Steel and Composite Structures

  • 제49권5호
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  • Pages.587-602
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  • 2023
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  • 1229-9367(pISSN)
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  • 1598-6233(eISSN)
테크노프레스 (Techno-Press)
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Transient heat transfer of unidirectional (1D) and multidirectional (2D/3D) functionally graded panels

  • Samarjeet Kumar (Department of Mechanical Engineering, National Institute of Technology Jamshedpur) ;
  • Vishesh Ranjan Kar (Department of Mechanical Engineering, National Institute of Technology Jamshedpur)
  • 투고 : 2022.08.06
  • 심사 : 2023.09.13
  • 발행 : 2023.12.10
⟨ 이전 논문 다음 논문 ⟩

초록

This article presents the numerical modelling of transient heat transfer in highly heterogeneous composite materials where the thermal conductivity, specific heat and density are assumed to be directional-dependent. This article uses a coupled finite element-finite difference scheme to perform the transient heat transfer analysis of unidirectional (1D) and multidirectional (2D/3D) functionally graded composite panels. Here, 1D/2D/3D functionally graded structures are subjected to nonuniform heat source and inhomogeneous boundary conditions. Here, the multidirectional functionally graded materials are modelled by varying material properties in individual or in-combination of spatial directions. Here, fully spatial-dependent material properties are evaluated using Voigt's micromechanics scheme via multivariable power-law functions. The weak form is obtained through the Galerkin method and solved further via the element-space and time-step discretisation through the 2D-isoparametric finite element and the implicit backward finite difference schemes, respectively. The present model is verified by comparing it with the previously reported results and the commercially available finite element tool. The numerous illustrations confirm the significance of boundary conditions and material heterogeneity on the transient temperature responses of 1D/2D/3D functionally graded panels.

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참고문헌

  1. Adhikari, B., Dash, P. and Singh, B.N. (2020), "Buckling analysis of porous FGM sandwich plates under various types non-uniform edge compression based on higher order shear deformation theory", Compos. Struct., 251, 112597. https://doi.org/10.1016/j.compstruct.2020.112597.
  2. Ahlawat, N. and Lal, R. (2016), "Buckling and vibrations of multidirectional functionally graded circular plate resting on elastic foundation", Procedia Eng., 144, 85-93. https://doi.org/10.1016/j.proeng.2016.05.010.
  3. Ameri, A., Fekrar, A., Bourada, F., Selim, M.M., Benrahou, K. H., Tounsi, A. and Hussain, M. (2021), "Hygro- thermo-mechanical bending of laminated composite plates using an innovative computational four variable refined quasi-3D HSDT model", Steel Compos. Struct., 41(1), 31-44. https://doi.org/10.12989/scs.2021.41.1.031.
  4. Aragh, B.S., Hedayati, H., Farahani, E.B. and Hedayati, M. (2011), "A novel 2-D six-parameter power-law distribution for free vibration and vibrational displacements of two-dimensional functionally graded fiber-reinforced curved panels", Eur. J. Mech. A/Solids., 30(6), 865-883. https://doi.org/10.1016/j.euromechsol.2011.05.002.
  5. Awaji, H. and Sivakumar, R. (2001), "Temperature and stress distributions in a hollow cylinder of functionally graded material: The case of temperature-independent material properties", J. Am. Ceram. Soc., 84(5), 1059-1065. https://doi.org/10.1111/j.1151-2916.2001.tb00790.x.
  6. Bayat, M., Mohazzab, A. H., Sahari, B. B. and Saleem, M. (2010), "Exact solution for functionally graded variable-thickness rotating disc with heat source", Proc. Inst. Mech. Eng. Part C, J. Mech. Eng. Sci., 224(11), 2316-2331. https://doi.org/10.1243/09544062JMES1812
  7. Bergheau, J.M. and Fortunier, R. (2013), Finite Element Simulation of Heat Transfer, John Wiley & Sons.
  8. Bot, I.K., Bousahla, A.A., Zemri, A., Sekkal, M., Kaci, A., Bourada, F., Tounsi, A., Ghazwani, M.H. and Mahmoud, S.R. (2022), "Effects of Pasternak foundation on the bending behavior of FG porous plates in hygrothermal environment", Steel Compos. Struct., 43(6), 821-837. https://doi.org/10.12989/scs.2022.43.6.821.
