Boundary conditions for axisymmetric circular cylinder in one-dimensional hexagonal quasicrystals

Through generalizing the method of a decay analysis technique determining the interior solution developed by Gregory and Wan, a set of necessary conditions on the end-data of axisymmetric circular cylinder in one-dimensional (1D) hexagonal quasicrystals (QCs) for the existence of a rapidly decaying solution is established. By accurate solutions for auxiliary regular state, and using the reciprocal theorem and general solution, these necessary conditions for the end-data to induce only a decaying elastostatic state (boundary layer solution) will be translated into appropriate boundary conditions for the circular cylinder with axisymmetric deformations in 1D hexagonal QCs. The results of the present paper enable us to establish a set of correct boundary conditions, most of which are obtained for the first time. Furthermore, corresponding necessary conditions for the case of axisymmetric circular cylinder with transversely isotropic are derived subsequently, and their isotropic elastic counterparts are also obtained. The accuracy of mixed boundary conditions of isotropic axisymmertic circular cylinder is proved at last.