On an Approximate Analysis Method of a Rectangular Plate with a Circular Hole

Abstract

As is well known, deflection caused by transverse loading of a plate with an arbitrary external form and a circular hole involves considerably complex problems of boundary values. It is very difficult to obtain exact solutions to these problems, and the author proposes an approximate solution by referring to the Collocation method and a general solution of a differential equation of plates in polar co-ordinate system.
In this paper, arbitrary constants in a general solution of a bi-harmonic differential equation of a plate are determined by exact boundary conditions on the edge of a circular hole and approximate boundary conditions which require exact boundary conditions only at the finite number of points selected on the external edge of the plate. Numerical examples for this analysis method are given, and stresses on the edge of a circular hole in a rectangular plate are calculated and compared with experimental values measured by means of a wire resistance strain gage.