Elastic solution for a hole in an infinite space

Dear All,

the solution of an elastic half space subjected to any generalized load may be seen as the solution of anotherelastic problem, that is elastic space with an infinite length hole when the hole radius goes to infinite.

Is there a "general" solution for thatelastic problem? For general I mean a solution that can be used e.g. like a kernel in a convolution operation.

I've expanded the Navier equation in cylindrical coordinate (radial, theta,z), with a Fourier approach; assigning periodicity to theta variable and the "square summability" along the z-direction, the problem is reduced to the r-direction.

However I'm not able to de-couple the displacements in order to obtain a Bessel-like equation... therefore the question!

Thanks for any suggestions!

MS