Bending of isotropic thin square plates by concentrated edge couples and forces

Abstract

In this paper the complex variable method of Muskhelishvili is applied to problems of bending for small deflections of thin, isotropic, homogeneous plates by concentrated edge couples and forces. The functional equation involved in Muskhelishvili's method is solved by using function theory. The necessary conformal mapping function is found from the Schwarz-Christoffel formula or expansion of elliptic functions. A general solution is given for plates which can be mapped on a unit circle by polynomial type mapping functions. Three particular problems are worked out in detail; namely those of approximately square plates subjected, respectively, to two bending couples, to two twisting couples, both applied at the ends of a diagonal, and to four forces applied at the four corners. Numerical results are presented in the form of tables and graphs.