A state-time finite element formulation for multibody dynamic systems simulation

This thesis presents the foundational ideas, theory and research effort associated with determining and demonstrating the feasibility and advantage of a new methodology, termed as state-time formulation, for dynamic simulation of multibody systems. The goal of this work is to advance the state of the art in multibody dynamic algorithms as a tool in the design, analysis and simulation for such systems. Additionally, the proposed algorithm is better able to fully exploit anticipated future massively parallel computing resources (e.g. peta flop machines and beyond). This methodology permits the treatment of time, appearing within the equations of motion, as a variable in much the same manner as what has been done on the spatial coordinates by the finite element community. This allows the parallelization of the corresponding computation over both space and time, resulting in a far greater level of coarse grain parallelization compared to the most advances of today's parallel multibody dynamic algorithms. As contemporary multibody algorithms are inherently sequential in time, the focus of all these formulations has been to parallelize the governing dynamical equations on the current integration step. Parallel implementation of these formulations is hobbled by sequential bottlenecks and the use of additional processors does not increase the speedup in a significant way unless these sequential bottlenecks can be reduced. Parallelizing the simulation and all related analysis both spatially and temporally results in a drastic increase in the number of coarse grain calculations that may be distributed over all the available processors. Another benefit of the state-time formulation relative to traditional approaches is its ability to effectively treat and consider multiple time scales. Similar to multi-rate integration schemes, the method provides the tool for accommodating multiple, grossly different time scales using this formalism. Additionally, the associated algorithm when constrained to sequential applications has the potential of acting as an efficient implicit integration scheme.