An element-free Galerkin method for probabilistic mechanics and reliability

A stochastic element-free Galerkin method was developed for reliability ana lysis of linear-elastic structures with spatially varying random material p roperties. A random field representing material properties was discretized into a set of random variables with statistical properties obtained from th e statistical properties of random field. In conjunction with meshless form ulations, the first-order reliability method was employed to predict the fu ll probabilistic characteristics of a structural response. Unlike the stoch astic finite element method, the stochastic mesh-free method does not requi re a structured mesh, instead only a scattered set of nodal points is requi red in the domain of interest. As well, there is no need for fixed connecti vities between nodes. Numerical examples show good agreement between the re sults 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 ti me-consuming and costly effort than solution of a discrete set of equations , the developed meshless method provides an attractive alternative to finit e element method for solving stochastic-mechanics problems. (C) 2001 Elsevi er Science Ltd. All rights reserved.