Analytical solutions for two-dimensional piezoelectric quasicrystal composite wedges and spaces

Abstract

Quasicrystals have aroused great interest and argument among researchers due to their unique atomic configurations. In this paper, based on the Stroh formalism and Barnett-Lothe matrices, we investigate the problems of two-dimensional piezoelectric quasicrystal composite wedges and spaces subjected to different loadings, such as line force and line dislocation. The special cases of the semi-infinite spaces, infinite spaces, and bi-material composite spaces are also taken into consideration. We derive the analytical expressions of displacements and stresses by considering the continuities of the displacements and surface tractions on the radial plane. After that, the comparative study regarding the infinite space problem, between solutions from Green’s function and solutions from our method, is performed to verify the accuracy of the formulation and numerical results. Numerical examples are given to present the mechanical behaviors of quasicrystal under different loadings. The results prove that line force affects phonon displacement more clearly than phason displacement, but line dislocation affects stresses and electric displacement little.