Hostname: page-component-78c5997874-dh8gc Total loading time: 0 Render date: 2024-11-15T01:31:27.638Z Has data issue: false hasContentIssue false
  • English
  • Français

Asymptotic shapes of inflated spheroidal nonlinearly elastic shells

Published online by Cambridge University Press:  24 October 2008

Stuart S. Antman  and
M. Carme Calderer
Stuart S. Antman
Affiliation:
Department of Mathematics, University of Maryland, College Park, MD 20742, U.S.A.
M. Carme Calderer
Affiliation:
Department of Mathematics, Oregon State University, Corvallis, OR 97331, U.S.A.
Get access Rights & Permissions [Opens in a new window]

Extract

In this paper we study the asymptotic behaviour of large axisymmetric deformations of closed axisymmetric nonlinearly elastic shells under internal hydrostatic pressure. These shells can suffer flexure, extension, and shear. Since there are spherical shells that can enclose an arbitrarily large volume at a finite pressure (cf. [1]), we take the volume rather than the pressure as the large parameter.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 97 , Issue 3 , May 1985 , pp. 541 - 549
Copyright
Copyright © Cambridge Philosophical Society 1985

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

[1]Antman, S. S.. Existence and nonuniqueness of axisymmetric equilibrium states of non-linearly elastic shells. Arch. Rational Mech. Anal. 40 (1971), 329–371.Google Scholar
[2]Antman, S. S.. Buckled states of nonlinearly elastic plates. Arch. Rational Mech. Anal. 67 (1978), 111–149.CrossRefGoogle Scholar
[3]Antman, S. S. and Calderer, M. C.. Asymptotic shapes of inflated noncircular elastic rings. Math. Proc. Cambridge Philos. Soc. 97 (1985), 357–379.CrossRefGoogle Scholar
[4]Destuynder, P.. A classification of thin shell theories. Acta Appl. Math., to appear.Google Scholar
[5]Isaacson, E.. The shape of a balloon. Comm. Pure Appl. Math. 18 (1965), 163–166.CrossRefGoogle Scholar
[6]Needleman, A.. Inflation of spherical rubber balloons. Internat. J. Solids and Structures 13 (1977), 409–421.CrossRefGoogle Scholar
[7]Wu, C-H.. Large finite strain membrane problems. Quart. Appl. Math. 36 (1979), 347–360.CrossRefGoogle Scholar