CAREER: Next-Generation Shape Optimization of Geometrically Complex Artifacts

该CAREER奖的研究目标是建立一个新一代的计算框架，用于几何复杂产品的形状优化。现有的形状优化方法通常是缓慢和繁琐的，并且缺乏鲁棒性，特别是当产品是几何复杂的。因此，在优化之前，通过特征去除，产品模型在几何上被简化。拟议的框架将取代脆弱的几何简化方法与强大的和数学上健全的代数简化方法。将使用伴随校正方法来避免由于简化而出现的误差。此外，将探索新的特征灵敏度方法，这将消除形状优化过程中重新分析的需要。建议的框架将应用于航空航天、汽车和精密机械行业中发现的复杂工件，并进行测试。如果成功，这项研究的成果将对工业和社会产生重大影响，主要是通过设计高度优化、成本更低和环境友好的产品。在设计过程中可以探索更广泛的产品设计，这将导致新颖的新产品。在计算方面，该框架将整合几何简化和形状优化，将这些研究领域与未来的发展潜力联系起来。作为一个测试平台，这项研究的结果将被来自威斯康星州大学和威斯康星州技术学院的研究生和本科生用于参加全国汽车设计挑战赛。研究成果也将通过技术选修课程和两个校区扩大学生设计经验嵌入本科课程。在工业界的支持下，参与的学生，特别是少数民族和妇女，将获得奖学金，完成必要的CAD培训，并参加全国性的比赛。

The research objective of this CAREER award is to establish a next-generation computational framework for shape optimization of geometrically complex products. Existing methods of shape optimization are typically slow and tedious, and lack robustness, especially when a product is geometrically complex. Product models are therefore geometrically simplified today, prior to optimization, through feature removal. The proposed framework will replace fragile geometric simplification methods with robust and mathematically sound algebraic simplification methods. An adjoint corrector method will be used to avoid errors that appear as a result of simplification. In addition, novel feature sensitivity methods will be explored that will eliminate the need for reanalysis during shape optimization. The proposed framework will be applied and tested against complex artifacts found in the aerospace, automobile and precision machinery industries.If successful, the results of this research will have a major impact on industry and society, primarily through the design of highly optimized, less expensive and environmentally friendly products. A wider range of product designs can be explored during the design process which will lead to novel new products. Computationally, this framework will integrate geometric simplification and shape optimization, linking these research areas with the potential for future advances. As a test bed, the results of this research will be used by graduate and undergraduate students from the University of Wisconsin and Wisconsin Technical Colleges to compete in national car design challenges. The research results will also be embedded within the undergraduate curricula through technical elective offerings and expanded student design experiences at both campuses. With support from industry, participating students, especially minority and women, will receive scholarships to complete necessary CAD training and take part in nation-wide competitions.