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。 为了预测这些虚拟对象的行为，分析师通常使用有限元分析（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，但它们都已成为高度复杂的数字孤岛，彼此之间只有松散的联系。其中一个重要原因是，在CAD和FEA工具中使用不同的数学描述来表示几何形状，这导致需要进行模型转换、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（伊加）对CAD和FEA使用相同的几何基函数。 该奖项支持使用三角贝塞尔样条作为等几何分析的基础函数的基础研究。如果成功的话，这项研究将导致破坏性的竞争优势，目前从CAD模型准备分析模型的漫长过程是设计分析integration.This研究的瓶颈行业主机利用的事实，技术可用于自动创建三角形网格从CAD模型。本研究的前提是，这种技术创建三角形网格可以扩展到技术的自动参数化的复杂对象与光滑的三角Bézier元素。因此，研究的目标是了解参数化质量的CAD模型自动分解成合理的三角贝塞尔样条元素（rTBS）和分析性能的收敛速度，一致性和稳定性方面的影响。 基于这些新知识，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组新的基于rTBS的算法计算设计，使无缝集成的设计通过分析。它代表了一个范式的转变，从目前费力的手工处理的CAD模型到有限元网格或手动参数化与张量积为基础的样条伊加。

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.