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On the General Theory of Heterogeneous Aeolotropic Plates

Published online by Cambridge University Press:  07 June 2016

Yehuda Stavsky
Yehuda Stavsky*
Affiliation:
Department of Mechanics, Israel Institute of Technology
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Summary

A large deflection theory is established for the bending and stretching of aeolotropic plates with elastic moduli that vary in the x, y, z directions. The theory is formulated in terms of two simultaneous non-linear differential equations, with variable coefficients, for the transverse deflection w and an Airy stress function F. Small deflection heterogeneous plate theory and some other sub-classes of plate problems are formulated by specialising the general non-linear plate equations. Effects of initial irregularities and of a variable elastic foundation are considered.

Type
Research Article
Information
Aeronautical Quarterly , Volume 15 , Issue 1 , February 1964 , pp. 29 - 38
Copyright
Copyright © Royal Aeronautical Society. 1964

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References

1. Stodola, A. Steam Turbines. Second Edition, pp. 335–342, Van Nostrand, New York, 1906.Google Scholar
2. Bert, C. W. Nonhomogeneous Polar-Orthotropic Circular Disk of Varying Thickness. Engineering Experiment Station Bulletin No. 190, March 1962.Google Scholar
3. Koronev, B. G. The Theory of Plates. Chapter IV in Structural Mechanics in the U.S.S.R. 1917-1957, p. 191, edited by Rabinovich, I. M., Pergamon Press, 1960.Google Scholar
4. Gran Olsson, R. Die Biegung der rechteckigen Platte von veranderlichen Dicke. Dissertation, Technische Hochschule Berlin, 1934.Google Scholar
5. Gran Olsson, R. Biegung der Rechteckplatte bei linear veränderlich Biegungssteifkeit. Ingenieur-Archiv, Vol. 5, p. 363, 1934.Google Scholar
6. Reissner, E. Remark On The Theory of Bending of Plates of Variable Thickness. Journal of Mathematics and Physics, Vol. 16, p. 43, 1937.Google Scholar
7. Federhofer, K. Die Grundgleichungen für elastische Platten veränderlicher Dicke und grosse Ausbiegung. Zeitschrift für Angewandte Mathematik und Mechanik, Vol. 25, p. 17, 1947.CrossRefGoogle Scholar
8. Mansfield, E. H. On the Analysis of Elastic Plates of Variable Thickness. Quarterly Journal of Mechanics and Applied Mathematics, Vol. 15, Part 2, p. 167, May 1962.Google Scholar
9. Stavsky, Y. Bending and Stretching of Laminated Aeolotropic Plates. Transactions of the American Society of Civil Engineers, Vol. 127, Part I, p. 1194, 1962.CrossRefGoogle Scholar
10. Stavsky, Y. Finite Deformations of a Class of Aeolotropic Plates With Material Heterogeneity. Israel Journal of Technology, Vol. 1, No. 2, January 1964.Google Scholar
11. Reissner, E. and Stavsky, Y. Bending and Stretching of Certain Types of Heterogeneous Aeolotropic Elastic Plates. Journal of Applied Mechanics, Vol. 28, No. 3, p. 402, September 1961.CrossRefGoogle Scholar
12. Shulezhko, P. G. Equations of Motion and Equilibrium for Anisotropic and Non-Uniform Thin Plates of Variable Thickness. Sbornik Ukrainskovo Nauchnoissledovatelskovo Instituta Sooruzhenij, No. 2, 1938.Google Scholar
13. Timoshenko, S. P. and Woinowski-Krieger, S. Theory of Plates and Shells. Second Edition, McGraw-Hill, p. 393, 1959.Google Scholar
14. Hetényi, M. Beams on Elastic Foundations. University of Michigan Press, pp. 1–3, 1946.Google Scholar