Abstract
The element-free Galerkin method (EFGM), which is one of the meshless method, has been tried to be applied to the stress concentration, crack and shells problems. Using the moving least square approximation (MLSM) as the interpolation function is a special feature for the EFGM. Another feature for the EFGM is that the EFGM has the continuity of the first derivative i.e. strain and stress for a structural analysis by selecting the weight function. Then we can obtain displacement, strain and stress anywhere. Calculating the fracture mechanics parameter, we can calculate more accurate fracture mechanics parameter for nonlinear fracture mechanics problems. Therefore, the EFGM is a promising method for treating problems such as crack growth because it can easily obtain the variations of the fracture mechanics parameters. The EFGM has not been applied to nonlinear problems such as elastic-plastic problems. If the EFGM will be able to applied to the nonlinear problems, it will be useful as a numerical method for solid mechanics. In the present paper, the EFGM is applied to elastic-plastic problems and to estimating J-integral. The results obtained from the EFGM agree well with those of the finite element method, and the EFGM is successfully applied to the elastic-plastic fracture mechanics problem.
