Comptes Rendus
no. 2
Vibration of a pre-constrained elastic thin shell I: Modeling and regularity of the solutions
[Vibration d'une coque élastique mince pré-contrainte I]
John Cagnol1 ; Jean-Paul Zolésio2
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
Comptes Rendus. Mathématique, Volume 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
John Cagnol 1 ; Jean-Paul Zolésio 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 = {John Cagnol and Jean-Paul Zol\'esio},
     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},
}
TY  - JOUR
AU  - John Cagnol
AU  - Jean-Paul Zolésio
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
DO  - 10.1016/S1631-073X(02)02182-9
LA  - en
ID  - CRMATH_2002__334_2_161_0
ER  - 
%0 Journal Article
%A John Cagnol
%A Jean-Paul Zolésio
%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
%R 10.1016/S1631-073X(02)02182-9
%G en
%F CRMATH_2002__334_2_161_0
John Cagnol; Jean-Paul Zolésio. 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. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/S1631-073X(02)02182-9/

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

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

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

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

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

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

Cité par Sources :

Commentaires - Politique

Ces articles pourraient vous intéresser

Vibration of a pre-constrained elastic thin shell II: Intrinsic exact model

John Cagnol; Jean-Paul Zolésio

C. R. Math (2002)

Uniqueness and continuous dependence on the initial data for a class of non-linear shallow shell problems

John Cagnol; Irena Lasiecka; Catherine Lebiedzik; ...

C. R. Math (2006)

Shape optimization for the Maxwell equations under weaker regularity of the data

John Cagnol; Matthias Eller

C. R. Math (2010)