Membrane caps

Dickey, R. W.

doi:10.1090/qam/917020

Membrane caps

Author: R. W. Dickey
Journal: Quart. Appl. Math. 45 (1987), 697-712
MSC: Primary 73K15
DOI: https://doi.org/10.1090/qam/917020
MathSciNet review: 917020
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Abstract: The exact theory for the rotationally symmetric deformation of a membrane cap under either a gravitational force or a normal force is derived. It is shown that in either case the exact theory can be reduced to a single, second-order, ordinary differential equation for the determination of a quantity related to the radial stress. This equation is specialized to the small strain case. Approximate theories are obtained from the exact equations. In particular, the correct approximate equations are obtained when the applied pressure is small and when the membrane cap is shallow. The shallow spherical cap is treated as a special example.

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