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

In this paper, we continue the development of the Direct Meshless Local Petrov–Galerkin (DMLPG) method for elasto-static problems. This method is based on the generalized moving least squares approximation. The computational efficiency is the most significant advantage of the new method in comparison with the original MLPG. Although, the “Petrov–Galerkin” strategy is used to build the primary local weak forms, the role of trial space is ignored and direct approximations for local weak forms and boundary conditions are performed to construct the final stiffness matrix. In this modification the numerical integrations are performed over polynomials instead of complicated MLS shape functions. In this paper, DMLPG is applied for two and three dimensional problems in elasticity. Some variations of the new method are developed and their efficiencies are reported. Finally, we will conclude that DMLPG can replace the original MLPG in many situations.