Steady-State Thermal Analysis of Functionally Graded Rotating Disks Using Finite Element and Analytical Methods

A steady-state thermal analysis for a hollow and axisymmetric functionally graded (FG) rotating disk with a uniform thickness was performed in this study. In the studied FG disk, metal and ceramic materials were considered for the inner and outer surfaces, respectively, when the material properties varied along the radial direction but not through material thickness variations. A power law distribution was employed to represent the material properties. Three different methods were used to present the temperature distribution along the radial direction of the FG disk, namely (1) an in-house finite element (FE) program, (2) the ANSYS parametric design language (APDL), and (3) an analytical solution. Furthermore, the in-house FE program presented the thermal stress and thermal strain of the FG disk. The weighted residual method in the FEM was used to present the temperature distribution when the material properties along an element are varying in contrast with using a commercial finite element software when the material properties are constant within an element to simulate FGMs. The accuracy of the in-house FE program was tested, and it was shown that the temperature distributions obtained by using the abovementioned methods were exactly the same. A parametric material gradation study was performed to understand the effects on the temperature, thermal strain, and stress. The material gradation was found to have a significant effect in this regard. The in-house finite element program enables one to perform a post-processing analysis in a more efficient and convenient manner than that through simulations in a finite element software program such as ANSYS. Lastly, this in-house code can be used to perform an optimization analysis to minimize the thermal strain and stress while the stiffness of the plate is maintained when the material properties within an element vary.