Bending of Circular Plates With Large Deflection

Publisher Website
Google Scholar
Abstract
In the design of thin plates bent by lateral loading, formulas based on the Kirchhoff theory which neglects stretching and shearing in the middle surface are quite satisfactory, providing the deflections are small compared to the thickness. If deflections are of the same order as the thickness, the Kirchhoff theory may yield results which are considerably in error and therefore a more rigorous theory which takes account of deformations in the middle surface should be applied. The fundamental equations for the more exact theory are known and approximate solutions have been developed for the case of a circular plate. This paper gives the general solution of the fundamental equations for the case of a circular plate bent to a figure of revolution. Particular solutions are found which satisfy one of the two boundary conditions, and stresses and deflections are calculated from these solutions. By interpolation, the stresses and deflections are then found for plates satisfying both boundary conditions. The deflections are compared with experimental results and with the approximate formulas. It is found that these deflections agree closely with the experimental results and also with those obtained by the approximate methods of A. Nadai and S. Timoshenko, as shown in Figs. 8 and 10.

This publication has 0 references indexed in Scilit: