Justification of a simplified model for shells in nonlinear elasticity

Dominique Blanchard; Georges Griso

doi:10.1016/j.crma.2010.02.015

Mathematical Problems in Mechanics/Calculus of Variations

Justification of a simplified model for shells in nonlinear elasticity

Presented by: Philippe G. Ciarlet

Dominique Blanchard ¹; Georges Griso ²

¹ Université de Rouen, UMR 6085, Laboratoire Raphaël-Salem, 76801 St Étienne-du-Rouvray cedex, France
² Laboratoire d'analyse numérique, université P. et M. Curie, case courrier 187, 75252 Paris cedex 05, France

Comptes Rendus. Mathématique, Volume 348 (2010) no. 7-8, pp. 461-465.

Abstract
Résumé

We introduce a simplified model for the minimization of the elastic energy in thin shells. The thickness of the shell remains a parameter in this new model.

Nous développons un modèle simplifié pour le problème de minimisation de l'énergie élastique d'une coque mince. L'épaisseur de la coque reste un paramètre du modèle.

Received: 2009-11-14
Accepted: 2010-02-15
Published online: 2010-03-09

DOI: 10.1016/j.crma.2010.02.015

Author's affiliations:

Dominique Blanchard ¹; Georges Griso ²

¹ Université de Rouen, UMR 6085, Laboratoire Raphaël-Salem, 76801 St Étienne-du-Rouvray cedex, France
² Laboratoire d'analyse numérique, université P. et M. Curie, case courrier 187, 75252 Paris cedex 05, France

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     title = {Justification of a simplified model for shells in nonlinear elasticity},
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     year = {2010},
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     language = {en},
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Dominique Blanchard; Georges Griso. Justification of a simplified model for shells in nonlinear elasticity. Comptes Rendus. Mathématique, Volume 348 (2010) no. 7-8, pp. 461-465. doi : 10.1016/j.crma.2010.02.015. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2010.02.015/

References
Cited by

[1] D. Blanchard; G. Griso Decomposition of shell deformations – Asymptotic behavior of the Green–St Venant strain tensor, C. R. Acad. Sci. Paris, Ser. I, Volume 347 (2009), pp. 1099-1103

[2] P.G. Ciarlet Mathematical Elasticity, vol. III, Theory of Shells, North-Holland, Amsterdam, 2000

[3] P.G. Ciarlet; C. Mardare An introduction to shell theory (P.G. Ciarlet; T.T. Li, eds.), Differential Geometry: Theory and Applications, World Scientific, Singapore, 2008, pp. 94-184

[4] P.G. Ciarlet; L. Gratie; C. Mardare A nonlinear Korn inequality on a surface, J. Math. Pures Appl., Volume 85 (2006), pp. 2-16

[5] G. Friesecke; R.D. James; M.G. Mora; S. Müller Derivation of nonlinear bending theory for shells from three-dimensional nonlinear elasticity by Gamma convergence, C. R. Acad. Sci. Paris, Ser. I, Volume 336 (2003), pp. 697-702

[6] G. Griso Décomposition des déplacements d'une poutre : simplification d'un problème d'élasticité, C. R. Mecanique, Volume 333 (2005), pp. 475-480

[7] G. Griso Obtention d'équations de plaques par la méthode d'éclatement appliquée aux équations tridimensionnelles, C. R. Acad. Sci. Paris, Ser. I, Volume 343 (2006), pp. 361-366

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