A Fourier–Karhunen–Loève discretization scheme for stationary random material properties in SFEM

Abstract

AbstractIn order to overcome the computational difficulties in Karhunen–Loève (K–L) expansions of stationary random material properties in stochastic finite element method (SFEM) analysis, a Fourier–Karhunen–Loève (F–K–L) discretization scheme is developed in this paper, by following the harmonic essence of stationary random material properties and solving a series of specific technical challenges encountered in its development. Three numerical examples are employed to investigate the overall performance of the new discretization scheme and to demonstrate its use in practical SFEM simulations. The proposed F–K–L discretization scheme exhibits a number of advantages over the widely used K–L expansion scheme based on FE meshes, including better computational efficiency in terms of memory and CPU time, convenient a priori error‐control mechanism, better approximation accuracy of random material properties, explicit methods for predicting the associated eigenvalue decay speed and geometrical compatibility for random medium bodies of different shapes. Copyright © 2007 John Wiley & Sons, Ltd.