An element-free Galerkin method for probabilistic mechanics and reliability

Abstract

A stochastic element-free Galerkin method was developed for reliability analysis of linear-elastic structures with spatially varying random material properties. A random field representing material properties was discretized into a set of random variables with statistical properties obtained from the statistical properties of random field. In conjunction with meshless formulations, the first-order reliability method was employed to predict the full probabilistic characteristics of a structural response. Unlike the stochastic finite element method, the stochastic mesh-free method does not require a structured mesh, instead only a scattered set of nodal points is required in the domain of interest. As well, there is no need for fixed connectivities between nodes. Numerical examples show good agreement between the results of the developed method and Monte Carlo simulation. Furthermore, the stochastic meshless method provides convergent solutions of the probability of failure. Since mesh generation of complex structures can be far more time-consuming and costly effort than solution of a discrete set of equations, the developed meshless method provides an attractive alternative to finite element method for solving stochastic-mechanics problems.