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Conceptual design and comparative study of very large telescope encluosures Sun, Meng 2004

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C O N C E P T U A L DESIGN AND C O M P A R A T I V E STUDY OF V E R Y L A R G E TELESCOPE ENCLOSURES By  Meng Sun B. A. Sc, Beijing University of Technology, 2001 A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF APPLIED SCIENCE in  THE FACULTY OF GRADUATE STUDIES Department of Civil Engineering We accept this thesis as conforming to the required standard  THE UNIVERSITY OF BRITISH COLUMBIA April, 2004 © Meng Sun, 2004  Library Authorization  In presenting this thesis in partial fulfillment of the requirements for an advanced degree at the University of British Columbia, I agree that the Library shall make it freely available for reference and study. I further agree that permission for extensive copying of this thesis for scholarly purposes may be granted by the head of my department or by his or her representatives. It is understood that copying or publication of this thesis for financial gain shall not be allowed without my written permission.  Name of Author (pleaspjirint)  Department of ClYi't (sftQ/Vig^fYv* The University of British Columbia Vancouver, BC Canada  Date (dd/mm/yyyy)  I.  A  B  S  T  R  A  C  T  The goal of the very large optical telescope (VLOT) project is to design and construct a 20 m segmented mirror telescope, which will surpass the limits of the current generation of telescopes. This significant expansion of the telescope's geometry will present many design and fabrication challenges simply through its sheer size of the structure and demand for fine accuracy. The telescope enclosure is a crucial component of the VLOT project; its feasibility will have a great effect in whether or not a project of this magnitude will ever see the light of day. The aim of this thesis is to determine an optimal enclosure design for the VLOT by comparing previous designs along with newer, innovative designs. A thorough investigation will be performed by an in-depth examination of available research material, conceptual designs, structural analysis and decision analysis. A review of telescopes as they have developed through out history will be conducted to illustrate the significance of VLOT's influence on the future of astronomy. Moreover, by collecting information on current design cases and ideas regarding telescope enclosures, an information database of enclosure designs will be prepared, providing valuable references for the VLOT enclosure development. Conceptual deigns of various types of potential VLOT enclosures are examined in this thesis. The telescope enclosure designs will be primarily based on structural safety and serviceability performance criteria. Furthermore, a finite element analysis will provide valuable insight into each enclosure design explored. Characteristics of enclosure designs are compared from various perspectives. With respect to the comparative analysis results, a comprehensive decision analysis will be used to determine the final optimal solution. The work within this thesis will provide academic and engineering references for the further development of the VLOT project.  ii  IL T A B L E O F C O N T E N T S I.  ABSTRACT  II.  TABLE OF CONTENTS  III.  FIGURES  IV.  TABLES  V.  ACKNOWLEDGMENTS  1  INTRODUCTION  II Ill VII X XII 1  1.1  REVIEW OF TELESCOPE DEVELOPMENT HISTORY  1.2  BACKGROUND AND OBJECTIVES OF VLOT PROJECT  1.3  DESIGN REQUIREMENTS OF  VLOT ENCLOSURE  1 ;  4 5  1.3.1  Enclosure size  5  1.3.2  Slit size  6  1.3.3  Environmental protection  7  1.3.4  Motion  9  1.4  DESIGN AND COMPARISON CRITERIA:  9  1.4.1  Structural performance criteria:  9  1.4.2  Mechanical performance criteria:  9  1.4.3  Cost criteria  10  1.4.4  Other criteria  10  1.5  THEORIES AND METHODS:  10  1.5.1  Finite element analysis  10  1.5.2  Design optimization  11  1.5.3  Decision analysis  12  1.6  DESIGN ALTERNATIVES RESEARCH AND STUDY  14  1.6.1  Gemini North enclosure  14  1.6.2  Subaru enclosure:  18  1.6.3  Large binocular telescope enclosure  20  iii  2  1.6.4  New ideas for VLOT enclosure  23  1.6.5  Discussion  25  PRELIMINARY DESIGN OF THREE TYPES OF ENCLOSURES 2.1  20 M C A L O T T E ENCLOSURE DESIGN  26  2.1.1  Enclosure geometry characteristics  26  2.1.2  Structural preliminary design  27  2.1.2.1  Main skeleton.....  2.1.2.2  Base ring  2.1.2.3  Interface rings  28  2.1.2.4  Aperture ring  28  2.1.2.5  Materials  28  2.1.2.6  Member sections  29  2.2  27 27  '.  20 M DOME-SHUTTER ENCLOSURE DESIGN  31  2.2.1  Enclosure geometry characteristics  31  2.2.2  Structural preliminary design  32  2.2.2.1  Main skeleton  32  2.2.2.2  Arch girders  33  2.2.2.3  Base  2.2.2.4  Materials  2.2.2.5  Member sections  2.3  3  26  ring  33 34 .....34  '.  20 M CAROUSEL ENCLOSURE DESIGN  35  2.3.1  Enclosure geometry characteristics  35  2.3.2  Structural preliminary design  36  2.3.2.1  Main skeleton  36  2.3.2.2  Mainframes  37  2.3.2.3  Base ring  37  2.3.2.4  Door track system  37  2.3.2.5  Materials  38  2.3.2.6  Member sections  •  ANALYSIS AND RESULTS  38  39  iv  3.1  MODELS FOR ANALYSIS  40  3.1.1  Type of model  40  3.1.2  Type of element  40  3.1.3  Assumptions  41  3.2  LOADS  42  3.2.1  Dead load  42  3.2.2  Live load  43  3.2.3  Wind load  43  3.2.4  Ice load and snow load  44  3.2.5  Thermal load  44  3.2.6  Load combination  44  3.3  BOUNDARY CONDITION  45  3.4  RESULTS  45  3.4.1  Mass information of the Calotte enclosure  45  3.4.1.2  Power and torque requirements for the Calotte enclosure  47  3.4.1.3  Modal analysis results  50  3.4.1.4  Linear static analysis results  51  Analysis results of the Dome-Shutter enclosure Mass information of the Dome-Shutter enclosure  58  3.4.2.2  Power and torque requirement of the Dome-Shutter enclosure  59  3.4.2.3  Modal analysis results  62  3.4.2.4  Linear static analysis results  62  Analysis results of the Carousel enclosure  68  3.4.3.1  Mass information of Carousel enclosure  68  3.4.3.2  Power and torque requirement of the Carousel enclosure  70  3.4.3.3  Modal analysis results  72  3.4.3.4  Linear static analysis results  73  CONCLUSION  78  COMPARATIVE STUDY 4.1  58  3.4.2.1  3.4.3  4  45  3.4.1.1  3.4.2  3.5  Analysis results of the Calotte enclosure  78  PREREQUISITES  78  V  4.2  79  4.2.1 Mass information  79  4.2.2 Power consumption  82  4.2.3 Frequency  85  4.3  STRUCTURAL RESPONSE  86  4.3.1 Stress  87  4.3.2 Deflection  87  4.3.3 Base reaction force  88  4.4  5  MECHANICAL CONTROL  CONCLUSION  .'. 91  DECISION ANALYSIS  91  5.1  PREANALYSIS  91  5.2  MODEL  92  5.3  VARIABLES  95  5.4  5.3.1.1  Preparation phase  95  5.3.1.2  Construction phase  99  5.3.1.3  Operation phase  5.3.1.4  Uncertainty  103 :  106  RESULTS  6  CONCLUSION  7  ABBREVIATION  8  REFERENCES  108  114 ,  118 119  vi  III.  FIGURES Figure 1-1 The first telescope in the world [Ref. 3]  1  Figure 1-2 Galileo's telescope [Ref. 3]  2  Figure 1-3 Lord Rosse's telescope [Ref. 8]  3  Figure 1-4 Otto Struve 2.1 telescope [Ref. 9]  3  Figure 1-5 20m optical telescope structure [Ref. 13]  6  Figure 1-6 Mauna Kea site, Hawaii [Ref. 16]..  7  Figure 1-7 Snow and ice on the Mauna Kea site [Ref. 17]  8  Figure 1-8 Gemini North 8.0 m telescope [Ref. 23]  15  Figure 1-9 Gemini North 8.0 m enclosure [Ref. 24]  16  Figure 1-10 Structural components of Gemini 8.0 m enclosure [Ref. 26]  17  Figure 1-11 Subaru 8.2 m telescope [Ref. 28]  18  Figure 1-12 Subaru 8.2 m enclosure [Ref. 29]  19  Figure 1-13 structural components of Subaru 8.2 m enclosure [Ref. 30]  20  Figure 1-14 Large binocular telescope [Ref. 31]  21  Figure 1-15 LBT enclosure, Arizona [Ref. 33]  22  Figure 1-16 Structure of LBT enclosure [Ref. 33]  22  Figure 1-17 3D Model of 20 m Calotte enclosure [Ref. 35]  24  Figure 2-1 Dimension of 20 m Calotte enclosure (mm)  26  Figure 2-2 Structural model of 20 m Calotte enclosure  29  Figure 2-3 Ring and rib truss section  30  Figure 2-4 Assembled box section  30  Figure 2-5 Dimension of 20 m Dome-Shutter enclosure (mm)  32  Figure 2-6 Structural model of 20 m Dome-Shutter enclosure  34  Figure 2-7 Dimension of 20 m Carousel enclosure (mm)  36  Figure 2-8 Structural model of 20 m Carousel enclosure  38  Figure 3-1 Global coordinate system for the Calotte enclosure  46  Figure 3-2 Local coordinate system for the Cap part of the Calotte enclosure  47  Figure 3-3 Driving torque of the Calotte enclosure  49  Figure 3-4 Power consumption of the Calotte enclosure  50  vii  Figure 3-5 First mode shape of the Calotte enclosure  51  Figure 3-6 Base reaction force of the Calotte enclosure  52  Figure 3-7 Deflected shape of the Calotte enclosure under load case 1  54  Figure 3-8 Deflected shape of the Calotte enclosure under load case 2  55  Figure 3-9 Displacement of the steel interface ring under load case 1  56  Figure 3-10 Displacement of the aluminum interface ring under load case 1  56  Figure 3-11 Displacement of steel interface ring under load case 2  57  Figure 3-12 Displacement of aluminum interface ring under load case 2  57  Figure 3-13 Global coordinate system for the Dome-Shutter enclosure  59  Figure 3-14 Driving torque of the Dome-Shutter enclosure  60  Figure 3-15 Power consumption of the Dome-Shutter enclosure  61  Figure 3-16 First mode shape of the Dome-Shutter enclosure  62  Figure 3-17 Base reaction force of the Dome-Shutter enclosure  63  Figure 3-18 Deflected shape of the Dome-Shutter enclosure under load case 1  65  Figure 3-19 Deflected shape of the Dome-Shutter enclosure under load case 2  65  Figure 3-20 Displacement of arch girder under load case 1  67  Figure 3-21 Displacement of arch girder under load case 2  67  Figure 3-22 Global coordinate system for the Carousel enclosure  69  Figure 3-23 Driving torque of the Carousel enclosure  71  Figure 3-24 Power consumption of the Carousel enclosure  71  Figure 3-25 First mode shape of the Carousel enclosure  72  Figure 3-26 Base reaction forces of the Carousel enclosure  73  Figure 3-27 Deflected shape of the Carousel enclosure under load case 1  75  Figure 3-28 Deflected shape of the Carousel enclosure under load case 2  76  Figure 3-29 Displacement of the main frame under load case 1  77  Figure 3-30 Displacement of the main frame under load case 2  77  Figure 4-1 Driving torque comparison of three enclosures  83  Figure 4-2 Power consumption comparison of three enclosures  84  Figure 4-3 Base reaction force comparison under the load case 1  89  Figure 4-4 Base reaction force comparison under the load case 2  90  Figure 5-1 Model layout of the decision analysis  93  viii  Figure 5-2 Model layout of the decision analysis  94  Figure 5-3 Decision tree layout a  109  Figure 5-4 Decision tree layout b..  109  Figure 5-5 Decision tree layout c  110  Figure 5-6 Decision tree layout d  110  Figure 5-7 Decision tree layout e  Ill  Figure 5-8 Decision tree layout f  Ill  Figure 5-9 Decision tree layout g  112  Figure 5-10 Decision tree layout h  112  Figure 5-11 Decision tree layout i  113  Figure 5-12 Decision tree layout j  113  ix  TABLES Table 2-1 Member section property of the Calotte enclosure  31  Table 2-2 Member section property of the Dome-Shutter enclosure  35  Table 2-3 Member section property of the Carousel enclosure  39  Table 3-1 Weight of the Calotte enclosure  46  Table 3-2 Mass moments of inertia of the Calotte enclosure (tons- mm )  47  Table 3-3 Driving torque and power consumption of the Calotte enclosure  49  Table 3-4 Member stress of the Calotte enclosure under load case 1  53  Table 3-5 Member stress of the Calotte enclosure under load case 2  53  Table 3-6 Weight of the Dome-Shutter enclosure  58  Table 3-7 Mass moments of inertia of the Dome-shutter enclosure (tonsmm )  59  2  Table 3-8 Driving torque and power consumption of the Dome-Shutter enclosure. 60 Table 3-9 Member stress of the Dome-Shutter enclosure under load case 1  63  Table 3-10 Member stress of the Dome-Shutter enclosure under load case 2  64  Table 3-11 Weight of the Carousel enclosure  68  Table 3-12 Mass moments of inertia of the Carousel enclosure (tonsmm ) 2  69  Table 3-13 Driving torque and power consumption of the Carousel enclosure  70  Table 3-14 Member stress of the Carousel enclosure under load case 1  74  Table 3-15 Member stress of the Carousel enclosure under load case 2  74  Table 4-1 Weight comparison of three enclosures  80  Table 4-2 Mass moment of inertia for three enclosures  81  Table 4-3 Driving torque and power consumption of three enclosures  83  Table 4-4 Frequency comparison of three enclosures  85  Table 4-5 Maximum global displacement comparison of three enclosures  87  Table 5-1 Preparation cost of the Gemini 8.0 m enclosure  96  Table 5-2 Preparation cost of the 20 m Dome-Shutter enclosure  97  Table 5-3 Preparation cost of the 20m Calotte enclosure  98  Table 5-4 Preparation cost of the 20 m Carousel enclosure  98  Table 5-5 Material cost of the 20 m Calotte enclosure  100  Table 5-6 Material cost of the 20 m Dome-Shutter enclosure  101  Table 5-7 Material cost of the 20 m Carousel enclosure  101  Table 5-8 Construction labor cost of three enclosures  102  Table 5-9 Facility cost of three enclosures  103  Table 5-10 Maintenance cost of three enclosures  104  Table 5-11 Daily power consumption cost of three enclosures  105  Table 5-12 Reparation cost of three enclosures  106  Table 5-13 Uncertainty cost of three enclosures  107  xi  V . ACKNOWLEDGMENTS I am deeply indebted to my thesis supervisor, Professor Siegfried F. Stiemer, for his advice, encouragement and help throughout my graduate study at the University of British Columbia. Special appreciation also goes to Mr. David J. Halliday, Vice president and Adjunct Professor, and Dr. Ye Zhou at A M E C Dynamic Structures, Ltd. I could not have done this work without their support and guidance. I also would like to thank my wife, Jing Zhang, for all her support in my life, and my parents, for their love to me.  The financial assistance of Professional Partnership Program with A M E C Dynamic Structures, Ltd., as well as of the Science Council of British Columbia, through a Technology B.C. Grant to A M E C Dynamic Structures, Ltd., are both gratefully acknowledged.  xii  1 INTRODUCTION  1.1 REVIEW OF TELESCOPE DEVELOPMENT HISTORY The telescope was one of the greatest inventions in human history. It not only changed people's basic ideas about the world, but also activated the unlimited curiosity of human being towards the universe.  The derivation of the telescope should be traced back to the thirteenth century, when the magnifying and diminishing properties of convex and concave transparent objects started to be applied to people's common life. Due to the improvement of glass techniques, magnifying glasses and spectacles became common used. [Ref. 1] With the development of lenses and mirrors through fifteenth century, the first telescope in the world was invented in October 1608 by a craftsman. [Ref. 2] It consisted of a convex and concave lens in a tube, a combination that magnified three or four times (See figure 1-1).  Figure 1-1 The first telescope in the world [Ref. 3]  After that, the telescope design quickly improved in Europe through seventeenth century. However, people did not realize the real significance of telescope until Galileo [Ref. 4] constructed his twenty-powered instruments. He discovered the mountains and craters of the Moon, four satellites of Jupiter, and resolved nebular patches into stars. These spectacular discoveries not only renewed the people's understanding towards the telescope, but also started an endless journey of human beings to explore another secret world.  l  Figure 1-2 Galileo's telescope [Ref. 3]  Due to the growth of people's curiosities and desires, Galileo's telescope could not meet the increasing demands with its mere 30 times of amplification. In 1671, Isaac Newton [Ref. 5] put the reflector theory of J. Gregory [Ref. 6] into practice and constructed his first reflector, with a 2.5-cm. metal mirror. And throughout the 18th century, telescopes with even larger sizes were built. In 1789, William Herschel [Ref. 7], a Hanoverian who settled in England, completed a huge reflector with a 122-cm. mirror. It was the largest telescope in the world until the installation of Lord Rosse's 183-cm mirror telescope in 1845. [Ref. 8] (See figure 1-3)  In the early twentieth century, the size of the telescopes continued to grow with an amazing speed. With a significant increase in the scale and the cost of telescopes, simple enclosure structures became necessary to protect telescopes from severe weather conditions and accommodate the auxiliary necessities for the telescope operation. The Otto Struve 2.1 m telescope, for example, was built in 1939 [Ref. 9]. Its enclosure is composed of two parts: a half-sphere dome and a cylinder base. On the body of the dome,  2  two parts of the door can move apart or together in order to open or close the aperture hole. The half sphere can rotate relatively to the base cylinder to reach different observation angles. (See figure 1-4)  Figure 1-4 Otto Struve 2.1 telescope [Ref. 9]  In the later twentieth century, several large-scaled telescopes were built, including Gemini 8.0 m telescope, Subaru 8.2 m telescope, Keck 10 m telescope, Large Binocular telescope and so on. With increase in observation capacities, these telescopes raise the 3  requirements for the operational environment. Even a gentle wind gust or a small temperature change can influence the observation quality severely. Therefore, more and more people have realized the significant influence of the enclosures to modern telescopes.  1.2 BACKGROUND AND OBJECTIVES OF VLOT PROJECT Very large optical telescope (VLOT) project aims at building extremely large telescopes in the early 21 century, which will start a new era in telescope development. The project st  was classified as a high priority project in the Long Range Plan for Astronomy (LRP) of Canada. Since the LRP was developed in 1999, there has been a rapid development of extremely large telescope  (ELT) concepts worldwide, including Canada. The  construction is now likely to begin within the next five years. [Ref. 10] VLOT is a 20 m segmented mirror telescope with an aggressive optical design (f/1 primary) that could meet the Mauna Kea Master Plan requirements and fit on the CFHT site [Ref. 11]. Compared with existing large-scaled telescopes with 8-10 m diameter mirror, a 20 m segment mirror telescope will be able to overcome the barrier of lightgathering power and angular resolution in current generation of telescope and will bring a spectacular improvement in observation.  However, when people feel excited about the prospect that more and more new galaxies and stars will be discovered, engineers are facing challenging problems in order to realize this idea. Besides the design and fabrication of the VLOT itself, the engineering work related to the VLOT enclosure will be the major challenge of the project. Determined by the geometry and operation of the telescope, the dimension of the VLOT enclosure is pushed to a new high level. The significant increase in size and weight of the enclosure structure may create new problems in various aspects, concerning structure, mechanic, and cost. Moreover, the effects of many old problems in previous telescope projects may be dramatically amplified in the VLOT project due to the geometric expansion. Therefore, the VLOT enclosure can neither be simply designed as a pure shelter for the  4  telescope, nor directly scaled up from existing enclosures. What kind of design can be considered to be optimal for this complex system? This question becomes critical to the VLOT enclosure work.  1.3  DESIGN R E Q U I R E M E N T S O F V L O T E N C L O S U R E  The objective of the telescope enclosure is to house and protect the telescope. Therefore, the design requirements of the VLOT enclosure are governed by the characteristics of the VLOT.  1.3.1  Enclosure size  The size of the enclosure, one of the key parameters to the entire system, is determined by the specifications of the VLOT. According to the layout of 20 m telescope structure (figure 1-5), some important data are shown as follows: [Ref. 12] •  The diameter of primary mirror of telescope is 20 m.  •  The diameter of secondary mirror is 2.5 m.  •  Telescope focal length is 20 m.  •  The distance between the elevation axis and the primary vertex is 2.1m.  •  The height of elevation axis above observatory floor.  •  The total distance from elevation axis to the enclosure wall is 22.02 m.  •  The clearance between the secondary socket and enclosure is 1 m.  5  Diameter of primary mirror  Diameter of secondary mirror  T  Height of elevation axis above observatory floor  Distance between primary mirror and secondary mirror Figure 1-5 20m optical telescope structure [Ref. 13]  The enclosure must provide enough space to accommodate the free motion to the telescope from zenith to 60° in elevation angles and 360° degrees in horizontal angles. [Ref. 14] Moreover, additional spaces for the maintenance, observation, facilities, and visitors need to be considered. Based on requirements above, the enclosure also should be as small as possible, in order to reduce the cost.  1.3.2 Slit size The enclosure must provide the visual access to the sky over some kind of astronomical opening. The dimension of the slit must be larger than the primary mirror of the telescope. The clear viewing access must be guaranteed at every observation angle. Also, a door system is needed to open or close the opening at any time.  Besides all  requirements above, the wind and thermal effects to the telescope also influence the size of the slit on the enclosure. The optimal size of the slit should lead wind buffets to the telescope structure and ambient effects to the optical images to be acceptable.  6  1.3.3  Environmental protection •  Site:  Mauna Kea is located about 300 km from the city of Honolulu, on the island of Hawaii. The highest point in the Pacific Basin, and the highest island-mountain in the world, Mauna Kea rises 9,750 m from the ocean floor to an altitude of 4,205 m above sea level, which places its summit above 40 percent of the Earth's atmosphere. [Ref. 15] The good weather and the low inversion layer lead Mauna Kea to be one of the best locations worldwide for the astronomy observation. A number of telescopes, including the CFHT, Gemini, Subaru, and Keck, have been built on the top of this mountain.  Figure 1-6 Mauna Kea site, Hawaii [Ref. 16]  •  Temperature:  Due to the high elevation level of the Mauna Kea site, the change of temperature from daytime to the night is considerable. A substantial, well-insulated and wellsealed enclosure is needed to minimize temperature differences between the telescope structure and outside environment. Also the structure -induced thermal disturbances problem should be considered. •  Snow and ice:  The VLOT enclosure should be able to resist the 100-year maximum snow and ice loads on the Mauna Kea site. [Ref. 16] Based on the weather statistics of 7  Mauna Kea winters, the survival cases will include 68 kg/m of ice and 150 kg/m 2  2  of snow accumulating on the surface of the enclosure. [Ref. 12] Even for some local area, snow and ice could be much thicker. Beside the structural issue, snow and ice will also influence other issues, including maintenance, mechanical equipment and system operation.  Figure 1-7 Snow and ice on the Mauna Kea site [Ref. 17]  •  Wind:  According to the weather of Mauna Kea site, the survival wind speed will be 65 m/sec from any direction and operational wind speed will be 33 m/sec from any direction. [Ref. 12] The transmission of wind-induced vibrations of the enclosure into the telescope through foundation should be considered.  8  1.3.4 Motion The enclosure will slew with a rate of 180° rotation in five minutes. The duty cycles and rates include: continuous slewing for up to fifteen minutes; one movement per two minutes during the observation; two full movement cycles of 15 minutes every hour. [Ref. 12] The motion of structure will introduce fatigue problems and mechanical control problems.  1.4 D E S I G N A N D C O M P A R I S O N CRITERIA: 1.4.1 Structural performance criteria: From the structural point of view, the basic structural performance criteria include: •  Member stress is controlled within allowable stress level  •  Global and local deformations of structures are controlled under acceptable limits  •  The whole structure and local members are stable  •  Disturbances of the enclosure to the telescope are minimized  •  Fatigue design requirements are satisfied  •  The structure is optimized to be efficient and economical  1.4.2 Mechanical performance criteria: From the mechanical point of view, the basic structural performance criteria include: •  High rigidity of the system  •  Low power consumption  •  Optimized weight of devices  •  High reliability of system  •  Harmony with structural parts  9  1.4.3 Cost criteria Although cost criteria are related to different aspects of the project, they can be unified into the total cost criterion: the lower the total cost is, the more desirable the design solution will be. However, since the cost on different aspects of the system may be correlated to each other, the evaluation of this criterion requires systematic analysis, which should consider the interaction between various factors.  1.4.4 Other criteria Besides the main criteria mentioned above, some additional issues should also be considered: •  Reliability of the whole system  •  Operational performance  •  Erection procedure  1.5 T H E O R I E S AND M E T H O D S : 1.5.1 Finite element analysis Finite element analysis utilizes mathematics to model and solve structural problems. By meshing a structure into finite elements, a complicated structural problem in one domain is converted into simple problems in subdomains. With the equilibrium conditions, geometry conditions and physic conditions, the problem in each subdomain is solved. Then the approximated results for the original problem are found. The essence of the finite element analysis is to get an approximate result by piecewise interpolation of a field quantity. [Ref. 18] The modeling can influence the quality of the final results of the analysis. A model for analysis can rarely reflects the real complexity of the structure completely. Based on the understanding of the structure, the model must be simplified so that the superfluous details are excluded while every essential feature of the structure is included. For the  10  VLOT enclosures, since the system is so huge and complex, some reasonable assumption and simplifications are necessary. With a simple and precise model, the structural characteristics of the enclosure designs are explored by finite element analysis. The software ANSYS 6.0 will be used during the analysis.  1.5.2 Design optimization Engineers are increasingly recognizing the importance of the structural optimization. An optimized system cannot only improve the structural efficiency and performance, but also minimize the cost. General approaches of the structural optimization are classified into two categories: member detail optimization and topology optimization. [Ref. 19] The member detail optimization is the conventional method in structural optimization. It usually focuses on the relationship between the member detail properties and the whole system performance. In this method, the objective function is usually defined as the minimum weight of the structure, or minimum cost of the system. Under several constraints associated with the stress level, the displacement amplitude or other responses, an optimum value for design valuables can be found.  The topology optimization is a relatively new method in  structural optimization. This method is concentrated on the relationship between the structural layout and the whole system performances. Since changing the topology of the structure could explore more spaces for the optimization than modification of member detail properties, topology optimization has been widely applied in engineering practices.  In process of the VLOT enclosure design, common optimization methods will meet great difficulties since systems are very huge and complex. As different types of problems are involved in one system and many variables are correlated, it seems nearly impossible to use simple objective functions, typical design variables, and common constrains to solve the problem. In this thesis, structural optimization will be concentrated on the relationship between member detail properties and comparable level of structures.  n  1.5.3 Decision analysis When projects grow in scale and complexity, risk becomes one of the focal issues. Especially in large invested engineering projects, correct decisions with the appropriate risk control become more valuable than before. Since the problem may involve many associated factors from various aspects, people should not depend on simple methods, such as experience, instincts or gambling, but apply systematic decision analysis to find the best solution. Decision analysis is a scientific process that can help people to think systematically and completely when faced with important and difficult decisions. The theories involved in this process include logics, statistics, probability, reliability and more. In a typical decision problem, the common steps of analysis include: [Ref. 20] •  Preanalysis Identify the basic elements and their relationship from the problem. The basic elements include:  •  •  Problem  •  Objectives  •  Alternatives  •  Consequences  •  Tradeoffs  •  Uncertainty  •  Risk  •  Linked decisions  Structural analysis Based on the results of preanalysis, the qualitative anatomy of the problem should be structured. According to different types of problem, different types of models are created with the help of appropriate tools.  •  Uncertainty analysis High uncertainty is one of the main characteristics of a complicated decision problem. By uncertainty analysis, probability value will be assigned to each chance node and final possibility of each alternative will be reflected clearly in  12  decision tree. The assignment of probability value is made by artful combination of different techniques and procedures based on experiment data, experience, expert's testimony and so force. It is one of the main procedures to quantify the problem •  Utility value analysis Another way to quantify the problem further is that the decision maker assigns utility value to consequences associated with the paths through the tree. Then the qualitative choice to the problem will be transformed to numerical calculation and comparison. The assignment of the utility number to consequences must be based the rule that maximization of expected utility becomes the appropriate criterion for the optimal selection.  •  Optimization analysis With different strategies, each analysis can generate different Expected Monetary Value (EMV). The optimal strategy, which can generate the highest EMV, should be found.  The spreadsheet is one of the traditional decision analysis tools. It is using generic mathematic concepts to transform a decision problem into a mathematic problem. By inputting different values into some functions, the decision outcomes could be presented by numerical results. Although spreadsheet is a very popular tool for the decision analysis, its limitation also becomes more obvious when the problem becomes more complicated. With the academic development, modern decision tools have overcome some hmitation of spreadsheet. Decision tree is one of the new tools in decision analysis. It provides an elegant framework for combining all information with consequence probabilities and outcome values to help select the best option, which has the highest expected monetary value, a measure of probabilistic value. It can divide a complex problem into several small parts and uses a hierarchy tree layout to simulate the logic relationship of each part. With the concept of "divide and conquer", the decision tree provides a new way to assess the impact of all possible outcomes simultaneously [Ref. 21].  13  For the VLOT enclosure, old telescope enclosure designs and novel ideas provide many options for the designers. In order to find the best design solution, designers should consider many problems including the structural performance, mechanical control, cost and reliability, and adopt a careful decision analysis to make a reasonable judgment. In this thesis, simple decision analysis will be performed using a commercial software product DecisionPro 4.0. Through narrowing the scope of options and comparing solid evidences, the ultimate design decision will be found.  1.6 D E S I G N A L T E R N A T I V E S R E S E A R C H A N D S T U D Y Many types of telescope enclosures have been tried around the world. The design information and engineering records of these existing structures provide valuable references for the VLOT enclosure design. Beside the real designs, a lot of new ideas about the telescope enclosure design are available. Although they may still exist in theory only, those ideas broaden and enrich the group of design candidates. In this thesis, several typical telescope enclosures designs and ideas, which can delegate the main styles of large telescope enclosure design, are discussed.  1.6.1 Gemini North enclosure Gemini North telescope, one of the world's largest and most advanced telescopes, was built on Mauna Kea, Hawaii in 1999. The telescope has an 8.0 m diameter f/1.8 primary mirror and a 2.4 m diameter f/6 secondary mirror. The structure can sweep in a radius of 15.09 m in elevation. The total weight of the telescope is 380 tons. [Ref. 22]  14  Figure 1-8 Gemini North 8.0 m telescope [Ref. 23]  In order to accommodate this huge structure, the Gemini enclosure adopts the traditional telescope enclosure layout: the combination of cylindrical base and hemispherical dome. The dome is connected to the base part by bogies, lateral guide rollers and anchor systems. The whole superstructure can rotate relatively to the cylindrical base to reach different observation angles. The observation opening is protected by the top shutter and the bottom shutter, which span on two arch girders. Along the body of the enclosure, there are some big vent gates, which can move up and down to control the wind effects to the telescope.  15  Figure 1-9 Gemini North 8.0 m enclosure [Ref. 24]  The major dimensions of the enclosure are: the total height of the structure is about 25 m; the internal radius of the dome is 17.3 m; the clearance between the secondary mirror to the enclosure is about 2.3 m; the thickness of the enclosure is 700 mm; the upper shutter spanning 92.5° and lower one spanning 19.5°; in the fully open position, the maximum viewing angle is 103.5°. [Ref. 25]  The whole structure mainly consists of steel members, except that the shutter and surface panels are made of aluminum. The hemispherical dome is supported by vertical rib trusses and horizontal ring trusses. The truss section is composed of angles and pipes. Two W shape vent girders are located between the dome and cylinder base. Big openings of vent gates require additional diagonal trusses to strengthen the structure. A heavy assembled section is assigned to two arch girders, which provide high lateral stiffness to accommodate the large opening of the structure, and offer enough strength to support two pieces of the shutter. Another heavy section is designed for the base ring, which supports  16  the superstructure and provides a solid foundation for bogie movement. The top shutter and the bottom shutter move upward and downward respectively. By this way, a considerable power could be conserved by reducing the total mass moving upward.  Figure 1-10 Structural components of Gemini 8.0 m enclosure [Ref. 26]  Some characteristics of this enclosure can be summarized as follows: [Ref. 27] • The weight of the enclosure is 1,250 Tons • The first frequency of the whole structure is 1.404 Hz • The maximum stress under the worst load case (wind + snow + dead) occurs at the arch girder. The member capacity ratio is 0.67. • The maximum member axial force occurs at the base ring with the value of 668 kN  17  • The maximum bending moment occur at the arch girder with the value of 936 kNm • Total cost of the whole system is about 9,000,000 US dollars.  1.6.2 Subaru enclosure: The Subaru Telescope, which is also located at Mauna Kea on the island of Hawaii, is another one of the new-generation telescopes. The diameter of its primary mirror is 8.2 meters. The whole telescope is 22 m in height and 27.2 m in maximum width. Total weight of the telescope is around 22.8 tons. [Ref. 28]  Figure 1-11 Subaru 8.2 m telescope [Ref. 28]  The geometry of the Subaru enclosure resembles a cylindrical shape. A cylindrical enclosure can prevent rising warm and turbulent air from entering the enclosure from the  18  outside. In addition, it allows warm air produced inside the enclosure to escape rapidly. Also, the regular shape of the structure can decrease manufacturing and construction costs. The observation opening is covered by two separated gates, which can travel along the base track and top track. The total height of the enclosure is 43 m and the base diameter is 40 m. The clearance between enclosure and telescope is larger than 15m. The total weight of the enclosure is 2,000 tons. The superstructure of the Subaru enclosure is mainly supported by a steel structure. The base is made from reinforced concrete. The main structural members in superstructure are vertical rib trusses and horizontal ring trusses. Two rigid frames were designed to compensate the large discontinuity of the structure caused by the big observation opening. Also, a composed section was selected for the base ring girder. Two gates are composed of a space truss system, which can provide high stiffness to satisfy the motion requirements.  Figure 1-12 Subaru 8.2 m enclosure [Ref. 29]  19  Figure 1-13 structural components of Subaru 8.2 m enclosure [Ref.  1.6.3  30]  Large binocular telescope enclosure  Large binocular telescope, part of the Mt. Graham International Observatory near Safford, Arizona, is one of the newest large telescopes in the world. The telescope has two 8.4 m primary mirrors on a common mount with 14.4 m center-center separation, which can provide equivalent ultimate image sharpness as 22.8 m telescope. By using swing arms to rotate the secondary mirrors and their supports, it is possible to switch the telescope from one mode of observation to another very quickly. The telescope is 25 m high from the elevation axis to the top of the secondary mirrors. The total weight of the telescope is 580 tons. [Ref. 31]  20  Figure 1-14 Large binocular telescope [Ref. 31]  In order to accommodate this huge telescope structure, the LBT enclosure design adopts a new concept, "co-rotating box". The main enclosure was designed as a huge box. Each wall of the box is composed of steel trusses. The whole box can rotate on a 23 m diameter circular rail above the reinforced concrete wall. Each aperture of the binocular telescope has a 10.4 m wide aperture for viewing. Sliding shutters, which move apart laterally to open the slits, covers these two apertures. Additional openings on the back and sides allow wind ventilation to flush the building. A windscreen can be raised to protect the telescope from buffeting at strong winds. [Ref. 32]  21  Figure 1-15 L B T enclosure, Arizona [Ref. 33]  1.6.4 New ideas for V L O T enclosure Beside several existing telescope enclosures mentioned above, more new concepts and ideas about the VLOT enclosure design can be found. With the novel characteristics, these imaginary designs have broadened the vision of VLOT enclosure designers. However, according to the characteristics of the 20 m optical telescope, many design ideas are not fully demonstrated or matured, which are not to be considered.  