Multibody System Dynamics

, Volume 19, Issue 1–2, pp 45–72 | Cite as

The discrete null space method for the energy-consistent integration of constrained mechanical systems. Part III: Flexible multibody dynamics

  • Sigrid Leyendecker
  • Peter Betsch
  • Paul Steinmann


In the present work, the unified framework for the computational treatment of rigid bodies and nonlinear beams developed by Betsch and Steinmann (Multibody Syst. Dyn. 8, 367–391, 2002) is extended to the realm of nonlinear shells. In particular, a specific constrained formulation of shells is proposed which leads to the semi-discrete equations of motion characterized by a set of differential-algebraic equations (DAEs). The DAEs provide a uniform description for rigid bodies, semi-discrete beams and shells and, consequently, flexible multibody systems. The constraints may be divided into two classes: (i) internal constraints which are intimately connected with the assumption of rigidity of the bodies, and (ii) external constraints related to the presence of joints in a multibody framework. The present approach thus circumvents the use of rotational variables throughout the whole time discretization, facilitating the design of energy–momentum methods for flexible multibody dynamics. After the discretization has been completed a size-reduction of the discrete system is performed by eliminating the constraint forces. Numerical examples dealing with a spatial slider-crank mechanism and with intersecting shells illustrate the performance of the proposed method.


Conserving time integration Constrained mechanical systems Flexible multibody dynamics Nonlinear structural dynamics Differential-algebraic equations 


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Copyright information

© Springer Science+Business Media B.V. 2007

Authors and Affiliations

  • Sigrid Leyendecker
    • 1
  • Peter Betsch
    • 2
  • Paul Steinmann
    • 1
  1. 1.Chair of Applied Mechanics, Department of Mechanical EngineeringUniversity of KaiserslauternKaiserslauternGermany
  2. 2.Chair of Computational Mechanics, Department of Mechanical EngineeringUniversity of SiegenSiegenGermany

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