Determination of thermal stresses in a long hollow thermo-sensitive cylinder made of functionally-graded material under complex convective heat exchage

An uncoupled quasi-static problem of thermoelasticity for a hollow cylinder is solved, taking into account the temperature dependence of the thermomechanical characteristics of the functionally graduated material (FGM). Convective heat transfer with an exponential in­crease of the temperature over time through cylinder surfaces is considered. The nonlinear nonstationary boundary value problem of thermal conductivity is solved numerically by reducing it to the Cauchy problem for a system of ordinary differential equations, solved using backward differentiation formulas. The corresponding problem of thermoelasticity is solved using the method of direct integration by reducing it to Fredholm’s integral equations. The influence of the radial temperature dependences on thermophysical and mechanical characteristics of a two-component metal-ceramic FGM, the characteristics of which are described by the simple mixture model, on the thermal stress state of a hollow cylinder is investigated.