This one of concepts to be considered for the VLOT enclosure is the "Calotte", which was introduced by David J. Halliday [Ref. 34]. The Calotte enclosure is divided into two parts: the cap part and the base part. There are two large ring girders mounted on each part respectively and connected by bogies and lateral guides in between. Through this interface, the cap part can rotate relatively to the base part to reach any elevation angle for the observation. Mover, the whole enclosure can also achieve different horizontal angles by the rotation of the base part along the base ring girder. The combination of these two movements offers a high speed of movement to capture any object in the sky.  23  Figure 1-17 3D Model of 20 m Calotte enclosure [Ref. 35]  The configuration of a calotte enclosure has been used at the Bernard Lyot telescope, a 2.0 m telescope built in Pic-du-Midi Observatory in 1980. [Ref. 36] The successful design of the Bernard Lyot enclosure provides valuable evidences to support the feasibility of the "Calotte" concept. However, because it is the first time to apply this concept to a very large-scaled enclosure, more detailed evaluations of this attempt are required.  24  Figure 1-18 Bernard Lyot telescope and enclosure [Ref. 37]  1.6.5 Discussion Based on the research and study above, the domain of the design candidates for VLOT enclosure should be optimized. The shutter layout of the Gemini enclosure and the carousel layout of the Subaru enclosure should be included in the new term of the study. Because they have been designed and built successfully as large-scaled telescopes, a lot of design data and performance records are available to provide references to the VLOT enclosure design. Although the Calotte enclosure doses not have extensive engineering records as the two alternatives above, the prospect of outstanding performance of this design idea deeply attracts engineers' attention. Therefore, the best design alternatives shall be selected from three candidates: Calotte enclosure, Dome-Shutter enclosure, and Carousel enclosure.  25  2  PRELIMINARY DESIGN OF THREE TYPES OF ENCLOSURES The preliminary structural design of Calotte, Dome-Shutter and Carousel enclosure for 20 m telescope will be introduced in this chapter. At this stage of design, global performance of the main structure is the focal point. Designs are referenced by real projects of Gemini enclosure, Subaru enclosure and Lyot enclosure.  2.1 20 M C A L O T T E E N C L O S U R E DESIGN 2.1.1 Enclosure geometry characteristics The shape of Lyot enclosure is adopted and scaled up for 20 m Calotte enclosure. According to the design requirements of VLOT enclosure in section 1.3, the dimension of the enclosure is shown in Fig 2-1.  Figure 2-1 Dimension of 20 m Calotte enclosure (mm)  26  The dome of Calotte enclosure is designed as a part of sphere. The average radius of the dome is 25.5 m, which leaves 3.5 m clearance between the secondary mirrors of the telescope and the interior wall of the enclosure. When the observation aperture is pointing to the zenith, the height of enclosure is 37.4 m, which leaves 1.4 m distance between the secondary mirror and outer air. An interface plane cut the dome in a 34.5° incline angle. Based on this angle, the observation aperture can reach the maximum zenith angel of. 60°. The diameter of the interface plane is 49.5 m. The entire dome can rotate along a 42 m diameter circle in the base ring plane. The aperture cover is a 22 m diameter disc, which is moved from a stowed position to the aperture, where it may be locked and sealed to the cap.  2.1.2 Structural preliminary design 2.1.2.1 Main skeleton Based on the geometry of the Calotte enclosure, a strong metal skeleton is designed and filled into this system. The skeleton consists of seventy-two vertical ribs and seven horizontal rings. Each rib or ring is composed of a plane truss. The spacing of vertical ribs is 5° measured from the center of the dome and the distance between each two horizontal rings is 6 meters. The skeleton is covered by 6 mm aluminum panels.  2.1.2.2 Base ring At the lower part of the enclosure, thirty-six heavy bogies support the structure in vertical direction, and thirty-six lateral guild rollers constrain the structure in lateral direction. Because these special mechanical connections and associated devices require high structural performances at the base part of the structure, a very strong and rigid base ring girder is designed.  27  2.1.2.3 Interface rings The interface between the cap part and base part plays the most important role in the Calotte enclosure design. The interface is formed by two ring girders. Between these two ring girders, thirty-six bogies support the cap in the vertical direction and thirty-six twoway lateral guide rollers prevent the cap sliding on the inclined interface plane. In order to meet the structural requirements for this interface, and to accommodate these mechanical devices, the interface ring girders must meet extremely high performance requirements.  2.1.2.4 Aperture ring On the top of the cap, the 25 m diameter observation aperture introduces a big discontinuity to the system. Because it is the only opening of the structure, the local rigidity of this part influences the global stiffness of the system. Moreover, the relatively heavy aperture cover requires a stable structure to support it. Therefore, another stiffening girder is designed on this part.  2.1.2.5 Materials Because of the motion mechanism of the enclosure, the weight of the cap part in the Calotte enclosure needs to be minimized, so that loads on the interface ring girders and power consumptions of the enclosure can be reduced. Therefore, aluminum is selected for the cap part while steel is used for the remainder. Although the strength capacity of aluminum is lower than the strength capacity of steel, the relatively low density of this material leads to an advantage in self weight of aluminum structure when compared with steel structure. Other issues such as heat expansion and costs need be considered, too.  28  Figure 2-2 Structural model of 20 in Calotte enclosure  2.1.2.6 Member sections The design of member sections should be guided by the following principles. Firstly, the section should have appropriate properties, which contribute to the strength and stiffness of the entire system. Secondly, the cost of fabrication should be minimized by proper section design. Finally, erection and assembling issues of structural members on the site need to be considered.  Because the majority of the structural members in Calotte enclosure belong to the ring truss and rib truss, the section design for these members are highly important. Sections of rib truss and ring truss are designed as assembled section with angles and pipes. (See figure 2-3). The upper chord and lower chord are angles, and the bracings in the middle are pipes. Angles have relatively balanced moment inertia along weak axis and strong axis, which is beneficial for chords and convenient for fabrication.  29  200x200x16 Angles  Figure 2-3 Ring and rib truss section  Assembled box sections are used to the base ring girder, interface ring girder, and aperture girder. (See figure 2-4) This type of cross section can be design to provide high strength and stiffness performances, required by heavy loads and high load cycles.  Figure 2-4 Assembled box section  30  The detailed information of member section properties is presented in the table 2-1.  Table 2-1 Member section property of the Calotte enclosure  Calotte Enclosure Ribs & rings Base ring Interface ring Aperture ring Axial area (mm )  6140  98780  24590  24540  4.44E+09  8.62E+09  2.55E+08  2.55E+08  4.51E+09  1.65E+10  5.93E+08  5.92E+08 .  Height of section (mm)  100  1000  400  400  Width of section (mm)  1200  900  300  300  2  Moment inertia for weak axis (mm ) 4  Moment inertia for strong axis (mm ) 4  2.2 20 M D O M E - S H U T T E R E N C L O S U R E D E S I G N 2.2.1 Enclosure geometry characteristics The sizes of 20 m Dome-Shutter enclosure are similar to characteristic parameters of the Calotte enclosure. The radius of the dome, measured from the center point of the sphere to the centerline of the dome skeleton, is 25 m. The diameter of the base ring circle is 42 m. A large slit on the body of dome is 25 m wide and spans from 0° to 120° relative to the horizontal axis. The total height of structure is 36.6 m.  31  Figure 2-5 Dimension of 20 m Dome-Shutter enclosure (mm)  2.2.2  Structural preliminary design  2.2.2.1 Main skeleton Similar to the Calotte enclosure design, the skeleton of shutter mainly consists of seventy-two vertical ribs and seven horizontal rings. Each rib or ring comprises a plane truss. The spacing of vertical ribs is 5° measured from the center of the dome and the distance between each two horizontal rings is 6 m. Above the skeleton, aluminum panels of 6 mm thickness cover the surface of the whole structure.  32  2.2.2.2 Arch girders The 25 m wide slit on the body of dome almost divides the structure in to two parts. The rigidity of the dome structure is severely decreased by this big discontinuity. Therefore, two arch girders are located at both edges of the slit to resist lateral loads. Tie beams, back ribs and bracings are situated between two arch girders, which can increase the lateral connections between two parts of dome. Similar to interface rings in the Calotte enclosure, two arch girders are the principle loadcarrying components of the DomeShutter enclosure. Besides compensating the discontinuity of the structure, arch girders also support the shutter, and provide mechanical environment for their movements. High strength and rigidity are required for the design of these two girders. The loads caused by the shutter are imposed on the method of equivalent loads.  2.2.2.3 Base ring At the lower part of the Dome-Shutter enclosure, same number of heavy bogies and lateral guide rollers as in the Calotte enclosure support the enclosure on the rail. Moreover, because two arch girders go all the way down to the base ring, high concentrated forces are created at the base part of the structure. Therefore, the base ring girder in the Dome-Shutter enclosure is designed stronger and stiffer than the one in the Calotte enclosure.  33  F i g u r e 2-6 Structural model of 20 m Dome-Shutter enclosure  2.2.2.4  Materials  Steel is the main material used for the Dome-Shutter enclosure. Considering the motion of two shutters, aluminum is used as dominate material for them, in order to reduce the weight of the shutter. The cover panels are also made of aluminum.  2.2.2.5 Member sections The truss sections of ribs and rings in the Dome-Shutter enclosure are the same as those in Calotte design. Base ring and arch girders also adopt the same heavy box sections as for the Calotte design, except that the section properties are different. For the tie beams, back ribs and bracings, similar plane truss sections as ribs and rings are chosen. The detail section property information is presented in the table 2-2.  34  Table 2-2 Member section property of the Dome-Shutter enclosure  Dome-Shutter Ribs & rings Base ring Arch girders Tie beam Back ribs Bracing Axial area (mm ) 2  6140  120000  105728  6140  6140  6140  Moment inertia for weak axis  4.44E+09  6.04+10 2.29E+19 8.88E+09 4.44E+09 4.44E+09  4.51E+09  1, 20+11  100  2300  2300  100  100  100  1200  2300  1350  1200  1200  1200  (mm ) 4  Moment inertia for strong axis  5.75E+10 9.02E+09 4.51E+09 4.51E+09  (mm ) 4  Height of section (mm) Width of section (mm)  2.3 20 M C A R O U S E L E N C L O S U R E DESIGN 2.3.1 Enclosure geometry characteristics The shape of the Carousel enclosure resembles a cylinder. By reviewing the geometry dimension of Subaru enclosure, the ratio of the total height and the width of the enclosure is around 1.0. This ratio is also applied to 20 m Carousel enclosure. The enclosure cylinder is 40 m high and 50 m in diameter. The slit is 25 m wide and start from 12 m above the base level to the roof of the enclosure.  35  00  o  2.3.2 Structural preliminary design 2.3.2.1 Main skeleton The advantages of "ribs & rings" type of skeleton in large spherical structures are evident in the Calotte enclosure and the Dome-Shutter enclosure. For the cylindrical shape of the Carousel enclosure, the concept of "ribs & rings" type of skeleton is still useful, although slightly modified. In order to fit the shape of cylinder, arch ribs in sphere structure become vertical columns. Each column has an axial strength to resist vertical loads and the lateral rigidity to resist lateral loads. Horizontal rings tie the columns together so that all individual structural members are integrated. The spacing between each column is still  36  a 5° angle measured from centerline of the cylinder and spacing between rings is 4 m. Each column or ring consists of a plane truss.  2.3.2.2 Mainframes Similar to the Dome-Shutter enclosure, the 25 m wide slit on the body of dome is a problem in regard of the strength of the structure. In order to improve it, two strong plane frames are designed to reinforce the both edges of the slit. Each frame consists of two columns and a crossbeam. By this way, the discontinuity of the enclosure is compensated by high lateral rigidity of these two frames.  2.3.2.3 Base ring Similar problems due to base reaction forces exist in the Carousel enclosure as in the Dome-Shutter enclosure. In order to accommodate the high concentrated forces introduced by two main frames, the base ring girder is similarly designed. Also, same number of bogies, lateral guide rollers and anchor bolts are designed to support the superstructure of the Carousel enclosure on the rail.  2.3.2.4 Door track system In contrast to the Calotte design and the Dome-Shutter design, the Carousel design has two parts of the door traveling apart or together to control the observation opening. Each part of the door consists of integrated truss systems and is supported at the top end and the bottom end. Therefore, two track girders and corresponding support systems are designed at the top part and middle part of the enclosure to support the dead loads and dynamic loads of the door.  37  M A I N GIRDERS  Figure 2-8 Structural model of 20 m Carousel enclosure  2.3.2.5 Materials Steel is the main material for the most of the structure of Carousel enclosure. Aluminum is only used for the door and surface panels.  2.3.2.6 Member sections In order to keep the three types of enclosure designs at a comparative level, most types of the member sections in the Carousel enclosure are similar to other two enclosures. Plane truss sections are used for the columns and rings. Box sections are used for members of the main frames, the base ring girder, and track girders. The detailed information of member property is shown as table 2-3:  38  Table 2-3 Member section property of the Carousel enclosure Carousel  Axial area (mm )  Columns  Base  Main  Main  Side  Track  & rings  ring  girders  columns  columns  girders  6140  61814  2  105728 9. 00E+06 1. 06E+05 61804  Bracing  9800  Front ribs  2. 25E+06  Moment inertia for weak axis  4. 44E+093. 02E+10 2. 29E+19 6. 75E+125. 75E+10 1. 38E+10 6. 26E+07' 4. 22E+11  (mm ) 4  Moment inertia for strong axis  4. 51E+095. 27E+105. 75E+106. 75E+128. 75E+10 3. 02E+10 4. 15E+09 4. 22E+11  (mm ) 4  Height of section  100  2300  2300  3000  2300  2300  1495  1500  1200  2300  1350  3000  2300  1350  203  1500  (mm) Width of section (mm)  3 ANALYSIS AND RESULTS In this chapter, the finite element analysis for three types of enclosures will be introduced. Following the analysis, various results associated with dynamic and static characteristics of each design will be discussed. A l l the data and discussion are prepared as the basis for a future comparative study. The finite element analysis is undertaken using the professional software ANSYS 6.0.  39  3.1 M O D E L S F O R A N A L Y S I S In order to explore the characteristics of the each preliminary design, a finite element model is set up for each type of enclosure. In this section, the concepts, methods and assumptions associated with modeling procedure are introduced.  3.1.1 Type of model According to the structure of each enclosure, a "stick model" for finite element analysis is adopted. In this type of model, each column or beam of the structure is modeled as a stick element and meshed by joint nodes, and the nodal forces and average stress of each element are calculated. In contrast to solid model, the stick model avoids the complicated and tedious process in modeling, and simplifies a complex structure to a simple but reasonably accurate model.  3.1.2 Type of element By reviewing the structural design of three enclosures, the types of members can be classified into three categories: truss section, assembled box section, and mechanical connections. Based on characteristics of each type of member section, the corresponding elements are selected in the element library of ANSYS [Ref. 38] for the model. As the truss sections and box sections are expected to resist uniform axial forces, shear forces, and bending moments, the 3D beam element is adopted for these members. Since bogies only work in contact and resist compression forces, the contact element in ANSYS should be the best choice. This kind of element is capable of supporting the compression in normal direction and coulomb friction in shear direction. However, because the contact element will introduce nonlinear problems to the analysis and thus increase the complexity of the problem, spring element is used during the analysis for similarity. The spring element can perform as a uniform axial member which only take tension and compression forces. In order to reflect the reality that bogies cannot resist tension forces, the "spring taken o f f method is used. The scenario of this method is as follows: by  40  checking the results from one cycle of analysis, springs in tension will be taken out of model and a new analysis will run. This procedure needs to be repeated until all springs are in compression. This approximate method can simplify the analysis with very close results to the reality. The spring element for the lateral guide roller is appropriate since three enclosures all have two-way roller systems, which will resist tension and compress forces. Moreover, several spring elements are added along the tangent direction of the interface ring circle and base ring circle, in order to simulate the brake/drive system and stabilize the structure.  3.1.3 Assumptions In the finite element model, 36 springs in normal directions and radial directions are distributed along the base ring and interface ring respectively. Also 3 springs in tangential direction are added to both the lower part of the interface ring and the certain part of the base ring. The stiffness is assumed to be 30 kN/mm for all springs. This value is estimated from the rigidity of the bogies, rollers and brake/drive system. Although some values may not be appropriate, they suffice for the comparative study. More accurate stiffness values can be introduced according to further analysis demands. All other structural members are modeled as 3D beam elements. The aluminum panels on the surface of each enclosure will not be modeled. This leads results of analysis to be conservative, because the rigidity contribution of panels will be ignored. The aperture cover, the shutter and the door will not be simulated in the model. Only the load effects of these components are considered. For the Calotte enclosure, various parking position of the cap will result in different structural characteristics. Therefore, structural performances under different parking position of the cap should be examined. However, since difference of the structure between those parking positions is supposedly small, at this stage of design, only the structure at the zenith poison is considered.  41  3.2 LOADS As in most structural designs, loads in the enclosure structure design can be divided into serviceability loads and survival loads. The main function of the telescope enclosure is to protect the telescope from severe weather conditions, thus survival loads govern the structural design for the enclosure. On the other hand, since the enclosure should also meet the mechanical requirements and the operational specifications, the structure performances of the structure under serviceability loads also need to be considered. In order to facilitate a comparative study, the analysis with the survival loads is included in this thesis.  