Abstract
Nonlinear transient heat conduction analysis is developed for hollow thick temperature-dependent 2D-FGM cylinders subjected to transient non-uniform axisymmetric thermal loads. It is demonstrated here that the temperature-dependency in addition to the material properties variation in the 2D- FGM would lead to highly nonlinear governing equations. To do this, the graded finite element method is employed to model the structures and a quadratic Lagrange shape function has been used to improve the accuracy of the temperature distribution for the two-dimensional heat conduction analysis. Furthermore, time variation of the temperatures and the effects of material distribution variability in two radial and axial directions and the temperature-dependency of the material properties on the temperature are discussed in detail. It is assumed that the material, geometry and volume fraction distribution are axisymmetric but not uniform along the axial direction. According to the results, the variation of the material properties in two dimensions has significant effect on temperature distribution; therefore, it gives more designing flexibility benefits to the designers to implement this kind of material for the thermal barriers purposes.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
N. Noda, Thermal stresses in functionally graded materials, J. Therm. Stresses, 22 (1999) 477–512.
B. D. Choules and K. Kokini, Architecture of functionally graded ceramic coating against surface thermal fracture, ASME J. Eng. Mater. Technol., 118 (1996) 522–528.
N. Noda, Thermal stresses in materials with temperaturedependent properties, Appl. Mech. Rev., 44 (1991) 83–97.
Y. Tanigawa, Some basic thermoelastic problems for non-homogeneous structural materials, Appl. Mech. Rev., 48 (1995) 287–300.
R. W. Zimmerman and M. P. Lutz, Thermal stress and thermal expansion in a uniformly heated functionally graded cylinder, J. Therm. Stresses, 22 (1999) 88–177.
Y. Obata and N. Noda, Steady thermal stresses in a hollow circular cylinder and a hollow sphere of a functionally gradient material, J. Therm. Stresses, 17 (1994) 471–487.
N. El-abbasi and S. A. Meguid, Finite element modeling of the thermo elastic behaviour of functionally graded plates and shells, Int. J. Comput. Eng. Sci., 1 (2000) 51–165.
M. Jabbari, S. Sohrabpour and M. R. Eslami, Mechanical and thermal stresses in a functionally graded hollow cylinder due to radially symmetric loads, Int. J.Press. Vess. Pip., 79 (2002) 493–497.
M. Jabbari, S. Sohrabpour and M. R. Eslami, General solution for mechanical and thermal stresses in a functionally graded hollow cylinder due to non-axisymmetric steady-state loads, ASME J. Appl. Mech.,70 (2003) 111–118.
K. M. Liew, S. Kitipornchai, X. Z. Zhang and C. W. Lim, Analysis of the thermal stress behaviour of functionally graded hollow circular cylinders, Int. J. Solids Struct., 40 (2003) 2355–2380.
H. S. Shen, Thermal post buckling behaviour of functionally graded cylindrical shells with temperature-dependent properties, Int. J. Solids Struct, 41 (2004) 1961–1974.
J. N. Reddy and C. D. Chin, Thermomechanical analysis of functionally graded cylinders and plates, J. Therm. Stresses, 21 (1998) 593–626.
Y. Ootao and M. Ishiharaa, Transient thermal stress problem of a functionally graded magneto-electro-thermoelastic hollow cylinder due to a uniform surface heating, Journal of Thermal Stresses, 35 (6) (2012) 517–533.
H. L. Lee, W. J. Chang, S. H. Sun and Y. Ch. Yang, Estimation of temperature distributions and thermal stresses in a functionally graded hollow cylinder simultaneously subjected to inner-and-outer boundary heat fluxes, Composites Part B: Engineering, 43 (2) (2012) 786–792.
S. M. Hosseini and M. H. Abolbashari, Analytical solution for thermoelastic waves propagation analysis in thick hollow cylinder based on green-naghdi model of coupled thermoelasticity, Journal of Thermal Stresses, 35 (4) (2012) 63–37.
T. Darabseh, N. Yilmaz and M. Bataineh, Transient thermoelasticity analysis of functionally graded thick hollow cylinder based on Green-Lindsay model, Int. J. Mech. Mater., 8 (2012) 247–255.
X. D. Zhang, Y. L Hong and A. H Li, Optimization of axial symmetrical FGM under the transient-state temperate field, International Journal of Minerals, Metallurgy and Materials, 19 (1) (2012) 59.
H. Awaji and R. Sivakumar, Temperature and stress distribution in a hollow cylinder of functionally graded material: The case of temperature-independent material properties, J. Am. Ceram. Soc., 84 (2001) 1059–1065.
K. S. Kim and N. Noda, Green’s function approach to unsteady thermal stresses in an infinite hollow cylinder of functionally graded material, Acta Mech., 156 (2002) 145–161.
