On the thermoelastic problem of uniform heat flow disturbed by a circular rigid lamellate inclusion

Abstract

A complete solution in elementary functions is given for the three-dimensional thermoelastic ï¬eld in an elastic space, containing an absolutely rigid circular inclusion (anticrack) under a normally incident uniform heat flow. The inclusion is assumed to be slightly conducting, with a certain thermal resistance. The analysis is based on the potential theory method. The resulting boundary-value problems are reduced to classical mixed problems of the potential theory. The temperature, fluxes, thermal stresses and displacements in the inclusion plane are given in closed forms and interpreted from the point of view of the failure theory.