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On the element free galerkin method in the static analysis for the 2-D elastic linear problem

The present method is a nieshless method, as it does not need a "finite element mesh" and it is only composed by the particles with theirs "compact support" (the influence domain) in the whole domain. Specially, the shape functions are not satisfying the Kronecker delta property, therefore, in this paper, we must enforce the esseutial boundary conditions by the Lagrangian multipliers method. | Vietnam Journal of Mecha.nics, NCST of Vietnam Vol. n, 1999, No 4 (239- 250) ON THE ELEMENT FREE G.ALERKIN METHOD IN THE STATIC-ANALYSIS FOR THE 2-D ELASTIC-LINEAR PROBLEM NGUYEN HOAI SON- NGUYEN THE QUANG Institute of Engineering Education, Ho Chi Minh City ABSTRACT. The Element Free Galerkin (EFG) method is a meshless method for solving partial differential equations in which the trial a.nd test functions employed in the discretization process result from moving least square interpolations (weak form of the variational principle). In this paper, the EFG method for solving problems in elastostatics {1-D, 2-D) is developed and numerically implemented. The present method is a nieshless method, as it does not need a "finite element mesh" and it is only composed by the particles with theirs "compact support" (the influence domain) in the whole domain. Specially, the shape functions are not satisfying the Kronecker delta property, therefore, in this paper, we must enforce the esseutial boundary conditions by the Lagrangian multipliers method. Finally, several numerical examples are presented to illustrate the performance of the EFG method. The results are compared with the other method (EFM) and also with the analytic solutions. It shows that the EFG method gives the good effectiveness of the proposed error estimator in the global energy norm and the high rates of convergence with the size of the "compact support". 1. Introduction The meshless methods are very attractive for the development of adaptive methods (h-adaptive, p-adaptive and h - p adaptive) for solving boundary value problems. The meshless approach is based on the local symmetric weak form and moving least squares approximations. The main advantage of this method over the widely used finite element method and other so called meshless methods, EFG method [Belytschko et al1994] . [Lu et al1994], [Zhu and Atluri 1998], reproducing kernel particle method (RKPM) [Liu et all1996], H-P cloud method [Duart .