Utilisation des nombres quasi-aléatoires dans la méthode des éléments finis stochastiques

Abstract

A non-intrusive stochastic finite element method is proposed for uncertainty propagation through mechanical systems with uncertain input described by random variables. A polynomial chaos expansion (PCE) of the random response is used. Each PCE coefficient is cast as a multi-dimensional integral when using a projection scheme. Common simulation schemes, e.g. Monte Carlo Sampling (MCS) or Latin Hypercube Sampling (LHS), may be used to estimate these integrals, at a low convergence rate though. As an alternative, quasi-Monte Carlo (QMC) methods, which make use of quasi-random sequences, are proposed to provide rapidly converging estimates. The Sobol' sequence is more specifically used in this paper. The accuracy of the QMC approach is illustrated on the case study of a truss structure with random member properties (Young's modulus and cross section) and random loading. It is shown that QMC outperforms MCS and LHS techniques for both moment and reliability analysis.