Comparison of two approaches for the discretization of elastodynamic contact problems

Houari Boumediène Khenous (1) , Patrick Laborde (1) , Yves Renard (2)

1 IMT - Institut de Mathématiques de Toulouse UMR5219
2 ICJ - Institut Camille Jordan

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.

Domaines: Analyse numérique [math.NA]

Houari Boumediène Khenous, Patrick Laborde, Yves Renard. Comparison of two approaches for the discretization of elastodynamic contact problems. Comptes Rendus. Mathématique, 2006, 342 (10), pp.791-796,. ⟨10.1016/j.crma.2006.03.011⟩. ⟨hal-00690583⟩