Torsion of Nonlinear Viscous Shafts

In this study, we reconsider the torsion of nonlinear viscous shafts. Attention is paid to the analytical solution of the nonlinear partial differential equation arising in the problem's formulation, and it is concluded that the stresses τ_xy, τ_xz, and the torque T(t) can be found in terms of the partial derivatives of the warping function ϕ. Theoretical results are given for circular cross sections, and it is shown that the present method gives the same results as those for elastic (m= 0) and perfectly plastic torsion (m→∞). It is further proved that it is not possible to give analytical solutions for nonregular boundaries, such as rectangular and triangular cross sections.