Stress analysis in an orthotropic non-homogeneous strip sandwiched between two piezoelectric layers weakened by multiple cracks

In the present paper, the problem of multiple cracks in a non-homogeneous orthotropic layer bonded between two piezoelectric layers is considered. The shear modulus of the middle layer is considered for a class of functional forms for which the equilibrium equation has an analytical solution. The elastic shear modulus of the functionally graded orthotropic layer is considered to vary exponentially. The analysis is based on the stress fields caused by Volterra-type screw dislocation in the functionally graded orthotropic strip. The solution for dislocation is obtained by means of the complex Fourier transform. The dislocation solution is then employed as strain nuclei to derive singular integral equations for a medium weakened by multiple smooth cracks. The integral equations are of Cauchy singular type at the location of dislocation which are solved numerically for dislocation density functions. Several examples are solved and the stress intensity factors for multiple cracks with different configuration are obtained.