Derivation of systems of fundamental equations for a three-dimensional thermoelastic field with nonhomogeneous material properties and pts application to a semi-infinite body

A method of analytical development of three-dimensional thermoelastic probl ems for a medium with nonhomogeneous material properties is developed in th is article. Assuming that the shear modulus elasticity G, the thermal condu ctivity lambda, and the coefficient of linear thermal expansion alpha vary with the power product form of axial coordinate variable z and introducing two kinds of displacement functions and the thermoelastic displacement func tion, the system of fundamental differential equations for such a three-dim ensional field is established. As an illustrative example, we consider the thermoelastic problem of a semi-infinite body. The three-dimensional temper ature solution in a steady state is obtained and the associated components of thermal displacement and stress are evaluated theoretically. Numerical c alculations are carried out for several cases taking into account the varie ty of the nonhomogeneous material properties of G, lambda, and alpha, and t hese results are shown graphically.