Método dos Elementos de Contorno para elasticidade linear bidimensional

Abstract

Starting from Betti's reciprocity theorem or from the application of the weighted residual method and using Kelvin's fundamental solution, a boundary integral equation is obtained, which is discretized, for computational implementation, using isoparametric linear elements. Applying the discretized integral equation at the boundary nodal points, a system of linear equations is obtained, having boundary displacements and/or tractions as unknowns. The traction discontinuity problem is considered by introducing addicional equations obtained from the elastic invariant properties, for the cases of corner points with prescribed displacements only. For body forces arising from a fixed gravitational field, two formulations are utilized for transforming the domain integrals into boundary integrals. A formulation which can consider a domain divided into aligned sub-regions is derived. Some applications are performed in order to obtain numerical results and to evaluate the performance of the formulation developed.