Modelagem de problemas bidimensionais através de formulação variacional auto-regularizada do método dos elementos de contorno

Abstract

This work deals with a numerical solution technique for evaluation of hypersingular two dimensional equations based on a non-symmetric variational approach for the Boundary Element Method (BEM) applied to Laplace and Poisson equations (potential problems) as well as Navier equation (elasticity problems). The relaxed continuity approach is the starting point for the formulations used along the work, which means that, instead of using approaches that assure the required C1,α inter-element continuity requirement, the formulation applied on this work uses only standard C0 isoparametric elements. The continuity requirement is enforced at smooth inter-element nodes through a subsidiary set of constraint equations included into the original system of equations. Numerical examples show that the developed algorithm based on the self-regular traction and flux-BIE are highly efficient, and quite straightforward in that no integral transformations are necessary to compute the singular integrals and even a small number of integration Gauss points gives very accurate results.