Axially Symmetric Thermal Stresses in a Semi-Infinite Solid

In a semi-infinite solid the problem of determination of the thermal stresses caused by a known initial heat source throughout the solid and a known time dependent heat source on the surface is considered. The heat sources are taken as axially-symmetric, and the physical properties of the solid are assumed to be constant. The equation of heat conduction is first integrated in order to obtain the temperature distribution throughout the solid. This result is then used in the equations of elastic equilibrium ex9ressed in terms of the displacements. The latter equations are integrated and integral expressions for the displacements are obtained. Conditions for convergence are discussed, and the integrals are evaluated for special choices of the initial and boundary heat sources.