The Interior Solution for Linear Problems of Elastic Plates

[+] Author and Article Information
R. D. Gregory

Department of Mathematics, University of Manchester, Manchester M13 9PL, England

F. Y. M. Wan

Department of Applied Mathematics, University of Washington, FS-20, Seattle, WA 98195

J. Appl. Mech 55(3), 551-559 (Sep 01, 1988) (9 pages) doi:10.1115/1.3125829 History: Received October 05, 1987; Revised January 13, 1988; Online July 21, 2009


Necessary conditions have been established recently for the prescribed data along the cylindrical edge(s) of an elastic flat plate to induce only an exponentially decaying elastostatic state. The present paper describes how these conditions may be used to determine the interior solution (or its various thin and thick plate theory approximations) of plate problems. The results in turn show that the necessary conditions for a decaying state are also sufficient conditions. Boundary conditions for the interior solution of circular plate problems with edgewise nonuniform boundary data are discussed in detail and then applied to two specific problems. One of them is concerned with a circular plate compressed by two equal and opposite point forces at the plate rim. The solution process for this problem illustrates for the first time how the stretching action in the plate interior induced by transverse loads can be properly analyzed.

Copyright © 1988 by ASME
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