Selection of Random Field Mesh in Finite Element Reliability Analysis

Abstract

Random fields are often used in reliability analysis to model the uncertainties that possess spatial variabilities. Within the framework of finite element reliability methods, the domain of each field is discretized into a mesh of random field elements and the value for each element is represented by a single random variable. The selection of random field mesh is important since it influences the accuracy of the reliability analysis. In this study, how to select and refine the random field mesh in finite element reliability analysis is investigated. An expression is derived to compare the improvements made by various refinements of a coarse mesh. Further exploration of the expression shows that the gradient of the limit‐state function plays a key role in the selection of a random field mesh. A criterion for selecting random field meshes is devised as follows: Adopt a coarse mesh in the area where the gradient of the limit‐state function with respect to the discretized variables is small, and a fine mesh in the area where the gradient is large. The selection rule developed in this study is verified by a beam and a plate examples.