An enforced essential boundary condition by penalty method in the element-free Galerkin (EFG) methods

Abstract

A meshless approach to the analysis of two-dimensional elasticity problems by the Element-Free Galerkin (EFG) method is presented. This method is based on moving least squares approximant (MLS). The unknown function of displacement $u(x)$ is approximated by moving least square approximants $u^h(x)$. These approximants are constructed by using a weight function, a monomial basis function and a set of nonconstant coefficients. A subdivision similar to finite element method is used to provide a background mesh for numerical integration. The essential boundary conditions are enforced by Penalty Method. The results are obtained for a two-dimensional problem using different EFG weight functions and compared with the results of finite element method and exact methods.