupant injury measure. Since the on road vehicles in the U.S. and Canada are similar and the current Canadian side impact standard does not properly address the occupant protection in side impacts, the FMVSS-214 and its requirements were utilized as the modeling baseline of a typical side impact collision in this research study. - 148-To satisfy the requirements of these standards, it is recognized by current researchers that automotive manufacturers and vehicle designers have adopted three primary approaches for enhancing their vehicles' crashworthiness in side impacts. 1) Improving the vehicle structure to absorb more side impact energy or redirect the impact energy away form the occupant, 2) Improving the vehicle interior side structure, and 3) Utilizing supplemental safety devices. While it is recognized that the optimum vehicle performance will most likely be achieved by employing some combination of these three approaches into a single strategy for occupant safety enhancement, the scope of the current research was focussed only on the first approach since the vehicle structure is both the dominant and the first line of defence for the occupant in side impact collisions. It was logical to assume that based upon the results of the current study, that further occupant protection enhancements such as using interior padding protection and supplemental devices would be added and optimized, and is addressed later in the future work section. Currently, vehicle designers develop and optimize their products based on requirements of one or both major side impact standards (i.e. FMVSS-214 and ECE-R95) to address their products' performance in side impacts. While this approach satisfies the current regulations, the efficiency and effectiveness of this approach in protecting the occupants for a realistic range of different side impact collision conditions is not apparent based on the current collision statistics and their associated cost to society. As such, the objective of the current research was to develop an improved strategy to optimize the vehicle structure for side impact collisions and provide recommendations to enhance vehicle structural design for such collisions. A numerical analysis and collision simulation approach based on FMVSS-214 dynamic test was utilized as the analysis tool for this research. It should be noted that this side impact condition (with - 149-associated SID injury criteria levels) is acceptable to current regulators as sufficiently severe for use in defining vehicle compliance levels. To achieve the objective of this study, the overall approach to this research program was broken down into five phases. The results and conclusions of each phase are summarized in the subsequent sections of this chapter. However, prior to reviewing these results, it is important to review the assumptions made while carrying out these analysis phases in order to properly assess the significance and recognize the limitations which should be placed on conclusions drawn from this research work. ASSUMPTIONS AND LIMITATIONS OF THE CURRENT RESEARCH STUDY To demonstrate the effectiveness of the developed approach and work towards achieving the objective of this research, a typical side impact collision scenario and a numerical model of its components were required. As mentioned earlier, since this research was carried out in North America, the FMVSS-214 was selected as a typical side impact collision. This standard does not address the occupant head injury likelihood within its injury requirements although it is recognized that head injuries do occur (typically as a result of hitting structure both inside - if unrestrained, and outside the vehicle -such as the bullet vehicle). As such, the results of the demonstrated example do not include any head injury criteria. In other words, the head injury criterion (HIC) is not defined on the SID and is not part of the FMVSS-214 standard. Furthermore, the study uses only one target vehicle model for all analysis cases, which does not include seatbelts and/or any supplementary safety devices such as airbags. Although the significance of the aforementioned limitations of the selected example on the actual results of this study are recognized by the author, they are somewhat irrelevant to the objective of the study as the limitations only affect the results of the utilized example and do not concern the developed state-of-the-art design approach. Also, while it is recognized that the material thickness of the target vehicle's structural components is only one of many parameters in defining and/or changing the stiffness characteristics of the vehicle - 150-structure, changes to the thickness does provide both efficient and representative stiffness changes in the vehicle structure suitable for use in the parametric study of the selected target vehicle (i.e. see Section 3.0 in Chapter 6). While other options of varying the vehicle components stiffness (i.e. changing the position of the existing material, and/or varying the material itself) might be more desirable for the vehicle designer, their implementation would reduce the efficiency of the parametric study of the vehicle structure at the early stages of the design. Thus, while, many methods exist to change the vehicle structure (and these can ultimately be selected by the vehicle designer), this study utilized the first option (i.e. changing the thickness of the components) to vary the stiffness of the vehicle structure and perform the parametric study. This assumption is not considered to be significant for the approach and the results of this study as the trends of results are expected to be similar once the other options of varying the vehicle structural stiffness are utilized. With the global assumptions used in the current study identified, the significance of the results and the conclusions from each of the defined phases can be discussed properly. This is done in the following sections. P H A S E 1: D E V E L O P M E N T AND V A L I D A T I O N O F T H E SIDE I M P A C T S I M U L A T I O N P A C K A G E The objective of this phase was to develop and verify a numerical analysis tool to be utilized as the investigation tool within this research study. Based on the FMVSS-214 compliance test, a complete side impact simulation package consisting of a validated SID, U.S. M D B , and finite element model of on the 1990 Ford Taurus was assembled to perform the side impact simulations. The following accomplishments and contributions were made in the process of completing this phase of the work: • A new and more efficient U.S. M D B model was developed and validated using L S - D Y N A software. - 151 -Efforts were made to simplify this model while maintaining accuracy for the purpose of increasing computational efficiency. The utilized approach for developing and simplifying this model is a contribution to the limited published methodologies for developing such a finite element model, and will benefit continued research by the current research group and potentially other independent researchers studying in this area. • The acquired US SID model was examined, and verified to ensure its accuracy and suitability for use in this research. Although this model was acquired from the N C A C website, subsequent verification using two sets of criterion within the current study has provided added confirmation and confidence for utilizing this software in both the current and future research. • The target vehicle model was acquired from N C A C website. This finite element model was previously validated by another independent researcher (i.e. [19]). As such, this model was utilized in its original form within this study. With the completion and verification of the simulation package, the objective of this phase was achieved. This package provided an essential tool required to complete the remaining phases of the work and achieve the objectives of this research study. The specific results of this phase are of particular interest to other software developers working in this area, while the benefits to other potential users of this document (i.e. regulators, vehicle designers and users, etc) will be achieved through application of this simulation package to make future vehicle crashworthiness enhancements. This simulation package should provide a useful tool for the other researchers working in area of vehicle side impact crashworthiness and contributes to the limited research tools available in this area. - 152-PHASE 2 : THE EFFECT OF SIDE IMPACT COLLISION PARAMETERS ON THE POTENTIAL FOR OCCUPANT INJURY In order to improve the current design strategy, the effects of the collision parameters on the occupant injury likelihood need to be well understood and addressed within the improved design strategy. As such, the objective of this phase was to investigate the effects of collision parameters on the FMVSS-214 defined injury indices (i.e. the TTI, the peak lateral pelvis acceleration). To achieve this objective, four sets of numerical analyses were performed utilizing the developed side impact simulation package. The following conclusions were drawn from the simulation results for the selected target vehicle within the specified limits of these collision parameters in this study. Although, these conclusions were drawn from the analysis results of one mid-sized target vehicle and within the assumptions of the studied example (i.e. as noted previously) the trends of these results are expected to be similar in the other types of mid-sized vehicles, but could potentially change for significantly different vehicle types (i.e. much smaller or much larger vehicle types). • The TTI was found to be the predominant injury index when compared to the peak lateral pelvic acceleration. This result is very significant (i.e. its value exceeded 141% of the acceptable limit in some analysis cases) in the studied target vehicle indicating high occupant injury likelihood in the thorax area. This trend was also supported by the current published literature as they reported the higher injury risk of the thorax area (i.e. 23-31% of the AIS >3 injuries) in comparison to the pelvic region (i.e. 6-12% of the AIS >3 injuries) [10] in side impact collisions. Clearly vehicle designers need to pay extra care to their design's performance for properly protecting the occupant thorax in such collisions. This conclusion leads one to recommend that the regulators may need to increase their penalty for thorax area injuries. This could be done easily by reducing the acceptable TTI limit while keeping the pelvic value the same. The results would be a priority shift towards more occupant protection in the thoracic area by manufacturers, and hopefully an associated reduction in injury risk in this area of the body. - 153 -They could also toughen their vehicle safety rating system (i.e. Star rating system) for the thorax related injuries to force the manufacturers to properly address these types of injury likelihood in their products. • The initial velocity of the bullet vehicle has the highest effect on the occupant injury indices in comparison to the other collision parameters. The TTI value increased by 55% when the M D B velocity was increased by 30% over the F M V A S S 214 test value (i.e. 54 Km/hr) striking the analyzed target Vehicle. Similar increases in the occupant injury likelihood by increasing the impact velocity have also been reported by other researchers (i.e. [6, 58]). However, its significance in comparison to the other collision parameters has not been previously addressed. The above results and conclusion lead one to propose that if the regulators reasonably increase the standard test velocity while keeping the injury measure limits unchanged, they could potentially cause a significant improvement in the current occupant protection level in side impact collisions. They could also define another side impact test procedure with higher speed as a safety rating test to encourage the manufacturers to improve their products crashworthiness. This test could be performed at say 80 km/hr, which would represent the impact velocity conditions for 99% of all side impacts in North America, in contrast to the current 54 km/hr which accounts for only 90% of side impacts. These results lead one to recommend strongly that vehicle designers consider a wider range of collision velocity for evaluating their design performance in such collisions. • The vertical position of the side impact point has the next greatest effect on injury potential after collision velocity. The results of the analyzed target vehicle showed that reducing the vertical position of the bullet vehicle reduces the injury level of the thorax region. The results of the analyzed target vehicle showed that once the vertical position of the M D B increased by 27% from its original position, the TTI value was increased by 25%. Such an increase of - 154-the occupant's thorax region injury likelihood with increasing height of the impacting vehicle has also been reported by other researchers (i.e. [6, 58]), however, its significance has not been addressed in comparison to the other collision parameters until now. Based on these results, it is apparent that the regulators need to pay specific attention to this parameter when they need to design or update a new side impact standard. The current U.S. M D B height is equal or higher than the bumper height for 70% of all the vehicles in North America. However, if the M D B height was increased by 27% (i.e. higher than 95% of the on-road vehicle height in North America), it could substantially improve the occupant protection by forcing the industry to improve their products crashworthiness in side impacts in order to satisfy the new standard. This could also be done by a rewarding program (i.e. safety rating program) and encourage the industry to pay attention to this parameter in their product design. • The bullet vehicle's mass is the next collision parameter that most affects the occupant injury measures in side impact collisions. Reducing this parameter below 1400 kg (i.e. close to the mass of the selected target vehicle) decreased the occupant injury measures, while increasing this parameter above 1400 kg did not cause a significant variation of the injury measures. The limited effect of increasing the striking vehicle mass has also been reported by Hobbs [6] based on performed full-scale physical tests. However, the performed tests did not include any small impacting vehicle (i.e. lighter vehicles), thus the results of the current work are significant for highlighting the potential effect of the bullet vehicle's mass on the occupant injury likelihood. This result provides insight to the regulators about the relative importance of this parameter in comparison to the other parameters when they consider updating the M D B design in the standard test. Since the early separation of the impacting vehicle from the target vehicle's door structure was found to be the main reason for small variations in the injury measure values for larger M D B mass cases, it indicates the benefit of delaying the energy transfer to the occupant in side collisions. This fact should be of interest to vehicle designers as it suggests that they can improve their product's crashworthiness by increasing the distance between the occupant and the intruding structure. - 155 -• The horizontal position of the collision has the least effect (of the parameters studied) on the injury measures in side impacts. The analyses of this phase indicated that this parameter only affects the injury likelihood in the thorax region once the C G of the striking vehicle directly hits the B-pillar of the target vehicle. The plastic failure of the B-pillar was found to be the main reason for such an increase in the injury likelihood of the thorax region. This failure significantly increased the depth of the intrusion profile and subsequently increased the occupant loading and injury likelihood. As such, if the regulators vary the current standard configuration so that the C G of the M D B hits the B-pillar directly, it represents the worse case scenario for the horizontal position of the bullet vehicle in side impact collisions. This could force the industry to improve the strength of the B-pillar so that it does not fail in the worst case scenario. As discussed within the above conclusions, the effects of the collision parameters on the occupant injury likelihood have been previously investigated. However, their significance relative to each other has not been previously addressed in the literature. As such, the results of this phase extend the state-of-the art knowledge about the relative effects of the identified collision parameters on the occupant injury likelihood. These results and conclusions also provide insight for the regulators, vehicle designers, and users to see the individual effects of these collision parameters on occupant injury likelihood in side impact collisions. The results of this phase were also crucial in implementing the effect of collision parameters in optimization process of the vehicle structure (i.e. Phase 5) as designers need to consider the effect of these parameters when designing for side impact crashworthiness of the vehicle. Although the objective of this phase was satisfied, it was recognized that the analyses performed in this phase were computationally expensive (i.e. each analysis required 48 hours of 2.8 GHz CPU time) making the simulation package less than desirable in terms of efficiency for use in the in the optimization process. The next phase of this study introduced an approach to reduce the analysis time, and thus increase the utility of the software tools developed in this study to vehicle designers and researchers alike. - 156-PHASE 3 : SIDE STRUCTURE PERFORMANCE CRITERION (SSPC) DEFINITION AND VALIDATION One of the problems that a designer