Inverse Problem Analysis of Thermal Deformation for a Nonhomogeneous Solid Cylinder under Axisymmetric Unsteady Heating

This paper deals with an inverse problem analysis of thermal deformation in a transient state for an infinitely long solid cylinder with nonhomogeneous material properties in a radial direction. Assuming that the solid cylinder is heated axisymmetrically by the unknown temperature function of the surrounding media, we have analyzed the inverse problem with the object of determination of the temperature function for the surrounding media so as to satisfy the prescribed transient thermal displacement component in the radial direction of the cylinder. The problems of transient heat conduction and the associated axisymmetric thermoelastic field are coupled for the theoretical developments, then the solutions of the temperature function for the surrounding media, the temperature change and the associated thermal stresses, thermal deformations for the cylinder are evaluated by making use of the method of Laplace transform. Thereafter, the numerical results for the temperature change and the stress distributions are shown in figures.