A stochastic element-free Galerkin method using Karhunen-Loève expansion of random field and wavelets

摘要

A stochastic meshless method is presented for solving solid-mechanics problems inrnlinear elasticity that involves random material properties. Using the Karhunen-Loève expansion,rnthe random field was modeled by a linear sum of orthonormal eigenfunctions with uncorrelatedrnrandom coefficients. The covariance and eigenfunctions were approximated by compactlysupportedrnwavelets and the integral eigenvalue problem was converted to a finite-dimensional eigenvaluernproblem that can be solved easily. In conjunction with meshless discretization, classicalrnNeumann expansion method was applied to predict the second-moment characteristics of structuralrnresponse. Numerical examples are presented to illustrate the proposed method. Since mesh generationrnof complex structures can be time-consuming and costly, the meshless method provides an attractivernalternative to finite element method for solving stochastic-mechanics problems.