Análise Isogeométrica com Elementos de Contorno e Superfícies de Subdivisão

Abstract

The boundary element method (BEM) is a numerical method widely employed for solving continuum mechanics problems. In the absence of body forces, the method is only based on a mesh of surface elements whose quality directly impacts the accuracy of the numerical solution. BEM is quite suited for isogeometric analysis (IGA). In IGA, the analysis model of a body is directly derived from its geometric model — usually defined in terms of parametric surface patches —, without the need for the explicit generation of a mesh of elements. The surface representation form adopted in this thesis for IGA is the subdivision surfaces. Subdivision surfaces have been the most used surface representation for geometric modeling in the animation industry since Pixar released the OpenSubdiv API. In conjunction with polygonal modeling software, it provides tools to build and edit continuous and smooth complex shapes with approximations as good as you want. Given the relevance of subdivision surfaces in computer graphics and considering their application in physics-based animation, this work presents a solution for elastostatic isogeometric analysis with boundary elements for solids represented by subdivision surfaces. As the core of this solution we introduced a method for load points’ positioning and a method for extracting curved elements from subdivision surfaces with boundaries, extraordinary points and creases. The experiments demonstrate that the efficiency and accuracy of the developed framework are comparable to related work found in the literature.

Keywords: subdivision surfaces, isogeometric analysis, boundary element method.