An Analytical Solution for Temperature Distribution and Thermal Strain of FGM Cylinders with Varying Thickness and Temperature-Dependent Properties Using Perturbation Technique

Document Type : Research Paper


1 Faculty of Mechanical And Mechatronics Engineering, Shahrood University of Technology, Semnan,Iran

2 Department of Mechanical Engineering, Shahrood University of Technology, Shahrood, Iran,


This research presents temperature distribution and thermal strain of functionally graded material cylinders with varying thickness and temperature-dependency properties that are subjected to heat fluxes in their inner and outer layers. The heterogeneous distribution of properties is modeled as a power function. Using first-order temperature theory and the energy method, governing equations are extracted. The system of governing differential equations is a system of nonlinear differential equations with variable coefficients, which are solved by using the analytical method of the matched asymptotic expansion of the perturbations technique. Results obtained from temperature distribution, heat flux, and thermal strain for different heterogeneous constants and temperature-dependency properties are discussed. They show that heterogeneity has a significant impact on the temperature field and thermal strain inside functionally graded cylinders. Moreover, it is observed that heterogeneity has no impact on the direction of heat flux vector inside the body; however, any changes in heterogeneity would change the magnitude of heat flux. The results obtained from the analytical method were compared with those of previous studies and FEM, which showed good agreement.


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Volume 51, Issue 1
June 2020
Pages 144-156
  • Receive Date: 28 December 2019
  • Revise Date: 07 May 2020
  • Accept Date: 20 May 2020