On inflating closed mylar shells

Vasyl A. Gorkavyy

doi:10.1016/j.crme.2010.07.019

On inflating closed mylar shells
[Sur le gonflage des ballons de mylar fermés]

Vasyl A. Gorkavyy ¹

¹ Verkin Institute for Low Temperature Physics and Engineering of NAS of Ukraine, 47, Lenin avenue, Kharkiv, Ukraine

Comptes Rendus. Mécanique, Volume 338 (2010) no. 12, pp. 656-662.

Résumé
Abstract

On étudie le gonflage d'un ballon mince fermé produit d'un matériel non-extensible et souple comme mylar. La question est de déterminer la forme extrémal du ballon, quand il est gonflé jusq'au volume maximal possible. On présente un problème variationnel qui décrit le gonflage des ballons de rotation. Le résultat essentiel est un critère pour un ballon de rotation d'admettre déformations qui accroissent le volume sans étendre la surface. En plus, des solutions explicites sont trouvées au cas des ballons cylindrique et biconique.

We discuss the inflating of a closed thin shell made of inextensible flexible material like mylar. The problem is to determine the extremal form of the shell, when it is inflated to the maximal possible volume. We introduce a variational problem which describes the inflating of rotationally symmetric shells. The main result presents a criteria for a rotationally symmetric shell to admit volume increasing deformations without surface stretching. Moreover explicit solutions are found for cylindrical and biconical shells.

Reçu le : 2010-07-06
Accepté le : 2010-07-26
Publié le : 2010-09-15

DOI : 10.1016/j.crme.2010.07.019

Keywords: Dynamics of rigid or flexible systems, Shell, Inflating, Volume, Mylar balloon, Short transformation
Mot clés : Dynamique des systèmes rigides ou flexibles, Ballon, Gonflage, Volume, Ballon de Mylar, Transformation courte

Affiliations des auteurs :

Vasyl A. Gorkavyy ¹

¹ Verkin Institute for Low Temperature Physics and Engineering of NAS of Ukraine, 47, Lenin avenue, Kharkiv, Ukraine

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     title = {On inflating closed mylar shells},
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     pages = {656--662},
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     language = {en},
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Vasyl A. Gorkavyy. On inflating closed mylar shells. Comptes Rendus. Mécanique, Volume 338 (2010) no. 12, pp. 656-662. doi : 10.1016/j.crme.2010.07.019. https://comptes-rendus.academie-sciences.fr/mecanique/articles/10.1016/j.crme.2010.07.019/

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