might face with the current strategy of designing the vehicle structural components for side impact crashworthiness is the high cost of examining the effectiveness of new design concepts at the early stages of product development. Since numerical modelling is the common analysis tool for evaluating such early design concepts (as has been selected for the current research), utilizing the current design strategy and available tools requires significant computational power thereby reducing its desirability for optimization of the vehicle structure. As such, the objective of this phase was to develop and validate a new criterion - the Side Structure Performance Criterion (SSPC) - that is defined based on the kinematics of the target vehicle's structure rather than the SID injury criteria, in order to reduce the computational cost of the required numerical analyses. The development of such an efficient evaluation tool for investigating the target vehicle crashworthiness should be of greater interest to the vehicle designer and automobile companies since other groups such as regulators and the vehicle users are only interested in the outcome of the vehicle design and how it can protect the occupant in the event of the crash rather than its designing issues. While the specific outcomes and conclusions of this phase will directly assist the vehicle designer, however other parties will also benefit indirectly in the long term when this new criterion is applied as part of the new vehicle design strategy developed in this study to increase vehicle occupant protection in side impacts. To achieve the objective of this phase, the SSPC was developed based on parameters related to the kinematics of the vehicle side structure and the potential effects on occupant injury. Implementation of the SSPC into the analysis process improved the efficiency of the side impact simulation in the following ways: • The SSPC is defined on the target vehicle's side structure. Therefore it eliminates the need for numerical model of the SID, and thus decreasing the complexity of the numerical simulation and increases the efficiency of the analysis. - 157-• The SSPC maximizes earlier than SID-based injury measures due to the fact that the vehicle structure experiences the severity of the crash prior to the occupant. Thus the total computer simulation time can be reduced causing an increase in the efficiency of the analysis. As the result, the analysis time for side impact simulations was reduced to 3.5 hours from its original 48 hours in 2.8 GHz CPU once the SSPC was utilized in place of the SID-based injury measures (i.e. 13 times faster than original analysis). This indicates a substantial efficiency improvement of the analysis tool which evaluates the vehicle performance in the side impact collisions. Thus, it could be very efficient analysis tool for vehicle designers in the early evaluation of their design concepts. To verify the SSPC, four sets of simulations were performed in which the collision parameters (such as impact velocity, position and the mass of the bullet vehicle) were altered, and the trend of the maximum injury measure (i.e. the TTI or the peak lateral pelvis acceleration) was compared with the SSPC trend for each simulation. The high correlation between the SSPC and the maximum injury measure (i.e. the maximum between normalized TTI and the peak lateral pelvic acceleration) indicated good accuracy of utilizing the SSPC as an evaluation tool for assessing of the target vehicle performance in side impact simulations. It should be noted that the predominant injury measure in the analyzed target vehicle for most cases was the TTI. Thus, the SSPC was utilized instead of the TTI to predict the occupant injury likelihood in this study. Suitability of the SSPC for use by vehicle designers is limited by the following issues. 1) This criterion (i.e. the SSPC) does not consider the effect of the door-occupant compliance. Therefore, it cannot assess the performance of the vehicle interior structure (i.e. padding system, etc) as well as supplementary safety devices such as side airbags. 2) The verification procedure of this criterion was also solely based the FMVSS-214 compliance requirements and performed with one target vehicle (i.e. 1990 Ford Taurus). As such, further - 158-efforts are required to validate this criterion based on other compliance requirements (i.e. ECE-R95) as well as other types of target vehicles. In spite of the above limitations of the developed criterion, the development and verification of the SSPC is one of the most significant contributions of this research study as currently there is no other evaluation criterion like the SSPC that could investigate the performance of the vehicle structure in side impacts with such efficiency. The results of this phase, developed confidence in employing the SSPC as an evaluation tool to assess the vehicle structure performance in side impact collisions. Thus, the objective of this phase was achieved and the SSPC utilized in subsequent analysis of the target vehicle side structure in this research. Also, it should be noted that once the limitations of this criterion are addressed, the SSPC could become very effective design tool at the early stages of a vehicle structural design. PHASE 4 : PARAMETRIC STUDY OF THE VEHICLE STRUCTURE To develop a strategy to optimize the vehicle structure for side impact collisions, it was recognized that two important issues needed to be properly addressed: 1) the critical components that affect the crashworthiness of the target vehicle need to be identified, and 2) the correlation between the design of these components and the vehicle performance in side impacts needs to be quantified. As such, the objective of this phase of study was to first, identify the critical components of the vehicle structure in providing the occupant protection in side impact collisions, and then perform a parametric study to develop a relationship between the SSPC and both collision parameters and the stiffness (i.e. the design variable) of the identified vehicle components which could be utilized in the final phase of the current research study (i.e. Phase 5). It should be noted that since the discussed parametric study is a part of vehicle structural design strategy, the individual results and conclusions of this phase should be of specific interest to the vehicle designer, while other parties (i.e. the vehicle users) will again benefit ultimately from the implementation of an improved design strategy (i.e. the main objective the study) leading to enhanced vehicle crashworthiness. - 159-To accomplish these objectives, initially, based upon a substantial review of previous side impact numerical modeling results using the mid-sized Ford Taurus and the M D B collisions (i.e. Phases 2 and 3), the B-pillar, rocker panel, door rail, roof, floor, upper door, and lower door structure were identified as the predominant vehicle structural elements involved in providing vehicle crashworthiness performance. Once these were identified, numerical simulations were used to obtain the correlation between the SSPC and the selected structural parameters (i.e. the thickness of the identified vehicle components) using the collision parameters specified for the FMVSS-214 compliance test condition. This correlation, in conjunction with the results of both previous phase (i.e. Phase 3) and the current phase (i.e. Phase 4), were utilized to develop a comprehensive equation to correlate the SSPC to both structural and collision parameters thus fulfilling the objectives of this phase. The performed analyses and results achieved in this phase demonstrate a successful example of the developed parametric study approach which quantifies the effect of the vehicle components stiffness on its performance in side impact collisions. The developed approach is a contribution to the methods of investigating the effects of vehicle design variables on the vehicle performance. This approach could benefit the vehicle designer to efficiently investigate the effects of the design variables on the defined performance criteria. Further analysis of the results of the analyzed target vehicle lead to the following conclusions for this particular vehicle design in FMVSS-214 compliance test condition: • Increasing the thickness of the B-pillar, upper and lower door decreases the SSPC value. This conclusion recommends that increasing the stiffness of these components would be beneficial and improves the analyzed vehicle's crashworthiness. • Increasing the thickness of the roof, floor pan, and rocker panel increased the SSPC value. This suggests that decreasing the stiffness of these components is beneficial and reduces the occupant injury risk for the analyzed target vehicle. - 160-• While the stiffness of the upper door had the highest effect, the door rail stiffness had little, if any effect on the SSPC level and occupant injury level. These results would lead the author to recommend that priority for crashworthiness improvement of the analyzed vehicle structure should be placed on improving the design of the vehicle upper door structure. The above recommendations and conclusions were drawn for the analyzed target vehicle in the FMVSS-214 test condition without considering the effect of the collision parameters. Similarly, the current vehicle design strategy does not consider the effect of the collision parameters in developing a new product. This could potentially be dangerous as the developed product might not provide enough occupant protection for other conditions of side impact collisions (i.e. other than FMVSS-214 test condition). As such, this could be one of the main issues of the current design strategy as it fails to consider the effect of the collision parameters on the vehicle design. This issue will be discussed more thoroughly at the end of the next section. PHASE 5: CALCULATION OF INJURY RISK AND OPTIMIZATION OF THE VEHICLE SIDE STRUCTURE The objective of this phase of study was to utilize the results of the previous phases and develop a state-of-the-art approach to optimize the vehicle structure for side impact collisions and satisfy the objective of the current research study. Similar to the previous phase, the individual results and approach of this phase will be of direct interest to the vehicle designer, while, its outcome as an improved approach to design the vehicle structure could ultimately improve the future vehicle's side impact crashworthiness and benefit all vehicle users. To achieve the above objective, a set of equations were developed that correlates the occupant injury likelihood to the selected structural parameters utilizing the results of the previous phases (i.e. Phase 3 and 4). Then, a series of Monte Carlo reliability analyses were performed to incorporate the effect - 161 -of collision parameters as well as structural parameters on the probability of occupant injury likelihood exceeding 3% (i.e. injury likelihood level which corresponds to the FMVSS-214 TTI limit). The generated database was represented with a full-quadratic response surface that was utilized in the optimization process of the vehicle structure. The results of the analyses performed on the analyzed target vehicle (i.e. Ford Taurus) lead the author to recommend that in order to optimize the side structure for this vehicle (within user-defined constraints) and enhance its side impact protection for the occupants in a North American driving environment, the following integrated set of structural design changes should be considered: • The thickness of the door and rocker panel was increased by 100% over the original design, while the thickness of B-pillar was increased by 40% over its original design. This suggests that increasing the stiffness of these components and improving their ability to absorb more impact energy would be beneficial in the analyzed target vehicle structural design. • The thickness of the roof was reduced by 50% over the original design. This recommends that transferring the impact energy away from the occupant and towards this more-compliant component by decreasing its stiffness would be desirable. • The thickness of door rail and floor pan did not substantially changed in the optimized structure. This indicates that the original stiffness of these components are at their optimum level for side impact crashworthiness in the current design of the analyzed target vehicle. Comparing the results of this phase - which includes the effects of the collision parameters - with those of the previous phase which does not include the effects of the collision parameters, shows the following similarities: • Both results recommend that increasing the stiffness of the door and B-pillar - 162-• Both results recommend reducing the stiffness of the roof improve the vehicle crashworthiness in side impact collisions. • The results of both phases confirm the limited effect of the door rail on the occupant injury likelihood. However, the conclusions of these two phases are controversial about the stiffness of the floor pan and the rocker panel. While the results of this phase (i.e. Phase 5) indicates that the current stiffness of the floor pan is around its optimum value and recommends increasing the stiffness of the rocker panel, the results of the previous phase suggests reducing the stiffness of both rocker panel and floor pan to improve the vehicle crashworthiness in side impact collisions. Such a contrast in the results of these two phases shows the danger of not considering the effect of the collision parameters in designing the vehicle structure. Currently, vehicle designers are only required to improve their design for the compliance test condition without considering the potential effect of the collision conditions on the occupant injury likelihood. However, the results of this study show that this could potentially increase the occupant injury likelihood for other side impact collision conditions as the vehicle structure performance could change in response to different collision conditions. This highlights the necessity of considering the effects of collision parameters in the vehicle structural design. The performed analyses of this phase demonstrated a successful example of the developed state-of the-art strategy to optimize the vehicle structure for side impact collisions, thus satisfying the objectives of the current research project. This strategy is another significant contribution of this research, which improves upon the current design strategy in two ways. 1) It recognizes the effects of the collision parameters on the occupant injury likelihood and addresses their effect on the optimization of the vehicle structure. 2) The developed strategy improves the efficiency of the design analysis tool by utilizing a new developed criterion (i.e. the SSPC) for assessing the vehicle structural side impact crashworthiness. - 163 -The development and verification of this criterion is also a significant contribution of this research, which could substantially improve the efficiency of the design process and benefits the vehicle designers. As such, the new and innovative approach for developing a more crashworthy vehicle side structure described and demonstrated within this thesis should help the vehicle designer to more efficiently optimize their design in the early stages of product development. This could substantially increase the vehicle's side impact crashworthiness and benefit the occupants by providing better protection is such collisions. This work also provides insight information for vehicle regulators by substantiating the relative effect of various key collision parameters on the occupant injury likelihood and how ignoring their effect could affect the risk of occupant injury in automotive collisions in North America. To improve the results of the current research and address its limitations, more research is still required. The next section of this chapter discusses potential work that should be performed to address these limitations and improve the results of the current study. P O T E N T I A L F U T U R E W O R K The overall aim of this A U T O 21 research project at U B C was to develop an approach to optimize the vehicle structure for side impact collisions and provide recommendations to enhance vehicle structural design. In addition to the work performed in the current study, numerous areas relating to vehicle design are still available for investigation, and potential future work related to the current research is outlined below: • The current vehicle structural design recommendations are based on one target vehicle's crashworthiness in side impact collisions. Therefore, although the general trends of the results are expected to be similar, further analyses with a variety of vehicle types are required to be performed, so that these guidelines can be verified and utilized as an approach to improve vehicle - 164-crashworthiness in side impact collisions. This would benefit all the parties involved in this matter (i.e. regulators, vehicle designers, users) by evaluating and potentially confirming the results of the current research study. The Side Structure Performance Criterion (SSPC) developed in this research is only verified based on the side impact compliance test in North America and only with one target vehicle model. This criterion needs to be validated based on the European side impact compliance test and with multiple target vehicles in order to be used globally in optimization process of the vehicle structure. Also the SSPC does not.consider the effects of the relative door-occupant compliance, which might reduce the occupant injury prediction capability of this criterion. This limitation especially prevents the vehicle designer from utilizing the SSPC to investigate the effects of a side airbag and/or padding system on the occupant injury