Torsion of elastic anisotropic micropolar cylindrical bars

The effects of a torque on a cylindrical bar, either solid or hollow, made of an anisotropic micropolar linear elastic material are analyzed. The elastic properties are supposed to be invariant along the cylinder axis. One of the principal directions of the material elasticity tensors is parallel to the cylinder axis; the other two are arbitrarily rotated in the plane of any cross-section of the bar. Closed-form, approximate solutions are obtained if the material internal length is much smaller or much larger than the cylinder outer radius; the latter solution applies for particular orientations of the material symmetry axes. In the general case, only numerical solutions of the governing equations can be derived. A parametric study is carried out on the effect of different parameters (material internal length, orientation of the symmetry axes, etc.) on the stress distribution and the torsional rigidity of the cylinder. The size effects associated with the material internal length are pointed out in terms of torsional rigidity, both for solid and hollow cylinders.