Thermoelastic Analysis of a Functionally Graded Rotating Thick-Walled Tube Subjected to Mechanical and Thermal Loads

Abstract

A thermoelastic solution for the functionally graded rotating thick-walled tube subjected to axisymmetric mechanical and thermal loads is given 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. By using the assumption of a uniform strain field within the representative volume element, the theoretical solutions of the displacement and the stresses are presented. 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, such as Young's modulus, thermal expansion coefficient, thermal conductivity, and density. The effects of the angular velocity, the volume fraction, the ratio of two thermal expansion coefficients, the ratio of two thermal conductivities, and the ratio of two densities on the displacement and stresses are systematically studied, which should help structural engineers and material scientists optimally design thick-walled tube comprised inhomogeneous materials.

Thermomechanical responses of functionally graded cylinders

“…Many of the studies deal with temperature, displacement and stress distribution of functionally graded hollow cylinders with different solution procedures. The solution methods used in the literature can be listed as: the perturbation method [2], the direct method [3], a novel limiting approach [4], generalized Bessel function and Fourier integral [5], Fredholm integral equation [6], a tolerance averaging approach [7], Differential quadrature method [8], representative volume element [9], the multilayer semi-analytical method [10], complementary functions method [11], the direct method and finite element method [12], an approximate method for a cylinder divided into N layers [13], the non-linear shooting method and the Runge-Kutta fourth-order algorithm [14].…”