Isogeometric Analysis with Bézier Tetrahedra

This paper presents an approach for isogeometric analysis of 3D objects using rational Bézier tetrahedral elements. In this approach, both the geometry and the physical field are represented by trivariate splines in Bernstein Bézier form over the tetrahedrangulation of a 3D geometry. Given a NURBS represented geometry, either untrimmed or trimmed, we first convert it to a watertight geometry represented by rational triangular Bézier splines (rTBS). For trimmed geometries, a compatible subdivision scheme is developed to guarantee the watertightness. The rTBS geometry preserves exactly the original NURBS surfaces except for an interface layer between trimmed surfaces where controlled approximation occurs. From the watertight rTBS geometry, a Bézier tetrahedral partition is generated automatically. By imposing continuity constraints on Bézier ordinates of the elements, we obtain a set of global Cr smooth basis functions and use it as the basis for analysis. Numerical examples demonstrate that our method achieve optimal convergence in Cr spaces and can handle complicated geometries.