The Theory of Torsion of Elastic Noncircular Cylinders Under Large Deformations

The Saint-Venant semi-inverse method generalization for the problem of torsion under large deformations is presented. The case where a prism cross-section possesses central symmetry is regarded. The torsion problem is reduced to a two-dimensional nonlinear boundary value problem. Differential balance equations and lateral conditions are satisfied by solving the boundary value problem. End conditions are implemented so that the stress system is equivalent to the torsion moment, and to the axial force passing through the cross-section center of inertia. The energy method, used to solve the torsion problem under small twist angles, is extended to the case of finite deformations. Approximate solutions of the torsion problem for elliptical, rectangular, and quadrantal cylinders made of Treloar and Blatz-Ko materials are obtained.