Torsion of a square isotropic plate by forces applied at the corners and by distributed torques

Abstract

We consider the classical problem of the theory of elastic plates, namely, the problem on the torsion of a square isotropic plane by forces applied at the corners. The traditional solution of this problem based on the classical theory of plates and Kirchhoff and Thomson–Tait transformations is compared with the solution obtained in the improved theory of plates and with experimental results. The solution, which does not exist in the classical theory of plates, of the problem on the torsion of a plate by torques uniformly distributed over the plate contour is presented as well.