A perturbation method for stochastic meshless analysis in elastostatics

A stochastic meshless method is presented for solving boundary-value problems in linear elasticity that involves random material properties. The material property was modelled as a homogeneous random eld. A meshless formulation was developed to predict stochastic structural response. Unlike the nite element method, the meshless method requires no structured mesh, since only a scattered set of nodal points is required in the domain of interest. There is no need for xed connectivities between nodes. In conjunction with the meshless equations, classical perturbation expansions were derived to predict second-moment characteristics of response. Numerical examples based on one- and two-dimensional problems are presented to examine the accuracy and convergence of the stochastic meshless method. A good agreement is obtained between the results of the proposed method and Monte Carlo simulation. Since mesh generation of complex structures can be a far more time-consuming and costly e ort than the solution of a discrete set of equations, the meshless method provides an attractive alternative to nite element method for solving stochastic mechanics problems