Structure-Preserving Integrators in Nonlinear Structural Dynamics and Flexible Multibody Dynamics

October 7, 2013 — October 11, 2013


  • Peter Betsch (Karlsruhe Institute of Technology (KIT) , Karlsruhe, Germany)

The course focuses on structure-preserving numerical methods for flexible multibody dynamics, including nonlinear elastodynamics and geometrically exact models for beams and shells. Starting with early developments in the eighties, structure-preserving time-stepping schemes are nowadays well-known to possess superior numerical stability and robustness properties.
Originally, energy-momentum conserving schemes have been mainly developed in the framework of nonlinear elastodynamics and structural dynamics. In this connection, nonlinear finite elements are typically used for the discretization in space. Moreover, the parametrization of finite rotations and their impact on the discretization in space and time plays a crucial role.
Due to their success in the field of nonlinear structural dynamics, the energy-momentum method, as well as energy-decaying variants thereof, have been extended to the framework of flexible multibody dynamics. In fact, the nonlinear finite element approach to flexible multibody dynamics has been strongly supported by the availability of structure-preserving discretization methods.
Concerning the discretization in space of nonlinear beams and shells, the course will address two alternative approaches. Firstly, geometrically exact formulations which are typically used in the finite element community and, secondly, the absolute nodal coordinate formulation which is quite popular in the multibody dynamics community.
The semi-discrete equations of motion resulting from the discretization in space of flexible multibody systems in general assume the form of differential-algebraic equations.
Concerning the discretization in time, the energy-momentum method and energy-decaying variants thereof will be treated. In addition to that, the newly emerging class of variational integrators as well as Lie-group integrators will be dealt with.
In the wake of the structure-preserving discretization in space and time a number of issues arise that will be addressed as well. Among them are the parametrization of finite rotations, the incorporation of algebraic constraints and the computer implementation of the various numerical methods. The practical application of structure-preserving methods will be illustrated by a number of examples dealing with, among others, nonlinear beams and shells, large deformation problems, long term simulations and coupled thermo-mechanical multibody systems. In addition to that the novel time integration methods are linked to frequently used methods in industrial multibody system simulation.
The target audience of this summer school are research scientists, postgraduate and graduate students from universities, research institutes and industry, who are interested in the theoretical background and the practical application of computer methods in nonlinear structural dynamics and flexible multibody dynamics.
Multibody system dynamics, Flexible multibody systems, Nonlinear structural dynamics, Structural preserving integrators.


See also