Assessment of variable step-size integration of multibody systems

When performing the numerical integration of multibody systems (MBS) dynamics, the analyst can choose from a wide variety of methods and implementations. Selecting the most appropriate option for a particular application is not a straightforward task; as a consequence, several benchmark examples have been formulated by the MBS research community with the intent to assess the accuracy and performance of different solution methods when applied to certain kinds of mechanical problems. This paper introduces a variation of the slider-crank mechanism, already employed as benchmark problem in the MBS literature, intended to evaluate the performance of variable-step MBS algorithms. Three cases, featuring singular configurations and variable-frequency external actions, were defined. The example is used to illustrate some necessary elements in the definition of a benchmark problem and in the process of comparing different solution methods, as well as difficulties that can arise during this task. The proposed example was used to evaluate the behaviour of a variable-step index-3 augmented Lagrangian algorithm with velocity and acceleration projections, as well as other well-known solution methods.