Solutions for behavior of a functionally graded thick-walled tube subjected to mechanical and thermal loads

Abstract

For the problem of a functionally graded thick-walled tube subjected to internal pressure, we have already presented the elasticity solution based on the Voigt method with the assumption of a uniform strain field within the representative volume element. This paper discusses the thermoelastic problem of the functionally graded thick-walled tube subjected to both axisymmetric mechanical and thermal loads, and gives the solution in terms of volume fractions of constituents. We assume that the tube consists of two linear elastic constituents and the volume fraction of one phase is a power function varied in the radial direction. The theoretical solutions of the displacement and the stresses are presented under the assumption of a uniform strain field within the representative volume element. Comparisons of the theoretical solutions and the finite element analysis demonstrate the validity of the assumption. Based on the relation of the volume average stresses of constituents and the macroscopic stresses of the composite material in micromechanics, the present method can avoid the assumption of the distribution regularities of unknown overall material parameters appeared in existing papers. Further, the present method is valid for the materials with different Poisson׳s ratios of constituents. The effects of the volume fraction, the ratio of two thermal expansion coefficients and the ratio of two thermal conductivities on the displacement and stresses are systematically studied.