[Dualité de Legendre–Fenchel en élasticité]
On montre que les formulations en déplacements et en déformations du problème de lʼélasticité linéarisée tri-dimensionnelle avec des conditions aux limites mixtes peuvent être vues comme des problèmes duaux de Legendre–Fenchel de la formulation en contraintes de ce même problème. On montre également que chacun des Lagrangiens correspondants a un point-selle, justifiant ainsi complètement cette nouvelle approche de lʼélasticité au moyen de la dualité de Legendre–Fenchel.
We show that the displacement and strain formulations of the displacement–traction problem of three-dimensional linearized elasticity can be viewed as Legendre–Fenchel dual problems to the stress formulation of the same problem. We also show that each corresponding Lagrangian has a saddle-point, thus fully justifying this new approach to elasticity by means of Legendre–Fenchel duality.
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@article{CRMATH_2011__349_9-10_597_0,
author = {Ciarlet, Philippe G. and Geymonat, Giuseppe and Krasucki, Fran\c{c}oise},
title = {Legendre{\textendash}Fenchel duality in elasticity},
journal = {Comptes Rendus. Math\'ematique},
pages = {597--602},
publisher = {Elsevier},
volume = {349},
number = {9-10},
year = {2011},
doi = {10.1016/j.crma.2011.03.007},
language = {en},
url = {http://www.numdam.org/articles/10.1016/j.crma.2011.03.007/}
}
TY - JOUR AU - Ciarlet, Philippe G. AU - Geymonat, Giuseppe AU - Krasucki, Françoise TI - Legendre–Fenchel duality in elasticity JO - Comptes Rendus. Mathématique PY - 2011 SP - 597 EP - 602 VL - 349 IS - 9-10 PB - Elsevier UR - http://www.numdam.org/articles/10.1016/j.crma.2011.03.007/ DO - 10.1016/j.crma.2011.03.007 LA - en ID - CRMATH_2011__349_9-10_597_0 ER -
%0 Journal Article %A Ciarlet, Philippe G. %A Geymonat, Giuseppe %A Krasucki, Françoise %T Legendre–Fenchel duality in elasticity %J Comptes Rendus. Mathématique %D 2011 %P 597-602 %V 349 %N 9-10 %I Elsevier %U http://www.numdam.org/articles/10.1016/j.crma.2011.03.007/ %R 10.1016/j.crma.2011.03.007 %G en %F CRMATH_2011__349_9-10_597_0
Ciarlet, Philippe G.; Geymonat, Giuseppe; Krasucki, Françoise. Legendre–Fenchel duality in elasticity. Comptes Rendus. Mathématique, Tome 349 (2011) no. 9-10, pp. 597-602. doi : 10.1016/j.crma.2011.03.007. http://www.numdam.org/articles/10.1016/j.crma.2011.03.007/
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