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

该学院早期职业发展（CAREER）拨款将通过开发一个强大的计算框架，用于三维几何结构设计方法的使用，开发和集成，弥合设计和工程之间的差距。这些方法被称为2-D图形静力学（GS），是强大的几何技术，在过去的150年中，已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。该计划将建立三维图形静力学的数学基础，这是最近开发的用于寻找高性能结构的建筑形式。这项研究将设计计算工具，以有效地建立，控制和优化三维结构形式。一个开源软件，一个互动的教育平台，以及推广活动将扩大学生，设计师和从业人员对3-D图形静态的可访问性和使用，以学习，分享，探索和设计创新，高性能，轻量级的空间结构解决方案。本项目的主要目标是开发数学方法和计算算法，（1）有效地构造凸和非凸的空间结构，（自相交）倒易多面体图与某些用户输入的几何约束：（2）优化的大小的外部负载和内力的几何;（3）操纵倒易多面体图而不破坏这些图的拓扑和几何依赖性;（4）允许结构形式及其力分布的即时拓扑编辑;以及（5）增强倒易图的可视化以提高设计效率。该计划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，用于使用三维图形静力学进行结构的设计，控制和优化。该软件平台将用于教育广泛的学生，研究人员和从业人员，并扩大使用三维图形静力学的设计和制造的高效，创新，高性能的结构系统。这个奖项反映了NSF的法定使命，并已被认为是值得支持的评估使用基金会的智力价值和更广泛的影响审查标准。

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.