ABSTRACT
This chapter considers the St. Venant theory of torsion for uniform prismatic elastic rods loaded by twisting couples at the ends of the rod. It utilizes 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 chapter illustrates the procedure for the Kantorovich method by considering the torsion of the shaft with a rectangular cross section as presented by Kantorovich and Krylov. It employs the familiar Ritz method to find approximate solutions to particular linear elastic and nonlinear elastic problems. The chapter describes the Ritz method in conjunction with the total potential energy and the Trefftz method to formulate lower and upper bounds, respectively, for the torsional rigidity.
