Iso-geometric Finite Element Analysis Based on Catmull-Clark Subdivision Solids

Abstract

We present a volumetric iso-geometric finite element analysis based on Catmull-Clark solids. This concept allows one to use the same representation for the modeling, the physical simulation, and the visualization, which optimizes the design process and narrows the gap between CAD and CAE. In our method the boundary of the solid model is a Catmull-Clark surface with optional corners and creases to support the modeling phase. The crucial point in the simulation phase is the need to perform efficient integration for the elements. We propose a method similar to the standard subdivision surface evaluation technique, such that numerical quadrature can be used. Experiments show that our approach converges faster than methods based on tri-linear and tri-quadratic elements. However, the topological structure of Catmull-Clark elements is as simple as the structure of linear elements. Furthermore, the Catmull-Clark elements we use are C2-continuous on the boundary and in the interior except for irregular vertices and edges.