Thermo-Elastic Static Behavior of Functionally Graded Shafts with Different Material Gradation Patterns

Improvement of new engineering materials is a prime challenge and an important research topic for material scientists and engineers. Functionally graded materials (FGMs) are developed as multifunctional, advanced heterogeneous materials with the smooth and continuous variation of thermo-elastic properties along a preferred direction(s) following various grading patterns, and potential uses in high-temperature applications. Therefore, the present work aims to present an analytical solution for bending and buckling behavior of FG shaft (FGS) in thermal environments.

The thermo-elastic behaviors are based on Timoshenko beam theory (TBT). Here, silicon nitride (Si₃N₄) and Ti-6Al-4V are considered as ceramic and metallic constituents for the FGS respectively, assuming Ti-6Al-4V content decreases gradually from inner diameter towards the outer diameter. First, temperature-dependent, and radially graded properties are obtained according to linear/power/exponential laws. Next, using the 1-D Fourier heat conduction equation, a radial variation of temperature distributions (TDs) is obtained using different grading patterns for achieving desired temperature-dependent material properties. Equations of motions are then derived using Hamilton’s principle for bending and buckling behavior of FGS.

Based on the analytical formulation, a MATLAB code is developed, and various numerical problems are solved for bending and buckling behavior of FGS. Finally, numerical results are produced to examine the influences of material grading patterns, temperature gradients, end conditions, and slenderness ratio on the thermo-elastic bending and critical buckling temperature of the FGS.

Results show that the material grading patterns, and temperature gradients have significant impact on thermo-elastic responses of the FGS. The present results will help in developing more accurate analytical formulations of dynamics of the FGS subjected to different thermal loads.