Vibration of a pre-constrained elastic thin shell I: Modeling and regularity of the solutions
[Vibration d'une coque élastique mince pré-contrainte I]
Comptes Rendus. Mathématique, Tome 334 (2002) no. 2, pp. 161-166.

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.

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.

Reçu le :
Révisé le :
Publié le :
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
@article{CRMATH_2002__334_2_161_0,
     author = {Cagnol, John and Zol\'esio, Jean-Paul},
     title = {Vibration of a pre-constrained elastic thin shell {I:} {Modeling} and regularity of the solutions},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {161--166},
     publisher = {Elsevier},
     volume = {334},
     number = {2},
     year = {2002},
     doi = {10.1016/S1631-073X(02)02182-9},
     language = {en},
     url = {http://www.numdam.org/articles/10.1016/S1631-073X(02)02182-9/}
}
TY  - JOUR
AU  - Cagnol, John
AU  - Zolésio, Jean-Paul
TI  - Vibration of a pre-constrained elastic thin shell I: Modeling and regularity of the solutions
JO  - Comptes Rendus. Mathématique
PY  - 2002
SP  - 161
EP  - 166
VL  - 334
IS  - 2
PB  - Elsevier
UR  - http://www.numdam.org/articles/10.1016/S1631-073X(02)02182-9/
DO  - 10.1016/S1631-073X(02)02182-9
LA  - en
ID  - CRMATH_2002__334_2_161_0
ER  - 
%0 Journal Article
%A Cagnol, John
%A Zolésio, Jean-Paul
%T Vibration of a pre-constrained elastic thin shell I: Modeling and regularity of the solutions
%J Comptes Rendus. Mathématique
%D 2002
%P 161-166
%V 334
%N 2
%I Elsevier
%U http://www.numdam.org/articles/10.1016/S1631-073X(02)02182-9/
%R 10.1016/S1631-073X(02)02182-9
%G en
%F CRMATH_2002__334_2_161_0
Cagnol, John; Zolésio, Jean-Paul. Vibration of a pre-constrained elastic thin shell I: Modeling and regularity of the solutions. Comptes Rendus. Mathématique, Tome 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/

[1] Bensoussan, A.; Da Prato, G.; Delfour, M.C.; Mitter, S.K., Representation and Control of Infinite Dimensional Systems, 1, Birkhäuser, 1993

[2] Cagnol, J.; Zolésio, J.-P. Hidden shape derivative in the wave equation (Khan, P.; Lasiecka, I.; Polis, M., eds.), System Modelling and Optimization, Addison-Wesley–Longman, 1998, pp. 42-52

[3] Cagnol, J.; Zolésio, J.-P. Hidden shape derivative in the wave equation with Dirichlet boundary condition, C. R. Acad. Sci. Paris, Série I, Volume 326 (1998) no. 9, pp. 1079-1084

[4] Cagnol, J.; Zolésio, J.-P. Shape derivative in the wave equation with Dirichlet boundary conditions, J. Differential Equations, Volume 158 (1999) no. 2, pp. 175-210

[5] Delfour, M.; Zolésio, J.-P. Hidden boundary smoothness in hyperbolic tangential problems of nonsmooth domains (Khan, P.; Lasiecka, I.; Polis, M., eds.), System Modelling and Optimization, Addison-Wesley–Longman, 1998

[6] Germain, P. Mecanique, Vol. I. Ellipses, École Polytechnique, 1986

[7] Sokolowski, J.; Zolésio, J.-P. Introduction to Shape Optimization, SCM, 16, Springer-Verlag, 1991

Cité par Sources :