likelihood in side impact collisions. Further efforts are required to incorporate this effect in the SSPC equation and verify and/or validate the new developed criterion. The improvement of this criterion could significantly benefit the vehicle designers by increasing the confidence level of utilizing the SSPC as an efficient evaluation tool of the vehicle performance in side impact collisions. The distributions of collision parameters utilized in this research were extracted from FARS database [1] and are only valid for North America, therefore further investigation is required to discover such statistical distributions of collision parameters from other parts of the world and investigate their effect on the vehicle side impact crashworthiness. This could help vehicle designers improve and maybe customize their products being sold in different parts of the world, which could benefit the occupant by improving its protection in such collisions. This could also help the regulators to develop more representative standards based on the vehicle and collision statistical distribution in that regional area. The current study utilized the thicknesses of the side components as being representative of the vehicle structural stiffness to optimize the vehicle structure. If may not be feasible or reasonable to alter the thicknesses of the materials in the real vehicle structural design due to manufacturing - 165 -difficulties, cost, etc. Thus other options of altering the vehicle side structure stiffness (i.e. changing the material, geometry, etc) need to be investigated to discover their effects on occupant injury likelihood in side impact collisions. This would benefit the vehicle manufacturers by recommending a more feasible design to improve their vehicle performance in side impacts. To expand the scope of the current research and improve the vehicle crashworthiness in side impact collisions, the other strategies normally applied to improve the vehicle performance in such collisions should be investigated. As previously discussed in Chapter 2, there are three major strategies to improve the vehicle crashworthiness in side impact collisions: 1) improving the vehicle structure, 2) improving the vehicle interior structure, and 3) implementing the supplemental safety devices such as side airbags in the vehicle. The current research has only investigated the first strategy and developed a method to optimize the vehicle side structure. However, the complete optimization of the vehicle performance in side impact collisions requires full investigation of all three strategies. Therefore, the next step to improve the current research work could be implementing various types of side impact airbags and different padding systems in the current computer simulation package to evaluate their effect on the occupant injury likelihood and ultimately optimize the vehicle design for better vehicle crashworthiness in side impact collisions. This would benefit the vehicle designer by providing a better and more general approach to improve the vehicle design for side impact crashworthiness. Thus, the developed vehicles would provide better occupant protection and benefit to the vehicle user. Finally, the effect of these recommendations in the case of other types of collisions (i.e. frontal impacts, rear end impacts, etc) should be investigated as implementing them without proper consideration might increase the occupant injury likelihood in the other types of collisions. This additional work would benefit all the parties involved in this matter (i.e. regulators, vehicle designers, users) by potentially improving the vehicle crashworthiness for all types of collisions. A l l of the aforementioned areas of future research involve varying degrees of complexity, and all are aimed at further improvement of the vehicle crashworthiness mostly in side impact collisions. - 166-However, i f funded, these investigations could potentially benefit the public and applied industry through significant reduction of societal costs associated with occupant injuries. - 167-Chapter 9. R E F E R E N C E S [1] Fatal Accident Reporting System (FARS), 2004, "Http://www-Fars.Nhtsa.Dot.gov/queryReport.Cfm?stateid=0&year=2004," 2006(3/21) pp. 1. [2] Insurance Corporation of British Columbia (ICBC), website: www.icbc.com, 2005, "Traffic Statistics, British Columbia 2004," 2006(11/1) pp. 1. [3] Careme, L. M . M . , 1991, "Occupant kinematics and injury causation in side impact," Proceedings of the 1991 SAE International Congress & Exposition, SAE, Warrendale, PA, USA, Detroit, MI, USA, 910316. [4] Lau, I. V. , Capp, J. P., and Obermeyer, J. 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G., Bourgund, U. , 1989/3, "On Efficient Computational Schemes to Calculate Structural Failure Probabilities," Probabilistic Engineering Mechanics, 4(1) pp. 10-18. [88] Mathworks, 2002, " M A T L A B Optimization Toolbox," 6.50. [89]Transport Canada, "http://www.tc.gc.ca/acts-regulations/GENERAL/m/mvsa/regulations/mvsrg/210/mvsr214.html" - 178-APPENDIX A. PARAMETRIC STUDY DATABASE - SIDE STRUCTURE THICKNESS - SSPC DATABASE Exp. Number B- Pillar thickness( mm) Inner Door-up thickness( mm) Inner Door-low thickness( mm) Door Rail thickness( mm) Rocker panel thickness( mm) Floor Pan thickness( mm) Roof thickness inm) SSPC m a x v-.o-gi;,^ , „ 0 91,;4 ,,-165 •;,Q95 • i- 1 3.- -• -.-..1 •. . 0:4724: , 1 2.01 E+00 7.22E-01 8.34E-01 1.55E+00 4.53E-01 0.5463 0.98871 0.4318 2 1.27E+00 6.64E-01 8.00E-01 1.03E+00 4.83E-01 0.57745 1.8 0.4522 3 9.67E-01 6.99E-01 4.70E-01 1.74E+00 4.68E-01 0.48005 0.96095 0.4589 4 1.62E+00 5.25E-01 9.18E-01 2.16E+00 4.64 E-01 0.48316 1.9749 0.4857 5 1.04E+00 9.35E-01 6.11 E-01 1.05E+00 5.98E-01 0.55137 0.52392 0.4439 6 1.78E+00 7.06E-01 4.40E-01 1.09E+00 5.27E-01 0.58123 1.5907 0.4399 7 9.72E-01 8.28E-01 7.12E-01 1.15E+00 5.66E-01 0.4778 1.2615 0.4481 8 1.39E+00 4.48E-01 6.75E-01 1.46E+00 5.66E-01 0.47869 2.0563 0.4763 9 1.04E+00 4.92E-01 5.14E-01 3.34E+00 4.80E-01 0.58453 0.69343 0.4922 10 1.05E+00 7.75E-01 6.43E-01 2.72E+00 4.83E-01 0.56871 1.612 0.4605 11 1.73E+00 8.14E-01 7.30E-01 3.17E+00 5.19E-01 0.51722 1.1203 0.4535 12 1.52E+00 4.83E-01 4.49E-01 2.50E+00 5.22E-01 0.47767 2.0189 0.4693 13 1.90E+00 4.97E-01 8.45E-01 3.03E+00 5.50E-01 0.57508 0.79701 0.4788 14 1.79E+00 7.64E-01 7.72E-01 2.29E+00 5.56E-01 0.55493 1.6333 0.5016 15 8.32E-01 8.07E-01 5.27E-01 2.80E+00 5.98E-01 0.50052 0.82438 0.5448 16 1.15E+00 7.87E-01 9.05E-01 2.52E+00 5.29E-01 0.5234 1.4473 0.4594 17 1.70E+00 6.07E-01 1.15E+00 1.11 E+00 5.01 E-01 0.58547 1.2014 0.4514 18 2.09E+00 7.54E-01 1.26E+00 2.11 E+00 4.51 E-01 0.60022 1.4642 0.4492 19 1.77E+00 6.67E-01 1.28E+00 1.78E+00 4.69E-01 0.49735 0.47806 0.4492 20 1.34E+00 5.18E-01 1.25E+00 8.21 E-01 4.94E-01 0.49676 1.6166 0.4594 21 1.35E+00 4.75E-01 9.63E-01 1.32E+00 5.95E-01 0.54666 1.1464 0.4857 22 1.51 E+00 8.22E-01 9.90E-01 1.66E+00 5.92E-01 0.57517 1.9089 0.452 23 1.65E+00 5.53E-01 9.68E-01 9.10E-01 5.25E-01 0.5131 0.83604 0.4614 24 2.16E+00 8.51 E-01 1.10E+00 1.34E+00 5.68E-01 0.48673 2.1381 0.4321 25 1.93E+00 9.29E-01 1.30E+00 2.63E+00 4.97E-01 0.59665 0.78229 0.4635 26 1.33E+00 8.93E-01 9.62E-01 2.23E+00 5.07E-01 0.57333 1.5676 0.4391 27 2.14E+00 8.97E-01 9.58E-01 3.45E+00 4.54E-01 0.49047 0.70973 0.4412 28 9.90E-01 5.51 E-01 1.04E+00 3.51 E+00 5.20E-01 0.52519 1.3231 0.4919 29 2.20E+00 8.23E-01 1.34E+00 3.16E+00 5.39E-01 0.5515 0.99719 0.4459 30 8.91 E-01 8.18E-01 1.42E+00 3.26E+00 5.33E-01 0.55324 1.4224 0.4579 31 1.24E+00 7.83E-01 1.12E+00 3.32E+00 5.83E-01 0.46611 0.56049 0.4526 32 2.12E+00 7.26E-01 9.98E-01 2.74E+00 5.53E-01 0.49511 2.0598 0.4583 33 1.26E+00 9.29E-01 1.94E+00 1.94E+00 4.79E-01 0.58876 0.50228 0.4466 34 1.32E+00 8.64E-01 1.84E+00 1.94E+00 4.54E-01 0.57597 2.1013 0.4379 35 8.93E-01 4.34E-01 1.68E+00 1.46E+00 5.16E-01 0.52544 0.76428 0.4848 36 8.58E-01 4.81 E-01 1.56E+00 1.17E+00 5.03E-01 0.46474 1.3349 0.4766 37 1.15E+00 5.61 E-01 1.61 E+00 1.35E+00 5.82E-01 0.55851 0.63694 0.4574 38 1.39E+00 7.82E-01 1.65E+00 8.72E-01 5.93E-01 0.56792 1.5306 0.4445 39 2.19E+00 7.04E-01 1.67E+00 1.72E+00 5.36E-01 0.4773 0.78089 0.4269 - 1 7 9 -P A R A M E T R I C STUDY D A T A B A S E - C O N T 40 2.14E+00 5.84E-01 1.63E+00 1.22E+00 5.78E-01 0.5164 1.5382 0.4499 41 1.32E+00 8.48E-01 1.74E+00 3.54E+00 5.03E-01 0.5591 1.306 0.431799 42 1.14E+00 6.94E-01 1.93E+00 3.37E+00 5.01 E-01 0.5573 1.5357 0.445467 43 1.71 E+00 6.65E-01 1.46E+00 3.32E+00 5.09E-01 0.49313 1.2352 0.465697 44 1.10E+00 4.73E-01 1.77E+00 3.41 E+00 4.96E-01 0.53127 1.3973 0.483 45 1.21 E+00 8.65E-01 1.69E+00 2.30E+00 5.47E-01 0.54085 1.0434 0.4395 46 8.21 E-01 9.27E-01 1.80E+00 2.47E+00 5.38E-01 0.59244 1.5183 0.4573 47 8.80E-01 5.12E-01 1.68E+00 2.32E+00 5.75E-01 0.47368 0.77525 0.4974 48 1.41 E+00 5.86E-01 1.95E+00 3.47E+00 5.97E-01 0.53063 2.145 0.51 49 1.53E+00 1.06E+00 8.20E-01 1.33E+00 4.77E-01 0.60002 0.67509 0.4347 50 8.70E-01 9.92E-01 4.90E-01 1.86E+00 4.84E-01 0.59429 2.1389 0.4363 51 1.80E+00 1.16E+00 5.27E-01 1.21 E+00 4.45E-01 0.50216 0.70241 0.4214 52 1.65E+00 9.78E-01 4.60E-01 1.72E+00 4.76E-01 0.50301 1.98 0.4361 53 1.90E+00 1.22E+00 5.75E-01 1.83E+00 5.97E-01 0.56185 0.75489 0.4245 54 1.77E+00 9.64E-01 4.77E-01 9.60E-01 5.93E-01 0.53472 1.3581 0.437585 55 1.45E+00 1.08E+00 6.85E-01 1.45E+00 5.49E-01 0.49498 0.78608 0.436574 56 1.17E+00 1.03E+00 7.81 E-01 1.48E+00 5.86E-01 0.52679 1.7456 0.441399 57 1.06E+00 1.20E+00 6.09E-01 2.88E+00 5.07E-01 0.58456 0.69738 0.462917 58 1.10E+00 1.36E+00 4.39E-01 3.10E+00 5.03E-01 0.56642 1.5387 0.442853 59 2.00E+00 1.26E+00 5.39E-01 2.97E+00 4.77E-01 0.50357 0.9488 0.455116 60 1.55E+00 9.63E-01 6.79E-01 2.88E+00 4.90E-01 0.46575 1.6488 0.437096 61 1.67E+00 9.78E-01 9.13E-01 3.53E+00 5.44E-01 0.54768 0.76996 0.44028 62 2.17E+00 1.22E+00 7.16E-01 2.89E+00 6.02E-01 0.59092 1.5126 0.427443 63 1.97E+00 1.35E+00 6.33E-01 2.37E+00 5.38E-01 0.47507 0.68649 0.451417 64 2.20E+00 1.23E+00 6.77E-01 3.39E+00 5.89E-01 0.46475 1.802 0.439922 65 1.61 E+00 1.04E+00 9.56E-01 1.36E+00 4.56E-01 0.58313 0.49952 0.422786 66 1.68E+00 1.14E+00 1.32E+00 1.94E+00 4.70E-01 0.56146 1.6095 0.447148 67 1.80E+00 9.65E-01 1.43E+00 1.16E+00 5.21 E-01 0.50733 0.76648 0.456585 68 1.82E+00 1.01 E+00 1.10E+00 1.66E+00 5.16E-01 0.47888 1.6222 0.438739 69 9.62E-01 1.15E+00 1.13E+00 1.46E+00 5.74E-01 0.58215 0.572 0.442144 70 8.09E-01 1.43E+00 1.23E+00 1.98E+00 5.22E-01 0.58949 1.4683 0.442287 71 1.26E+00 1.08E+00 1.31 E+00 1.99E+00 5.73E-01 0.47581 0.75943 0.452034 72 1.64E+00 1.18E+00 1.14E+00 9.84E-01 5.51 E-01 0.48084 1.5752 0.428026 73 8.48E-01 1.16E+00 1.04E+00 2.62E+00 4.51 E-01 0.54906 0.93526 0.447706 74 1.24E+00 1.40E+00 1.21 E+00 2.31 E+00 5.05E-01 0.55021 1.7245 0.451284 75 8.87E-01 9.39E-01 1.14E+00 2.65E+00 4.80E-01 0.48549 1.1732 0.467863 76 1.91 E+00 1.04E+00 9.66E-01 2.98E+00 4.41 E-01 0.48507 1.4522 0.424177 77 1.81 E+00 1.34E+00 1.06E+00 2.73E+00 5.44 E-01 0.54009 0.49336 0.442079 78 8.16E-01 1.36E+00 1.31 E+00 2.19E+00 5.62E-01 0.55355 2.0731 0.447148 79 2.18E+00 1.31 E+00 1.24E+00 3.49E+00 5.56E-01 0.46838 1.209 0.439652 80 1.98E+00 9.72E-01 1.41 E+00 3.42E+00 5.30E-01 0.50166 2.0477 0.450493 81 9.12E-01 1.28E+00 1.57E+00 1.29E+00 4.47E-01 0.59608 1.2444 0.451932 82 1.63E+00 1.06E+00 1.52E+00 1.62E+00 4.79E-01 0.58339 1.7271 0.445057 83 1.33E+00 1.36E+00 1.72E+00 1.84E+00 5.11 E-01 0.51906 0.90895 0.433816 84 1.15E+00 1.34E+00 1.68E+00 1.63E+00 4.89E-01 0.53329 1.8909 0.432899 - 180-P A R A M E T R I C STUDY D A T A B A S E - C O N T 85 8.77E-01 1.04E+00 1.75E+00 1.85E+00 5.52E-01 0.59105 1.121 0.467234 86 8.79E-01 1.14E+00 1.86E+00 1.11E+00 5.39E-01 0.60193 1.5351 0.446507 87 1.37E+00 9.71 E-01 1.81 E+00 1.63E+00 5.51 E-01 0.49758 1.2493 0.450361 88 2.06E+00 9.37E-01 1.95E+00 1.89E+00 5.28E-01 0.51933 1.8161 0.421157 89 1.83E+00 1.44E+00 1.61 E+00 2.26E+00 4.88E-01 0.5446 1.2053 0.436896 90 1.73E+00 9.68E-01 1.68E+00 2.33E+00 4.96E-01 0.53598 1.9439 0.443659 91 1.91 E+00 1.44E+00 1.85E+00 3.32E+00 4.42E-01 0.49231 0.80754 0.445699 92 8.95E-01 1.35E+00 1.52E+00 3.03E+00 4.73E-01 0.47965 1.4167 0.456841 93 1.88E+00 1.17E+00 1.86E+00 3.25E+00 5.59E-01 0.55417 0.58946 0.436486 94 1.54E+00 1.36E+00 1.54E+00 3.19E+00 5.85E-01 0.53686 1.9857 0.445102 95 1.07E+00 1.45E+00 1.55E+00 2.39E+00 5.43E-01 0.53275 1.1513 0.446479 96 1.85E+00 1.01 E+00 1.55E+00 3.31 E+00 5.37E-01 0.48377 1.8588 0.451971 97 1.41 E+00 1.84E+00 7.72E-01 1.00E+00 5.13E-01 0.54728 1.1744 0.424228 98 1.91 E+00 1.53E+00 8.68E-01 1.86E+00 5.14E-01 0.58267 1.9299 0.405384 99 1.82E+00 1.83E+00 9.03E-01 2.05E+00 4.48E-01 0.51815 0.98324 0.429457 100 1.73E+00 1.68E+00 8.25E-01 1.54E+00 4.63E-01 0.48894 1.6358 0.425779 101 1.53E+00 1.78E+00 5.22E-01 1.25E+00 5.50E-01 0.54115 0.74754 0.425779 102 2.16E+00 1.84E+00 9.04E-01 9.04E-01 5.86E-01 0.58045 2.0977 0.423027 103 1.68E+00 1.65E+00 7.51 E-01 1.29E+00 5.63E-01 0.49282 0.4865 0.424491 104 2.02E+00 1.93E+00 8.84E-01 2.01 E+00 5.41 E-01 0.50835 1.4285 0.418399 105 1.58E+00 1.49E+00 6.63E-01 2.26E+00 4.57E-01 0.56578 0.85822 0.45441 106 2.12E+00 1.65E+00 4.32E-01 2.84E+00 5.02E-01 0.59402 1.3277 0.411229 107 2.09E+00 1.60E+00 7.21 E-01 3.20E+00 4.58E-01 0.49316 0.97638 0.453493 108 1.34E+00 1.89E+00 7.73E-01 2.68E+00 4.47E-01 0.52652 2.1185 0.436493 109 1.93E+00 1.56E+00 4.43E-01 2.59E+00 5.63E-01 0.58959 1.0709 0.436493 110 1.53E+00 1.79E+00 5.86E-01 3.40E+00 5.61 E-01 0.54465 1.958 0.420336 111 7.99E-01 1.53E+00 8.48E-01 2.99E+00 5.31 E-01 0.51504 1.0189 0.443457 112 1.52 E+00 1.54E+00 6.52E-01 2.26E+00 5.54E-01 0.48362 1.9749 0.441251 113 1.13E+00 1.63E+00 1.44E+00 1.74E+00 4.63E-01 0.57849 1.0433 0.432428 114 2.06E+00 1.54E+00 9.48E-01 1.61 E+00 4.72E-01 0.54228 1.9926 0.400757 115 2.14E+00 1.67E+00 1.44E+00 9.59E-01 5.14E-01 0.52297 1.1662 0.426416 116 1.62E+00 1.47E+00 1.43E+00 1.35E+00 5.09E-01 0.51178 1.5748 0.436404 117 8.42E-01 1.66E+00 1.00E+00 8.10E-01 5.25E-01 0.54009 0.60316 0.42247 118 1.93E+00 1.62E+00 1.33E+00 1.64E+00 5.92E-01 0.56773 1.6021 0.421101 119 1.45E+00 1.80E+00 1.39E+00 1.06E+00 5.42E-01 0.49254 0.72283 0.428935 120 1.51 E+00 1.59E+00 9.99E-01 1.09E+00 5.45E-01 0.49187 1.3469 0.410399 121 2.00E+00 1.80E+00 1.20E+00 3.40E+00 4.93E-01 0.54467 0.67759 0.440027 122 2.10E+00 1.58E+00 1.08E+00 2.59E+00 4.67E-01 0.59388 2.0906 0.430055 123 1.23E+00 1.74E+00 1.23E+00 2.60E+00 5.04E-01 0.47729 1.226 0.441209 124 9.35E-01 1.72E+00 1.03E+00 2.67E+00 4.91 E-01 0.50631 1.9878 0.442873 125 1.16E+00 1.64E+00 1.35E+00 2.94E+00 5.28E-01 0.57473 1.1647 0.444899 126 1.17E+00 1.52E+00 1.16E+00 2.70E+00 5.50E-01 0.56274 1.6607 0.44774 127 1.12E+00 1.80E+00 1.44E+00 3.12E+00 5.48E-01 0.48241 0.90106 0.439741 128 1.44E+00 1.51 E+00 1.22E+00 2.48E+00 5.58E-01 0.4905 1.9406 0.444669 129 2.05E+00 1.76E+00 1.76E+00 1.19E+00 4.63E-01 0.54262 1.1362 0.411991 130 2.09E+00 1.61 E+00 1.81 E+00 1.31 E+00 5.14E-01 0.54039 1.6042 0.4099 -181 -P A R A M E T R I C STUDY DATABASE - C O N T 130 2.09E+00 1.61 E+00 1.81 E+00 1.31 E+00 5.14E-01 0.54039 1.6042 0.4099 131 2.14E+00 1.73E+00 1.84E+00 1.63E+00 5.13E-01 0.48494 0.6907 0.4025 132 1.20E+00 1.63E+00 1.69E+00 1.69E+00 4.97E-01 0.51917 1.3368 0.4184 133 1.22E+00 1.73E+00 1.72E+00 1.11E+00 5.79E-01 0.53718 0.84251 0.4167 134 9.64 E-01 1.82E+00 1.56E+00 1.92E+00 5.95E-01 0.53626 1.8946 0.41 135 1.46E+00 1.77E+00 1.68E+00 8.78E-01 5.61 E-01 0.52175 1.0474 0.4198 136 1.62E+00 1.60E+00 1.73E+00 1.52E+00 5.51 E-01 0.51767 1.5216 0.4141 137 1.39E+00 1.59E+00 1.91 E+00 3.27E+00 4.99E-01 0.59448 0.76691 0.4331 138 2.21 E+00 1.83E+00 1.73E+00 2.86E+00 4.51 E-01 0.58734 1.5014 0.4178 139 1.20E+00 1.80E+00 1.70E+00 3.30E+00 4.81 E-01 0.48887 0.79253 0.4307 140 1.54E+00 1.79E+00 1.56E+00 2.71 E+00 4.71 E-01 0.48625 1.9574 0.4261 141 1.44E+00 1.88E+00 1.91 E+00 3.44E+00 5.52E-01 0.5408 0.57974 0.419518 142 1.82E+00 1.52E+00 1.58E+00 2.62E+00 5.78E-01 0.59383 1.8409 0.432717 143 1.55E+00 1.73E+00 1.71 E+00 2.22E+00 5.79E-01 0.47866 0.89397 0.416321 144 2.11 E+00 1.95E+00 1.73E+00 2.85E+00 5.99E-01 0.51493 1.3729 0.40381 145 2.23E+00 6.33E-01 5.93E-01 1.18E+00 5.06E-01 0.59558 0.84669 0.461281 146 3.22E+00 4.99E-01 7.10E-01 8.04E-01 4.50E-01 0.5763 1.6355 0.44811 147 3.37E+00 6.24E-01 4.54E-01 1.92E+00 4.75E-01 0.5323 0.8032 0.453482 148 2.52E+00 7.72E-01 4.99E-01 1.83E+00 4.61 E-01 0.49322 1.5739 0.42854 149 3.12E+00 9.31 E-01 5.44E-01 1.45E+00 5.89E-01 0.56718 1.0459 0.426196 150 2.85E+00 6.74E-01 8.91 E-01 8.66E-01 5.39E-01 0.56245 1.8834 0.443123 151 3.33E+00 7.18E-01 6.38E-01 1.25E+00 5.45E-01 0.49504 1.1899 0.442673 152 2.42E+00 4.92E-01 6.88E-01 2.01 E+00 5.77E-01 0.53288 1.3423 0.467662 153 2.38E+00 6.05E-01 4.62E-01 2.51 E+00 5.08E-01 0.55698 0.97217 0.442086 154 3.08E+00 5.36E-01 8.76E-01 2.59E+00 5.13E-01 0.56474 1.6032 0.468294 155 2.34E+00 6.28E-01 7.33E-01 2.20E+00 5.01 E-01 0.52261 0.7145 0.457653 156 2.69E+00 5.93E-01 9.33E-01 3.53E+00 5.18E-01 0.47644 1.6593 0.457634 157 2.32E+00 7.83E-01 7.18E-01 2.34E+00 5.68E-01 0.58698 0.77478 0.442032 158 2.33E+00 5.16E-01 6.09E-01 2.90E+00 5.97E-01 0.55304 1.3637 0.467256 159 3.46E+00 7.67E-01 5.04E-01 3.41 E+00 6.00E-01 0.48936 0.67767 0.438394 160 3.32E+00 6.12E-01 5.54E-01 2.45E+00 5.98E-01 0.48419 2.0746 0.451059 161 2.25E+00 9.29E-01 1.31 E+00 1.39E+00 4.55E-01 0.53481 0.79008 0.460354 162 2.85E+00 5.28E-01 1.05E+00 1.44E+00 5.13E-01 0.5356 2.0263 0.442654 163 2.68E+00 5.85E-01 1.44E+00 2.16E+00 4.57E-01 0.5175 0.961 0.43458 164 2.82E+00 5.46E-01 1.27E+00 1.75E+00 4.76E-01 0.51554 1.8488 0.439776 165 2.89E+00 4.67E-01 1.07E+00 1.96E+00 5.78E-01 0.57616 0.64151 0.439704 166 3.27E+00 6.95E-01 1.22E+00 1.57E+00 5.56E-01 0.5829 1.3416 0.444877 167 3.04E+00 4.90E-01 1.23E+00 1.13E+00 5.55E-01 0.52989 1.0978 0.444586 168 3.63E+00 5.36E-01 1.13E+00 1.12E+00 5.35E-01 0.48847 1.7498 0.440088 169 2.60E+00 8.97E-01 1.00E+00 2.79E+00 4.84E-01 0.59432 1.3044 0.436612 170 3.34E+00 8.30E-01 1.27E+00 3.24E+00 5.04E-01 0.55936 2.0287 0.430209 171 2.80E+00 8.42E-01 1.03E+00 3.24E+00 5.17E-01 0.48887 0.87504 0.441898 172 2.37E+00 