An elasticity solution of a nonhomogeneous half-plane problem

We employ fundamental equations of non-homogeneous elasticity and Fourier integral transformations to obtain the general solutions of the stress function. On the basis of these points of view and when the forces on the boundary are arbitrary for non-homogeneous half-plane problems with the Young’s modulus E(x)=E₀expβx], accurate solutions are obtained. At last with the degeneracy it is obtained that the famous Boussnesq solution and this method is successful.