Nonuniform torsion of bars of variable cross section

In this paper a boundary element method is developed for the nonuniform torsion of simply or multiply connected bars of arbitrary variable cross section. The bar is subjected to an arbitrarily concentrated or distributed twisting moment, while its edges are restrained by the most general linear torsional boundary conditions. The developed procedure takes into account the variable torsional and warping rigidities along the member length. Three boundary value problems with respect to the variable along the beam angle of twist and to the primary and secondary warping functions are formulated and solved employing a pure BEM approach, that is only boundary discretization used. Both the variable warping and torsion constants together with the torsional shear stresses and the warping normal and shear stresses are computed. Numerical results are presented to illustrate the method and demonstrate its efficiency and accuracy. The discrepancy in the analysis of a thin-walled cross section beam employing the FEM and using a fine mesh of shell elements or employing shape functions after calculating the torsion and warping constants adopting the thin tube theory demonstrates the importance of the proposed procedure even in thin-walled beams, since it approximates better the torsion and warping constants and takes also into account the warping of the walls of the cross section.