TY - JOUR AU - Oliveira, Tiago da Silva AU - Portela, Artur PY - 2017/01/19 Y2 - 2024/03/29 TI - COMPARATIVE STUDY OF THE WEAK-FORM COLLOCATION MESHLESS FORMULATION AND OTHER MESHLESS METHODS JF - Revista Interdisciplinar de Pesquisa em Engenharia JA - Rev. Interd. Pesq. Eng. VL - 2 IS - 6 SE - Artigos DO - 10.26512/ripe.v2i6.21472 UR - https://periodicos.unb.br/index.php/ripe/article/view/21472 SP - 60-78 AB - <p>This paper is concerned with the numerical comparison of the weak-form collocation,&nbsp;a new local meshless method, and other meshless methods, for the solution of two-dimensional&nbsp;problems in linear elasticity. Four methods are compared, namely, the Generalized-Strain&nbsp;Mesh-free (GSMF) formulation, the Rigid-body Displacement Mesh-free (RBDMF) formulation,&nbsp;the Element-free Galerkin (EFG) and the Meshless Local Petrov-Galerkin Finite Volume&nbsp;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,&nbsp;working as a weighted-residual weak-form collocation. This weak-form collocation readily&nbsp;overcomes the well-known difficulties of the strong-form collocation, such as low accuracy and&nbsp;instability of the solution. A numerical example was analyzed with these methods, in order to&nbsp;assess the accuracy and the computational effort. The results obtained are in agreement with&nbsp;those of the available analytical solution. The numerical results show that the GSMF, when&nbsp;compared to the other methods, is superior not only regarding the computational efficiency, but&nbsp;also regarding the accuracy.</p> ER -