An Electrically Permeable Mode-Iii Nano-Elliptical Hole Embedded In One-Dimensional Hexagonal Piezoelectric Quasicrystals With Surface Effect

Under the electrical permeable boundary condition, an antiplane problem of a nano-elliptic hole and a nano-crack in one-dimensional (1D) hexagonal piezoelectric quasicrystals (PQCs) with surface effect is studied. Exact solutions of phonon stresses, phason stresses and electric displacement are obtained by using the technique of conformal mapping and the method of complex variable function. The special case such as nano-crack can be reduced from the present model. The effects of surface layer properties, elliptic hole aspect ratio and crack length on generalized stress and field intensity factor near the crack tip under different electrical boundary conditions are analyzed show by numerical examples. The results show that the surface effect and the electrically permeable boundary have great influence on field concentration of the nano-hole and the field intensity factor of the crack. This method is universal and can be used to optimize the design of PQC nanocomposites in engineering practice.