ANALYTICAL TREATMENT OF AXISYMMETRICAL THERMOELASTIC FIELD WITH KASSIR'S NONHOMOGENEOUS MATERIAL PROPERTIES AND ITS ADAPTATION TO BOUNDARY VALUE PROBLEM OF SLAB UNDER STEADY TEMPERATURE FIELD

The method of an analytical development of thermoelastic problems for a medium with Kassir's nonhomogeneous material properties is developed. For isothermal problems of such a nonhomogeneous body, an analytical method of development has already been proposed by M. K. Kassir under the assumption that the shear modulus of elasticity G is changed arbitrarily with the variable z of the axial coordinate according to the relation G(z) = G_oz^m. However, the analytical procedure for the thermoelastic field has not been established. In this article, introducing the thermoelastic displacement potential function, the analytical method of development for the axisymmetrical thermoelastic field is established. As an illustrative example, we consider the thermoelastic problem of a slab. Assuming that the shear modulus of elasticity G, the thermal conductivity λ, and the coefficient of linear thermal expansion α vary with the variable [zcirc] of the dimension-less axial coordinate according to the relation G([zcirc]) = G_o[zcirc]^m, λ([zcirc]) = λ₀[zcirc]^l, α([zcirc]) = α₀[zcirc]ⁿ, the axisymmetric temperature solution in a steady state for the slab is obtained and the associated thermal stress components are evaluated theoretically. Numerical calculations are carried out for several cases, taking into account the variety of the nonhomogeneous material properties. Numerical results are shown graphically.