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Thermal Stresses in Rectangular Plates*

Published online by Cambridge University Press:  07 June 2016

J. S. Przemieniecki*
Affiliation:
Bristol Aircraft Limited
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Summary

The characteristic functions for beam vibration modes are used to derive an approximate solution for the calculation of thermal stresses in rectangular isotropic flat plates subjected to arbitrary temperature distributions in the plane of the plate and constant temperatures through the plate thickness. The thermal stresses are obtained in the form of generalised Fourier expansions in terms of the characteristic functions, and their derivatives, representing normal modes of vibration of a clamped-clamped beam. Since these functions have recently been tabulated, the practical application of this new method to the thermoelastic stress analysis of plates presents no difficulty.

Type
Research Article
Copyright
Copyright © Royal Aeronautical Society. 1959

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Footnotes

*

This paper is based on Chapter 8 of a Ph.D. thesis approved by the University of London(5);it was written while the author was at the Imperial College of Science and Technology, London.

References

1. Heldenfels, R. R. and Roberts, W. M. Experimental and Theoretical Determination of Thermal Stresses in Flat Plates. N.A.C.A. T.N. 2769, August 1952.Google Scholar
2. Singer, J., Anliker, M. and Lederman, S. Thermal Stresses and Thermal Buckling. Wright Air Development Center Technical Report 57-69, Polytechnic Institute of Brooklyn, April 1957.Google Scholar
3. Horvay, G. The End Problem of Rectangular Strips. Journal of Applied Mechanics, Vol. 20, pp. 8794, March 1953 and pp. 576-582, December 1953.CrossRefGoogle Scholar
4. Mendelson, A. and Hirschberg, M. Analysis of Elastic Thermal Stress in Thin Plate with Spanwise and Chordwise Variation of Temperature and Thickness. N.A.C.A. T.N. 3778, November 1956.Google Scholar
5. Przemieniecki, J. S. Temperature Stresses in Aircraft Structures. Ph.D. Thesis, Chapter 8, University of London, 1958.Google Scholar
6. Young, D. and Felgar, R. P. Tables of Characteristic Functions Representing Normal Modes of Vibration of a Beam. Publication No. 4913, University of Texas, 1949.Google Scholar
7. Timoshenko, S. Theory of Plates and Sliells. First Edition, p. 227. McGraw-Hill, New York, 1940.Google Scholar
8. Timoshenko, S. Vibration Problems in Engineering, pp. 331336. Constable, London, 1937.Google Scholar