Relationships between the solutions to the Saint-Venant torsion of an anisotropic circular cylinder and of an isotropic elliptical cylinder are proven. It is shown that if the geometrical data describing an isotropic elliptical cylinder are certain functions of the shear rigidities of an anisotropic circular cylinder, then the torsional functions and torsional rigidities of the considered cross-sections are the same. The material of both cylinders is homogeneous. The class of anisotropy taken into account has at least one plane of elastic symmetry normal to the axis of the circular cylinder.
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