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

9983708Jay 这项工作得到了国家科学基金会教师早期职业发展奖的支持。 该项目涉及力学中约束系统的微分代数方程 (DAE) 的数值求解。 许多力学问题的模型方程采用 DAE 的形式，而不是常微分方程 (ODE)。 这些 DAE 的数值积分非常困难，主要是由于几何和/或运动学约束的存在。 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 数值积分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 DAE 的结构，并且它们完美地适合保留其基本属性。 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；经典分子动力学。 该项目的教育和研究方面是相互交织的。研究生将撰写他们的硕士学位。或博士学位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。将创建与该项目密切相关的新课程。航天器、凝胶中的 DNA 环、飞机的起落架、卡车的悬架系统以及分子与另一个分子碰撞之间有什么共同点？ 它们都是力学（物理学的一个分支）系统的例子，其运动可以通过某些称为“微分代数方程”的方程组进行数学建模。 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改进车辆安全和车辆开发的研究。 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体，从而减少昂贵的物理原型的数量、提高设计质量并缩短产品开发时间。 拥有多个协调航天器的概念已被确定为 NASA 21 世纪许多任务的一项支持技术。在实际发送之前对协调航天器进行准确模拟有助于降低任务失败的风险。了解 DNA 的机制是生命的核心，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转移过程中重要的参数，从而减少化学反应中不需要的副产物和污染物。 这些都是这项研究在将要考虑的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，使这些工具能够准确有效地模拟“力学中的约束系统”。国家科学基金会大力鼓励学术人员作为教育者和研究人员的早期发展。 教师早期职业发展（CAREER）计划是一项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。 它将最广泛意义上的高质量研究和教育的支持以及传统上在科学和工程领域代表性不足的人们的充分参与结合在一个计划中。 该计划增强并强调了基金会对包括研究和教育在内的全面、平衡的学术职业发展的重视。

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.