Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

Online ISSN 1552-4485; Print ISSN 0033-569X



On the everted state of spherical and cylindrical shells

Author: Andrew J. Szeri
Journal: Quart. Appl. Math. 48 (1990), 49-58
MSC: Primary 73G05; Secondary 73H05, 73K15
DOI: https://doi.org/10.1090/qam/1040233
MathSciNet review: MR1040233
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: The existence, uniqueness, and qualitative nature of the everted state of spherical and cylindrical shells is examined for elastic materials with stress functions satisfying relatively simple restrictions. Qualitative analysis of the governing nonlinear ordinary differential equation is facilitated by recasting it in stress-stretch coordinates. One finds a continuum of solutions which meet the boundary conditions. Each corresponds uniquely to a shell of a particular thickness. We present numerical solutions which demonstrate the claims of the analysis.

References [Enhancements On Off] (What's this?)

  • [1] S. S. Antman, The eversion of thick spherical shells, Arch. Rational Mech. Anal. 70, 113-123 (1979) MR 546629
  • [2] A. E. Green and J. E. Adkins, Large Elastic Deformations, Clarendon Press, Oxford, 1960 MR 0269158
  • [3] R. Hill, On uniqueness and stability in the theory of finite elastic strain, J. Mech. Phys. Solids 5, 229-241 (1957) MR 0092379
  • [4] J. E. Marsden and T. J. R. Hughes, Mathematical Foundations of Elasticity, Prentice-Hall, Englewood Cliffs, New Jersey, 1983
  • [5] J. Sivaloganathan, Uniqueness of regular and singular equilibria for spherically symmetric problems of nonlinear elasticity, Arch. Rational Mech. Anal. 96 (2), 97-136 (1986) MR 853969
  • [6] C. Truesdell and W. Noll, The nonlinear field theories of mechanics, Handbuch der Physik, vol. III/3, Springer-Verlag, Berlin, 1965 MR 1215940
  • [7] R. von Mises and K. O. Friedrichs, Fluid Dynamics, Springer-Verlag, New York, 1971 MR 0521580

Similar Articles

Retrieve articles in Quarterly of Applied Mathematics with MSC: 73G05, 73H05, 73K15

Retrieve articles in all journals with MSC: 73G05, 73H05, 73K15

Additional Information

DOI: https://doi.org/10.1090/qam/1040233
Article copyright: © Copyright 1990 American Mathematical Society

American Mathematical Society