Isogeometric triangular Bernstein-Bezier discretizations: Automatic mesh generation and geometrically exact finite element analysis

摘要

Isogeometric analysis (IGA) was introduced as a way to bypass the design-to-analysis bottleneck inherent in the traditional Computer Aided Design (CAD) through Finite Element Analysis (FEA) paradigm. However, an outstanding problem in the field of IGA is that of surface-to-volume parameterization. In CAD packages, solid objects are represented by a collection of NURBS or T-spline bounding surfaces, but to perform engineering analysis on real world problems, we must find a way to parameterize the volumes of these objects as well. This has proven to be difficult using traditional IGA, as the tensor-product nature of trivariate NURBS and T-splines limit their ability to create analysis suitable parameterizations of arbitrarily complex volumes.