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In this paper, we continue the development of the Direct Meshless LocalPetrov-Galerkin (DMLPG) method for elasto-static problems. This method is basedon the generalized moving least squares approximation. The computationalefficiency is the most significant advantage of the new method in comparisonwith the original MLPG. Although, the "Petrov-Galerkin" strategy is used tobuild the primary local weak forms, the role of trial space is ignored anddirect approximations for local weak forms and boundary conditions areperformed to construct the final stiffness matrix. In this modification thenumerical integrations are performed over polynomials instead of complicatedMLS shape functions. In this paper, DMLPG is applied for two and threedimensional problems in elasticity. Some variations of the new method aredeveloped and their efficiencies are reported. Finally, we will conclude thatDMLPG can replace the original MLPG in many situations.

A new low-cost meshfree method for two and three dimensional problems in elasticity