On the Stress State of a Heterogeneous Plate Made of a Material with a Step Change in Elastic Characteristics in the Presence of an Inclusion System and Temperature Influence

Abstract

In the formulation of thermoelasticity and in the framework of the conventional theory of thermal stresses, the problem on the stress state of an elastic piecewise-homogeneous plane or an infinite plate at non-uniform steady-state heating is considered. On the interface of dissimilar materials, the compound plane is reinforced by a collinear system of absolutely rigid thin inclusions and is subjected to mechanical and thermal influences. First, to determine the temperature distribution in a piecewise-homogeneous plane the corresponding boundary value problem of the theory of steady-state heat conduction is solved using the integral Fourier transform. Solving this problem is reduced to solving a singular integral equation (SIE) that allows an exact solution. Further, the elastic displacements of points of the compound plane, caused by mechanical and temperature influence, are determined by the known methods of thermoselasticity. Based on these results, solving the problem of the contact interaction between the system of inclusions and a compound plane is again reduced to solving SIE, which also allows an exact solution. A special case is considered.