Thermo-elastic Analysis of Functionally Graded Thick- Walled Cylinder with Novel Temperature – Dependent Material Properties using Perturbation Technique
الموضوعات : فصلنامه شبیه سازی و تحلیل تکنولوژی های نوین در مهندسی مکانیکAlireza Nadafoskoue 1 , hadi mohammadi hooyeh 2
1 - Assistant Professor, Faculty Member of Imam Hossein University (AS)
2 - Department of Solid Mechanics, Faculty of Engineering, Imam Hossein University, Tehran, Iran
الکلمات المفتاحية: Functionally graded material, : Infinite thick – walled cylinder, nonlinear heat transfer, classical perturbation method, Temperature-dependent properties,
ملخص المقالة :
In this work, thermo – elastic analysis for functionally graded thick – walled cylinder with temperature - dependent material properties at steady condition is carried out. The length of cylinder is infinite and loading is consist of internal hydrostatic pressure and temperature gradient. All of physical and mechanical properties expect the Poisson's ratio are considered as multiplied an exponential function of temperature and power function of radius. With these assumptions, the nonlinear differential equations for temperature distribution at cylindrical coordinate is obtained. Temperature distribution is achieved by solving this equation using classical perturbation method. With considering strain – displacement, stress – strain and equilibrium relations and temperature distribution that producted pervious, the constitutive differential equation for cylinder is obtained. By employing mechanical boundary condition the radial displacement is yield. With having radial displacement, stresses distribution along the thickness are achieved. The results of this work show that by increasing the order of temperature perturbation series the convergence at curves is occurred and also dimensionless radial stress decrease and other stresses with dimensionless radial displacement increase.
[1] S. Suresh, and A. Mortensen, Fundamentals of functionally graded materials, Barnes and Noble Publications, 1998.
[2] M.Yamanouchi, and M. Koizumi, Functionally gradient materials. Proceeding of the first international symposium on functionally graded materials, Sendai, Japan, 1991.
[3] M.M. Najafizadeh, and H.R. Heydari, An exact solution for buckling of functionally graded circular plates based on higher order shear deformation plate theory under uniform radial compression, Int. J. Mech. Sci., vol. 50, pp. 603–612, 2008.
[4] H.J. Xiang, and J. Yang, Free and forced vibration of a laminated FGM Timoshenko beam of variable thickness under heat conduction, Compos. Part B (Eng), vol. 39, pp. 292–303, 2008.
[5] R. Ansari, and M. Darvizeh, Prediction of dynamic behaviour of FGM shells under arbitrary boundary conditions, Compos. Struct., vol. 85, pp. 284–292, 2008.
[6] A. Allahverdizadeh, M.H. Naei, and M. Nikkhah Bahrami, Vibration amplitude and thermal effects on the nonlinear behavior of thin circular functionally graded plates, Int. J. Mech. Sci., vol. 50, pp. 445–454, 2008.
[8] M. Jabbaria, S. Sohrabpourb, and M.R. Eslamic, Mechanical and thermal stresses in a functionally graded hollow cylinder due to radially symmetric loads, Int. J. Pressure Vessels Piping, vol. 79, pp. 493–497, 2002.
[9] Z.S. Shao, and G.W. Ma, Thermo-mechanical stresses in functionally graded circular hollow cylinder with linearly increasing boundary temperature, Compos. Struct., vol.83 pp. 259–265, 2008.
[10] H.L. Dai, and Y.M. Fu, Magnetothermoelastic interactions in hollow structures of functionally graded material subjected to mechanical loads, Int. J. Pressure Vessels Piping vol. 84 pp. 132–138, 2007.
[11] N.Tutuncu, and B. Temel, A novel approach to stress analysis of pressurized FGM cylinders, disks and spheres, Compos. Struct., vol. 91, pp. 385–390, 2009.
[12] Z. Shao, T.J. Wang, Three-dimensional solutions for the stress fields in functionally graded cylindrical panel with finite length and subjected to thermal/mechanical loads, Int. J. Solids. Struct., vol.43, pp. 3856-3874, 2006.
[13] N. Tutuncu, Stresses in thick-walled FGM cylinders with exponentially-varying properties, Eng. Struct., vol.29, pp.2032-2035, 2007.
[14] M. Azadi, and M. Azadi, Nonlinear transient heat transfer and thermoelastic analysis of thick-walled FGM cylinder with temperature-dependent material properties using Hermitian transfinite element, J. Mech. Sci Tech., vol. 23, pp. 2635-2644, 2009.
[15] X.L. Peng, and X.F. Li, Thermoelastic analysis of a cylindrical vessel of functionally graded materials, Int. J. Pressure Vessels Piping, vol. 87 pp. 203 - 210, 2010.
[16] R. Seifi, Exact and approximate solutions of thermoelastic stresses in functionally graded cylinders, J. Thermal Stresses, vol. 38, pp. 1163–1182, 2015.
