On the thermal stresses of a semi-infinite plate with a circular inclusion under uniform heat flow

Abstract

The present paper gives a theoretical solution for a semi-infinite plate with a circular hole, which is filled with an elastic inclusion of another material, and subjected to uniform heat flow of the temperature gradient μ in the direction of the straight edge. The analysis is developed on the basis of the Airy's stress function in the generalized plane stress and by applying the bipolar coordinates. Here the plate is supposed to be insulated and the boundaries are free from the traction. The method of perturbation is adopted for the determination of unknown coefficients involved in the solution. Numerical calculations about the stress distributions along main parts of the semi-infinite plate and the inclusion are worked out in some detail, in order to clarify the effects of an inclusion. The maximum stresses on the common boundary are also calculated and compared with the results available.