A nonlinear theory for shells with slowly varying thickness

Marta Lewicka; Maria Giovanna Mora; Mohammad Reza Pakzad

doi:10.1016/j.crma.2008.12.017

Mathematical Problems in Mechanics/Calculus of Variations

A nonlinear theory for shells with slowly varying thickness

Presented by: Philippe G. Ciarlet

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

Comptes Rendus. Mathématique, Volume 347 (2009) no. 3-4, pp. 211-216.

Abstract
Résumé

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

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.

Received: 2008-04-16
Accepted: 2008-12-16
Published online: 2009-02-01

DOI: 10.1016/j.crma.2008.12.017

Author's affiliations:

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/

References
Cited by

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[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

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[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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