Asymptotically exact Kornʼs constant for thin cylindrical domains

Paroni, Roberto; Tomassetti, Giuseppe

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

Paroni, Roberto ¹ ; Tomassetti, Giuseppe 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, Tome 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 :

Paroni, Roberto ¹ ; Tomassetti, Giuseppe ²

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     title = {Asymptotically exact {Korn's} constant for thin cylindrical domains},
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Paroni, Roberto; Tomassetti, Giuseppe. Asymptotically exact Kornʼs constant for thin cylindrical domains. Comptes Rendus. Mathématique, Tome 350 (2012) no. 15-16, pp. 749-752. doi : 10.1016/j.crma.2012.09.013. http://www.numdam.org/articles/10.1016/j.crma.2012.09.013/

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