Design Space Parametrizations and Their Role in Mechanical Design Space Exploration

In its broadest sense, mechanical design is an ill-posed and intractable problem. There are known examples of design domains, such as structural vehicle hood design, where explicit design space parameterizations transform the design problem into a tractable one, but generalizations remain poorly understood. These issues are further exacerbated by the zoo of geometric representations used in computational design. Consequently, the process of design ideation remains difficult to automate.

We review the role of parameterizations in the ideation process within the context of design space exploration and introduce a new hierarchical geometric representation based on maximal balls. We show that this new representation known as MDBD, which is a structured and hierarchical collection of tangent d-dimensional balls and its associated connectivity graph, induces a hierarchical parameterization of geometry that is unique, rotation-invariant, representation-agnostic, and fully supports design, analysis, and optimization, while avoiding the degradation of model accuracy seen with other volumetric representations (e.g., voxels and octrees). We show that these maximal balls can be used to efficiently represent and learn shapes in topology optimization and geometric/manufacturability similarity search. Moreover, we demonstrate that, when coupled with automatic differentiation, MDBD can be used to simultaneously optimize two independently NP hard problems, namely the packaging (layout) and routing of complex engineered systems, driven by intricate yet functionally meaningful objective functions.

Horea Ilies headshotHorea Ilies, University of Connecticut 

Horea Ilies is the Pratt and Whitney Professor and Director of the School of Mechanical, Aerospace, and Manufacturing Engineering at the University of Connecticut (UConn), and a director of the DREAM research center at UConn. He earned his Ph.D. in Mechanical Engineering from the University of Wisconsin–Madison and holds M.S. degrees in Mechanics and Mechanical Engineering from Michigan State University and the Technical University of Cluj, Romania. Before transitioning to academia, Dr. Ilies gained extensive industrial experience at Ford Motor Company, working in research, manufacturing, and product design and development. His research focuses on geometric and physical computing, shape synthesis, geometric reasoning, and the theoretical and computational foundations of the systematic design and manufacturing of engineered systems. Dr. Ilies is a recipient of the NSF CAREER Award (2007) and together with his graduate students received several Best Paper awards for his contributions to the field. He is also an elected member of the Connecticut Academy of Science and Engineering and a Fellow of ASME.