Thermal stresses in a functionally graded rotating disk: An approximate closed form solution

Abstract

The purpose of this study is to analyze a circular annulus made of a functionally graded material (FGM) subjected to thermomechanical loading. The governing nonlinear differential equation for heat transfer, comprising of all the modes of heat transfer, such as conduction, convection, radiation, and internal heat generation, was formulated and then solved using the homotopy perturbation method (HPM). The stress field in the circular annulus due to thermomechanical loading was obtained using a HPM based approximate closed-form solution for a steady-state nonhomogeneous temperature field coupled with the solution of the classical theory of elasticity. The present work considered both Dirichlet and Neumann boundary conditions. A rigorous study on the effect of various thermomechanical parameters and grading parameters on temperature as well as the stress field is presented. The present approximate closed-form solution was validated with the finite element method (FEM) based solution. The close agreement between HPM based solutions of this work with the results of the ANSYS based FEM confirms the effectiveness and the viability of the present solution method for a FGM rotating disk with multiple variable nonlinearities. The present closed-form solution is more rational and computationally efficient over FEM and other numerical solutions.

Keywords:

• Functionally graded materials (FGM)
• generalized boundary conditions
• homotopy perturbation method (HPM)
• rotating disk
• thermal stresses
• variable thermal parameters

Acknowledgment

The authors are grateful to Dr. Satyabratta Sahoo, Dept. of Mechanical Engineering, IIT(ISM) Dhanbad and the reviewers for their critical comments and suggestions that greatly improved the manuscript.