The nonlinear circular membrane under a vertical force-Reference-Cited by-同舟云学术

The nonlinear circular membrane under a vertical force

Published:1983 Issue:3 Volume:41 Page:331-338
ISSN:0033-569X
Container-title:Quarterly of Applied Mathematics
language:en
Short-container-title:Quart. Appl. Math.

Author:

Dickey R. W.

Abstract

The exact theory for the deformation of a plane circular membrane under a vertical force is derived. It is shown that the system of equations can be reduced to a single, nonlinear, ordinary differential equation. In addition it is shown that the Foppl approximation is the first term in an asymptotic expansion of the exact theory.

Publisher

American Mathematical Society (AMS)

Subject

Applied Mathematics

Link

http://www.ams.org/qam/1983-41-03/S0033-569X-1983-0721423-8/S0033-569X-1983-0721423-8.pdf

Reference5 articles.

1. A. Foppl, Vorlesungen über technische Mechanik, Bd. 5, P. Teubner, Leipzig, 1907

2. H. Hencky, Über der Spannungszustand in kreisrunden Platten, Z. Math. Phys. 63, 311–317 (1915)

3. The plane circular elastic surface under normal pressure;Dickey, R. W.;Arch. Rational Mech. Anal.,1967

4. Non-linear boundary value problems for the circular membrane;Callegari, Andrew J.;Arch. Rational Mech. Anal.,1968

5. Membrane buckling: A study of solution multiplicity;Callegari, Andrew J.;Comm. Pure Appl. Math.,1971

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