Análise numérica de problemas de estado plano por meio de métodos sem malha com formulação local

Abstract

This study deals with analysis of solids in Plane State, based on the Meshless Method. To this method, it will be used the Moving Least Squares Method (MLS) as the approximation function. In order to verify precision and stability, results will be compares with analytical solutions or numerical solutions obtained by means of Boundary Elements Method (BEM). Meshless Method formulations will be employed to the assembly of the global stiffness matrix and the independent vector: the Collocation Method; in which formulation the Dirac-Delta will be used as the weighting function, thus, the numerical integration is not necessary and the MLPG-1. As the weighting function, the fourth-order Spline functions and the gaussiana with radius will be used. To the numerical integration, the radius of circular local support similar to the shortest distance between two points (one of them is the base point) and is registered, concentrically, in another approximation local support. This way, the distribution of Gauss points is closer to the base point, avoiding mistakes due to the integration of the global domain. So, it is not necessary the construction of the support for each Gauss point, deacreasing the method’s computational cost.