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An energy-momentum formulation for nonlinear dynamics of planar co-rotating beams
KTH, School of Architecture and the Built Environment (ABE), Civil and Architectural Engineering. Université Bretagne, France.
KTH, School of Architecture and the Built Environment (ABE), Civil and Architectural Engineering.ORCID iD: 0000-0003-2104-382X
2017 (English)In: COMPDYN 2017 - Proceedings of the 6th International Conference on Computational Methods in Structural Dynamics and Earthquake Engineering, National Technical University of Athens , 2017, Vol. 2, p. 3682-3696Conference paper, Published paper (Refereed)
Abstract [en]

This article presents an energy-momentum integration scheme for the nonlinear dynamic analysis of planar Bernoulli/Timoshenko 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 can be 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 two numerical examples.

Place, publisher, year, edition, pages
National Technical University of Athens , 2017. Vol. 2, p. 3682-3696
Keywords [en]
2D beams, Conserving energy, Corotational formulation, Energy-momentum method, Nonlinear dynamic
National Category
Other Engineering and Technologies
Identifiers
URN: urn:nbn:se:kth:diva-224408Scopus ID: 2-s2.0-85042298112ISBN: 9786188284425 OAI: oai:DiVA.org:kth-224408DiVA, id: diva2:1191207
Conference
6th International Conference on Computational Methods in Structural Dynamics and Earthquake Engineering, COMPDYN 2017, Rhodes Island, Greece, 15 June 2017 through 17 June 2017
Note

QC 20180316

Available from: 2018-03-16 Created: 2018-03-16 Last updated: 2018-03-16Bibliographically approved

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Battini, Jean-Marc

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Citation style
  • apa
  • harvard1
  • ieee
  • modern-language-association-8th-edition
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More styles
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Output format
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