COMPARATIVE STUDY OF THE WEAK-FORM COLLOCATION MESHLESS FORMULATION AND OTHER MESHLESS METHODS - Oliveira, Tiago da Silva; Portela, Artur (Revista Interdisciplinar de Pesquisa em Engenharia, 2017)
This paper is concerned with the numerical comparison of the weak-form collocation, a new local meshless method, and other meshless methods, for the solution of two-dimensional problems in linear elasticity. Four methods are compared, namely, the Generalized-Strain Mesh-free (GSMF) 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, when compared to the other methods, is superior not only regarding the computational efficiency, but also regarding the accuracy.