Bending of a Circular Plates with Many Circular Holes : Case of Circular Holes with Free Edges

Abstract

For bending problems of a circular plate with many circular holes is presented in this study a method of solution in which the general solution for the biharmonic equation in the polar coordinates is recurrently used until all boundary conditions are satisfied. This method is used to solve bending problems of a circular plate with one circular hole in eccentric position or with two circular holes of equal diameters in symmetric position. Two loading conditions are assumed; bending moment distributes uniformly at the outer edge of the plate, and the load concentrates at its center. As for the boundary condition, it is assumed that the edges of the holes are free and that the outer edge of the plate is simply supported for the first loading condition and simply supported or clamped for the second loading condition. Calculated results are indicated in some diagrams which are considered useful in design of thin-walled structures.