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Error analysis of generalized-\(\alpha \) Lie group time integration methods for constrained mechanical systems

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Abstract

Generalized-\(\alpha \) methods are very popular in structural dynamics. They are methods of Newmark type and combine favourable stability properties with second order convergence for unconstrained second order systems in linear spaces. Recently, they were extended to constrained systems in flexible multibody dynamics that have a configuration space with Lie group structure. In the present paper, the convergence of these Lie group methods is analysed by a coupled one-step error recursion for differential and algebraic solution components. It is shown that spurious oscillations in the transient phase result from order reduction that may be avoided by a perturbation of starting values or by index reduction. Numerical tests for a benchmark problem from the literature illustrate the results of the theoretical investigations.

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Authors and Affiliations

  1. Institute of Mathematics, Martin Luther University Halle-Wittenberg, 06099 , Halle (Saale), Germany

    Martin Arnold

  2. Department of Aerospace and Mechanical Engineering (LTAS), University of Liège, Chemin des Chevreuils, 1 (B52), 4000 , Liège, Belgium

    Olivier Brüls

  3. CIMEC, Universidad Nacional del Litoral, Conicet, Güemes 3450, 3000 , Santa Fe, Argentina

    Alberto Cardona

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Correspondence to Martin Arnold.

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Arnold, M., Brüls, O. & Cardona, A. Error analysis of generalized-\(\alpha \) Lie group time integration methods for constrained mechanical systems. Numer. Math. 129, 149–179 (2015). https://doi.org/10.1007/s00211-014-0633-1

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  • DOI: https://doi.org/10.1007/s00211-014-0633-1

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