Zeitschrift für angewandte Mathematik und Physik

, Volume 66, Issue 4, pp 1939–1947 | Cite as

Higher-order asymptotic result for the wrinkling of an everted Varga spherical shell

  • M. SanjaranipourEmail author
  • N. Abdolalian


This paper applies the WKB method to the buckling analysis of an everted spherical shell composed of Varga material. The same problem has been studied by Haughton and Chen in 2003, but they only obtained the leading-order value for the critical radius ratio B/A because they did not seem to realize that the second-order ODE with variable coefficients satisfied by the eigenfunctions could be solved explicitly, where A and B are the inner and outer radii of the undeformed sphere. In the current paper, we managed to find the leading-order and next-order eigenfunctions explicitly in the WKB expansion, and hence obtained two more terms in the asymptotic expansion of B/A. We believe that the same idea can be employed to find the eigenfunctions at higher orders.

Mathematics Subject Classification

Primary 99Z99 Secondary 00A00 


Compound matrix method Eversion Incompressible Spherical Varga material WKB method 


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Copyright information

© Springer Basel 2014

Authors and Affiliations

  1. 1.Faculty of MathematicsUniversity of Sistan and BaluchestanZahedanIran

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