Geodesic
Energy conservative finite element semi-discretization for vibro-impacts of plates on rigid obstacles
Pozzolini, Cédric1  ; Renard, Yves1  ; Salaün, Michel2 
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.
ESAIM: Mathematical Modelling and Numerical Analysis , Tome 50 (2016) no. 6, pp. 1585-1613

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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.

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DOI : 10.1051/m2an/2015094
Classification : 35L85, 65M12, 74H15, 74H45
Keywords: Variational inequalities, finite element method, elastic plates, dynamics, unilateral constraints

Pozzolini, Cédric 1 ; Renard, Yves 1 ; Salaün, Michel 2

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. 
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     title = {Energy conservative finite element semi-discretization for vibro-impacts of plates on rigid obstacles},
     journal = {ESAIM: Mathematical Modelling and Numerical Analysis },
     pages = {1585--1613},
     publisher = {EDP-Sciences},
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Pozzolini, Cédric; Renard, Yves; Salaün, Michel. Energy conservative finite element semi-discretization for vibro-impacts of plates on rigid obstacles. ESAIM: Mathematical Modelling and Numerical Analysis , Tome 50 (2016) no. 6, pp. 1585-1613. doi: 10.1051/m2an/2015094

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