3.2.1 Dead load The effect of dead load will be predominant, which is typical for large-scaled structure. The dead load can be divided into three parts: •  The self weight of structural skeletons  •  The self weight of secondary structural components to each enclosure, including, cover panels, stairs, elevators, and so on  •  The self weight of mechanical devices, including bogies, guide rollers, motor drive system, power system, ventilation system, air condition system and so on  •  Transformed dead load effects from the aperture cover, the shutter, and the door  All these weights are calculated by following methods: •  The weight of the structural skeleton is included automatically by the analysis software  •  The weight of secondary structural components will be uniformly added to the structure by amplification factors of the materials density. The values of amplification factors are as follows:  •  •  1.8 for the Calotte enclosure  •  2.3 for the Dome-Shutter enclosure  •  3.5 for the Carousel enclosure  The weight of mechanical equipments in three types of enclosures are considered in different ways  42  •  In the Calotte enclosure, a lumped mass of 430 tons is uniformly added to the base interface ring.  •  In the Dome-Shutter enclosure, the weight of mechanical system is included in the weight of the shutter.  •  In the Carousel enclosure, the weight of mechanical devices is included in the weight of the door  •  Additional lumped masses will be added to reflect the weight of from the aperture cover, the shutter and the door. •  In the Calotte enclosure, 30 tons lumped mass is uniformly distributed along the aperture girder  •  In the Shutter enclosure, 400 tons lumped mass is for self weight of shutter and mechanical equipments is distributed along two arch girders  •  In the Carousel enclosure, 250 tons lumped mass for self weight of shutter and mechanical equipments is distributed along two track girders  3.2.2 Live load Live loads are mainly caused during the construction, maintenance, and operation. Because these loads are ignorable when compared with dead loads on enclosure structures, they are not included at this stage of design and study.  3.2.3 Wind load Based on the site information as mentioned in section 1.3.3, the survival wind speed is 67 m/s in any directions. Based on this speed, wind loads are calculated according to the NBCC specification [Ref. 39]. The results of nodal forces are applied to each node of the model.  43  3.2.4 Ice load and snow load Under the survival conditions, the average weight of accumulated snow on the surface of the enclosure is 150 kg/m and the average weight of accumulated ice is 68 kg/m . The load values are calculated based on the surface area of the telescope enclosure, and applied to node points of rings on each enclosure. In some severe weather condition, the ice on some local part of the enclosure will exceed the global survival value of ice load. However, they will not influence the global response of the structure much, and is not included at this stage of design and analysis.  3.2.5 Thermal load Thermal effects to the enclosure structure caused by radiation of sunshine, temperature difference of daytime and night, air conditioning effects, heat effects of mechanical and power equipments are included in the analysis. Aluminum has a high heat expansion ratio; therefore the thermal effects on this material in the enclosure structure require special attention.  3.2.6 Load combination With the combination of different loads, more load cases are involved in enclosure design. In order to simplify the problem, only two typical load cases are included at this study: 1. Gravity load + Ice load + Snow 2. Gravity load + Wind load (the direction along y axis) These two load cases are typical enough to reflect the vertical and lateral loading effects to the structure.  44  3.3  B O U N D A R Y CONDITION  In order to simplify the problem, similar boundary constraints are applied to each enclosure design: each structure is fixed to the ground through each node of the base ring girder. Six degrees of freedom of each node point are restricted.  3.4  RESULTS  Based on the preliminary design of each type of enclosure, the finite element analysis is performed. According to the structural response, each model is simply optimized. The final analysis results, including mass, mode shape, frequency, member forces, member stress and deflection, will be presented in the following.  3.4.1 Analysis results of the Calotte enclosure 3.4.1.1 Mass information of the Calotte enclosure The weight information of the Calotte enclosure is listed in table 3-1. The total weight of the enclosure is 950 tons, which include 30 tons of the aperture cover and associated mechanical system, 482 tons of structural components of enclosure and 430 tons of mechanical equipments of enclosure. The total weight of cap part, including aperture cover, is 155 tons and the total weight of the base part, including mechanical equipments, is 831 tons.  45  Table 3-1 Weight of the Calotte enclosure  Calotte 20m enclosure Components  Weight (tons)  Aperture cover  25  Door drive system  5  Shell rib (aluminum)  40  Shell rib (steel)  112  Shell plate (aluminum)  45  Shell plate (steel)  215  B a s e ring  183  Interface ring (aluminum)  19  Interface ring (steel)  53  7.5  Hole ring  150  Drive/brake/idler bogie Track rail  95  Total  950  The origin of the global coordinate system for the whole structure is located at the center of the base ring circle. The origin of the local coordinate system for the cap part only is located at the center of the interface plane.  Figure 3-1 Global coordinate system for the Calotte enclosure  46  Figure 3-2 Local coordinate system for the Cap part of the Calotte enclosure  Mass moment inertias of the Calotte enclosure are shown in the table 3-1. For different parts of structure, including the cap part, the base part and the whole structure, six types of mass moments of inertia referring to the origin of the global coordinate system are listed.  Table 3-2 Mass moments of inertia of the Calotte enclosure (tonsmm ) 2  'xx  Cap 3.60E+07  Base 4.69E+08  Cap and Base 5.92E+08  'yy  3.08E+07  5.10E+08  6.33E+08  'zz  4.05E+07  4.18E+08  4.53E+08  •xy  1.17E+04  -2.81 E+05  -2.66E+05  'xz  5.56E+03  -6.75E+04  -5.55E+04  'yz  5.00E+06  7.05E+07  6.23E+07  3.4.1.2 Power and torque requirements for the Calotte enclosure The driving torque and corresponding power consumption are associated with various aspects of the system, including weight, mass moment inertia, acceleration, friction ratio, ice load, and wind load. In order to simplify the problem, the driving torque and corresponding power consumptions are calculated by following steps:  47  Step 1. Based on the telescope specification, the angular acceleration of the VLOT enclosure is assumed to be 0.05 °/sec . The inertia torque will be calculated 2  from the angular acceleration and mass moment inertia. Step 2.  The tangent friction force is calculated from the total weight of the enclosure (including ice loads) and friction ratio between bogies and the rail. This force multiplied by radius to give the value of the friction torque.  Step 3.  The torque to overcome wind load will be calculated according to two types of wind speeds: 25 m/s and 35 m/s.  Step 4.  By summing all torque together, the total driving torque requirement is calculated.  Step 5.  Based on the total driving torque requirement, the power requirements are determined by the following formula: P=T a  Where P: power T: torque 0): angular speed The driving torque and corresponding power consumption for the rotation of the base part and cap part are calculated respectively. In table 3-2, the results are listed under different loading conditions, which are associated with "dead load", "inertia load from acceleration", "ice load", "wind load with 25 m/s speed" and "wind load with 35 m/s speed". Also, the results are plotted in figure 3-3 and figure 3-4.  48  Table 3-3 Driving torque and power consumption of the Calotte enclosure  Base Load C a s e dead + acc + ice + wind 25 m/s + wind 35 m/s all  Torque (kNm) 840.70 1151.33 1238.55 1437.48 1968.61  Cap Power (kW) 8.80 12.06 12.97 15.05 20.62  Figure 3-3 Driving torque of the Calotte enclosure  49  Torque (kNm) 2058.96 2541.78 2562.04 3177.83 3585.45  Power (kW) 54.07 66.63 67.20 83.32 94.02  Figure 3-4 Power consumption of the Calotte enclosure  According to the results presented above, in the Calotte enclosure, the total torque required for the cap rotation is 3,585.45 kN-m and the total power needed is 94.02 kW; for the whole enclosure movement, the total torque required is 1,968.6 kN-m and the total power needed is 20.62 kW. It is obvious that the torque and power for driving cap part is much higher than for the whole enclosure, because that the cap rotates within an inclined plane, thus introducing a big mass eccentricity and results in a large inertia torque.  3.4.1.3 Modal analysis results Modal analysis is performed in order to find the vibration characteristics of the structure. Natural frequency and mode shapes are two major results from this analysis. From the natural frequencies, the rigidity of the structure can be reflected. The higher the frequency is, the stiffer the structure will be. The mode shape is represented by a deflected shape of the structure during the vibration. Based on the structural mode shapes, dynamic characteristics of the structure can be directly detected.  50  The first frequency of the Calotte enclosure is 1.9 Hz and the corresponding mode shape shows the whole structure swaying along the global x-axis (in global coordinate system). Also a large deformation occurs in the observation aperture, which reflects the rigidity weakness of structure due to this big opening.  Figure 3-5 First mode shape of the Calotte enclosure 3.4.1.4  Linear static analysis results  Linear static analysis is based on the assumption that all the stress level is lower than the yielding level so that the stress is proportional to the strain. Under this assumption, structural responses of each enclosure under different load cases are presented.  3.4.1.4.1 Base reaction force Base reaction force is one of the important structural responses, which is related to the base ring design, foundation design and associated mechanical system design. The results of base reaction forces of the Calotte enclosure under two load cases are plotted in figure 3-6.  51  NORMAL B A S E REACTION FORCES OF C A L O T T E ENCLOSURE  700  — — gravity+ice+snow —  gravity+wind  100  0  60  120  180  240  300  360  A n g l e s in the b a s e r i n g c i r c l e ( d e g r e e s )  Figure 3-6 Base reaction force of the Calotte enclosure  According to the results, the maximum value of the base reaction force due to two load cases is 656 kN, and the minimum value is 371 kN. The largest difference of force values is 285 kN.  3.4.1.4.2 Member stress The member stress is a common means to evaluate the structural design. The comparison between the maximum member stress and allowable stress can not only reflect the strength level of the structure, but also indicate efficiency of the structure.  The stress  values of structural members under two load cases are summarized in the tables 3-4.  52  Load case 1: gravity load + wind load (survival) Table 3-4 Member stress of the Calotte enclosure under load case 1  Ribs & rings Base ring Elem number  Interface rings  Aperture girder  1125  550  346  16  76  14  Elem number  957  8  1157  557  Min iMpji  -46  -9  - )0  -17  Max (Mpa)  51 : *•.-.*..  r  21  Load case 2: gravity load + ice load + snow load (survival) Table 3-5 Member stress of the Calotte enclosure under load case 2  Ribs & rings Base ring  Interface rings  Aperture girder  1245  572  101  11  Elem number  360  16  Max (Mpa)  123  v.--17  Elem number  681  1.8  1159  557  Min (Mpa)  -82  -18  -31  -38  '  It is obvious that the member stress is higher in load case 2 than in load case 1. The self weight of the structure is rather severe and its contribution to the vertical loads governs final effects of each load case. Especially in load case 2, the highest tension stress value of 123 Mpa happens in a member of horizontal rings and highest compression stress value of 82 Mpa happens in a member of vertical ribs. These results prove the mechanism of the dome structure to resist vertical loads: the vertical ribs, which are mainly in compression, resist the vertical loads and horizontal rings behave as the tie beams in tension to prevent the ribs expanding outside.  53  3.4.1.4.3 Displacement The displacements of the structure under various load cases can reflect the rigidity of the structure. The smaller the structural deformations are, the stiffer the structure is. The deflected shape and maximum structural displacement value are plotted in figure 3-7 and 3-8.  Load case 1: gravity load + wind load (survival) DISPLACEMENT STEM. S U B =1 TIME=1 DMX = 1 8 . 9 7 8  20M C a l o t t e E n c l o s u r e  F i g u r e 3-7 Deflected shape of the C a l o t t e enclosure u n d e r l o a d case 1  54  Load case 2: gravity load + ice load + snow load (survival) DISPLACEMENT  NCV 21 2003 10:42:35  o T p n - i  sriR=i T S E = I  P  U  J  C  M  -  1  DMX =38.898  20M Calotte Enclosure F i g u r e 3-8 D e f l e c t e d shape o f the C a l o t t e enclosure u n d e r l o a d case 2  The maximum displacement of the structure under load case 1 is 19 mm in lateral direction, and under load case 2 is 39 mm in vertical direction. Compared with the total height of the structure, these displacements are acceptable.  3.4.1.4.4 Interface rings The structural performance of interface rings directly influences the quality of the Calotte enclosure design.  Beside the member stress of this part as mentioned before, the  deformations of the interface rings, which are measured in the local cylinder coordinates, will be shown as figures below. The origin of cylinder coordinates is located at the center of the interface circle and displacements in radial, tangential and normal directions are measured  55  Load case 1: gravity load + wind load (survival) Structural displacement of interface ring (steel part) (mm)  radial direction tangential direction normal direction  Angles in interface circle (degrees)  Figure 3-9 Displacement of the steel interface ring under load case 1  Structural displacement of interfacer ring (aluminum part) (mm)  radial direction tangential direction normal direction  Angles in interface circle (degrees)  Figure 3-10 Displacement of the aluminum interface ring under load case 1  Under the load case one, the maximum absolute displacements of the base interface ring are 27 mm in radial direction, 15 mm in tangent direction and 6 mm in normal direction.  56  The maximum absolute displacements of the top interface ring are 25 mm in radial direction, 12 mm in tangent direction and 5 mm in normal direction.  Load case 2: gravity load + ice load + snow load (survival) Structural displacement of interface ring (steel part) (mm) 30  Figure 3-11 Displacement of steel interface ring under load case 2  Figure 3-12 Displacement of aluminum interface ring under load case 2  57  Under the load case two, the maximum absolute displacements of the base interface ring are 26 mm in radial direction, 15 mm in tangent direction and 12 mm in normal direction. The maximum absolute displacements of the top interface ring are 28 mm in radial direction, 26 mm in tangential direction and 13 mm in normal direction.  3.4.2 Analysis results of the Dome-Shutter enclosure 3.4.2.1 Mass information of the Dome-Shutter enclosure In table 3-6, the weight summary of the Dome-Shutter enclosure is presented. The total weight of the enclosure is 1,482 tons, which include 200 tons of the structural members. of the shutter, 30 tons of the mechanical system of the shutter, 981 tons of the structural weight for the base part and 271 tons of mechanical equipments on the base part. The total weight of shutter part is 230 tons, and the total weight of the base part is 1,252 tons.  Table 3-6 Weight of the Dome-Shutter enclosure  Dome-Shutter 20 m enclosure  Components Shutter Shutter drive system Shell rib (steel) Shell plate (aluminum) Base ring Arch girder (steel) Drive/brake bogie Idler bogie Track rail Total  Weight (tons) 200 30 142 190 220 250 60 270 120 1482  The origin of the global coordinate system in the Dome-Shutter enclosure model is located at the center of the dome, as shown in figure 3-13.  58  Mass moments of inertia of the Dome-Shutter enclosure to the origin of global coordinates are shown in the table 3-7.  Table 3-7 Mass moments of inertia of the Dome-shutter enclosure (tons-mm ) 2  B a s e and shutter  'xx  5.90E+08  'yy Izz  5.40E+08  'xy  4.10E+03  Ixz  6.90E+06  'yz  3.40E+03  5.60E+08  3.4.2.2 Power and torque requirement of the Dome-Shutter enclosure The calculation of power and torque for the Dome-shutter enclosure is based on a similar scenario as the Calotte enclosure. According to the motional mechanism of the upper shutter and the lower shutter, two pieces of the shutter can be simplified as two lumped mass points. The driving torque is calculated by the sum of inertia torque and friction 59  torque, and the power consumption is calculated based on total torque values. The calculation of torque and power requirements for the whole enclosure is based on the same steps as for the Calotte enclosure. The results are presented in the tables and figures below.  Table 3-8 Driving torque and power consumption of the Dome-Shutter enclosure  No. Load Case  Upper Shutter Power Torque (kW) (kNm)  Base  Lower Shutter Power Torque (kW) (kNm)  Torque (kNm)  Power (kW)  dead + acc  49082.74  452.12  13056.52  120.27  1200.78  12.57  2  + Ice  66007.44  608.02  17238.60  158.79  1511.40  15.83  3a  + Wind 25 m/s  50554.30  465.68  13082.58  120.51  1769.03  18.53  3b  +Wind 35 m/s  50606.43  466.16  13095.61  120.63  2053.16  21.50  4  all  68056.52  626.90  17290.22  159.27  2584.29  27.06  1  Figure 3-14 Driving torque of the Dome-Shutter enclosure  60  Figure 3-15 Power consumption of the Dome-Shutter enclosure  Considering various loading conditions, during the movement of the upper shutter, the total torque required is 68,056.52 k N m and the total power needed is 626.9 kW; during the movement of lower shutter, the total torque required is 17,290.22 k N m and the total power consumed is 159.27 kW; during the rotation of entire enclosure, the total torque required is 2,584.9 k N m and the total power consumed is 27.06 kW. It is obvious that the driving torque and power consumption for the upper shutter are much higher than those for other parts. When the upper shutter moves upward, a large torque is required to react to the high gravity load of the shutter. In the case of single shutter design, much higher torque will be required.  61  3.4.2.3 Modal analysis results  The first mode of the dome-shutter enclosure happens at the frequency of 1.4 Hz. In this mode, two upper parts of enclosure, which are divided by the shutter opening, sway oppositely. This mode shape reflects a significant decrease in rigidity of the structure due to the large structural discontinuity.  Figure 3-16 First mode shape of the Dome-Shutter enclosure  3.4.2.4 Linear static analysis results  3.4.2.4.1 Base reaction force Base reaction forces of the Dome-Shutter enclosure for two load cases are plotted as two curves in the figure 3-17. Each curve has two prominent peaks and each peak consists of two reaction force points. The values of these peak points are above 5,000 kN, while values of other points are below 1,000 kN. The maximum base reaction force value is 5,173 kN from the load case 1, and the maximum amplitude of value fluctuation is 5,300 kN. These characteristics are caused by the two arch girders in the Dome-Shutter enclosure. The highest base reaction forces occur right under these arch girders, which pass high concentrated forces from superstructures. The shapes of two curves are similar, which proves that the gravity load in the Dome-Shutter enclosure governs the vertical effects of each load cases.  