Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

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



Buckling of an elastic membrane on a surface of revolution

Author: Murray Schechter
Journal: Quart. Appl. Math. 23 (1965), 121-132
MSC: Primary 73.99
DOI: https://doi.org/10.1090/qam/193830
MathSciNet review: 193830
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Abstract: This paper is concerned with a generalization of the following problem in nonlinear membrane theory studied by S. Lubkin [1] and C. Sensenig [2]: a membrane in the shape of an annulus is deformed by the application of a hydrostatic pressure to the outer boundary while the inner boundary remains stress free. The membrane is constrained to lie between two lubricated plates, so that no work is done at these surfaces during the deformation. The deformation is rotationally symmetric, each point on the membrane moving along a radius so that the deformed membrane is still in the shape of an annulus. What is to be determined is the stability of this deformation with respect to asymmetric disturbances satisfying the same stress conditions at the two boundaries and the same constraint imposed by the plates.

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

  • [1] S. Lubkin, Determination of buckling criteria by minimization of total energy, New York Univ., Institute of Math. Sciences, Report No. 241, 1957
  • [2] C. Sensenig, Instability of thick elastic solids, New York Univ., Courant Institute of Math. Sciences, Report No. 310, 1963 MR 0169453
  • [3] F. John, Plane strain problems for a perfectly elastic material of harmonic type, Comm. Pure Appl. Math. 13 (1960) MR 0118022

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DOI: https://doi.org/10.1090/qam/193830
Article copyright: © Copyright 1965 American Mathematical Society

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