Abstract
Levinson's solution for the problem of a simply supported rectangular plate of arbitrary thickness by normal surface loads is extended to the transversely isotropic and layered case. The exact closed form solution is obtained by using the propagator matrix method in a system of vector functions. As a special case of the layered medium, the normal displacement or deflection of a homogeneous plate of arbitrary thickness by normal surface loads is also given. It is shown that it approaches the classical solution for the transversely isotropic thin plate as the thickness approaches zero on the one hand, and on the other hand reduces to the thick plate expression as given by Levinson when the medium is isotropic.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
A.P.S. Selvadurai, Elastic Analysis of Soil-Foundation Interaction. Elsevier, Amsterdam (1979).
V. Panc, Theories of Elastic Plates. Noordhoff, Leyden (1975).
M. Levinson, A novel approach to thick plate theory suggested by studies in foundation theory. Int. J. Mech. Sci. 26 (1984) 427–436.
M. Levinson, The simply supported rectangular plate: An exact, three dimensional, linear elasticity solution. J. Elasticity 15 (1985) 283–291.
J.C. Small and J.R. Booker, Finite layer analysis of layered elastic materials using a flexibility approach. Part 1—strip loadings. Int. J. Numer. Methods Eng. 20 (1984) 1025–1037.
J.C. Small and J.R. Booker, Finite layer analysis of layered elastic materials using a flexibility approach. Part 2—circular and rectangular loadings. Int. J. Numer. Methods Eng. 23 (1986) 959–978.
J.E. Ashton and J.M. Whitney, Theory of Laminated Plates. Technomic, Stamford (1970).
Y.M. Tsai, Symmetrical contact problem of a thick transversely isotropic plate. J. Elasticity 16 (1986) 179–188.
E. Pan, Static response of a transversely isotropic and layered half-space to general surface loads. Phys. Earth Planet. Inter. 54 (1989) 353–363.
F. Gilbert and G. Backus, Propagator matrices in elastic wave and vibration problems. Geophysics 31 (1966) 326–332.
S.G. Lekhnitskii, Theory of Elasticity of an Anisotropic Elastic Body. Holden-Day, San Francisco (1963).
P.M. Morse and H. Feshbach, Methods of Theoretical Physics. McGraw-Hill, New York (1953).
A.F. Ulitko, Method of Special Vector Functions in Three Dimensional Elasticity (in Russian). Naukova Dumka, Kiev (1979).
E. Pan, The static responses of multilayered foundations to general surface loading and body force. Acta Mechanica Sinica (in Chinese, with English abstract) 21 (1989) 344–353.
E. Pan, A general analysis of layered linear elastostatic problems. Prepared to submit.
S. Timoshenko and S. Woinowsky-Krieger, Theory of Plates and Shells. 2nd edn, McGraw-Hill, New York (1959).
N.J. Pagano, Exact solutions for rectangular bidirectional composites and sandwich plates. J. Comp. Mater. 4 (1970) 20–36.
S. Srinivas and A.K. Rao, Bending, vibration and buckling of simply supported thick orthotropic rectangular plates and laminates. Int. J. Solids Structures 6 (1970) 1463–1481.
M. Levinson, Generalized Vlasov-Jones foundation model: a foundation of grade 4. Int. J. Mech. Sci. 25 (1983) 149–154.
R. Jones and J. Mazumdar, A note on the behavior of plates on an elastic foundation. J. Appl. Mech. 47 (1980) 191–192.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Pan, E. An exact solution for transversely isotropic, simply supported and layered rectangular plates. J Elasticity 25, 101–116 (1991). https://doi.org/10.1007/BF00042460
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF00042460