Um Método de Refinamento Local de T-splines Conformes para Análise

Abstract

In the context of computational simulation of physical problems, isogeometric analysis (IGA) of a solid is one in which the analysis model has the same order of continuity as the geometric model of the solid. The most commonly used geometric representation in the IGA literature is based on NURBS (non-uniform rational B-splines) surface patches, as this is the most commonly employed representation in the computer-aided design and manufacturing (CAD/CAM) industry. A NURBS surface, and consequently the analysis model derived from it in IGA, has its geometry defined by rational interpolation functions acting on a structured mesh of control point}. A recently adopted alternative in CAD/CAM software are T-splines. These generalize NURBS with watertight surfaces that allow unstructured control point meshes with T-junctions, called T-meshes. Additionally, they enable local refinement, which results in the addition of vertices and edges and the subdivision of faces in a T-mesh.

Although various studies confirm the feasibility of T-splines in IGA, there are still limitations regarding the characteristics of the T-splines used. These restrictions motivate the definition of a subset of T-splines referred to as analysis-suitable. This work explores refinement methods for analysis-suitable T-splines under unstructured meshes. To this end, a hierarchical data structure for the computational representation of T-meshes, called HBDS (handle-body data structure), is employed. The objectives of this work include developing an interactive graphical application capable of presenting T-splines, manipulating their topological elements, refining their T-mesh, prescribing crease edges, besides flexible scene composition, either with T-splines generated by the developed application or by importing pre-existing meshes from third-party sources.