Elementos de Contorno para Análise Isogeométrica de Sólidos Elásticos com Vincos

Abstract

The boundary element method (BEM) is an important alternative applied to the numerical solution of various problems derived from continuum mechanics. In solids mechanics, more specifically, the method is attractive as it may require only a discretization of the surfaces of the bodies under analysis, with a consequent decrease in the dimensionality of the discrete system. In the context of isogeometric analysis (IGA), the BEM is even more naturally attractive, since the idea behind IGA is to use the geometric model of an object - generally defined by NURBS surface patches generated from a CAD tool - as the analysis model, without the employment of a particular process of mesh generation. Recently, several papers demonstrating the feasibility of IGA can be found in the literature. However, there are still several limitations that prevent the practical use of IGA, mainly due to the difficulty of imposing non-homogeneous boundary conditions. In this thesis, a study of those limitations is carried out, and a solution based on the MEC for isogeometric analysis of elastic solids is proposed. The resulting framework allows the modeling of traction discontinuities by using discontinuous elements and/or multiple nodes, where the multiplicity of a node is given by surface regions delimited by crease curves. The boundary elements are defined as Bézier patches associated with the faces of the elemental mesh of a T-spline surface. T-splines are employed instead of NURBS since they allow non-structured control point meshes, with T-joints and extraordinary points, without the need for trimming curves. Nevertheless, any geometric representation that can be transformed into Bézier patches is supported. A Bézier extraction procedure for generic T-splines with creases and a robust numerical integration scheme for the boundary integral equation are introduced. The framework is implemented in C ++. A prototype in MATLAB allows the interactive selection of groups of elements for specifying boundary conditions that represent generic constraints and uniformly distributed tractions, pressures, and torques, as well as the numerical analysis and visualization of results.