Axisymmetric Stress-Strain State of a Body with Thin Rigid Disk-Shaped Heat-Resistant Inclusion

We construct a solution of the problem of thermoelasticity for a body with thin rigid heat-resistant inclusion in the class of functions specifying the stress-strain state with constant displacements normal to the plane of inclusion at infinity. The inclusion is modeled by a boundary layer corresponding, from the mathematical viewpoint, to a sheet of moment dipoles and forces and the jump of radial displacements and stresses normal to the plane of inclusion serves as its mechanical manifestation. The solution of the heat-conduction and thermoelasticity equations with satisfying the requirement of continuous dependence of the solutions on boundary conditions is reduced to integral equations of the first kind and realized by the method of Neumann generalized series. We also determine the jump of normal stresses on the surfaces of the inclusion, which guarantees the realization of perfect mechanical contact between the rigid inclusion and the elastic matrix. © 2015, Springer Science+Business Media New York.