Decomposition of shell deformations – Asymptotic behavior of the Green–St Venant strain tensor

Dominique Blanchard; Georges Griso

doi:10.1016/j.crma.2009.06.018

Mathematical Problems in Mechanics/Calculus of Variations

Decomposition of shell deformations – Asymptotic behavior of the Green–St Venant strain tensor

Presented by: Philippe G. Ciarlet

Dominique Blanchard ¹; Georges Griso ²

¹ Université de Rouen, UMR 6085, laboratoire Raphaël-Salem, 76801 St Etienne 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 347 (2009) no. 17-18, pp. 1099-1103.

Abstract
Résumé

This Note deals with a new method, based on a decomposition of the deformations, to study thin shells. In particular, we give the asymptotic behavior of the Green–St Venant's strain tensor.

Dans cette Note nous présentons une nouvelle méthode, basée sur une décomposition des déformations, pour l'étude des coques minces. En particulier, nous donnons le comportement asymptotique du tenseur de Green–St Venant.

Received: 2009-06-03
Accepted: 2009-06-30
Published online: 2009-07-25

DOI: 10.1016/j.crma.2009.06.018

Author's affiliations:

Dominique Blanchard ¹; Georges Griso ²

¹ Université de Rouen, UMR 6085, laboratoire Raphaël-Salem, 76801 St Etienne 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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     author = {Dominique Blanchard and Georges Griso},
     title = {Decomposition of shell deformations {\textendash} {Asymptotic} behavior of the {Green{\textendash}St} {Venant} strain tensor},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {1099--1103},
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     volume = {347},
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     year = {2009},
     doi = {10.1016/j.crma.2009.06.018},
     language = {en},
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Dominique Blanchard; Georges Griso. Decomposition of shell deformations – Asymptotic behavior of the Green–St Venant strain tensor. Comptes Rendus. Mathématique, Volume 347 (2009) no. 17-18, pp. 1099-1103. doi : 10.1016/j.crma.2009.06.018. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2009.06.018/

References
Cited by

[1] D. Blanchard; G. Griso Decomposition of deformations of thin rods. Application to nonlinear elasticity, Anal. Appl., Volume 7 (2009) no. 1, pp. 21-71

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

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[4] 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

[5] G. Friesecke; R.D. James; S. Müller A theorem on geometric rigidity and the derivation of nonlinear plate theory from the three-dimensional elasticity, Comm. Pure Appl. Math., Volume LV (2002), pp. 1461-1506

[6] G. Friesecke; R.D. James; S. Müller A hierarchy of plate models derived from nonlinear elasticity by Γ-convergence, Arch. Rational Mech. Anal., Volume 130 (2006), pp. 183-236

[7] 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

[8] G. Griso Decomposition of displacements of thin structures, J. Math. Pures Appl., Volume 89 (2008), pp. 199-233

[9] G. Griso Asymptotic behavior of structures made of plates, Anal. Appl., Volume 3 (2005) no. 4, pp. 325-356

[10] O. Pantz On the justification of the nonlinear inextensional plate model, Arch. Rational Mech. Anal., Volume 167 (2003) no. 3, pp. 179-209

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