62  NORMAL B A S E REACTION F O R C E S O F DOME-SHUTTER E N C L O S U R E  6000 5000 4000  fl  3000  - gravity+ice+snow -gravity+wind  2000  I  1000 0 60  -1000  120  180  240  300  360  A n g l e s i n the b a s e ring circle (degrees)  Figure 3-17 Base reaction force of the Dome-Shutter enclosure  3.4.2.4.2 Member stress The results of the member stress under different load cases are summarized in table 3-9 and table 3-10. Load case 1: gravity load + wind load (survival) Table 3-9 Member stress of the Dome-Shutter enclosure under load case 1  Ribs&rings Tie beam  Back ribs  Bracing  Base ring  Arch girders  2041  5063  136  101  Elem num  2602  3204  3408  3638  Max (Mpa)  105  56  31  73  Elem num  1156  3200  4001  485  2041  5062  Min (Mpa)  -63.23  -146  -37  -25  5 .141  -107  63  :  Load case 2: gravity load + ice load + snow load (survival) Table 3-10 Member stress of the Dome-Shutter enclosure under load case 2  Ribs&rings Tie beam Back ribs Bracing  Base ring  Arch girders  Elem num  2401  3204  3404  3600  2041  5028  Max (Mpai  110.6  49  11  62  120  79  Elem num  1156  3200  3407  3600  3614  5062  Min (Mpa)  -60  -123:  -102  -132  -93  . -40  According the results above, although the member stresses from both load cases are almost identical, the stress in load case 1 is a little higher than in load case 2. The big discontinuity of the structure increases the effects of lateral loads to the structure. Under the heavy wind load, the large lateral deformations of the structure lead to high bending stresses and axial stresses in some members. Also, comparing the stress value in each member, the higher stresses occur in base ring part and arch girder part. High stresses in the base ring are caused by high concentrated forces from the two arch girders. In load case 1, the highest stress values of base ring member are 208 Mpa in tension and 231 Mpa in compression. The stress value here is for combined stress, which includes axial stresses, bending stresses and torsion stresses. Based on the basic structural principle that more rigid a member is, the more loads it will attract, two arch girders with their predominate high rigidity and strength, absorb high loads resulting in high stresses. The highest stress values of arch girders are 101 Mpa in tension and 107 Mpa in compression under load case 1.  3.4.2.4.3 Displacement The deformation of the entire enclosure under load case 1 is depicted in the figure 3-18. Due to effects of the wind load pattern, the two parts of enclosure on each side of shutter opening deform towards each other. The maximum displacement of the whole structure under load case 1 is 74.5 mm in lateral direction.  64  Load case 1: gravity load + wind load (survival) AN  DISPLACEMENT STEP-1 SIB -1 TIME-1 DMX =74.537  NOV 25 2003 10:54:00 PLOT NO. 1  20M done Enclosure  Figure 3-18 Deflected shape of the Dome-Shutter enclosure under load case 1  Load case 2: gravity load + ice load + snow load (survival) AN  DISPLACEMENT STEP-1 SUB =1 TIME=1 •MX -52.571  NCW 25 2003 10:58:31 PLOT NO. 1  20M dome Enclosure  Figure 3-19 Deflected shape of the Dome-Shutter enclosure under load case 2  65  Under load case 2, the top part of enclosure is compressed under the vertical load and the ribs in the middle expand outside. The deformed shape is depicted in the figure 3-19. The maximum displacement of the whole structure under load case 2 is 53 mm in vertical direction. These displacements can be considered as acceptable. One can conclude that the big opening of the Dome-Shutter enclosure is directly associated with the amount of structural displacements under various load case. Since two arch girders are located at both edges of the opening and have higher rigidity and strength than other members, the performances these two girders are directly influence the amplitude of the maximum displacement of the whole structure.  3.4.2.4.4 Arch girders The importance of two arch girders in the Dome-Shutter enclosure is obvious. Their structural performances directly influence the quality of the Dome-Shutter enclosure design. The special location and layout of two arch girders require them to compensate for the large discontinuity of the structure. They have to resist heavy lateral loads and vertical loads. They must also provide good working environment for the shutter and mechanical devices too.  Therefore, the evaluation of the structural design for arch  girders should be centered on these duties.  Since the Dome-Shutter enclosure is symmetrical about the y-axis in global coordinate system (see figure 3-13), the structural response of each arch girder ought to be same under symmetric loads. The deformations of an arch girder under the two load cases are depicted in figure 3-20 and 3-21. Under each load case, absolute displacements of each node on the arch girder are plotted versus corresponding node numbers. Displacements are measured in the global coordinate system of Dome-Shutter model, as shown in figure 3-13.  66  Load case 1: gravity load + wind load (survival) Structural displacement of an arch girder  —— along global x axis —— along global y axis —» along global z axis  1  3  5  7  9 11. 13 15 17 19 21 23 25 27 29 31 33 35 37 Node number  Figure 3-20 Displacement of arch girder under load case 1  Load case 2: gravity load + ice load + snow load (survival) Structural displacement of an arch girder  -— along global x axis — along global y axis -  1  3  5  7  along global z axis  9 11 13 15 17 19 21 23 25 27 29 31 33 35 37 Node number  Figure 3-21 Displacement of arch girder under load case 2  The maximum displacement of arch girders is 65 mm along global x-axis direction under load case one. It indicates that strong wind load will govern the displacements of arch girders. Due to the lateral load, in global y direction, the lateral displacements of the arch girder are larger in load case 1 than in load case 2. In vertical direction, the self weight of  67  enclosure dominates the vertical effects of various loads so that the displacements of arch girders in load case 1 are similar to those in load case 2. Compared with the total height of the structure, the displacements of the enclosure are acceptable at this stage of design.  3.4.3 Analysis results of the Carousel enclosure 3.4.3.1 Mass information of Carousel enclosure  As shown in the table 3-11, the total weight of the Carousel enclosure is 2,354 tons, which include 250 tons for two parts of the door and associated mechanical devices, and 2,104 tons for total weight of base part. The structural weight of enclosure is 1,300 tons, which includes 600 tons for the skeleton and 700 tons for the panels. The weight of all mechanical devices and secondary structures is 1,054 tons.  Table 3-11 Weight of the Carousel enclosure Carousel 20 m enclosure Components  Weight (tons)  Aperture door  230  Door drive system  20  Shell rib (steel)  800  Shell plate (aluminum)  500  B a s e ring  180  Main frame (steel)  160  Rail b e a m  84  Drive /brake bogie  .30  Idler bogie  250  Track rail  100  Total  2354  The origin of the global coordinates in the Carousel enclosure model is located at the center of the base ring circle, which is shown as figure 3-22.  68  Figure 3-22 Global coordinate system for the Carousel enclosure  Mass moments of inertia of the Carousel enclosure to the origin of global coordinate system are shown in the table 3-12.  Table 3-12 Mass moments of inertia of the Carousel enclosure (tonsmm ) 2  Door and Base 1.98E+09 yy  2.02E+09  kz  1.38E+09  Iv  3.46E+06 -1.30E+08 -4.20E+06  69  3.4.3.2 Power and torque requirement of the Carousel enclosure The power and torque demands for the Carousel enclosure are shown in table 3-13. When the Carousel enclosure is in the operation, two types of movements are involved: the rotation of whole enclosure along base ring and the linearly shding of two pieces of the door. Because of the linear movement, the motion of two parts of the door can be simplified as motions of two mass points. The power consumption for the door is related to the linear inertia forces and friction forces. The driving torque and power consumption of the Carousel enclosure are calculated according to the same method as for other two enclosures above, and results are also plotted as figure 3-21 and figure 3-22.  Table 3-13 Driving torque and power consumption of the Carousel enclosure Doors Load C a s e  __lPI9  Base Power  Torque  Power  (kNm)  (kW)  (kNm)  (kW)  dead + a c c  390.51  6.51  2994.33  31.36  + ice  406.00  6.77  3269.95  34.24  + wind 25 m/s  427.12  7.12  4266.17  44.68  + wind 35 m/s  446.08  7.43  4902.09  51.33  all  484.82  8.08  5591.16  58.55  ue  70  Considering various loading effects, the movement of the door requires 484.82 k N m of the driving torque, and consumes 8.08 kW of power; the rotation of whole enclosure requires 5,591.16 k N m of driving torque, and consumes 58.55 kW of power. Thus the driving torque and power consumption for the rotation of the enclosure are higher than those for the door alone.  3.4.3.3 Modal analysis results  The first mode shape of Carousel enclosure is shown as figure 3-25. The first frequency of the Carousel enclosure is 1.7 Hz and the corresponding mode shape is that the whole structure sway along global x-axis. This mode shape indicates that the lateral stiffness of the whole structure is lower than the local stiffness of the door opening in the Carousel enclosure.  72  3.4.3.4 Linear static analysis results  3.4.3.4.1 Base reaction force The Normal base reaction forces of the Carousel enclosure under two load cases are plotted as two curves in the figure 3-26. On each curve, four peak points represent the highest base reaction forces. These forces occur under four main columns, which are located at both sides of the observation opening. Because these columns are much suffer and stronger than other members, they attract more loads, which results in the highest reaction forces. The highest reaction force happens in load case 1, gravity load + wind load (survival), with the value of 1,067 kN. The lowest base reaction force in load case 1 is 137 kN and the maximum fluctuation is 930 kN.  NORMAL BASE REACTION FORCES OF CAROUSEL ENCLOSURE  A 0  h  — gravity+ice+snow  \  1  1  1  1  60  120  180  240  —— gravity+wind  1  300  360  Angles In the base ring circle (degrees)  Figure 3-26 Base reaction forces of the Carousel enclosure  3.4.3.4.2 Member stress The stresses of various structural members in the Carousel enclosure are summarized in table 3-14 and 3-15 for two load cases respectively.  73  Load case 1: gravity load + wind load (survival) Table 3-14 Member stress of the Carousel enclosure under load case 1 Columns&rings  Rail beam  Bracing  Basering  Main colunmns  Main girder  Elem num  791  4800  4185  100  3219  3600  Max (Mpa)  79  35  5fi  20  50  46  Elem num Win (Mpa)  790 -47  4805 -50  4192 '0  116 -13  3219 63  3600 -49  Load case 2: gravity load + ice load + snow load (survival) Table 3-15 Member stress of the Carousel enclosure under load case 2 Columns&rings  Rail beam  Bracing  Basering  Main colunmns  Main girder  Elem num  791  4800  4185  147  3209  3600  Max (Mpa)  68  39  68  2  55,  46  Elem num Mm (Mpa)  790 60  4805 -50  4192 G9  160 -4  3209 -71  3600 58  The member stresses from both load cases are very close. In load case 1, the highest combined tensile stress value is 79 Mpa and is located at one of "horizontal ring" members; the highest combined compression stress value is 76 Mpa and happens in one of "bracing" members. In load case 2, the highest combined tensile stress is 68 Mpa in one of "bracing" members; the highest combined compression stress is 71 Mpa in one of "main column" members. The vertical columns in the Carousel enclosure are closely spaced to resist vertical and lateral loads. The large weight of the aperture door is carried by the rail beams and the bracing systems. Members with extreme stress levels cannot be found in the Carousel enclosure.  3.4.3.4.3 Displacement The deflected shape of the Carousel enclosure under load case 1 is depicted in the figure 3-27. Due to the wind load, along global x-axis direction, one side of the enclosure deforms under compression and the other side of enclosure deforms under suction; along global y-axis direction, both sides of enclosure deform under suction. The top track beam  74  sags in the middle due to the dead loads of the aperture door. Because the deformation of the top track beam governs the total deformations of the enclosure, the maximum displacements of the whole structure under both load cases are all about 27 mm.  20M carousel Enclosure  Figure 3-27 Deflected shape of the Carousel enclosure under load case 1  75  Load case 2: gravity load + ice load + snow load (survival) A N  DISPLACEMENT STEP=1 SUB =1 TIME=1 •MX =27.377  DEC  4 2003 12:30:53 PLOT NO. 1  20M carousel Enclosure Figure 3-28 Deflected shape of the Carousel enclosure under load case 2  3.4.3.4.4 Main frames The two main frames are key components of the Carousel enclosure. Each frame is composed of two columns and a crossbeam. Two crossbeams support the roof structure and the top rail beam. Four columns, located at both sides of the observation opening, are supported by the base ring on one side, and bottom rail beam on the other side. The performance of the frames is directly related to the rigidity of the whole enclosure and behaviors of the aperture door. The stress of the main frames has been mentioned in section 3.4.2.4.2. Under both load cases, the stress level of the frames is around 50 Mpa. Since the Carousel enclosure is also symmetric to y-axis in global coordinate system (see figure 3-22), the structural response of two main frames under symmetric loads are same.  76  Under asymmetric loads, the frame with the larger deflection is identified. The deformations of one piece of frame under both load cases are plotted in figure 3-29 and 330. Under each load case, absolute displacements of each node are plotted corresponding node numbers. Displacements are measured in the global coordinates of the Carousel enclosure model, as shown in figure 3-22.  Load case 1: gravity load + wind load (survival) Structural displacement of the main frame  15 E E  1 I  1 0  5 0  -5 8 -10 8" -15 -20 -25  _l  -3  I  I  - — along global x axis  L  5—7 9—14  ^3 25 27 29  along global y axis along global z axis  Q  Node Number  Figure 3-29 Displacement of the main frame under load case 1  Load case 2: gravity load + ice load + snow load (survival) Structural displacement of the main frame  t(m  5 0 E -5 c -10 CU E CD  O cd Q. CO  -3  5 7- 9 11 13 15 17 19 21 23 25 27 26 along global x axis along global y axis  -15  along global z axis  -20 Q -25 -30 Node Number  Figure 3-30 Displacement of the main frame under load case 2  77  The maximum displacement of two main frames is 25 mm in vertical direction under load case 2. The dead load from top rail girder governs the most severe case of the frame deformation. The maximum lateral displacement, which is 14 mm in wind blowing direction (global x direction), is caused by loads of case 1.  3.5  CONCLUSION  Based on the analysis and study in this chapter, a general picture for each VLOT enclosure candidate has been formed. According to various design concepts, the structure of each candidate presents its unique characteristics. By checking functional specifications and performance requirements of the VLOT enclosure, the prehminary structural design of each candidate can be deemed acceptable. The design characteristics and analysis results of each type of enclosure represent the database for a comparative study and decision analysis as conducted in the following chapters.  4 COMPARATIVE STUDY In this chapter, a systematic comparative study on three types of VLOT enclosure designs is conducted. Based on the information gathered in chapter 3, three types of enclosures are compared by their structural and mechanical aspects, including mechanical control, dynamic characteristics, and static characteristics. Comparisons focus on both the entire structure of the enclosure and certain local critical members. Unique characteristics of each enclosure are highlighted in order to prepare a decision analysis.  4.1  PREREQUISITES  Before starting the comparative study, a question is raised: are those candidates for the comparison in a comparable level? The answer to this question is the most important prerequisite for this comparative study. Because each type of the enclosure represents a rather complex system, a precise and complete comparable level for all candidates is unrealistic. Therefore, the stress level has been selected as a measure of comparison for  78  the candidates. By changing the type and section property of structural members, the global member stresses in each enclosure are approximately at the same level. Based on the stress criterion, structural designs of three enclosures are in a comparable level.  4.2 MECHANICAL CONTROL The challenges in the VLOT enclosure design are that the structure is huge, complex, and movable. According to the specification of VLOT telescope, the enclosure should meet several motion requirements as follows: •  36 degree/min of slew rate.  •  Continuous slewing for up to 15 minutes, once per hour.  •  1 movement per 2 minutes during observation.  •  2 start/stop cycles / minute for a maximum of 15 minutes per hour  •  Maximum 25% for duty rate  Therefore, the control of the motion of VLOT enclosure during the routine operation is one of the important design objectives. In this section, three types of enclosures are compared under the mechanical control aspect. The study focuses on various specific aspects, including weight, power, and frequency.  4.2.1  Mass information  The first concern from the mechanical control aspect is the mass information of the enclosure. Before moving or stopping the system, it will be useful to know the weight and mass eccentricity of the system. The mass information determines the mechanical design and influences the structural design for the VLOT enclosures.  79  According to the various concepts of the enclosures, the motion mechanism differs for each system. The main movements of the Calotte enclosure include the rotation of the whole structure along the base ring, rotation of the cap part along the interface ring and movement of aperture cover (not considered in this study). The movements of the DomeShutter enclosure include vertical movements of two pieces of the shutter and rotation of the whole enclosure. The Carousel enclosure has movements like Dome-Shutter enclosure, except that the horizontal movements of two pieces of the door replace vertical movements of two pieces of the shutter. The mass information for each candidate is determined as weight and mass moments of inertia for different components. In table 4-1, the mass information for three enclosures is presented. The components listed in the table include "Door/shutter" for the three enclosures, "Cap" and "Cap + door" for the Calotte enclosure, "Base" for the base part of the three enclosures, "Panels" for the surface panels of three enclosures and "Total" for the total weight. The weight of each component is represented by "skeleton weight", which is the structural weight of the components, and the "total weight", which is the overall weight of components, including the weight of main structures, the weight of mechanical devices and the weight of secondary structures.  