Asymptotically exact Kornʼs constant for thin cylindrical domains

Roberto Paroni; Giuseppe Tomassetti

doi:10.1016/j.crma.2012.09.013

Mathematical Analysis/Mathematical Problems in Mechanics

Asymptotically exact Kornʼs constant for thin cylindrical domains
[Développement asymptotique précis de la constante de Korn dans une poutre mince]

Présenté par : Philippe G. Ciarlet

Roberto Paroni ¹ ; Giuseppe Tomassetti ²

¹ Dipartimento di Architettura e Pianificazione, Università degli Studi di Sassari, 07041 Alghero, Italy
² Dipartimento di Ingegneria Civile, Università degli Studi di Roma “Tor Vergata”, 00133 Roma, Italy

Comptes Rendus. Mathématique, Volume 350 (2012) no. 15-16, pp. 749-752.

Résumé
Abstract

On considère une poutre verticale $Ω^{ε}$ de hauteur fixée et de petite section εω avec $ω \subset R^{2}$ . Soit $1 / K^{ε}$ la constante de Korn dans $Ω^{ε}$ . On démontre que, lorsque ε tend vers zéro, $K^{ε} / ε^{2}$ converge vers une constante positive. On caractérise la limite en fonction de paramètres qui dépendent de ω.

We consider a cylinder $Ω^{ε}$ having fixed length and small cross-section εω with $ω \subset R^{2}$ . Let $1 / K^{ε}$ be the Korn constant of $Ω^{ε}$ . We show that, as ε tends to zero, $K^{ε} / ε^{2}$ converges to a positive constant. We provide a characterization of this constant in terms of certain parameters that depend on ω.

Reçu le : 2012-09-17
Accepté le : 2012-09-19
Publié le : 2012-08-01

DOI : 10.1016/j.crma.2012.09.013

Affiliations des auteurs :

Roberto Paroni ¹ ; Giuseppe Tomassetti ²

¹ Dipartimento di Architettura e Pianificazione, Università degli Studi di Sassari, 07041 Alghero, Italy
² Dipartimento di Ingegneria Civile, Università degli Studi di Roma “Tor Vergata”, 00133 Roma, Italy

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     author = {Roberto Paroni and Giuseppe Tomassetti},
     title = {Asymptotically exact {Korn's} constant for thin cylindrical domains},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {749--752},
     publisher = {Elsevier},
     volume = {350},
     number = {15-16},
     year = {2012},
     doi = {10.1016/j.crma.2012.09.013},
     language = {en},
}

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Roberto Paroni; Giuseppe Tomassetti. Asymptotically exact Kornʼs constant for thin cylindrical domains. Comptes Rendus. Mathématique, Volume 350 (2012) no. 15-16, pp. 749-752. doi : 10.1016/j.crma.2012.09.013. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2012.09.013/

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