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

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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.