Flattening of membranes of revolution by large stretching—Asymptotic solution with boundary layer
Authors:
Daniel Y. P. Perng and Chien-Heng Wu
Journal:
Quart. Appl. Math. 30 (1973), 407-420
DOI:
https://doi.org/10.1090/qam/99720
MathSciNet review:
QAM99720
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Abstract: The problem is solved explicitly by the method of matching asymptotics. The stretching of a flat membrane with an inclusion is studied as an example. Asymptotic stress and strain concentration ratios are derived. It is shown that the stress concentration ratio tends to unity as the stretching tends to infinity. This is justified by the exact numerical solution.
C. H. Wu, Tube to annulus—an exact nonlinear membrane solution, Quart. Appl. Math. 27, 489–496 (1970)
W. H. Yang and W. W. Feng, On axisymmetrical deformations of nonlinear membranes, J. Appl. Mech. 37, 1002–1011 (1970)
- A. E. Green and W. Zerna, Theoretical elasticity, Oxford, at the Clarendon Press, 1954. MR 0064598
- A. E. Green and J. E. Adkins, Large elastic deformations, Clarendon Press, Oxford, 1970. Second edition, revised by A. E. Green. MR 0269158
C. H. Wu, On certain integrable nonlinear membrane solutions, Quart. Appl. Math. 28, 81–90 (1970)
C. H. Wu and D. Y. P. Perng, On the asymptotically spherical deformations of arbitrary membranes of revolution fixed along an edge and inflated by large pressures—a nonlinear boundary layer phenomenon, SIAM J. Appl. Math. 23, 133–152 (1972)
- Julian D. Cole, Perturbation methods in applied mathematics, Blaisdell Publishing Co. Ginn and Co., Waltham, Mass.-Toronto, Ont.-London, 1968. MR 0246537
W. H. Yang, Stress concentration in a rubber sheet under axially symmetric stretching, J. Appl. Mech. 34, 943–947 (1967)
C. H. Wu, Tube to annulus—an exact nonlinear membrane solution, Quart. Appl. Math. 27, 489–496 (1970)
W. H. Yang and W. W. Feng, On axisymmetrical deformations of nonlinear membranes, J. Appl. Mech. 37, 1002–1011 (1970)
A. E. Green and W. Zerna, Theoretical elasticity, Clarendon Press, Oxford, 1954
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)
C. H. Wu and D. Y. P. Perng, On the asymptotically spherical deformations of arbitrary membranes of revolution fixed along an edge and inflated by large pressures—a nonlinear boundary layer phenomenon, SIAM J. Appl. Math. 23, 133–152 (1972)
J. D. Cole, Perturbation methods in applied mathematics, Blaisdell Publishing Company, 1968
W. H. Yang, Stress concentration in a rubber sheet under axially symmetric stretching, J. Appl. Mech. 34, 943–947 (1967)
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Article copyright:
© Copyright 1973
American Mathematical Society
