Thermoelastic Analysis of Functionally Graded Hollow Cylinder Subjected to Uniform Temperature Field

Document Type : Research Paper

Authors

1 Head Department of Mathematics, R.M. G. College, Saoli, Chandrapur, India

2 Head Deptt. of Mathematics Shri Lemdeo Patil Mahavidyalaya, Nagpur, INDIA

Abstract

This paper deals with the determination of displacement function and thermal stresses of a finite length isotropic functionally graded hollow cylinder subjected to uniform temperature field. The solution of the governing thermoelastic equation is obtained, as suggested by Spencer et al. for anisotropic laminates.  Numerical calculations are also carried out for FGM (Functionally graded material) system consisting of ceramic Alumina (Al2O3), along with Nickel (Ni) as the metallic component varying with distance in one direction and illustrated graphically.

Keywords

Main Subjects

[1]           Noda, N., “Thermal stresses in functionally graded materials”, Journal of Thermal Stresses, Vol. 22, pp. 477-512, 1999.
[2]           Horgan, C. O. and Chan, A. M., “The pressurized Hollow cylinder or Disk problem for functionally graded isotropic linearly Elastic material”, Journal of Elasticity, Vol. 55, pp. 43-59, 1999.
[3]           Lutz, M. P. and Zimmerman, R. W., “Thermal stresses and thermal expansion in a uniformly heated functionally graded cylinder”, Journal of Thermal Stresses, Vol. 22, pp. 177-188, 1999.
[4]           Chen, W.,  Ye, G. and Cai, J., “Thermoelastic Stresses in a uniformly heated functionally graded isotropic hollow cylinder”, Journal of Zhejiang University Science, Vol. 3, No. 1, pp. 1-5, 2002.
[5]           Eraslan, A.N., and Akis, T., “Elastoplastic Response of a Long Functionally Graded Tube Subjected to Internal Pressure”, Turkish J. Eng. Env. Sci., Vol. 29, pp. 361-368, 2005.           
[6]           Lekhnitskii, S. G., “Theory of Elasticity of an Anisotropic Body”, Mir, Moscow, 1981.
[7]           Spencer, A. J. M., Watson, P. and Rogers, T. G., “Thermoelastic Distortions in laminated anisotropic tubes and channel section”, Journal of Thermal Stresses, Vol. 15, pp. 129-141, 1992.
[8]            Noda, N., Hetnarski, R.B.,  and Tanigawa, Y., “Thermal stresses”, First Edition, Lastran, Rochester, 2000.
[9]            Shariyat, M., “Dynamic thermal buckling of suddenly heated temperature-dependent FGM cylindrical shells, under combined axial compression and external pressure”, International Journal of Solids and Structures, Volume 45 , pp. 2598–2612 , 2008.
[10]         Na, S., Kim, K.W., Lee, B. H. and Marzocca, P., “Dynamic Response Analysis Of Rotating Functionally Graded Thin-Walled Blades Exposed To Steady Temperature And External Excitation”, Journal of Thermal Stresses, vol. 32, pp. 209–225, 2009.
[11]         Ootao, Y., “Transient Thermoelastic and Piezothermoelastic Problems of Functionally Graded Materials”, Journal of Thermal Stresses, vol. 32, pp. 656–697, 2009.
[12]         Houari, M. S. A., Benyoucef, S., Mechab, I., Tounsi, A. and Bedia, El A. A., “Two-Variable Refined Plate Theory For Thermoelastic Bending Analysis Of Functionally Graded Sandwich Plates”, Journal of Thermal Stresses, vol. 34, pp. 315–334, 2011.
[13]         Marzocca, P., Fazelzadeh, S. A. and Hosseini, M., “A Review of Nonlinear Aero-Thermo-Elasticity of Functionally Graded Panels”, Journal of Thermal Stresses, vol. 34, pp. 536–568, 2011.
[14]         Chang, W.J., Lee, H.L. and Yang, Y. C., “Estimation of Heat Flux and Thermal Stresses in Functionally Graded Hollow Circular Cylinders”, Journal of Thermal Stresses, vol. 34, pp. 740–755, 2011.
[15]         Fazelzadeh, S. A., Hosseini, M. and Madani, H., “Thermal Divergence of Supersonic Functionally Graded Plates, Journal of Thermal Stresses”, vol. 34, pp. 759–777, 2011.
[16]         Sheng, G. G. and Wang, X., “Non-Linear Response of Functionally Graded Cylindrical Shells under Mechanical and Thermal Loads”, Journal of Thermal Stresses, vol. 34, pp.1105–1118, 2011.
[17]         Sumi,  N., Tanigawa,  Y., Eslami, M. R.,  Hetnarski, R.,  Noda, N. and Ignaczak, J., Theory of Elasticity and Thermal Stresses, Springer, 2013.
[18]         Bayat, M., Rahimi, M., Saleem, M., Mohazzab, A.H., Wudtke, I., and Talebi, H., “One-dimensional analysis for magneto-thermo-mechanical response in a functionally graded annular variable-thickness rotating disk”,  Applied Mathematical Modeling, vol. 38 , pp. 4625–4639 , 2014.
[19]         Ashida, F., Morimoto, T., and Ohtsuka, T., “Dynamic Behavior of Thermal Stress in a Functionally Graded Material Thin Film Subjected to Thermal Shock”, Journal of Thermal Stresses, volume 37, pp. 1037–1051, 2014.