Obtenção de matriz de rigidez utilizando o método dos elementos de contorno

Abstract

This work is concerned with the development of a stiffness matrix for a body, using a direct Boundary Element Method Approach (BEM), in a suitable way to couple into a global Finite Element Method formulation (FEM). The main property of this matrix must be the simmetry, to allow the use of FEM computational techniques. The stiffness matrix developed with BEM does not exhibit the inherent symmetry property, and the perturbations of the solutions are examined when the simple simmetrisation (by considering the simetric part of the matrix) is adopted. In the first part of this work the 2-Dimensional Potential problem is examined, and results obtained from the symmetric "stiffness matrix" of some formulations are compared. Then this research is developed for 2-Dimensional Elastostatics, and the surface discontinuous tractions at nodal points are examined in depth. These discontinuities are considered with the introduction of extra 'corner conditions', or with the Galerkin Method concept, that uses weighting functions at these nodal points divided into two components.