Geng, YN, Huang, JX and Fu, YB (2016) Shape bifurcation of a pressurized ellipsoidal balloon. International Journal of Engineering Science, 101. pp. 115-125. ISSN 0090-6913

[thumbnail of geng-huang-fu-ijes-2016.pdf]
geng-huang-fu-ijes-2016.pdf - Accepted Version
Available under License Creative Commons Attribution Non-commercial No Derivatives.

Download (939kB) | Preview


It is well-known that for most spherical and cylindrical rubber balloons the pressure versus volume curve associated with uniform inflation both has an N-shape, but their shape bifurcation has different characters: whereas a spherical balloon tends to bifurcate into a pear shape through localized thinning near one of the poles, a cylindrical balloon would always bulge out locally in a symmetric manner. To understand the connection between these two different bifurcation behaviors, we study in this paper the shape bifurcation of an ellipsoidal balloon which becomes a spherical balloon when the three axes are identical, and approximates a cylindrical balloon when one axis is much larger than the other two axes. The ellipsoidal shape is obtained by rotating an ellipse about one of its axes, that gives rise to two possibilities: a rugby shape or a pumpkin shape. It is shown that for a rugby-shaped balloon, there exists a threshold axes ratio below which the slender ellipsoidal balloon behaves more like a tube and bifurcation into a pear shape becomes impossible, whereas for a pumpkin-shaped balloon bifurcation into a pear shape is always possible.

Item Type: Article
Uncontrolled Keywords: nonlinear elasticity; balloons; bifurcation; localization
Subjects: Q Science > QA Mathematics
Divisions: Faculty of Natural Sciences > School of Computing and Mathematics
Depositing User: Symplectic
Date Deposited: 11 Feb 2016 11:58
Last Modified: 15 Apr 2019 11:28

Actions (login required)

View Item
View Item