Refined theory of axisymmetric circular cylinder with transversely isotropic

To analyze the exact stress field and displacement field in axisymmetric circular cylinder with transversely isotropic, the refined theory of torsional deformation of a circular shaft was converted for being applicable to the case of axisymmetric circular cylinder with transversely isotropic. Without employing ad hoc assumptions, the refined theory of an axisymmetric circular cylinder with transversely isotropic could be applied, which would yield the solution of the cylinder directly from the general solution and Bessel function. With the homogenous boundary condition, the refined theory provided exact solutions which satisfied all of the governing equations. The exact solutions could be decomposed into two parts: the 1-orders equation and the transcendental equation. The solutions of two equations reflected directly the axially loading solution and the transcendental solution, respectively. The transcendental solution satisfied the boundary condition under self-equilibrated end loading, and the stress distribution on the end of the stress field could be known clearly.