Bounds for the Critical Value of a Nonlinear Circular Membrane under Normal Pressure

  • Jürgen Sprekels
  • Heinrich Voss
Part of the International Series of Numerical Mathematics / Internationale Schriftenreihe zur Numerischen Mathematik / Serie Internationale D’Analyse Numerique book series (ISNM, volume 48)


In this note we use the finite dimensional iteration techniques developed in [3] to include the critical value of a circular membrane under constant normal pressure.


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  1. [1]
    E. Bohl: On Two Boundary Value Problems in Nonlinear Elasticity from a Numerical Viewpoint. In: Lecture Notes in Mathematics No, 679, Ed.: R. Ansorge, W. Törnig. Springer, Berlin-Heidelberg-New York 1977, 1–14.Google Scholar
  2. [2]
    R. W. Dickey: The Plane Circular Elastic Surface Under Normal Pressure. Arch. Rat. Mech. Anal. 26 (1967), 219–236.CrossRefGoogle Scholar
  3. [3]
    J. Sprekels, H. Voss: Pointwise Inclusions of Fixed Points by Finite Dimensional Iteration Schemes. To appear in Numer. Math.Google Scholar
  4. [4]
    H. J. Weinitschke: Endliche Deformationen elastischer Membranen. ZAMM 53 (1973), 89–91.Google Scholar
  5. [5]
    H. J. Weinitschke: Verzweigungsprobleme bei kreisförmigen elastischen Platten. Intern. Ser. Numer. Math. 38 (1977), 195–212.Google Scholar

Copyright information

© Springer Basel AG 1979

Authors and Affiliations

  • Jürgen Sprekels
    • 1
  • Heinrich Voss
    • 2
  1. 1.Institut für Angewandte MathematikUniversität HamburgHamburg 13Bundesrepublik Deutschland
  2. 2.Fachbereich MathematikUniversität Essen — GHSEssenBundesrepublik Deutschland

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