J. Sladek, V. Sladek and C. Zhang, Transient heat conduction analysis in functionally graded materials by the meshless local boundary integral equation method, Comput.Mater. Sci., 28 (2003) 494–504.
B. L. Wang, Y. W. Mai and X. H. Zhang, Thermal shock resistance of functionally graded materials, ActaMater., 52 (2004) 4961–4972.
B. L. Wang and Y. W. Mai, Transient one-dimensional heat conduction problems solved by finite element, Int. J. Mech. Sci., 47 (2005) 303–317.
S. M. Hosseini, M. Akhlaghi and M. Shakeri, Transient heat conduction in functionally graded thick hollow cylinders by analytical method, Heat Mass Trans., 43 (2007) 669–675.
Z. S. Shao, T. J. Wang and K. K. Ang, Transient thermomechanical analysis of functionally graded hollow circular cylinders, J. Therm. Stresses, 30 (1) (2007) 81–104.
Z. S. Shao and G. W. Ma, Thermo-mechanical stresses in functionally graded circular hollow cylinder with linearly increasing boundary temperature, Compos. Struct., 83 (2008) 259–265.
Y. S. Touloukian, Thermophysical properties of high temperature solid materials, McMillan, New York (1967).
M. Shariyat, S. M. H. Lavasani and M. Khaghani, Nonlinear transient thermal stress and elastic wave propagation analyses of thick temperature-dependent FGM cylinders, Using A Second-Order Point-Collocation Method, Appl. Math. Model, 34 (2010) 898–918.
M. Shariyat, M. Khaghani and S. M. H. Lavasani, Nonlinear thermoelasticity, vibration, and stress wave propagation analyses of thick FGM cylinders with temperaturedependent material properties, Eur. J. Mech. A. Solids., 29 (2010) 378–391.
M. Shariyat, Nonlinear transient stress and wave propagation analyses of the FGM thick cylinders, Employing a Unified Generalized Thermoelasticity Theory, Int. J. Mech. Sci., 65 (1) (2012) 24–37.
J. R. Cho and D. Y. Ha, Optimal tailoring of 2D volumefraction distributions for heat-resisting functionally graded materials using FDM, Comput. Method Appl. Mech. Eng., 191 (2002) 3195–3211.
J. Abudi and M. J. Pindera, Thermoelastic theory for the response of materials functionally graded in two directions, Int. J. Solid Struct., 33 (1996) 931–966.
M. Nemat-Alla, Reduction of thermal stresses by developing two dimensional functionally graded materials, Int. J. Solids Struct., 40 (2003) 7339–7356.
M. Nemat-Alla, Kh.I.E. Ahmed, I. Hassab-Allah, Elasticplastic analysis of two-dimensional functionally graded materials under thermal loading, Int. J. Solids Struct., 46 (2009) 2774–2786.
M. H. Santare and J. Lambros, Use of a graded finite element to model the behaviour of non-homogeneous materials, J. Appl. Mech., 67 (2000) 819–822.
M. Asgari and M. Akhlaghi, Transient heat conduction in two-dimensional functionally graded hollow cylinder with finite length, Heat Mass Transfer, 45 (2009) 1383–1392.
H. S. Shen, Functionally graded materials: Nonlinear analysis of plates and shells, CRC Press, Taylor & Francis Group (2009).
J. H. Kim and G. H. Paulino, Isoparametric graded finite elements for non-homogeneous isotropic and orthotropic materials, ASME J. Appl. Mech., 69 (4) (2002) 502–514.
O. C. Zienkiewicz and R. L. Taylor, The finite element method, 5th edn. VII: Solid mechanics, Elsevier Ltd. (2000).
P. Deuflhard, A modified newton method for the solution of ill-conditioned systems of nonlinear equations with application to multiple shooting, Numer. Math., 22 (1974) 289–315.
Author information
Authors and Affiliations
Corresponding author
Additional information
Recommended by Associate Editor Dae Hee Lee
Mohammad Hasan Shojaeefard is a Professor and Head of Automotive Eng. Research Center (AERC) & Automotive Eng. Dept (AED) in the Iran University of Science and Technology. His work is relating to automotive engineering (vehicle engine and body design). His work also is dedicated to research in the field of Mechanical and Automotive Engineering and training of the students.
Amir Najibi is a Ph.D. Student of Automotive Engineering in the Iran university of Science and Technology. His work is related to vehicle body design and crashworthiness capability of structures and pedestrian safety. He is also working on the application of FGM’s in the vehicle engine.
Rights and permissions
About this article
Cite this article
Shojaeefard, M.H., Najibi, A. Nonlinear transient heat conduction analysis of hollow thick temperature-dependent 2D-FGM cylinders with finite length using numerical method. J Mech Sci Technol 28, 3825–3835 (2014). https://doi.org/10.1007/s12206-014-0846-3
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s12206-014-0846-3