On décrit et analyse une approche du problème de traction pure en élasticité linéarisée tridimensionnelle, dont la nouveauté consiste à considérer le tenseur linéarisé des déformations comme l'inconnue principale, au lieu du déplacement lui-même selon l'habitude. Cette approche conduit à un problème bien posé de minimisation sous contraintes, celles-ci consistant en une forme affaiblie des conditions de compatibilité de St Venant. Cette approche conduit aussi à une nouvelle démonstration de l'inégalité de Korn.
We describe and analyze an approach to the pure traction problem of three-dimensional linearized elasticity, whose novelty consists in considering the linearized strain tensor as the ‘primary’ unknown, instead of the displacement itself as is customary. This approach leads to a well-posed minimization problem, constrained by a weak form of the St Venant compatibility conditions. It also provides a new proof of Korn's inequality.
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@article{CRMATH_2004__339_4_307_0,
author = {Ciarlet, Philippe G. and Ciarlet, Patrick Jr.},
title = {Another approach to linearized elasticity and {Korn's} inequality},
journal = {Comptes Rendus. Math\'ematique},
pages = {307--312},
publisher = {Elsevier},
volume = {339},
number = {4},
year = {2004},
doi = {10.1016/j.crma.2004.06.021},
language = {en},
url = {http://www.numdam.org/articles/10.1016/j.crma.2004.06.021/}
}
TY - JOUR AU - Ciarlet, Philippe G. AU - Ciarlet, Patrick Jr. TI - Another approach to linearized elasticity and Korn's inequality JO - Comptes Rendus. Mathématique PY - 2004 SP - 307 EP - 312 VL - 339 IS - 4 PB - Elsevier UR - http://www.numdam.org/articles/10.1016/j.crma.2004.06.021/ DO - 10.1016/j.crma.2004.06.021 LA - en ID - CRMATH_2004__339_4_307_0 ER -
%0 Journal Article %A Ciarlet, Philippe G. %A Ciarlet, Patrick Jr. %T Another approach to linearized elasticity and Korn's inequality %J Comptes Rendus. Mathématique %D 2004 %P 307-312 %V 339 %N 4 %I Elsevier %U http://www.numdam.org/articles/10.1016/j.crma.2004.06.021/ %R 10.1016/j.crma.2004.06.021 %G en %F CRMATH_2004__339_4_307_0
Ciarlet, Philippe G.; Ciarlet, Patrick Jr. Another approach to linearized elasticity and Korn's inequality. Comptes Rendus. Mathématique, Tome 339 (2004) no. 4, pp. 307-312. doi : 10.1016/j.crma.2004.06.021. http://www.numdam.org/articles/10.1016/j.crma.2004.06.021/
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