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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Additional Information

DOI:
https://doi.org/10.1090/qam/917020

Article copyright:
© Copyright 1987
American Mathematical Society