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Isogeometric analysis of nonlinear Euler–Bernoulli beam vibrations

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Abstract

In this paper we analyze the vibrations of nonlinear structures by means of the novel approach of isogeometric finite elements. The fundamental idea of isogeometric finite elements is to apply the same functions, namely B-Splines and NURBS (Non-Uniform Rational B-Splines), for describing the geometry and for representing the numerical solution. In case of linear vibrational analysis, this approach has already been shown to possess substantial advantages over classical finite elements, and we extend it here to a nonlinear framework based on the harmonic balance principle. As application, the straight nonlinear Euler–Bernoulli beam is used, and overall, it is demonstrated that isogeometric finite elements with B-Splines in combination with the harmonic balance method are a powerful means for the analysis of nonlinear structural vibrations. In particular, the smoother k-method provides higher accuracy than the p-method for isogeometric nonlinear vibration analysis.

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Acknowledgements

The authors were supported by the 7th Framework Programme of the European Union, project TERRIFIC (FP7-2011-NMP-ICT-FoF 284981) [40].

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Authors and Affiliations

  1. TU Kaiserslautern, Felix-Klein-Center for Mathematics, Paul-Ehrlich-Straße 31, 67663, Kaiserslautern, Germany

    Oliver Weeger & Bernd Simeon

  2. Siemens AG, Corporate Technology, Otto-Hahn-Ring 6, 81739, Munich, Germany

    Oliver Weeger & Utz Wever

Authors
  1. Oliver Weeger
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  2. Utz Wever
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  3. Bernd Simeon
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Correspondence to Oliver Weeger.

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Weeger, O., Wever, U. & Simeon, B. Isogeometric analysis of nonlinear Euler–Bernoulli beam vibrations. Nonlinear Dyn 72, 813–835 (2013). https://doi.org/10.1007/s11071-013-0755-5

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