Application of a stochastic finite element procedure to reliability analysis

The stochastic finite element procedure presented in this paper consists in representing in a probabilistic form the response of a system whose material properties and loading are random. Each random variable is expanded into Hermite polynomial series. The response is expanded onto the so-called polynomial chaos. The coefficients of the expansion of the response (e.g. the nodal displacement vector) are obtained by a Galerkin-type method in the space of probability. This stochastic finite element procedure is applied to the parametric study of the reliability of a foundation on a two-layer elastic soil mass. The method reveals accurate and more efficient than a direct coupling between a finite element code and a probabilistic code.