Boundary Conditions for Torsional Circular Shaft with Two-Dimensional Dodecagonal Quasicrystals

Abstract

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 torsional circular shaft in two-dimensional dodecagonal quasicrystals (2D dodecagonal QCs) for the existence of a rapidly decaying solution is established. By accurate solutions for auxiliary regular state, using the reciprocal theorem, 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 torsional circular shaft in 2D dodecagonal QCs. The results of the present paper enable us to establish a set of boundary conditions.