Abstract
This paper describes a new two-dimensional (2-D) control volume finite element method (CV-FEM) for transient heat conduction in multilayer functionally graded materials (FGMs). To deal with the mixed-grid problem, 9-node quadrilateral grids and 6-node triangular grids are used. The unknown temperature and material properties are stored at the node. By using quadratic triangular grids and quadratic quadrilateral grids, the present method offers greater geometric flexibility and the potential for higher accuracy than the linear CV-FEM. The properties of the FGMs are described by exponential, quadratic and trigonometric grading functions. Some numerical tests are studied to demonstrate the performance of the developed method. First, the present CV-FEM with mixed high-order girds provides a higher accuracy than the linear CV-FEM based on the same grid size. Second, the material properties defined location is proved to have a significant effect on the accuracy of the numerical results. Third, the present method provides better numerical solutions than the conventional FEM for the FGMs in conjunction with course high-order grids. Finally, the present method is also capable of analysis of transient heat conduction in multilayer FGM.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
Koizumi M., Niino M., Overview of FGM research in Japan. Mrs Bulletin, 1995, 20: 19–21.
Chan S.H., Khor K.A., The effect of thermal barrier coated piston crown on engine characteristics. Journal of Materials Engineering and Performance, 2000, 9: 103–109.
Buyukkaya E., Thermal analysis of functionally graded coating alsi alloy and steel pistons. Surface and Coatings Technology, 2008, 202: 3856–3865.
Zhao B., Thermal stress analysis of ceramic-coated diesel engine pistons based on the wavelet finite-element method. Journal of Engineering Mechanics, 2012, 138(1): 143–149.
Thieme M., Wieters K.P., Bergner F., Titanium sintering for preparation of a porous functionally graded material destined for orthopaedic implants. Journal of Materials Science Materials in Medicine, 2001, 12(3): 225–231.
Suk M.J., Choi S.I., Kim J.S., Kim Y. Do, Kwon Y.S., Fabrication of a porous material with a porosity gradient by a pulsed electric current sintering process. Metals and Materials International, 2003, 9(6): 599–603.
Hideki S., Katsumi K., Hitoshi O., Application feasibility of permittivity graded fgm (functionally graded materials) for gas insulated equipment. IEEJ Transactions on Power and Energy, 2005, 125(7): 695–700.
Kato K., Kurimoto M., Shumiya H., Application of functionally graded material for solid insulator in gaseous insulation system. IEEE Transactions on Dielectrics and Electrical Insulation, 2006, 13(2): 362–372.
Ootao Y., Tanigawa Y., Fukuda T., Axisymmetric transient thermal stress analysis of a multilayered composite hollow cylinder. Journal of Thermal Stresses, 1991, 14(2): 201–213.
Ootao Y., Akai T., Tanigawa Y., Three-dimensional transient thermal stress analysis of a nonhomogeneous hollow circular cylinder due to a moving heat source in the axial direction. Journal of Thermal Stresses, 1995, 18(5): 497–512.
Tanigawa, Ootao Y., Yoshinobu, Three-dimensional transient thermal stresses of functionally graded rectangular plate due to partial heating. Journal of Thermal Stresses, 1999, 22(1): 35–55.
Vel S., Batra R., C,. Exact solution for thermoelastic deformations of functionally graded thick rectangular plate. Aiaa Journal, 2012, 40(7): 1421–1433.
Lutz M.P., Zimmerman R.W., Thermal stresses and effective thermal expansion coefficient of a functionally gradient sphere. Journal of Thermal Stresses, 1996, 19(1): 39–54.
Zhou Y.T., Lee K.Y., Yu D.H., Transient heat conduction in a functionally graded strip in contact with well stirred fluid with an outside heat source. International Journal of Heat and Mass Transfer, 2011, 54(25-26): 5438–5443.
