The refined analysis about mechanical behavior for torsional circular shaft of cubic quasicrystal

Cheng's refined theory is extended to investigate torsional circular shaft of cubic quasicrystal, and Lur'e method about harmonic function is extended to harmonic function in the respective cylindrical coordinate. The refined theory of torsional circular shaft of cubic quasicrystal under reverse direction surface loading is proposed on the basis of the classical elasticity theory and stress-displacement relations of cubic quasicrystal, and the refined theory provides the solutions about torsional deformation of a circular shaft without ad hoc assumptions. Exact solutions are obtained for circular shaft from boundary conditions. Using Taylor series of the Bessel functions and then dropping all the terms associated with the higher-order terms, we obtain the approximate expressions for circular shaft of cubic quasicrystal under reverse direction surface. To illustrate the application of the theory developed, one example is examined.