CGV: Small: Discrete Variational Contact, Impact, and Dissipative Dynamics

CGV：小：离散变分接触、冲击和耗散动力学

• 批准号: 1117257
• 负责人: Eitan Grinspun
• 金额: $ 49.99万
• 依托单位: Columbia University
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2011
• 资助国家: 美国
• 起止时间: 2011-08-15 至 2015-07-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1117257&HistoricalAwards=false
• 关键词: CGV; Small; Discrete; Variational; Contact

This project investigates computational techniques for modeling dissipative physical systems experiencing contact, impact, friction and plasticity. The attendant optimization problems are strongly nonlinear, nonsmooth, and nonconvex in nature, necessitating the development of novel numerical methods. The research grounds the development of these methods by building on discrete geometric mechanics and variational integrators, which restate the fundamental principles of physics in a discrete, hence immediately computable form. The research examines five core behaviors arising from the Principle (momentum/energy/symmetry preservation, breaking contact, and non-interpenetration) and thereby derives computer algorithms whose outputs capture these physical behaviors. The project success is measured by (a) the production of novel computer algorithms that are able to simulate dissipative physical phenomena more accurately and efficiently than ever before, (b) new theoretical results on what can be expected of computer algorithms that simulate these phenomena, and (c) the successful adoption of the novel techniques by industry partners. The project results are publicly disseminated via articles in journals, release of source code on the world wide web, and transfer of technological expertise and data to industrial partners. Improving computational techniques for the simulation of contact, impact, and dissipative phenomena helps make engineering safety analyses, biomechanical models, computer visualizations, surgical training tools, and industrial manufacturing simulations that better predict reality. Algorithms that accurately capture the physics help to gain important new insights into many open questions that influence our understanding of large-scale geophysics of earthquakes and calving of icebergs, small-scale dissipation in high-frequency micro- and nano-electronic mechanical devices, prosaic domestic phenomena such as the chattering of chalk on a board and even the excitation of violin strings.

该项目研究对经历接触、冲击、摩擦和塑性的耗散物理系统进行建模的计算技术。随之而来的优化问题本质上是强非线性、非光滑和非凸的，因此需要开发新的数值方法。该研究通过建立在离散几何力学和变分积分器的基础上，为这些方法的发展奠定了基础，这些方法以离散且可立即计算的形式重申了物理学的基本原理。该研究检查了该原理产生的五种核心行为（动量/能量/对称性保持、断开接触和非互穿），从而推导出其输出捕获这些物理行为的计算机算法。该项目的成功是通过以下指标来衡量的：（a）新型计算机算法的产生，这些算法能够比以往更准确、更有效地模拟耗散物理现象，（b）关于模拟这些现象的计算机算法的预期结果的新理论结果， (c) 行业合作伙伴成功采用新技术。该项目的成果通过期刊文章、在万维网上发布源代码以及向工业合作伙伴转让技术专长和数据来公开传播。改进接触、冲击和耗散现象模拟的计算技术有助于更好地预测现实的工程安全分析、生物力学模型、计算机可视化、手术训练工具和工业制造模拟。准确捕捉物理现象的算法有助于对许多悬而未决的问题获得重要的新见解，这些问题影响我们对地震和冰山崩解的大规模地球物理学、高频微纳米电子机械设备中的小尺度耗散、平淡无奇的地球物理学的理解。国内现象，如粉笔在木板上的颤动，甚至小提琴琴弦的激励。