  9. Bouafia, K., Selim, M.M., Bourada, F., Bousahla, A.A., Bourada, M., Tounsi, A., Bedia, E.A. and Tounsi, A. (2021), "Bending and free vibration characteristics of various compositions of FG plates on elastic foundation via quasi 3D HSDT model", Steel Compos. Struct., 41(4), 487-503. https://doi.org/10.12989/scs.2021.41.4.487.
  10. Bounouara, F., Aldosari, S.M., Chikh, A., Kaci, A., Bousahla, A.A., Bourada, F., Tounsi, A., Benrahou, K.H. and Albalawi, H. (2023), "The effect of visco-Pasternak foundation on the free vibration behavior of exponentially graded sandwich plates with various boundary conditions", Steel Compos. Struct., 46(3), 367-383. https://doi.org/10.12989/scs.2023.46.3.367.
  11. Byrd, L. and Birman, V. (2010), "An investigation of numerical modeling of transient heat conduction in a one-dimensional functionally graded material", Heat Transf. Eng., 31(3), 212-221. https://doi.org/10.1080/01457630903304384
  12. Chaht, F.L., Kaci, A., Houari, M.S.A., Tounsi, A., Beg, O.A. and Mahmoud, S.R. (2015), "Bending and buckling analyses of functionally graded material (FGM) size-dependent nanoscale beams including the thickness stretching effect", Steel Compos. Struct., 18(2), 425-442. https://doi.org/10.12989/scs.2015.18.2.425.
  13. Chen, B., Tong, L., Gu, Y., Zhang, H. and Ochoa, O. (2004), "Transient heat transfer analysis of functionally graded materials using adaptive precise time integration and graded finite elements", Numer. Heat Transf. B: Fundam., 45(2), 181-200. https://doi.org/10.1080/1040779049025384.
  14. Chen, X., Lu, Y., Zhu, B., Zhang, X. and Li, Y. (2019), "Nonlinear resonant behaviors of bi-directional functionally graded material microbeams: one-/two-parameter bifurcation analyses", Compos. Struct., 223, 110896. https://doi.org/10.1016/j.compstruct.2019.110896.
  15. Choi, C.K. and Noh, H.C. (1996), "Stochastic finite element analysis of plate structures by weighted integral method", Struct. Eng. Mech., 4(6), 703-715. https://doi.org/10.12989/sem.1996.4.6.703.
  16. Cuong-Le, T., Nguyen, K.D, Le-Minh, H., Phan-Vu, P., Nguyen-Trong, P. and Tounsi, A. (2022), "Nonlinear bending analysis of porous sigmoid FGM nanoplate via IGA and nonlocal strain gradient theory", Adv. Nano Res, 12(5), 441. https://doi.org/10.12989/anr.2022.12.5.441.
  17. Daneshjou, K., Bakhtiari, M., Alibakhshi, R. and Fakoor, M. (2015), "Transient thermal analysis in 2D orthotropic FG hollow cylinder with heat source", Int. J. Heat Mass Transf., 89, 977-984. https://doi.org/10.1016/j.ijheatmasstransfer.2015.05.104.
  18. Demirbas, M.D. and Apalak, M.K. (2019), "Thermal stress analysis of one-and two-dimensional functionally graded plates subjected to in-plane heat fluxes", Proc. Inst. Mech. Eng. Pt. L J. Mater. Des. Appl., 233(4), 546-562. https://doi.org/10.1177/1464420716675507.
  19. Ghatage, P.S., Kar, V.R. and Sudhagar, P.E. (2020), "On the numerical modelling and analysis of multidirectional functionally graded composite structures: a review", Compos. Struct., 236, 111837. https://doi.org/10.1016/j.compstruct.2019.111837.
  20. Hachemi, H., Bousahla, A.A., Kaci, A., Bourada, F., Tounsi, A., Benrahou, K.H., Tounsi, A., Al-Zahrani, M.M. and Mahmoud, S.R. (2021), "Bending analysis of functionally graded plates using a new refined quasi-3D shear deformation theory and the concept of the neutral surface position", Steel Compos. Struct., 39(1), 51-64. https://doi.org/10.12989/scs.2021.39.1.051.
