An augmented Lagrangian and reduced index formulation for the analysis of multibody systems with impacts.

OLIVIER BRULS; VINCENT ACARY; FEDERICO CAVALIERI; GEOFFREY VIRLEZ; ALBERTO CARDONA

Zagreb

Congreso; ECCOMAS Multibody Dynamics 2013; 2013

University of Zagreb

In multibody dynamics, contact conditions can lead to impacts and/or abrupt changes in the velocities and, as a consequence, the design of a consistent and stable time integration scheme requires great care. There exist two main groups of numerical integration schemes for nonsmooth systems, namely, event-driven schemes and time-stepping schemes. Event driven schemes are based on an accurate event detection and the time step is adapted such that the end of the step coincides with an event. At this time instant, the event is solved with the help of an impact law. Such schemes are accurate for the free flight smooth motions, but fail to handle frequent transitions in a short time. In practice, they are especially suitable for small multibody systems with a limited number of events. Contrary to the event-driven schemes, time-stepping schemes, e.g. the Moreau-Jean scheme [1, 2] and the Schatzman-Paoli scheme [3, 4], do not adapt their time step size on events but only on some accuracy requirements if needed. Time-stepping methods have been proven to be convergent and robust, and are extensively applied as the solution to the nonsmooth system models. In contrast to event-driven schemes, time-stepping schemes are expected to have order-one accuracy even in the smooth part of the motion. Therefore, the accuracy is less satisfactory unless a very small step size is applied. However, it remains robust and efficient even for a large number of events as it is usual in  structural dynamics.