Axisymmetric Loading of a Class of Inhomogeneous Transversely Isotropic Half-Spaces with Quadratic Elastic Moduli

Some axisymmetric problems are considered for a class of inhomogeneous anisotropic elastic materials for which the elastic moduli vary continuously as a quadratic function of the spatial coordinates. For a restricted class of transversely isotropic materials, loading of a half-space and a layer on a rigid foundation are considered and integral expressions for the displacement and stress are obtained. Particular attention is given to cases when the values of the elastic moduli near to the plane boundary of the half-space and the layer approach zero. Numerical results are obtained for some example transversely isotropic and isotropic materials.