Reliability-based Structural Optimization For Frequency And Stability

Engineering structures are affected by lots of random factors. To get a more rational,economical and safe design, relevant reliability requirements should be considered in thestructural optimization design. Based on the success of the intermediate variable method inthe structural optimization and reliability-based optimization of truss structure, thisdissertation investigates the use of intermediate variables in structural reliability analysis andreliability-based structural optimization. Both the reliability index and failure probability areused in the study.It is assumed that the random factors are time-invariant and can be described by usingrandom variables with known probability distributions. Based on the theory and algorithms ofstructural design optimization, studies in the following three aspects have been conducted:(1) For the reliability analysis of frame structures, different performance functions suchas displacement, stress and frequency are considered;(2) In the reliability-based stability optimization of frame structures, a new sequentiallinear programming algorithm is proposed using intermediate variables;(3) For the plate bending problem, a similar algorithm if presented for the optimizationof plate structures considering the reliability constraints on lateral deflections and bucklingload factors.All algorithms have been implemented in Fortran. Numerical examples are conducted,and the results obtained are compared with those of the available methods, to demonstrate theeffectiveness and accuracy of the new algorithms using intermediate variables.Main conclusions of this dissertation are as follows:(1) For structural reliability analysis, we can improve the computational efficiency byusing intermediate variables for different performance functions;(2) For reliability-based optimizations of frame structures and bending plates, we canalso improve the computational efficiency by using intermediate variables;(3) It is important to choose the appropriate form of an intermediate variable, and theselection of different forms of intermediate variables must be made by considering the types of structures and performance functions.