5.74E-01 1.33E+00 3.47E+00 5.01 E-01 0.46468 1.5377 0.438738 173 3.20E+00 7.82E-01 9.40E-01 3.20E+00 5.52E-01 0.56715 1.155 0.435503 174 2.53E+00 9.12E-01 1.33E+00 3.53E+00 5.25E-01 0.58122 1.8611 0.437257 - 182-P A R A M E T R I C STUDY D A T A B A S E - C O N T 175 2.28E+00 6.37E-01 9.71 E-01 3.07E+00 5.45E-01 0.4767 0.78399 0.458175 176 3.49E+00 9.07E-01 1.26E+00 2.64E+00 5.46E-01 0.48605 1.6951 0.454163 177 3.02E+00 5.78E-01 1.81 E+00 1.43E+00 4.86E-01 0.59997 0.69013 0.415742 178 2.44E+00 7.06E-01 1.90E+00 1.17E+00 5.09E-01 0.57317 1.363 0.433817 179 2.89E+00 5.59E-01 1.62E+00 1.65E+00 5.04E-01 0.46975 0.94483 0.422338 180 2.41 E+00 7.80E-01 1.94E+00 1.43E+00 4.61 E-01 0.52364 1.9023 0.41821 181 3.50E+00 4.60E-01 1.63E+00 1.47E+00 5.86E-01 0.59558 1.0189 0.442552 182 3.54E+00 7.55E-01 1.73E+00 1.46E+00 6.03E-01 0.56849 1.33 0.419313 183 3.12E+00 7.21 E-01 1.85E+00 1.44E+00 5.89E-01 0.49411 0.51373 0.421384 184 2.53E+00 8.42E-01 1.90E+00 2.13E+00 5.91 E-01 0.51324 1.4335 0.431297 185 2.54E+00 4.42E-01 1.54E+00 3.26E+00 4.44 E-01 0.59723 0.67187 0.458895 186 3.18E+00 8.55E-01 1.95E+00 2.57E+00 5.15E-01 0.54302 2.1136 0.426181 187 3.50E+00 8.63E-01 1.46E+00 2.68E+00 4.47E-01 0.52704 1.2695 0.446951 188 3.42E+00 6.79E-01 1.65E+00 3.30E+00 4.75E-01 0.52092 1.5811 0.433746 189 2.59E+00 7.85E-01 1.88E+00 3.10E+00 5.62E-01 0.54244 1.1852 0.43533 190 2.55E+00 8.06E-01 1.63E+00 2.69E+00 5.30E-01 0.5924 1.3927 0.427834 191 2.46E+00 4.89E-01 1.58E+00 2.65E+00 5.88E-01 0.4839 0.48363 0.457684 192 3.20E+00 9.03E-01 1.66E+00 2.16E+00 5.51 E-01 0.52502 1.7599 0.426076 193 2.31 E+00 1.24E+00 9.32E-01 1.57E+00 4.85E-01 0.60265 0.64703 0.413521 194 2.50E+00 1.07E+00 7.92E-01 8.23E-01 5.02E-01 0.59094 1.5265 0.411963 195 3.54E+00 1.07E+00 5.46E-01 7.99E-01 5.20E-01 0.49065 1.2816 0.408001 196 2.54E+00 1.27E+00 8.95E-01 1.57E+00 4.53E-01 0.48491 2.0763 0.398003 197 2.39E+00 1.24E+00 6.41 E-01 1.05E+00 5.54E-01 0.56825 0.87991 0.415275 198 2.79E+00 9.43E-01 6.43E-01 1.38E+00 5.84E-01 0.55917 2.0839 0.435072 199 3.33E+00 1.16E+00 7.18E-01 1.55E+00 5.38E-01 0.52805 1.0889 0.416954 200 3.20E+00 1.20E+00 8.39E-01 1.18E+00 5.59E-01 0.53097 1.4798 0.404981 201 3.42E+00 1.07E+00 9.12E-01 2.68E+00 4.93E-01 0.56794 0.68363 0.420456 202 3.60E+00 1.19E+00 5.59E-01 2.23E+00 5.16E-01 0.60015 1.319 0.434806 203 3.14E+00 1.34E+00 8.70E-01 2.41 E+00 4.59E-01 0.4833 0.73774 0.426301 204 2.81 E+00 1.24E+00 8.28E-01 2.75E+00 4.75E-01 0.48392 1.745 0.419877 205 3.14E+00 1.06E+00 7.52E-01 3.07E+00 5.34E-01 0.53751 0.81182 0.424203 206 3.57E+00 1.45E+00 6.42E-01 3.00E+00 5.86E-01 0.58711 1.63 0.440407 207 2.46E+00 1.25E+00 4.76E-01 2.40E+00 5.31 E-01 0.53082 0.74424 0.444536 208 3.08E+00 1.27E+00 6.62E-01 3.45E+00 5.49E-01 0.48761 1.3313 0.448237 209 2.48E+00 1.39E+00 1.27E+00 2.03E+00 4.87E-01 0.58778 0.71474 0.43632 210 3.30E+00 1.39E+00 1.18E+00 2.04E+00 4.54E-01 0.5512 1.3542 0.42931 211 3.03E+00 1.42E+00 1.21 E+00 1.77E+00 4.79E-01 0.51041 1.1314 0.427153 212 3.24E+00 1.03E+00 1.30E+00 1.46E+00 4.95E-01 0.50112 2.0457 0.435606 213 2.22E+00 1.03E+00 9.76E-01 1.87E+00 5.27E-01 0.59202 0.88775 0.412866 214 2.98E+00 1.29E+00 1.13E+00 2.09E+00 5.52E-01 0.55953 1.7454 0.429438 215 2.82E+00 1.40E+00 1.24E+00 1.41 E+00 5.54E-01 0.52234 0.88891 0.432143 216 2.98E+00 1.29E+00 1.11E+00 1.91 E+00 5.88E-01 0.50401 1.5685 0.420966 217 3.63E+00 1.03E+00 1.04E+00 2.89E+00 4.67E-01 0.58539 1.0007 0.425778 218 2.90E+00 1.02E+00 1.28E+00 2.96E+00 4.68E-01 0.54482 1.3446 0.457223 219 3.18E+00 1.29E+00 9.62E-01 2.28E+00 4.44E-01 0.50248 0.76738 0.416976 - 183 -P A R A M E T R I C STUDY D A T A B A S E - C O N T 220 2.37E+00 1.15E+00 1.19E+00 2.62E+00 4.78E-01 0.48345 1.5294 0.450642 221 2.29E+00 1.44E+00 1.17E+00 3.23E+00 5.67E-01 0.5754 0.88626 0.43952 222 2.75E+00 1.33E+00 1.03E+00 2.51 E+00 5.90E-01 . 0.54791 1.5174 0.417373 223 2.65E+00 1.25E+00 1.40E+00 3.52E+00 5.78E-01 0.50948 1.2723 0.439908 224 3.06E+00 1.43E+00 1.16E+00 3.52E+00 5.88E-01 0.5252 1.6575 0.424101 225 2.73E+00 1.18E+00 1.73E+00 8.54E-01 4.78E-01 0.58996 0.4784 0.447838 226 2.73E+00 9.50E-01 1.91 E+00 9.69E-01 5.04E-01 0.58109 2.1329 0.430186 227 3.59E+00 1.45E+00 1.62E+00 8.40E-01 4.61 E-01 0.53162 1.2456 0.433739 228 2.60E+00 1.08E+00 1.61 E+00 1.14E+00 5.08E-01 0.49506 2.0862 0.432054 229 2.94E+00 1.34E+00 1.52E+00 1.75E+00 5.26E-01 0.53679 0.70842 0.428688 230 2.39E+00 1.00E+00 1.81 E+00 7.94E-01 5.85E-01 0.57364 1.8573 0.431993 231 2.27E+00 1.15E+00 1.52E+00 7.97E-01 5.99E-01 0.50093 0.73284 0.437848 232 3.16E+00 9.87E-01 1.79E+00 8.51 E-01 5.56E-01 0.46818 2.0859 0.428163 233 2.26E+00 1.41 E+00 1.59E+00 2.53E+00 4.54E-01 0.56151 0.60411 0.444669 234 3.04E+00 1.44E+00 1.79E+00 2.44E+00 4.56E-01 0.58223 1.4796 0.431115 235 2.89E+00 9.44E-01 1.89E+00 3.54E+00 4.59E-01 0.50583 0.84532 0.424867 236 2.34E+00 1.19E+00 1.52E+00 2.68E+00 4.41 E-01 0.48773 2.0915 0.45078 237 3.07E+00 1.07E+00 1.56E+00 3.43E+00 5.58E-01 0.57308 1.0514 0.445471 238 2.57E+00 1.06E+00 1.56E+00 2.28E+00 5.71 E-01 0.54386 1.9209 0.454355 239 3.13E+00 1.12E+00 1.61 E+00 3.17E+00 5.64E-01 0.49738 0.93562 0.440555 240 3.13E+00 1.36E+00 1.54E+00 3.08E+00 5.48E-01 0.53192 1.5236 0.434505 241 2.61 E+00 1.65E+00 8.68E-01 1.64E+00 5.18E-01 0.59865 1.1673 0.416943 242 2.75E+00 1.84E+00 5.52E-01 1.54E+00 4.43E-01 0.5896 2.1053 0.405807 243 3.45E+00 1.82E+00 6.86E-01 1.64E+00 4.51 E-01 0.52475 1.0088 0.424847 244 3.21 E+00 1.65E+00 4.60E-01 2.01 E+00 4.97E-01 0.5239 1.8068 0.400069 245 2.58E+00 1.57E+00 4.67E-01 1.39E+00 5.98E-01 0.56677 1.1238 0.41304 246 3.57E+00 1.78E+00 6.36E-01 1.59E+00 5.87E-01 0.57018 1.8692 0.411656 247 3.18E+00 1.51 E+00 7.28E-01 1.46E+00 5.72E-01 0.51655 1.2351 0.434992 248 2.56E+00 1.58E+00 6.17E-01 2.00E+00 5.97E-01 0.4979 2.0121 0.436794 249 2.71 E+00 1.77E+00 7.16E-01 3.33E+00 5.12E-01 0.55457 0.75283 0.437015 250 3.27E+00 1.63E+00 6.54E-01 2.97E+00 4.76E-01 0.57757 1.5617 0.427888 251 2.86E+00 1.46E+00 4.71 E-01 2.60E+00 4.45E-01 0.50435 0.57079 0.429107 252 3.57E+00 1.74E+00 8.76E-01 2.35E+00 5.09 E-01 0.4775 1.5974 0.430531 253 3.31 E+00 1.73E+00 6.20E-01 2.63E+00 5.67E-01 0.58516 1.0096 0.422679 254 2.95E+00 1.59E+00 4.24E-01 2.98E+00 5.62E-01 0.55643 1.8245 0.400465 255 3.05E+00 1.46E+00 8.75E-01 2.26E+00 5.62E-01 0.51381 0.7218 0.435069 256 2.57E+00 1.83E+00 5.30E-01 3.01 E+00 5.84E-01 0.52751 1.9003 0.404193 257 2.76E+00 1.46E+00 1.26E+00 1.65E+00 4.52E-01 0.59296 1.0064 0.430143 258 2.93E+00 1.56E+00 1.36E+00 7.84E-01 4.88E-01 0.58091 1.9642 0.420023 259 3.27E+00 1.69E+00 1.03E+00 1.90E+00 4.59E-01 0.53263 0.55178 0.426781 260 2.89E+00 1.91 E+00 1.03E+00 2.03E+00 5.11 E-01 0.46583 1.4172 0.420479 261 3.62E+00 1.83E+00 1.27E+00 9.54E-01 5.22E-01 0.5486 1.0737 0.416423 262 2.56E+00 1.95E+00 1.26E+00 8.31 E-01 5.72E-01 0.58695 2.0956 0.409474 263 2.86E+00 1.63E+00 9.54E-01 8.09E-01 5.91 E-01 0.47675 0.69232 0.42804 264 2.57E+00 1.47E+00 9.81 E-01 8.62E-01 5.72E-01 0.53216 1.8787 0.402322 - 184-P A R A M E T R I C STUDY D A T A B A S E - C O N T 265 3.40E+00 1.93E+00 9.85E-01 2.44E+00 4.67E-01 0.59509 1.1806 0.421981 266 2.23E+00 1.67E+00 1.20E+00 2.45E+00 4.85E-01 0.57829 1.5538 0.433591 267 2.91 E+00 1.62E+00 1.23E+00 2.88E+00 5.12E-01 0.49436 0.92293 0.435648 268 2.44E+00 1.49E+00 9.49E-01 2.79E+00 4.79E-01 0.48081 1.5611 0.437018 269 3.56E+00 1.94E+00 1.09E+00 2.34E+00 5.33E-01 0.56013 0.9453 0.423276 270 3.39E+00 1.86E+00 1.17E+00 2.76E+00 5.65E-01 0.58397 2.1338 0.421556 271 2.70E+00 1.59E+00 1.21 E+00 3.27E+00 6.02E-01 0.48507 0.7796 0.432424 272 3.56E+00 1.60E+00 1.09E+00 2.29E+00 5.98E-01 0.48333 2.1407 0.426579 273 2.76E+00 1.67E+00 1.53E+00 8.64E-01 4.41 E-01 0.57649 0.70991 0.431918 274 2.59E+00 1.95E+00 1.68E+00 2.14E+00 5.03E-01 0.54999 1.8937 0.397099 275 2.56E+00 1.57E+00 1.57E+00 1.14E+00 4.81 E-01 0.49637 1.1738 0.426126 276 2.50E+00 1.79E+00 1.51 E+00 1.95E+00 5.16E-01 0.47267 2.1506 0.407501 277 2.32E+00 1.69E+00 1.55E+00 2.08E+00 5.89E-01 0.57361 0.61371 0.415318 278 2.51 E+00 1.79E+00 1.51 E+00 1.76E+00 5.37E-01 0.55673 1.6031 0.405406 279 2.29E+00 1.54E+00 1.78E+00 1.01 E+00 5.45E-01 0.52673 0.57741 0.425414 280 3.49E+00 1.52E+00 1.88E+00 1.81 E+00 5.97E-01 0.47894 1.656 0.39944 281 2.74E+00 1.73E+00 1.91 E+00 2.87E+00 5.21 E-01 0.58141 0.51838 0.417246 282 2.99E+00 1.79E+00 1.53E+00 3.39E+00 5.14E-01 0.57035 1.9669 0.41408 283 2.78E+00 1.64E+00 1.78E+00 2.95E+00 4.91 E-01 0.49231 1.3029 0.422582 284 3.06E+00 1.77E+00 1.67E+00 3.47E+00 5.00E-01 0.4686 1.3504 0.415034 285 3.45E+00 1.84E+00 1.83E+00 3.14E+00 5.57E-01 0.58416 1.1022 0.40403 286 2.27E+00 1.68E+00 1.62E+00 3.51 E+00 5.86E-01 0.53726 1.8724 0.419647 287 2.85E+00 1.80E+00 1.49E+00 2.63E+00 5.45E-01 0.48812 0.842 0.422119 288 3.33E+00 1.78E+00 1.91 E+00 2.88E+00 5.25E-01 0.49638 2.093 0.402732 289 1.69 0.91 0.91 1.65 7.00E+00 1.3 1 0.41961 290 1.69 0.91 0.91 1.65 8.00E-01 1.3 1 0.466309 291 1.69 0.91 0.91 1.65 1.00E+00 1.3 1 0.47334 292 1.69 0.91 0.91 1.65 1.10E+00 1.3 1 0.477007 293 1.69 0.91 0.91 1.65 1.20E+00 1.3 1 0.470191 294 1.69 0.91 0.91 1.65 1.30E+00 1.3 1 0.493046 295 1.69 0.91 0.91 1.65 1.40E+00 1.3 1 0.491009 296 1.69 0.91 0.91 1.65 1.50E+00 1.3 1 0.495697 297 1.69 0.91 0.91 1.65 1.60E+00 1.3 1 0.499477 298 1.69 0.91 0.91 1.65 1.70E+00 1.3 1 0.494875 299 1.69 0.91 0.91 1.65 1.80E+00 1.3 1 0.489101 300 1.69 0.91 0.91 1.65 1.90E+00 1.3 1 0.489883 301 1.69 0.91 0.91 1.65 2.00E+00 1.3 1 0.488902 302 1.69 0.91 0.91 1.65 9.50E-01 0.7 1 0.462046 303 1.69 0.91 0.91 1.65 9.50E-01 0.8 1 0.466089 304 1.69 0.91 0.91 1.65 9.50E-01 0.9 1 0.467335 305 1.69 0.91 0.91 1.65 9.50E-01 1 1 0.466989 306 1.69 0.91 0.91 1.65 9.50E-01 1.2 1 0.471731 307 1.69 0.91 0.91 1.65 9.50E-01 1.4 1 0.474863 - 185 -P A R A M E T R I C STUDY D A T A B A S E - C O N T 308 1.69 0.91 0.91 1.65 9.50E-01 1.5 1 0.475864 309 1.69 0.91 0.91 1.65 9.50E-01 1.6 1 0.473643 310 1.69 0.91 0.91 1.65 9.50E-01 1.7 1 0.476874 311 1.69 0.91 0.91 1.65 9.50E-01 1.8 1 0.477055 312 1.69 0.91 0.91 1.65 9.50E-01 1.9 1 0.478241 313 1.69 0.91 0.91 1.65 9.50E-01 2 1 0.480195 314 1.69 0.91 0.91 1.65 9.50E-01 2.1 1 0.482055 315 1.69 0.91 0.91 1.65 9.50E-01 2.2 1 0.484807 316 1.69 0.91 0.91 1.65 9.50E-01 2.3 1 0.487568 317 1.69 0.91 0.91 1.65 9.50E-01 2.4 1 0.489085 318 1.69 0.91 0.91 1.65 9.50E-01 2.5 1 0.491019 319 1.69 0.91 0.91 1.65 9.50E-01 2.6 1 0.494238 320 1.69 0.91 0.91 1.65 9.50E-01 2.7 1 0.490918 321 1.69 0.91 0.91 1.65 9.50E-01 2.8 1 0.492723 - 186-APPENDIX B. RELIABILITY ANALYSIS DATABASE - SIDE STRUCTURE THICKNESS - PROBABILITY OF SERIOUS INJURY DATABASE Exp. Number B- Pillar thickness( mm) Inner Door-up thickness( mm) Inner Door-low thickness( mm) Door Rail thickness( mm) Rocker panel thickness( mm) Floor Pan thickness( mm) Roof thickness (mm) injury probability (Pinj>0.03) (AIS>3) Original 1.69 0.91 0.91 1.65 0.95 1.3 1 0.2919 1 2.00640 0.72163 0.83371 1.54780 0.45268 0.54630 0.98871 0.27180 2 1.27390 0.66350 0.80049 1.03410 0.48298 0.57745 1.80000 0.27840 3 0.96655 0.69927 0.46983 1.73530 0.46841 0.48005 0.96095 0.28290 4 1.61550 0.52525 0.91843 2.15880 0.46419 0.48316 1.97490 0.28420 5 1.04320 0.93497 0.61073 1.05430 0.59811 0.55137 0.52392 0.27930 6 1.78180 0.70606 0.44025 1.08610 0.52739 0.58123 1.59070 0.27080 7 0.97204 0.82811 0.71241 1.14550 0.56624 0.47780 1.26150 0.28240 8 1.38950 0.44841 0.67459 1.45560 0.56608 0.47869 2.05630 0.29600 9 1.04400 0.49197 0.51378 3.34290 0.48026 0.58453 0.69343 0.30100 10 1.05320 0.77485 0.64333 2.71650 0.48275 0.56871 1.61200 0.28800 11 1.73350 0.81372 0.72955 3.17200 0.51903 0.51722 1.12030 0.28450 12 1.52370 0.48300 0.44867 2.49990 0.52215 0.47767 2.01890 0.29390 13 1.90390 0.49734 0.84460 3.03180 0.54968 0.57508 0.79701 0.29260 14 1.78680 0.76402 0.77184 2.28950 0.55643 0.55493 1.63330 0.28340 15 0.83233 0.80738 0.52653 2.80320 0.59836 0.50052 0.82438 0.30320 16 1.15250 0.78654 0.90536 2.52260 0.52878 0.52340 1.44730 0.29110 17 1.69600 0.60674 1.14700 1.10530 0.50118 0.58547 1.20140 0.27990 18 2.09300 0.75355 1.25790 2.11110 0.45080 0.60022 1.46420 0.27400 19 1.76670 0.66669 1.27840 1.78210 0.46914 0.49735 0.47806 0.27860 20 1.34040 0.51843 1.25340 0.82051 0.49354 0.49676 1.61660 0.28240 21 1.34990 0.47512 0.96269 1.31960 0.59514 0.54666 1.14640 0.29560 22 1.50890 0.82170 0.99042 1.65580 0.59189 0.57517 1.90890 0.28510 23 1.65070 0.55256 0.96829 0.91013 0.52527 0.51310 0.83604 0.27950 24 2.16430 0.85116 1.10070 1.34020 0.56797 0.48673 2.13810 0.27270 25 1.93040 0.92868 1.29610 2.63140 0.49697 0.59665 0.78229 0.27480 26 1.33350 0.89346 0.96209 2.22620 0.50671 0.57333 1.56760 0.28120 27 2.13580 0.89749 0.95784 3.45250 0.45397 0:49047 0.70973 0.27710 28 0.99039 0.55063 1.03910 3.50720 0.51969 0.52519 1.32310 0.30680 29 2.19560 0.82257 1.34060 3.16480 0.53881 0.55150 0.99719 0.27630 30 0.89079 0.81753 1.42410 3.25620 0.53291 0.55324 1.42240 0.29560 31 1.23880 0.78345 1.12070 3.32340 0.58281 0.46611 0.56049 0.29720 32 2.12180 0.72576 0.99840 2.73990 0.55326 0.49511 2.05980 0.28560 33 1.25570 0.92872 1.93770 1.94360 0.47901 0.58876 0.50228 0.27370 34 1.32400 0.86372 1.83980 1.93680 0.45383 0.57597 2.10130 0.27500 35 0.89292 0.43373 1.67810 1.45630 0.51644 0.52544 0.76428 0.29440 36 0.85827 0.48094 1.56050 1.17200 0.50340 0.46474 1.33490 0.29160 37 1.15190 0.56134 1.60680 1.35440 0.58233 0.55851 0.63694 0.28890 38 1.38960 0.78234 1.65250 0.87238 0.59254 0.56792 1.53060 0.27740 39 2.19070 0.70442 1.67320 1.72400 0.53565 0.47730 0.78089 0.26930 - 187-RELIABILITY ANALYSIS D A T A B A S E - C O N T 40 2.13860 0.58413 1.63260 1.21550 0.57838 0.51640 1.53820 0.27690 41 1.32420 0.84769 1.74310 3.54120 0.50252 0.55910 1.30600 0.28130 42 1.14020 0.69428 1.92980 3.37020 0.50147 0.55730 1.53570 0.28580 43 1.70910 0.66527 1.45580 3.31890 0.50947 0.49313 1.23520 0.28540 44 1.09620 0.47329 1.77140 3.40590 0.49612 0.53127 1.39730 0.29660 45 1.21300 0.86493 1.69300 2.30060 0.54660 0.54085 1.04340 0.28090 46 0.82083 0.92746 1.79690 2.46620 0.53750 0.59244 1.51830 0.28470 47 0.87980 0.51200 1.67730 2.31700 0.57463 0.47368 0.77525 0.29760 48 1.41120 0.58639 1.94520 3.47380 0.59694 0.53063 2.14500 0.29760 49 1.53410 1.06320 0.82013 1.33080 0.47743 0.60002 0.67509 0.27070 50 0.86952 0.99214 0.48964 1.86160 0.48431 0.59429 2.13890 0.27340 51 1.80090 1.15810 0.52749 1.20610 0.44495 0.50216 0.70241 0.26160 52 1.64650 0.97826 0.45988 1.71570 0.47578 0.50301 1.98000 0.26240 53 1.90320 1.22120 0.57512 1.83420 0.59653 0.56185 0.75489 0.26650 54 1.77280 0.96372 0.47723 0.96022 0.59313 0.53472 1.35810 0.26550 55 1.45280 1.08250 0.68536 1.45040 0.54892 0.49498 0.78608 0.27170 56 1.16890 1.03100 0.78101 1.48230 0.58613 0.52679 1.74560 0.27780 57 1.06160 1.20090 0.60861 2.87740 0.50727 0.58456 0.69738 0.28140 58 1.09830 1.36320 0.43858 3.10230 0.50337 0.56642 1.53870 0.28170 59 1.99520 1.26470 0.53940 2.97420 0.47732 0.50357 0.94880 0.26940 60 1.54970 0.96263 0.67888 2.88290 0.49024 0.46575 1.64880 0.27870 . 61 1.66530 0.97848 0.91309 3.52800 0.54421 0.54768 0.76996 0.28380 62 2.16580 1.21510 0.71628 2.89030 0.60192 0.59092 1.51260 0.27050 63 1.96950 1.35200 0.63336 2.37020 0.53839 0.47507 0.68649 0.26890 64 2.19700 1.22530 0.67652 3.38740 0.58866 0.46475 1.80200 0.27540 65 1.60540 1.03890 0.95643 1.36180 0.45635 0.58313 0.49952 0.27260 66 1.68390 1.14110 1.31590 1.93890 0.47037 0.56146 1.60950 0.26780 67 1.79750 0.96519 1.43190 1.16370 0.52147 0.50733 0.76648 0.26810 68 1.82350 1.00970 1.10190 1.66230 0.51641 0.47888 1.62220 0.26950 69 0.96245 1.14840 1.12680 1.46270 0.57366 0.58215 0.57200 0.27250 70 0.80919 1.42510 1.23160 1.97560 0.52228 0.58949 1.46830 0.27210 71 1.25510 1.08090 1.31450 1.99490 0.57314 0.47581 0.75943 0.27770 72 1.64480 1.17590 1.13880 0.98350 0.55149 0.48084 1.57520 0.26200 73 0.84763 1.15770 1.04080 2.62050 0.45111 0.54906 0.93526 0.28260 74 1.24150 1.39820 1.21170 2.30980 0.50497 0.55021 1.72450 0.26870 75 0.88686 0.93942 1.14280 2.65430 0.47997 0.48549 1.17320 0.28840 76 1.91440 1.03600 0.96604 2.98460 0.44121 0.48507 1.45220 0.27190 77 1.80950 1.33710 1.06050 2.73440 0.54404 0.54009 0.49336 0.27210 78 0.81647 1.35740 1.31410 2.19320 0.56183 0.55355 2.07310 0.27590 79 2.18040 1.30980 1.23660 3.48730 0.55607 0.46838 1.20900 0.27010 80 1.97560 0.97186 1.40930 3.42080 0.53025 0.50166 2.04770 0.27780 81 0.91232 1.28090 1.57120 1.28750 0.44734 0.59608 1.24440 0.27020 82 1.63020 1.06030 1.51720 1.62320 0.47913 0.58339 1.72710 0.26870 83 1.32550 1.35720 1.71970 1.84270 0.51083 0.51906 0.90895 0.26580 84 1.14820 1.34100 1.68220 1.62770 0.48928 0.53329 1.89090 0.26430 85 0.87710 1.03540 1.75040 1.85270 0.55185 0.59105 1.12100 0.27840 - 188-RELIABILITY ANALYSIS DATABASE - C O N T 86 0.87854 1.14030 1.86210 1.10960 0.53896 0.60193 1.53510 0.27060 87 1.37360 0.97114 1.81150 1.63470 0.55098 0.49758 1.24930 0.27060 88 2.06140 0.93660 1.94590 1.88510 0.52801 0.51933 1.81610 0.26460 89 1.82640 1.43760 1.60930 2.25580 0.48780 0.54460 1.20530 0.26200 90 1.72620 0.96785 1.67800 2.32630 0.49564 0.53598 1.94390 0.25100 91 1.91240 1.43790 1.84620 3.32490 0.44246 0.49231 0.80754 0.26390 92 0.89484 1.34900 1.52340 3.02510 0.47288 0.47965 1.41670 0.27720 93 1.87770 1.16510 1.85950 3.24850 0.55913 0.55417 0.58946 0.26230 94 1.53520 1.35530 1.54320 3.19340 0.58476 0.53686 1.98570 0.26940 95 1.07090 1.44780 1.54740 2.39310 0.54272 0.53275 1.15130 0.27010 96 1.84770 1.01140 1.54700 3.30510 0.53715 0.48377 1.85880 0.27610 97 1.40810 1.84180 0.77150 1.00210 0.51312 0.54728 1.17440 0.25150 98 1.90840 1.52910 0.86784 1.86140 0.51363 0.58267 1.92990 0.25500 99 1.82080 1.82950 0.90253 2.04630 0.44756 0.51815 0.98324 0.26370 100 1.73400 1.68440 0.82479 1.54190 0.46332 0.48894 1.63580 0.25310 101 1.52780 1.77920 0.52190 1.25010 0.54952 0.54115 0.74754 0.25420 102 2.16230 1.84280 0.90446 0.90446 0.58576 0.58045 2.09770 0.24070 103 1.68460 1.64560 0.75142 1.29480 0.56282 0.49282 0.48650 0.26010 104 2.01850 1.93290 0.88422 2.00570 0.54069 0.50835 1.42850 0.25040 105 1.58260 1.49050 0.66347 2.26010 0.45699 0.56578 0.85822 0.26650 106 2.11740 1.65450 0.43221 2.84050 0.50221 0.59402 1.32770 0.25540 107 2.09420 1.60460 0.72105 