Solution of Elasto-Statics Problems Using the Element-Free Galerkin Method with Local Maximum Entropy Shape Functions

The element free Galerkin method (EFGM) [1] is one of the most robust meshless methods for the solution of elasto-statics problems. In the EFGM, moving least squares (MLS) shape functions are used for the approximation of the field variable. The essential boundary conditions cannot be implemented directly as in the case of Finite Element Method (FEM), because the MLS shape functions do not possess the Kronecker-delta property and use Lagrange multipliers instead. In this paper the recently developed local maximum entropy shape functions are used in the EFGM for the approximation of the field variable instead of MLS. As the local maximum entropy shape functions possess the Kroneckerdelta property at the boundaries so the essential boundary conditions are enforced directly as in the case of FEM. Two benchmark problems, a cantilever beam subjected to parabolic traction at the free end and an infinite plate with circular hole subjected to unidirectional tension are solved to show the implementation and performance of the current approach. The displacement and stresses calculated by the current approach show good agreement with the analytical results