Stochastic FEM Based on Local Averages of Random Vector Fields

Abstract

The formula for the covariances of the local averages of homogeneous random scalar fields over rectangular domains is first generalized to include the case of homogeneous random vector fields with quadrant symmetry. For nonhomogeneous random fields and/or nonrectangular domains, Gaussian quadrature is proposed to evaluate the means and covariances of the local averages of random vector fields. The stochastic finite‐element analysis based on the local averages of random vector fields is then formulated for static, eigenvalue, and stress‐intensity factor problems. The present stochastic finite‐element method (SFEM) is a generalization of the SFEM based on the local averages of random scalar fields and can be applied to any configuration of structure with several correlated random parameters and several correlated random loads. Numerical examples are examined to show the advantages of the present SFEM over the SFEM based on midpoint discretization, i.e., more rapid convergence and more efficiency.