Infinitely stretched Mooney surfaces of revolution are uniformly stressed catenoids
Author:
Chien-Heng Wu
Journal:
Quart. Appl. Math. 32 (1974), 273-284
DOI:
https://doi.org/10.1090/qam/99679
MathSciNet review:
QAM99679
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Abstract: Axially and radially stretched Mooney surfaces of revolution are found to tend to catenoids as the stretching tends to infinity. Moreover, two catenoids are found to exist for any given set of stretching parameters. A formal two-term asymptotic solution is obtained explicitly and the stretching of a cylindrical surface is given as an example.
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C. H. Wu, Spherelike deformations of a balloon, Quart. Appl. Math. 30, 183–194 (1972)
D. Y. P. Perng and C. H. Wu, Flattening of membranes of revolution by large stretching—asymptotic solution with boundary layer, Quart. Appl. Math. 32, 407–420 (1973)
L. P. Eisenhart, A treatise on the differential geometry of curves and surfaces, Ginn and Company, 1909
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C. H. Wu, On certain integrable nonlinear membrane solutions, Quart. Appl. Math. 28, 81–90 (1970)
E. Isaacson, The shape of a balloon, Comm. Pure Appl. Math. 18, 163–166 (1965)
C. H. Wu, Spherelike deformations of a balloon, Quart. Appl. Math. 30, 183–194 (1972)
D. Y. P. Perng and C. H. Wu, Flattening of membranes of revolution by large stretching—asymptotic solution with boundary layer, Quart. Appl. Math. 32, 407–420 (1973)
L. P. Eisenhart, A treatise on the differential geometry of curves and surfaces, Ginn and Company, 1909
A. E. Green and J. E. Adkins, Large elastic deformations, Clarendon Press, Oxford, 1960
C. H. Wu, On certain integrable nonlinear membrane solutions, Quart. Appl. Math. 28, 81–90 (1970)
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Article copyright:
© Copyright 1974
American Mathematical Society
