Transient thermoelastic analysis of FGM rotating thick cylindrical pressure vessels under arbitrary boundary and initial conditions

Document Type : Research Paper


1 Mechanical Engineering Department, Yasouj University, P.O.Box: 75914-353, Yasouj, Iran

2 Mechanical Engineering Department, Yasouj University, Yasouj, Iran

3 School of Mechanical Engineering, College of Engineering, University of Tehran, Tehran, Iran


Assuming arbitrary boundary and initial conditions, a transient thermo-elastic analysis of a rotating thick cylindrical pressure vessel made of functionally graded material (FGM) subjected to axisymmetric mechanical and transient thermal loads is presented. Time-dependent thermal and mechanical boundary conditions are assumed to act on the boundaries of the vessel. Material properties of the vessel are assumed to be graded in the radial direction according to a power law function. The Poisson’s ratio is assumed to be constant. Method of separation of variables has been used to analytically calculate the time dependent temperature distribution as a function of radial direction. In a case study, the distribution of radial and hoop stresses along the thickness is derived and plotted. In order to validate the model, the analytical results have been compared with finite element method modeling results presented in literature. Any arbitrary boundary and initial conditions can be handled using the equations derived in the present research. In order to investigate the inhomogeneity effect on time dependent stress distribution and displacements, values of the parameters have been set arbitrary in the present study. To the best of the authors’ knowledge, in previous researches, transient thermo-elastic analysis of thick cylindrical FGM pressure vessels is investigated by numerical methods, while in the present research, an exact solution is derived for the same problem.


