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.

该项目研究了用于建模耗散物理系统的计算技术，以进行接触，影响，摩擦和可塑性。随之而来的优化问题本质上是强烈的非线性，非平滑和非凸的，因此需要开发新的数值方法。该研究通过建立离散的几何力学和变分集成剂来为这些方法的发展开发，这些整合物以离散的物理原理重新以离散的形式重述了基本原理，因此立即可计算。该研究研究了由原理（动量/能量/对称性保存，断裂接触和非互操作）产生的五种核心行为，从而得出了计算机算法的计算机算法，其输出捕获了这些物理行为。该项目的成功是通过（a）生产新型计算机算法来衡量的，这些算法能够比以往任何时候都更准确，更有效地模拟耗散性的物理现象，（b）关于模拟这些现象的计算机算法可以期待的新理论结果，以及（c）行业伙伴成功地采用了新型技术。该项目的结果通过期刊中的文章公开传播，在万维网上发布源代码，以及将技术专业知识和数据传输给工业合作伙伴。改进计算技术以模拟接触，影响和耗散现象有助于进行工程安全分析，生物力学模型，计算机可视化，手术培训工具以及工业制造模拟，以更好地预测现实。 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.