On integration of the Green function in a discontinuous temperature field in a 2D domain

The paper discusses the problem of Green's functions application to stress calculations in the case of a discontinuous temperature field acting in a 2D domain. It is proved that the double integral of the Green function for the stresses does not exist. A new method of finding iterrated integrals of Green's functions which enables obtaining correct functions for the stress $\sigma_{\alpha\beta}$ is presented as well.