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.
Publié le :
@article{CRMATH_2004__339_4_307_0,
author = {Philippe G. Ciarlet and Patrick Ciarlet},
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},
}
Philippe G. Ciarlet; Patrick Ciarlet. Another approach to linearized elasticity and Korn's inequality. Comptes Rendus. Mathématique, Volume 339 (2004) no. 4, pp. 307-312. doi : 10.1016/j.crma.2004.06.021. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2004.06.021/
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