Guaranteeing the Absence of Radial Stresses in a Long Hollow Cylinder by the Inhomogeneity of Material

We propose a method for the determination of the thermomechanical characteristics of a functionally graded material guaranteeing the absence of radial stresses in a long hollow cylinder inhomogeneous along the radius if the mass forces are equal to zero. Under given thermal loads applied to the surfaces, we deduce an exact analytic formula playing the role of the condition of vanishing of radial and circumferential stresses in the cylinder and connecting the coefficients of linear thermal expansion, thermal conductivity, Poisson’s ratio of the material, axial loads, and temperature fields. The numerical analysis of the thermomechanical characteristics of an actually existing two-component material is performed on the basis of the Voigt model of simple mixture.