Fundamental solution of a power-law orthotropic and half-space functionally graded material under line loads

The problems of a power-law orthotropic and half-space functionally graded material (FGM) subjected to a line load are studied. The material is assumed to be linearly elastic and locally orthotropic. The material properties vary with the depth according to a power-law function. The governing partial differential equations are solved exactly in terms of elementary functions. The analytical solutions of the stress and the displacement fields are derived, which have the forms similar to those of functionally graded isotropic materials.