Non-uniform torsion of functionally graded anisotropic bar of an elliptical cross section

An analytical solution is given to the problem of non-uniform torsion of an elliptical cylinder made of functionally graded anisotropic linear elastic material. The material moduli of the considered anisotropic non-homogeneous elastic bar are smooth functions of the axial coordinate. The contour of the elliptical cross section depends on the elastic constants. This dependence provides the zero warping property of the considered elliptical cross section. The obtained stress field is independent of the axial coordinate as in the case of Saint-Venant’s torsion problem, but the rate of twist depends on the axial coordinate.