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A Review on the Finite Element Methods for Heat Conduction in Functionally Graded Materials

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Abstract

The review presented in this paper focuses mainly on the application of finite element methods for investigating the effect of heat transfer, variation of temperature and other parameters in the functionally graded materials. Different methods have been investigated for thermal conduction in functionally graded materials. The use of FEM for steady state heat transfer has been addressed in this work. The authors have also discussed the utilization of FEM based shear deformation theories and FEM in combination with other methods for the problems involving complexity of the shape and geometry of functionally graded materials. Finite element methods proved to be effective for the solution of heat transfer problem in functionally graded materials. These methods can be used for steady state heat transfer and as well as for transient state.

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References

  1. Y. Xu, et al., “Analysis of convective heat transfer steady thermal stresses in a ZrO2/FGM/Ti-6Al-4 V composite ECBF plate by FEM,” Int. Joint Conf. on Computational Sciences and Optimization, pp 266–269 (2009)

  2. J. Zhao, et al., Analysis of transient thermal stress in sandwich plate with functionally graded coatings. Thin Solid Films 516, 7581–7587 (2008)

    Article  Google Scholar 

  3. B.-L. Wang , Y.-W. Mai, Transient one-dimensional heat conduction problems solved by finite element. Int. J. Mech. Sci. 47, 303–317 (2005)

    Article  Google Scholar 

  4. S. Suresh, A. Mortensen, Fundamentals of Functionally Graded Materials (IOM Communications, London, 1998)

    Google Scholar 

  5. Y. Miyamoto, W.A. Kaysser, B.H. Rabin, A. Kawasaki, R.G. Ford, Functionally Graded Materials: Design, Processing and Applications (Kluwer Academic, Dordrecht, 1999)

    Book  Google Scholar 

  6. O.C. Zienkiewicz, The Finite Element Method in engineering Science (McGraw- Hill, London, 1971)

    MATH  Google Scholar 

  7. C.S. Desai, J.F. Abel, Introduction to Finite Element Method (Van Nostrand Reinhold, New York, 1972)

    MATH  Google Scholar 

  8. B. Nath, Fundamentals of Finite Element for engineers (Athlone press, London, 1974)

    Google Scholar 

  9. R. Fenner, Finite Element Methods for engineers (Imperial College Press, London, 1996)

    Book  Google Scholar 

  10. R.D. Cook, Concepts and Applications of Finite Element Analysis, 3rd edn. (John Wiley & Sons, New York, 1989)

    MATH  Google Scholar 

  11. H.G. Wang, Introduction of thermal elasticity (Tsing hua Univ. Press, Beijing, 1989)

    Google Scholar 

  12. Y. J. Xu, J. J. Zhang and D. H. Tu. “Transient thermal stress analysis of functionally gradient material plate with temperature- dependent material properties under convective heat transfer boundary”, China J. Mech. Engrg.,CMES, Beijing, 27 (2005),pp. 198-204

  13. B. L. Wang , Z. H. Tian, Application of finite element – finite difference method to the determination of transient temperature field in functionally graded materials. Finite Elem. Anal. Des. 41, 335–349 (2005)

    Article  MATH  Google Scholar 

  14. S. Kakaç, Y. Yener, Heat Conduction (Taylor & Francis, Washington, 1993)

    Google Scholar 

  15. J.N. Reddy, D.K. Gartling, The Finite Element Method in Heat Transfer and Fluid Dynamics (CRC Press Inc., Boca Raton, 1994), p. 67

    MATH  Google Scholar 

  16. T. Fujimoto, N. Noda, Crack Propagation in a Functionally Graded Plate Under Thermal. Shock 70, 377–386 (2000)

    MATH  Google Scholar 

  17. F. Erdogan, B.H. Wu, Crack problem in FGM layers under thermal stresses. J. Therm. Stress. 19, 237–265 (1996)

    Article  Google Scholar 

  18. E. Reissner, The effect of transverse shear deformation on the bending of elastic plates. J. Appl. Mech. 12, A69–A77 (1945)

    MATH  MathSciNet  Google Scholar 

  19. E. Reissner , Small bending and stretching of sandwich type shells. NACA-TN- 1832, 1949

  20. R.D. Mindlin, Influence of rotary inertia and shear in flexural motion of isotropic elastic plates. ASME J. Appl. Mech. 18, 31–38 (1951)

    MATH  Google Scholar 

  21. J.M. Whitney, Shear correction factors for orthotropic laminates under static loads. J. Appl. Mech. 40, 302–304 (1973)

    Article  Google Scholar 

  22. J.M. Whitney, The effect of transverse shear deformation in the bending of laminated plates. J. Compos. Mater. 3, 534–547 (1969)

    Article  Google Scholar 

  23. J.M. Whitney, N.J. Pagano, Shear deformation in heterogeneous anisotropic plates. J. Appl. Mech. 37, 1031–1036 (1970)

    Article  MATH  Google Scholar 

  24. E. Reissner, A consistent treatment of transverse shear deformations in laminated anisotropic plates. AIAA J 10, 716–718 (1972)

