Time-integration schemes for the finite element dynamic Signorini problem

David Doyen (1) , Alexandre Ern (2) , Serge Piperno (3)

1 EDF - EDF
2 CERMICS - Centre d'Enseignement et de Recherche en Mathématiques, Informatique et Calcul Scientifique
3 CERMICS - Centre d'Enseignement et de Recherche en Mathématiques et Calcul Scientifique

The discretization of the dynamic Signorini problem with finite elements in space and a time-stepping scheme is not straightforward. Consequently a large variety of methods for this problem have been designed over the last two decades. Up to date, no systematic comparison of such methods has been performed. The aim of the present work is to classify and compare them. For each method, we discuss the presence of spurious oscillations and the energy conservation. For explicit approaches, the stability condition on the time step is also discussed. Numerical simulations on two 1D benchmark problems with analytical solutions illustrate the properties of the different methods. Most of the discretizations considered herein can be found in the literature, but the semi-explicit modified mass method is new and features, in our opinion, several attractive properties.

Mots clés: elastodynamics; frictionless unilateral contact; time-integration schemes; finite elements; modified mass method

Domaines: Analyse numérique [math.NA]

David Doyen, Alexandre Ern, Serge Piperno. Time-integration schemes for the finite element dynamic Signorini problem. SIAM Journal on Scientific Computing, 2011, 33 (1), pp.223-249. ⟨10.1137/100791440⟩. ⟨hal-00440128⟩