Quasistatic Thermoelastic State of a Layered Functionally Graded Cylinder with Regard for Thermal Radiation

We propose a methodology aimed at determining the quasistatic thermoelastic state of layered cylinders with functionally graded components with regard for the presence of thermal radiation. The solution of the problem of heat conduction involves the approximation of thermal characteristics by piecewise constant functions of the radial coordinate and determination of temperatures of the bounding surfaces at fixed times according to the linear recurrence relations. In this case, we use the Green function of the nonstationary problem of heat conduction for a multilayer cylinder, linear splines, and generalized functions. The strains and stresses are found by using the analytic solution of the system of integro-algebraic equations of the problem of thermoelasticity in displacements. This solution was obtained by the method of successive approximations restricted to the first approximation. The solution of the problem of thermoelasticity for a cylinder with piecewise-constant physical and mechanical characteristics is chosen as the zero-order approximation. The results of numerical analyses performed for a three-layer cylinder are presented.