Sladek J., Sladek V., Krivacek J., Local BIEM for transient heat conduction analysis in 3-D axisymmetric functionally graded solids. Computational Mechanics, 2003, 32(3): 169–176.
Sutradhar A., Paulino G.H., Gray L.J., Transient heat conduction in homogeneous and non-homogeneous materials by the Laplace transform Galerkin boundary element method. Engineering Analysis with Boundary Elements, 2002, 26(2): 119–132.
Sutradhar A., Paulino G.H., Gray L.J., On hypersingular surface integrals in the symmetric Galerkin boundary element method: application to heat conduction in exponentially graded materials. International Journal for Numerical Methods in Engineering, 2005, 62(1): 122–157.
Wang H., Qin Q. H., Kang Y.L., A meshless model for transient heat conduction in functionally graded materials. Computational Mechanics, 2006, 38(1): 51–60.
Wang B.L., Mai Y.W., Zhang X.H., Thermal shock resistance of functionally graded materials. Acta Materialia, 2004, 52(17): 4961–4972.
Yu Y., Cui J., Han F., The statistical second-order two-scale analysis method for heat conduction performances of the composite structure with inconsistent random distribution. Computational Materials Science, 2009, 46(1): 0–161.
Aboudi J., Pindera M.J., Arnold S.M., Higher-order theory for functionally graded materials. Composites Part B Engineering, 1999, 30(8): 777–832.
Bansal Y., Pindera M.J., Efficient reformulation of the thermoelastic higher-order theory for functionally graded materials. Journal of Thermal Stresses, 2003, 26(11-12): 1055–1092.
Zhong Y., Bansal Y., Pindera M.J., Efficient reformulation of the thermal high reorder theory for fgms with locally variable thermal conductivity. International Journal of Computational Engineering Science, 2004, 5: 795–831.
Bansal Y., Finite-volume direct averaging micromechanics of heterogeneous media. Engineering and Applied Science University of Virginia, VA; 2005. Virginia, USA.
Gong J.F., Xuan L.K., Ming P.J., Application of the staggered cell-vertex finite volume method to thermoelastic analysis in heterogeneous materials. Journal of Thermal Stresses, 2014, 37(4): 506–531.
Gong J., Xuan L., Ming P., An unstructured finite-volume method for transient heat conduction analysis of multilayer functionally graded materials with mixed grids. Numerical Heat Transfer, Part B: Fundamentals, 2013, 63(3): 222–247.
Charoensuk J., Vessakosol P., A high order control volume finite element procedure for transient heat conduction analysis of functionally graded materials. Heat and Mass Transfer, 2010, 46(11-12): 1261–1276.
Wang X.C., Finite element method. Tsinghua University Press, Beijing, 2003.
Liu Y., Zhang X., Lu M.W., A meshless method based on least-squares approach for steady- and unsteady-state heat conduction problems. Numerical Heat Transfer, Part B, 2005, 47(3): 257–275.
Ching H.K., Yen S.C., Transient thermoelastic deformations of 2-D functionally graded beams under nonuniformly convective heat supply. Composite Structures, 2006, 73(4): 381–393.
Sutradhar A., Paulino G.H., The simple boundary element method for transient heat conduction in functionally graded materials. Computer Methods in Applied Mechanics and Engineering, 2004, 193(42-44): 4511–4539.
Pisani S.R., Rencis J.J., Investigating CURVIC coupling behavior by utilizing two- and three-dimensional boundary and finite element methods. Engineering Analysis with Boundary Elements, 2000, 24(3): 271–275.
Acknowledgement
The financial support from the Fundamental Research Funds for the Central Universities HEUCFP201711 is gratefully acknowledged.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Liu, Q., Ming, P., Zhao, H. et al. A High Order Control Volume Finite Element Method for Transient Heat Conduction Analysis of Multilayer Functionally Graded Materials with Mixed Grids. J. Therm. Sci. 29, 144–158 (2020). https://doi.org/10.1007/s11630-019-1167-8
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11630-019-1167-8