The three-dimensional isogeometric Boundary Element Method for concentrated boundary conditions

Resumo

The Isogeometric Boundary Element Method (IGABEM) is a recent and robust strategy for the me-
chanical modelling of solids. One remarkable advantage of the isogeometric approach is the direct mechanical

analysis from geometries modelled by Computer-Aided Design (CAD) software, in which complex geometries
can be accurately represented. In this context, the non-uniform rational B-splines (NURBS) surfaces approximate

both geometry and mechanical fields. Besides, the non-requirement of the domain mesh contributes to the cou-
pling IGA and BEM, once CAD surfaces are the mesh itself. However, the application of concentrated boundary

conditions in IGABEM is quite challenging, because of two main aspects: the extension of the NURBS curves and
the singular nature of the fundamental solutions. Commonly, few NURBS surfaces are necessary to represent the
entire boundary and trimming these curves is not an easy task. Besides, boundary conditions over small areas may
require small NURBS, which is non-sense in this domain. Additionally, the use of small elements may lead to the
ill-positioned algebraic system of equations, due to the small distance between the source points. Therefore, this
study presents an IGABEM formulation (IGABEM) to account such boundary conditions in three-dimensional
solids. Concentrated loads and supports are introduced by the addition of the Dirac Delta function over the traction
mechanical field. One application demonstrates the accuracy of the proposed formulation, in which its results are
compared against the responses of Finite Element equivalent model. The proposed IGABEM approach predicts
the mechanical behaviour accurately, which proves the accuracy and robustness of the proposed improvements.