The Exact Deformation Theory of Two-Dimensional Dodecagonal Quasicrystal Shaft
Cheng’s refined theory is extended to investigate torsional circular shaft of two-dimensional dodecagonal quasicrystal (2D dodecagonal QCs), and Lur’e method about harmonic function is extended to harmonic function in the respective cylindrical coordinate. The exact deformation of torsional circular shaft of 2D dodecagonal QCs under reverse direction surface loading is proposed on the basis of the classical elasticity theory and stress-displacement relations of 2D dodecagonal QCs, and the exact deformation 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 2D dodecagonal QCs under reverse direction surface. To illustrate the application of the theory developed, one example is examined.
B. S. Zhao et al., "The Exact Deformation Theory of Two-Dimensional Dodecagonal Quasicrystal Shaft", Advanced Materials Research, Vol. 213, pp. 276-280, 2011