Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

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



The nonlinear circular membrane under a vertical force

Author: R. W. Dickey
Journal: Quart. Appl. Math. 41 (1983), 331-338
MSC: Primary 73K15
DOI: https://doi.org/10.1090/qam/721423
MathSciNet review: 721423
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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.

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

  • [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] R. W. Dickey, The plane circular elastic surface under normal pressure, Arch. Rational Mech. Anal. 26, 219-236 (1967) MR 1553496
  • [4] A. J. Callegari and E. L. Reiss, Nonlinear boundary value problems for the circular membrane, Arch. Rational Mech. Anal. 31, 390-400 (1970) MR 0233538
  • [5] A. J. Callegari, H. B. Keller, and E. L. Reiss, Membrane buckling: A study of solution multiplicity, Comm. Pure Appl. Math. 24, 499-521 (1971) MR 0290638

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DOI: https://doi.org/10.1090/qam/721423
Article copyright: © Copyright 1983 American Mathematical Society

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