  21. Haghighi, M.G., Eghtesad, M. and Malekzadeh, P. (2008), "Coupled DQ-FE methods for two-dimensional transient heat transfer analysis of functionally graded material", Energy Convers. Manag., 49(5), 995-1001. https://doi.org/10.1016/j.enconman.2007.10.004.
  22. Hamidi, A., Tounsi, A., Houari, M.S.A. and Mahmoud, S.R. (2015), "A sinusoidal plate theory with 5-unknowns and stretching effect for thermomechanical bending of functionally graded sandwich plates", Steel Compos. Struct., 18(1), 235-253. https://doi.org/10.12989/scs.2015.18.1.235
  23. Hamza-Cherif, S. M., Houmat, A. and Hadjoui, A. (2007), "Transient heat conduction in functionally graded materials", Int. J. Comput. Methods, 4(4), 603-619. https://doi.org/10.1142/S0219876207001254.
  24. Hidayat, M.I.P., Ariwahjoedi, B., Parman, S. and Irawan, S. (2018), "A meshfree approach for transient heat conduction analysis of nonlinear functionally graded materials", Int. J. Comput. Methods, 15(02), 1850007. https://doi.org/10.1142/S021987621850007X.
  25. Huynh, T.A., Lieu, X.Q. and Lee, J. (2017), "NURBS-based modeling of bidirectional functionally graded Timoshenko beams for free vibration problem", Compos. Struct., 160, 1178-1190. https://doi.org/10.1016/j.compstruct.2016.10.076.
  26. Jeffers, A.E. (2013). "Heat transfer element for modeling the thermal response of non-uniformly heated plates", Finite Elem. Anal. Des., 63, 62-68. https://doi.org/10.1016/j.finel.2012.08.009.
  27. Joshi, K.K. and Kar, V.R. (2021), "Effect of material heterogeneity on the deformation behaviour of multidirectional (1D/2D/3D) functionally graded composite panels", Eng. Comput., 38(8), 3325-3350. https://doi.org/10.1108/EC-06-2020-0301.
  28. Kar, V.R. and Panda, S.K. (2015), "Nonlinear flexural vibration of shear deformable functionally graded spherical shell panel", Steel Compos. Struct., 18(3), 693-709. https://doi.org/10.12989/scs.2015.18.3.693.
  29. Katiyar, V., Gupta, A. and Tounsi, A. (2022), "Microstructural/geometric imperfection sensitivity on the vibration response of geometrically discontinuous bi-directional functionally graded plates (2D FGPs) with partial supports by using FEM", Steel Compos. Struct., 45(5), 621-640. https://doi.org/10.12989/scs.2022.45.5.621.
  30. Kermani, I.D., Ghayour, M. and Mirdamadi, H.R. (2012), "Free vibration analysis of multidirectional functionally graded circular and annular plates", J. Mech. Sci. Technol., 26(11), 3399-3410. https://doi.org/10.1007/s12206-012-0860-2.
  31. Kumar, S., Kar, V.R., and Khudayarov, B.A. (2022), "Analytical solution for the steady-state heat transfer analysis of porous nonhomogeneous material structures", Adv. Compos. Mater. Struct., CRC Press. https://doi.org/10.1201/9781003158813-3.
  32. Kumar, Y., Gupta, A. and Tounsi, A. (2021), "Size-dependent vibration response of porous graded nanostructure with FEM and nonlocal continuum model", Adv. Nano Res, 11(1), 001. https://doi.org/10.12989/anr.2021.11.1.001.
  33. Lee, P.S., Noh, H.C. and Choi, C.K. (2008), "Geometry-dependent MITC method for a 2-node iso-beam element", Struct. Eng. Mech., 29(2), 203-222. https://doi.org/10.12989/sem.2008.29.2.203.
  34. Lezgy-Nazargah, M. (2015), "Fully coupled thermo-mechanical analysis of bi-directional FGM beams using NURBS isogeometric finite element approach", Aerosp. Sci. Technol., 45, 154-164. https://doi.org/10.1016/j.ast.2015.05.006.
  35. Malek, M., Izem, N. and Seaid, M. (2020), "A three-dimensional enriched finite element method for nonlinear transient heat transfer in functionally graded materials", Int. J. Heat Mass Transf., 155, 119804. https://doi.org/10.1016/j.ijheatmasstransfer.2020.119804.
