LAUSR

The three-dimensional QCs include icosahedral QCs and cubic QCs. Cubic QC has a 3D structure quasiperiodic in three orthogonal directions that supports simultaneously phonon and phason fields [1]. Feng et al. [2–4] have reported cubic QCs with cubic symmetry and Wang et al. [5] have discussed the projection description of the cubic QCs. Yang et al. [6] have studied the linear elasticity theory. There are still many physical properties of the cubic quasicrystals which have not been studied yet. In the literature, there is not much work on solutions of the cubic QCs. For elasticity problems of cubic QCs, a large number of analytical results have been obtained for static cases. In [7–9], plane problems with simpler structure of the cubic QCs have been studied for static case. Based on the complex potential method, plane problems of cubic QC media containing an elliptic hole subjected to uniform remote loadings have been solved in [7]. Equations of plane elasticity of cubic QCs have been simplified to an eighth-order partial differential governing equation and general solutions have been established by using an operator method [8]. The problem of an infinite plane which is composed of two halfplanes with different cubic QC has been investigated in [9]. A method for analyzing the static elasticity problem of cubic QC has been given and the solutions of elastic field of cubic QC with a penny-shaped crack have been obtained in [10]. The equations of wave propagation in the cubic QCs and the analytical expression of the phase velocity of wave propagation have been derived in [11]. Based on the variation of the general potential function of QCs, the 3D finite element formulation for cubic QCs has been developed in [12].