A good agreement is obtained between the results of the proposed method and the Monte Carlo simulation. Several numerical examples are presented to examine the accuracy and convergence of the stochastic meshless method. In conjunction with meshless discretization, the classical Neumann expansion method was applied to predict second-moment characteristics of the structural response. The second method is more general than the first, and can solve problems involving a multi-dimensional random field with arbitrary covariance functions. In the second method, a Galerkin-based approach in conjunction with meshless discretization was developed in which the integral eigenvalue problem was also converted to a matrix eigenvalue problem.

In the first method, the eigenfunctions were approximated as linear sums of wavelets and the integral eigenvalue problem was converted to a finite-dimensional matrix eigenvalue problem that can be easily solved. Two numerical methods were developed for solving the integral eigenvalue problem associated with K-L expansion. Using Karhunen-Loève (K-L) expansion, the homogeneous random field representing material properties was discretized by a set of orthonormal eigenfunctions and uncorrelated random variables. This paper presents a stochastic meshless method for probabilistic analysis of linear-elastic structures with spatially varying random material properties.

Eigen meshfree