Comptes Rendus
no. 12
On inflating closed mylar shells
[Sur le gonflage des ballons de mylar fermés]
Vasyl A. Gorkavyy1
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.

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 :
Accepté le :
Publié le :
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
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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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/

[1] A.V. Pogorelov Bendings of Surfaces and Stability of Shells, Translations of Mathematical Monographs, vol. 72, American Mathematical Society (AMS), Providence, RI, 1988

[2] K. Brakke Surface evolver http://www.susqu.edu/brakke/evolver/evolver.html

[3] D.D. Bleecker Volume increasing isometric deformations of convex polyhedra, J. Differential Geom., Volume 43 (1996), pp. 505-526

[4] D.D. Bleecker Isometric deformations of compact hypersurfaces, Geom. Dedicata, Volume 64 (1997), pp. 193-227

[5] W. Paulsen What is the shape of a mylar balloon?, Amer. Math. Monthly, Volume 101 (1994), pp. 953-958

[6] I. Mladenov; J. Oprea The mylar balloon revisited, Amer. Math. Monthly, Volume 110 (2003), pp. 761-784

[7] I. Pak Inflating polyhedral surfaces http://www.math.ucla.edu/~/papers/pillow4.pdf

[8] G.A. Samarin Volume increasing isometric deformations of polyhedra, Comput. Math. Math. Phys., Volume 50 (2010) no. 1, pp. 54-64

[9] N.H. Kuiper Isometric and short imbeddings, Indag. Math., Volume 21 (1959), pp. 11-25

[10] W.P. Reinhardt; P.L. Walker Jacobian elliptic functions (F.W.J. Olver; D.M. Lozier; R.F. Boisvert et al., eds.), NIST Handbook of Mathematical Functions, Cambridge University Press, 2010

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