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.
In engineering, products are optimized to meet several objectives such as cost, performance, manufacturability, recyclability, etc. Product optimization can be a tedious and time-consuming process if carried out manually by human engineers. Therefore, computers are typically used for this purpose. There are several commercially available software systems that are configured to optimize products. However, there are several challenges that these commercial systems face. Two primary challenges being: (1) lack of automation where the software system may require human intervention to complete the optimization, and (2) the software system may require an inordinately long time due to high computational costs. Intellectual Outcome: The first intellectual outcome of the project was in a clear understanding the two challenges. It was determined through careful research that: (1) "lack of automation" could typically attributed to what is referred to as "meshing failure", and (2) "high computational cost" was typically attributed to certain class of products that are long and slender (such as beam structures). The next outcome was creating practical solutions for the two challenges. The first challenge of "automation" was addressed through a new methodology of carrying out product analysis (a critical step in optimization). The new methodology, namely, "tangled finite element analysis" allows the computer to bypass the challenges in automation. It is based on a new interpretation of an existing methods that engineers rely on, and can be easily incorporated into existing commercial software systems. A patent has been filed through Wisconsin Alumni Research Foundation (WARF), a non-profit organization. The second challenge of "speed" was addressed by combining two existing methods into a new "dual" method that is more efficient and robust (as compared to the two existing ones). A patent has been approved by the US Patent office; potential commercialization of this concept is being pursued through WARF. Broader Impacts: An immediate impact of the project is that it has led to fundamental discoveries that translates into less expensive and environmentally friendly products. In practice, the findings can be integrated with commercial product optimization tools. From an educational perspective, trained graduate students were trained on understanding and isolating some of the research challenges faced by the engineering industry. They received formal mentoring on various computational techniques used in product design. The project also trained undergraduate students from the UW Formula SAE team on the use of commercial software systems for optimizing car components.
