Collaborative Research: Simulation of Multibody Dynamics. Leveraging New Numerical Methods and Multiprocessor Capabilities

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This project capitalizes on new numerical integration methods and recent breakthroughs in multi-processor technologies (software and midrange hardware) to provide the theoretical and computational foundation that will enable a paradigm shift in mechanical system simulation. Recent numerical integration methods developed for mechanical system simulation of large industrial problems (e.g. vehicles, aircraft, spacecraft, gears, chains/track, contact/impact, etc.) have demonstrated the ability to reduce simulation times by a factor of two to three. The proposed work draws on these results to (a) investigate and extend the use of Hilber-Hughes-Taylor (HHT)-type integrators in mechanical system simulation, and (b) investigate and extend new specialized partitioned additive Runge-Kutta methods that have excellent stability properties, adjustable numerical damping, and a wide range of convergence orders. This effort will also lead to accurate integration formulas with adjustable numerical damping for the solution of first order differential equations. These formulas will enable the simulation of mechatronic systems (mixed multibody dynamics and controls problems) in a unified framework. A second direction of research will investigate mechanical system simulation techniques that leverage recent advances in software and midrange hardware support for parallel computation. Multibody dynamics specific load balancing and inter-process communication management that account for the topology of the mechanical system, along with an asynchronous Jacobian evaluation strategy, will enable scalable equation formulation and numerical solution on multiprocessor platforms.Together, the two thrusts of this research (new numerical integration techniques and the associated parallel computation support) will yield one to two orders of magnitude reduction in simulation times for large industrial-type mechanical systems. In economic terms, this work benefits design engineers relying on simulation-based engineering by enhancing their productivity. In educational terms, this work provides material and examples for hands-on classes in Computational Dynamics and Numerical Analysis, as well as the foundation for a longer term initiative aimed at introducing under-represented groups to the field of Computational Science through a series of seminars and workshops offered to High School students and teachers.