CAREER: Incorporating Geometric Rules and Cost in Topology Optimization for Efficient Design of Manufacturable and Economically-Viable Structures

拓扑优化是一个强大的计算辅助探索新的结构设计概念，而不需要预先设想结构的形状。由此产生的设计为其应用进行了高度优化，实现了轻质高性能结构。然而，这些设计往往具有复杂的有机外观结构，这使得它们难以可靠和经济地制造。先前在拓扑优化过程中施加制造约束的尝试取得了有限的成功。此外，目前的方法不能直接考虑制造成本，使设计师难以考虑经济目标或限制因素。该学院早期职业发展计划（Career）奖支持基础研究，以制定第一个框架，系统地将几何设计规则和制造成本纳入拓扑优化，并将该框架与教育活动相结合，以改善代表性不足的少数群体对STEM领域的态度。这项研究将使轻量化、高性能和经济可行的结构的概念设计和优化成为可能，并在广泛的工程行业中得到应用。新的设计能力将有可能显著降低制造和研发成本，从而提高美国制造商的经济竞争力。该奖项还将通过一项旨在提高学生自我效能感和刺激他们参与STEM的综合教育计划，对代表性不足的少数族裔产生积极影响。该教育项目包括一个吸引人的、基于虚拟现实的中学生课后项目。该项目还将吸引和影响K-12教师、本科生和研究生，并将成为向更广泛的公众和研究界交流研究成果的渠道。虽然拓扑优化是一种成功的结构设计技术，但其影响受到将制造限制和经济考虑纳入优化过程的挑战的限制。这些差距的根源在于，根据现有技术使用的设计表示，难以表达许多制造驱动的几何需求，一些几何特征的离散性，以及制造成本可能是设计的非平滑函数。这个CAREER项目将对结构的计算设计做出三个主要的智力贡献，即基于特征的设计表示与1)全局优化方法的耦合，以避免在存在许多几何设计规则的情况下陷入不希望的局部最小值；2)适应离散几何特征的离散优化方法；3)参数化代价模型和非光滑优化方法，将代价纳入拓扑优化问题。新技术将与行业合作伙伴合作，在基准测试和工程问题上进行验证。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。

Topology optimization is a powerful computational aid for exploring novel structural design concepts without requiring a preconceived shape of the structure. The resulting designs are highly optimized for their application, enabling lightweight high-performance structures. However, the designs tend to have an intricate organic-looking structure making them challenging to manufacture reliably and economically. Prior attempts to impose manufacturing constraints during the topology optimization process have had limited success. Furthermore, current methods cannot directly consider manufacturing costs, making it difficult for designers to factor in economic objectives or constraints. This Faculty Early Career Development Program (CAREER) award supports fundamental research to formulate the first framework to systematically incorporate geometric design rules and manufacturing cost in topology optimization, and to integrate this framework with educational activities that improve the attitudes of underrepresented minorities towards STEM fields. This research will enable the conceptual design and optimization of lightweight, high-performance, and economically-viable structures with applications across a wide range of engineering industries. The new design capabilities will have the potential to significantly reduce manufacturing and R&D costs and thereby increase the economic competitiveness of American manufacturers. This award will also positively impact underrepresented minorities through an integrated education plan aimed at increasing student self-efficacy and stimulating their participation in STEM. The educational program includes an engaging, virtual-reality based after-school program for middle school students. This program will also engage and impact K-12 teachers and undergraduate and graduate students, and it will be a conduit to communicate research outcomes to the wider public and the research community.Although topology optimization is a successful technique for structural design, its impact is limited by challenges in incorporating manufacturing constrains and economic considerations into the optimization process. These gaps are rooted in the difficulty to express many manufacturing-driven geometric requirements in terms of the design representations used by existing techniques, the discrete nature of some geometric features, and the fact that manufacturing cost can be a non-smooth function of the design. This CAREER project will make three major intellectual contributions to the computational design of structures, namely the coupling of feature-based design representations with 1) global optimization methods to escape entrapment in undesired local minima in the presence of many geometric design rules; 2) discrete optimization methods to accommodate discrete geometric features; and 3) parametric cost models and non-smooth optimization methods to incorporate cost in the topology optimization problem. The new techniques will be validated against benchmarks and demonstrated on engineering problems in collaboration with industry partners.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.