Solutions for Certain Circular Plate Problems

by Amir K. Naghdi, Prof. of Aeronautical-Astronautical Engrg. and Mathematical Sciences; Indiana-Purdue Univ., Indianapolis, Ind.,

Serial Information: Journal of the Engineering Mechanics Division, 1978, Vol. 104, Issue 5, Pg. 1241-1251

Document Type: Journal Paper


The exact closed-form solutions have been obtained for the problems of transverse displacements in clamped thin solid circular elastic plates subject to partial loadings as described in the following. The transverse load per unit area, which varies as a closed form polynomial only in the direction perpendicular to a secant line in the circular plate, exists on one side of this line. The included examples are the case in which the plate is subject to hydrostatic pressure on one side of a secant line, and the case of a uniform line load along a chord. The technique of solution is by first deriving a closed-form particular integral of the governing differential equation. Next, the complementary solution of the equation in polar coordinates satisfying the necessary edge conditions is derived in the form of an infinite series. Finally the involved series are summed to obtain the desired closed-form solution.

Subject Headings: Closed form solutions | Load factors | Plates | Transverse loads | Case studies | Displacement (mechanics) | Elastic analysis | Polynomials

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