[Comparaison entre deux approches de la discrétisation du problème de contact en élastodynamique]
Dans cette Note, on compare deux approches de la discrétisation du problème élastodynamique de contact. La première correspond à un schéma qui conserve strictement l'énergie du problème. Ce schéma résulte d'une méthode de point milieu standard avec une loi de contact exprimée en fonction de la vitesse. Dans la deuxième approche, on considère une distribution équivalente de la masse du corps de telle sorte que les points du bord de contact n'aient plus d'inertie. Ceci permet d'aboutir à une conservation de l'énergie pour le problème semi-discrétisé en espace. Enfin, on présente des tests numériques en dimension deux.
The purpose of this Note is to compare two approaches for the discretization of elastodynamic contact problems. First, we introduce an energy conserving method based on a standard midpoint scheme and a contact condition expressed in terms of velocity. The second approach consists in considering an equivalent distribution of the body mass so that the nodes on the contact boundary have no inertia. We prove that this method leads to an energy conservation for the space semi-discretized elastodynamic contact problem. Finally, some numerical results are presented in the two dimensional case.
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@article{CRMATH_2006__342_10_791_0,
author = {Khenous, Houari Boumedi\`ene and Laborde, Patrick and Renard, Yves},
title = {Comparison of two approaches for the discretization of elastodynamic contact problems},
journal = {Comptes Rendus. Math\'ematique},
pages = {791--796},
publisher = {Elsevier},
volume = {342},
number = {10},
year = {2006},
doi = {10.1016/j.crma.2006.03.011},
language = {en},
url = {http://www.numdam.org/articles/10.1016/j.crma.2006.03.011/}
}
TY - JOUR AU - Khenous, Houari Boumediène AU - Laborde, Patrick AU - Renard, Yves TI - Comparison of two approaches for the discretization of elastodynamic contact problems JO - Comptes Rendus. Mathématique PY - 2006 SP - 791 EP - 796 VL - 342 IS - 10 PB - Elsevier UR - http://www.numdam.org/articles/10.1016/j.crma.2006.03.011/ DO - 10.1016/j.crma.2006.03.011 LA - en ID - CRMATH_2006__342_10_791_0 ER -
%0 Journal Article %A Khenous, Houari Boumediène %A Laborde, Patrick %A Renard, Yves %T Comparison of two approaches for the discretization of elastodynamic contact problems %J Comptes Rendus. Mathématique %D 2006 %P 791-796 %V 342 %N 10 %I Elsevier %U http://www.numdam.org/articles/10.1016/j.crma.2006.03.011/ %R 10.1016/j.crma.2006.03.011 %G en %F CRMATH_2006__342_10_791_0
Khenous, Houari Boumediène; Laborde, Patrick; Renard, Yves. Comparison of two approaches for the discretization of elastodynamic contact problems. Comptes Rendus. Mathématique, Tome 342 (2006) no. 10, pp. 791-796. doi : 10.1016/j.crma.2006.03.011. http://www.numdam.org/articles/10.1016/j.crma.2006.03.011/
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