Force at a point in the interior of a layered elastic half space

This study formulates, by the technique of integral transforms, the solution of a layered half space subjected to a concentrated force which may act either vertically or horizontally in the interior of the system. Accurate approximations of the reciprocals of the common denominators in the solution integrals are suggested in such a way that the latter are in standard closed forms and can be identified by two parts. The first part is the singular part of Mindlin's solution which is singular at the point of application of the force, and the second is non-singular. The solutions for plane problems are also obtained in closed forms by performing appropriate integrations of the solutions for the corresponding three-dimensional cases.