Determination of thermostressed state of cylindrical bodies with multilayer inhomogeneous coatings

The method of determining the thermal stress state in a long cylinder with the inhomogeneous in the radial direction multilayer coating under a constant force surface load and a given temperature field is proposed. The corresponding problem of uncoupled thermoelasticity in terms of stresses is reduced by direct integration of the equations of equilibrium and compatibility to a set of integral equations relative to radial stresses and the sum of radial and circular stresses. The approximate analytical solutions to these integral equations were obtained taking into account the thinness of each coating layer. The method was verified by comparison with the results obtained from the exact solutions of the cor¬responding thermoelasticity problem for the power-law dependence of the thermomechanical characteristics of the coating materials on the radial variable. The method can be applied to determine the thermal stress state of the relatively thick coatings which consist of a large number of thin ones.