An Element-free Galerkin Method for Probabilistic Mechanics and Reliability

A stochastic element-free Galerkin method was developed for reliability analysis of linear-elastic structures with spatially varying random material properties. A random ®eld representing material properties was discretized into a set of random variables with statistical properties obtained from the statistical properties of random ®eld. In conjunction with meshless formulations, the ®rst-order reliability method was employed to predict the full probabilistic characteristics of a structural response. Unlike the stochastic ®nite 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 ®xed 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 con-vergent solutions of the probability of failure. Since mesh generation of complex structures can be far more time-consuming and costly e€ort than solution of a discrete set of equations, the developed meshless method provides an attractive alternative to ®nite element method for solving stochastic-mechanics problems.