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
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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.
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J. E. Marsden and T. J. R. Hughes, Mathematical Foundations of Elasticity, Prentice-Hall, Englewood Cliffs, New Jersey, 1983
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- R. von Mises and K. O. Friedrichs, Fluid dynamics, Springer-Verlag, New York-Heidelberg, 1971. Applied Mathematical Sciences, Vol. 5. MR 0521580
S. S. Antman, The eversion of thick spherical shells, Arch. Rational Mech. Anal. 70, 113–123 (1979)
A. E. Green and J. E. Adkins, Large Elastic Deformations, Clarendon Press, Oxford, 1960
R. Hill, On uniqueness and stability in the theory of finite elastic strain, J. Mech. Phys. Solids 5, 229–241 (1957)
J. E. Marsden and T. J. R. Hughes, Mathematical Foundations of Elasticity, Prentice-Hall, Englewood Cliffs, New Jersey, 1983
J. Sivaloganathan, Uniqueness of regular and singular equilibria for spherically symmetric problems of nonlinear elasticity, Arch. Rational Mech. Anal. 96 (2), 97–136 (1986)
C. Truesdell and W. Noll, The nonlinear field theories of mechanics, Handbuch der Physik, vol. III/3, Springer-Verlag, Berlin, 1965
R. von Mises and K. O. Friedrichs, Fluid Dynamics, Springer-Verlag, New York, 1971
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Article copyright:
© Copyright 1990
American Mathematical Society