3.19530 0.45805 0.49316 0.97638 0.26790 108 1.33510 1.88830 0.77294 2.67810 0.44698 0.52652 2.11850 0.25450 109 1.93450 1.55780 0.44280 2.59160 0.56255 0.58959 1.07090 0.26000 110 1.52960 1.79090 0.58584 3.40300 0.56095 0.54465 1.95800 0.26240 111 0.79925 1.52680 0.84816 2.99240 0.53084 0.51504 1.01890 0.27980 112 1.51920 1.53990 0.65204 2.25890 0.55408 0.48362 1.97490 0.26200 113 1.12930 1.63270 1.44300 1.73950 0.46318 0.57849 1.04330 0.26640 114 2.05550 1.53630 0.94845 1.60690 0.47217 0.54228 1.99260 0.25250 115 2.14150 1.66520 1.44390 0.95886 0.51407 0.52297 1.16620 0.25280 116 1.62130 1.46780 1.42790 1.34520 0.50938 0.51178 1.57480 0.25790 117 0.84232 1.66090 1.00110 0.81004 0.52481 0.54009 0.60316 0.26470 118 1.92960 1.61730 1.32830 1.63970 0.59193 0.56773 1.60210 0.25390 119 1.45080 1.79740 1.39210 1.06120 0.54246 0.49254 0.72283 0.25700 120 1.50660 1.59100 0.99896 1.09270 0.54535 0.49187 1.34690 0.25510 121 1.99710 1.80370 1.20330 3.40440 0.49338 0.54467 0.67759 0.26780 122 2.10270 1.58360 1.07990 2.59330 0.46710 0.59388 2.09060 0.25590 123 1.23330 1.73810 1.22650 2.59930 0.50383 0.47729 1.22600 0.26860 124 0.93547 1.71520 1.02580 2.67400 0.49118 0.50631 1.98780 0.26650 125 1.16310 1.63530 1.34940 2.93760 0.52797 0.57473 1.16470 0.26880 126 1.16540 1.51980 1.16150 2.69880 0.55005 0.56274 1.66070 0.27000 127 1.12470 1.80020 1.43710 3.12130 0.54844 0.48241 0.90106 0.27080 128 1.44360 1.50760 1.21500 2.47540 0.55812 0.49050 1.94060 0.26680 129 2.05160 1.75570 1.76490 1.19280 0.46300 0.54262 1.13620 0.25530 130 2.08840 1.61280 1.81380 1.30550 0.51389 0.54039 1.60420 0.25000 - 1 8 9 -RELIABILITY ANALYSIS DATABASE - C O N T 131 2.13880 1.72940 1.83780 1.63240 0.51263 0.48494 0.69070 0.25430 132 1.20490 1.62930 1.69100 1.68640 0.49715 0.51917 1.33680 0.26010 133 1.22310 1.72940 1.72040 1.11010 0.57867 0.53718 0.84251 0.25280 134 0.96445 1.82070 1.56490 1.91740 0.59523 0.53626 1.89460 0.25630 135 1.46360 1.76610 1.67570 0.87817 0.56141 0.52175 1.04740 0.24960 136 1.62090 1.60280 1.72650 1.51890 0.55050 0.51767 1.52160 0.25300 137 1.39080 1.59440 1.90650 3.26750 0.49881 0.59448 0.76691 0.26100 138 2.20690 1.83300 1.72690 2.86390 0.45139 0.58734 1.50140 0.25490 139 1.19520 1.79620 1.69830 3.29810 0.48140 0.48887 0.79253 0.27020 140 1.53570 1.78580 1.56110 2.70840 0.47100 0.48625 1.95740 0.25850 141 1.43590 1.87600 1.91230 3.44220 0.55159 0.54080 0.57974 0.25660 142 1.82350 1.51650 1.57920 2.62410 0.57810 0.59383 1.84090 0.25900 143 1.54990 1.73230 1.70720 2.21750 0.57851 0.47866 0.89397 0.25620 144 2.10790 1.95160 1.73280 2.84650 0.59934 0.51493 1.37290 0.24690 145 2.23380 0.63313 0.59324 1.18450 0.50613 0.59558 0.84669 0.27150 146 3.21800 0.49896 0.71049 0.80370 0.44953 0.57630 1.63550 0.26470 147 3.37140 0.62433 0.45435 1.92220 0.47459 0.53230 0.80320 0.26450 148 2.52010 0.77156 0.49867 1.83070 0.46065 0.49322 1.57390 0.25730 149 3.11970 0.93101 0.54378 1.45310 0.58927 0.56718 1.04590 0.26180 150 2.85180 0.67370 0.89094 0.86579 0.53887 0.56245 1.88340 0.26940 151 3.32900 0.71759 0.63824 1.24570 0.54456 0.49504 1.18990 0.26300 152 2.41850 0.49209 0.68849 2.00740 0.57668 0.53288 1.34230 0.28410 153 2.38120 0.60510 0.46161 2.51150 0.50774 0.55698 0.97217 0.27630 154 3.07730 0.53619 0.87574 2.58920 0.51302 0.56474 1.60320 0.27720 155 2.33890 0.62752 0.73279 2.20430 0.50112 0.52261 0.71450 0.27640 156 2.68830 0.59265 0.93284 3.53340 0.51792 0.47644 1.65930 0.28230 157 2.31540 0.78334 0.71817 2.33530 0.56774 0.58698 0.77478 0.27650 158 2.32970 0.51647 0.60904 2.90310 0.59688 0.55304 1.36370 0.29170 159 3.46320 0.76749 0.50402 3.41210 0.59958 0.48936 0.67767 0.27360 160 3.31830 0.61241 0.55423 2.44950 0.59770 0.48419 2.07460 0.28000 161 2.24560 0.92929 1.30650 1.39060 0.45472 0.53481 0.79008 0.26780 162 2.85000 0.52833 1.04990 1.44080 0.51311 0.53560 2.02630 0.27620 163 2.67760 0.58518 1.43540 2.15670 0.45734 0.51750 0.96100 0.27150 164 2.81520 0.54555 1.26570 1.75140 0.47645 0.51554 1.84880 0.27340 165 2.88670 0.46676 1.07480 1.95910 0.57758 0.57616 0.64151 0.27830 166 3.26510 0.69512 1.22260 1.57020 0.55583 0.58290 1.34160 0.27080 167 3.04000 0.48956 1.22890 1.12760 0.55454 0.52989 1.09780 0.27260 168 3.63340 0.53564 1.12660 1.11790 0.53467 0.48847 1.74980 0.26990 169 2.59750 0.89710 1.00210 2.78970 0.48417 0.59432 1.30440 0.27010 170 3.34150 0.82980 1.27080 3.24450 0.50363 0.55936 2.02870 0.27020 171 2.80280 0.84171 1.03180 3.23630 0.51662 0.48887 0.87504 0.27330 172 2.37240 0.57388 1.32820 3.47180 0.50128 0.46468 1.53770 0.28170 173 3.19680 0.78222 0.94012 3.19590 0.55202 0.56715 1.15500 0.27250 174 2.52520 0.91226 1.32670 3.53230 0.52452 0.58122 1.86110 0.27340 175 2.28300 0.63715 0.97120 3.07050 0.54511 0.47670 0.78399 0.28320 - 190-RELIABILITY ANALYSIS DATABASE - C O N T 176 3.48640 0.90654 1.26340 2.63850 0.54616 0.48605 1.69510 0.26690 177 3.02490 0.57783 1.80730 1.43260 0.48634 0.59997 0.69013 0.26740 178 2.44090 0.70567 1.89740 1.16770 0.50902 0.57317 1.36300 0.26690 179 2.88810 0.55852 1.62080 1.65110 0.50367 0.46975 0.94483 0.26690 180 2.40690 0.77978 1.93930 1.43250 0.46056 0.52364 1.90230 0.26410 181 3.49560 0.46049 1.63380 1.47340 0.58552 0.59558 1.01890 0.27180 182 3.53500 0.75455 1.73230 1.46130 0.60327 0.56849 1.33000 0.25180 183 3.11780 0.72055 1.85080 1.43780 0.58861 0.49411 0.51373 0.25510 184 2.53320 0.84193 1.90420 2.12740 0.59098 0.51324 1.43350 0.26340 185 2.53670 0.44210 1.54480 3.26080 0.44354 0.59723 0.67187 0.27540 186 3.17840 0.85537 1.95140 2.56850 0.51543 0.54302 2.11360 0.26260 187 3.50380 0.86261 1.45610 2.67500 0.44662 0.52704 1.26950 0.26410 188 3.42100 0.67871 1.64560 3.29760 0.47513 0.52092 1.58110 0.26580 189 2.59380 0.78472 1.87790 3.09900 0.56190 0.54244 1.18520 0.26510 190 2.55240 0.80636 1.62890 2.68840 0.52985 0.59240 1.39270 0.27020 191 2.45520 0.48917 1.57780 2.64590 0.58784 0.48390 0.48363 0.27630 192 3.19940 0.90295 1.65610 2.16370 0.55126 0.52502 1.75990 0.26400 193 2.30700 1.24170 0.93184 1.57490 0.48471 0.60265 0.64703 0.26470 194 2.49860 1.06520 0.79192 0.82255 0.50248 0.59094 1.52650 0.25720 195 3.54170 1.07310 0.54602 0.79893 0.51992 0.49065 1.28160 0.25130 196 2.53810 1.27460 0.89524 1.56650 0.45272 0.48491 2.07630 0.25330 197 2.39420 1.24020 0.64129 1.05300 0.55411 0.56825 0.87991 0.25620 198 2.79430 0.94325 0.64314 1.37970 0.58442 0.55917 2.08390 0.26540 199 3.32710 1.15720 0.71844 1.55420 0.53802 0.52805 1.08890 0.25780 200 3.20350 1.19630 0.83941 1.17700 0.55865 0.53097 1.47980 0.25530 201 3.42130 1.06930 0.91190 2.68020 0.49327 0.56794 0.68363 0.26550 202 3.60340 1.19390 0.55864 2.23250 0.51559 0.60015 1.31900 0.25830 203 3.13830 1.33720 0.87009 2.41220 0.45924 0.48330 0.73774 0.26490 204 2.80890 1.23830 0.82781 2.74990 0.47508 0.48392 1.74500 0.26130 205 3.13750 1.06080 0.75233 3.07430 0.53362 0.53751 0.81182 0.26690 206 3.56920 1.44570 0.64184 3.00460 0.58558 0.58711 1.63000 0.25760 207 2.45590 1.24590 0.47627 2.40410 0.53051 0.53082 0.74424 0.26400 208 3.07830 1.27030 0.66217 3.44730 0.54883 0.48761 1.33130 0.26050 209 2.48030 1.39120 1.26930 2.02750 0.48653 0.58778 0.71474 0.26360 210 3.29670 1.38880 1.18090 2.03860 0.45400 0.55120 1.35420 0.26050 211 3.02800 1.42010 1.21150 1.77000 0.47908 0.51041 1.13140 0.25960 212 3.23560 1.03330 1.29600 1.46210 0.49460 0.50112 2.04570 0.26030 213 2.21940 1.03100 0.97599 1.87480 0.52651 0.59202 0.88775 0.26870 214 2.97640 1.29250 1.12510 2.09010 0.55165 0.55953 1.74540 0.25960 215 2.81900 1.39810 1.24190 1.41010 0.55362 0.52234 0.88891 0.25600 216 2.97910 1.29210 1.11370 1.91430 0.58770 0.50401 1.56850 0.25890 217 3.62830 1.03080 1.03760 2.88650 0.46729 0.58539 1.00070 0.26490 218 2.89830 1.02050 1.28310 2.96030 0.46809 0.54482 1.34460 0.26550 219 3.18120 1.29020 0.96242 2.28060 0.44401 0.50248 0.76738 0.26490 220 2.36500 1.14570 1.19400 2.62440 0.47775 0.48345 1.52940 0.26610 -191 -RELIABILITY ANALYSIS D A T A B A S E - C O N T 221 2.29250 1.44370 1.16510 3.22540 0.56653 0.57540 0.88626 0.26400 222 2.74980 1.32540 1.02890 2.50540 0.59020 0.54791 1.51740 0.26160 223 2.64670 1.24610 1.39920 3.51500 0.57758 0.50948 1.27230 0.26410 224 3.06340 1.43140 1.16450 3.51790 0.58831 0.52520 1.65750 0.26090 225 2.73070 1.17530 1.72800 0.85387 0.47833 0.58996 0.47840 0.26150 226 2.73170 0.94967 . 1.90940 0.96916 0.50367 0.58109 2.13290 0.26190 227 3.58600 1.44730 1.62250 0.83974 0.46137 0.53162 1.24560 0.25920 228 2.59560 1.08210 1.60550 1.13600 0.50790 0.49506 2.08620 0.25800 229 2.94110 1.33850 1.51500 1.74890 0.52626 0.53679 0.70842 0.25770 230 2.38790 1.00430 1.80980 0.79429 0.58461 0.57364 1.85730 0.26070 231 2.27330 1.14990 1.51560 0.79740 0.59902 0.50093 0.73284 0.25400 232 3.15590 0.98671 1.78680 0.85068 0.55589 0.46818 2.08590 0.25530 233 2.25970 1.41060 1.58530 2.52620 0.45399 0.56151 0.60411 0.26530 234 3.03850 1.43680 1.78990 2.43580 0.45560 0.58223 1.47960 0.25580 235 2.88670 0.94399 1.88750 3.54000 0.45862 0.50583 0.84532 0.25780 236 2.34450 1.18880 1.51850 2.68210 0.44134 0.48773 2.09150 0.26160 237 3.06960 1.07380 1.56270 3.42730 0.55754 0.57308 1.05140 0.26020 238 2.56880 1.05950 1.55600 2.27660 0.57099 0.54386 1.92090 0.26340 239 3.13280 1.11570 1.60990 3.17220 0.56351 0.49738 0.93562 0.25820 240 3.12810 1.35790 1.54000 3.07630 0.54842 0.53192 1.52360 0.25680 241 2.61250 1.65180 0.86754 1.64140 0.51837 0.59865 1.16730 0.25430 242 2.75120 1.84490 0.55249 1.53550 0.44319 0.58960 2.10530 0.24140 243 3.44930 1.81570 0.68586 1.63760 0.45118 0.52475 1.00880 0.26080 244 3.21120 1.64990 0.45995 2.01060 0.49748 0.52390 1.80680 0.24790 245 2.57630 1.56550 0.46653 1.39470 0.59779 0.56677 1.12380 0.24800 246 3.56520 1.78440 0.63594 1.59070 0.58717 0.57018 1.86920 0.24650 247 3.18430 1.50910 0.72770 1.45810 0.57247 0.51655 1.23510 0.25180 248 2.56370 1.58370 0.61665 2.00420 0.59674 0.49790 2.01210 0.25210 249 2.71410 1.76670 0.71604 3.32910 0.51195 0.55457 0.75283 0.26360 250 3.26520 1.62580 0.65378 2.97340 0.47640 0.57757 1.56170 0.25540 251 2.85920 1.46220 0.47110 2.60210 0.44466 0.50435 0.57079 0.26460 252 3.57210 1.74270 0.87610 2.34590 0.50873 0.47750 1.59740 0.25700 253 3.31280 1.73130 0.61994 2.62870 0.56665 0.58516 1.00960 0.25490 254 2.94570 1.58640 0.42407 2.97910 0.56224 0.55643 1.82450 0.25380 255 3.04860 1.46060 0.87516 2.26220 0.56204 0.51381 0.72180 0.25980 256 2.56560 1.82670 0.52988 3.00800 0.58393 0.52751 1.90030 0.25360 257 2.76220 1.45560 1.25710 1.64740 0.45231 0.59296 1.00640 0.26170 258 2.92580 1.56120 1.36270 0.78433 0.48755 0.58091 1.96420 0.25180 259 3.27220 1.69220 1.02930 1.89910 0.45896 0.53263 0.55178 0.26710 260 2.88850 1.91230 1.02580 2.03270 0.51070 0.46583 1.41720 0.25540 261 3.61660 1.83170 1.26600 0.95393 0.52219 0.54860 1.07370 0.25680 262 2.56070 1.94540 1.25820 0.83127 0.57171 0.58695 2.09560 0.24120 263 2.86200 1.62970 0.95421 0.80885 0.59118 0.47675 0.69232 0.24890 264 2.56550 1.47450 0.98104 0.86204 0.57151 0.53216 1.87870 0.24870 265 3.40180 1.92550 0.98503 2.43820 0.46684 0.59509 1.18060 0.26170 - 192-RELIABILITY ANALYSIS D A T A B A S E - C O N T 266 2 .22840 1.67200 1.20390 2 .45310 0 .48495 0 .57829 1.55380 0 .25740 267 2 .91110 1.61730 1.23370 2 .88400 0 .51184 0 .49436 0 .92293 0 .26180 268 2 .44230 1.48840 0 .94925 2 .79310 0 .47946 0.48081 1.56110 0 .26160 2 6 9 3 .55550 1.93950 1.08540 2 .33880 0 .53265 0 .56013 0 .94530 0 .25960 2 7 0 3 .38660 1.86200 1.16570 2 .75740 0 .56459 0 .58397 2 .13380 0 .25160 271 2 .70000 1.58500 1.20900 3 .27340 0 .60183 0 .48507 0 .77960 0 .26000 272 3 .55900 1.59960 1.08540 2 .29220 0 .59767 0 .48333 2 .14070 0 .25470 273 2 .75640 1.66860 1.52860 0 .86387 0.44121 0 .57649 0.70991 0 .26370 274 2 .59150 1.94740 1.68290 2 .13570 0 .50334 0 .54999 1.89370 0 .24910 275 2 .56040 1.56960 1.56760 1.13540 0 .48052 0 .49637 1.17380 0 .25480 276 2 .50230 1.78580 1.51460 1.94910 0 .51560 0 .47267 2 .15060 0 .24990 277 2 .31620 1.69200 1.55290 2 .08280 0 .58888 0.57361 0.61371 0 .25230 278 2 .51310 1.79100 1.51110 1.76470 0 .53729 0 .55673 1.60310 0 .25010 2 7 9 2 .28750 1.54270 1.77580 1.00570 0.54451 0 .52673 0.57741 0 .25140 2 8 0 3 .48650 1.52200 1.87970 1.81270 0 .59724 0 .47894 1.65600 0 .24430 281 2 .74440 1.72530 1.90740 2 .86870 0 .52066 0.58141 0 .51838 0 .25140 282 2 .98590 1.79180 1.52610 3 .38530 0 .51380 0 .57035 1.96690 0 .25200 2 8 3 2 .77650 1.63550 1.77810 2 .95450 0 .49133 0.49231 1.30290 0 .25420 284 3 .06030 1.77030 1.66990 3 .46850 0 .50024 0 .46860 1.35040 0 .25520 285 3 .44940 1.83630 1.83430 3 .14060 0 .55742 0 .58416 1.10220 0 .24610 286 2 .27100 1.67900 1.62130 3 .51450 0 .58567 0 .53726 1.87240 0 .25420 287 2 .85060 1.79820 1.48910 2 .62560 0 .54464 0 .48812 0 .84200 0 .25640 288 3 .32560 1.78190 1.90780 2 .88240 0 .52485 0 .49638 2 .09300 0 .24720 2 8 9 1.69000 0 .91000 0 .91000 1.65000 0 .70000 1.30000 1.00000 0 .28570 2 9 0 1.69000 0 .91000 0 .91000 1.65000 0 .80000 1.30000 1.00000 0 .28830 291 1.69000 0 .91000 0 .91000 1.65000 1.00000 1.30000 1.00000 0 .29300 292 1.69000 0 .91000 0 .91000 1.65000 1.10000 1.30000 1.00000 0 .29500 293 1.69000 0 .91000 0 .91000 1.65000 1.20000 1.30000 1.00000 0 .29700 294 1.69000 0 .91000 0 .91000 1.65000 1.30000 1.30000 1.00000 0 .29910 295 1.69000 0 .91000 0 .91000 1.65000 1.40000 1.30000 1.00000 0 .30090 296 1.69000 0 .91000 0 .91000 1.65000 1.50000 1.30000 1.00000 0 .30270 297 1.69000 0 .91000 0 .91000 1.65000 1.60000 1.30000 1.00000 0 .30450 298 1.69000 0 .91000 0 .91000 1.65000 1.70000 1.30000 1.00000 0 .30620 2 9 9 1.69000 0 .91000 0 .91000 1.65000 1.80000 1.30000 1.00000 0 .30760 300 1.69000 0 .91000 0 .91000 1.65000 1.90000 1.30000 1.00000 0 .30900 301 1.69000 0 .91000 0 .91000 1.65000 2 .00000 1.30000 1.00000 0 .31010 302 1.69000 0 .91000 0 .91000 1.65000 0 .95000 0 .70000 1.00000 0 .28950 303 1.69000 0 .91000 0 .91000 1.65000 0 .95000 0 .80000 1.00000 0 .28970 304 1.69000 0 .91000 0 .91000 1.65000 0 .95000 0 .90000 1.00000 0 .29000 305 1.69000 0 .91000 0 .91000 1.65000 0 .95000 1.00000 1.00000 0 .29040 306 1.69000 0 .91000 0 .91000 1.65000' 0 .95000 1.20000 1.00000 0 .29140 307 1.69000 0 .91000 0 .91000 1.65000 0 .95000 1.40000 1.00000 0 .29260 308 1.69000 0 .91000 0 .91000 1.65000 0 .95000 1.50000 1.00000 0 .29340 309 1.69000 0 .91000 0 .91000 1.65000 0 .95000 1.60000 1.00000 0 .29410 310 1.69000 0 .91000 0 .91000 1.65000 0 .95000 1.70000 1.00000 0 .29490 - 193 -RELIABILITY ANALYSIS DATABASE - C O N T 311 1.69000 0.91000 0.91000 1.65000 0.95000 1.80000 1.00000 0.29580 312 1.69000 0.91000 0.91000 1.65000 0.95000 1.90000 1.00000 0.29690 313 1.69000 0.91000 0.91000 1.65000 0.95000 2.00000 1.00000 0.29800 314 1.69000 0.91000 0.91000 1.65000 0.95000 2.10000 1.00000 0.29890 315 1.69000 0.91000 0.91000 1.65000 0.95000 2.20000 1.00000 0.30020 316 1.69000 0.91000 0.91000 1.65000 0.95000 2.30000 1.00000 0.30150 317 1.69000 0.91000 0.91000 1.65000 0.95000 2.40000 1.00000 0.30270 318 1.69000 0.91000 0.91000 1.65000 0.95000 2.50000 1.00000 0.30420 319 1.69000 0.91000 0.91000 1.65000 0.95000 2.60000 1.00000 0.30590 320 1.69000 0.91000 0.91000 1.65000 0.95000 2.70000 1.00000 0.30730 321 1.69000 0.91000 0.91000 1.65000 0.95000 2.80000 1.00000 0.30880 - 194-A P P E N D I X C . T A R G E T V E H I C L E -1990 FORD TAURUS - SPECIFICS Figure C - l : Target vehicle model (i.e. 1990 Ford Taurus) Table C-4: The target vehicle specifics Occupan t compar tment height (mm) Overa l l length (mm) Overa l l width (mm) We igh t (Kg) Bumpe r height (mm) W h e e l b a s e (mm) 1214 4530 1760 1200 520 2720 - 195 -APPENDIX D. T A R G E T V E H I C L E - 1990 FORD TAURUS - M A T E R I A L PROPERTIES (LS-DYNA VERSION 970): This appendix contains the material property input file for the target vehicle model used in this research. The input data has been prepared for use in LS-Dyna version 970. $...+.