Table 4-1 Weight comparison of three enclosures  Components Door/shutter Cap part Cap+door Base Panels Total  Calotte Dome-Shutter Carousel skeleton total weight skeleton skeleton total weight total weight weight (tons) (tons) weight (tons) (tons) (tons) weight (tons) 25 30 200 230 230 250 45 81 0 0 0 0 152 70 0 0 0 0 427 270 781 1062 1100 1604 260 260 190 190 500 500 600 950 1171 1482 1830 2354  The Calotte enclosure is the lightest enclosure according to this summary, with 537 tons for the pure structural skeleton weight and 950 tons for the whole system weight. The Dome-Shutter enclosure is 43% heavier than the Calotte enclosure, with 1,181 tons for the pure structural skeleton weight and 1,482 tons for the whole system weight. The  80  heaviest enclosure is Carousel enclosure, with 1,810 tons for tons for the pure structural skeleton weight and 2,354 tons for the whole system weight, which are 2.5 times of the weight of Calotte enclosure and 1.9 times of the weight of the Dome-Shutter enclosure. The large weight for the Carousel enclosure when compared with other two alternatives is mainly due to the geometry of the enclosure. According to the space demands of the 20 m telescope, the cylinder shape of the Carousel enclosure results in a large volume of the structure, which is approximately twice as large as the volume of the sphere shape of the Calotte and the Dome-Shutter enclosure. The advantage of the spherical shape on the efficiency of space occupation is proven again. The layout of the Calotte enclosure results in a lighter weight than the Dome-Shutter enclosure. It is mainly due to the fact that the cap part of the calotte enclosure, which occupies 50% of the whole structure, is made of aluminum, while the enclosure structure of the Dome-Shutter, except the shutter, is made of steel.  The mass moments of inertia for three enclosures are compared in table 4-2. I and I xx  yy  are mass moment of inertia of whole enclosure respect to x-axis and y-axis through the model centroid. They reflect the rotational characteristics of the system.  Table 4-2 Mass moment of inertia for three enclosures Calotte enclosure  Dome-Shutter enclosure  Carousel enclosure  Ixx (mm )  5.92E+08  4.46E+08  1.98E+09  lyy(mm )  6.33E+08  4.03E+08  2.02E+09  4  4  Based on the table above, the Calotte enclosure and the Dome-Shutter enclosure share the similar characteristics. The reason is that these two enclosures have the similar geometry and mass distribution. In the Calotte enclosure, because two different materials are used for the cap part and the base part respectively, and prominent lumped mass is added to the interface rings, the whole enclosure has a mass eccentricity. Therefore, when compared with the Dome-Shutter enclosure, which has a relative uniform mass distribution, the Calotte enclosure has higher mass moments of inertia. The values for the Carousel enclosure are approximately four times higher than the values for other two 81  types of enclosures. The dramatic increase in mass and radius of the Carousel enclosure is the major reason for the large values of mass moment of inertia.  4.2.2 Power consumption In order to accommodate 20 m telescope, VLOT enclosures become larger and heavier than any currently existing telescope enclosures in the world. On the top of the Mauna Kea Mountain, the power supply for the operation of this kind of huge system will be a challenging problem. Besides the lighting system, air conditioners, vent system, elevators and other electrical equipments, the major power consumption of the enclosure stems from the driving system of enclosures. Friction forces and inertia forces result in main resistances to the driving torque during the movements of enclosures. The amount of driving torque determines the amount of the power that the system will consume. In the table 4-3, the total driving torque and associated power consumptions of three types of enclosures are listed. For the Calotte enclosure, the total torque includes the driving torque for the rotation of the base part and the driving torque for the movement of the cap part. For the Dome-Shutter enclosure, the total torque includes the driving torque for the rotation of the base part and the driving torque for movements of the shutter. For Carousel enclosure, the total torque includes the driving torque for the rotation of the base part and the driving torque for the movement of the door. During the calculation of torque values, several loading conditions are considered, including "dead load", "inertia load", "ice load", "wind load with 25m/s speed" and "wind load with 35m/s speed". The results are also shown in figure 4-1 and figure 4-2.  82  Table 4-3 Driving torque and power consumption of three enclosures Dome-Shutter  Calotte Load Case  Torque (kNm)  Dead + Acc  2899.66 3693.10  + Ice + Wind 25 rrVs +Wind 35 rrVs All  3800.59 4615.30 5554.06  Carousel  Power (kW) 62.89 78.69 80.17  Toque (kNm)  Power (kW)  Torque (kNm)  Power (kW)  63340.03 84757.45 65405.91  584.97 782.64 604.71  3384.83 3675.96 4693.29  98.38 114.64  65755.19 87931.03  608.29 813.23  5348.17 6075.99  37.86 41.01 51.79 58.77  Figure 4-1 Driving torque comparison of three enclosures  83  66.63  Figure 4-2 Power consumption comparison of three enclosures  The total driving torque for the Dome-Shutter enclosure is 5,554.06 k N m and the corresponding power consumption is 114.64 kW. The total driving torque for the DomeShutter enclosure is 87,931.03 k N m and corresponding power consumption is 813.23 kW. The total driving torque for the Carousel enclosure is 6,075.99 k N m and corresponding power consumption is 66.63 kW. The driving torque and corresponding power consumption for the Dome-Shutter enclosure are much larger when compared to the other two enclosures. Though having a similar shape like the Calotte enclosure, the Dome-Shutter enclosure requires nearly sixteen times of the driving torque and power consumptions. This is mainly caused by the different moving mechanism. For the DomeShutter enclosure, vertical movements of two pieces of the shutter require a large amount of driving torque to overcome the high vertical inertia loads, which consumes a lot of energy. For the Calotte enclosure however, either rotations of the cap part or rotations of base part requires relative low driving torque to overcome friction loads and inertia loads. The driving torque for the Carousel enclosure is a little higher than for the Calotte  84  enclosure, caused by the significant differences in weight. The total power consumption of the Carousel enclosure is lower than that of the Calotte enclosure since the angular speed of the cap part in Calotte enclosure is higher than that of the base parts.  4.2.3 Frequency It is a known fact in mechanical design that the rigidity of a system directly influences the mechanical performance. The poor rigidity of a structure usually causes problems for the mechanical design. When the telescope tries to point to a certain object in the sky, the enclosure should start, move and stop to the right position within proper response time. If the enclosure is too flexible and takes a long time to complete its motion, observation activities will be influenced. From the structural point of view, the rigidity of the structure cannot be always as high as desired. Therefore, the objective a high rigidity for structure should be pursued based on a good structural design. The natural frequency of the structure is a good measure of rigidity. It is equal to the vibration cycles per unit time during the harmonic motion. This parameter is only related to the stiffness and mass of the object. Therefore, under the same mass level, the higher the frequency is, the stiffer the structure. Different mode shapes are presented during the vibrations of the system, with its corresponding natural frequency. Since the first several modes contribute most to the total response of the structure, they are mainly considered in this analysis. Based on preUminary designs of three types of enclosures, frequencies of each structure are listed in table 4-4.  Table 4-4 Frequency comparison of three enclosures  Calotte  Dome-Shutter  Carousel  1st mode frequency (Hz)  1.9  1.3  1.7  2nd mode frequency (Hz)  2.4  1.5  1.9  3rd mode frequency (Hz)  2.7  1.7  2.2  85  It is found that the highest first natural frequency of 1.9 Hz belongs to the Calotte enclosure. The Calotte enclosure takes advantage of the dome layout, in which each rib performs as a part of arch and contributes its strong axial capacity into the high rigidity and strength of the whole system. Moreover, the idea of a rotating cap reduces the observation opening to the minimum size and preserves the integrity of the whole structure. The lowest first natural frequency value ofl.3 Hz belongs to the Dome-Shutter enclosure. Since the mass of this enclosure is close to the one of the Calotte enclosure, the lower natural frequency indicates the lower rigidity of the Dome-Shutter system. The discontinuity of the structure caused by the big opening for the shutter is the main reason for this result. With its first natural frequency, the carousel enclosure ranks second among three types of enclosures. While the total mass increases significantly, the densely arrayed columns and tie rings give the Carousel enclosure a high rigidity. The resulting natural frequency of the Carousel enclosure is still higher than that of the Dome-Shutter enclosure, although the total mass of the Carousel enclosure is more than twice of the total mass of the DomeShutter enclosure.  4.3  STRUCTURAL RESPONSE  Under various loading conditions, responses of the structure are presented by parameters of stress, deformation and base reaction. Member stresses indicate the strength of the structure. They are related to member forces and section properties. Deformations reflect the rigidity of the system. Global deformation and local deformation of the structure are determined by the stiffness of the structure and loads. Base reaction forces summarize all loading effects to the foundation of the structure. They are determined by resultants of various loads acting on the structure. In this section, stress, deflection and base reaction force of three enclosures are compared.  86  4.3.1 Stress The stress comparison between three enclosures is not so straightforward as comparisons on other aspects. The stress level of each member can be controlled by the choice of section properties. Therefore, pure numerical comparison of member stress in VLOT enclosure design is not feasible. The stress comparison here only aims to prove the compatibility of three candidates based on the simple criteria of strength level and efficiency level of the structural design. Global member stresses of three enclosures are all below the yielding stresses of materials and are roughly at the same level. It indicates that three candidates are comparable to each other. More stress studies are deemed to be necessary for the further design of each enclosure. In particular for some members that provide mechanical interface, the stress analysis should according to the fatigue stress specifications, as well as the strength capacity requirements. The members in question are the base ring girder of all three enclosures, the interface rings and the aperture ring of the Calotte enclosure, the two arch girders of the Dome-Shutter enclosure, and the main frames and the rail beams of the Carousel enclosure.  4.3.2 Deflection The maximum global deflections of three enclosures under two load cases are listed in the table 4-5. The load case 1 is composed of gravity load and survival wind load. The load case 2 is composed of gravity load, survival ice load and snow load.  Table 4-5 Maximum global displacement comparison of three enclosures  Type of enclosure Calotte Dome-Shutter Carousel  Displacement (mm) load c a s e 1 load c a s e 2 19 39 52 75 27 27  87  The maximum displacement of the Calotte enclosure is 19 mm under load case 1 and 39 mm under load case 2, which are much less than 75 mm and 52 mm of Dome-Shutter enclosure in load case 1 and 2 respectively. Because the mass distribution and geometric characteristics of these two enclosures are similar to each other, the loads on these two structures are in the same level. Therefore, it is reasonable to conclude that the smaller deflection of Calotte enclosure indicates a higher structural rigidity of its whole structure when compared with Dome-Shutter enclosure, which has big discontinuity due to its large shutter opening.  The loads on the Carousel enclosure are not comparable to the loads on other two enclosures. However, the maximum deflection of Carousel enclosure is 27 mm in both load cases, indicating a strong rigidity of the structure.  4.3.3 Base reaction force Base reactions are directly related to base ring design of VLOT enclosures. Considering the location and functions of the base ring girder, its member stress level should be kept below the permissible fatigue stress values. Its maximum deformation should stay within a certain limit in order to accommodate the mechanical systems mounted on the girder. The foundation design of the structure is directly related to amount and distribution of base reaction forces. A good foundation design should have enough strength and rigidity to support the superstructure, and isolate the enclosure from the telescope. Base reaction forces of three types of enclosure under two load cases are plotted as several curves in the figure 4-3 and 4-4. The curves of the Dome-Shutter enclosure, with their outstanding peaks, are prominent when compared with curves of other two enclosures. Values of the peak points are about ten times higher than values of the left points.  88  Compared with the Dome-Shutter enclosure, the Calotte enclosure has almost uniformly distributed base reactions. The force values are close to the non-peak values of the DomeShutter enclosure. The curves of Carousel enclosure for both load cases are similar to the curves of Calotte enclosure, except for the small peaks that occur under the feet of main columns. Especially under the load case 1, the peak reaction force value is around three times higher than the values of left base constraint nodes. Even though, the highest reaction force of the Carousel enclosure is still five times less than the peak reaction values of the Dome-Shutter enclosure  BASE REACTION FORCES COMPARISON (Load case: gravity + wind)  6000  — Calotte enclosure —— Dome-Shutter enclosure - Carousel enclosure  CD O  O  ra CD  rr  60  120  180  240  300  360  Angles in the base ring circle (degrees)  Figure 4-3 Base reaction force comparison under the load case 1  89  BASE REACTION FORCES COMPARISON (Load case: gravity + ice + snow)  6000 5000 P  4000  — Calotte enclosure — Dome-Shutlerll enclosure — - Carousel enclosure  3000 o  CO CD  rr  2000 1000 0 60  120  180  240  300  360  Angles in the base ring circle (degrees)  Figure 4-4 Base reaction force comparison under the load case 2  The large structural opening and the special layout of two arch girders in Dome-Shutter enclosure result in high values and uneven distributions of base reaction force. Although the strong structural layout of the Carousel enclosure compensates a lot for the discontinuity of the structure, high values for the base reaction forces are still found under the two main frames. Therefore, advantages of high integrity of the Calotte enclosure are strengthened by the facts of relatively uniform distributions and relatively low values of base reaction force.  90  4.4  C O N C L U S I O N  The comparative study in this chapter presents unique characteristics of each VLOT enclosure design. Because the telescope enclosure is a very complex system, it is very difficult to design three types of VLOT enclosure to a completely comparable level. Some assumptions and optimizations are applied before the comparative study, so that candidates are comparable on several aspects. By this way, the results of comparison are useful for the decision analysis, and for the further research and design.  5  DECISION ANALYSIS  The main objective of this study is to find the best design solution for the VLOT enclosure structure. Based on the research about the telescope enclosure design alternatives mentioned above, the scope of design candidates for VLOT enclosure is concentrated on three types of enclosures. According to prehminary designs and the comparative study, main characteristics of each type of enclosure have been highlighted. In this chapter, a systematic decision analysis is approached in order to find an indication that which design is the most promising one.  5.1  P R E A N A L Y S I S  According to the complexity of the VLOT enclosures, more than one objective may be involved in the analysis, including the minimum cost, the best structural performance, the best mechanical performance, and the reliability of system, and each objective is even correlated to each other. In order to simplify the problem, variables for different objectives are converted to the cost variables. Reliability objective is considered during the analysis procedure by the possibility coefficients. Then, a multi-objective problem is simplified into a single objective problem—the minimum cost objective problem. A l l the data and evidences used in the design analysis are based on preliminary designs and comparative studies as mentioned before.  91  5.2  MODEL  The model for the decision analysis is built based on the results of the preanalysis. The function for the minimum cost objective is described as follows:  C — min(gj  ,x, 2  ...), g  2  (^4 > ^5 >  x$ •••)» £ 3 ( ^ 7 > - ^ 8 » ^ 9  ••••))  Where C:  The minimum cost of the enclosure design  g : The cost of the Calotte enclosure design l  g:  The cost of Dome-Shutter enclosure design  g :  The cost of Carousel enclosure design  2  3  x ,x ,x ...: Variables for the Calotte enclosure solution 1  2  3  x ,x ,x ...: 4  5  6  Variables for the Dome-Shutter enclosure solution  JC , x , x ...: Variables for the Carousel enclosure solution 7  s  g  The total cost of each enclosure design consists of three parts: the cost during preparation, the cost during construction and the cost during operation. The cost during preparation includes the cost of design and the cost of fabrication. The amount of time spent in the design office and shop for each enclosure is estimated, and then converted into cost values. The cost of material, labor and facilities mainly constitutes the cost during construction. The cost of materials is estimated according to the total weight of each preliminary design model. The cost of labors and facilities is roughly estimated based on the amount of time spent on the construction site. The cost during operation comprises of the cost of regular maintenance, the cost of power consumption and the cost of reparation. These values are calculated based on the operation time of ten yeas. The structure of the model is plotted in figure 5-1 and 5-2.  92  Total cost of Calotte enclosure Final decision  Cost during preparation Cost during construction Cost during operation  Cost during preparation The design solution with the minimum cost  Total cost of Dome-Shutter enclosure  Cost during construction Cost during operation  Cost during preparation Total cost of Carousel enclosure  Cost during construction  Cost during operation Figure 5-1 Model layout of the decision analysis  93  Cost of design efforts  Cost during preparation  Cost of fabrication  Cost of materials  Cost during construction  Cost of labors  Cost of facilities Input values of variables Cost of maintenance  Cost during operation  Cost of power consumption  Cost of reparation Figure 5-2 Model layout of the decision analysis  94  5.3 VARIABLES Based on the prehminary design, the cost estimation for different phases of the project will be a difficult procedure. The complexity of the system will also increase the uncertainty of the project. Based on simple assumptions, engineering experiences and expert advices, the values of variables are estimated. The design records and practice experiences of current existing large-scaled enclosures provide references for the VLOT enclosure design. Particularly, the design information of the Gemini 8.0 m enclosure is summarized. According to the comparison between the VLOT enclosure and the Gemini 8.0 m enclosure, scale factors are evaluated.  