Scattering of anti-plane stress waves by a crack in a non-homogeneous orthotropic medium

Scattering of anti-plane harmonic waves by a finite crack in the functionally graded orthotropic medium is investigated by means of the Schmidt method. By using the Fourier transform and defining the jump of displacement components across the crack surface as the unknown function, a pair of dual integral equations are derived. To solve the dual integral equations, the jump of the displacement components across the crack surface is expanded in a series of Jacobi polynomial. The dynamic stress intensity factor is obtained as functions of the incident wavelength, gradient parameter of the functionally graded materials. Numerical examples are provided to show the effects of material properties upon the dynamic fracture behavior of the functionally graded materials.