Multibody System Dynamics

, Volume 37, Issue 1, pp 29–48 | Cite as

Validation of flexible multibody dynamics beam formulations using benchmark problems

  • Olivier A. BauchauEmail author
  • Peter Betsch
  • Alberto Cardona
  • Johannes Gerstmayr
  • Ben Jonker
  • Pierangelo Masarati
  • Valentin Sonneville


As the need to model flexibility arose in multibody dynamics, the floating frame of reference formulation was developed, but this approach can yield inaccurate results when elastic displacements becomes large. While the use of three-dimensional finite element formulations overcomes this problem, the associated computational cost is overwhelming. Consequently, beam models, which are one-dimensional approximations of three-dimensional elasticity, have become the workhorse of many flexible multibody dynamics codes. Numerous beam formulations have been proposed, such as the geometrically exact beam formulation or the absolute nodal coordinate formulation, to name just two. New solution strategies have been investigated as well, including the intrinsic beam formulation or the DAE approach. This paper provides a systematic comparison of these various approaches, which will be assessed by comparing their predictions for four benchmark problems. The first problem is the Princeton beam experiment, a study of the static large displacement and rotation behavior of a simple cantilevered beam under a gravity tip load. The second problem, the four-bar mechanism, focuses on a flexible mechanism involving beams and revolute joints. The third problem investigates the behavior of a beam bent in its plane of greatest flexural rigidity, resulting in lateral buckling when a critical value of the transverse load is reached. The last problem investigates the dynamic stability of a rotating shaft. The predictions of eight independent codes are compared for these four benchmark problems and are found to be in close agreement with each other and with experimental measurements, when available.


Multibody dynamics Beam models Benchmark problems 


Conflict of interest

The authors declare that they have no conflict of interest. This article does not contain any studies with human participants or animals performed by any of the authors. Informed consent was obtained from all individual participants included in the study.


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Copyright information

© Springer Science+Business Media Dordrecht 2016

Authors and Affiliations

  • Olivier A. Bauchau
    • 1
    Email author
  • Peter Betsch
    • 2
  • Alberto Cardona
    • 3
  • Johannes Gerstmayr
    • 4
  • Ben Jonker
    • 5
  • Pierangelo Masarati
    • 6
  • Valentin Sonneville
    • 7
  1. 1.University of MarylandCollege ParkUSA
  2. 2.Karlsruhe Institute of TechnologyKarlsruheGermany
  3. 3.CIMEC (UNL/Conicet)Santa FeArgentina
  4. 4.Leopold-Franzens Universität InnsbruckInnsbruckAustria
  5. 5.University of TwenteEnschedeThe Netherlands
  6. 6.Politecnico di MilanoMilanoItaly
  7. 7.Université de LiègeLiègeBelgium

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