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Existence theorems for some boundary value problems in the nonlinear theory of annular elastic membranes

Published online by Cambridge University Press:  16 July 2009

Hans Grabmüller  and
Robert Pirner
Hans Grabmüller
Affiliation:
Institut für Angewandte Mathematik, Friedrich-Alexander-Universität Erlangen-Nürnberg, D-8520 Erlangen, Germany
Robert Pirner
Affiliation:
Institut für Angewandte Mathematik, Friedrich-Alexander-Universität Erlangen-Nürnberg, D-8520 Erlangen, Germany
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Abstract

A simplified version of Reissner's theory of thin shells of revolution suffering small strains but arbitrarily large deflections and rotations reduces, when specialized to axi-symmetric deformations of annular membranes under a vertical surface load, to a nonlinear ordinary differential equation which is free of Poisson'ratio. Within this framework the questions of existence and non-existence of non-negative solutions of the associated stress and displacement boundary value problem are brought to a final answer. Progress in this direction was made in an earlier study (Grabmüller & Pirner 1987). In this paper a continuous monotone curve is constructed which effects a subdivision of the respective ranges of boundary data into complementary domains of existence and non-existence of strictly positive solutions

Type
Research Article
Information
European Journal of Applied Mathematics , Volume 3 , Issue 3 , September 1992 , pp. 299 - 317
Copyright
Copyright © Cambridge University Press 1992

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