Main Subjects

[1]          M. Yamanouchi, M. Koizumi, T. Hirai, I. Shiota, FGM-90, in Proceeding of.
[2]          A. H. Sofiyev, Influences of shear stresses on the dynamic instability of exponentially graded sandwich cylindrical shells, Composites Part B: Engineering, Vol. 77, pp. 349-362, 2015.
[3]          M. Ghannad, G. H. Rahimi, M. Z. Nejad, Elastic analysis of pressurized thick cylindrical shells with variable thickness made of functionally graded materials, Composites Part B: Engineering, Vol. 45, No. 1, pp. 388-396, 2013.
[4]          M. Zamani Nejad, A. Afshin, Transient thermoelastic analysis of pressurized rotating disks subjected to arbitrary boundary and initial conditions, Chinese Journal of Engineering, Vol. 2014, 2014.
[5]          M. Z. Nejad, M. D. Kashkoli, Time-dependent thermo-creep analysis of rotating FGM thick-walled cylindrical pressure vessels under heat flux, International Journal of Engineering Science, Vol. 82, pp. 222-237, 2014.
[6]          M. Z. Nejad, A. Rastgoo, A. Hadi, Effect of exponentially-varying properties on displacements and stresses in pressurized functionally graded thick spherical shells with using iterative technique, Journal of Solid Mechanics, Vol. 6, No. 4, pp. 366-377, 2014.
[7]          M. Z. Nejad, A. Rastgoo, A. Hadi, Exact elasto-plastic analysis of rotating disks made of functionally graded materials, International Journal of Engineering Science, Vol. 85, pp. 47-57, 2014.
[8]          M. Z. Nejad, P. Fatehi, Exact elasto-plastic analysis of rotating thick-walled cylindrical pressure vessels made of functionally graded materials, International Journal of Engineering Science, Vol. 86, pp. 26-43, 2015.
[9]          M. Jabbari, M. Z. Nejad, M. Ghannad, Thermo-elastic analysis of axially functionally graded rotating thick cylindrical pressure vessels with variable thickness under mechanical loading, International journal of engineering science, Vol. 96, pp. 1-18, 2015.
[10]        M. Z. Nejad, M. Jabbari, M. Ghannad, Elastic analysis of FGM rotating thick truncated conical shells with axially-varying properties under non-uniform pressure loading, Composite Structures, Vol. 122, pp. 561-569, 2015.
[11]        Z. H. Jin, An asymptotic solution of temperature field in a strip a functionally graded material, International communications in heat and mass transfer, Vol. 29, No. 7, pp. 887-895, 2002.
[12]        Y. Ootao, Y. Tanigawa, Transient thermoelastic problem of functionally graded thick strip due to nonuniform heat supply, Composite Structures, Vol. 63, No. 2, pp. 139-146, 2004.
[13]        N. A. Apetre, B. V. Sankar, D. R. Ambur, Low-velocity impact response of sandwich beams with functionally graded core, International Journal of Solids and Structures, Vol. 43, No. 9, pp. 2479-2496, 2006.
[14]        B. V. Sankar, An elasticity solution for functionally graded beams, Composites Science and Technology, Vol. 61, No. 5, pp. 689-696, 2001.
[15]        J. R. Cho, J. T. Oden, Functionally graded material: a parametric study on thermal-stress characteristics using the Crank–Nicolson–Galerkin scheme, Computer methods in applied mechanics and engineering, Vol. 188, No. 1, pp. 17-38, 2000.
[16]        M. Bahraminasab, B. B. Sahari, K. L. Edwards, F. Farahmand, T. S. Hong, M. Arumugam, A. Jahan, Multi-objective design optimization of functionally graded material for the femoral component of a total knee replacement, Materials & Design, Vol. 53, pp. 159-173, 2014.
[17]        F. Tornabene, A. Ceruti, Mixed static and dynamic optimization of four-parameter functionally graded completely doubly curved and degenerate shells and panels using GDQ method, Mathematical Problems in Engineering, Vol. 2013, 2013.
[18]        P. Shanmugavel, G. B. Bhaskar, M. Chandrasekaran, S. P. Srinivasan, Determination of Stress Intensity Factors and Fatigue Characteristics for Aluminium, Aluminium-Alumina Composite Material and Aluminium-Alumina FGM Specimens with Edge Crack by Simulation, International Journal of Applied Environmental Sciences, Vol. 9, No. 4, pp. 1759-1768, 2014.
[19]        S. Bhattacharya, K. Sharma, V. Sonkar, Numerical simulation of elastic plastic fatigue crack growth in functionally graded material using the extended finite element method, Mechanics of Advanced Materials and Structures, pp. 1-14, 2017.
[20]        M. Pant, K. Sharma, S. Bhattacharya, Application of EFGM and XFEM for Fatigue Crack growth Analysis of Functionally Graded Materials, Procedia Engineering, Vol. 173, pp. 1231-1238, 2017.
[21]        K. Sharma, S. Bhattacharya, V. Sonkar, XFEM simulation on Mixed-Mode Fatigue Crack Growth of Functionally Graded Materials, Journal of Mechanical Engineering and Biomechanics, Vol. 1, 2016.
[22]        B. Gupta, Few Studies on Biomedical Applications of Functionally Graded Material.
[23]        S. Mohammadi, M. Z. Nejad, A. Afshin, Transient Thermoelastic Analysis of Pressurized Thick Spheres Subjected to Arbitrary Boundary and Initial Conditions, Indian Journal of Science and Technology, Vol. 8, No. 36, 2015.
[24]        X. Han, D. Xu, G. R. Liu, Transient responses in a functionally graded cylindrical shell to a point load, Journal of Sound and Vibration, Vol. 251, No. 5, pp. 783-805, 2002.
[25]        K. S. Kim, N. Noda, Green's function approach to unsteady thermal stresses in an infinite hollow cylinder of functionally graded material, Acta Mechanica, Vol. 156, No. 3-4, pp. 145-161, 2002.
[26]        C. H. Chen, H. Awaji, Transient and residual stresses in a hollow cylinder of functionally graded materials, in Proceeding of, Trans Tech Publ, pp. 665-670.
[27]        K. M. Liew, S. Kitipornchai, X. Z. Zhang, C. W. Lim, Analysis of the thermal stress behaviour of functionally graded hollow circular cylinders, International Journal of Solids and Structures, Vol. 40, No. 10, pp. 2355-2380, 2003.
[28]        Y. Ootao, Y. Tanigawa, Three-dimensional solution for transient thermal stresses of functionally graded rectangular plate due to nonuniform heat supply, International Journal of Mechanical Sciences, Vol. 47, No. 11, pp. 1769-1788, 2005.
[29]        Y. Heydarpour, M. M. Aghdam, Transient analysis of rotating functionally graded truncated conical shells based on the Lord–Shulman model, Thin-Walled Structures, Vol. 104, pp. 168-184, 2016.
[30]        K. C. Mishra, J. N. Sharma, P. K. Sharma, Analysis of vibrations in a nonhomogeneous thermoelastic thin annular disk under dynamic pressure, Mechanics Based Design of Structures and Machines, Vol. 45, No. 2, pp. 207-218, 2017.
[31]        M. Ghannad, M. P. Yaghoobi, 2D thermo elastic behavior of a FG cylinder under thermomechanical loads using a first order temperature theory, International Journal of Pressure Vessels and Piping, Vol. 149, pp. 75-92, 2017.
[32]        A. Najibi, R. Talebitooti, Nonlinear transient thermo-elastic analysis of a 2D-FGM thick hollow finite length cylinder, Composites Part B: Engineering, Vol. 111, pp. 211-227, 2017.
[33]        S. M. Hosseini, M. Akhlaghi, M. Shakeri, Transient heat conduction in functionally graded thick hollow cylinders by analytical method, Heat and Mass Transfer, Vol. 43, No. 7, pp. 669-675, 2007.
[34]        M. Jabbari, A. R. Vaghari, A. Bahtui, M. R. Eslami, Exact solution for asymmetric transient thermal and mechanical stresses in FGM hollow cylinders with heat source, Structural Engineering and Mechanics, Vol. 29, No. 5, pp. 551-565, 2008.
[35]        M. Shariyat, A rapidly convergent nonlinear transfinite element procedure for transient thermoelastic analysis of temperature-dependent functionally graded cylinders, Journal of Solid Mechanics, Vol. 1, No. 4, pp. 313-327, 2009.
[36]        M. Azadi, M. Azadi, Nonlinear transient heat transfer and thermoelastic analysis of thick-walled FGM cylinder with temperature-dependent material properties using Hermitian transfinite element, Journal of Mechanical Science and Technology, Vol. 23, No. 10, pp. 2635-2644, 2009.
Volume 48, Issue 1
June 2017
Pages 15-26
  • Receive Date: 20 May 2017
  • Revise Date: 17 June 2017
  • Accept Date: 25 June 2017