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、飞机和船舶的分析设计周期中，薄壁结构的两种独立几何表示会导致许多互操作性问题。具体地，在计算机辅助设计（CAD）软件中使用基于修剪的NURBS的几何表示，并且在有限元分析（FEA）软件中使用基于拉格朗日多项式的几何表示。具有非常点（EP）的样条为在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EP的样条曲线会产生水密曲面和一致参数化。此外，具有EP的样条的元件间连续性导致在计算取决于解的导数的物理量（例如，应力），并增强了处理严重网格变形的鲁棒性。这个工程研究启动（ERI）项目的目标是进行基础研究，大大提高我们对特定EP结构更适合实现CAD和FEA之间无缝集成的理解。CAD和FEA的综合愿景以及该项目的结果将被纳入为底特律大都市社区服务的本科和研究生课程。在当地高中的推广活动将以基于项目结果的基于样条的碰撞模拟为特色，并提供专注于上大学的问答环节。该项目将在三个至关重要的主题上产生全新的理解，以实现使用带EP的样条的薄壁结构的CAD和FEA之间的无缝集成：（i）带EP的样条在频谱分析中的准确性，即，研究样条与EP在解决本征值问题的性能;（ii）一个新的EP建设的基础上施加G^1约束，具有最佳逼近性能的发展，这还没有被证明无论是在数值上或数学文献;（iii）研究表面质量时，每个面多个EP被认为是。对不同类型的带EP的样条在频谱分析中的表现缺乏了解，限制了我们自信地将该技术应用于耐撞性仿真，噪声，振动和声振粗糙度（NVH）仿真以及形状优化等方面的能力。此外，目前文献中用于评估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，每个表面都有多个EP，因此需要评估这些配置的表面质量。该奖项反映了NSF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.