On temperature and stresses in a thermoelastic half-space with temperature dependent properties

Abstract

The paper deals with the axisymmetric problem of the thermoelastic half-space with temperature dependent properties. The thermal coefficients: heat conductivity and coefficient of linear expansion are assumed to be functions of temperature. The mechanical properties: Young modulus and Poisson ratio are taken into account as constants. Two cases of boundary conditions are considered: a normal heat flux acting on a circle with given radius and two variants of the boundary conditions on the outside of the heated region: (1) a thermal insulation, or (2) a constant temperature, taken as reference. The boundary is assumed to be free of mechanical loadings. The linear dependences of thermal properties on temperature is considered as a special case. The obtained exact results are presented in the forms of multiple integrals and the detailed analysis are derived for linear dependences of the thermal properties on temperature.