Revisiting the Indirect-BEM's Fulfillment of Equilibrium Conditions in Internal Problems
Josue Labaki1; Persio Leister de Almeida Barros1; Euclides Mesquita1
1 Unicamp
doi:10.20906/CPS/CILAMCE2017-0584
Resumo
In light of new evidence, in this paper the authors reconsider conclusions made seven years ago regarding the suitability of the Indirect Boundary Element Method (I-BEM) to closed-domain (internal) problems. The Indirect version of the Boundary Element Method (I-BEM) is a numerical method of discretization based on the superposition of Green functions to approximate the solution of differential equations. The I-BEM differs from its Direct-BEM (D-BEM) counterpart in that it relates tractions and displacements at the discretized boundary through a set of fictitious stresses, rather than physical displacements and tractions. Previous investigations by the authors had shown that I-BEM's feature of employing non-singular Green's functions was evened out by it being significantly more computationally expensive. More critical was the observation that the application of I-BEM to closed-domain problems failed to satisfy elementary equilibrium criteria, which was then attributed to the formulation's inability to comply with Dumont's criteria on the spectral properties of the influence matrices. A harder look at the formulation of the I-BEM has revealed recently that the "problem" of equilibrium, contrarily to those previous conclusions, arose from an incorrect interpretation of traction discontinuities at the boundary of the problem. These must be interpreted differently whether the problem is an external or an internal one, and the appropriate numerical implementation must take this into account. This article investigates a new implementation of the I-BEM that considers the correct traction discontinuity for closed-domain problems. For this implementation, a classical but representative closed-form solution of an isotropic, elastodynamic full-space is used for influence function. The results show that the discretized problem satisfies both static and dynamic equilibrium, provided that an adequate discretization is chosen. Additionally, the authors also present a derivation of the equilibrium condition in I-B
Palavras-chave: Indirect-BEM; Green's functions; Elastodynamics