SFEM for Reliability of Structures with Material Nonlinearities

A stochastic finite element method (SFEM) is developed to study the reliability of structures with material nonlinearities. Bilinear stress-strain relationships that involve two correlated random fields are used to model the material nonlinearities. Random fields are represented as continuous functions by using general orthogonal series expansions, and are incorporated directly into the nonlinear finite element analysis and first-order reliability formulation. The proposed method is illustrated by two examples involving a fixed-end beam and a frame. Random spatial fluctuations in the material properties or distributed loads may have a significant effect on reliability if correlation lengths of random fields are less than the lengths of members, meaning that local fluctuations in the fields are relatively high.