Résumé
L’objet de ce travail est de démontrer, dans le cas du modèle linéaire de W.T. KOITEE, l’ellipticité de l’énergie de déformation d’une coque assujettie à des conditions aux limites convenables. Une étape essentielle consiste à démontrer que si les tenseurs de déformation et de changement de courbure de la surface moyenne de la coque sont nuls au sens des distributions, le champ de déplacement est nécessairement un mouvement rigide.
Abstract
The purpose of this paper is to show, in the case of W.T. KOITER’s linear model, that the strain energy of a shell is elliptic, when it is subjected to appropriate boundary conditions. An essential step consists in showing that if the strain tensor and change of curvature tensor vanish in the sense of distributions along the middle surface of the shell, the displacement field is necessarily that of a rigid body motion.
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Bernadou, M., Ciarlet, P.G. (1976). Sur L’Ellipticite du Modele Lineaire de coques de W.T. Koiter. In: Glowinski, R., Lions, J.L. (eds) Computing Methods in Applied Sciences and Engineering. Lecture Notes in Economics and Mathematical Systems, vol 134. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-85972-4_7
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DOI: https://doi.org/10.1007/978-3-642-85972-4_7
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