Inverse problem on the identification of temperature and thermal stresses in an FGM hollow cylinder by the surface displacements

A problem on the identification of time-dependent temperature on one of the limiting surfaces of a radially inhomogeneous hollow cylinder is formulated and solved under the temperature and radial displacement given on the other limiting surface. The analysis of temperature and thermal stress distribution in the cylinder is performed. The solution has been constructed by the reduction to an inverse thermoelasticity problem. By making use of the finite difference method, a stable solution algorithm is suggested for the analysis of inverse problem. The solution technique is verified numerically by making use of the solution to a relevant direct problem. It is shown that the proposed technique can be efficiently used for the identification of a heat flux or unknown parameters (the surrounding temperature or the heat-exchange coefficient) in the third-kind boundary conditions.