Validation of flexible multibody dynamics beam formulations using benchmark problems

Olivier A. Bauchau*, Peter Betsch, Alberto Cardona, Johannes Gerstmayr, Ben Jonker, Pierangelo Masarati, Valentin Sonneville

*Corresponding author for this work

    Research output: Contribution to journalConference articleAcademicpeer-review

    67 Citations (Scopus)
    210 Downloads (Pure)


    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.

    Original languageEnglish
    Pages (from-to)29-48
    Number of pages20
    JournalMultibody system dynamics
    Issue number1
    Early online date9 Mar 2016
    Publication statusPublished - 1 May 2016
    Event7th Asian Conference on Multibody Dynamics, ACMD 2014 - Busan Exhibition and Convention Center (BEXCO), Busan, Korea, Republic of
    Duration: 30 Jun 20143 Jul 2014
    Conference number: 7


    • Beam models
    • Benchmark problems
    • Multibody dynamics
    • 2023 OA procedure


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