The Stress and Displacement Fields Produced in a Semi-Infinite Solid by a Uniform Heat Source Over a Rectangular Area on the Surface

An important problem in thermo-mechanical contacts is the determination of the stress and displacement fields caused by heat flow. Heat flow may come from a difference in temperature between the contacting solids, or from frictional heating at the sliding interface. Generally, the distribution of heat flow in a contact area is unknown. In many cases, however, it is approximately uniform or one may divide the contact area into small parts, and in each part the heat flow may be treated as approximately uniform. This work provides closed-form solutions of the stress and displacement fields in a semi-infinite solid caused by uniform steady-state heat flow over a rectangular area on the surface. The material is assumed to be homogeneous and isotropic.