Penalty, semi-recursive and hybrid methods for MBS real-time dynamics in the context of structural integrators

In a previous work, the authors presented a new real-time formulation for the dynamics of multibody systems, which encompasses high ranks of efficiency, accuracy, robustness and easiness of implementation. The new method, called hybrid, was obtained as a combination of a topological semi-recursive formulation based on velocities transformation, and a global penalty formulation for closed-loops consideration. It was proven to be more robust and efficient that its predecessors for large problems. For the three methods compared, the implicit, single-step trapezoidal rule was used as numerical integrator. In this paper, the influence of the integration scheme on the performance of the three mentioned methods is studied. Since the hybrid formulation becomes competitive for large multibody systems, a rather demanding simulation of the full model of a car vehicle is selected as benchmark problem. Computer codes implementing the three dynamic formulations in combination with different structural integrators, like Newmark, HHT and Generalized-alpha algorithms, are used to run the simulation, so that the performance of each couple dynamic-formulation/numerical-integrator can be appraised. The example is also analyzed through a commercial tool, so as to provide the readers with a well-known reference for comparison.