This paper is concerned with the torsion of anisotropic, linearly elastic cylindrical bars. The solution of the problem in the case where the medium has a plane of elastic symmetry which contains the axis of the cylinder is established. We consider the case of inhomogeneous cylinders where the elastic coefficients are independent of the axial coordinate. We prove that, in general, the torsion induces extension and bending. The solution is new even for homogeneous bodies. The results are used to study the torsion of an anisotropic circular cylinder.
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