Deflection of uniformly loaded circular plates upon equispaced point supports

Abstract

A simple formula is derived for predicting the flexure of uniformly loaded point-supported circular plates. The classical solution of Michell for a clamped plate under a single point load is extended for any number of point loads regularly spaced around a circle concentric with the plate edge. The resulting series for the edge moments and shears are summed and are shown to be very similar to a simple sine wave. Replacing the exact expressions by single sine waves enables the clamped edges to be set free by a simple superposition of solutions. The point reactions are equilibrated by a uniform load and the resulting deflection surface for a free uniformly loaded point-supported plate is obtained immediately. Deflection curves for the particular case of a plate supported at three points are given in the form of contours of equal deflection. This particular case is compared with some experimental results which were obtained by optical methods.

For three supports, maximum deviation from the flat is least when the supports are equispaced around a circle of radius approximately two-thirds that of the plate. The contours for this case show that the central area is remarkably flat and that there are three diameters along which the deflections are almost constant.

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