A consistent and efficient framework for the time integration of multibody systems with impacts and friction

In this work, we discuss time integration schemes for the dynamic simulation of nonsmooth flexible multibody systems.

We develop a framework for the consistent treatment of velocity jumps, e.g. due to impacts. A non-impulsive trajectory of state-variables is improved by an impulsive correction after each time-step if necessary.

This correction is automatically chosen starting from a non-impulsive base integration scheme, which discretizes the propagation within the time-step. Consistency is achieved due to the impulsive corrections on the same kinematic level as the treatment of non-impulsive constraints. This idea stems from a time-discontinuous Galerkin setting, but is generalized concerning the splitting of non-impulsive and impulsive force propagation. In this work, we compare the behaviour of four different base integration schemes in the newly developed framework as well as a classical Moreau-Jean timestepping scheme concerning selected criteria and examples from academics and industry.

It turns out that the half-explicit timestepping is a very robust and the most efficient method as far as we deal with non-stiff problems. The timestepping schemes based on the generalized-alpha method, the Bathe method and the ED-alpha method become most efficient for stiff problems with spurious oscillations. In our test cases the generalized-alpha method is the most efficient base integration scheme concerning computing time, however it may get unstable in the nonlinear regime. The ED-alpha method satisfies exactly the opposed characteristics. It is the Bathe-method, which seems to be the best compromise concerning stability and efficiency in the nonlinear regime. We propose it as a base integration scheme for timestepping methods whenever stiff problems with impacts and friction have to be solved.

• Since 2015: Senior Scientist, ABB Corporate Research Center Germany
  • Development of next generation breaker prototypes in an interdisciplinary group of mechanical and electrical engineers.
  • Statistical optimization of robust designs in simulation and testing.
  • Sophisticated mechanical modeling including clearance, impact and friction models.
  • Coupling and co-simulation of mechanical, electro-magnetical and hydrodynamical phenomena.

• 2011-2015: Research group leader 'numerical simulation' and habilitation candidate, Institute of Applied Mechanics, TU München
  Thesis: Consistent Time-Integration Schemes for Flexible Multibody Systems with Friction and Impacts. Examiner: Prof. Dr. Daniel Rixen, Prof. Dr. Wolfgang Wall, Prof. Dr. Christoph Glocker
• 2010-2011: PostDoc, BiPoP team, INRIA Grenoble Rhône-Alpes
  Publication: Timestepping schemes for nonsmooth dynamics based on discontinuous Galerkin methods: definition and outlook. Collaborator: Dr. Vincent Acary
• 2006-2010: Scientific research assistant and PhD student, Institute of Applied Mechanics, TU München
  Thesis: Spatial Dynamics of Pushbelt CVTs, Examiner: Prof. Dr. Heinz Ulbrich, Prof. Dr. Martin Arnold 
• 2001-2006: Diploma (M.S.) Technomathematik, TU München
  Thesis: Domain decomposition methods for parabolic partial differential equations. Advisor: Prof. Dr. Bernd Simeon