Improving Virtual Product Development Through Isogeometric Analysis Based on Rational Triangular Bezier Splines

在现代产品开发中，使用计算机辅助设计(CAD)模型以数字方式表示对象的几何形状。为了预测这些虚拟物体的行为，分析人员经常使用有限元分析(FEA)。然而，尽管这些技术在越来越广泛的应用中得到越来越多的使用，但它们各自都已成为高度复杂的数字岛屿，彼此之间只有松散的联系。这样做的一个重要原因是，在CAD和FEA工具中使用不同的数学描述来表示几何图形，从而需要进行模型转换、近似和网格化。为了绕过这一繁琐的网格划分过程，等距几何分析(IGA)对CAD和FEA使用相同的几何基函数。该奖项支持将三角贝塞尔曲线作为等距分析的基函数的基础研究。如果成功，这项研究将为许多行业带来颠覆性的竞争优势，目前从CAD模型准备分析模型的漫长过程是设计-分析集成的瓶颈。本研究利用了从CAD模型自动创建三角网格的技术。本研究的前提是，这种三角网格生成技术可以扩展为具有光滑三角Bézier单元的复杂对象的自动参数化技术。因此，研究的目的是了解CAD模型自动分解为有理三角Bézier样条元(RTBS)时的参数化质量及其对收敛速度、一致性和稳定性等分析性能的影响。基于这一新知识，将开发基于rTBS的参数化完成算法和分析技术。这项研究的成功完成将导致一套新的基于rTBS的计算设计算法，使通过分析设计的无缝集成成为可能。它代表了一种范式的转变，从目前繁琐的人工处理CAD模型到有限元网格或基于张量积样条的人工参数化。

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.