AN EXTENDED BOUNDARY ELEMENT FORMULATION FOR PUNCTUAL BOUNDARY CONDITIONS MODELLING

Resumo

The Boundary Element Method (BEM) is a numerical approach accurate in the solution of
several elastostatic problems. Because the method formulation involves integrals written at the
boundary, solely the bodies’ boundaries are discretised. Then, in three-dimensional problems, the BEM
mesh is composed of plane elements. However, the standard BEM formulation is limited in the solution
of problems where punctual boundary conditions are present. Then, concentrated loads and punctual
support conditions are not properly represented by the standard BEM. Such boundary conditions may

be approximately represented through small BEM elements. However, this strategy may lead to the ill-
positioned algebraic system of equations because of the small distance among the source points in such

elements. In this regard, this study presents an enriched BEM formulation (XBEM) capable to represent
properly punctual boundary conditions in three-dimensional problems. The Dirac’s function is utilized
in this enrichment process. Three numerical applications illustrate the accuracy of the proposed XBEM
scheme. The results achieved by the proposed XBEM formulation are compared with responses
provided by equivalent models constructed on Finite Element Method.