Transient thermo-visco-elastic response of a functionally graded non-axisymmetric cylinder

Document Type : Research Paper


1 Mechanical Properties Research Lab (MPRL), Faculty of Mechanical Engineering, K.N. Toosi Univeristy of Technology, Iran

2 Composites Research Laboratory, Center of Excellence in Experimental Solid Mechanics and Dynamics, School of Mechanical Engineering, Iran University of Science and Technology, Iran


In this study, the analysis of transient thermoelastic response of a functionally graded (FG) non-axisymmetric viscoelastic cylinder is presented. The material properties are assumed to be time- dependent and radially and circumferentially non-homogeneous. The finite element (FE) formulations of the thermoelastic problem are obtained using the virtual work method and all the coupling terms are considered. According to material dependencies and nonlinearity of the constitutive equation, an iterative-based FE solution is suggested in order to solve thermo-elastic equations. The effects of material in homogeneities on the time-dependent response of mechanical and thermal components are investigated. From the results of this study, it is concluded that, using appropriate material inhomogeneities can improve the magnitudes of stress components, especially shear stress.


Main Subjects

[1].Chen TC, Weng CI., 1989, Coupled transient thermoelastic response in an axi-symmetric circular cylinder by Laplace transform-finite element method. Comput Struct 33(2): 533-542.
[2].Lee ZY., 2006, Generalized coupled transient thermoelastic problem of multilayered hollow cylinder with hybrid boundary conditions. Int Commun Heat Mass 33(4): 518–528.
[3].Chitikireddy R, Datta SK, Shah AH, Bai H., 2011, Transient thermoelastic waves in an anisotropic hollow cylinder due to localized heating. Int J Solids Struct 48(21): 3063–3074.
[4].Jabbari M, Bahtui A, Eslami MR., 2009, Axisymmetric mechanical and thermal stresses in thick short length FGM cylinders. Int J Pres Ves Pip 86(5): 296–306.
[5].Ying J, Wang HM., 2010, Axisymmetric thermoelastic analysis in a finite hollow cylinder due to nonuniform thermal shock. Int J Pres Ves Pip 87(12): 714–720.
[6].Sadd M., 2005, Elasticity, theory, applications and numeric. Elsevier, Kingston Elsevier.
[7].Takeut Y, Nod N., 1980, Three-dimensional transient thermal stresses in a finite circular cylinder under nonaxisymmetric temperature distribution. J Therm Stresses 3(2): 159-183.
[8].Jabbari M, Sohrabpour S, Eslami MR., 2003, General Solution for Mechanical and Thermal Stresses in a Functionally Graded Hollow Cylinder due to Nonaxisymmetric Steady-State Loads. J Appl Mech 70(1): 111–118.
[9].Tokovyy YV, Ma CC., 2008, Analysis of 2D non-axisymmetric elasticity and thermoelasticity problems for radially inhomogeneous hollow cylinders. J Eeg Math 61(2-4): 171-184.
[10]. Tokovyy YV, Ma CC., 2009, Analytical solutions to the planar non-axisymmetric elasticity and thermoelasticity problems for homogeneous and inhomogeneous annular domains. Int J Eng Sci 47(3): 413–437.
[11]. Li H, Liu Y., 2014, Functionally graded hollow cylinders with arbitrary varying material properties under nonaxisymmetric loads. Mech Res Commun 55: 1–9.
[12]. Zheng BJ., Gao XW., Yang K., Zeng C., A novel meshless local Petrov–Galerkin method for dynamic coupled thermoelasticity analysis under thermal and mechanical shock loading. Eng Anal Bound Elem, doi:10.1016/j.enganabound.2014.12.001, in press.
[13]. Jin ZH., 2006, Some Notes on the Linear Viscoelasticity of Functionally Graded Materials. Math Mech Solids 11(2): 216–224.
[14]. Zhang NH, Wang ML., 2007, Thermoviscoelastic deformations of functionally graded thin plates. Eur J Mech A-Solid 26(5): 872–886.
[15]. Altenbach H., Eremeyev VA., 2008, Analysis of the viscoelastic behavior of plates made of functionally graded materials. J Appl Math Mech-Uss 88(5): 332–341.
[16]. Chen SS, Xu CJ, Tong GS., 2015, A meshless local natural neighbour interpolation method to modeling of functionally graded viscoelastic materials. Eng Anal Bound Elem 52: 92–98.
[17]. Temel B, Yildirim S, Tutuncu N., Elastic and viscoelastic response of heterogeneous annular structures under Arbitrary Transient Pressure. Int J Mech Sci, doi: 10.1016/j.ijmecsci.2014.08.021, in press.
[18]. Lakes R., 2009, Viscoelastic materials, Cambridge University Press, New York.
[19]. Moreau S., Chrysochoos A., Muracciole JM., Wattrisse B., 2005, Analysis of thermoelastic effects accompanying the deformation of PMMA and PC polymers. Comptes Rendus Mécanique, 333(8): 648-653.
[20]. Volodin VP., Slutsker, AI., 1994, Specific features of the thermoelastic effect in polymers. Thermochimica acta, 247(1): 121-128.
[21]. Hetnarski R, Eslami MR., 2008 Thermal stresses – Advanced theory and applications, Springer, New York.
[22]. Payette GS, Reddy JN., 2010, Nonlinear quasi-static finite element formulations for viscoelastic Euler–Bernoulli and Timoshenko beams. Int J Numer Method Biomed Eng 26(12): 1736–1755.
[23]. Luche J, Rogaume T, Guillaume E., 2011, Characterization of thermal properties and analysis of combustion behavior of PMMA in a cone calorimeter. Fire Safety J 46(7): 451-461.
[24]. Ashby MF., 2005 Materials selection in mechanical design, Elsevier, Cambridge.
[25]. Guedes RM., 2010, Nonlinear viscoelastic analysis of thick-walled cylindrical composite pipes. Int J Mech Sci 52(8): 1064–1073.
  • Receive Date: 24 May 2015
  • Revise Date: 12 July 2015
  • Accept Date: 12 July 2015