Reliability Based Structural Design using Continuum Sensitivity Analysis

摘要

Reliability based design of structural systems is necessary to account for the randomness in loads, structural geometry, material properties, manufacturing processes, and operational environment. Probabilistic methods are commonly used for reliability based design. Gradients of the objective and limit state functions that are required during stochastic optimization procedure are almost always calculated using finite difference method. However, calculating gradients in this way is very computationally expensive. In this paper, we propose a stochastic optimization procedure, which makes use of continuum sensitivity analysis for obtaining gradients. It is expected that this would not only result in significant savings in computational efforts, but also accurate design derivatives than those obtained with other numeric design sensitivity analysis methods. Another part of the current work is to investigate the most appropriate polynomial family and order of expansion to use for polynomial chaos expansion. The use of Jacobi and Hermite polynomials is compared. It is seen that if the input variables follow a beta distribution, then second order Jacobi polynomials give the best stochastic optimization result.