Solution of non-uniform torsion of bars by an integral equation method

In this paper, a boundary element method (BEM) is developed for the non-uniform torsion of simply or multiply connected cylindrical bars of arbitrary cross-section. The bar is subjected to an arbitrarily distributed twisting moment while its edges are restrained by the most general linear torsional boundary conditions. Since warping is prevented, besides the Saint-Venant torsional shear stresses, the warping normal stresses are also computed. Two boundary value problems with respect to the variable along the beam angle of twist and to the warping function are formulated and solved employing a BEM approach. Both the warping and the torsion constants are computed by employing an effective Gaussian integration over the domains of arbitrary shape. Numerical results are presented to illustrate the method and demonstrate its efficiency and accuracy. The contribution of the normal stresses due to a restrained warping is investigated, by numerical examples, with great practical interest.