An analysis for the elasto-plastic fracture problem by the meshless local Petrov-Galerkin method

A meshless local Petrov-Galerkin method (MLPG) for the analysis of the elastoplastic fracture problem is presented in this paper. The meshless method uses the moving least squares (MLS) to approximate the field functions. The shape function has not Kronecker Delta properties for the trial-function interpolation, and a direct interpolation method is adopted to impose essential boundary conditions. The MLPG method does not involve any domain and singular, integrals if body force is ignored. It only involves a regular boundary Integral. Two numerical examples show that results obtained by the present method have a good agreement with that by FEM software-ANSYS. However, in the present method, the computational time is greatly reduced in forming the tangent stiffness matrix because there is no domain integral, and the pre and post-processing time are also greatly reduced because no element connectivity and no remeshing are required. The proposed method is valid and feasible for the solution of the elasto-plastic fracture problem.