5.3.1.1 Preparation phase In this phase, the cost of design and fabrication for three enclosures are estimated according to the formula below:  Where C\: Cost in preparation phase with the unit of Canadian dollars TJ: Time consumed with the unit of hours p : Unit cost with the unit of dollars/hour  The design office hours and shop hours for each structural component of enclosures are estimated. Design office hours represent the time consumed on the design procedure, while shop hours include the time for fabrication, installation and paint in the shop. Under the common labor price, which is approximately 60 $/hour for design office and 60 $/hour for fabrication shop, the total cost in this phase is calculated.  95  In the table 5-1, the cost of the Gemini 8.0 enclosure in the preparation phase is presented. Main structural and mechanical components are listed. Other components, such as vent system, platform and so on, are summarized in the "other" part. According to the results, the total design office hours for the Gemini 8.0 enclosure are approximately 13,220 hours and cost 793,200 Canadian dollars, and the total shop hours are approximately 63,900 hours and cost 383,400 Canadian dollars.  Table 5-1 Preparation cost of the Gemini 8.0 m enclosure  G e m i n i 8.0 m e n c l o s u r e Components Shutters Shell ribs Shell plate Base ring Arch girders Drive /brake/idler bogie Track rail Wind blind Other Subtotal  Hawaii  Design office (hours) Cost (CAN $) 800 48000 400 24000 30 1800 450 27000 650 39000 600 36000 250 15000 40 2400 10000 600000 13220 793200  Shop (hours) Cost (CAN $) 8000 480000 5000 300000 1200 72000 2800 168000 8000 480000 6000 360000 200 12000 2700 162000 30000 1800000 63900 3834000  The 20 m Dome-Shutter enclosure is very similar to the expanded Gemini enclosure, so that its cost can be estimated by scaling the cost of the Gemini enclosure. According to the increasing workloads and complexity for general components such as shell ribs, shell plates, track rails, and wind blind, the scale factor for the design hours is 1.5 and for the shop hours is 3.0. For some critical components such as the shutter, arch girders and base ring girders, the growth of workloads and complexity for the design and the fabrication is more significant than for other common components. Therefore, for these components, the scale factors are 3.0 for the design hours and 4.0 for the shop hours. According to the results listed in the table 5-2, the total design office hours of the 20 m Dome-Shutter enclosure are 39,660 hours and related cost is 2,379,600 Canadian dollars, which are 1.76 times of those for the 8.0 m Gemini enclosure. The total shop office hours of the 20 m Dome-Shutter enclosure are 210,500 hours and related cost is 12,630,000 Canadian dollars, which are 3.2 times of those for the Gemini 8.0 m enclosure.  96  Table 5-2 Preparation cost of the 20 m Dome-Shutter enclosure  Components Shutter Shell rib Shell plate Base ring Arch girder Drive/brake/idler bogie Track rail Wind blind Other Total  Dome-Shutter 219 m e n c l o s u r e Design office hours Cost (CAN $) 2400 144000 1200 72000 90 5400 1350 81000 1950 117000 1800 108000 750 45000 120 7200 30000 1800000 39660 2379600  Shop hours 32000 15000 3600 11200 32000 18000 600 8100 90000 210500  Cost (CAN $) 1920000 900000 216000 672000 1920000 1080000 36000 486000 5400000 12630000  Because the 20 m Calotte enclosure has a similar shape and weight to the 20 m DomeShutter enclosure, the estimation of the Dome-Shutter enclosure can provide guidance for the estimation of the Calotte enclosure. For general members of the Calotte enclosure, including shell ribs and shell plates, the same scale factors are used as those in the DomeShutter enclosure, so that the design time and shop time are same in both types of enclosures. However, the difference between these two enclosures cannot be ignored. The interface ring part is the unique feature of the Calotte enclosure, which has no engineering experience to follow. Therefore, the scale factors for this part is 6.0 for design office hours and 4.5 for the shop hours. According to the characteristics of base reactions of the Calotte enclosure, the scale factors of the base ring girder in the Calotte enclosure are 1.5 for design office hours and 3.0 for the shop hours. The aperture cover of the Calotte enclosure does not need high performance requirements as the shutter in the Dome-Shutter enclosure, so that the scale factors for this part are 1.5 for the design office and 2.0 for the shop. According to the results in table 5-3, the total design office hours of the Calotte enclosure are 22,695 hours and cost 1,361,700 Canadian dollars, and total shop hours of the Calotte enclosure are 145,200 hours and cost 8,712,000 Canadian dollars.  97  Table 5-3 Preparation cost of the 20m Calotte enclosure  Components Aperture cover Shell rib Shell plate Base ring Interface ring Drive/brake/idlerbogie Track rail Wind blind Other Total  Cost (CAN $) DesignCalotte office hours 20 m enclosure 1200 72000 600 36000 45 2700 675 40500 3900 234000 900 54000 375 22500 0 0 15000 900000 22695 1361700  Shop hours 16000 10000 2400 8400 36000 12000 400 0 60000 145200  Cost (CAN $) 960000 600000 144000 504000 2160000 720000 24000 0 3600000 8712000  The 20 m Carousel enclosure is much larger and heavier than the other two enclosures. Which results in higher workloads of the design and fabrication. So the scale factors are 4.5 for the design office hours and 6.0 for the shop hours. According to the results listed in the table 5-4, the total design office hours of the Carousel enclosure are 59,490, which cost 3,569,400 Canadian dollars, and the total shop hours are 48,000, which cost 8,712,000 Canadian dollars.  Table 5-4 Preparation cost of the 20 m Carousel enclosure  Components Door Shell rib Shell plate Base ring Interface ring Drive/brake/idler bogie Track rail Wind blind Other Total  Design office hours (CAN $) Carousel 20 m Cost enclosure 3600 216000 1800 108000 135 8100 2025 121500 2925 175500 2700 162000 1125 67500 180 10800 45000 2700000 59490 3569400  98  Shop hours 48000 22500 5400 16800 48000 27000 900 12150 135000 315750  Cost (CAN $) 2880000 1350000 324000 1008000 2880000 1620000 54000 729000 8100000 18945000  5.3.1.2 Construction phase During this phase, the cost calculation is according to the formula as follows:  C =c + +c 2  m  Cl  f  Where: C : Cost of during the construction phase with the unit of Canadian dollars 2  c : Cost of materials c, : Cost of labors c : Cost of facilities f  The cost of this phase is mainly composed of three components: the material cost, the labor cost and the facility cost. The material cost refers to the materials of main structural and mechanical components of the enclosure. The labor cost is related to the labors during the construction of main structural and mechanical components. The facility cost is the cost of engineering facilities during the construction, including cranes, falsework, formworks, trailers, trucks and so on.  5.3.1.2.1 Material cost The material cost is calculated based on the weight of the structure and the unit price of materials, which is shown as the following formula:  Where:  w:  Weight of each component with the unit of metric tons  p : Unit price of materials with the unit of Canadian dollars m  In table 5-5, the material cost estimation of the Calotte enclosure is listed. The Unit price of each component is roughly estimated. According to the results, the total unit cost of  99  material in Calotte enclosure is 93,500 Canadian dollars per ton and the total material cost is 4,176,000 Canadian dollars. These results provide a reference for the material cost estimation of other two enclosures.  Table 5-5 Material cost of the 20 m Calotte enclosure Calotte 2 0 m enclosure  Components Aperture cover (aluminum) Door drive system Shell rib (aluminum) Shell rib (steel) Shell plate (aluminum) Shell plate (steel) Base ring Interface ring (aluminum) Interface ring (steel) Hole ring Drive/brake bogie Idler bogie Track rail Total  Weight (tons) 25 5 40 112 45 215 183 19 53 7.5 20 130 95 950  Unit price(CAN $/ton) 6000 20000 6500 4500 5000 2500 3500 5000 10000 15000 8000 4000 3500 93500  Total cost (CAN $) 150000 100000 260000 504000 225000 537500 640500 95000 530000 112500 160000 520000 332500 4167000  The material cost estimation of the Dome-Shutter enclosure is presented in table 5-6. For components including shell ribs and shell plate, the same unit prices as in Calotte enclosure are used. The unit prices of certain components are modified in order to reflect the unique characteristics of Dome-Shutter enclosure. For example, although the shutter has the same unit material price as the aperture cover in the Calotte enclosure, the unit price of shutter drive system is much higher than that of the door drive system. This is because that the shutter needs higher capacity and performance requirements for the drive system. Due to the uneven distribution and high values of base reactions in the DomeShutter enclosure, the base ring girder and associated drive/brake bogies require significant improvements in strength and stiffness, which leads to almost doubled unit material price for these components when compared with the Calotte enclosure. According to table 5-6, the total unit price of the Dome-Shutter enclosure is 84,500 Canadian dollars per ton and the total material cost is 11,599,000 Canadian dollars.  100  Table 5-6 Material cost of the 20 m Dome-Shutter enclosure  Components Shutter (aluminum) Shutter drive system Shell rib Shell plate (aluminum) Base ring Arch girder Drive/brake bogie Idler bogie Track rail Total  Dome-Shutter 20 m enclosure Weight (tons) Unit price(CAN $/ton) 200 6000 30 25000 142 4500 190 5000 220 7000 250 10000 60 12000 270 10000 120 5000 1482 84500  Total cost (CAN $) 1200000 750000 639000 950000 1540000 2500000 720000 2700000 600000 11599000  In the Carousel enclosure, shell ribs, shell plates and aperture door use the same unit material price as in other two enclosures. Due to the motion mechanism of aperture door, the unit price of door drive systems is lower than in the Calotte enclosure. Because the base reactions of the Carousel enclosure are not extreme, the unit price of base ring girder and drive/brake bogies is much lower than those in Dome-Shutter enclosure. However, it is still higher than the unit material price of corresponding components in the Calotte enclosure since the Carousel enclosure is much heavier. According to table 5-7, the total unit price 65,500 Canadian dollars per ton and the total material cost is 12,104,000 Canadian dollars.  Table 5-7 Material cost of the 20 m Carousel enclosure  Components Aperture door (aluminum) Door drive system Shell rib Shell plate (aluminum) Base ring Main frame Rail beam Drive /brake bogie Idler bogie Track rail Total  Carousel 20 m enclosure Weight (tons) Unit price (CAN $/ton) 230 6000 20 15000 800 4500 500 5000 180 3500 160 10000 84 6000 30 8000 250 4000 3500 100 2354 65500  101  Total cost (CAN $) 1380000 300000 3600000 2500000 630000 1600000 504000 240000 1000000 350000 12104000  5.3.1.2.2 Labor cost The labor cost during the construction phase is influenced by various factors, including scale, complexity, schedule, labor quality, weather, site environment and so on. In order to simplify the problem, the construction labor cost of three enclosures is estimated according to the following formula: c, = Wxp, Where W : Total weight of the system p, : Unit labor price with the unit of Canadian dollars per ton  Especially due to the severe site environment on the Mauna Kea Mountain, the unit labor price is assumed to be 1,340 C A N $ per ton of total structure weight. The results of three types of enclosures are listed in the table 5-8. The labor cost in construction phase is 1,273,000 Canadian dollars for the Calotte enclosure, 1,985,880 Canadian dollars for the Dome-Shutter enclosure, and 3,154,360 Canadian dollars for the Carousel enclosure.  Table 5-8 Construction labor cost of three enclosures  T y p e of enclsoure  Total weight (tons)  Construction labor c o s t ( C A N $)  Calotte 20 m enclosure  950  1273000  Dome-Shutter 20 m enclosure  1482  1985880  Carousel 20 m enclosure  2354  3154360  5.3.1.2.3 Facility cost General construction facilities include construction machines, tucks, equipments and temporary buildings. The facility cost is estimated according to the following formula:  102  c = Wxp f  f  Where W : Total weight of enclosure p :Unit price of facihty cost with the unit of Canadian dollars per ton f  The unit facility cost is roughly assumed to be 200 C A N $ per ton. According to table 59, the total facility cost estimation is 190,000 Canadian dollars for the Calotte enclosure, 296,400 Canadian dollars for the Dome-Shutter enclosure and 470,800 Canadian dollars for the Carousel enclosure.  Table 5-9 Facility cost of three enclosures  Type of enclsoure  Total weight (tons)  Construction facility cost(CAN $)  Calotte 20 m enclosure  950  190000  Dome-Shutter 20 m enclosure  1482  296400  Carousel 20 m enclosure  2354  470800  5.3.1.3 Operation phase During this phase, the cost is composed of three components: the cost of maintenance, the cost of power consumption and the cost of reparation. Therefore, the total cost in this phase is calculated as the following formula:  C 3 =  C m  +  C  p  +  C  r  Where" C : Total cost estimation in the operation phase with the unit of Canadian dollars 3  c : The cost estimation of maintenance m  c : The cost estimation of power consumption p  c : The cost estimation of reparation r  103  5.3.1.3.1 Maintenance cost The maintenance cost is mainly associated with the mechanical systems of the enclosure. The qualities, features, and workloads of mechanical equipments may influence their maintenance cost. In order to simplify the problem, the maintenance cost of the VLOT enclosure is roughly assumed to be proportional to the cost of its mechanical system. The calculations are according to the following formula:  c  =C  m  meh  * f J  Where : Total cost of the mechanical system  / :  Scale factor, which is assumed to be 0.4 Table 5-10 Maintenance cost of three enclosures Type of enclsoure  Mechanical equipment cost (CAN $)  Maintenance cost(CAN $)  Calotte 20 m enclosure  1112500  445000  Dome-Shutter 20 m enclosure  4770000  1908000  Carousel 20 m enclosure  1890000  756000  According to table 5-10, the maintenance cost estimation is 445,000 C A N $ for the Calotte enclosure, 1,908,000 C A N $ for the Dome-Shutter enclosure, and 756,000 C A N $ for the Carousel enclosure.  5.3.1.3.2 Power consumption cost During the operation, the motions of the enclosure consume the most part of the power. The estimation of the power consumption cost is then simply according to the following formula:  c  p  =Pxtx  Pp  104  Where P: Total power demands for motion of the enclosure t: Time required for daily motions p : Unit price of power p  The total power consumption for the daily motions of enclosures shares the results in section 4.2.2. The daily motion time is assumed to be one hour. The unit price of the power is assumed to be 0.6 C A N $/kWhour including influences of the site environment on the top of Mauna Kea Mountain. According to table 5-11, the daily power cost is 68.784 Canadian dollars for the Calotte enclosure, 487.878 Canadian dollars for the Dome-Shutter enclosure, and 39.978 Canadian dollars for the Carousel enclosure.  Table 5-11  Daily power consumption cost of three enclosures  Type of enclsoure  Daily power consumption (KW)  Daily power cost(CAN $)  Calotte 20 m enclosure  114.64  68.784  Dome-Shutter 20 m enclosure  813.13  487.878  Carousel 20 m enclosure  66.63  39.978  5.3.1.3.3 Reparation cost The reparation cost is mainly related to the mechanical system of the enclosure, which is estimated according to a simple formula as follows:  c =C m  meh  *f J  Where C : Total cost of the mechanical system on the enclosure meh  / :  Scale factor, which is assumed to be 0.6  105  Table 5-12 Reparation cost of three enclosures Type of enclsoure  Mechanical equipment cost (CAN $)  Reparation cost(CAN $)  Calotte 20 m enclosure  1112500  667500  Dome-Shutter 20 m enclosure  4770000  2862000  Carousel 20 m enclosure  1890000  1134000  According to table 5-12, the reparation cost for the Calotte enclosure is 667,500 Canadian dollars, is 2,862,000 Canadian dollars for the Dome-Shutter enclosure, and is 1,134,000 Canadian dollars for the Carousel enclosure.  5.3.1.4 Uncertainty  Uncertainty means something that people cannot control or predict. With the growth of scale and complexity of the project, more and more uncertainty factors will be involved in the project. The significant effects of these factors may lead the real results of a project to be far away from people initially predicted. In order to reflect the effects of uncertainty to the VLOT project, the risk coefficient and uncertainty cost are introduced to the analysis. The risk coefficient utilizes a number between zero and one to present the possibility of an unforeseen outcome. The uncertainty cost represents the additional cost caused by an unforeseen outcome, which is calculated by the original cost and cost factors. The values of these parameters are determined by various characteristics of each enclosure.  106  Table 5-13 Uncertainty cost of three enclosures  Calotte enclosure 20m  Dome-Shutter enclosure 20m  costiofsdesignleffort cost of design effort OC (CAN $) RC CF UC (CAN $) OC (CAN $) RC CF UC (CAN $) 1361700 0.5 0.5 680850 2379600 0.3 0.5 1189800 cost of fabrication cost of fabrication OC (CAN $) RC CF UC (CAN $) OC (CAN $) RC CF UC (CAN $) 145200 0.5 0.5 72600 12630000 0.3 0.5 6315000 cost of material cost of material OC (CAN $) RC CF UC (CAN $) OC (CAN $) RC CF UC (CAN $) 4167000 0.5 0.3 1250100 11599000 0.2 0.3 3479700 cost of labors costoflabors OC (CAN $) RC CF UC (CAN $) OC (CAN $) RC CF UC (CAN $) 1273000 0.5 0.5 636500 1985880 0.2 0.5 992940 ' <>> L < cost of facilities " '<• > j <>, cost of facilities OC (CAN $) RC CF UC (CAN $) OC (CAN $) RC CF UC (CAN $) 190000 0.5 0.5 95000 296400 0.2 0.5 148200 cost of maintaintence cost of maintaintence OC (CAN $) RC CF UC (CAN $) OC (CAN $) RC CF UC (CAN $) 445000 0.1 0.1 44500 1908000 0.5 0.3 572400 cost of power consumption • cost of power consumption OC (CAN $) RC CF UC (CAN $) OC (CAN $) RC CF UC (CAN $) 68.784 0.1 0.1 6.8784 487.878 0.5 0.2 97.5756 cost of reparation cost of resarahon CF UC (CAN $) OC (CAN $) RC CF UC (CAN $) OC (CAN $) RC 667500 0.1 0.1 66750 2862000 0.5 0.3 858600 Total OC Total UC Total OC Total UC 8249468.784 2846306.878 33661367.88 13556737.58  Carousel enclosure 20m  cost of design effort OC (CAN $) RC CF UC (CAN $) 3569400 0.2 0.5 1784700 cost of fabrication OC (CAN $) RC CF UC (CAN $) 9472500 18945000 0.2 0.5 cost of material OC (CAN $) RC CF UC (CAN $) 12104000 0.1 0.3 3631200 cost of labors OC (CAN $) RC CF UC (CAN $) 1577180 3154360 0.2 0.5 cost of facilities OC (CAN $) RC CF UC (CAN $) 470800 0.2 0.5 235400 cost!pf|maintaintence OC (CAN $) RC CF UC (CAN $) 756000 0.3 0.3 226800  cost tfpSSrefl^nsurnption  OC (CAN $) RC CF UC (CAN $) 39.978 0.2 0.2 7.9956 cost of reparation OC (CAN $) RC CF UC (CAN $) 1134000 0.3 0.3 340200 Total OC Total UC 17267988 40133599.98  In table 5-13, values of the original cost (OC), risk coefficient (RC), cost factor (CF) and uncertainty cost (UC) of three types of VLOT enclosures are listed. For each type of enclosure, uncertainty cost is calculated from eight aspects, including the cost of design efforts, the cost of fabrication, the cost of material, the cost of construction labor, the cost of facilities, the cost of maintenance, the cost of power consumption and the cost of reparation. The sum of these eight costs is equal to the total uncertainty cost. For the Calotte enclosure, the lack of the engineering references and experiences increase the uncertainty of the project. Therefore, during the preparation phase, 50% of possibility for design delay and fabrication delay is considered, which leads to additional 50% of original cost estimation; during the construction phase, also 50% of possibility for the construction delay is assumed, which causes addition labor cost and facility cost; During the operation phase, 10% of possibility for uncertain conditions is considered, which causes additional 10% of original cost.  107  For the Dome-Shutter enclosure, references and experiences from the existing enclosures reduce the uncertainty of the project. However, there are still a lot of question marks mainly caused by two arch girders. Therefore, during the preparation phase, 30% of possibility for the design delay and fabrication delay is considered; during the construction phase, 20% of possibility for the construction delay is considered; during the operation phase, because of the extremely high power consumption due to two pieces of the shutter and effects of high base reaction forces, 50% of possibility for unusual maintenance with extra 30% of original cost, 50% of possibility for increase the power capacity with extra 20% of original power cost, and 50% of possibility of unusual reparation with additional 30% of original cost are considered.  