CAREER: 3D/Polyhedral Graphic Statics for Education, Design, and Optimization of High-Performance Structures

University Of Pennsylvania, Philadelphia PA

Investigators

Abstract

This Faculty Early Career Development (CAREER) grant will bridge the gap between design and engineering by developing a robust computational framework for the use, development, and integration of geometry-based structural design methods in three dimensions. These methods, known as 2-D graphic statics (GS), are powerful geometric techniques that have been used to find efficient structural forms of many iconic bridges and long-span structures over the past 150 years. This program will establish the mathematical foundations of 3-D graphic statics, which has been very recently developed for finding architectural forms for high-performance structures. This research will devise computational tools to effectively build, control, and optimize structural forms in three dimensions. An open-source software, an interactive educational platform together with outreach activities will extend the accessibility and use of 3-D graphic statics by students, designers, and practitioners to learn, share, explore, and design innovative, high-performance, lightweight spatial structural solutions. The result of this project will open a new horizon for an unexplored realm of efficient spatial structural designs. The primary objective of this CAREER project is to develop mathematical methods and computational algorithms that (1) effectively construct convex and non-convex (self-intersecting) reciprocal polyhedral diagrams with certain user-input geometric constraints; (2) optimize the magnitude of external loads and the internal forces geometrically; (3) manipulate reciprocal polyhedral diagrams without breaking the topological and geometric dependencies of these diagrams; (4) allow for instant topological editing of both structural form and its force distribution; and (5) enhance the visualization of the reciprocal diagrams to increase design efficiency. This program will also provide a robust software platform and its related application programming interface for design, control and optimization of structures using 3D graphic statics. The software platform will be used in the education of a wide range of students, researchers, and practitioners and broaden the use of 3-d graphic statics in the design and fabrication of highly efficient, innovative, high-performance structural systems. 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.