The radially nonhomogeneous thermoelastic axisymmetric problem

Abstract

The plane axisymmetric thermoelastic problem with axisymmetric geometry, loading and temperature field is studied. Considering the radial dependence of the stress, displacement fields, of the stiffness matrix and the linear thermal expansion coefficient, after a series of admissible functional manipulations, the general differential system solving the radially nonhomogeneous circular cylinder results. The exact thermoelastic solution is proposed for a radially nonhomogeneous hollow circular cylinder of exponential shear modulus and constant Poisson ratio and also for a radially nonhomogeneous hollow circular cylinder of power law shear modulus and constant Poisson's ratio. For the isotropic elastic axisymmetric thermoelastic problem, a general solution is derived. Defining the elastic reduced stress, strain and displacement fields and using the nonhomogeneous compatibility equations of strain and the equilibrium equations of the thermoelastic problem, a nonhomogeneous differential equation in terms of the reduced displacements field, results. In the cases that the shear modulus is expressed by an exponential or a power law form, the displacements and stress fields are deduced analytically. Two applications have been performed for a radially nonhomogeneous hollow cylinder where the stress and displacements fields are determined for thermal loading.