An element-free method for in-plane notch problems with anisotropic materials

This study developed an element-free Galerkin method (EFGM) to simulate notched anisotropic plates containing stress singularities at the notch tip. Two-dimensional theoretical complex displacement functions are first deduced into the moving least-squares interpolation. The interpolation functions and their derivatives are then determined to calculate the nodal stiffness using the Galerkin method. In the numerical validation, an interface layer of the EFGM is used to combine the mesh between the traditional finite elements and the proposed singular notch EFGM. The H-integral determined from finite element analyses with a very fine mesh is used to validate the numerical results of the proposed method. The comparisons indicate that the proposed method obtains more accurate results for the displacement, stress, and energy fields than those determined from the standard finite element method.