[Dualité de Legendre–Fenchel en élasticité]
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.
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.
Accepté le :
Publié le :
Philippe G. Ciarlet 1 ; Giuseppe Geymonat 2 ; Françoise Krasucki 3
@article{CRMATH_2011__349_9-10_597_0,
author = {Philippe G. Ciarlet and Giuseppe Geymonat and Fran\c{c}oise Krasucki},
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},
}
Philippe G. Ciarlet; Giuseppe Geymonat; Françoise Krasucki. Legendre–Fenchel duality in elasticity. Comptes Rendus. Mathématique, Volume 349 (2011) no. 9-10, pp. 597-602. doi : 10.1016/j.crma.2011.03.007. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2011.03.007/
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