—l —+— 2 — + — - 3 — + — - 4 — + — 5 — + — - 6 — + — 7 — + — - 8 $ $ $ M A T E R I A L C A R D S $ $ $ $ „ . + — 1 — . + — 2 — - + — - 3 — + — 4 — + — 5 — - + — 6 — + — 7 — + — 8 * M A T _ P I E C E W I S E _ L I N E A R _ P L A S T I C I T Y $ A M A T 0 0 0 1 $ M I D R O E P R S I G Y E T A N F A I L T D E L 17.8500E-09 200000.0 0.30 215.0 0.05.0000E+08 0.0 $ C P L C S S L C S R V P 0.0 0.0 0.0 0.0 0.0 $ EPS1 EPS2 EPS3 EPS4 EPS5 EPS6 EPS7 EPS8 0.0 0.0040 0.030 0.15 0.30 0.40 0.0 0.0 $ E S I ES2 ES3 ES4 ES5 ES6 ES7 ES8 215.0 300.0 390.0 440.0 460.0 400.0 0.0 0.0 * M A T _ P I E C E W I S E _ L I N E A R _ P L A S T I C I T Y $ A M A T 0 0 0 2 $ M I D R O E P R S I G Y E T A N F A I L T D E L 27.8500E-09 200000.0 0.30 215.0 0.05.0000E+08 0.0 $ C P L C S S L C S R V P 0.0 0.0 0.0 0.0 0.0 $ EPS1 EPS2 EPS3 EPS4 EPS5 EPS6 EPS7 EPS8 0.0 0.0040 0.030 0.15 0.30 0.40 0.0 0.0 $ E S I ES2 ES3 ES4 ES5 ES6 ES7 ES8 215.0 300.0 390.0 440.0 460.0 400.0 0.0 0.0 * M A T _ P I E C E W I S E _ L I N E A R _ P L A S T I C I T Y $ A M A T 0 0 0 3 $ M I D R O E P R S I G Y E T A N F A I L T D E L 37.8500E-09 200000.0 0.30 215.0 0.05.0000E+08 0.0 $ C P L C S S L C S R V P 0.0 0.0 0.0 0.0 0.0 $ EPS1 EPS2 EPS3 EPS4 EPS5 EPS6 EPS7 EPS8 0.0 0.0040 0.030 0.15 0.30 0.40 0.0 0.0 $ E S I ES2 ES3 ES4 ES5 ES6 ES7 ES8 215.0 300.0 390.0 440.0 460.0 400.0 0.0 0.0 * M A T _ P I E C E W I S E _ L I N E A R _ P L A S T I C I T Y $ A M A T 0 0 0 4 $ M I D R O E P R S I G Y E T A N F A I L T D E L 47.8500E-09 200000.0 0.30 215.0 0.05.0000E+08 0.0 - 196-$ C P L C S S L C S R V P 0.0 0.0 0.0 0.0 0.0 $ EPS1 EPS2 EPS3 EPS4 EPS5 EPS6 EPS7 EPS8 0.0 0.0040 0.030 0.15 0.30 0.40 0.0 0.0 $ E S I ES2 ES3 ES4 ES5 ES6 ES7 ES8 215.0 300.0 390.0 440.0 460.0 400.0 0.0 0.0 * M A T _ P I E C E W I S E _ L I N E A R _ P L A S T I C I T Y $ A M A T 0 0 0 5 $ M I D R O E P R S I G Y E T A N F A I L T D E L 57.8500E-09 200000.0 0.30 215.0 0.05.0000E+08 0.0 $ C P L C S S L C S R V P 0.0 0.0 0.0 0.0 0.0 $ EPS1 EPS2 EPS3 EPS4 EPS5 EPS6 EPS7 EPS8 0.0 0.0040 0.030 0.15 0.30 0.40 0.0 0.0 $ E S I ES2 ES3 ES4 ES5 ES6 ES7 ES8 215.0 300.0 390.0 440.0 460.0 400.0 0.0 0.0 * M A T _ P I E C E W I S E _ L I N E A R _ P L A S T I C I T Y $ A M A T 0 0 0 6 $ M I D R O E P R S I G Y E T A N F A I L T D E L 67.8500E-09 200000.0 0.30 215.0 0.05.0000E+08 0.0 $ C P L C S S L C S R V P 0.0 0.0 0.0 0.0 0.0 $ EPS1 EPS2 EPS3 EPS4 EPS5 EPS6 EPS7 EPS8 0.0 0.0040 0.030 0.15 0.30 0.40 0.0 0.0 $ E S I ES2 ES3 ES4 ES5 ES6 ES7 ES8 215.0 300.0 390.0 440.0 460.0 400.0 0.0 0.0 * M A T _ P I E C E W I S E _ L I N E A R _ P L A S T I C I T Y $ A M A T 0 0 0 7 $ M I D R O E P R S I G Y E T A N F A I L T D E L 77.8500E-09 200000.0 0.30 215.0 0.05.0000E+08 0.0 $ C P L C S S L C S R V P 0.0 0.0 0.0 0.0 0.0 $ EPS1 EPS2 EPS3 EPS4 EPS5 EPS6 EPS7 EPS8 0,0 0.0040 0.030 0.15 0.30 0.40 0.0 0.0 $ E S I ES2 ES3 ES4 ES5 ES6 ES7 ES8 215.0 300.0 390.0 440.0 460.0 400.0 0.0 0.0 * M A T _ P I E C E W I S E _ L I N E A R _ P L A S T I C I T Y $ A M A T 0 0 0 8 $ M I D R O E P R S I G Y E T A N F A I L T D E L 87.8500E-09 200000.0 0.30 215.0 0.05.0000E+08 0.0 $ C P L C S S L C S R V P 0.0 0.0 0.0 0.0 0.0 $ EPS1 EPS2 EPS3 EPS4 EPS5 EPS6 EPS7 EPS 8 0.0 0.0040 0.030 0.15 0.30 0.40 0.0 0.0 $ E S I ES2 ES3 ES4 ES5 ES6 ES7 ES8 215.0 300.0 390.0 440.0 460.0 400.0 0.0 0.0 - 197-* M A T _ P I E C E W I S E _ L I N E A R _ P L A S T I C I T Y $ A M A T 0 0 0 9 $ M I D R O E P R S I G Y E T A N F A I L T D E L 97.8500E-09 200000.0 0.30 215.0 0.05.0000E+08 0.0 $ C P L C S S L C S R V P 0.0 0.0 0.0 0.0 0.0 $ EPS1 EPS2 EPS3 EPS4 EPS5 EPS6 EPS7 EPS8 0.0 0.0040 0.030 0.15 0.30 0.40 0.0 0.0 $ E S I ES2 ES3 ES4 ES5 ES6 ES7 ES8 215.0 300.0 390.0 440.0 460.0 400.0 0.0 0.0 * M A T _ P I E C E W I S E _ L I N E A R _ P L A S T I C I T Y $ A M A T 0 0 1 0 $ M I D R O E P R S I G Y E T A N F A I L T D E L 107.8500E-09 200000.0 0.30 215.0 0.05.0000E+08 0.0 $ C P L C S S L C S R V P 0.0 0.0 0.0 0.0 0.0 $ EPS1 EPS2 EPS3 EPS4 EPS5 EPS6 EPS7 EPS8 0.0 0.0040 0.030 0.15 0.30 0.40 0.0 0.0 $ E S I ES2 ES3 ES4 ES5 ES6 ES7 ES8 215.0 300.0 390.0 440.0 460.0 400.0 0.0 0.0 * M A T _ P I E C E W I S E _ L I N E A R _ P L A S T I C I T Y $ A M A T 0 0 1 1 $ M I D R O E P R S I G Y E T A N F A I L T D E L 112.5000E-09 76000.0 0.30 138.0 0.0 0.00050 0.0 $ C P L C S S L C S R V P 0.0 0.0 0.0 0.0 0.0 $ EPS1 EPS2 EPS3 EPS4 EPS5 EPS6 EPS7 EPS8 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 $ E S I ES2 ES3 ES4 ES5 ES6 ES7 ES8 138.0 138.0 138.0 0.0 0.0 0.0 0.0 0.0 * M A T _ P I E C E W I S E _ L I N E A R _ P L A S T I C I T Y $ A M A T 0 0 1 2 $ M I D R O E P R S I G Y E T A N F A I L T D E L 127.8500E-09 200000.0 0.30 215.0 0.05.0000E+08 0.0 $ C P L C S S L C S R V P 0.0 0.0 0.0 0.0 0.0 $ EPS1 EPS2 EPS3 EPS4 EPS5 EPS6 EPS7 EPS8 0.0 0.0040 0.030 0.15 0.30 0.40 0.0 0.0 $ E S I ES2 ES3 ES4 ES5 ES6 ES7 ES8 215.0 300.0 390.0 440.0 460.0 400.0 0.0 0.0 * M A T _ P I E C E W I S E _ L I N E A R _ P L A S T I C I T Y $ A M A T 0 0 1 3 $ M I D R O E P R S I G Y E T A N F A I L T D E L 137.8500E-09 200000.0 0.30 215.0 0.05.0000E+08 0.0 $ C P L C S S L C S R V P 0.0 0.0 0.0 0.0 0.0 - 198-$ EPS1 EPS2 EPS3 EPS4 EPS5 EPS6 EPS7 EPS8 0.0 0.0040 0.030 0.15 0.30 0.40 0.0 0.0 $ E S I ES2 ES3 ES4 ES5 ES6 ES7 ES8 215.0 300.0 390.0 440.0 460.0 400.0 0.0 0.0 * M A T _ P I E C E W I S E _ L I N E A R _ P L A S T I C I T Y $ A M A T 0 0 1 4 $ M I D R O E P R S I G Y E T A N F A I L T D E L 147.8500E-09 200000.0 0.30 215.0 0.05.0000E+08 0.0 $ C P L C S S L C S R V P 0.0 0.0 0.0 0.0 0.0 $ EPS1 EPS2 EPS3 EPS4 EPS5 EPS6 EPS7 EPS8 0.0 0.0040 0.030 0.15 0.30 0.40 0.0 0.0 $ E S I ES2 ES3 ES4 ES5 ES6 ES7 ES8 215.0 300.0 390.0 440.0 460.0 400.0 0.0 0.0 * M A T _ P I E C E W I S E _ L I N E A R _ P L A S T I C I T Y $ A M A T 0 0 1 5 $ M I D R O E P R S I G Y E T A N F A I L T D E L 157.8500E-09 200000.0 0.30 215.0 0.05.0000E+08 0.0 $ C P L C S S L C S R V P 0.0 0.0 0.0 0.0 0.0 $ EPS1 EPS2 EPS3 EPS4 EPS5 EPS6 EPS7 EPS8 0.0 0.0040 0.030 0.15 0.30 0.40 0.0 0.0 $ E S I ES2 ES3 ES4 ES5 ES6 ES7 ES8 215.0 300.0 390.0 440.0 460.0 400.0 0.0 0.0 * M A T _ P I E C E W I S E _ L I N E A R _ P L A S T I C I T Y $ A M A T 0 0 1 6 $ M I D R O E P R S I G Y E T A N F A I L T D E L 167.8500E-09 200000.0 0.30 215.0 0.05.0000E+08 0.0 $ C P L C S S L C S R V P 0.0 0.0 0.0 0.0 0.0 $ EPS1 EPS2 EPS3 EPS4 EPS5 EPS6 EPS7 EPS8 0.0 0.0040 0.030 0.15 0.30 0.40 0.0 0.0 $ E S I . ES2 ES3 ES4 ES5 ES6 ES7 ES8 215.0 300.0 390.0 440.0 460.0 400.0 0.0 0.0 * M A T _ P I E C E W I S E _ L I N E A R _ P L A S T I C I T Y $ A M A T 0 0 1 7 $ M I D R O E P R S I G Y E T A N F A I L T D E L 177.8500E-09 200000.0 0.30 215.0 0.05.0000E+08 0.0 $ C P L C S S L C S R V P 0.0 0.0 0.0 0.0 0.0 $ EPS1 EPS2 EPS3 EPS4 EPS5 EPS6 EPS7 EPS8 0.0 0.0040 0.030 0.15 0.30 0.40 0.0 0.0 $ ESI ES2 ES3 ES4 ES5 ES6 ES7 ES8 215.0 300.0 390.0 440.0 460.0 400.0 0.0 0.0 * M A T _ P I E C E W I S E _ L I N E A R _ P L A S T I C I T Y $ A M A T 0 0 1 8 - 199-$ M I D R O E P R S I G Y E T A N F A I L T D E L 187.8500E-09 200000.0 0.30 215.0 0.05.0000E+08 0.0 $ C P L C S S L C S R V P 0.0 0.0 0.0 0.0 0.0 $ EPS1 EPS2 EPS3 EPS4 EPS5 EPS6 EPS7 EPS8 0.0 0.0040 0.030 0.15 0.30 0.40 0.0 0.0 $ E S I ES2 ES3 ES4 ES5 ES6 ES7 ES8 215.0 300.0 390.0 440.0 460.0 400.0 0.0 0.0 * M A T _ P I E C E W I S E _ L I N E A R _ P L A S T I C I T Y $ A M A T 0 0 1 9 $ M I D R O E P R S I G Y E T A N F A I L T D E L 197.8500E-09 200000.0 0.30 215.0 0.05.0000E+08 0.0 $ C P L C S S L C S R V P 0.0 0.0 0.0 0.0 0.0 $ EPS1 EPS2 EPS3 EPS4 EPS5 EPS6 EPS7 EPS8 0.0 0.0040 0.030 0.15 0.30 0.40 0.0 0.0 $ E S I ES2 ES3 ES4 ES5 ES6 ES7 ES8 215.0 300.0 390.0 440.0 460.0 400.0 0.0 0.0 * M A T _ P I E C E W I S E _ L I N E A R _ P L A S T I C I T Y $ A M A T 0 0 2 0 $ M I D R O E P R S I G Y E T A N F A I L T D E L 202.7000E-09 70000.0 0.0 248.3 0.05.0000E+08 0.0 $ C P L C S S L C S R V P 0.0 0.0 0.0 0.0 0.0 $ EPS1 EPS2 EPS3 EPS4 EPS5 EPS6 EPS7 EPS8 0.0 0.0085 0.035 0.0616 0.0 0.0 0.0 0.0 $ E S I ES2 ES3 ES4 ES5 ES6 ES7 ES8 0.0 254.8 258.0 262.8 0.0 0.0 0.0 0.0 * M A T _ P I E C E W I S E _ L I N E A R _ P L A S T I C I T Y $ A M A T 0 0 2 1 $ M I D R O E P R S I G Y E T A N F A I L T D E L 217.8500E-09 200000.0 0.30 215.0 0.05.0000E+08 0.0 $ C P L C S S L C S R V P 0.0 0.0 0.0 0.0 0.0 $ EPS1 EPS2 EPS3 EPS4 EPS5 EPS6 EPS7 EPS8 0.0 0.0040 0.030 0.15 0.30 0.40 0.0 0.0 $ E S I ES2 ES3 ES4 ES5 ES6 ES7 ES8 215.0 300.0 390.0 440.0 460.0 400.0 0.0 0.0 * M A T _ P I E C E W I S E _ L I N E A R _ P L A S T I C I T Y $ A M A T 0 0 2 2 $ M I D R O E P R S I G Y E T A N F A I L T D E L 227.8500E-09 200000.0 0.30 215.0 0.05.0000E+08 0.0 $ C P L C S S L C S R V P 0.0 0.0 0.0 0.0 0.0 $ EPS1 EPS2 EPS3 EPS4 EPS5 EPS6 EPS7 EPS8 0.0 0.0040 0.030 0.15 0.30 0.40 0.0 0.0 - 2 0 0 -$ ESI ES2 ES3 ES4 ES5 ES6 ES7 ES8 215.0 300.0 390.0 440.0 460.0 400.0 0.0 0.0 * M A T _ P I E C E W I S E _ L I N E A R _ P L A S T I C I T Y $ A M A T 0 0 2 3 $ M I D R O E P R S I G Y E T A N F A I L T D E L 237.8500E-09 200000.0 0.30 215.0 0.05.0000E+08 0.0 $ C P L C S S L C S R V P 0.0 0.0 0.0 0.0 0.0 $ EPS1 EPS2 EPS3 EPS4 EPS5 EPS6 EPS7 EPS8 0.0 0.0040 0.030 0.15 0.30 0.40 0.0 0.0 $ E S I ES2 ES3 ES4 ES5 ES6 ES7 ES8 215.0 300.0 390.0 440.0 460.0 400.0 0.0 0.0 * M A T _ P I E C E W I S E _ L I N E A R _ P L A S T I C I T Y $ A M A T 0 0 2 4 $ M I D R O E P R S I G Y E T A N F A I L T D E L 247.8500E-09 200000.0 0.30 215.0 0.05.0000E+08 0.0 $ C P L C S S L C S R V P 0.0 0.0 0.0 0.0 0.0 $ EPS1 EPS2 EPS3 EPS4 EPS5 EPS6 EPS7 EPS8 0.0 0.0040 0.030 0.15 0.30 0.40 0.0 0.0 $ E S I ES2 ES3 ES4 ES5 ES6 ES7 ES8 215.0 300.0 390.0 440.0 460.0 400-0 0.0 0.0 * M A T _ P I E C E W I S E _ L I N E A R _ P L A S T I C I T Y $ A M A T 0 0 2 5 $ M I D R O E P R S I G Y E T A N F A I L T D E L 257.8500E-09 200000.0 0.30 215.0 0.05.0000E+08 0.0 $ C P L C S S L C S R V P 0.0 0.0 0.0 0.0 0.0 $ EPS1 EPS2 EPS3 EPS4 EPS5 EPS6 EPS7 EPS 8 0.0 0.0040 0.030 0.15 0.30 0.40 0.0 0.0 $ E S I ES2 ES3 ES4 ES5 ES6 ES7 ES8 215.0 300.0 390.0 440.0 460.0 400.0 0.0 0.0 * M A T _ P I E C E W I S E _ L I N E A R _ P L A S T I C I T Y $ A M A T 0 0 2 6 $ M I D R O E P R S I G Y E T A N F A I L T D E L 267.8500E-09 200000.0 0.30 215.0 0.05.0000E+08 0.0 $ C P L C S S L C S R V P 0.0 0.0 0.0 0.0 0.0 $ EPS1 EPS2 EPS3 EPS4 EPS5 EPS6 EPS7 EPS8 0.0 0.0040 0.030 0.15 0.30 0.40 0.0 0.0 $ E S I ES2 ES3 ES4 ES5 ES6 ES7 ES8 215.0 300.0 390.0 440.0 460.0 400.0 0.0 0.0 * M A T _ P I E C E W I S E _ L I N E A R _ P L A S T I C I T Y $ A M A T 0 0 2 7 $ M I D R O E P R S I G Y E T A N F A I L T D E L 277.8500E-09 200000.0 0.30 215.0 0.05.0000E+08 0.0 -201 -$ C P L C S S L C S R V P 0.0 0.0 0.0 0.0 0.0 $ EPS1 EPS2 EPS3 EPS4 EPS 5 EPS6 EPS7 EPS8 0.0 0.0040 0.030 0.15 0.30 0.40 0.0 0.0 $ E S I ES2 ES3 ES4 ES5 ES6 ES7 ES8 215.0 300.0 390.0 440.0 460.0 400.0 0.0 0.0 * M A T _ P I E C E W I S E _ L I N E A R _ P L A S T I C I T Y $ A M A T 0 0 2 8 $ M I D R O E P R S I G Y E T A N F A I L T D E L 287.8500E-09 200000.0 0.30 215.0 0.05.0000E+08 0.0 $ C P L C S S L C S R V P 0.0 0.0 0.0 0.0 0.0 $ EPS1 EPS2 EPS3 EPS4 EPS5 EPS6 EPS7 EPS8 0.0 0.0040 0.030 0.15 0.30 0.40 0.0 0.0 $ E S I ES2 ES3 ES4 ES5 ES6 ES7 ES8 215.0 300.0 390.0 440.0 460.0 400.0 0.0 0.0 * M A T _ P I E C E W I S E _ L I N E A R _ P L A S T I C I T Y $ A M A T 0 0 2 9 $ M I D R O E P R S I G Y E T A N F A I L T D E L 297.8500E-09 200000.0 0.30 215.0 0.05.0000E+08 0.0 $ C P L C S S L C S R V P 0.0 0.0 0.0 0.0 0.0 $ EPS1 EPS2 EPS3 EPS4 EPS5 EPS6 EPS7 EPS8 0.0 0.0040 0.030 0.15 0.30 0.40 0.0 0.0 $ E S I ES2 ES3 ES4 ES5 ES6 ES7 ES8 215.0 300.0 390.0 440.0 460.0 400.0 0.0 0.0 * M A T _ P I E C E W I S E _ L I N E A R _ P L A S T I C I T Y $ A M A T 0 0 3 0 $ M I D R O E P R S I G Y E T A N F A I L T D E L 307.8500E-09 200000.0 0.30 215.0 0.05.0000E+08 0.0 $ C P L C S S L C S R V P 0.0 0.0 0.0 0.0 0.0 $ EPS1 EPS2 EPS3 EPS4 EPS5 EPS6 EPS7 EPS8 0.0 0.0040 0.030 0.15 0.30 0.40 0.0 0.0 $ ESI ES2 ES3 ES4 ES5 ES6 ES7 ES8 215.0 300.0 390.0 440.0 460.0 400.0 0.0 0.0 * M A T _ P I E C E W I S E _ L I N E A R _ P L A S T I C I T Y $ A M A T 0 0 3 1 $ M I D R O E P R S I G Y E T A N F A I L T D E L 317.8500E-09 200000.0 0.30 215.0 0.05.0000E+08 0.0 $ C P L C S S L C S R V P 0.0 0.0 0.0 0.0 0.0 $ EPS1 EPS2 EPS3 EPS4 EPS5 EPS6 EPS7 EPS8 0.0 0.0040 0.030 0.15 0.30 0.40 0.0 0.0 $ E S I ES2 ES3 ES4 ES5 ES6 ES7 ES8 215.0 300.0 390.0 440.0 460.0 400.0 0.0 0.0 -202 -* M A T _ P I E C E W I S E _ L I N E A R _ P L A S T I C I T Y $ A M A T 0 0 3 2 $ M I D R O E P R S I G Y E T A N F A I L T D E L v 327.8500E-09 200000.0 0.30 215.0 0.05.0000E+08 0.0 $ C P L C S S L C S R V P 0.0 0.0 0.0 0.0 0.0 $ EPS1 EPS2 EPS3 EPS4 EPS5 EPS6 EPS7 EPS8 0.0 0.0040 0.030 0.15 0.30 0.40 0.0 0.0 $ E S I ES2 ES3 ES4 ES5 ES6 ES7 ES8 215.0 300.0 390.0 440.0 460.0 400.0 0.0 0.0 * M A T _ P I E C E W I S E _ L I N E A R _ P L A S T I C I T Y $ A M A T 0 0 3 3 $ M I D R O E P R S I G Y E T A N F A I L T D E L 337.8500E-09 200000.0 0.30 215.0 0.05.0000E+08 0.0 $ C P L C S S L C S R V P 0.0 0.0 0.0 0.0 0.0 $ EPS1 EPS2 EPS3 EPS4 EPS5 EPS6 EPS7 EPS8 0.0 0.0040 0.030 0.15 0.30 0.40 0.0 0.0 $ E S I ES2 ES3 ES4 ES5 ES6 ES7 ES8 215.0 300.0 390.0 440.0 460.0 400.0 0.0 0.0 * M A T _ P I E C E W I S E _ L I N E A R _ P L A S T I C I T Y $ A M A T 0 0 3 4 $ M I D R O E P R S I G Y E T A N F A I L T D E L 347.8500E-09 200000.0 0.30 215.0 0.05.0000E+08 0.0 $ C P L C S S L C S R V P 0.0 0.0 0.0 0.0 0.0 $ EPS1 EPS2 EPS3 EPS4 EPS5 EPS6 EPS7 EPS8 0.0 0.0040 0.030 0.15 0.30 0.40 0.0 0.0 $ E S I ES2 ES3 ES4 ES5 ES6 ES7 ES8 215.0 300.0 390.0 440.0 460.0 400.0 0.0 0.0 * M A T _ P I E C E W I S E _ L I N E A R _ P L A S T I C i T Y $ A M A T 0 0 3 5 $ M I D R O E P R S I G Y E T A N F A I L T D E L 357.8500E-09 200000.0 0.30 215.0 0.05.0000E+08 0.0 $ C P L C S S L C S R V P 0.0 0.0 0.0 0.0 0.0 $ EPS1 EPS2 EPS3 EPS4 EPS5 EPS6 EPS7 EPS8 0.0 0.0040 0.030 0.15 0.30 0.40 0.0 0.0 $ E S I ES2 ES3 ES4 ES5 ES6 ES7 ES8 215.0 300.0 390.0 440.0 460.0 400.0 0.0 0.0 * M A T _ P I E C E W I S E _ L I N E A R _ P L A S T I C I T Y $ A M A T 0 0 3 6 $ M I D R O E P R S I G Y E T A N F A I L T D E L 367.8500E-09 200000.0 0.30 215.0 0.05.0000E+08 0.0 $ C P L C S S L C S R V P 0.0 0.0 0.0 0.0 0.0 -203 -$ EPS1 EPS2 EPS3 EPS4 EPS5 EPS6 EPS7 EPS8 0.0 0.0040 0.030 0.15 0.30 0.40 0.0 0.0 $ E S I ES2 ES3 ES4 ES5 ES6 ES7 ES8 215.0 300.0 390.0 440.0 460.0 400.0 0.0 0.0 * M A T _ P I E C E W I S E _ L I N E A R _ P L A S T I C I T Y $ A M A T 0 0 3 7 $ M I D R O E P R S I G Y E T A N F A I L T D E L 377.8500E-09 200000.0 0.30 215.0 0.05.0000E+08 0.0 $ C P L C S S L C S R V P 0.0 0.0 0.0 0.0 0.0 $ EPS1 EPS2 EPS3 EPS4 EPS5 EPS6 EPS7 EPS 8 0.0 0.0040 0.030 0.15 0.30 0.40 0.0 0.0 $ E S I ES2 ES3 ES4 ES5 ES6 ES7 ES8 215.0 300.0 390.0 440.0 460.0 400.0 0.0 0.0 * M A T _ P I E C E W I S E _ L I N E A R _ P L A S T I C I T Y $ A M A T 0 0 3 8 $ M I D R O E P R S I G Y E T A N F A I L T D E L 387.8500E-09 200000.0 0.30 215.0 0.05.0000E+08 0.0 $ C P L C S S L C S R V P 0.0 0.0 0.0 0.0 0.0 $ EPS1 EPS2 EPS3 EPS4 EPS5 EPS6 EPS7 EPS8 0.0 0.0040 0.030 0.15 0.30 0.40 0.0 0.0 $ E S I ES2 ES3 ES4 ES5 ES6 ES7 ES8 215.0 300.0 390.0 440.0 460.0 400.0 0.0 0.0 * M A T J P I E C E W I S E _ L I N E A R _ P L A S T I C I T Y $ A M A T 0 0 3 9 $ M I D R O E P R S I G Y E T A N F A I L T D E L 397.8500E-09 200000.0 0.30 215.0 0.05.0000E+08 0.0 $ C P L C S S L C S R V P 0.0 0.0 0.0 0.0 0.0 $ EPS1 EPS2 EPS3 EPS4 EPS5 EPS6 EPS7 EPS8 0.0 0.0040 0.030 0.15 0.30 0.40 0.0 0.0 $ E S I ES2 ES3 ES4 ES5 ES6 ES7 ES8 215.0 300.0 390.0 440.0 460.0 400.0 0.0 0.0 * M A T _ P I E C E W I S E _ L I N E A R _ P L A S T I C I T Y $ A M A T 0 0 4 0 $ M I D R O E P R S I G Y E T A N F A I L T D E L 407.8500E-09 200000.0 0.30 215.0 0.05.0000E+08 0.0 $ C P L C S S L C S R V P 0.0 0.0 0.0 0.0 0.0 $ EPS1 EPS2 EPS3 EPS4 EPS5 EPS6 EPS7 EPS8 0.0 0.0040 0.030 0.15 0.30 0.40 0.0 0.0 $ E S I ES2 ES3 ES4 ES5 ES6 ES7 ES8 215.0 300.0 390.0 440.0 460.0 400.0 0.0 0.0 * M A T _ P I E C E W I S E _ L I N E A R _ P L A S T I C I T Y $ A M A T 0 0 4 1 - 2 0 4 -$ M I D R O E P R S I G Y E T A N F A I L T D E L 417.8500E-09 200000.0 0.30 215.0 0.05.0000E+08 0.0 $ C P L C S S L C S R V P 0.0 0.0 0.0 0.0 0.0 $ EPS1 EPS2 EPS3 EPS4 EPS5 EPS6 EPS7 EPS 8 0.0 0.0040 0.030 0.15 0.30 0.40 0.0 0.0 $ E S I ES2 ES3 ES4 ES5 ES6 ES7 ES8 215.0 300.0 390.0 440.0 460.0 400.0 0.0 0.0 * M A T _ P I E C E W I S E _ L I N E A R _ P L A S T I C I T Y $ A M A T 0 0 4 2 $ M I D R O E P R S I G Y E T A N F A I L T D E L 426.8730E-08 200000.0 0.30 215.0 0.05.0000E+08 0.0 $ C P L C S S L C S R V P 0.0 0.0 0.0 0.0 0.0 $ EPS1 EPS2 EPS3 EPS4 EPS5 EPS6 EPS7 EPS8 0.0 0.0040 0.030 0.15 0.30 0.40 0.0 0.0 $ ESI ES2 ES3 ES4 ES5 ES6 ES7 ES8 215.0 300.0 390.0 440.0 460.0 400.0 0.0 0.0 * M A T J J I E C E W I S E _ L I N E A R _ P L A S T I C I T Y $ A M A T 0 0 4 3 $ M I D R O E P R S I G Y E T A N F A I L T D E L 437.8500E-09 200000.0 0.30 215.0 0.05.0000E+08 0.0 $ C P L C S S L C S R V P 0.0 0.0 0.0 0.0 0.0 $ EPS1 EPS2 EPS3 EPS4 EPS5 EPS6 EPS7 EPS 8 0.0 0.0040 0.030 0.15 0.30 0.40 0.0 0.0 $ E S I ES2 ES3 ES4 ES5 ES6 ES7 ES8 215.0 300.0 390.0 440.0 460.0 400.0 0.0 0.0 * M A T _ P I E C E W I S E _ L I N E A R _ P L A S T I C I T Y $ A M A T 0 0 4 4 $ M I D R O E P R S I G Y E T A N F A I L T D E L 447.8500E-09 200000.0 0.30 215.0 0.05.0000E+08 0.0 $ C P L C S S L C S R V P 0.0 0.0 0.0 0.0 0.0 $ EPS1 EPS2 EPS3 EPS4 EPS5 EPS6 EPS7 EPS8 0.0 0.0040 0.030 0.15 0.30 0.40 0.0 0.0 $ E S I ES2 ES3 ES4 ES5 ES6 ES7 ES8 215.0 300.0 390.0 440.0 460.0 400.0 0.0 0.0 * M A T _ P I E C E W I S E _ L I N E A R _ P L A S T I C I T Y $ A M A T 0 0 4 5 $ M I D R O E P R S I G Y E T A N F A I L T D E L 457.8500E-09 200000.0 0.30 215.0 0.05.0000E+08 0.0 $ C P L C S S L C S R V P 0.0 0.0 0.0 0.0 0.0 $ EPS1 EPS2 EPS3 EPS4 EPS5 EPS6 EPS7 EPS8 0.0 0.0040 0.030 0.15 0.30 0.40 0.0 0.0 -205 -$ E S I ES2 ES3 ES4 ES5 ES6 ES7 ES8 215.0 300.0 390.0 440.0 460.0 400.0 0.0 0.0 * M A T _ P I E C E W I S E _ L I N E A R _ P L A S T I C I T Y $ A M A T 0 0 4 6 $ M I D R O E P R S I G Y E T A N F A I L T D E L 467.8500E-09 200000.0 0.30 215.0 0.05.0000E+08 0.0 $ C P L C S S L C S R V P 0.0 0.0 0.0 0.0 0.0 $ EPS1 EPS2 EPS3 EPS4 EPS5 EPS6 EPS7 EPS8 0.0 0.0040 0.030 0.15 0.30 0.40 0.0 0.0 $ E S I ES2 ES3 ES4 ES5 ES6 ES7 ES8 215.0 300.0 390.0 440.0 460.0 400.0 0.0 0.0 * M A T _ P I E C E W I S E _ L I N E A R _ P L A S T I C I T Y $ A M A T 0 0 4 7 $ M I D R O E P R S I G Y E T A N F A I L T D E L 477.8500E-09 200000.0 0.30 215.0 0.05.0000E+08 0.0 $ C P L C S S L C S R V P 0.0 0.0 0.0 0.0 0.0 $ EPS1 EPS2 EPS3 EPS4 EPS5 ( EPS6 EPS7 EPS8 0.0 0.0040 0.030 0.15 0.30 0.40 0.0 0.0 $ E S I ES2 ES3 ES4 ES5 ES6 ES7 ES8 215.0 300.0 390.0 440.0 460.0 400.0 0.0 0.0 * M A T _ P I E C E W I S E _ L I N E A R _ P L A S T I C I T Y $ A M A T 0 0 4 8 $ M I D R O E P R S I G Y E T A N F A I L T D E L 487.8500E-09 200000.0 0.30 215.0 0.05.0000E+08 0.0 $ C P L C S S L C S R V P 0.0 0.0 0.0 0.0 0.0 $ EPS1 EPS2 EPS3 EPS4 EPS5 EPS6 EPS7 EPS8 0.0 0.0040 0.030 0.15 0.30 0.40 0.0 0.0 $ E S I ES2 ES3 ES4 ES5 ES6 ES7 ES8 215.0 300.0 390.0 440.0 460.0 400.0 0.0 0.0 * M A T _ P I E C E W I S E _ L I N E A R _ P L A S T I C I T Y $ A M A T 0 0 4 9 $ M I D R O E P R S I G Y E T A N F A I L T D E L 497.8500E-09 200000.0 0.30 215.0 0.05.0000E+08 0.0 $ C P L C S S L C S R V P 0.0 0.0 0.0 0.0 0.0 $ EPS1 EPS2 EPS3 EPS4 EPS5 EPS6 EPS7 EPS8 0.0 0.0040 0.030 0.15 0.30 0.40 0.0 0.0 $ E S I ES2 ES3 ES4 ES5 ES6 ES7 ES8 215.0 300.0 390.0 440.0 460.0 400.0 0.0 0.0 * M A T _ P I E C E W I S E _ L I N E A R _ P L A S T I C I T Y $ A M A T 0 0 5 0 $ M I D R O E P R S I G Y E T A N F A I L T D E L 507.8500E-09 200000.0 0.30 215.0 0.05.0000E+08 0.0 -206 -$ C P L C S S L C S R V P 0.0 0.0 0.0 0.0 0.0 $ EPS1 EPS2 EPS 3 EPS4 EPS5 EPS6 EPS7 EPS8 0.0 0.0040 0.030 0.15 0.30 0.40 0.0 0.0 $ E S I ES2 ES3 ES4 ES5 ES6 ES7 ES8 215.0 300.0 390.0 440.0 460.0 400.0 0.0 0.0 * M A T _ P I E C E W I S E _ L I N E A R _ P L A S T I C I T Y $ A M A T 0 0 5 1 $ M I D R O E P R S I G Y E T A N F A I L T D E L 517.8500E-09 200000.0 0.30 215.0 0.05.0000E+08 0.0 $ C P L C S S L C S R V P 0.0 0.0 0.0 0.0 0.0 $ EPS1 EPS2 EPS3 EPS4 EPS5 EPS6 EPS7 EPS8 0.0 0.0040 0.030 0.15 0.30 0.40 0.0 0.0 $ E S I ES2 ES3 ES4 ES5 ES6 ES7 ES8 215.0 300.0 390.0 440.0 460.0 400.0 0.0 0.0 * M A T _ P I E C E W I S E _ L I N E A R _ P L A S T I C I T Y $ A M A T 0 0 5 2 $ M I D R O E P R S I G Y E T A N F A I L T D E L 527.8500E-09 200000.0 0.30 215.0 