Bending of Isotropic Thin Plates by Concentrated Edge Couples and Forces

Abstract

Abstract In this paper the complex variable method of Muschelišvili for solving the biharmonic equation is applied to problems of bending of isotropic thin plates by concentrated edge couples and forces. The results of the method as applied to plate problems by previous authors are presented first. Methods of handling concentrated edge couples and forces are developed. These are then applied to the circular plate as an example, for which exact solutions in closed forms are obtained. Worked out in detail are three particular problems; namely, those of circular plates subjected, respectively, to two bending couples, to two twisting couples, both applied at the ends of a diameter, and to four forces applied at the ends of two diameters perpendicular to each other. Numerical results are presented in the form of graphs.