Generalized surface Green's functions for an elastic half-space

Using generalized functions are constructed Green's functions for homogeneous elastic isotropic half-planes and half-spaces. Airy and Maxwell stress functions to find the Green's functions are used. One-dimensional and two-dimensional integral Fourier transforms to solve the boundary value problems are used. Taking into account the properties of generalized functions with a point support, singular components of displacement images are distinguished. It is shown that they correspond to the displacements of a rigid body. If there are no singular components, then the stresses and displacements coincide with the known classical solutions of the Flaman, Boussinesq and Cerutti problems.