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Isogeometric analysis of nonlinear Euler-Bernoulli beam vibrations

  • 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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Author:Oliver Weeger, Utz Wever, Bernd Simeon
URN (permanent link):urn:nbn:de:hbz:386-kluedo-37184
Document Type:Preprint
Language of publication:English
Publication Date:2013/01/04
Year of Publication:2013
Publishing Institute:Technische Universität Kaiserslautern
Date of the Publication (Server):2014/02/10
Number of page:17
Faculties / Organisational entities:Fachbereich Mathematik
DDC-Cassification:5 Naturwissenschaften und Mathematik / 510 Mathematik
MSC-Classification (mathematics):65-XX NUMERICAL ANALYSIS
Licence (German):Standard gemäß KLUEDO-Leitlinien vom 10.09.2012