Comptes Rendus
no. 3-4
Mathematical Problems in Mechanics/Calculus of Variations
A nonlinear theory for shells with slowly varying thickness
[Une théorie des coques d'épaisseurs faiblement variables]

Présenté par : Philippe G. Ciarlet

Marta Lewicka1 ; Maria Giovanna Mora2 ; Mohammad Reza Pakzad3
1 University of Minnesota, Department of Mathematics, 206 Church St. S.E., Minneapolis, MN 55455, USA
2 Scuola Internazionale Superiore di Studi Avanzati, via Beirut 2-4, 34014 Trieste, Italy
3 University of Pittsburgh, Department of Mathematics, 139 University Place, Pittsburgh, PA 15260, USA
Comptes Rendus. Mathématique, Volume 347 (2009) no. 3-4, pp. 211-216.

On étudie la Γ-limite de la théorie de l'élasticité non linéaire pour une coque mince à épaisseur variable autour d'une surface arbitraire de dimension 2.

We study the Γ-limit of 3d nonlinear elasticity for shells of small, variable thickness, around an arbitrary smooth 2d surface.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2008.12.017
Marta Lewicka 1 ; Maria Giovanna Mora 2 ; Mohammad Reza Pakzad 3

1 University of Minnesota, Department of Mathematics, 206 Church St. S.E., Minneapolis, MN 55455, USA
2 Scuola Internazionale Superiore di Studi Avanzati, via Beirut 2-4, 34014 Trieste, Italy
3 University of Pittsburgh, Department of Mathematics, 139 University Place, Pittsburgh, PA 15260, USA 
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Marta Lewicka; Maria Giovanna Mora; Mohammad Reza Pakzad. A nonlinear theory for shells with slowly varying thickness. Comptes Rendus. Mathématique, Volume 347 (2009) no. 3-4, pp. 211-216. doi : 10.1016/j.crma.2008.12.017. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2008.12.017/

[1] P.G. Ciarlet Mathematical Elasticity, North-Holland, Amsterdam, 2000

[2] G. Friesecke; R. James; M.G. Mora; S. Müller Derivation of nonlinear bending theory for shells from three-dimensional nonlinear elasticity by Γ-convergence, C. R. Math. Acad. Sci. Paris, Ser. I, Volume 336 (2003) no. 8, pp. 697-702

[3] G. Friesecke; R. James; S. Müller A theorem on geometric rigidity and the derivation of nonlinear plate theory from three dimensional elasticity, Comm. Pure Appl. Math., Volume 55 (2002), pp. 1461-1506

[4] G. Friesecke; R. James; S. Müller A hierarchy of plate models derived from nonlinear elasticity by Γ-convergence, Arch. Ration. Mech. Anal., Volume 180 (2006) no. 2, pp. 183-236

[5] H. Le Dret; A. Raoult The nonlinear membrane model as a variational limit of nonlinear three-dimensional elasticity, J. Math. Pures Appl., Volume 73 (1995), pp. 549-578

[6] H. Le Dret; A. Raoult The membrane shell model in nonlinear elasticity: a variational asymptotic derivation, J. Nonlinear Sci., Volume 6 (1996), pp. 59-84

[7] M. Lewicka, M.G. Mora, M.R. Pakzad, Shell theories arising as low energy Γ-limit of 3d nonlinear elasticity, submitted for publication (2008), available at | arXiv

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