Anti-plane crack problem of a functionally graded piezoelectric materials strip with arbitrarily distributed properties

This paper treats the anti-plane crack problem of a functionally graded piezoelectric material (FGPM) strip with arbitrarily distributed properties. It is assumed that the elastic stiffness, piezoelectric constant, and dielectric constant of the FGPM vary continuously along the thickness of the medium, and the strip is under anti-plane mechanical and in-plane electric impact loadings. By using the Fourier transform and defining unknown discontinuous functions across the crack surfaces, the anti-plane crack problem of FGPM is reduced to a group of singular integral equations, which are solved numerically. The stress and electric displacement intensity factors are presented, and the influences of the nonhomogeneous and geometric parameters on stress and electric displacement intensity factors are also included.