Membrane caps under hydrostatic pressure

Dickey, R. W.

doi:10.1090/qam/934684

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.

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