CAREER: Development, Analysis, Implementation, and Application of Innovative Structure Preserving Integrators for Constrained Systems in Mechanics

职业：力学约束系统创新结构保持积分器的开发、分析、实现和应用

• 批准号: 9983708
• 负责人: Laurent Jay
• 金额: $ 20万
• 依托单位: University of Iowa
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2000
• 资助国家: 美国
• 起止时间: 2000-06-01 至 2006-05-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9983708&HistoricalAwards=false
• 关键词: CAREER; Development; Analysis; Implementation; Application

9983708JayThis work is supported by a National Science Foundation Faculty Early Career Development Award. This project is concerned with the numerical solution of differential-algebraic equations (DAEs) of constrained systems in mechanics. The model equations of numerous problems in mechanics take the form of DAEs, not of ordinary differential equations (ODEs). The numerical integration of these DAEs is notoriously difficult, mainly due to the presence of geometrical and/or kinematic constraints. The main research and development objectives of this project are to develop, analyze, implement, and apply numerical methods and techniques related to the numerical integration of these DAEs. The methods proposed, which are based on Runge-Kutta type methods, make great use of the structure of the DAEs considered and they are perfectly fitted to preserve their underlying properties. Several applications in the following areas will be considered: rigid and flexible multibody dynamics; flight formation of multiple coordinated spacecraft; classical molecular dynamics. The educational and research aspects of this project are intertwined. Graduate students will write their M.Sc. or Ph.D. thesis as part of the project. They will spend part of their time with partners in industry and in research laboratories/centers. New courses closely related to the project will be created.What is common between a spacecraft, a DNA loop in a gel, the landing gear of an aircraft, the suspension system of a truck, and a molecule colliding with another one? They are all examples of systems in mechanics (a branch of physics) whose motion can be mathematically modeled by certain sets of equations called "differential-algebraic equations". Being able to simulate these systems on a computer can have various impacts depending on the applications considered. Vehicle-system simulation can help improve research in vehicle safety and vehicle development. Mechanical system simulation software enables users to relatively quickly analyze multiple design variations, thereby reducing the number of costly physical prototypes, improving the quality of the design, and reducing product development time. The concept of having multiple coordinated spacecraft has been identified as an enabling technology for many of the NASA's 21st century missions. The accurate simulation of coordinated spacecraft before they are actually sent can help reduce the risk of mission failure. Understanding the mechanics of DNA, which is at the heart of life, can have some fundamental potential medical benefits. Understanding the collision dynamics of molecules can help to delineate the parameters that are important in the energy transfer process, so that unwanted byproducts and pollutants in chemical reactions can be reduced. Those are all examples of possible impacts that this research can have in the different application areas that will be considered. The work primarily in designing and developing tools that will enable the accurate and efficient simulation of those "constrained systems in mechanics".The National Science Foundation strongly encourages the early development of academic faculty as both educators and researchers. The Faculty Early Career Development (CAREER) Program is a Foundation-wide program that provides for the support of junior faculty within the context of their overall career development. It combines in a single program the support of quality research and education in the broadest sense and the full participation of those traditionally underrepresented in science and engineering. This program enhances and emphasizes the importance the Foundation places on the development of full, balanced academic careers that include both research and education.

9983708 jay本研究获得国家自然科学基金教师早期职业发展奖资助。本课题研究力学中约束系统微分代数方程的数值解。力学中许多问题的模型方程都采用微分方程形式，而不是常微分方程形式。这些DAEs的数值积分是出了名的困难，主要是由于几何和/或运动约束的存在。该项目的主要研究和开发目标是开发、分析、实施和应用与这些dae的数值集成相关的数值方法和技术。所提出的方法基于龙格-库塔类型方法，充分利用了所考虑的DAEs的结构，并且可以很好地拟合以保留其底层属性。将考虑以下领域的几个应用：刚性和柔性多体动力学；多航天器协同飞行编队研究经典分子动力学。这个项目的教育和研究方面是相互交织的。研究生将写他们的硕士或博士论文作为项目的一部分。他们将花部分时间与工业界和研究实验室/中心的合作伙伴一起工作。将开设与项目密切相关的新课程。宇宙飞船、凝胶中的DNA环、飞机的起落架、卡车的悬挂系统，以及一个分子与另一个分子的碰撞，三者之间有什么共同之处？它们都是力学（物理学的一个分支）中系统的例子，其运动可以用某些称为“微分代数方程”的方程集来数学建模。能够在计算机上模拟这些系统可能会产生不同的影响，具体取决于所考虑的应用程序。车辆系统仿真有助于提高车辆安全研究水平和车辆发展水平。机械系统仿真软件使用户能够相对快速地分析多种设计变化，从而减少昂贵的物理原型数量，提高设计质量，缩短产品开发时间。拥有多个协调航天器的概念已被确定为美国宇航局21世纪许多任务的使能技术。协调的航天器在实际发射前的精确模拟可以帮助减少任务失败的风险。DNA是生命的核心，了解它的机制可以带来一些基本的潜在医学益处。了解分子的碰撞动力学有助于描述能量传递过程中重要的参数，从而减少化学反应中不需要的副产物和污染物。这些都是本研究在不同应用领域可能产生的影响的例子。这项工作主要是设计和开发工具，使那些“力学约束系统”的精确和有效的模拟。美国国家科学基金会强烈鼓励教师作为教育工作者和研究人员的早期发展。教师早期职业发展（Career）计划是一个基金会范围内的计划，为初级教师的整体职业发展提供支持。它在一个项目中结合了对最广泛意义上的高质量研究和教育的支持，以及那些传统上在科学和工程领域代表性不足的人的充分参与。该项目加强并强调了基金会对包括研究和教育在内的全面、平衡的学术生涯发展的重要性。