Multi-field coupling solutions of functionally graded two-dimensional piezoelectric quasicrystal wedges and spaces

Abstract

Quasicrystal materials have aroused extensive attentions of researchers due to their excellent properties. In this paper, for the first time, functionally graded two-dimensional piezoelectric QC wedges and spaces which subjected to line force, charge or dislocation are investigated. By virtue of equilibrium and constitutive equations, the real form expressions of stresses and displacements are directly derived without introducing complex vectors. All expressions can be degraded to the classical solutions of homogeneous materials when material parameters have no concern with angle. Before the numerical results are presented, the comparative study between solutions of homogeneous materials from Stroh formalism and solutions of homogeneous materials from our method is performed to verify the accuracy of the formulation and numerical procedure. The mechanical behaviors of QC wedges and spaces under different loads are analyzed carefully by numerical examples. The numerical results reveal that the variations of stress and displacement in each field have much to do with the wedge angle and boundary conditions; line force has little effect on lattice rearrangement. Moreover, the numerical results can be used as references in engineering application when analyzing functionally graded materials.