Semi-exact elastic solutions for thermo-mechanical analysis of functionally graded rotating disks

In this paper, distributions of stress and strain components of rotating disks with non-uniform thickness and material properties subjected to thermo-elastic loading under different boundary conditions are obtained by semi-exact methods of Liao’s homotopy analysis method (HAM), Adomian’s decomposition method and He’s variational iteration method (VIM). The materials are assumed to be perfectly elastic and isotropic. A two dimensional plane stress analysis is used. The distribution of temperature over the disk radius is assumed to have power forms with the higher temperature at the outer surface.The results of the three methods are compared with those obtained by Runge–Kutta’s numerical method that shows good agreement. This verifies the implementation of the proposed methods and demonstrates the applicability of the HAM, ADM and VIM to provide accurate solution for a complicated case with no exact solution. It is also shown that the rate of convergence of ADM is faster than that of VIM and modified HAM; whereas the rates of convergence of VIM and modified HAM are approximately same.

► Distributions of stress and strain components of FGM rotating disks subjected to thermo-elastic loading are obtained.
► Homotopy analysis, Adomian’s decomposition and He’s variational iteration methods have been utilized.
► The results of the three methods are compared with those obtained by Runge–Kutta’s method that shows good agreement.
► The rate of convergence of modified HAM is faster than that of VIM; while that of ADM is faster than the rate for MHAM.