Bending of a Uniformly Loaded Circular Plate with a Clamped Boundary on a Single-Beam Grid with Clamped Edges

Abstract

This paper treats the problem of the bending of a uniformly loaded circular plate with a clamped boundary which is supported by a single-beam grid formed of two beams intersecting at the center of the plate at right angles and clamped at edges. The deflection of the plate due to the reaction of the grid can be obtained by the Duhamel's method of superposition from the solution for the unit concentrated load. The reaction can be determined by solving an integral equation expressing that the deflections are equal on the grid for the plate and the grid. Hence superposing the deflections due to the reaction of the grid and the uniform load, we obtain the deflection of the plate, and hence stresses.