Efficient Algorithm for Stochastic Structural Optimization

Abstract

A stochastic structural optimization procedure using element‐level reliabilities as constraints is proposed here. The procedure is robust and efficient and closely resembles the practical approach used in design offices. The procedure is developed in modules which can be linked and unlinked. Element‐level reliabilities are estimated using the stochastic finite element method or Monte Carlo simulation with variance reduction techniques whenever necessary. The method can consider different limit states with different desired levels of reliability as well as the system reliability as constraints, resulting in a balanced distribution of weight. A constrained optimization algorithm is used which is tailored to the information and the requirements of the structural optimization problem considered here. The algorithm contains a simple and efficient search procedure that uses variable, discrete step sizes. Several alternatives for reliability analysis and trial structure selection, and strategies for reduction of the number of constraints are included and explained with the help of numerical examples to show the desirability of the proposed method.