Optimum Design of Thin Circular Plates on an Elastic Foundation

Abstract

An analysis is given of a thin, constant-thickness, circular plate subjected to uniform lateral pressure. The plate is assumed to rest on an elastic foundation and to be elastically restrained at the edges against rotation and vertical deflection. The equations for the magnitude and location of the maximum stress in the plate were programmed for an electronic computer and curves obtained for both these quantities for various values of two dimensionless parameters. These curves are presented in the paper and it is shown how the optimum design of a constant-thickness circular plate can be quickly effected with their aid.

One interesting result of the analysis is that it is possible to design plates in which the maximum stress is between 25 and 50 per cent smaller than that in similar plates with simply supported ends. This possibility does not appear to have been appreciated before and its utilization has obvious economic advantages. Another result of interest is that the value of the dimensionless elastic rotational restraint parameter giving minimum thickness is almost a constant for most cases occurring in practice.

A brief discussion is also included of the application of the curves obtained for homogeneous plates to the design of perforated tube-plates.

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