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A bstract . 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 uh (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 resul ts of finite element method and exact methods .

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