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

这项学院早期职业发展(Career)补助金将通过开发一个强大的计算框架来使用、开发和整合基于几何的三维结构设计方法，从而弥合设计和工程之间的差距。这些方法被称为二维图形静力学(GS)，是一种强大的几何技术，在过去的150年里已经被用于寻找许多标志性桥梁和大跨度结构的有效结构形式。该程序将建立3-D图形静力学的数学基础，这是最近为寻找高性能结构的建筑形式而开发的。这项研究将设计计算工具，以有效地构建、控制和优化三维结构形式。一个开源软件，一个互动教育平台，以及推广活动，将扩大学生、设计师和从业者对3D图形静力学的访问和使用，以学习、分享、探索和设计创新的、高性能的、轻型的空间结构解决方案。这个项目的结果将为有效的空间结构设计开辟一个新的领域。这个职业项目的主要目标是开发数学方法和计算算法，以(1)有效地构建具有某些用户输入几何约束的凸和非凸(自交)互易多面体图；(2)从几何上优化外部载荷和内力的大小；(3)在不打破这些图的拓扑和几何依赖的情况下操作互易多面体图；(4)允许对结构形式及其力分布进行即时的拓扑编辑；以及(5)增强互易图的可视化，以提高设计效率。该程序还将提供一个强大的软件平台及其相关的应用程序编程接口，用于使用3D图形静力学对结构进行设计、控制和优化。该软件平台将用于广泛的学生、研究人员和从业人员的教育，并扩大三维图形静力学在设计和制造高效、创新、高性能结构系统中的使用。该奖项反映了NSF的法定使命，并通过使用基金会的智力优势和更广泛的影响审查标准进行评估，被认为值得支持。

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.