Keywords: parallel processing, multibody dynamics, parallelization, numerical simulation.

Multibody dynamics plays a crucial role in today's research and development. New methods, better computational environments and growing demands on accuracy and complexity lead to increasing degrees of freedom and a high number of uni- and bi-lateral constraints. This trend has the main drawback that the computational times for the simulations are steadily increasing which conflicts with the main purposes of the simulation method in general. Simulation methods are mainly used for saving time using techniques such as numerical optimization or parameter variation which are only profitable if the simulation times are low enough. But exactly these systems with a high number of uni- and bi-lateral constraints are of great interest. Uni- and bi- lateral constraints can mainly be modelled by means of smooth (single-valued) or non-smooth (set-valued) force laws [1]. Using single-valued force laws leads to numerical stiff equations of motion which need special time-consuming integration methods or small time step sizes. Alternatively, set-valued force laws can be taken into account. These force laws also need special integration schemes such as time-stepping methods, however solving them by the proximal point to a convex set, they are about three times faster as single-valued force laws [2]. But now, the solution of the force laws itself is not the most time-consuming part, rather the calculation of the "system update", meaning calculating the gap-distances, gap-velocities, right-hand sides, mass-matrices, etc. in every time step.

The method described in this paper proposes the parallel calculation of the system-update. Shared-memory parallelization has some difficulties, named data-races, dead-locks and most important computational overhead for the management of the parallelization which is depends on the number of used cores. If the computational costs for the management are higher than the saved time as a result of the parallelization, the parallelized simulation is slower than the sequential. The algorithm of the proposed method determines during runtime which parts of the system-update should be calculated in parallel and which sequentially. The algorithm therefore uses two criterions, the number of used cores and the computational time needed for each individual calculation.

The parallelization method is applied to three examples, two academic examples and one large industrial example from the field of rotor dynamics. The method is discussed on selected update-processes of these three examples leading to the result that the chosen criterions are very important for the effectiveness of the parallelization. After having discussed the method in detail, the method is applied to different update-methods within these examples. For every method the best choice of the criterions and the possible speedups are shown. Using one of the academic examples, the difference between smooth- and non-smooth contact mechanics is shown concerning the required computational time. Hence, different "state of the art" integrators are chosen to integrate the system.

1

J. Clauberg, et al., "Simulation of a Non-Smooth Continuous System", in "Vibration Problems ICOVP - Proceedings in Physics", 978-94-007-2068-8, Springer, Berlin, 2011. doi:10.1007/978-94-007-2069-5_39

2

M. Förg, et al., "Contacts within Valve Train Simulations: a Comparison of Models", JSME Technical Journal, 1(1), 2006.

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