Energy conservative finite element semi-discretization for vibro-impacts of plates on rigid obstacles
1 Université de Lyon, CNRS, INSA-Lyon, ICJ UMR5208, LaMCoS UMR5259, 69621 Villeurbanne, France.
2 Université de Toulouse, CNRS, ISAE-SUPAERO, Institut Clément Ader (ICA), 31077 Toulouse cedex 4, France.
Received: 9 March 2015
Revised: 18 September 2015
Accepted: 1 December 2015
Our purpose is to describe and compare some families of fully discretized approximations and their properties, in the case of vibro-impact of plates between rigid obstacles with non-penetration Signorini’s conditions. To this aim, the dynamical Kirchhoff–Love plate model is considered and an extension to plates of the singular dynamic method, introduced by Renard and previously adapted to beams by Pozzolini and Salaün, is described. A particular emphasis is given in the use of an adapted Newmark scheme in which intervene a discrete restitution coefficient. Finally, various numerical results are presented and energy conservation capabilities of several numerical schemes are investigated and discussed.
Mathematics Subject Classification: 35L85 / 65M12 / 74H15 / 74H45
Key words: Variational inequalities / finite element method / elastic plates / dynamics / unilateral constraints
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