Finite Element Reliability of Geometrically Nonlinear Uncertain Structures

A general framework for finite element reliability analysis based on the first‐ and second‐order reliability methods, FORM and SORM, is presented. New expressions for the required gradients of the response of geometrically nonlinear structures are derived and implemented in an existing finite element code, which is then merged with a FORM/SORM reliability code. The gradient computation does not require repeated solutions of the nonlinear response and is free of the errors inherent in the perturbation method. The proposed reliability method offers significant advantages over the conventional Monte Carlo simulation approach. The method is illustrated for a plate problem with random field properties, random geometry, and subjected to random static loads. The example represents the first application of the finite element method in conjunction with SORM, for a system reliability problem, and involving non‐Gaussian random fields. Extensive analyses of reliability sensitivities with respect to parameters defining the random fields are carried out.