Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

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

   
 
 

 

Membrane caps under hydrostatic pressure


Author: R. W. Dickey
Journal: Quart. Appl. Math. 46 (1988), 95-104
MSC: Primary 73K15
DOI: https://doi.org/10.1090/qam/934684
MathSciNet review: 934684
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Abstract: It is shown that the exact nonlinear theory for a rotationally symmetric membrane cap deformed by hydrostatic pressure is statically determinant. A small strain theory is obtained without any assumptions on the relative magnitudes of the displacements. This small strain theory can be reduced to a single second-order ordinary differential equation for the determination of the radial stress. A linear shallow cap theory is obtained and solved explicitly for the case of the shallow spherical cap.


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

  • [1] E. Bromberg and J. J. Stoker, Non-linear theory of curved elastic sheets, Quart. Appl. Math. 3, 246-265 (1945/46) MR 0013355
  • [2] E. Reissner, Rotationally symmetric problems in the theory of thin elastic shells, 3rd U.S. Natl. Congress of Applied Mechanics, 59-69, 1958 MR 0101672
  • [3] M. A. Goldberg, An iterative solution for rotationally symmetric non-linear membrane problems, Internat. J. of Non-linear Mechs. 1, 169-178 (1966)
  • [4] R. W. Dickey, Membrane caps, Quart. Appl. Math. 45, 697-712 (1987); erratum: this issue, p. 192. MR 917020

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DOI: https://doi.org/10.1090/qam/934684
Article copyright: © Copyright 1988 American Mathematical Society

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