Exact Thermomechanical Analysis of Functionally Graded (FG) Thick-Walled Spheres

Abstract The present study aims to provide a deeper understanding for the thermo-mechanical analysis of spheres made of non-homogeneous isotropic materials. To this end, Navier equations are solved analytically based on the spherically-symmetric plain-strain assumptions and closed-form formulas are proposed for the elastic fields in a simple-power-law graded spheres subjected to steady-state thermal and internal/external pressure loads. A comprehensive parametric study is then performed with both functionally-graded hypothetical and physical materials. Two benchmark examples are reconsidered with hypothetically chosen inhomogeneity indexes. Effects of inhomogeneity indexes are reviewed in these examples. Differently from the literature, thickness effects are also examined under separate and combined loads together with the thermo-mechanical behavioral differences in spheres and cylinders. Finally three physical metal-ceramic pairs are studied originally with appropriate inhomogeneity indexes which are defined as the inner surface is full ceramic and the outer surface is full metal. Results are presented in graphical and tabular forms.