Exact solution of two collinear cracks normal to the boundaries of a 1D layered hexagonal piezoelectric quasicrystal

Abstract

The electroelastic problem related to two collinear cracks of equal length and normal to the boundaries of a one-dimensional hexagonal piezoelectric quasicrystal layer is analysed. By using the finite Fourier transform, a mixed boundary value problem is solved when antiplane mechanical loading and inplane electric loading are applied. The problem is reduce to triple series equations, which are then transformed to a singular integral equation. For uniform remote loading, an exact solution is obtained in closed form, and explicit expressions for the electroelastic field are determined. The intensity factors of the electroelastic field and the energy release rate at the inner and outer crack tips are given and presented graphically.

Keywords:

• Quasicrystals
• collinear cracks
• triple series equations
• electroelastic field
• intensity factors
• energy release rate

Notes

No potential conflict of interest was reported by the authors.

Additional information

Funding

This work was Central South University Doctoral Student Innovation Project [No. 2017zzts085].