Elastic Ellipsoidal Inclusion in a Body Under the Action of Constant Temperature on Their Boundary

We obtain the exact solution of a system of three singular integrodifferential equations of a thermoelastic problem for the space containing an elastic heat-conducting ellipsoidal inclusion. It is assumed that the temperature on the interface of the matrix and inclusion is constant. As a result, we deduce the formulas for the stress concentration near the inclusion, stresses inside the inclusion, and the stress intensity factors KI for an elliptic crack and for a perfectly rigid lamellar elliptic inclusion. The influence of the shape of the inclusion on the stress concentration is analyzed in some special cases.