Vibration of a pre-constrained elastic thin shell I: Modeling and regularity of the solutions
Comptes Rendus. Mathématique, Volume 334 (2002) no. 2, pp. 161-166.

We study the vibration of an elastic thin shell which is pre-constrained by a large displacement with a small deformation. In this first Note we prove the solutions exist and we investigate both the interior regularity and the boundary regularity which is known to be important in the shape differentiation of hyperbolic equations.

On étudie la vibration d'une coque élastique pré-contrainte par grand déplacement en petites déformations. Dans cette première Note on modélise la vibration et on démontre l'existence des solutions et la régularité intérieure. On termine par une étude de la régularité sur le bord, laquelle est connue pour intervenir dans la dérivée par rapport au domaine dans les équations hyperboliques.

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DOI: 10.1016/S1631-073X(02)02182-9
Cagnol, John 1; Zolésio, Jean-Paul 2

1 Pôle Universitaire Léonard de Vinci, ESILV, DER-CS, 92916 Paris La Défense cedex, France
2 CNRS research director at INRIA, OPALE project, 2004 route des Lucioles, BP 93, 06902 Sophia Antipolis cedex, France
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Cagnol, John; Zolésio, Jean-Paul. Vibration of a pre-constrained elastic thin shell I: Modeling and regularity of the solutions. Comptes Rendus. Mathématique, Volume 334 (2002) no. 2, pp. 161-166. doi : 10.1016/S1631-073X(02)02182-9. http://www.numdam.org/articles/10.1016/S1631-073X(02)02182-9/

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