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