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Boundary layer solutions for some nonlinear elastic membrane problems

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Summary

The method of matched asymptotic expansions is used to describe finite axisymmetric deformations of two thin elastic membrane problems: a circular membrane with a small radial traction at the edge, an annular membrane with a small circular hole at the center. In both problems, the surface load is assumed to be an axial pressure. There is a boundary layer at the outer edge in the first problem, and at the hole in the second problem.

Zusammenfassung

Mit Hilfe der in der singulären Störungsrechnung benutzten Methode einer inneren und äußeren asymptotischen Entwicklung werden endliche, axialsymmetrische Deformationen bei zwei Membranproblemen beschrieben: eine dünne elastische Kreismembran mit kleiner radialer Zugspannung am Rande, und eine Kreisringmembran mit einem kleinen konzentrischen Loch. In beiden Problemen wird die Belastung als ein axial gerichteter Oberflächendruck angenommen. Im ersten Problem zeigt die Lösung am äußeren Rand Grenzschichtverhalten, welches im zweiten Problem am Lochrand vorliegt.

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Authors and Affiliations

  1. Dept. of Applied Mathematics FS-20, University of Washington, 98195, Seattle, WA, USA

    Frederic Y. M. Wan

  2. Institut für Angewandte Mathematik, Universität Erlangen-Nürnberg, 8520, Erlangen, Germany

    Hubertus J. Weinitschke

Authors
  1. Frederic Y. M. Wan
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  2. Hubertus J. Weinitschke
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Wan, F.Y.M., Weinitschke, H.J. Boundary layer solutions for some nonlinear elastic membrane problems. Z. angew. Math. Phys. 38, 79–91 (1987). https://doi.org/10.1007/BF00944922

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  • DOI: https://doi.org/10.1007/BF00944922

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