An isogeometric Boundary Element formulation for solids containing trimmed surfaces

Resumo

The Isogeometric Boundary Element Method (IGABEM) is an accurate and recent approach for solving
boundary value problems. This approach is especially accurate in the representation of complex geometries and
mechanical responses. Besides, it enables the direct application over Computer Aided Design (CAD) models, once
they utilise same basis functions in the parametrization of geometric entities. In the context of elasticity problems,

the Non-Uniform Rational B-Splines (NURBS) functions approximate both geometry and mechanical fields. Ad-
ditionally, CAD models often represent complex solids with trimmed NURBS surfaces. The generation of these

type of surfaces rely on the trimming operation, in which NURBS curves represent the edges of a cut. Conse-
quently, a robust IGABEM analysis must account for trimmed surfaces, which is a challenging task nowadays.

Hence, the present research deals with the mechanical analysis within IGABEM and trimmed geometries. For this
purpose, an identification task based on the ray-casting algorithm detects regions and control points unaffected by
trimming operation, trimmed or inactivated. Afterwards, the collocation points in surfaces’ corners are moved into
the surface, which follows the modified Greville Abscissae (GA) strategy. Besides, the integration process applies
the transformations proposed by Kim et al (2009). The proposed formulation applies a non-singular strategy, which
avoids additional singularities’ treatment. One application demonstrates the accuracy of the proposed formulation,
in which the responses have been compared against analytical solutions. A new extension of mechanical analysis
within IGABEM has been reached herein, once trimmed surfaces are also incorporated in this numerical method.