    Article  Google Scholar 

  25. P.C. Yang, C.H. Norris, Y. Stavsky, Elastic wave propagation in heterogeneous plates. Int. J. Solids Struct. 2, 665–684 (1966)

    Article  Google Scholar 

  26. C.W. Bert, T.L. Chen, Effect of shear deformation on vibration of antisymmetric angle-ply laminated rectangular plates. Int. J. Solids Struct. 14, 465–473 (1978)

    Article  MATH  Google Scholar 

  27. R.C. Fortier, J.N. Rossetto, On the vibration of shear deformable curved anisotropic composite plates. J. Appl. Mech. 40, 299–301 (1973)

    Article  Google Scholar 

  28. K.M. Liew, C.M. Wang, Y. Xiang, S. Kitipornchai, Vibration of Mindlin plates: programming the p-version Ritz method (Elsevier, Amsterdam, 1998)

    MATH  Google Scholar 

  29. J.N. Reddy, Exact solutions of moderately thick laminated shells. J. Eng. Mech. 110, 05–794 (1984)

    Article  Google Scholar 

  30. A.K. Noor, Stability of multilayered composite plates. Fibre Sci. Technol. 8, 81–89 (1975)

    Article  Google Scholar 

  31. D. Saji, et al., “Finite element analysis for thermal buckling behaviour in functionally graded plates with cut-outs”, Proceedings of the International conference on Aerospace Science and Technology 26–28 June 2008, Bangalore India

  32. H. S. Shen, Thermal postbuckling behavior of shear deformable FGM plates with temperature-dependent properties. Int. J. Mech. Sci. 49(2007), 466–478 (2007)

    Article  Google Scholar 

  33. A. Bhimaraddi, K. Chandashekhara, Nonlinear vibrations of heated antisymmetric angle-ply laminated plates. Int. J. Solids Struct. 30, 1255–1268 (1993)

    Article  MATH  Google Scholar 

  34. K. Ramkumar, N. Ganesan, Finite-element buckling and vibration analysis of functionally graded box columns in thermal environments. J. Mater. Des. Appl. 222, 53–64 (2007)

    Google Scholar 

  35. O.C. Zienkiewicz, The finite element method in engineering science (McGraw-Hill Publishing Company Limited, London, 1971)

    MATH  Google Scholar 

  36. K. Ramkumar, J.N. Reddy, An introduction to the finite element method (McGraw-Hill International Editions, Singapore, 1984)

    Google Scholar 

  37. L. Leon, Mishnaevsky Jr, Functionally gradient metal matrix composites: numerical analysis of the microstructure–strength relationships. Compos. Sci. Technol. 66, 1873–1887 (2006)

    Article  Google Scholar 

  38. Y. M. Shabana, N. Noda, Numerical evaluation of the thermomechanical effective properties of a functionally graded material using the homogenization method. Int. J. Solids Struct. 45, 3494–3506 (2008)

    Article  MATH  Google Scholar 

  39. N. Takano, M. Zako, Integrated design of graded microstructures of heterogeneous materials. Arch. Appl. Mech. 70, 585–596 (2000)

    Article  MATH  Google Scholar 

  40. C. Cho-Hsien, 1992. Modeling of the thermal elasto-plastic behavior for composite materials using the homogenization method. PhD thesis, University of Michigan, USA

  41. M. Grujicic, Y. Zhang, Determination of effective elastic properties of functionally graded materials using voronoi cell finite element method. Mater. Sci. Eng. A251, 64–76 (1998)

    Article  Google Scholar 

  42. X.Y. Kou, S.T. Tan, W.S. Sze, Modeling complex heterogeneous objects with non-manifold heterogeneous cells. Comput. Aided Des. 38(5), 457 (2006)

    Article  Google Scholar 

  43. Y.K. Siu, S.T. Tan, Source-based heterogeneous solid modeling. Comput. Aided Des. 34(1), 41 (2002)

    Article  Google Scholar 

  44. X. Qian, D. Dutta, Design of heterogeneous turbine blade. Comput. Aided Des. 35(3), 319 (2003)

    Article  Google Scholar 

  45. K. Samanta, B. Koc, Feature-based design and material blending for free-form heterogeneous object modeling. Comput. Aided Des. 37(3), 287 (2005)

    Article  Google Scholar 

  46. D. Natekar, X. Zhang, G. Subbarayan, Constructive solid analysis: a hierarchical, geometry-based meshless analysis procedure for integrated design and analysis. Comput. Aided Des. 36(5), 473 (2004)

    Article  Google Scholar 

  47. W. Martin, E. Cohen, “Representation and extraction of volumetric attributes using trivariate splines: a mathematical framework”. In: Proceedings of the sixth ACM symposium on solid modeling and applications; 2001. p. 234

  48. V. Kumar, D. Dutta, Approach to modeling & representation of heterogeneous objects. J. Mech. Des., Trans. ASME 120(4), 659 (1998)

    Article  Google Scholar 

  49. W. Sun, X. Hu, Reasoning Boolean operation based modeling for heterogeneous objects. Comput. Aided Des. 34(6), 481 (2002)

