Contact stresses in an infinite plate containing a smooth circular insert under thermal load

Summary. A solution is presented for the contact problem with a smooth circular elastic insert in an infinite, linearly elastic plate under thermal load. The thermal load considered here includes the temperature gradient applied at infinity and a uniform temperature change. One of the major difficult parts in solving the present problem is that separation may occur between an insert or inclusion and the surrounding matrix under a nonuniform expansion of the matrix and the insert due to a temperature change. Based on the complex potential theory and the method of analytical continuation, the problem is reduced to a singular integro-differential equation which is solved numerically. Results are presented for the contact angle and for the normal and circumferential stresses at the plate-insert interface. Exact solutions are found for the current problem for a special case when the material properties of the plate and the insert are identical.