Analysis of Temperature, Displacement, and Stress in Shafts Made of Functionally Graded Materials with Various Grading Laws

An exact solution for thermo-elastic analyses of radially graded circular hollow shafts made of functionally graded materials (FGMs) is studied. The material properties of functionally graded (FG) shafts are assumed to be temperature-dependent (TD) and graded in the radial direction according to various grading patterns such as linear law of material gradation (LLMG), power law of material gradation (PLMG), and exponential law of material gradation (ELMG). Temperature fields of radially graded FG shafts are obtained analytically for the different grading patterns, using a steady-state Fourier equation of heat conduction. Subsequently, based on linear strain-displacement relations, thermo-elastic equations are solved analytically to obtain displacement and stress fields as functions of radial distances, material gradient indices, and temperature gradients. The present mathematical derivations for thermo-elastic analyses and solution methods are successfully validated by comparing with the results of published literature. Numerical results are presented to highlight the importance of material parameters, temperature distributions, radial distances, and aspect ratios on the temperature profiles, displacement, and stress fields of the FG shafts under thermal/mechanical loads. The numerical results have explicitly shown that the thermo-elastic analyses of FG shafts are significantly influenced by material gradient indices, temperature gradients, and temperature-dependent properties in high-temperature environmental applications.