Structural and System Reliability

Many problems in structural reliability require the use of a computational platform, such as a finite-element code, to evaluate the limit-state function. Chapter 12 describes the framework for such coupling between a finite-element code and FORM/SORM analysis. The chapter begins with a brief review of the finite-element formulation for inelastic problems. Because FORM requires the gradients of the limit-state function, it is necessary for the finite-element code to compute not only the response vector but also its gradient with respect to selected outcomes of the random variables. The use of finite-differences for this purpose is not practical because of accuracy issues and computational demand. The direct-differentiation method (DDM) presented in this chapter provides an accurate and efficient means for this purpose. It is shown that the DDM requires a linear solution at the convergence of each iterative step in the nonlinear finite-element analysis. Next, a method for discrete representation of random fields of material properties or loads in the context of finite-element analysis is presented. The chapter concludes with a review of alternative approaches for finite-element reliability analysis or uncertainty propagation, including the use of polynomial chaos and various response-surface methods with efficient selection of experimental design points.