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This paper is concerned with the overall performance of the Generalized-strain Meshfree formulation, a new local meshless method, when compared to other meshless methods, for solving two-dimensional linear elastic problems.
Four methods are compared in this study, namely, the Generalized-Strain Mesh-free (GSMF) formulation, also known as the weak-form collocation meshless formulation; the Rigid-body Displacement Mesh-free (RBDMF) formulation, the Element-free Galerkin (EFG) and the Meshless Local Petrov-Galerkin Finite Volume Method (MLPG FVM). While the RBDMF, EFG and MLPG FVM rely on integration and quadrature process to obtain the stiffness matrix, the GSMF is completely integration-free, working as a weighted-residual weak-form collocation. This weak-form collocation readily overcomes the well-known difficulties of the strong-form collocation, such as low accuracy and instability of the solution.
A numerical example was analyzed with these methods, in order to assess the accuracy and the computational effort. The results obtained are in agreement with those of the available analytical solution. The numerical results show that the GSMF is superior not only regarding the computational efficiency, but also regarding the accuracy, when compared to the other methods.

Local Meshless; Generalized-strain; Weak-form collocation; Element-free Galerkin; Meshless Local Petrov-Galerkin