In modern product development, the geometry of objects is represented digitally using computer-aided design (CAD) models. To predict the behavior of these virtual objects, analysts often use finite element analysis (FEA). However, despite the growing usage of these technologies in an increasingly broad range of applications, they each have become highly sophisticated digital islands, only loosely connected to each other. An important reason for this is that different mathematical descriptions are used to represent geometry in CAD and FEA tools, leading to the need for model conversion, approximation, and meshing. To bypass this laborious meshing process, isogeometric analysis (IGA) uses the same geometric basis functions for both CAD and FEA. This award supports the fundamental study of using triangular Bézier splines as basis functions for isogeometric analysis. If successful, this research will lead to disruptive competitive advantages to a host of industries where currently the lengthy processes of preparing analysis models from CAD models is the bottleneck in design-analysis integration.
This research exploits the fact that techniques are available for automatic creation of triangular meshes from CAD models. The premise of this research is that such techniques for creating triangular meshes can be extended into techniques for automatic parametrization of complex objects with smooth triangular Bézier elements. The research objective is thus to understand the parametrization quality during the automatic decomposition of CAD models into rational Triangular Bézier Spline elements (rTBS) and its influence on analysis performances in terms of convergence rate, consistency and stability. Based on this new knowledge, rTBS based parametrization completion algorithms and analysis techniques will be developed. Successful completion of this research will lead to a new set of rTBS-based algorithms for computational design that enable seamless integration of design-through-analysis. It represents a paradigm shift from current laborious manual processing of CAD models into finite element meshes or manual parametrization with tensor-product based splines for IGA.
