Fracture analysis using parametric meshless Galerkin method

The recently introduced parametric meshless Galerkin method (PMGM) uses meshless shape functions which are mapped from a parametric space. The PMGM improves the efficiency of the meshless methods via the capability of using the meshless shape functions of an existing elements library and no necessity to construct all meshless shape functions in the running time. In this paper, the application of the PMGM to calculate the crack-tip stress intensity factors (SIFs) is studied. Some modifications are performed on the original PMGM to eliminate the restrictions arisen from the compulsory use of the whole of the parametric data. In doing so, some of the mapped nodes are inactivated due to their confliction with the problem geometry or extra node patterns and some of the Gaussian cells are also replaced with new ones. Numerical examples show a computational time saving of more than 20% as well as accurate obtained SIFs.