Stochastic Finite Element Analysis: an Introduction

With the aid of the finite element method, the present paper deals with the problem of structural response variability resulting from the spatial variability of material properties of structures, when they are subjected to static loads of a deterministic nature. Several forms of spatial variability of Young’s modulus and Poisson’s ratio are considered; they are assumed to be two-dimensional Gaussian or non-Gaussian stochastic fields. The finite element discretization is performed in such a way that the size of each element is sufficiently small. A Neumann expansion method is developed and used in deriving the finite element solution of such stochastic systems within the framework of the Monte Carlo method. Then the results from the Neumann expansion method are compared with those from the first- and second-order perturbation approximation methods and direct Monte Carlo simulation method with respect to accuracy, convergence and computational efficiency.