A novel class of graded cylinders neutral to host shafts of arbitrary cross-sections under torsion

A novel class of graded cylinders is proposed as neutral inclusions inside host shafts of arbitrary cross-section under Saint-Venant's torsion. The graded cylinder is made of cylindrically orthotropic materials with position varying quantities. The profiles of the two distinct shear moduli in the radial and tangential directions follow specific forms based on an arbitrarily selected function along the radial distance. We show that this type of graded cylinders can serve as universal neutral inclusions within host shafts of arbitrary cross-sections. In addition, we find that the associated warping fields can be exactly determined in terms of simple exponents of the selected function. This suggests that, by tuning the gradation parameter, one can manipulate the warping field of the inserted cylinder without disturbing the fields inside the host shaft. This finding is an original contribution to the existing solvable configurations of composite shafts under torsion.