ERI: Seamless Integration Between CAD and FEA of Thin-Walled Structures Using Splines With Extraordinary Points

该奖项全部或部分由《2021年美国救援计划法案》（公法117-2）资助。在汽车、飞机和船舶的从设计到分析的周期中，薄壁结构的两种不同的几何表示导致了许多互操作性问题。具体来说，计算机辅助设计（CAD）软件中使用了基于修剪NURBS的几何表示，而有限元分析（FEA）软件中使用了基于拉格朗日多项式的几何表示。具有异常点（EPs）的样条曲线为在CAD和FEA软件中使用相同的薄壁结构几何表示打开了大门。与修剪的NURBS相比，带有EPs的样条曲线产生水密表面和一致性参数化。此外，具有EPs的样条的元素间连续性导致计算依赖于解的导数的物理量（例如，应力）的准确性提高，并增强了处理严重网格畸变的鲁棒性。这个工程研究启动（ERI）项目的目标是进行基础研究，以显著提高我们对哪种特定的EP结构更适合实现CAD和FEA之间的无缝集成的理解。这种CAD和FEA的综合愿景以及该项目的结果将包括在为底特律大都市社区服务的本科和研究生课程中。在当地高中的推广活动将以基于项目结果的样条碰撞模拟为特色，并提供以上大学为重点的问答环节。该项目将从根本上对三个主题产生新的理解，这些主题对于使用EPs样条实现薄壁结构CAD和FEA之间的无缝集成至关重要：(i) EPs样条在光谱分析中的准确性，即研究EPs样条在解决特征值问题中的性能；（ii）基于施加具有最佳近似特性的G^1约束的新EP结构的发展，这在文献中尚未在数值或数学上得到证明；（iii）在考虑每个面有多个EPs时研究表面质量。由于缺乏对不同类型的EPs样条曲线在频谱分析中的表现的了解，我们无法自信地将这项技术应用于耐撞性模拟、噪声、振动和粗糙度（NVH）模拟以及形状优化等领域。此外，目前文献中用于评价表面质量的控制网通常只有一个孤立的EP。然而，在汽车和航空航天应用中，每个表面普遍存在多个EPs，因此需要评估这些配置的表面质量。该奖项反映了美国国家科学基金会的法定使命，并通过使用基金会的知识价值和更广泛的影响审查标准进行评估，被认为值得支持。

This award is funded in whole or in part under the American Rescue Plan Act of 2021 (Public Law 117-2).In the design-through-analysis cycle of automobiles, aircrafts, and ships, numerous interoperability issues are caused by having two separate geometric representations of thin-walled structures. Specifically, a geometric representation based on trimmed NURBS is used within computer-aided design (CAD) software, and a geometric representation based on Lagrange polynomials is used within finite-element analysis (FEA) software. Splines with extraordinary points (EPs) open the door to having the same geometric representation of thin-walled structures used in both CAD and FEA software. In contrast with trimmed NURBS, splines with EPs result in watertight surfaces and conforming parameterizations. Furthermore, the inter-element continuity of splines with EPs leads to increased accuracy in computing physical quantities that depend on the derivatives of the solution (e.g., stresses) and enhanced robustness in handling severe mesh distortion. The objective of this Engineering Research Initiation (ERI) project is to perform fundamental research that significantly advances our understanding of which particular EP construction is more suitable to achieve a seamless integration between CAD and FEA. This integrated vision of CAD and FEA and the results of this project will be included in undergraduate and graduate courses serving the metropolitan Detroit community. Outreach activities at local high schools will feature spline-based crash simulations based on project results and provide Q&A sessions focused on attending college.This project will generate fundamentally new understanding in three topics of critical importance to achieving a seamless integration between CAD and FEA of thin-walled structures using splines with EPs: (i) the accuracy of splines with EPs in spectrum analysis, i.e., studying the performance of splines with EPs in solving eigenvalue problems; (ii) the development of a new EP construction based on imposing G^1 constraints that has optimal approximation properties, which has not yet been shown either numerically or mathematically in the literature; and (iii) studying the surface quality when multiple EPs per face are considered. The lack of understanding of how well different types of splines with EPs perform in spectrum analysis is limiting our capability to confidently apply this technology to crashworthiness simulations, noise, vibration, and harshness (NVH) simulations, and shape optimization, among others. In addition, the control nets that are currently used in the literature to evaluate surface quality often have only one isolated EP. However, in automotive and aerospace applications, multiple EPs per face are ubiquitous, and thus, evaluating the surface quality for these configurations is needed.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.