Space time discretization for flexible multibody systems and multisymplectic variational integrators

Internally funded project

Project Details

Project leader:
Prof. Dr.-Ing. Sigrid Leyendecker

Project members:
Thomas Leitz

Contributing FAU Organisations:
Chair of Applied Dynamics

Start date: 01/10/2011

Research Fields

structure preserving simulation and optimal control
Chair of Applied Dynamics
multibody dynamics and robotics
Chair of Applied Dynamics

Abstract (technical / expert description):

Variational integrators are based on the discretization of the variational principle. It is applied to an approximation of the action functional and results in the discrete Euler-Lagrange equations. If space time is discretized in one step, the resulting integrator is multisymplectic, i.e. symplectic in both space and time.Those integrators are suitable for the simulation of flexible multibody systems including beams, shells and 3D continua. Some of the symmetries present in the continuous system are carried over to the discrete setting which leads to the conservation of the associated discrete momentum maps. Furthermore, variational integrators show a very good energy behaviour, i.e. they do not artificially dissipate or gain total energy in a conservative system.


Leitz, T., & Leyendecker, S. (2016). Multisymplectic variational (Lie group) integrators for PDEs of geometrically exact beam dynamics using algorithmic differentiation. In Proceedings of the GAMM. Braunschweig, DE.
Leitz, T., Ober-Blöbaum, S., & Leyendecker, S. (2014). Variational Lie group formulation of geometrically exact beam dynamics: synchronous and asynchronous integration. In Computational Methods in Applied Sciences. (pp. 175-203). Berlin: Springer.
Demoures, F., Gay-Balmaz, F., Leitz, T., Leyendecker, S., Ober-Blöbaum, S., & Ratiu, T.S. (2013). Asynchronous variational Lie group integration for geometrically exact beam dynamics. In Proceedings in Applied Mathematics and Mechanics (Eds.), Proceedings of the GAMM (pp. 1-2). Novi Sad, RS.
Leitz, T., Leyendecker, S., Demoures, F., Gay-Balmaz, F., & Ober-Blöbaum, S. (2013). Asynchronous variational Lie group integration for geometrically exact beam dynamics. In Proceedings of the Multibody Dynamics 2013, ECCOMAS Thematic Conference (pp. DVD, 10 Seiten). Zagreb, HR.

Last updated on 2019-08-01 at 16:46