Mathematical Problems in Mechanics
Comparison of two approaches for the discretization of elastodynamic contact problems
Comptes Rendus. Mathématique, Volume 342 (2006) no. 10, pp. 791-796.

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.

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.

Received:
Accepted:
Published online:
DOI: 10.1016/j.crma.2006.03.011
Khenous, Houari Boumediène 1; Laborde, Patrick 2; Renard, Yves 1

1 INSA Toulouse, département GMM, 135, avenue Rangueil, 31077 Toulouse cedex 4, France
2 Université Paul-Sabatier, Laboratoire MIP, 118, route de Narbonne, 31062 Toulouse cedex 4, France
@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, Volume 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/

[1] H.B. Khenous, PhD thesis, INSA de Toulouse, November 2005

[2] Khenous, H.B.; Pommier, J.; Renard, Y. Hybrid discretization of the Signorini problem with Coulomb friction. Theoretical aspects and comparison of some numerical solvers, Appl. Numer. Math., Volume 56 (2006) no. 2, pp. 163-192

[3] Kim, J.U. A boundary thin obstacle problem for a wave equation, Comm. Partial Differential Equations, Volume 14 (1989) no. 8–9, pp. 1011-1026

[4] Lebeau, G.; Schatzman, M. A wave problem in a half-space with a unilateral constraint at the boundary, J. Differential Equations, Volume 55 (1984), pp. 309-361

[5] Laursen, T.A.; Chawla, V. Design of energy conserving algorithms for frictionless dynamic contact problems, Int. J. Numer. Methods Engrg., Volume 40 (1997), pp. 863-886

[6] Moreau, J.J. Numerical aspects of the sweeping process, Comput. Methods Appl. Mech. Engrg., Volume 177 (1999), pp. 329-349

[7] Paoli, L. Time discretization of vibro-impact, Philos. Trans. Roy. Soc. London Ser. A, Volume 359 (2001), pp. 2405-2428

[8] Paumier, J.-C.; Renard, Y. Surface perturbation of an elastodynamic contact problem with friction, Eur. J. Appl. Math., Volume 14 (2003), pp. 465-483

Cited by Sources: