Stationary Temperature Field Ensuring the Absence of Thermal Stresses in an Inhomogeneous Rectangular Beam

Abstract

We consider the inverse problem of thermoelasticity for a long inhomogeneous rectangular beam under the conditions of constant axial strains in the presence of a stationary temperature field and convective heat exchange with ambient media. The elastic and thermal characteristics of the beam material in its cross section are arbitrary functions of coordinates. We establish the formulas for the temperature distributions on the lateral surfaces of the beam, heat-transfer coefficients, and densities of the internal heat sources guaranteeing the absence of thermal stresses in the beam. We also deduce analytic dependences of the thermal conductivity and the coefficients of linear thermal expansion on the coordinates corresponding to the absence of stresses in the beam without internal heat sources.