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UBC Theses and Dissertations

Reliability-based structural design optimization for nonlinear structures in OpenSees Liang, Hong


The aspiration of this thesis is to provide a tool for engineers in making rational decisions based on the balance between cost and safety. This objective is accomplished by merging the optimization and reliability analyses with sophisticated finite element models that predict structural response. In particular, two state-of-the-art reliability-based design optimization approaches are implemented in OpenSees, a modern and comprehensive finite element software that has recently been extended with reliability and response sensitivity analysis capabilities. These new implementations enable reliability-based design optimization for comprehensive real-world structures that exhibit nonlinear behaviour. This thesis considers the problem of minimizing the initial cost plus the expected cost of failure subject to reliability and structural constraints. This involves reliability terms in both objective and constraint functions. In the two implemented approaches, the reliability analysis and the optimization evaluation are decoupled, although they are not bi-level approaches, thus allowing flexibility in the choice of the optimization algorithm and the reliability method. Both solution approaches employ the same reformulation of the optimization problem into a deterministic optimization problem. The decoupled sequential approach using the method of outer approximation (DSA-MOOA) applies a semi-infinite optimization algorithm to solve this deterministic optimization problem. An important feature of the DSA-MOOA approach is that a convergence proof exists in the first-order approximation. The simplified decoupled sequential approach (DSA-S) utilizes an inequality constrained optimization algorithm to solve the deterministic optimization problem. The DSA-S approach is demonstrated to result in a consistent design, which lacks the convergence proof but requires less computational time than the DSA-MOOA approach. The gradients of the finite element response with respect to model parameters are needed in reliability-based design optimization. These gradients are obtained using the direct differentiation method, which entails the derivation and implementation of analytical derivatives of the finite element response. The potential negative effect of response gradient discontinuities due to sudden yielding events is stressed in the thesis. The problem is remedied through the use of the smooth material model and a section discretization scheme. Object-oriented programming is utilized when extending optimization and sensitivity capabilities to OpenSees. The superior extensibility and maintainability features of this approach are emphasized. A numerical example involving a nonlinear finite element analysis of a three-bay, sixstorey building is presented in the thesis to demonstrate new implementations in OpenSees. Three cases are studied: a linear pushover analysis using elasticBeam elements, a nonlinear pushover analysis using beamWithHinges elements, and a nonlinear pushover analysis using dispBeamColumn elements with fibre sections. This thesis also touches on practical experiences by comparing two implemented approaches, two gradient computation methods, and linear and nonlinear analyses. The experience of speeding up the convergence procedure by removing inactive constraints and scaling the involved functions is also discussed.

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