0.05.0000E+08 0.0 $ C P L C S S L C S R V P 0.0 0.0 0.0 0.0 0.0 $ EPS1 EPS2 EPS3 EPS4 EPS5 EPS6 EPS7 EPS8 0.0 0.0040 0.030 0.15 0.30 0.40 0.0 0.0 $ E S I ES2 ES3 ES4 ES5 ES6 ES7 ES8 215.0 300.0 390.0 440.0 460.0 400.0 0.0 0.0 * M A T _ P I E C E W I S E _ L I N E A R _ P L A S T I C I T Y $ A M A T 0 0 5 3 $ M I D R O E P R S I G Y E T A N F A I L T D E L 537.8500E-09 200000.0 0.30 215.0 0.05.0000E+08 0.0 $ C P L C S S L C S R V P 0.0 0.0 0.0 0.0 0.0 $ EPS1 EPS2 EPS3 EPS4 EPS5 EPS6 EPS7 EPS8 0.0 0.0040 0.030 0.15 0.30 0.40 0.0 0.0 $ E S I ES2 ES3 ES4 ES5 ES6 ES7 ES8 215.0 300.0 390.0 440.0 460.0 400.0 0.0 0.0 * M A T _ P I E C E W I S E _ L I N E A R _ P L A S T I C I T Y $ A M A T 0 0 5 4 $ M I D R O E P R S I G Y E T A N F A I L T D E L 547.8500E-09 200000.0 0.30 215.0 0.05.0000E+08 0.0 $ C P L C S S L C S R V P 0.0 0.0 0.0 0.0 0.0 $ EPS1 EPS2 EPS3 EPS4 EPS5 EPS6 EPS7 EPS8 0.0 0.0040 0.030 0.15 0.30 0.40 0.0 0.0 $ E S I ES2 ES3 ES4 ES5 ES6 ES7 ES8 215.0 300.0 390.0 440.0 460.0 400.0 0.0 0.0 - 2 0 7 -* M A T _ P I E C E W I S E _ L I N E A R _ P L A S T I C I T Y $ A M A T 0 0 5 5 $ M I D R O E P R S I G Y E T A N F A I L T D E L 552.5000E-09 76000.0 0.30 138.0 0.0 0.00050 0.0 $ C P L C S S L C S R V P 0.0 0.0 0.0 0.0 0.0 $ EPS1 EPS2 EPS3 EPS4 EPS5 EPS6 EPS7 EPS8 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 $ ESI ES2 ES3 ES4 ES5 ES6 ES7 ES8 138.0 138.0 138.0 0.0 0.0 0.0 0.0 0.0 * M A T _ P I E C E W I S E _ L I N E A R _ P L A S T I C I T Y $ A M A T 0 0 5 6 $ M I D R O E P R S I G Y E T A N F A I L T D E L 567.8500E-09 200000.0 0.30 215.0 0.05.0000E+08 0.0 $ C P L C S S L C S R V P 0.0 0.0 0.0 0.0 0.0 $ EPS1 EPS2 EPS3 EPS4 EPS5 EPS6 EPS7 EPS8 0.0 0.0040 0.030 0.15 0.30 0.40 0.0 0.0 $ E S I ES2 ES3 ES4 ES5 ES6 ES7 ES8 215.0 300.0 390.0 440.0 460.0 400.0 0.0 0.0 * M A T J > I E C E W I S E _ L I N E A R _ P L A S T I C I T Y $ A M A T 0 0 5 7 $ M I D R O E P R S I G Y E T A N F A I L T D E L 577.8500E-09 200000.0 0.30 215.0 0.05.0000E+08 0.0 $ C P L C S S L C S R V P 0.0 0.0 0.0 0.0 0.0 $ EPS1 EPS2 EPS3 EPS4 EPS5 EPS6 EPS7 EPS8 0.0 0.0040 0.030 0.15 0.30 0.40 0.0 0.0 $ E S I ES2 ES3 ES4 ES5 ES6 ES7 ES8 215.0 300.0 390.0 440.0 460.0 400.0 0.0 0.0 * M A T _ P I E C E W I S E _ L I N E A R _ P L A S T I C I T Y $ A M A T 0 0 5 8 $ M I D R O E P R S I G Y E T A N F A I L T D E L 587.8500E-09 200000.0 0.30 215.0 0.05.0000E+08 0.0 $ C P L C S S L C S R V P 0.0 0.0 0.0 0.0 0.0 $ EPS1 EPS2 EPS3 EPS4 EPS5 EPS6 EPS7 EPS8 0.0 0.0040 0.030 0.15 0.30 0.40 0.0 0.0 $ E S I ES2 ES3 ES4 ES5 ES6 ES7 ES8 215.0 300.0 390.0 440.0 460.0 400.0 0.0 0.0 * M A T _ P I E C E W I S E _ L I N E A R _ P L A S T I C I T Y $ A M A T 0 0 5 9 $ M I D R O E P R S I G Y E T A N F A I L T D E L 597.8500E-09 200000.0 0.30 215.0 0.05.0000E+08 0.0 $ C P L C S S L C S R V P 0.0 0.0 0.0 0.0 0.0 -208 -$ EPS1 EPS2 EPS3 EPS4 EPS5 EPS6 EPS7 EPS8 0.0 0.0040 0.030 0.15 0.30 0.40 0.0 0.0 $ E S I ES2 ES3 ES4 ES5 ES6 ES7 ES8 215.0 300.0 390.0 440.0 460.0 400.0 0.0 0.0 * M A T _ P I E C E W I S E _ L I N E A R _ P L A S T I C I T Y $ A M A T 0 0 6 0 $ M I D R O E P R S I G Y E T A N F A I L T D E L 607.8500E-09 200000.0 0.30 215.0 0.05.0000E+08 0.0 $ C P L C S S L C S R V P 0.0 0.0 0.0 0.0 0.0 $ EPS1 EPS2 EPS3 EPS4 EPS5 EPS6 EPS7 EPS8 0.0 0.0040 0.030 0.15 0.30 0.40 0.0 0.0 $ E S I ES2 ES3 ES4 ES5 ES6 ES7 ES8 215.0 300.0 390.0 440.0 460.0 400.0 0.0 0.0 * M A T _ P I E C E W I S E _ L I N E A R _ P L A S T I C I T Y $ A M A T 0 0 6 1 $ M I D R O E P R S I G Y E T A N F A I L T D E L 617.8500E-09 200000.0 0.30 215.0 0.05.0000E+08 0.0 $ C P L C S S L C S R V P 0.0 0.0 0.0 0.0 0.0 $ EPS1 EPS2 EPS3 EPS4 EPS5 EPS6 EPS7 EPS8 0.0 0.0040 0.030 0.15 0.30 0.40 0.0 0.0 $ ESI ES2 ES3 ES4 ES5 ES6 ES7 ES8 215.0 300.0 390.0 440.0 460.0 400.0 0.0 0.0 * M A T _ P I E C E W I S E _ L I N E A R _ P L A S T I C I T Y $ A M A T 0 0 6 2 $ M I D R O E P R S I G Y E T A N F A I L T D E L 627.8500E-09 200000.0 0.30 215.0 0.05.0000E+08 0.0 $ C P L C S S L C S R V P 0.0 0.0 0.0 0.0 0.0 $ EPS1 EPS2 EPS3 EPS.4 EPS5 EPS6 EPS7 EPS8 0.0 0.0040 0.030 0.15 0.30 0.40 0.0 0.0 $ E S I ES2 ES3 ES4 ES5 ES6 ES7 ES8 215.0 300.0 390.0 440.0 460.0 400.0 0.0 0.0 * M A T _ P I E C E W I S E _ L I N E A R _ P L A S T I C I T Y $ A M A T 0 0 6 3 $ M I D R O E P R S I G Y E T A N F A I L T D E L 637.8500E-09 200000.0 0.30 215.0 0.05.0000E+08 0.0 $ C P L C S S L C S R V P 0.0 0.0 0.0 0.0 0.0 $ EPS1 EPS2 EPS3 EPS4 EPS5 EPS6 EPS7 EPS8 0.0 0.0040 0.030 0.15 0.30 0.40 0.0 0.0 $ E S I ES2 ES3 ES4 ES5 ES6 ES7 ES8 215.0 300.0 390.0 440.0 460.0 400.0 0.0 0.0 * M A T _ P I E C E W I S E _ L I N E A R _ P L A S T I C I T Y $ A M A T 0 0 6 4 - 2 0 9 -$ M I D R O E P R S I G Y E T A N F A I L T D E L 647.8500E-09 200000.0 0.30 215.0 0.05.0000E+08 0.0 $ C P L C S S L C S R V P 0.0 0.0 0.0 0.0 0.0 $ EPS1 EPS2 EPS3 EPS4 EPS5 EPS6 EPS7 EPS8 0.0 0.0040 0.030 0.15 0.30 0.40 0.0 0.0 $ E S I ES2 ES3 ES4 ES5 ES6 ES7 ES8 215.0 300.0 390.0 440.0 460.0 400.0 0.0 0.0 * M A T _ P I E C E W I S E _ L I N E A R _ P L A S T I C I T Y $ A M A T 0 0 6 5 $ M I D R O E P R S I G Y E T A N F A I L T D E L 657.8500E-09 200000.0 0.30 215.0 0.05.0000E+08 0.0 $ C P L C S S L C S R V P 0.0 0.0 0.0 0.0 0.0 $ EPS1 EPS2 EPS3 EPS4 EPS5 EPS6 EPS7 EPS8 0.0 0.0040 0.030 0.15 0.30 0.40 0.0 0.0 $ E S I ES2 ES3 ES4 ES5 ES6 ES7 ES8 215.0 300.0 390.0 440.0 460.0 400.0 0.0 0.0 * M A T _ P I E C E W I S E _ L I N E A R _ P L A S T I C I T Y $ A M A T 0 0 6 6 $ M I D R O E P R S I G Y E T A N F A I L T D E L 667.8500E-09 200000.0 0.30 215.0 0.05.0000E+08 0.0 $ C P L C S S L C S R V P 0.0 0.0 0.0 0.0 0.0 $ EPS1 EPS2 EPS3 EPS4 EPS5 EPS6 EPS7 EPS 8 0.0 0.0040 0.030 0.15 0.30 0.40 0.0 0.0 $ E S I ES2 ES3 ES4 ES5 ES6 ES7 ES8 215.0 300.0 390.0 440.0 460.0 400.0 0.0 0.0 * M A T _ P I E C E W I S E _ L I N E A R _ P L A S T I C I T Y $ A M A T 0 0 6 7 $ M I D R O E P R S I G Y E T A N F A I L T D E L 677.8500E-09 200000.0 0.30 215.0 0.05.0000E+08 0.0 $ C P L C S S L C S R V P 0.0 0.0 0.0 0.0 0.0 $ EPS1 EPS2 EPS3 EPS4 EPS5 EPS6 EPS7 EPS8 0.0 0.0040 0.030 0.15 0.30 0.40 0.0 0.0 $ ESI ES2 ES3 ES4 ES5 ES6 ES7 ES8 215.0 300.0 390.0 440.0 460.0 400.0 0.0 0.0 * M A T _ P I E C E W I S E _ L I N E A R _ P L A S T I C I T Y $ A M A T 0 0 6 8 $ M I D R O E P R S I G Y E T A N F A I L T D E L 687.8500E-09 200000.0 0.30 215.0 0.05.0000E+08 0.0 $ C P L C S S L C S R V P 0.0 0.0 0.0 0.0 0.0 $ EPS1 EPS2 EPS3 EPS4 EPS5 EPS6 EPS7 EPS8 0.0 0.0040 0.030 0.15 0.30 0.40 0.0 0.0 - 2 1 0 -$ E S I ES2 ES3 ES4 ES5 ES6 ES7 ES8 215.0 300.0 390.0 440.0 460.0 400.0 0.0 0.0 * M A T _ P I E C E W I S E _ L I N E A R _ P L A S T I C I T Y $ A M A T 0 0 6 9 $ M I D R O E P R S I G Y E T A N F A I L T D E L 697.8500E-09 200000.0 0.30 215.0 0.05.0000E+08 0.0 $ C P L C S S L C S R V P 0.0 0.0 0.0 0.0 0.0 $ EPS1 EPS2 EPS3 EPS4 EPS5 EPS6 EPS7 EPS8 0.0 0.0040 0.030 0.15 0.30 0.40 0.0 0.0 $ E S I ES2 ES3 ES4 ES5 ES6 ES7 ES8 215.0 300.0 390.0 440.0 460.0 400.0 0.0 0.0 * M A T _ P I E C E W I S E _ L I N E A R _ P L A S T I C I T Y $ A M A T 0 0 7 0 $ M I D R O E P R S I G Y E T A N F A I L T D E L 707.8500E-09 200000.0 0.30 215.0 0.05.0000E+08 0.0 $ C P L C S S L C S R V P 0.0 0.0 0.0 0.0 0.0 $ EPS1 EPS2 EPS3 EPS4 EPS5 EPS6 EPS7 EPS8 0.0 0.0040 0.030 0.15 0.30 0.40 0.0 0.0 $ E S I ES2 ES3 ES4 ES5 ES6 ES7 ES8 215.0 300.0 390.0 440.0 460.0 400.0 0.0 0.0 * M A T _ P I E C E W I S E _ L I N E A R _ P L A S T I C I T Y $ A M A T 0 0 7 1 $ M I D R O E P R S I G Y E T A N F A I L T D E L 717.8500E-09 200000.0 0.30 215.0 0.05.0000E+08 0.0 $ C P L C S S L C S R V P 0.0 0.0 0.0 0.0 0.0 $ EPS1 EPS2 EPS3 EPS4 EPS5 EPS6 EPS7 EPS8 0.0 0.0040 0.030 0.15 0.30 0.40 0.0 0.0 $ ESI ES2 ES3 ES4 ES5 ES6 ES7 ES8 215.0 300.0 390.0 440.0 460.0 400.0 0.0 0.0 * M A T _ P I E C E W I S E _ L I N E A R _ P L A S T I C I T Y $ A M A T 0 0 7 2 $ M I D R O E P R S I G Y E T A N F A I L T D E L 727.8500E-09 200000.0 0.30 215.0 0.05.0000E+08 0.0 $ C P L C S S L C S R V P 0.0 0.0 0.0 0.0 0.0 $ EPS1 EPS2 EPS3 EPS4 EPS5 EPS6 EPS7 EPS 8 0.0 0.0040 0.030 0.15 0.30 0.40 0.0 0.0 $ E S I ES2 ES3 ES4 ES5 ES6 ES7 ES8 215.0 300.0 390.0 440.0 460.0 400.0 0.0 0.0 * M A T _ P I E C E W I S E _ L I N E A R _ P L A S T I C I T Y $ A M A T 0 0 7 3 $ M I D R O E P R S I G Y E T A N F A I L T D E L 737.8500E-09 200000.0 0.30 215.0 0.05.0000E+08 0.0 -211 -$ C P L C S S L C S R V P 0.0 0.0 0.0 0.0 0.0 $ EPS1 EPS2 EPS3 EPS4 EPS5 EPS6 EPS7 EPS8 0.0 0.0040 0.030 0.15 0.30 0.40 0.0 0.0 $ E S I ES2 ES3 ES4 ES5 ES6 ES7 ES8 215.0 300.0 390.0 440.0 460.0 400.0 0.0 0.0 * M A T _ P I E C E W I S E _ L I N E A R _ P L A S T I C I T Y $ A M A T 0 0 7 4 $ M I D R O E P R S I G Y E T A N F A I L T D E L 747.8500E-09 200000.0 0.30 215.0 0.05.0000E+08 0.0 $ C P L C S S L C S R V P 0.0 0.0 0.0 0.0 0.0 $ EPS1 EPS2 EPS3 EPS4 EPS5 EPS6 EPS7 EPS8 0.0 0.0040 0.030 0.15 0.30 0.40 0.0 0.0 $ E S I ES2 ES3 ES4 ES5 ES6 ES7 ES8 215.0 300.0 390.0 440.0 460.0 400.0 0.0 0.0 * M A T _ P I E C E W I S E _ L I N E A R _ P L A S T I C I T Y $ A M A T 0 0 7 5 $ M I D R O E P R S I G Y E T A N F A I L T D E L 757.8500E-09 200000.0 0.30 215.0 0.05.0000E+08 0.0 $ C P L C S S L C S R V P 0.0 0.0 0.0 0.0 0.0 $ EPS1 EPS2 EPS3 EPS4 EPS5 EPS6 EPS7 EPS8 0.0 0.0040 0.030 0.15 0.30 0.40 0.0 0.0 $ E S I ES2 ES3 ES4 ES5 ES6 ES7 ES8 215.0 300.0 390.0 440.0 460.0 400.0 0.0 0.0 * M A T _ P I E C E W I S E _ L I N E A R _ P L A S T I C I T Y $ A M A T 0 0 7 6 $ M I D R O E P R S I G Y E T A N F A I L T D E L 767.8500E-09 200000.0 0.30 215.0 0.05.0000E+08 0.0 $ C P L C S S L C S R V P 0.0 0.0 0.0 0.0 0.0 $ EPS1 EPS2 EPS3 EPS4 EPS5 EPS6 EPS7 EPS8 0.0 0.0040 0.030 0.15 0.30 0.40 0.0 0.0 $ E S I ES2 ES3 ES4 ES5 ES6 ES7 ES8 215.0 300.0 390.0 440.0 460.0 400.0 0.0 0.0 * M A T _ P I E C E W I S E _ L I N E A R _ P L A S T I C I T Y $ A M A T 0 0 7 7 $ M I D R O E P R S I G Y E T A N F A I L T D E L 772.5000E-09 76000.0 0.30 138.0 0.0 0.00050 0.0 $ C P L C S S L C S R V P 0.0 0.0 0.0 0.0 0.0 $ EPS1 EPS2 EPS3 EPS4 EPS5 EPS6 EPS7 EPS8 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 $ E S I ES2 ES3 ES4 ES5 ES6 ES7 ES8 138.0 138.0 138.0 0.0 0.0 0.0 0.0 0.0 - 2 1 2 -* M A T _ P I E C E W I S E _ L I N E A R _ P L A S T I C I T Y $ A M A T 0 0 7 8 $ M I D R O E P R S I G Y E T A N F A I L T D E L 782.5000E-09 76000.0 0.30 138.0 0.0 0.00050 0.0 $ C P L C S S L C S R V P 0.0 0.0 0.0 0.0 0.0 $ EPS1 EPS2 EPS3 EPS4 EPS5 EPS6 EPS7 EPS8 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 $ E S I ES2 ES3 ES4 ES5 ES6 ES7 ES8 138.0 138.0 138.0 0.0 0.0 0.0 0.0 0.0 * M A T _ P I E C E W I S E _ L I N E A R _ P L A S T I C I T Y $ A M A T 0 0 7 9 $ M I D R O E P R S I G Y E T A N F A I L T D E L 797.8500E-09 200000.0 0.30 215.0 0.05.0000E+08 0.0 $ C P L C S S L C S R V P 0.0 0.0 0.0 0.0 0.0 $ EPS1 EPS2 EPS3 EPS4 EPS5 EPS6 EPS7 EPS8 0.0 0.0040 0.030 0.15 0.30 0.40 0.0 0.0 $ E S I ES2 ES3 ES4 ES5 ES6 ES7 ES8 215.0 300.0 390.0 440.0 460.0 400.0 0.0 0.0 * M A T _ P I E C E W I S E _ L I N E A R _ P L A S T I C I T Y $ A M A T 0 0 8 0 $ M I D R O E P R S I G Y E T A N F A I L T D E L 807.8500E-09 200000.0 0.30 215.0 0.05.0000E+08 0.0 $ C P L C S S L C S R V P 0.0 0.0 0.0 0.0 0.0 $ EPS1 EPS2 EPS3 EPS4 EPS5 EPS6 EPS7 EPS8 0.0 0.0040 0.030 0.15 0.30 0.40 0.0 0.0 $ E S I ES2 ES3 ES4 ES5 ES6 ES7 ES8 215.0 300.0 390.0 440.0 460.0 400.0 0.0 0.0 * M A T _ P I E C E W I S E _ L I N E A R _ P L A S T I C I T Y $ A M A T 0 0 8 1 $ M I D R O E P R S I G Y E T A N F A I L T D E L 817.8500E-09 200000.0 0.30 215.0 0.05.0000E+08 0.0 $ C P L C S S L C S R V P 0.0 0.0 0.0 0.0 0.0 $ EPS1 EPS2 EPS3 EPS4 EPS5 EPS6 EPS7 EPS8 0.0 0.0040 0.030 0.15 0.30 0.40 0.0 0.0 $ E S I ES2 ES3 ES4 ES5 ES6 ES7 ES8 215.0 300.0 390.0 440.0 460.0 400.0 0.0 0.0 * M A T _ P I E C E W I S E _ L I N E A R _ P L A S T I C I T Y $ A M A T 0 0 8 2 $ M I D R O E P R S I G Y E T A N F A I L T D E L 827;8500E-09 200000.0 0.30 215.0 0.05.0000E+08 0.0 $ C P L C S S L C S R V P 0.0 0.0 0.0 0.0 0.0 -213 -$ EPS1 EPS2 EPS3 EPS4 EPS5 EPS6 EPS7 EPS8 0.0 0.0040 0.030 0.15 0.30 0.40 0.0 0.0 $ ESI ES2 ES3 ES4 ES5 ES6 ES7 ES8 215.0 300.0 390.0 440.0 460.0 400.0 0.0 0.0 * M A T _ P I E C E W I S E _ L I N E A R _ P L A S T I C I T Y $ A M A T 0 0 8 3 $ M I D R O E P R S I G Y E T A N F A I L T D E L 837.8500E-09 200000.0 0.30 215.0 0.05.0000E+08 0.0 $ C P L C S S L C S R V P 0.0 0.0 0.0 0.0 0.0 $ EPS1 EPS2 EPS3 EPS4 EPS5 EPS6 EPS7 EPS8 0.0 0.0040 0.030 0.15 0.30 0.40 0.0 0.0 $ ESI ES2 ES3 ES4 ES5 ES6 ES7 ES8 215.0 300.0 390.0 440.0 460.0 400.0 0.0 0.0 * M A T _ P I E C E W I S E _ L I N E A R _ P L A S T I C I T Y $ A M A T 0 0 8 4 $ M I D R O E P R S I G Y E T A N F A I L T D E L 847.8500E-09 200000.0 0.30 215.0 0.05.0000E+08 0.0 $ C P L C S S L C S R V P 0.0 0.0 0.0 0.0 0.0 $ EPS1 EPS2 EPS3 EPS4 EPS5 EPS6 EPS7 EPS 8 0.0 0.0040 0.030 0.15 0.30 0.40 0.0 0.0 $ E S I ES2 ES3 ES4 ES5 ES6 ES7 ES8 215.0 300.0 390.0 440.0 460.0 400.0 0.0 0.0 * M A T _ E L A S T I C $ A M A T 0 0 8 5 $ M I D R O E P R D A D B 857.8500E-09 200000.0 0.30 0.0 0.0 * M A T _ P I E C E W I S E _ L I N E A R _ P L A S T I C I T Y $ A M A T 0 0 8 6 $ M I D R O E P R S I G Y E T A N F A I L T D E L 867.8500E-09 200000.0 0.30 215.0 0.05.0000E+08 0.0 $ C P L C S S L C S R V P 0.0 0.0 0.0 0.0 0.0 $ EPS1 EPS2 EPS3 EPS4 EPS5 EPS6 EPS7 EPS8 0.0 0.0040 0.030 0.15 0.30 0.40 0.0 0.0 $ E S I ES2 ES3 ES4 ES5 ES6 ES7 ES8 215.0 300.0 390.0 440.0 460.0 400.0 0.0 0.0 * M A T _ P I E C E W I S E _ L I N E A R _ P L A S T I C I T Y $ A M A T 0 0 8 7 $ M I D R O E P R S I G Y E T A N F A I L T D E L 877.8500E-09 200000.0 0.30 215.0 0.05.0000E+08 0.0 $ C P L C S S L C S R V P 0.0 0.0 0.0 0.0 0.0 $ EPS1 EPS2 EPS3 EPS4 EPS5 EPS6 EPS7 EPS8 0.0 0.0040 0.030 0.15 0.30 0.40 0.0 0.0 - 2 1 4 -$ ESI ES2 ES3 ES4 ES5 ES6 ES7 ES8 215.0 300.0 390.0 440.0 460.0 400.0 0.0 0.0 * M A T _ P I E C E W I S E _ L I N E A R _ P L A S T I C I T Y $ A M A T 0 0 8 8 $ M I D R O E P R S I G Y E T A N F A I L T D E L 887.8500E-09 200000.0 0.30 215.0 0.05.0000E+08 0.0 $ C P L C S S L C S R V P 0.0 0.0 0.0 0.0 0.0 $ EPS1 EPS2 EPS3 EPS4 EPS5 EPS6 EPS7 EPS8 0.0 0.0040 0.030 0.15 0.30 0.40 0.0 0.0 $ ESI ES2 ES3 ES4 ES5 ES6 ES7 ES8 215.0 300.0 390.0 440.0 460.0 400.0 0.0 0.0 * M A T _ P I E C E W I S E _ L I N E A R _ P L A S T I C I T Y $ A M A T 0 0 8 9 $ M I D R O E P R S I G Y E T A N F A I L T D E L 896.6620E-08 200000.0 0.30 215.0 0.05.0000E+08 0.0 $ C P L C S S L C S R V P 0.0 0.0 0.0 0.0 0.0 $ EPS1 EPS2 EPS3 EPS4 EPS5 EPS6 EPS7 EPS8 0.0 0.0040 0.030 0.15 0.30 0.40 0.0 0.0 $ E S I ES2 ES3 ES4 ES5 ES6 ES7 ES8 215.0 300.0 390.0 440.0 460.0 400.0 0.0 0.0 * M A T _ E L A S T I C $ A M A T 0 0 9 0 $ M I D R O E P R D A D B 907.8500E-09 200000.0 0.30 0.0 0.0 * M A T _ E L A S T I C $ A M A T 0 0 9 1 $ M I D R O E P R D A D B 917.8500E-09 200000.0 0.30 0.0 0.0 * M A T _ E L A S T I C $ A M A T 0 0 9 2 $ M I D R O E P R D A D B 927.8500E-09 200000.0 0.30 0.0 0.0 * M A T _ E L A S T I C $ A M A T 0 0 9 3 $ M I D R O E P R D A D B 937.8500E-09 200000.0 0.30 0.0 0.0 * M A T _ E L A S T I C $ A M A T 0 0 9 4 $ M I D R O E P R D A D B 947.8500E-09 200000.0 0.30 0.0 0.0 * M A T _ E L A S T I C $ A M A T 0 0 9 5 $ M I D R O E P R D A D B 957.8500E-09 200000.0 0.30 0.0 0.0 -215 -* M A T _ E L A S T I C $ A M A T 0 0 9 6 $ M I D R O E P R D A D B 967.8500E-09 200000.0 0.30 0.0 0.0 * M A T _ E L A S T I C $ A M A T 0 0 9 7 $ M I D R O E P R D A D B 977.8500E-09 200000.0 0.30 0.0 0.0 * M A T _ E L A S T I C $ A M A T 0 0 9 8 $ M I D R O E P R D A D B 987.8500E-09 200000.0 0.30 0.0 0.0 * M A T _ E L A S T I C $ A M A T 0 0 9 9 $ M I D R O E P R D A D B 997.8500E-09 2000000.0 0.30 0.0 0.0 * M A T _ E L A S T I C $ A M A T 0 1 0 0 $ M I D R O E P R D A D B 1007.8500E-09 200000.0 0.30 0.0 0.0 * M A T _ E L A S T I C $ A M A T 0 1 0 1 $ M I D R O E P R D A D B T017.8500E-09 2000000.0 0.30 0.0 0.0 * M A T _ E L A S T I C $ A M A T 0 1 0 2 $ M I D R O E P R D A D B 1027.8500E-09 2000000.0 0.30 0.0 0.0 * M A T _ E L A S T I C $ A M A T 0 1 0 3 $ M I D R O E P R D A D B 1037.8500E-09 200000.0 0.30 0.0 0.0 * M A T _ P I E C E W I S E _ L I N E A R _ P L A S T I C I T Y $ A M A T 0 1 0 4 $ M I D R O E P R S I G Y E T A N F A I L T D E L 1047.8500E-09 200000.0 0.30 215.0 0.05.0000E+08 0.0 $ C P L C S S L C S R V P 0.0 0.0 0.0 0.0 0.0 $ EPS1 EPS2 EPS3 EPS4 EPS5 EPS6 EPS7 EPS8 0.0 0.0040 0.030 0.15 0.30 0.40 0.0 0.0 $ E S I ES2 ES3 ES4 ES5 ES6 ES7 ES8 215.0 300.0 390.0 440.0 460.0 400.0 0.0 0.0 * M A T _ E L A S T I C $ A M A T 0 1 0 5 $ M I D R O E P R D A D B 1057.8500E-09 200000.0 0.30 0.0 0.0 - 2 1 6 -* M A T _ P I E C E W I S E _ L I N E A R _ P L A S T I C I T Y $ A M A T 0 1 0 6 $ M I D R O E P R S I G Y E T A N F A I L T D E L 1061.0600E-09 2462.0 0.323 24.77 0.05.0000E+08 0.0 $ C P L C S S L C S R V P 0.0 0.0 0.0 0.0 0.0 $ EPS1 EPS2 EPS3 EPS4 EPS5 EPS6 EPS7 EPS8 0.0 0.029 0.070 0.40 0.0 0.0 0.0 0.0 $ E S I ES2 ES3 ES4 ES5 ES6 ES7 ES8 24.77 29.9 32.91 35.91 0.0 0.0 0.0 0.0 * M A T _ P I E C E W I S E _ L I N E A R _ P L A S T I C I T Y $ A M A T 0 1 0 7 $ M I D R O E P R S I G Y E T A N F A I L T D E L 1077.8500E-09 200000.0 0.30 215.0 0.05.0000E+08 0.0 $ C P L C S S L C S R V P 0.0 0.0 0.0 0.0 0.0 $ EPS1 EPS2 EPS3 EPS4 EPS5 EPS6 EPS7 EPS 8 0.0 0.0040 0.030 0.15 0.30 0.40 0.0 0.0 $ ESI ES2 ES3 ES4 ES5 ES6 ES7 ES8 215.0 300.0 390.0 440.0 460.0 400.0 0.0 0.0 * M A T _ P I E C E W I S E _ L I N E A R _ P L A S T I C I T Y $ A M A T 0 1 0 8 $ M I D R O E P R S I G Y E T A N F A I L T D E L 1087.8500E-09 200000.0 0.30 215.0 0.05.0000E+08 0.0 $ C P L C S S L C S R V P 0.0 0.0 0.0 0.0 0.0 $ EPS1 EPS2 EPS3 EPS4 EPS5 EPS6 EPS7 EPS8 0.0 0.0040 0.030 0.15 0.30 0.40 0.0 0.0 $ E S I ES2 ES3 ES4 ES5 ES6 ES7 ES8 215.0 300.0 390.0 440.0 460.0 400.0 0.0 0.0 * M A T _ P I E C E W I S E _ L I N E A R _ P L A S T I C I T Y $ A M A T 0 1 0 9 $ M I D R O E P R S I G Y E T A N F A I L T D E L 1097.8500E-09 200000.0 0.30 215.0 0.05.0000E+08 0.0 $ C P L C S S L C S R V P 0.0 0.0 0.0 0.0 0.0 $ EPS1 EPS2 EPS3 EPS4 EPS5 EPS6 EPS7 EPS8 0.0 0.0040 0.030 0.15 0.30 0.40 0.0 0.0 $ E S I ES2 ES3 ES4 ES5 ES6 ES7 ES8 215.0 300.0 390.0 440.0 460.0 400.0 0.0 0.0 * M A T _ P I E C E W I S E _ L I N E