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An energy-momentum co-rotational formulation for nonlinear dynamics of planar beams
KTH, School of Architecture and the Built Environment (ABE), Civil and Architectural Engineering, Building Technology and Design. Université Bretagne Loire, France.
KTH, School of Architecture and the Built Environment (ABE), Civil and Architectural Engineering, Building Technology and Design.
2017 (English)In: Computers & structures, ISSN 0045-7949, E-ISSN 1879-2243, Vol. 187, 50-63 p.Article in journal (Refereed) Published
Abstract [en]

This article presents an energy-momentum integration scheme for the nonlinear dynamic analysis of planar Euler-Bernoulli beams. The co-rotational approach is adopted to describe the kinematics of the beam and Hermitian functions are used to interpolate the local transverse displacements. In this paper, the same kinematic description is used to derive both the elastic and the inertia terms. The classical midpoint rule is used to integrate the dynamic equations. The central idea, to ensure energy and momenta conservation, is to apply the classical midpoint rule to both the kinematic and the strain quantities. This idea, developed by one of the authors in previous work, is applied here in the context of the co-rotational formulation to the first time. By doing so, we circumvent the nonlinear geometric equations relating the displacement to the strain which is the origin of many numerical difficulties. It is rigorously shown that the proposed method conserves the total energy of the system and, in absence of external loads, the linear and angular momenta remain constant. The accuracy and stability of the proposed algorithm, especially in long term dynamics with a very large number of time steps, is assessed through four numerical examples.

Place, publisher, year, edition, pages
Elsevier, 2017. Vol. 187, 50-63 p.
Keyword [en]
Co-rotational formulation, Energy-momentum method, Conserving energy, Nonlinear dynamic, 2D beam
National Category
Other Engineering and Technologies
Identifiers
URN: urn:nbn:se:kth:diva-208776DOI: 10.1016/j.compstruc.2017.03.021ISI: 000401675600004Scopus ID: 2-s2.0-85017346411OAI: oai:DiVA.org:kth-208776DiVA: diva2:1109696
Note

QC 20170614

Available from: 2017-06-14 Created: 2017-06-14 Last updated: 2017-06-14Bibliographically approved

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CiteExportLink to record
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Citation style
  • apa
  • harvard1
  • ieee
  • modern-language-association-8th-edition
  • vancouver
  • Other style
More styles
Language
  • de-DE
  • en-GB
  • en-US
  • fi-FI
  • nn-NO
  • nn-NB
  • sv-SE
  • Other locale
More languages
Output format
  • html
  • text
  • asciidoc
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