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Energy-momentum method for nonlinear dynamic of 2D corotational beams

Abstract : This paper presents an energy-momentum method for nonlinear dynamics of 2D Bernoulli corotational beams. It is shown that the time stepping algorithm conserves energy, linear momentum and angular momentum. To be consistent in the corotational approach, cubic interpolations of Bernoulli element are employed to derive both inertia and elastic terms. The shallow arch strain definition is used to get an element which produce accurate results for less number of elements. To avoid membrane locking, we use a constant and average value of the axial strains. In addition, the energy-momentum method is used to preserve the conserving properties, which is able to maintain the stability and accuracy in a non-dissipative system for a long period. The midpoint velocities of kinematic fields and strains are used to tackle any non-linear form of strain displacement relations. Finally, two examples including large overall displacement are presented to illustrate the stability and efficiency of the proposed algorithms.
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Contributor : Laurent Jonchère Connect in order to contact the contributor
Submitted on : Wednesday, December 14, 2016 - 3:08:55 PM
Last modification on : Monday, January 24, 2022 - 11:30:13 AM


  • HAL Id : hal-01416481, version 1


S. Chhang, Mohammed Hjiaj, J.-M. Battini, C. Sansour. Energy-momentum method for nonlinear dynamic of 2D corotational beams. 7th European Congress on Computational Methods in Applied Sciences and Engineering, ECCOMAS Congress 2016, Jun 2016, Hersonissos, Greece. pp.5496--5506. ⟨hal-01416481⟩



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