Contact stresses in an infinite plate containing a rigid circular inclusion under thermal loads

Summary

The problem of an infinite plate containing a rigid circular inclusion under thermal loads is solved in this paper. The thermal loads considered here include 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 non-uniform expansion of the matrix due to a temperature change. Unlike the corresponding problem with perfect contact along the interface between the inclusion and the surrounding matrix, there is no exact solution available for the current problem with incomplete contact. Based on the complex potential theory and the method of analytical continuation, a Prandtl type of integro-differential equation corresponding to the incomplete contact problem is derived. By expressing the normal stress function in terms of series form, the system of simultaneous equations is then established and solved numerically. Numerical results of the normal compressive stress and the circumferential stress for different thermal loading conditions are discussed in detail and shown in graphic form.