ABSTRACT
In this chapter, the authors consider the St. Venant theory of torsion for uniform prismatic elastic rods loaded by twisting couples at the ends of the rod. They examine the principle of total potential energy for the assumed deformation field. The authors also consider methods arising from the variational approach to reach approximate solutions to the torsion problem. They find that it is often desirable in this regard to use the total complementary energy functional for torsion. The authors use the total complementary energy coupled with the Ritz method to formulate approximate solutions to the torsion problem for a linear elastic body. A serious shortcoming of the Ritz method as well as the Galerkin method is that the results obtained have a strong dependence on the coordinate functions chosen. The method of Kantorovich will decrease the strong dependence of the results on the choice of the coordinate function, thereby making the process more effective.
