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

University Of Iowa, Iowa City IA

Investigators

Abstract

9983708 Jay This 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.