Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

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

   
 
 

 

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 | References | Additional Information

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.


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

  • [1] C. H. Wu, Tube to annulus--an exact nonlinear membrane solution, Quart. Appl. Math. 27, 489-496 (1970)
  • [2] W. H. Yang and W. W. Feng, On axisymmetrical deformations of nonlinear membranes, J. Appl. Mech. 37, 1002-1011 (1970)
  • [3] A. E. Green and W. Zerna, Theoretical elasticity, Clarendon Press, Oxford, 1954 MR 0064598
  • [4] A. E. Green and J. E. Adkins, Large elastic deformations, Clarendon Press, Oxford, 1960 MR 0269158
  • [5] C. H. Wu, On certain integrable nonlinear membrane solutions, Quart. Appl. Math. 28, 81-90 (1970)
  • [6] 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)
  • [7] J. D. Cole, Perturbation methods in applied mathematics, Blaisdell Publishing Company, 1968 MR 0246537
  • [8] W. H. Yang, Stress concentration in a rubber sheet under axially symmetric stretching, J. Appl. Mech. 34, 943-947 (1967)


Additional Information

DOI: https://doi.org/10.1090/qam/99720
Article copyright: © Copyright 1973 American Mathematical Society

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