Thermal stresses and thermal expansion in a uniformly heated functionally graded cylinder

The exact solution is derived for the problem of uniformly heating a cylinder whose elastic moduli and thermal expansion coefficient vary linearly with radius. The solution shows that the radial and tangential stresses are largest in magnitude at the center of the cylinder whereas the deviatoric stress is largest in magnitude at the outer edge of the cylinder The effective thermal expansion coefficient is found to be essentially given by the volumetric average of the local thermal expansion coefficient, with the variation in moduli having only a small effect. In the case of a material with uniform moduli but a spatially variable thermal expansion coefficient, the effective thermal expansion coefficient is exactly equal to the volumetric average; this result is an extension of those derived by Levin and Schapery for n-component materials.