A R _ P L A S T I C I T Y $ A M A T 0 1 1 0 $ M I D R O E P R S I G Y E T A N F A I L T D E L 1107.8500E-09 200000.0 0.30 215.0 0.05.0000E+08 0.0 $ C P L C S S L C S R V P 0.0 0.0 0.0 0.0 0.0 - 2 1 7 -$ EPS1 EPS2 EPS3 EPS4 EPS5 EPS6 EPS7 EPS8 0.0 0.0040 0.030 0.15 0.30 0.40 0.0 0.0 $ ESI ES2 ES3 ES4 ES5 ES6 ES7 ES8 215.0 300.0 390.0 440.0 460.0 400.0 0.0 0.0 * M A T _ P I E C E W I S E _ L I N E A R _ P L A S T I C I T Y $ A M A T 0 1 1 1 $ M I D R O E P R S I G Y E T A N F A I L T D E L 1117.8500E-09 200000.0 0.30 215.0 0.05.0000E+08 0.0 $ C P L C S S L C S R V P 0.0 0.0 0.0 0.0 0.0 $ EPS1 EPS2 EPS3 EPS4 EPS5 EPS6 EPS7 EPS8 0.0 0.0040 0.030 0:15 0.30 0.40 0.0 0.0 $ ESI ES2 ES3 ES4 ES5 ES6 ES7 ES8 215.0 300.0 390.0 440.0 460.0 400.0 0.0 0.0 * M A T _ P I E C E W I S E _ L I N E A R _ P L A S T I C I T Y $ A M A T 0 1 1 2 $ M I D R O E P R S I G Y E T A N F A I L T D E L 1127.8500E-09 200000.0 0.30 215.0 0.05.0000E+08 0.0 $ C P L C S S L C S R V P 0.0 0.0 0.0 0.0 0.0 $ EPS1 EPS2 EPS3 EPS4 EPS5 EPS6 EPS7 EPS8 0.0 0.0040 0.030 0.15 0.30 0.40 0.0 0.0 $ E S I ES2 ES3 ES4 ES5 ES6 ES7 ES8 215.0 300.0 390.0 440.0 460.0 400.0 0.0 0.0 * M A T _ P I E C E W I S E _ L I N E A R _ P L A S T I C I T Y $ A M A T 0 1 1 3 $ M I D R O E P R S I G Y E T A N F A I L T D E L 1137.8500E-09 200000.0 0.30 215.0 0.05.0000E+08 0.0 $ C P L C S S L C S R V P 0.0 0.0 0.0 0.0 ' 0.0 $ EPS1 EPS2 EPS3 EPS4 EPS5 EPS6 EPS7 EPS8 0.0 0.0040 0.030 0.15 0.30 0.40 0.0 0.0 $ E S I ES2 ES3 ES4 ES5 ES6 ES7 ES8 215.0 300.0 390.0 440.0 460.0 400.0 0.0 0.0 * M A T _ E L A S T I C $ A M A T 0 1 1 4 $ M I D R O E P R D A D B 1147.8500E-09 2000000.0 0.30 0.0 0.0 * M A T _ P I E C E W I S E _ L I N E A R _ P L A S T I C I T Y $ A M A T 0 1 1 5 $ M I D R O E P R S I G Y E T A N F A I L T D E L 1157.8500E-09 200000.0 0.30 215.0 0.05.0000E+08 0.0 $ C P L C S S L C S R V P 0.0 0.0 0.0 0.0 0.0 $ EPS1 EPS2 EPS3 EPS4 EPS5 EPS6 EPS7 EPS8 0.0 0.0040 0.030 0.15 0.30 0.40 0.0 0.0 -218 -$ E S I ES2 ES3 ES4 ES5 ES6 ES7 ES8 215.0 300.0 390.0 440.0 460.0 400.0 0.0 0.0 * M A T _ P I E C E W I S E _ L I N E A R _ P L A S T I C I T Y $ A M A T 0 1 1 6 $ M I D R O E P R S I G Y E T A N F A I L T D E L 1167.8500E-09 200000.0 0.30 215.0 0.05.0000E+08 0.0 $ C P L C S S L C S R V P 0.0 0.0 0.0 0.0 0.0 $ EPS1 EPS2 EPS3 EPS4 EPS5 EPS6 EPS7 EPS8 0.0 0.0040 0.030 0.15 0.30 0.40 0.0 0.0 $ E S I ES2 ES3 ES4 ES5 ES6 ES7 ES8 215.0 300.0 390.0 440.0 460.0 400.0 0.0 0.0 * M A T _ E L A S T I C $ A M A T 0 1 1 7 $ M I D R O E P R D A D B 1177.8500E-09 2000000.0 0.30 0.0 0.0 * M A T _ P I E C E W I S E _ L I N E A R _ P L A S T I C I T Y $ A M A T 0 1 1 8 $ M I D R O E P R S I G Y E T A N F A I L T D E L 1187.6830E-08 2000000.0 0.30 215.0 0.05.0000E+08 0.0 $ C P L C S S L C S R V P 0.0 0.0 0.0 0.0 0.0 $ EPS1 EPS2 EPS3 EPS4 EPS5 EPS6 EPS7 EPS 8 0.0 0.0040 0.030 0.15 0.30 0.40 0.0 0.0 $ E S I ES2 ES3 ES4 ES5 ES6 ES7 ES8 215.0 300.0 390.0 440.0 460.0 400.0 0.0 0.0 * M A T _ P I E C E W I S E _ L I N E A R _ P L A S T I C I T Y $ A M A T 0 1 1 9 $ M I D R O E P R S I G Y E T A N F A I L T D E L 1197.8500E-09 200000.0 0.30 215.0 0.05.0000E+08 0.0 $ C P L C S S L C S R V P 0.0 0.0 0.0 0.0 0.0 $ EPS1 EPS2 EPS3 EPS4 EPS5 EPS6 EPS7 EPS8 0.0 0.0040 0.030 0.15 0.30 0.40 0.0 0.0 $ E S I ES2 ES3 ES4 ES5 ES6 ES7 ES8 215.0 300.0 390.0 440.0 460.0 400.0 0.0 0.0 * M A T _ P I E C E W I S E _ L I N E A R _ P L A S T I C I T Y $ A M A T 0 1 2 0 $ M I D R O E P R S I G Y E T A N F A I L T D E L 1207.8500E-09 200000.0 0.30 215.0 0.05.0000E+08 0.0 $ C P L C S S L C S R V P 0.0 0.0 0.0 0.0 0.0 $ EPS1 EPS2 EPS3 EPS4 EPS5 EPS6 EPS7 EPS8 0.0 0.0040 0.030 0.15 0.30 0.40 0.0 0.0 $ E S I ES2 ES3 ES4 ES5 ES6 ES7 ES8 215.0 300.0 390.0 440.0 460.0 400.0 0.0 0.0 - 2 1 9 -* M A T _ P I E C E W I S E _ L I N E A R _ P L A S T I C I T Y $ A M A T 0 1 2 1 $ M I D R O E P R S I G Y E T A N F A I L T D E L 1217.8500E-09 200000.0 0.30 215.0 0.05.0000E+08 0.0 $ C P L C S S L C S R V P 0.0 0.0 0.0 0.0 0.0 $ EPS1 EPS2 EPS3 EPS4 EPS5 EPS6 EPS7 EPS 8 0.0. 0.0040 0.030 0.15 0.30 0.40 0.0 0.0 $ ESI ES2 ES3 ES4 ES5 ES6 ES7 ES8 215.0 300.0 390.0 440.0 460.0 400.0 0.0 0.0 * M A T _ P I E C E W I S E _ L I N E A R _ P L A S T I C I T Y $ A M A T 0 1 2 2 $ M I D R O E P R S I G Y E T A N F A I L T D E L 1227.8500E-09 200000.0 0.30 215.0 0.05.0000E+08 0.0 $ C P L C S S L C S R V P 0.0 0.0 0.0 0.0 0.0 $ EPS1 EPS2 EPS3 EPS4 EPS5 EPS6 EPS7 EPS 8 0.0 0.0040 0.030 0.15 0.30 0.40 0.0 0.0 $ E S I ES2 ES3 ES4 ES5 ES6 ES7 ES8 215.0 300.0 390.0 440.0 460.0 400.0 0.0 0.0 * M A T H O N E Y C O M B $ A M A T 0 1 2 3 $ M I D R O E P R S I G Y V F M U B U L K 1231.4750E-10 2070.0 0.0 140.0 0.20 0.0 0.0 L C A L C B L C C L C S L C A B L C B C L C C A L C S R $ $ 3.0 3.0 3.0 E A A U E B B U 3.0 E C C U 2.1 A l 0.0 T S E F 0.0 0.0 0.0 G A B U G B C U 2.1 2.1 0.0 A 2 A3 0.0 0.0 SSEF 0.0 G C A U A O P T 20.7 20.7 20.7 $ X P Y P ZP 0.0 0.0 0.0 $ D l D2 D3 0.0 0.0 0.0 0.0 0.0 * M A T _ E L A S T I C $ A M A T 0 1 2 4 $ M I D R O E P R D A D B 1247.8480E-09 200000.0 0.30 0.0 0.0 * M A T _ R I G I D $ A M A T 0 1 2 5 $ M I D R O E P R N C O U P L E 1267.8890E-10 200000.0 0.30 0.0 0.0 $ C M O C O N 1 C O N 2 0.0 0.0 M 0.0 A L I A S 0.0 $ L C O _ O R _ A l 0.0 0.0 * M A T _ R I G I D $ A M A T 0 1 2 6 A 2 0.0 . A 3 0.0 V I 0.0 V 2 V 3 0.0 - 2 2 0 -$ M I D R O E P R N 1277.8890E-10 200000.0 0.30 $ C M O C O N 1 C O N 2 0.0 0.0 A 2 A 3 0.0 0.0 C O U P L E M 0.0 0.0 0.0 V I 0.0 $ L C O _ O R _ A l 0.0 0.0 * M A T _ R I G I D $ A M A T 0 1 2 7 $ M I D R O E P R N 1287.8890E-10 200000.0 0.30 $ C M O CON1 C O N 2 0.0 0.0 A 2 A 3 0.0 0.0 V 2 V 3 V I 0.0 $ L C O _ O R _ A l 0.0 0.0 * M A T _ R I G I D $ A M A T 0 1 2 8 $ M I D R O E P R N 1297.8890E-10 200000.0 0.30 $ C M O C O N 1 C O N 2 0.0 0.0 A 2 A 3 0.0 0.0 V I 0.0 A 3 0.0 V I 0.0 V I 0.0 V 2 V 3 $ L C O _ O R _ A l 0.0 0.0 * M A T _ R I G I D $ A M A T 0 1 2 9 $ M I D R O E P R N 1307.8890E-10 200000.0 0.30 $ C M O CON1 C O N 2 0.0 0.0 A 2 0.0 $ L C O _ O R _ A l 0.0 0.0 * M A T _ R I G I D $ A M A T 0 1 3 0 $ M I D R O E P R N 1317.8890E-10 200000.0 0.30 $ C M O CON1 C O N 2 0.0 0.0 A 2 A 3 0.0 0.0 V 2 V 3 $ L C O _ O R _ A l 0.0 0.0 * M A T _ R I G I D $ A M A T 0 1 3 1 $ M I D R O E P R N 1327.8890E-10 200000.0 0.30 $ C M O C O N 1 C O N 2 0.0 0.0 $ L C O _ O R _ A l A 2 A 3 V I 0.0 0.0 0.0 0.0 0.0 V 2 V 3 V 2 V 3 A L I A S 0.0 0.0 C O U P L E M 0.0 0.0 0.0 A L I A S 0.0 0.0 C O U P L E M 0.0 0.0 0.0 V 2 V 3 0.0 C O U P L E M 0.0 0.0 0.0 A L I A S 0.0 A L I A S 0.0 0.0 C O U P L E M 0.0 0.0 0.0 A L I A S 0.0 0.0 C O U P L E M 0.0 0.0 0.0 A L I A S 0.0 0.0 -221 -* M A T _ R I G I D $ A M A T 0 1 3 2 $ M I D R O E P R N C O U P L E M A L I A S 1337:8890E-10 200000.0 0.30 0.0 0.0 0.0 0.0 $ C M O CON1 C O N 2 0.0 0.0 $ L C O _ O R _ A l A 2 A 3 V I V 2 V 3 0.0 0.0 0.0 0.0 0.0 0.0 * M A T _ P I E C E W I S E _ L I N E A R _ P L A S T I C I T Y $ A M A T 0 1 3 3 $ M I D R O E P R S I G Y E T A N F A I L T D E L 2002.8700E-09 69000.0 0.33 145.0 0.0 0.12 0.0 $ C P L C S S L C S R V P 0.0 0.0 0.0 0.0 0.0 $ EPS1 EPS2 EPS3 EPS4 EPS5 EPS6 EPS7 EPS 8 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 $ E S I ES2 ES3 ES4 ES5 ES6 ES7 ES8 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 * M A T _ P I E C E W I S E _ L I N E A R _ P L A S T I C I T Y $ A M A T 0 1 3 4 $ M I D R O E P R S I G Y E T A N F A I L T D E L 2147.8300E-09 207000.0 0.28 215.0 0.0 0.0 0.0 $ C P L C S S L C S R V P 0.0 0.0 0.0 0.0 0.0 $ EPS1 EPS2 EPS3 EPS4 EPS5 EPS6 EPS7 EPS8 0.0 0.0040 0.030 0.15 0.30 0.40 0.0 0.0 $ E S I ES2 ES3 ES4 ES5 ES6 ES7 ES8 215.0 300.0 390.0 440.0 460.0 400.0 0.0 0.0 * M A T _ S P R I N G _ G E N E R A L _ N O N L I N E A R $ A M A T 0 1 3 5 $ M I D L C D L L C D U B E T A T Y I C Y I 134 2 2 0.0 0.0 0.0 * M A T _ S P R I N G _ G E N E R A L _ N O N L I N E A R $ A M A T 0 1 3 6 $ M I D L C D L L C D U B E T A T Y I C Y I 213 213 213 0.050 0.0 0.0 * M A T _ S P R I N G _ G E N E R A L _ N O N L I N E A R $ A M A T 0 1 3 7 $ M I D L C D L L C D U B E T A T Y I C Y I 215 215 215 0.050 0.0 0.0 * M A T _ D A M P E R _ V I S C O U S $ A M A T 0 1 3 8 $ M I D D C 212 10.0 * M A T _ P I E C E W I S E _ L I N E A R _ P L A S T I C I T Y $ A U P P E R D O O R - 2 2 2 -$ M I D R O E P R S I G Y E T A N F A I L T D E L 6007.8500E-09 200000.0 0.30 215.0 0.05.0000E+08 0.0 $ C P L C S S L C S R V P 0.0 0.0 0.0 0.0 0.0 $ EPS1 EPS2 EPS3 EPS4 EPS5 EPS6 EPS7 EPS8 0.0 0.0040 0.030 0.15 0.30 0.40 0.0 0.0 $ E S I ES2 ES3 ES4 ES5 ES6 ES7 ES8 215.0 300.0 390.0 440.0 460.0 400.0 0.0 0.0 * M A T _ P I E C E W I S E _ L I N E A R _ P L A S T I C I T Y $ A L O W E R D O O R $ M I D R O E P R S I G Y E T A N F A I L T D E L 6017.8500E-09 200000.0 0.30 215.0 0.05.0000E+08 0.0 $ C P L C S S L C S R V P 0.0 0.0 0.0 0.0 0.0 $ EPS1 EPS2 EPS3 EPS4 EPS5 EPS6 EPS7 EPS 8 0.0 0.0040 0.030 0.15 0.30 0.40 0.0 0.0 $ E S I ES2 ES3 ES4 ES5 ES6 ES7 ES8 215.0 300.0 390.0 440.0 460.0 400.0 0.0 0.0 -223 -APPENDIX E . T H E SID M A T E R I A L PROPERTIES (LS-DYNA VERSION 970): This appendix contains the material property input fde for the US Side Impact Dummy model used in this research. The input data has been prepared for use in LS-Dyna version 970. * M A T _ R I G I D 1 7.79900-9 2.07300+5 0.3500000 0.0000000 0.0000000 0.0000000 1.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 * M A T _ R I G I D 2 7.80000-9 2.07300+5 0.3500000 0.0000000 0.0000000 0.0000000 1.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 * M A T _ R I G I D 3 7.80000-9 2.07300+5 0.3500000 0.0000000 0.0000000 0.0000000 1.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 * M A T _ M O O N E Y - R I V L I N _ R U B B E R 4 1.06800-9 0.4950000 0.1243000 0.6140000 0.0000000 0.0000000 0.0000000 0 * M A T _ R I G I D 5 2.67100-9 69110.000 0.3000000 0.0000000 0.0000000 0.0000000 1.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 * M A T _ R I G I D 6 2.68000-9 69110.000 0.3000000 0.0000000 0.0000000 0.0000000 1.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 * M A T _ E L A S T I C 7 1.38700-9 69.110001 0.3500000 * M A T _ R I G I D 8 7.94000-9 2.07300+5 0.3500000 0.0000000 0.0000000 0.0000000 1.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 * M A T _ R I G I D 9 7.94000-9 2.07300+5 0.3500000 0.0000000 0.0000000 0.0000000 1.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 * M A T _ R J G I D 10 1.01500-8 2.07300+5 0.3500000 0.0000000 0.0000000 0.0000000 1.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 0.0000000 * M A T _ R I G I D 11 1.01500-8 2.07300+5 0.3500000 0.0000000 0.0000000 0.0000000 - 2 2 4 -- szz-00001WI 000Z3££"0 0000S6F0 6-00890'! 6Z a^earra NiiAra-AHNOOW ivn* 0 OOOOOOO'O OOOOOOO'O OOOOOOO'O 00001WI 000ZZ££"0 0000S6fr'0 6-00890"l_8Z "aaeerra NiiAra-AHNOOiAi IVJAI* 0 OOOOOOO'O OOOOOOO'O OOOOOOO'O 0000H9'0 000£WI'0 0000£6fr'0 6-00890'T LZ xaeerra NiiAra-AHNOOH ivn* OOOOOSfr'O 6666698'C 6"00t769'I_93 3 I I S V 1 3 I V I M * 00000S£'0 S+00eZ,0'3 6-00008"Z,_S3 D I I S V 1 H I VIM* OOOOOSe'O S+00££0"3 6-00008'A_b3 3 I I S V 1 3 IVn* ooooooe'o ooooe'^ oz 6-oooos'i_oz ousvia ivn* OOOOOOO'O OOOOOOO'O OOOOOOO'O OOOOOOO'O OOOOOOO'O OOOOOOO'O OOOOOOO'O OOOOOOO'O OOOOOOO'O OOOOOOO'O 0000000'I OOOOOOO'O OOOOOOO'O OOOOOOO'O OOOOOSfr'O I000IT69 6-0068£'l_8I aiora ivn* OOOOOOO'O OOOOOOO'O OOOOOOO'O OOOOOOO'O OOOOOOO'O OOOOOOO'O OOOOOOO'O OOOOOOO'O OOOOOOO'O OOOOOOO'O 0000000'I OOOOOOO'O OOOOOOO'O OOOOOOO'O OOOOOSe'O 000'0c"8£I 8-0000£'l LI aiora ivn* OOOOOOO'O OOOOOOO'O OOOOOOO'O OOOOOOO'O OOOOOOO'O OOOOOOO'O OOOOOOO'O OOOOOOO'O OOOOOOO'O OOOOOOO'O 0000000'I OOOOOOO'O OOOOOOO'O OOOOOOO'O OOOOOSS'O S+00£Z,0"Z 6-00008"Z._9I aiora ivn* OOOOOOO'O OOOOOOO'O OOOOOOO'O OOOOOOO'O OOOOOOO'O OOOOOOO'O OOOOOOO'O OOOOOOO'O OOOOOOO'O OOOOOOO'O 0000000'I OOOOOOO'O OOOOOOO'O OOOOOOO'O 00000S£'0 000'038£I s-oooonji aiora ivn* OOOOOOO'O OOOOOOO'O OOOOOOO'O OOOOOOO'O OOOOOOO'O OOOOOOO'O OOOOOOO'O OOOOOOO'O OOOOOOO'O OOOOOOO'O 0000000'I OOOOOOO'O OOOOOOO'O OOOOOOO'O 00000££'0 000'038£I 8-0000£'I M aiora ivn* OOOOOOO'O OOOOOOO'O OOOOOOO'O OOOOOOO'O OOOOOOO'O OOOOOOO'O OOOOOOO'O OOOOOOO'O OOOOOOO'O OOOOOOO'O 0000000'I OOOOOOO'O OOOOOOO'O OOOOOOO'O 00000S£'0 000'038£l 8-0000£'I_£l aiora ivn* OOOOOOO'O OOOOOOO'O OOOOOOO'O OOOOOOO'O OOOOOOO'O OOOOOOO'O OOOOOOO'O OOOOOOO'O OOOOOOO'O OOOOOOO'O 0000000'I OOOOOOO'O OOOOOOO'O OOOOOOO'O 00000SO 000'0G"8£1 8-0080c"I_3l aiora ivn* OOOOOOO'O OOOOOOO'O OOOOOOO'O OOOOOOO'O OOOOOOO'O OOOOOOO'O OOOOOOO'O OOOOOOO'O OOOOOOO'O OOOOOOO'O OOOOOOO'l -9ZZ-OOOOOOO'O OOOOOOO'O 0000000" I OOOOOOO'O OOOOOOO'O OOOOOOO'O 000008l"0 S+OOOZ.0'3 6-008Z,Z/c"_9t> aiora ivn* OOOOOOO'O OOOOOOO'O OOOOOOO'O OOOOOOO'O OOOOOOO'O OOOOOOO'O OOOOOOO'O OOOOOOO'O OOOOOOO'O OOOOOOO'O OOOOOOO'I OOOOOOO'O OOOOOOO'O OOOOOOO'O 0000083'0 S+OOOZ.0'2 6-00SLLZ& aiora ivn* OOOOOOO'O OOOOOOO'O OOOOOOO'O OOOOOOO'O OOOOOOO'O OOOOOOO'O OOOOOOO'O OOOOOOO'O OOOOOOO'O OOOOOOO'O OOOOOOO'I OOOOOOO'O OOOOOOO'O OOOOOOO'O 000008l*'0 S+000Z,0'3 6-00SLLZp aiora ivn* OOOOOOO'O OOOOOOO'O OOOOOOO'O OOOOOOO'O OOOOOOO'O OOOOOOO'O OOOOOOO'O OOOOOOO'O OOOOOOO'O OOOOOOO'O 0000000' I OOOOOOO'O OOOOOOO'O OOOOOOO'O 0000083'0 S+000/.0'3 6-008Z,Z,T_£t7 aiora ivn* 000000£'0 £+000Z,0T 6 - 0 0 0 0 8 ' ^ DLLSVTH ivn* OOOOOOC'O 5+000Z,0T 6-00008"Z._Ifr D U S V T H ivn* OOOOOOO'O OOOOOOO'O OOOOOOO'O OOOOOOO'O OOOOOOO'O OOOOOOO'O OOOOOOO'O OOOOOOO'O OOOOOOO'O OOOOOOO'O OOOOOOO'I OOOOOOO'O OOOOOOO'O OOOOOOO'O 000008l"0 S+000/,0'3 8-00££rSj6£ aiora ivn* 00066^0 0000000'8 6-000£U_8£ Diisvia ivn* OOOOOOO'O OOOOOOO'O OOOOOOO'O OOOOOOO'O OOOOOOO'O OOOOOOO'O OOOOOOO'O OOOOOOO'O OOOOOOO'O OOOOOOO'O OOOOOOO'I ooooooo'o ooooooo'o ooooooo'o ooooo8ro g+oooz.0'3 8-oosers_9£ aiora ivn* 000000£'0 0000000'8 6 - 0 0 0 £ U J £ D L L S V I H ivn* OOOOOOO'O OOOOOOO'O OOOOOOO'O OOOOOOO'O OOOOOOO'O OOOOOOO'O OOOOOOO'O OOOOOOO'O OOOOOOO'O OOOOOOO'O. 0000000" I OOOOOOO'O 0000000"0 0000000"0 000008r0 S+000/.O'Z: 8"0000rrfr£ aiora ivn* OOOOOOO'O OOOOOOO'O OOOOOOO'O OOOOOOO'O OOOOOOO'O OOOOOOO'O OOOOOOO'O OOOOOOO'O OOOOOOO'O OOOOOOO'O OOOOOOO'I OOOOOOO'O OOOOOOO'O OOOOOOO'O 0000083'0 S+000Z,0T 8-00003'3_££ aiora ivn* OOOOOOO'O OOOOOOO'O OOOOOOO'O OOOOOOO'O 0000000"0 0000000"0 OOOOOOO'O OOOOOOO'O OOOOOOO'O OOOOOOO'O OOOOOOO'I OOOOOOO'O OOOOOOO'O OOOOOOO'O 0000083'0 S+000Z,0'3 6-00998'5_3£ aiora ivn* OOOOOSfr'O 0000000'8 6-000SI'I_0£ oiisvia ivn* 0 OOOOOOO'O OOOOOOO'O OOOOOOO'O - LZZ-OOOOOOO'O OOOOOOO'O OOOOOOO'I OOOOOOO'O OOOOOOO'O OOOOOOO'O OOOOOSfO 0000000'8 6-000Sl'l_39 aiora ivn* OOOOO^'O 6666698'£ 6-00*69'I_l 9 3IJLSV13 IVn* OOOOOOe'O 00000'003 OOOOOOO'O OOOOOOO'O OOOOOOO'O OOOOOOO'O 11-0000'1^)9 nriN ivn* OOOOOOO'O OOOOOOO'O OOOOOOO'O OOOOOOO'O OOOOOOO'O OOOOOOO'O OOOOOOO'O OOOOOOO'O OOOOOOO'O OOOOOOO'O OOOOOOO'I OOOOOOO'O OOOOOOO'O OOOOOOO'O 000000£'0 OOOOOOO'S I l-0000'I_6S aiora ivn* OOOOOOO'O OOOOOOO'O OOOOOOO'O OOOOOOO'O OOOOOOO'O OOOOOOO'O OOOOOOO'O OOOOOOO'O OOOOOOO'O OOOOOOO'O OOOOOOO'I OOOOOOO'O OOOOOOO'O OOOOOOO'O 00000££'0 I 0 0 0 l l ' 6 9 6-00890'I_8£ aiora ivn* 00000S1/'0 000000'03 6-00000'I LS . DiisviH ivn* 00000St>'0 000000'03 6"00000T_9S oiisvia ivn* OOOOOSt/'O 000000'03 6-00000" OLLSVIH ivn* OOOOOOO'O OOOOOOO'O OOOOOOO'O OOOOOOO'O OOOOOOO'O OOOOOOO'O OOOOOOO'O OOOOOOO'O OOOOOOO'O OOOOOOO'O OOOOOOO'I OOOOOOO'O OOOOOOO'O OOOOOOO'O 0000083'0 S+OOOAO'3 8"0081K)'\p aiora ivn* OOOOOOO'O OOOOOOO'O OOOOOOO'O OOOOOOO'O OOOOOOO'O OOOOOOO'O OOOOOOO'O OOOOOOO'O OOOOOOO'O OOOOOOO'O 0000000" I OOOOOOO'O OOOOOOO'O OOOOOOO'O 0000083'0 S+000Z,0'3 8-008W)'I_£S aiora ivn* 000000£'0 S+OOOZ.0'3 6-0090S '£^S oiisvia ivn* 000000£'0 S+000/.0T 6-00t>0S'£J£ OIISVTH ivn* OOOOOOO'O OOOOOOO'O OOOOOOO'O OOOOOOO'O OOOOOOO'O OOOOOOO'O OOOOOOO'O OOOOOOO'O OOOOOOO'O OOOOOOO'O OOOOOOO'I OOOOOOO'O OOOOOOO'O OOOOOOO'O 0000083'0 S+OOOZ-0'3 8-00S9l"I_0e aiora I V I A I * OOOOOOO'O OOOOOOO'O OOOOOOO'O OOOOOOO'O OOOOOOO'O OOOOOOO'O OOOOOOO'O OOOOOOO'O OOOOOOO'O OOOOOOO'O OOOOOOO'I OOOOOOO'O OOOOOOO'O OOOOOOO'O 0000083'0 S+000/,0'3 8-00S91' 16V aiora ivn* OOOOOOO'O OOOOOOO'O OOOOOOO'O OOOOOOO'O OOOOOOO'O OOOOOOO'O OOOOOOO'O OOOOOOO'O OOOOOOO'O OOOOOOO'O OOOOOOO'I OOOOOOO'O OOOOOOO'O OOOOOOO'O 0000083'0 S+000/.0'3 6-0066Z/Z. LP aiora ivn* OOOOOOO'O OOOOOOO'O OOOOOOO'O OOOOOOO'O OOOOOOO'O OOOOOOO'O OOOOOOO'O OOOOOOO'O - 8 3 3 -OOOOOOO'O OOOOOOO'O OOOOOOO'O OOOOOOO'O OOOOOOO'O OOOOOOO'O OOOOOOO'O OOOOOOO'O APPENDIX F. T H E M D B M A T E R I A L PROPERTIES (LS-DYNA VERSION 970): This appendix contains the material property input file for the Moving Deformable Barrier model used in this research. The input data has been prepared for use in LS-Dyna version 970. $—+--.-1— -+--.-2—-+—-3—-+—-4—-+—5—-+—-6—-+—7—-+—-8 $ $ $ M A T E R I A L C A R D S $ $ $ $...+.. . .1—+—2—-+-—3—-+—4—-+-—5—+—6—+—7—+—8 * M A T _ P L A S T I C _ K I N E M A T I C $ A F A C E 1 $ M I D R O E P R S I G Y E T A N B E T A 2162.6800E-09 70300.0 0.33 214.0 494.0 $ S R C SRP FS V P * M A T _ P L A S T I C _ K I N E M A T I C $ A F A C E 2 $ M I D R O E P R S I G Y E T A N B E T A 2172.7800E-09 73100.0 0.33 345.0 774.0 0.0 $ S R C SRP FS V P * M A T _ H O N E Y C O M B $ A H O N E Y 2 4 5 $ M I D R O E P R S I G Y V F M U B U L K 2188.3333E-11 70146.65 0.33 160.4 0.0308 0.0 0.0 $ L C A L C B L C C L C S L C A B L C B C L C C A L C S R 9122.0 9123.0 9124.0 9125.0 0.0 0.0 0.0 0.0 $ E A A U E B B U E C C U G A B U G B C U G C A U A O P T 1022.82 340.71 340.71 435.39 435.39 214.24 0.0 $ X P Y P Z P A l A 2 A 3 $ D l D2 D3 T S E F SSEF * M A T _ H O N E Y C O M B $ A H O N E Y 4 5 $ M I D R O E P R S I G Y V F M U B U L K 2192.5619E-11 8293.2 0.33 160.40.00949199 0.0 0.0 $ L C A L C B L C C L C S L C A B L C B C L C C A L C S R 9126.0 9127.0 9128.0 9129.0 0.0 0.0 0.0 0.0 $ E A A U E B B U E C C U G A B U G B C U G C A U A O P T 172.77 57.36 57.36 145.13 145.13 76.02 0.0 - 2 2 9 -$ X P Y P Z P A l A 2 A 3 $ D I D2 D3 T S E F SSEF * M A T _ R I G I D $ A R I G I D B $ M I D R O E P R N C O U P L E M A L I A S 2201.3955E-08 213000.0 0.33 0.0 0.0 0.0 $ C M O CON1 C O N 2 1.0 3.0 1 $ L C O _ O R _ A l A 2 A 3 V I V 2 V 3 - 2 3 0 -

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