On the Bending of a Circular Plate with a Circular Hole at the Center under a Concentrated Load

Abstract

Expressing the distribution of load, on a circular plate with a hole at the center under a concentrated load, by means of δ-function, and performing the integral of particular solution by the property of δ-function, we reduced the differential equation for the bending of the plate to a plane biharmonic equation. Expressing the solution of this biharmonic equation and boundary conditions by Fourier series and comparing the coefficients of both sides of the equations, we derived the exact solution of the deflection for the following cases ; (i) Both boundaries are clamped, (ii) One boundary is clamped and the other is free supported, (iii) Both boundaries are free supported, (iv) One boundary is clamped and the other is a free edge, (v) One boundary is free supported and the other is a free edge.