In this work, we design a time-stepping scheme, which can ensure either conservation of energy or dissipation of energy of high (unresolved) modes for nonlinear dynamic analysis. The latter is needed to improve the performance in stress computation and long-term numerical stability. Finite element implementation details are given for finite-strain three-dimensional solid model with independent rotational degrees of freedom. The addition of a rotation field requires a particular choice of large strain measures, allowing one to separate large rotation and large displacement. Several numerical simulations illustrate a very satisfying performance of the proposed time-stepping scheme.
Dans cet article, nous développons un schéma implicite d'intégration temporelle capable d'assurer, soit la conservation de l'énergie, soit la dissipation de l'énergie d'un système dynamique non linéaire. Ce dernier est particulièrement intéressant pour améliorer la stabilité numérique pour le calcul sur un grand intervalle du temps. L'implémentation de la méthode des éléments finis est présentée en détail pour un modèle de solide tridimensionnel en grandes transformations qui fait intervenir des degrés de liberté de rotation indépendants. La prise en compte de la rotation implique un choix judicieux de la mesure des grandes déformations pour séparer les grands déplacements des grandes rotations. La performance du schéma proposé est illustrée à travers de nombreux exemples de simulations.
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Mot clés : Solide 3D, Dynamique non linéaire, Grandes transformations, Algorithme de conservation/dissipation
Abir Boujelben 1; Adnan Ibrahimbegovic 2
@article{CRMECA_2018__346_7_571_0,
author = {Abir Boujelben and Adnan Ibrahimbegovic},
title = {Conserving and decaying energy for finite-strain three-dimensional solids with rotational degrees of freedom in nonlinear dynamics},
journal = {Comptes Rendus. M\'ecanique},
pages = {571--580},
publisher = {Elsevier},
volume = {346},
number = {7},
year = {2018},
doi = {10.1016/j.crme.2018.04.006},
language = {en},
}
TY - JOUR AU - Abir Boujelben AU - Adnan Ibrahimbegovic TI - Conserving and decaying energy for finite-strain three-dimensional solids with rotational degrees of freedom in nonlinear dynamics JO - Comptes Rendus. Mécanique PY - 2018 SP - 571 EP - 580 VL - 346 IS - 7 PB - Elsevier DO - 10.1016/j.crme.2018.04.006 LA - en ID - CRMECA_2018__346_7_571_0 ER -
%0 Journal Article %A Abir Boujelben %A Adnan Ibrahimbegovic %T Conserving and decaying energy for finite-strain three-dimensional solids with rotational degrees of freedom in nonlinear dynamics %J Comptes Rendus. Mécanique %D 2018 %P 571-580 %V 346 %N 7 %I Elsevier %R 10.1016/j.crme.2018.04.006 %G en %F CRMECA_2018__346_7_571_0
Abir Boujelben; Adnan Ibrahimbegovic. Conserving and decaying energy for finite-strain three-dimensional solids with rotational degrees of freedom in nonlinear dynamics. Comptes Rendus. Mécanique, Volume 346 (2018) no. 7, pp. 571-580. doi : 10.1016/j.crme.2018.04.006. https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.1016/j.crme.2018.04.006/
[1] Non-linear dynamics of three dimensional rods: exact energy and momentum conserving algorithms, Int. J. Numer. Methods Eng., Volume 38 (1995), pp. 1431-1473
[2] Nonlinear dynamics of flexible beams in planar motion: formulation and time-stepping scheme for stiff problems, Comput. Methods Appl. Mech. Eng., Volume 191 (1999), pp. 4241-4258
[3] Energy conserving/decaying implicit time-stepping scheme for nonlinear dynamics of three-dimensional beams undergoing finite rotations, Comput. Struct., Volume 70 (2002), pp. 1-22
[4] The discrete energy-momentum method. Conserving algorithms for nonlinear elastodynamics, Z. Angew. Math. Phys. ZAMP, Volume 43 (1992), pp. 757-792
[5] An energyconserving corotational procedure for the dynamics of shell structures, Eng. Comput. (1998), pp. 552-576
[6] Nonlinear Solid Mechanics: Theoretical Formulations and Finite Element Solution Methods, Springer Science and Business Media, 2009
[7] Solved Problems in Lagrangian and Hamiltonian Mechanics, Springer, Netherlands, 2009
[8] The Finite Element Method: Basic Formulation and Linear Problems, vol. I, McGraw-Hill, Maidenhead, England, 1989
[9] On the choice of finite rotation parameters, Int. J. Numer. Methods Eng., Volume 149 (1997), pp. 49-71
[10] Lectures on Mechanics, Cambridge University Press, 1991
[11] Euler parameters and the use of quaternion algebra in the manipulation of finite rotations, Mech. Mach. Theory, Volume 21 (1986), pp. 365-373
[12] On the role of frame-invariance in structural mechanics models at finite rotations, Comput. Methods Appl. Mech. Eng., Volume 191 (2002), pp. 5159-5176
[13] Numerical integration of non-linear elastic multi-body systems, Int. J. Numer. Methods Eng., Volume 38 (1995), pp. 2727-2751
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