Eventos Anais de eventos
MecSol 2017
6th International Symposium on Solid Mechanics
Performance of the Weak-form Collocation Meshless Formulation
Submission Author:
Tiago da Silva Oliveira , DF
Co-Authors:
Artur Portela
Presenter: Tiago da Silva Oliveira
doi://10.26678/ABCM.MecSol2017.MSL17-0017
Abstract
This paper is concerned with the overall performance of the weak-form collocation, a new local meshless method, for solving two-dimensional linear elastic problems when compared to other meshless methods. 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, the computational effort and the convergence rate. The results obtained with all methods 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 regarding the computational efficiency and accuracy, leading to remarkable results using only one collocation point on each boundary of the local domain.
Keywords
Local Meshless, Generalized-strain, Weak-form collocation, Element-free Galerkin, Meshless Local Petrov-Galerkin
