[Non existence de minimiseurs pour une plaque membranaire non linéaire comprimée]
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.
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.
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@article{CRMATH_2003__337_8_553_0,
author = {Trabelsi, Karim},
title = {Non-existence of minimizers for a nonlinear membrane plate under compression},
journal = {Comptes Rendus. Math\'ematique},
pages = {553--558},
publisher = {Elsevier},
volume = {337},
number = {8},
year = {2003},
doi = {10.1016/j.crma.2003.09.008},
language = {en},
url = {http://archive.numdam.org/articles/10.1016/j.crma.2003.09.008/}
}
TY - JOUR AU - Trabelsi, Karim TI - Non-existence of minimizers for a nonlinear membrane plate under compression JO - Comptes Rendus. Mathématique PY - 2003 SP - 553 EP - 558 VL - 337 IS - 8 PB - Elsevier UR - http://archive.numdam.org/articles/10.1016/j.crma.2003.09.008/ DO - 10.1016/j.crma.2003.09.008 LA - en ID - CRMATH_2003__337_8_553_0 ER -
%0 Journal Article %A Trabelsi, Karim %T Non-existence of minimizers for a nonlinear membrane plate under compression %J Comptes Rendus. Mathématique %D 2003 %P 553-558 %V 337 %N 8 %I Elsevier %U http://archive.numdam.org/articles/10.1016/j.crma.2003.09.008/ %R 10.1016/j.crma.2003.09.008 %G en %F CRMATH_2003__337_8_553_0
Trabelsi, Karim. Non-existence of minimizers for a nonlinear membrane plate under compression. Comptes Rendus. Mathématique, Tome 337 (2003) no. 8, pp. 553-558. doi : 10.1016/j.crma.2003.09.008. http://archive.numdam.org/articles/10.1016/j.crma.2003.09.008/
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