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Nonlinear symmetric bending of circular elastic plates

Published online by Cambridge University Press:  09 April 2009

B. P. Garfoot
B. P. Garfoot
Affiliation:
Department of Mathematics and Computer Science, Queensland Institute of Technology, Australia
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In recent years, there has been considerable interest in the refining of thin plate theories. In this paper, the method of matching asymptotic expansions is used to obtain one such refinement which is believed to be an improvement on several previous results. Previous authors(Habip (1967), Widera (1969)) attempted such refinemnts within the framework of a partially nonlinear theory of elasticity whereas in the present work all terms neglected by these authors have been retained.

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 19 , Issue 4 , June 1975 , pp. 481 - 504
Copyright
Copyright © Australian Mathematical Society 1975

References

Van Dyke, M. (1964), Perturbation methods in Fluid Mechaincs. (Academic Press, New York, 1964).Google Scholar
Eringen, A. C. (1962), Nonlinear Theory of Cantinuous Media. (McGraw-Hill Book Company, Inc., New York, 1962).Google Scholar
Habip, L. M. (1967), ‘Moderately large deflection of asymmetrically elastic plate’, Int. Solids Strucutres, 3, 207–215.CrossRefGoogle Scholar
Hart, V. G. and Evans, D. J. (1964), ‘Non-linear bending of an annular plate by transverse edge forces’, J. Math. and Physics. 43, 275–303.CrossRefGoogle Scholar
von Kármán, Th. (1910), Enzyklopädie der Mathematischen Wissenschaften. IV. 4, 1910 p. 349.Google Scholar
Widera, O. E. (1969), ‘An Asymptotic Theory for Moderately Large Deflections of Anisotropic Plates’, Journal of Engineering Math. 3, 239–244.CrossRefGoogle Scholar
Friedrichs, K. O. and Dressler, R. F. (1961), ‘A Boundary Layer Theory for Elasticity Bending of Plates’, Comm. on Pure and Appl. Math. 14, 1–33.CrossRefGoogle Scholar
Garfoot, B. P. (1970), Ph. D. Thesis. (University of Queensland, 1970).Google Scholar
Gol'denveizer, A. L. and Kolos, A. V. (1965), ‘On the Derivation of Two-Dimensional Equations in the Theory of Thin Elastic Plates’, PMM, 29, 141–155.Google Scholar
Kolos, A. V. (1964), ‘On a Refinement of the Classical Theory of Bending of Circular Plates’, PMM, 28, 582–589.Google Scholar
Reiss, E. L. (1962), ‘Symmetric Bending of Thick Circular Plates’, J. Soc. Indust. Appl. Math. 10, 596–609.CrossRefGoogle Scholar
Riess, E. L. and Locke, S. (1961), ‘On the Theory of Plane Stress’, Quatrt. Appl. Math. 19, 195–203.Google Scholar
Reissner, E. (1963), ‘On the Derivation of Boundary Conditions for Plate Theory’, Proc. Royal. Soc. A, 276, 178–186.Google Scholar
Gusein-Zade, M. I. (1965), ‘On necessary and sufficient conditions for the existence of decaying solutions of the plane problem of the theory of elasticity for a semistrip’, PMM 29, 892–901.Google Scholar