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The local Petrov-Galerkin methods (MLPG) have attracted much attention due to their great flexibility in dealing with numerical model in elasticity problems. It is derived from the local weak form (WF) of the equilibrium equations and by inducting the moving last square approach for trial and test functions in (WF) is discussed over local sub-domain. In this paper, we studied the effect of the configuration parameters of the size of the support or quadrature domain, and the effect of the size of the cells with nodes distribution number on the accuracy of the methods. It also presents a comparison of the results for the Shear stress, the deflections and the error in energy.

Atluri and Zhu (1998) have advocated the meshless local Petrov-Galerkin methods (MLPG). It is derived from the local weak form (WF) of the equilibrium equations and by inducting the moving last square approach for trial and test functions in (WF). Finally is discussed over local sub-domains. However, the convergence of the method presents dependency to number of parameters deriving from local weak form and different subdomains. This paper deals with the effect of sizing parameter of subdomains on the convergence and accuracy of the methods and numerical values are presented to specifying the convergence domain by precising maximum and minimum values as a function of distribution nodes number. It also presents a comparison with numerical results for different materials. Numerical results agree with the analytical solution of the deflection.

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