Study of uniqueness and stability of solution of transient problem of thermoelasticity for hollow orthotropic cylinder under nonlinearity of contact thermal resistance (Q2759472)

A hollow cylinder is placed into a rigid becket; temperatures at its inner surface and that of the becket are prescribed. Thermal resistance between the cylinder and the becket is some experimentally determined function of gap thickness and contact pressure. The problem of determination of temperature and stresses in cylinder is described by one-dimensional non-stationary equation of heat conduction for temperature and one-dimensional quasistatic equation for elastic displacement under nonlinear boundary conditions. By application of Laplace transform with respect to time, a system of Volterra-Hammerstein equations was obtained and solved numerically. It was found that when there exist one or two stationary solutions they are asymptotically stable. If three solutions exist, the middle of them is unstable and the outermost ones are asymptotically stable.