An efficient meshless method for fracture analysis of cracks

This paper presents an efficient meshless method for analyzing linear-elastic cracked structures subject to single- or mixed-mode loading conditions. The method involves an element-free Galerkin formulation in conjunction with an exact implementation of essential boundary conditions and a new weight function. The proposed method eliminates the shortcomings of Lagrange multipliers typically used in element-free Galerkin formulations. Numerical examples show that the proposed method yields accurate estimates of stress-intensity factors and near-tip stress field in two-dimensional cracked structures. Since the method is meshless and no element connectivity data are needed, the burdensome remeshing required by finite element method (FEM) is avoided. By sidestepping remeshing requirement, crack-propagation analysis can be dramatically simplified. Example problems on mixed-mode condition are presented to simulate crack propagation. The predicted crack trajectories by the proposed meshless method are in excellent agreement with the FEM or the experimental data.