An axisymmetric problem of elasticity theory for a transversely isotropic inhomogeneous half-space

The problem of the equilibrium of a transversally-isotropic half-space which is non-homogeneous is depth under the influence of perpendicular forces applied to the boundary is discussed. A method of solution, based on the integral transformation with respect to certain variables, and on a special approach to the system of ordinary differential equations which arises is proposed. The case where Young's and the shear moduli vary exponentially with depth, and Poisson's ratios are constant is considered as an example.