GOVERNING EQUATIONS AND GENERAL SOLUTIONS OF PLANE ELASTICITY OF TWO-DIMENSIONAL DECAGONAL QUASICRYSTALS

Abstract

Two-dimensional problem is systematically investigated for the coupled equations in two-dimensional decagonal quasicrystals, and three general solutions are presented by an operator method. To simplify governing equations, each general solution shall take three different forms expressed in terms of three displacement functions, which satisfy partial three differential equations of second order. To illustrate its utility, the closed-form solutions are obtained for problems of point phonon forces and phason force acting at the apex of a quasicrystal wedge, all in terms of the general solutions. Furthermore, these solutions can be degenerated to those of problems of point forces applied on the boundary of a quasicrystal half-plane.