Element-free Galerkin method (EFGM) based on moving least-square curve fitting concept is presented and applied to elastic fracture problems. Because no element connectivity data are needed, EFGM is very convenient and effective numerical method for crack growth analysis. This paper is intended as an investigation of crack trajectory for different notch locations under three-point bending test. The initial crack growth angles obtained by element-free Galerkin method in comparison with those obtained by lab test reveal that both results are very close. However, numerical results also show that the location of an original notch can stronger affect the variation of crack path for different increment. The stress intensity factors (SIF) of cracks under three-point bending test with different increment are also investigated by EFGM.

In this paper, a modified numerical integration scheme is presented that improves the accuracy of the numerical integration of the Galerkin weak form, within the integration cells of the analyzed domain in the element-free methods. A geometrical interpretation of the Gaussian quadrature rule is introduced to map the effective weighting territory of each quadrature point in an integration cell. Then, the conventional quadrature rule is extended to cover the overlapping area between the weighting territory of each quadrature point and the physical domain. This modified numerical integration scheme can lessen the errors due to misalignment between the integration cell and the boundary or interface of the physical domain. Some numerical examples illustrate that this newly proposed integration scheme for element-free methods does effectively improve the accuracy when solving solid mechanics problems.