For the Carousel enclosure, abundant references and experiences, plus regular structural layout, reduce the uncertainty of the project to the lowest level among three types of enclosure. Therefore, during the preparation phase, 20% of possibility for design delay and fabrication delay are considered; during the construction phase, 10% of possibility for the extension of construction time is assumed; and during the operation phase, 30% of possibility for unusual maintenance, 20% of possibility for the increase of power capacity and 30% of possibility for reparation and replacement are assumed.  Based on the analysis above, the uncertainty of the project is expressed numerically. Based on various cost and associated possibilities, the Expected Monetary Values are calculated as following formula:  '  N  EMV =  values x possibility„ n  n=l  5.4 RESULTS Based on the model and variables presented before, the decision tree is built with DecisionPro 4.0 and shown from figure 5-3 to 5-12. Variables with corresponding  108  possibilities are expressed as Expected Monetary Values. According the total value of each type of enclosure, the optimal solution with the minimum cost value is found.  Calotte design delivery 50% Calotte cost of design efforts $1,702,125.00  $1,361,700.00 Calotte design delay  (  .50% Calotte cost during the preparation phase  $2,042,550.00  ^  Calotte fabrication delivery  $1,884,625.00 50% Calotte cost of fabrication  $146,200.00 Calotte fabrication delay  $182,500.00 ,50%  $218,800.00  Figure 5-3 Decision tree layout a Cost of the Calotte enclosure during the preparation phase  Calotte budget material 50% Calotte cost of materials  $4,167,000.00  ^  Calotte overbudget material  $4,792,050.00 , 50%  $5,417,100.00 Calotte budget labor 50% Calotte cost during the construction phase / $6,620,800.00  Calotte cost of labors  $1,273,000.00  ^  Calotte overbudget labor  $1,591,250.00 ,50%  $1,909,500.00  ^  Calotte budget facilities 50% Calotte cost of facilities  $190,000.00 Calotte overbudget facilities  $237,500.00 .50%  $285,000.00  Figure 5-4 Decision tree layout b  Cost of the Calotte enclosure during the construction phase  1 0 9  Calotte regular maintenance  90%  Calotte cost of maintenance  $445,000.00  1  Calotte uncommon maitenance  $449,450.00 .10%  $489,500.00 Calotte budget power 90% Calotte cost during the operation phase  Calotte cost of power  $1,377,197.22  $253,572.22  $251,061.60  «  Calotte overbudget power .10% $276,167.76  ^  Calotte common reparation 90% Calotte cost of reparation  $667,500.00  ^  Calotte emergent reparation  $674,175.00 ,10%  $734,250.00 Figure 5-5 Decision tree layout c  Cost estimation of the Calotte enclosure during the operation phase  Dome design delivery 70% Dome cost of design efforts $2,736,540.00  $2,379,600.00 Dome design delay  (  . 30% Dome cost during the preparation phase  $3,569,400.00  ^  Dome fabrication delivery  $17,261,040.00 70% Dome cost of fabrication  $12,630,000.00 Dome fabrication delay  $14,524,500.00 ,30%  $18,945,000.00 Figure 5-6 Decision tree layout d  Cost estimation of the Dome-Shutter enclosure during the preparation phase  110  Dome budget material 80% Dome cost of materials  $11,599,000.00  '  Dome overbudget material  $12,294,940.00 ,20%  $15,078,700.00 Dome budget labor 80% Dome cost during the construction phase / $14,805,448.00  Dome cost of labors  $1,985,880.00  ^  Dome overbudget labor  $2,184,468.00 ,20%  $2,978,820.00  '  Dome budget facilities 80% Dome cost of facilities  $296,400.00  ^  Dome overbudget facilities  $326,040.00 ,20%  $444,600.00 Figure 5-7 Decision tree layout e  Cost estimation of the Dome-Shutter enclosure during the construction phase  Dome regular maintenance 50% Dome cost of maintenance  $1,908,000.00  ^  Dome uncommon maintenance  $2,194,200.00 ,50%  $2,480,400.00 Dome budget power 50% Dome cost during the operation phase  Dome cost of power  $7,444,330.17  $1,958,830.17  $1,780,754.70  '  Dome overbudget power , 50% $2,136,905.64  ^  Dome common reparation 50% Dome cost of reparation  $2,862,000.00  Dome emergent reparation  $3,291,300.00 ,50%  $3,720,600.00 Figure 5-8 Decision tree layout f  Cost estimation of the Dome-Shutter enclosure during the operation phase  111  ^  Carousel design delivery 80% Carousel cost of design efforts $3,926,340.00  $3,569,400.00 Carousel design delay  <  .20% Carousel cost during the preparation phase  $5,354,100.00^ Carousel fabrication delivery  $24,765,840.00 80% Carousel cost of fabrication  $18,945,000.00 Carousel fabrication delay  $20,839,500.00 ,20%  $28,417,500.00 Figure 5-9 Decision tree layout g  Cost estimation of the Carousel enclosure during the preparation phase  Carousel budget material 90% Carousel cost of materials  $12,104,000.00  '  Carousel overbudget material  $12,467,120.00 .10%  $15,735,200.00 Carousel budget labor 80% Carousel cost during the construction phase / $16,454,796.00  Carousel cost of labors  $3,154,360.00  ^  Carousel overbudget labor  $3,469,796.00 ,20%  $4,731,540.00 Carousel budget facilities 80% Carousel cost of facilities  $470,800.00  Carousel overbudget facilities  $517,880.00 ,20%  $706,200.00 Figure 5-10 Decision tree layout h  Cost estimation of the Carousel enclosure during the construction phase  112  ^  Carousel regular maitenance 70%  Carousel cost of maintenance  $756,000.00  1  Carousel uncommon maintenance  $824,040.00 ,30%  $982,800.00 Carousel budget power 80%  Carousel cost during the operation phase  Carousel cost of power  $2,211,940.00  $151,840.00  $146,000.00 Carousel overbudget power ,20% $175,200.00  ^  Carousel regular reparation 70% Carousel cost of reparation  $1,134,000.00  *  Carousel emergent reparation  $1,236,060.00 ,30%  $1,474,200.00  Figure 5-11 Decision tree layout i Cost estimation of the Carousel enclosure during the operation phase  Calotte cost during the preparation phase Page  $1,884,625.00 Total cost estimaion of Calotte enclosure / Calotte cost during the construction phase $9,882,622.22  \  • Page  $6,620,800.00 Calotte cost during the operation phase  k  Page  $1,377,197.22 Dome cost during the preparation phase / S 1 7 , 2 6 1 , 0 4 0 . 0 0  Minimum cost estimation  H  Page  Total cost estimaion of Dome enclosure / Dome cost during the construction phase  0  $9,882,622.22  $39,510,818.17  $14,805,448.00  • Page  \ Dome cost during the operation phase $7,444,330.17  i  !  |"  Carousel cost during the preparation phase  \  I  Page  /  •  $^4776^4000  *  Page  /  •! Total cost estimaion of Carousel enclosure / Carousel cost during the construction phase $43,432,576.00  \  $16,454,796.00  Page  \  \ Carousel cost during the operation phase $2,211,940.00  Figure 5-12 Decision tree layout j Minimum cost estimation  113  Page  The total cost estimation for the Calotte enclosure is 9,882,622.22 Canadian dollars, for the Dome-Shutter enclosure is 39,510,818.17 Canadian dollars, and for the Carousel enclosure is 43,432,576.00 Canadian dollars. These numbers relatively reflect the comprehensive characteristics of each type of enclosure, and form a solid reference for the final decision. The Calotte enclosure with the minimum cost estimation has been primarily proven as the best design solution for the VLOT project.  6  CONCLUSION  The goal of this thesis is to seek the best design solution to the VLOT enclosure. The research explores characteristics of several typical enclosure designs, and attempts to provide helps for the decision on the optimum solution.  Through the review of the telescope development history, rapid progress and continuous human efforts in this field during the past decades are presented. In order to satisfy people's curiosity towards the universe, telescopes with increasing capacities have been designed and built. With the dramatic increase in scale, complexity, functions and cost of the latest telescopes, the importance of their enclosures has been recognized. Through evaluation of various enclosure design cases and ideas, a candidate database for the 20 m optical telescope enclosure design has been established. Based on the study and research on this database, three types of enclosure designs, including the Calotte enclosure, the Dome-Shutter enclosure and the Carousel enclosure, are proven to be superior to other candidates for the VLOT enclosure design. Conceptual designs of three types of enclosures are mainly based on two basic criteria: the functional specification and the structural requirement. The functional specification requires the design of the enclosure to have certain functions, so that it can satisfy requirements for protecting and accommodating the telescope. The structural requirement, on the other hand, evaluates the design of enclosure from the strength, stability, efficiency, and reliability of the structure. Under the structural and mechanical analysis characteristics of each design solution are presented. 114  In addition to the general  characteristics of each type of enclosure, several unique features of each system are emphasized, including the performance of the interface rings in the Calotte enclosure, performance of the arch girders in the Dome-Shutter enclosure and the performance of the main frames in the Carousel enclosure. These may directly determine the final evaluation of each enclosure design. The comparative study is performed from emphasizing aspects: the structural performance and the mechanical control. In the structural performance aspect, three candidates are compared in stress level, deflection amplitude and base reaction force. In the mechanical control aspect, three enclosures are compared in mass information, power consumption and frequency. In order to summarize results of the comparative study, characteristics of three enclosures are classified into categories of "advantages" and "disadvantages", which are presented as follows: •  Calotte enclosure Advantages: With the rotational cap, the Calotte enclosure reduces the observation opening to the minimum size, preserving the integrity and the stiffness of the dome structure. The global stress level and the deflection amplitude of the structure are well controlled. The base reaction forces of the enclosure are relatively low and uniformly distributed. The total weight of the Calotte enclosure is the lowest one among total weights of three enclosures. Due to the motion mechanism, the power consumption of the Calotte enclosure is relatively low. The high rigidity and the low self weight of the Calotte enclosure result in the highest natural frequency for the system, when compared with other two candidates. Disadvantages: The main disadvantage of the Calotte enclosure design is caused by its novelty. Although the idea of the Calotte enclosure has been demonstrated in the Bernard Lyot telescope in 1980, the implementation of this idea in the extremely largescale telescope must still be considered new and therefore risky. Especially for the inclined interface between the Cap part and the base part, the mechanical system  115  including the bogies, lateral guide rollers and drive/brake system directly influence the structural performance of the interface rings. The structural performance of the interface rings also determines the design of mechanical systems on the interface. How to harmonize and optimize these two aspects is still a major question mark. •  Dome-Shutter enclosure Advantages: The Dome-Shutter enclosure is a well-developed and proven design with abundant engineering reference and technical supports. This type of enclosure is the most conventional enclosure and has been frequently built. The enclosures of Gemini 8.0 m and Keck 10.0 m telescope provide valuable design information and practical experience. Practices of scaring and simulating old designs result in lower risk. Disadvantages: The main disadvantage of the Dome-Shutter enclosure is caused by its shutter. The shutter requires a large opening in the body of enclosure, which disrupts the integrity of the dome structure significantly. Because of the dramatic decrease in the stiffness of the whole system, the natural frequency of the Dome-Shutter enclosure is the lowest among the three. Vertical movements of the shutter result in the highest power demand among three enclosures. In order to support the shutter, the design of two arch girders is necessary. These two strong members result in extreme values and distributions of base reactions. For certain components of the enclosure, simple scaling and simulating measures are not feasible.  •  Carousel enclosure Advantages: Experience from previous enclosure projects, especially from the 8.2 m Subaru enclosure, reduces the risk of the 20 m Carousel enclosure solution. The strong  116  and uniform structural layout of the Carousel enclosure gives the system the high strength and stiffness, leading to a low global stress level, acceptable structural deformation and mild base reaction forces. In addition, simple horizontal motion of two pieces of the door results in the lowest power consumption among the power consumption of three candidates. Disadvantages:  Due to the cylindrical shape of the Carousel enclosure, the high self weight of the whole system is its main disadvantage. Under its influence, the natural frequency of the system is low although the stiffness of the structure is high. The decision analysis adopts a mathematic method to solve a complex decision-making problem. In order to quantify the problem, characteristics of each type of enclosure are expressed as cost values. In order to reflect uncertainty of the project, additional cost values and certain possibility values are added to the analysis. By calculation of expected monetary values, characteristics of each type of enclosure are reflected with the consideration of the risk issue. A complex qualitative problem is transformed into a minimum-cost problem. The design of the Calotte enclosure seems to be the best design solution to the VLOT enclosure among three types of enclosures.  In this thesis, structural designs for three types of enclosures remain in the preliminary stage. Although the Calotte enclosure design basically leads the competition, there are still more work needed to further reinforce that this solution is feasible, practical, and reliable. These tasks include the interface ring performance study, mechanical system design on the interface, member section detail design, connection design between the interface rings and ribs, aperture cover design, base ring and associated mechanical system design, structural optimization and so on.  117  7  ABBREVIATION  VLOT  P.4  LRP  P.4  ELP  P.4  FEM  P.10  LBT  P.20  EMV  P.13  OC  P.107  RC  P.107  CF  P.107  UC  P.107  8  REFERENCES  Ref. 1 Vincent Ilardi, Eyeglasses and Concave Lenses in Fifteenth-Century Florence and Milan: New Documents, Renaissance Quarterly 29(1976): 341-360 Ref. 2 Albert van Helden, The Invention of the Telescope, the Transactions of the American Philosophical Society, 67, no. 4 (1977) Ref. 3 Rice University, The Telescope, http://es.rice.edu/ES/humsoc/Galileo/Things/ telescope.html Ref. 4 Rice University, The Galileo Project, http://es.rice.edu/ES/humsoc/Galileo/ Ref. 5 Isaac Newton (1642-1727), a British mathematician and physicist, http://www. newton.cam. ac.uk/newtlife.html Ref. 6 James Gregory (1638-1675), a Scottish mathematician, invented the first reflecting telescope in 1663 Ref. 7 William Herschel (1738-1822), astronomer, http://www.seds.org/messier/xtra/ Bios/wherschel.html Ref. 8 Lord Rosse's 72" Telescope, http://www.ioncmaste.ca/homepage/resources/ web_resources/CSA_Astro/files/contentyhtml/unit7/rosse_telescope.html Ref. 9 Otto Struve telescope, Macdonald adversary, http://www.as.utexas.edu/mcdonald/ facilities/2, lm/2.1 .html  119  Ref. 10 Dennis Crabtree, Canadian Efforts towards Very Large Optical Telescope (VLOT), National Research Council Canada-Herzberg Institute of Astrophysics, http://www.casca.ca/ecass/issues/2003-me/features/crabtreeA^LOT-%20E.htm Ref. 11 The Canada-France-Hawaii Telescope, http://www.cfht.hawaii.edu/ Ref. 12 Ray Carlberg, Joeleff Fitzsimmons, Nathan Loewen, Scott Roberts, Sigi Stiemer, Ye Zhou, VLOT Enclosure Design Specification, July 16, 2003 Ref. 13 A M E C Dynamic Structure Ltd., The 3D model of the 20 m telescope, 2001 Ref. 14 CELT Steering Committee, California Extremely Large Telescope (CELT) Performance Requirements, CELT Report #13, Revision 3,12 March 2001 Ref. 15 University of Hawaii, Institute for Astronomy, Mauna Kea Observatories, http://www.ifa.hawaii.edu/mko/about_maunakea.htm Ref. 16 University of Hawaii, Institute for Astronomy, Mauna Kea Observatories, http://www.ifa.hawaii.edu/mko/ Ref. 17 Michael Gedig, A M E C Dynamic Structures Ltd, Presentation of VLOT enclosure design approaches, 2001 Ref. 18 Robert D. Cook, David S.Malkus, Michael E.Plesha, Robert J.Witt, Concepts And Applications Of Finite Element Analysis, Fourth Edition, 2001  Ref.19 A. Azid, A.S.K. Kawn, A Layout Optimization Technique With Displacement Constraint, Optimization And Control In Civil And Structural Engineering, 1999  Ref. 20 Ralph L. Keeney, Howard Raiffa, Decisions With Multiple Objectives: Preferences and Value Tradeoffs, 1976  120  Ref. 21 Vanguard Software Corporation, DecisionPro 4.0 for windows Help Contents Ref. 22 Telescope Structure, Building, and Enclosure Group, Gemini 8.0m telescope project, Gemini 8m Telescope Design Requirements Document, SPE-TE-G0012, Revision 1, 1992 Ref. 23 The Gemini Observatory, http://www.gemini.edu/gallery/telescope/ telescope.html Ref. 24 The Gemini Observatory, http://www.germni.edu/gallery/enclosure/maunakea/ mk_construction.html Ref. 25 Telescope Structure, Building, and Enclosure Group, Gemini 8.0m telescope  project, Gemini 8m Telescope Enclosure Design Requirements Document, SPETE-G0012, Revision 2, 1993 Ref. 26 The Gemini Observatory, http://www.gemini.edu/gallery/enclosure/maunakea/ mk_construction.html Ref. 27 A M E C Dynamic Structures Ltd., Gemini 8.0 m Telescope enclosure design  report, 1996 Ref. 28 Subaru Telescope National Astronomical Observatory of Japan, http://www. naoj.org/Introduction/Outline.html Ref. 29 Subaru Telescope National Astronomical Observatory of Japan, http://www. naoj.org/Gallery/tele_dome.html Ref. 30 Subaru Telescope National Astronomical Observatory of Japan, http://www. naoj.org/ Introduction/history.html  121  Ref. 31 Large Binocular Telescope, LBT Telescope, http://medusa.as.arizona.edu /lbtwww/telescop.html Ref. 32 Large Binocular Telescope, Technical Description, http://medusa.as.arizona.edu/ lbtwww/tech/lbtbook.htm Ref. 33 Large Binocular Telescope, LBT site & enclosure construction process, http:// medusa.as.arizona.edu/lbtwww/site.html Ref. 34 David Halliday, P. Eng., Adjunct professor of UBC, Vice-president/Director of special projects, AMEC Dynamic Structures Ltd Ref. 35 AMEC Dynamic Structures Ltd, New approaches of next generation telescope enclosure design, 2002 Ref. 36 Telescope Bernard Lyot, http://bigoire.bagn.obs-mip.fr/tbl/indexeh.htm Ref. 37 Telescope Bernard Lyot, Gallery, http://bigorre.bagn.obsmip.fr/tbl/Ehtml/ mainvisitf.htm Ref. 38 ANSYS Inc. ANSYS User Manuals, ANSYS Element Reference, Ver. 7.0, ANSYS Inc. 2000 Ref. 39 Canadian Commission on Building and Fire Codes, National Building Code of Canada 1995, Institute for Research in Construction, National Research Council of Canada, 1995  122  

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