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A Simple Approximation for Plate Deflection Problems

Published online by Cambridge University Press:  28 July 2016

R. K. Kaul  and
V. Cadambe
R. K. Kaul
Affiliation:
National Physical Laboratory of India, New Delhi
V. Cadambe
Affiliation:
National Physical Laboratory of India, New Delhi
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Extract

The problem of bending of thin elastic plates has interested mathematicians and engineers for many years. Various methods have been put forward for determining the approximate solutions among which the variational method of Ritz is most common. This procedure leads to a system of linear simultaneous equations, the solution of which is often quite tedious, although generally by taking a few rows and columns quite accurate results are obtained. The purpose of this note is to show that by using bar eigen-functions for plates which are either clamped, or when some edges are freely supported, certain simplifications can be made in the process and the difficulty of solving simultaneous equations can be avoided; and that the deflection surface of the plate can be derived directly in a series form.

Type
Technical Notes
Information
The Aeronautical Journal , Volume 59 , Issue 539 , November 1955 , pp. 778 - 780
Copyright
Copyright © Royal Aeronautical Society 1955

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References

1. Kaul, R. K. and Cadambe, V. The Frequency of Vibration of Thin Isotropic Oblique Plates (to be published).Google Scholar
2. Young, D. (1950). Vibration of Rectangular Plates by the Ritz Method. Journal of Applied Mechanics, Trans, A.S.M.E., Vol. 72, p. 448, 1950.CrossRefGoogle Scholar
3. Young, D. and Felgar, R. P. (1945). Table of Characteristic Functions representing the Normal Modes of Vibration of a Beam. Engineering Research Series, No. 44, University of Texas, Austin, Texas, July 1945.Google Scholar
4. Huang, M. K. and Conway, H. D. (1952). Bending of a Uniformly Loaded Rectangular Plate with Two Adjacent Edges Clamped and the Other Two either Simply Supported or Free. Journal of Applied Mechanics, Trans. A.S.M.E., Vol. 19, No. 4, pp. 451–460, December 1952.Google Scholar