Efficient ways to construct boundary-element codes: case of 3D problems

FRANCISCO CELIO DE ARAUJO¹

¹ Programa de Pós-Graduação em Eng.Civil, Universidade Federal de Ouro Preto

doi:10.20906/CPS/CILAMCE2017-0842

Resumo

Compared to domain methods, applying boundary-element formulations to solve 3D complex solids (e.g. general composites) may be quite advantageous as domain discretizations are avoided. This statement has been recurrently mentioned in the boundary-element literature. Indeed, the Finite Element Method (FEM) has been the tool of choice for analyzing structural systems by means of simplified theories as beam or plate ones. On the other hand, the modeling of 3D domains with finite elements may pose special difficulties, e.g. in case of describing complex (microstructural) geometrical details or large (infinite) regions. And in fact, discretizing only the boundary of the domain, as typically happens in applying the Boundary Element Method (BEM), alleviates considerably the modeling of geometrically complex solids. Besides, as boundary-element formulations start from the analytical integral representations of sought-after responses, they provide high-accurate solutions, fulfill radiation conditions, and allow for easily deriving unified processes for dealing with thick-walled and thin-walled domains. The BEM also does not require interelement compatibility (in the finite-element sense). And all this together conspires to make the BEM convenient to deal with continuum mechanics problems. This paper discusses efficient ways to construct boundary-element codes, taking into account the relevance of the method to solve real-life problems. In this aspect, three points are considered: (1) subregioning techniques to model heterogeneous problems, (2) special numerical quadratures for singular and quasi-singular integrals, and (3) the solution of the non-hermitian system of equations via direct and iterative solvers. Details of the involved formulations are presented. The performance of the technique is verified by solving complex 3D solids and composites.

Palavras-chave: Boundary Element Method (BEM); subregion-by-subregion (SBS) technique, 3D solids and composites; 3D solids and composites; Krylov solvers