Mathematical Problems in Mechanics
Another approach to linearized elasticity and Korn's inequality
Comptes Rendus. Mathématique, Volume 339 (2004) no. 4, pp. 307-312.

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.

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.

Published online:
DOI: 10.1016/j.crma.2004.06.021
Ciarlet, Philippe G. 1; Ciarlet, Patrick Jr. 2

1 Department of Mathematics, City University of Hong Kong, 83 Tat Chee Avenue, Kowloon, Hong Kong
2 École Nationale Supérieure de Techniques Avancées, 32, boulevard Victor, 75015 Paris, France
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     title = {Another approach to linearized elasticity and {Korn's} inequality},
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     publisher = {Elsevier},
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     language = {en},
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Ciarlet, Philippe G.; Ciarlet, Patrick Jr. 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.

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