Local maximum entropy shape functions based FE-EFGM coupling.

Abstract

In this paper, a new method for coupling the finite element method (FEM) and the element-free Galerkin method (EFGM) is proposed for linear elastic and geometrically nonlinear problems using local maximum entropy shape functions in the EFG zone of the problem domain. These shape functions possess a weak Kronecker delta property at the boundaries which provides a natural way to couple the EFG and the FE regions as compared to the use of moving least square basis functions. In this new approach, there is no need for interface/transition elements between the EFG and the FE regions or any other special treatment for shape function continuity across the FE-EFG interface. One- and two-dimensional linear elastic and twodimensional geometrically nonlinear benchmark numerical examples are solved by the new approach to demonstrate the implementation and performance of the current approach.