Session: Rising Stars of Mechanical Engineering Celebration & Showcase

Paper Number: 149577

149577 - Breaking Space for Making Shape: Partitive Geometry for Design and Manufacturing 

Motivation & Need: Generative design is gaining tremendous impetus in engineering, especially after the popularity of topology optimization combined with unprecedented access to additive manufacturing. While inverse design and even generative design in particular, as concepts, have been around for a few decades, it is the recent rise of computational power, commodification of cloud computing, and the development of advanced artificial intelligence platforms that has brought these paradigms to mainstream engineering design. Current methodologies for complex shape generation are, by and large, inverse design strategies wherein the designer co-explores the design space with an algorithmic back-end that generates solution instances based on some prescribed design requirements (if the designer knows what they are). However, in doing so, the designer also forfeits explicit control over the form. Therefore, it is the computer that has taken over the task of inventing new shapes leaving designers to specify parameters and then choose from a vast collection computer-generated shapes. There is a need for a new representation of geometric solids that allows for real-time forward design of complex shapes while also simplifying physical evaluation (e.g. finite element simulation) for inverse design. In contrast to the existing modeling systems, this research proposes partitive geometry, a new shape representation that allows the designer to create a family of space-filling shapes in a single shot by using the principles of spatial symmetry and arrangements.

Methodology: Partitive geometry takes inspiration from the fact that natural systems, organic or inorganic, embody spatial growth as one of the working principles that is central to the development of complex forms with a wide range of mechanical functions. By distilling the underlying geometric principles of growth in physical, chemical, and biological systems, the idea behind partitive geometry is to develop the theoretical, computational, and experimentally validated principles for designing space-filling shapes. Specifically, this research integrates currently disconnected methodologies such as implicit modeling, medial axis representations, and Voronoi tessellations into a single unified methodology for a low information-footprint shape representation in complex 2D and 3D lattices. The main advantage of this representation is that it will simultaneously enable interactive forward design as well as computationally efficient inverse design. Modeling techniques for pattern generation are currently restrictive in the amount of control users have over the end outcome. The current progress in the development of partitive modeling has established algorithms to enable interactive design of extremely complex structures with simple and intuitive Voronoi site representation governed by well-categorized 2D, 2.5D, and 3D symmetries.

Results: Many entirely new classes of structural patterns have thus come to light through the application of this approach including a wide variety of topologically interlocking shapes, functionally graded cellular structures, and auxetic meta-materials. Experimental evaluation of some of the auxetic structures has led to significant multi-functional mechanical and piezo-resistive performance under tensile loading. A completely new class of design space has also been discovered to represented volumetric woven structures and is being leveraged for the design of volumetric cellular structures with unique mechanical properties. The development of topologically interlocked space-filling shapes enabled by partitive geometry have recently been applied to collision-free path planning algorithms for Cooperative 3D printing where multiple robots optimally print large-scale parts. The algorithms developed using partitive geometry have not only significantly reduced the time to print medium-to-large scale parts, they also promise parts with higher impact resistance owing to topological interlocking.

Future Outlook: This research seeks to promote disruptive methodological innovations in engineering disciplines including automotive and aerospace industry, construction science (architectural design), additive manufacturing (swarm 3D printing), structural mechanics (architected materials), heat transfer (design of heat fins), and even acoustics (using topologically interlocking energy dissipating structures). Several application areas will also be transformed including protective gear for military and sports, and curved miniaturized electronics. Emerging trends in the maker culture and open design movement have led to several small scale enterprises that have adopted generative design as a core enabling technology for customized and personalized products. 

Presenting Author: Vinayak Krishnamurthy Texas A&M University

Presenting Author Biography: Vinayak Krishnamurthy is an Associate Professor and Morris E. Foster Faculty Fellow in the J. Mike Walker’66 Department of Mechanical Engineering and an affiliated faculty in the Department of Computer Science at Texas A&M University. He joined Texas A&M in Fall 2016. He earned his Ph.D. in 2015 from the School of Mechanical Engineering at Purdue University. Dr. Krishnamurthy currently directs the Mixed-Initiative Design Lab (MIDL) at Texas A&M University. His research is at the interface of geometric & topological computing, human-computer interaction, and artificial intelligence. He applies the knowledge gained in these areas to various domains such as metamaterial design, extended reality for design, computational fabrication, data-driven design, collaborative design, autonomous systems, surgical training, and engineering education. His dissertation research led to the commercial deployment of zPots, a virtual pottery app using Leap Motion controller in collaboration with zeroUI, a California-based startup. He is the recipient of multiple awards including the NSF CAREER award, ASME CIE Young Engineer Award, two ASME CIE best paper awards, and the Peggy L. and Charles L. Brittan Teaching Award for Outstanding Undergraduate Teaching and the TAMU Association of Former Students College Level Teaching Award.

Authors:

Vinayak Krishnamurthy Texas A&M University