    Article  MathSciNet  Google Scholar 

  50. H. Liu et al., Methods for feature-based design of heterogeneous solids. Comput. Aided Des. 36(12), 1141 (2004)

    Article  Google Scholar 

  51. K.-H. Shin, D. Dutta, Constructive representation of heterogeneous objects. J. Comput. Inform. Sci. Eng. 1, 205 (2001)

    Article  Google Scholar 

  52. J. Cheng, F. Lin, Approach of heterogeneous bio-modeling based on material features. Comput. Aided Des. 37(11), 1115 (2005)

    Article  MathSciNet  Google Scholar 

  53. X.Y. Kou, S.T. Tan, A systematic approach for Integrated computer-aided design and finite element analysis of functionally-graded-material objects. Mater. Des. 28, 2549–2565 (2007)

    Article  Google Scholar 

  54. S.M. Hosseini et al., Heat Conduction and heat wave propagation in functionally graded thick hollow cylinder base on coupled thermoelasticity without energy dissipation. Heat Mass Transf. 44, 1477–1484 (2008)

    Article  Google Scholar 

  55. J.G. Andrew, S.V. Senthil, Multi-objective optimization of functionally graded materials with temperature-dependent material properties. Mater. Des. 28(6), 1861–1879 (2007)

    Article  Google Scholar 

  56. L.F. Qian, R.C. Batra, Transient thermoelastic deformations of a thick functionally graded plate. J. Therm. Stress. 27, 705–740 (2004)

    Article  Google Scholar 

  57. L.F. Qian, R.C. Batra, L.M. Chen, Static and dynamic deformations of thick functionally graded elastic plate by using higher-order shear and normal deformable plate theory and meshless local Petrov-Galerkin method. Compos. Part B 35, 685–697 (2004)

    Article  Google Scholar 

  58. L.F. Qian, R.C. Batra, L.M. Chen, Analysis of cylindrical bending thermoelastic deformations of functionally graded plates by a meshless local Petrov-Galerkin method. Comput. Mech. 33, 263–273 (2004)

    Article  MATH  Google Scholar 

  59. L.F. Qian, R.C. Batra, Design of bidirectional functionally graded plate for optimal natural frequencies. J. Sound Vib. 280, 415–424 (2005)

    Article  Google Scholar 

  60. A.J.M. Ferreira, R.C. Batra, C.M.C. Roque, L.F. Qian, P.A.L.S. Martins, Static analysis of functionally graded plates using third-order shear deformation theory and a meshless method. Compos. Struct. 69, 449–457 (2005)

    Article  Google Scholar 

  61. L.F. Qian, R.C. Batra, Three-dimensional transient heat conduction in a functionally graded thick plate with a higher-order plate theory and a meshless local Petrov-Galerkin method. Comput. Mech. 35, 214–226 (2005)

    Article  MATH  Google Scholar 

  62. A.J.M. Ferreira, R.C. Batra, C.M.C. Roque, L.F. Qian, R.M.N. Jorge, Natural frequencies of functionally graded plates by a meshless method. Compos. Struct. 75, 593–600 (2006)

    Article  Google Scholar 

  63. D.F. Gilhooley, R.C. Batra, J.R. Xiao, M.A. McCarthy, J.W. Gillespie, Analysis of thick functionally graded plates by using higher-order shear and normal deformable plate theory and MLPG method with radial basis functions. Compos. Struct. 80, 539–552 (2007)

    Article  Google Scholar 

  64. A.J.M. Ferreira, G.E. Fasshauer, R.C. Batra, J.D. Rodrigues, Static deformations and vibration analysis of composite and sandwich plates using a Layerwise theory and RBF-PS discretizations with optimal shape parameter. Compos. Struct. 86, 328–343 (2008)

    Article  Google Scholar 

  65. A.J.M. Ferreira, G.E. Fasshauer, R.C. Batra, Natural frequencies of thick plates made of orthotropic, monoclinic, and hexagonal materials by a meshless method. J. Sound Vib. 319, 984–992 (2009)

    Article  Google Scholar 

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Acknowledgments

This paper is a revised and expanded version of an article entitled, “A Review on the Finite Element Methods for Heat Conduction in Functionally Graded Materials” presented in “National Conference on Recent Advancements in Mechanical Engineering” held at ‘North East Regional Institute of Science and Technology’, Arunachal Pradesh, India on November 8–9, 2013.

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Authors and Affiliations

  1. Chandigarh College of Engineering and Technology, Chandigarh, India

    R. Sharma

  2. Gian Jyoti Group of Institutions, Punjab, India

    V. K. Jadon

  3. Punjab Technical University, Jalandhar, India

    B. Singh

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  1. R. Sharma
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Correspondence to R. Sharma.

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Sharma, R., Jadon, V.K. & Singh, B. A Review on the Finite Element Methods for Heat Conduction in Functionally Graded Materials. J. Inst. Eng. India Ser. C 96, 73–81 (2015). https://doi.org/10.1007/s40032-014-0125-1

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