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）模型对物体的几何形状进行数字化表示。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，尽管这些技术的应用范围越来越广泛，但它们都变成了高度复杂的数字孤岛，彼此之间只是松散地连接在一起。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，导致需要模型转换，近似和网格划分。为了绕过这个费力的网格划分过程，等几何分析（IGA）在CAD和FEA中使用相同的几何基函数。该奖项支持使用三角形bsamizier样条作为等几何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。本研究利用了可用于从CAD模型自动创建三角形网格的技术。本研究的前提是，这种创建三角形网格的技术可以扩展到具有光滑三角形bsamizier元素的复杂对象的自动参数化技术。因此，研究目的是了解CAD模型自动分解为有理三角b<s:1>样条元（rTBS）过程中的参数化质量及其在收敛速度、一致性和稳定性方面对分析性能的影响。基于这一新知识，将开发基于rTBS的参数化完井算法和分析技术。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，使设计通过分析的无缝集成。它代表了一种范式的转变，从目前手工处理CAD模型到有限元网格或手工参数化与基于张量积样条的IGA。

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.