Non-existence of minimizers for a nonlinear membrane plate under compression

Karim Trabelsi

doi:10.1016/j.crma.2003.09.008

Mathematical Problems in Mechanics

Non-existence of minimizers for a nonlinear membrane plate under compression

Presented by: Philippe G. Ciarlet

Karim Trabelsi ¹

¹ Laboratoire Jacques-Louis Lions, Université Pierre et Marie Curie, BP 187, 75252 Paris cedex 05, France

Comptes Rendus. Mathématique, Volume 337 (2003) no. 8, pp. 553-558.

Abstract
Résumé

The classical equations of a nonlinearly elastic membrane plate, made of Saint Venant–Kirchhoff material, have been justified by Fox et al. (Arch. Rational Mech. Anal. 124 (2) (1993) 157–199). We show that, under compression, the associated minimization problem admits no solution. The proof is based on a result of non-existence of minimizers of non-convex functionals due to Dacorogna and Marcellini (Arch. Rational Mech. Anal. 131 (4) (1995) 359–399). We generalize the application of their result from plane elasticity to membrane plates.

Les équations classiques de plaques membranaires non linéairement élastique, constituées d'un matériau de Saint Venant–Kirchhoff ont été justifiées par Fox et al. (Arch. Rational Mech. Anal. 124 (2) (1993) 157–199). On montre que le problème de minimisation associé à une telle plaque comprimée n'admet pas de solution. La preuve fait appel à un résultat de non existence de minimiseurs de fonctionnelles non convexes dû à Dacorogna et Marcellini (Arch. Rational Mech. Anal. 131 (4) (1995) 359–399). On généralise l'application de leur résultat de l'élasticité plane aux plaques membranaires.

Received: 2003-05-28
Accepted: 2003-09-03
Published online: 2003-10-15

DOI: 10.1016/j.crma.2003.09.008

Author's affiliations:

Karim Trabelsi ¹

¹ Laboratoire Jacques-Louis Lions, Université Pierre et Marie Curie, BP 187, 75252 Paris cedex 05, France

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Karim Trabelsi. Non-existence of minimizers for a nonlinear membrane plate under compression. Comptes Rendus. Mathématique, Volume 337 (2003) no. 8, pp. 553-558. doi : 10.1016/j.crma.2003.09.008. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2003.09.008/

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Cited by

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[11] K. Trabelsi, Non-existence of minimizers for the nonlinear plate membrane under compression, Preprint

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