Weeger, Oliver ; Wever, Utz ; Simeon, Bernd (2022)
Isogeometric analysis of nonlinear Euler-Bernoulli beam vibrations.
In: Nonlinear Dynamics, 72 (4)
doi: 10.26083/tuprints-00019802
Article, Secondary publication, Postprint
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 isogeometricfinite elements is to apply the same functions, namely B-Splines and NURBS (Non-Uniform Rational B-Splines), fordescribing the geometry and for representing the numericalsolution. In case of linear vibrational analysis, this approachhas already been shown to possess substantial advantages over classical finite elements, and we extend it here to a non-linear framework based on the harmonic balance principle. As application, the straight nonlinear Euler-Bernoulli beamis 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 analysisof nonlinear structural vibrations. In particular, the smoother k-method provides higher accuracy than the p-method forisogeometric nonlinear vibration analysis.
| Item Type: | Article |
|---|---|
| Erschienen: | 2022 |
| Creators: | Weeger, Oliver ; Wever, Utz ; Simeon, Bernd |
| Type of entry: | Secondary publication |
| Title: | Isogeometric analysis of nonlinear Euler-Bernoulli beam vibrations |
| Language: | English |
| Date: | 2022 |
| Publisher: | Springer |
| Journal or Publication Title: | Nonlinear Dynamics |
| Volume of the journal: | 72 |
| Issue Number: | 4 |
| Collation: | 17 Seiten |
| DOI: | 10.26083/tuprints-00019802 |
| URL / URN: | https://tuprints.ulb.tu-darmstadt.de/19802 |
| Corresponding Links: | |
| Origin: | Secondary publication service |
| 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 isogeometricfinite elements is to apply the same functions, namely B-Splines and NURBS (Non-Uniform Rational B-Splines), fordescribing the geometry and for representing the numericalsolution. In case of linear vibrational analysis, this approachhas already been shown to possess substantial advantages over classical finite elements, and we extend it here to a non-linear framework based on the harmonic balance principle. As application, the straight nonlinear Euler-Bernoulli beamis 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 analysisof nonlinear structural vibrations. In particular, the smoother k-method provides higher accuracy than the p-method forisogeometric nonlinear vibration analysis. |
| Status: | Postprint |
| URN: | urn:nbn:de:tuda-tuprints-198020 |
| Additional Information: | Keywords: Isogeometric analysis, finite element method, nonlinear vibration, harmonic balance, nonlinear beam |
| Classification DDC: | 600 Technik, Medizin, angewandte Wissenschaften > 600 Technik 600 Technik, Medizin, angewandte Wissenschaften > 620 Ingenieurwissenschaften und Maschinenbau |
| Divisions: | 16 Department of Mechanical Engineering 16 Department of Mechanical Engineering > Cyber-Physical Simulation (CPS) |
| Date Deposited: | 06 Jan 2022 13:02 |
| Last Modified: | 07 Jan 2022 08:09 |
| PPN: | |
| Corresponding Links: | |
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