000021527 001__ 21527
000021527 005__ 20170622131250.0
000021527 04107 $$aeng
000021527 046__ $$k2017-06-15
000021527 100__ $$aCchang, Sophy
000021527 24500 $$aAN ENERGY-MOMENTUM FORMULATION FOR NONLINEAR DYNAMICS OF PLANAR CO-ROTATING BEAMS

000021527 24630 $$n6.$$pComputational Methods in Structural Dynamics and Earhquake Engineering
000021527 260__ $$bNational Technical University of Athens, 2017
000021527 506__ $$arestricted
000021527 520__ $$2eng$$aThis 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.

000021527 540__ $$aText je chráněný podle autorského zákona č. 121/2000 Sb.
000021527 653__ $$aCorotational formulation; energy-momentum method; conserving energy; nonlinear dynamic; 2D Beams

000021527 7112_ $$aCOMPDYN 2017 - 6th International Thematic Conference$$cRhodes Island (GR)$$d2017-06-15 / 2017-06-17$$gCOMPDYN2017
000021527 720__ $$aCchang, Sophy$$iSansour, Carlo$$iBattini, Jean-Marc$$iHjiaj, Mohammed
000021527 8560_ $$ffischerc@itam.cas.cz
000021527 8564_ $$s481210$$uhttps://invenio.itam.cas.cz/record/21527/files/16886.pdf$$yOriginal version of the author's contribution as presented on CD, section: [RS11] Nonlinear dynamics
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000021527 962__ $$r21500
000021527 980__ $$aPAPER