Torsion of cylindrically orthotropic elastic circular bars with radial inhomogeneity: some exact solutions and end effects

Torsion of elastic circular bars of radially inhomogeneous, cylindrically orthotropic materials is studied with emphasis on the end effects. To examine the conjecture of Saint-Venant’s torsion, we consider torsion of circular bars with one end fixed and the other end free on which tractions that results in a pure torque are prescribed arbitrarily over the free end surface. Exact solutions that satisfy the prescribed boundary conditions point by point over the entire boundary surfaces are derived in a unified manner for cylindrically orthotropic bars with or without radial inhomogeneity and for their counterparts of Saint-Venant’s torsion. Stress diffusion due to the end effect is examined in the light of the exact solutions.