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

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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. | Vietnam Journal of Mechanics, VAST, Vol.31 , No.2 (2009), pp. 122 - 132 AN ENFORCED ESSENTIAL BOUNDARY CONDITION BV PENALT Y M ETHOD IN THE ELEMENT-FREE GALERKIN (EFG ) METHODS N g uyen H oai Son University of Technical Education Ho Chi Minh City 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 . Keywords. weight function , pena lty method, moving least squares, meshfree. 1. INTRODUCTION As for now the finite element method has been a powerful tool for solving partial differential equations. It has successfully been applied for a large number of engineering applications, for example solid mechanics, structure mechanics, electro magnetism, geo mechanics, bio mechanics and so on. But for t he last fifteen years a new mesh free met hod has been subject to extensive research. The element free Galerkin (EFG) method is a meshless method for solving partial differential equations which uses only a set of nodal points and a CAD _ like description of t he body to formulate the discrete model. It has been used extensively for fracture problems and has yielded good results when adequate refinement is used near the crack tip. In this paper, a meshless approach to the analysis of two-dimensional elasticity problems by the Element-Free Galerkin (EFG) .