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A Lagrange–Eulerian formulation of an axially moving beam based on the absolute nodal coordinate formulation

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Abstract

In the scope of this paper, a finite-element formulation for an axially moving beam is presented. The beam element is based on the absolute nodal coordinate formulation, where position and slope vectors are used as degrees of freedom instead of rotational parameters. The equations of motion for an axially moving beam are derived from generalized Lagrange equations in a Lagrange–Eulerian sense. This procedure yields equations which can be implemented as a straightforward augmentation to the standard equations of motion for a Bernoulli–Euler beam. Moreover, a contact model for frictional contact between an axially moving strip and rotating rolls is presented. To show the efficiency of the method, simulations of a belt drive are presented.

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Acknowledgements

The first author acknowledges support of the Austrian Science Fund FWF under project grant I 337-N18. The second author acknowledges support of the Comet-K2 Austrian Center of Competence in Mechatronics ACCM.

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Authors and Affiliations

  1. Institute of Technical Mechanics, Johannes Kepler University Linz, Altenbergerstr. 69, 4040, Linz, Austria

    Astrid Pechstein

  2. Austrian Center of Competence in Mechatronics, Altenbergerstr. 69, 4040, Linz, Austria

    Johannes Gerstmayr

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  1. Astrid Pechstein
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  2. Johannes Gerstmayr
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Correspondence to Astrid Pechstein.

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Pechstein, A., Gerstmayr, J. A Lagrange–Eulerian formulation of an axially moving beam based on the absolute nodal coordinate formulation. Multibody Syst Dyn 30, 343–358 (2013). https://doi.org/10.1007/s11044-013-9350-2

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  • DOI: https://doi.org/10.1007/s11044-013-9350-2

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