[17] S.S.Vel, Exact thermoelastic analysis of functionally graded anisotropic hollow cylinders with arbitrary material gradation, Mech. Adv. Mater. Struct., vol. 18, pp.14–31, 2011.
[18] A. Loghman, and H. Parsa, Exact solution for magneto-thermo-elastic behaviour of double-walled cylinder made of an inner FGM and an outer homogeneous layer, Int. J. Mech. Sci., vol. 88, pp. 93-99, 2014.
[19] A. Ghorbanpour Arani, A. Loghman, A. Abdollahitaheri, and V. Atabakhshian, Electrothermomechanical behavior of a radially polarized rotating functionally graded piezoelectric cylinder, J. Mech. Mater. Struct., vol.6, pp.869-882, 2011.
[19] A. Atrin, J. Jafari Fesharaki, and S. H. Nourbakhsh, Thermo-electromechanical behavior of functionally graded piezoelectric hollow cylinder under non-axisymmetric loads, Appl. Math. Mech. Engl. Ed., vol. 35, pp. 939–954, 2015.
[20] M. Arefi, and G.H. Rahimi, The effect of nonhomogeneity and end supports on the thermo elastic behavior of a clamped-clamped FG cylinder under mechanical and thermal loads, Int. J. Press Vessels Piping, vol. 96, pp. 30-37, 2012.
[21] J.H. Zhang, G.Z. Li, S.R. Li, and Y.B. Ma, DQM-based thermal stresses analysis of a functionally graded cylindrical shell under thermal shock, J. Thermal Stresses, vol. 38, pp. 959–982, 2015.
[22] H. Gharooni, M. Ghannad, and M.Z.Nejad, Thermo-elastic analysis of clamped-clamped thick FGM cylinders by using third-order shear deformation theory, Latin American Journal of Solids and Structures, vol. 13, pp. 750-774, 2016.
[23] M. Arefi, Two – dimensional thermoelastic analysis of a FG cylinder for different functionalities by using the higher – order shear deformation theory, J. Appl. Mech. Tech. Phys, vol. 56, pp. 494–501, 2015.
[24] M. Arefi , A.R. Abbasi, and M.R.Vaziri Sereshk, Two-dimensional thermoelastic analysis of FG cylindrical shell resting on the Pasternak foundation subjected to mechanical and thermal loads based on FSDT formulation, J. Thermal stresses, vol. 39, pp. 554-570, 2016.
[25] M. Arefi, Nonlinear thermal analysis of a functionally graded hollow cylinder with temperature variable material properties, J. Appl. Mech. Tech. Phys., vol. 56, pp. 267-273, 2015.
[26] A. loghman, and M. Moradi, The analysis of time-dependent creep in FGPM thick walled sphere under electro-magneto-thermo-mechanical loadings, Mech. Time-Dependent Materials, vol. 17, pp. 315–329, 2013.
[27] A.M. Wazwaz, Partial differential equations and solitary Waves theory, Nonlinear Physical Science, Springer, 2009.
[28] A. Sadighi, and D.D. Ganji, Exact solutions of Laplace equation by homotopy-perturbation and Adomian decomposition methods, Phys. Lett. A., vol. 367, pp. 83-87, 2007.
[29] R. Vatankhah, M.H. Kahrobaiyan, A. Alasty, and M.T. Ahmadian, Nonlinear forced vibration of strain gradient microbeams, Appl. Math. Model., vol. 37, pp. 8363–8382, 2013.
[30] A. Moosaie, Axisymmetric steady temperature field in FGM cylindrical shells with temperature-dependent heat conductivity and arbitrary linear boundary conditions, Arch. Mech., vol. 67, pp. 233–251, 2015.
[31] A.C., Ugural, and S.K., Fenster, Advanced strength and applied elasticity, New Jersey Institute of Thechnology, 2003.
[31] A. Alibeigloo, A.M. Kani, and M.H. Pashaei, Elasticity solution for the free vibration analysis of functionally graded cylindrical shell bonded to thin piezoelectric layers, Int. J. Pressure Vessels Piping, vol. 89, pp. 98-111, 2012.
[32] A. Loghman, S.M.A. Aleayoub, and M. Hasani Sadi, Time-dependent magnetothermoelastic creep modeling of FGM spheres using method of successive elastic solution, Appl. Math. Model., vol. 36, pp. 836-845, 2012.
[33] J. Jafari Fesharaki, A. Loghman, M. Yazdipoor, and S. Golabi, Semi-analytical solution of time-dependent thermomechanical creep behavior of FGM hollow spheres, Mech. Time-Dependent Materials, vol. 18, pp. 41–53, 2014.
[34] A. Loghman, A. Ghorbanpour Arani, S. Amir, and A. Vajedi, Magnetothermoelastic creep analysis of functionally graded cylinders, Int. J. Pressure Vessels Piping, vol. 87, pp. 389-395, 2010.
