On the Volterra's Distortions Theory

This paper has been spurred by the great influence of the Volterra's distortions theory on the modern theory of dislocations and particularly of the ones which study the crystals, aelotropic materials. Volterra developed his theory, as well as the explicit solutions, for elastic, homogeneous, isotropic, and right hollow cylinders. Here we are subduing the assumptions developing the theory for transversely isotropic hollow cylinders.