An improved meshfree method for fracture analysis of cracks

This paper presents an improved meshless method for analyzing linear-elastic cracked structures subject to singleor mixed-mode loading conditions. The method involves an element-free Galerkin formulation in conjunction with an improved moving least-square approximation. The conventional moving least-square approximation which is one of the bases of element-free Galerkin method may form an ill-conditioned system of equations so that the solution cannot be correctly obtained. Hence, in this paper, an improved moving least-square approximation is adopted for fracture analysis of cracks. In the improved moving least-square approximation, the orthogonal function system with a weight function is used as the basis function. The improved moving least-square approximation has higher computational efficiency and precision than the moving least-square approximation, and will not lead to an ill-conditioned system of equations. Numerical examples show that the current method yields accurate estimates of stress-intensity factors and near-tip stress field in two-dimensional cracked structures.