Reliability-based optimization using SFEM

Consideration of element level reliabilities in design optimization ensures a distribution of weight such that there is uniform risk in the structure failure modes and ensures overall safety. Therefore an optimization algorithm that considers both types of reliability is desirable. The Stochastic Finite Element Method (SFEM) appears capable of efficiently solving the aforementioned problems. Given a probabilistic description of the basic parameters, SFEM is able to compute the stochastic response of the structure in terms of either the response statistics such as mean, variance, etc. or the probability of failure considering a particular limit state. This is done by keeping account of the variation of the quantities computed at every step of the deterministic analysis, in terms of the variation of the basic variables. This capability makes SFEM attractive for application to reliability-based optimum design of large structures. Such an optimization procedure is presented in this paper using SFEM-based reliability analysis, and illustrated with the help of a numerical example.