  36. Merazka, B., Bouhadra, A., Menasria, A., Selim, M.M., Bousahla, A.A., Bourada, F., Tounsi, A., Benrahou, K.H., Tounsi, A. and Al-Zahrani, M.M. (2021), "Hygro-thermo-mechanical bending response of FG plates resting on elastic foundations", Steel Compos. Struct., 39(5), 631-643. https://doi.org/10.12989/scs.2021.39.5.631.
  37. Moradi-Dastjerdi, R. and Payganeh, G. (2017), "Transient heat transfer analysis of functionally graded CNT reinforced cylinders with various boundary conditions", Steel Compos. Struct., 24(3), 359-367. https://doi.org/10.12989/scs.2017.24.3.359.
  38. Nie, G. and Zhong, Z. (2010), "Dynamic analysis of multidirectional functionally graded annular plates" Appl. Math. Model, 34(3), 608-616. https://doi.org/10.1016/j.apm.2009.06.009.
  39. Ramteke, P.M. and Panda, S.K. (2021), "Free vibrational behaviour of multi-directional porous functionally graded structures", Arab. J. Sci. Eng., 1-16. https://doi.org/10.1007/s13369-021-05461-6.
  40. Rathore, S.S., Kar, V.R. and Sanjay (2023), "Thermoelastic eigenfrequency of pre-twisted FG-sandwich straight/curved blades with rotational effect", Struct. Eng. Mech., 86(4), 519-533. https://doi.org/10.12989/sem.2023.86.4.000.
  41. Sah, S.K. and Ghosh, A. (2021), "Influence of porosity distribution on free vibration and buckling analysis of multi-directional functionally graded sandwich plates", Compos. Struct., 114795. https://doi.org/10.1016/j.compstruct.2021.114795.
  42. Tian, J., Jing, G., Han, X., Hu, G. and Huo, S. (2021), "Understanding the thermal problem of variable gradient functionally graded plate based on hybrid numerical method under linear heat source", Adv. Mech. Eng., 13(5), 16878140211017810. https://doi.org/10.1177/16878140211017810.
  43. Van Vinh, P., Van Chinh, N. and Tounsi, A. (2022), "Static bending and buckling analysis of bi-directional functionally graded porous plates using an improved first-order shear deformation theory and FEM", Eur. J. Mech. A/Solids, 96, 104743. https://doi.org/10.1016/j.euromechsol.2022.104743.
  44. Wang, B.L. and Mai, Y.W. (2005), "Transient one-dimensional heat conduction problems solved by finite element", Int. J. Mech. Sci., 47(2), 303-317. https://doi.org/10.1016/j.ijmecsci.2004.11.001.
  45. Wang, B.L. and Tian, Z.H. (2005), "Application of finite element-finite difference method to the determination of transient temperature field in functionally graded materials", Finite Elem. Anal. Des., 41(4), 335-349. https://doi.org/10.1016/j.finel.2004.07.001.
  46. Wang, B.L., Mai, Y.W. and Zhang, X.H. (2004), "Thermal shock resistance of functionally graded materials", Acta Mater., 52(17), 4961-4972. https://doi.org/10.1016/j.actamat.2004.06.008.
  47. Wang, X., Yuan, Z. and Jin, C. (2019), "3D free vibration analysis of multidirectional FGM parallelepipeds using the quadrature element method", Appl. Math. Model, 68, 383-404. https://doi.org/10.1016/j.apm.2018.11.030.
  48. Yang, H.S., Dong, C.Y. and Wu, Y.H. (2020), "Postbuckling analysis of multidirectional perforated FGM plates using NURBS-based IGA and FCM", Appl. Math. Model, 84, 466-500. https://doi.org/10.1016/j.apm.2020.03.043.
  49. Yildirim, V. (2017), "Exact thermal analysis of functionally graded cylindrical and spherical vessels", Int. J. Appl. Sci., 9(2), 112-126. https://doi.org/10.24107/ijeas.318459.
  50. Zhao, J., Ai, X. and Li, Y.Z. (2007), "Transient temperature fields in functionally graded materials with different shapes under convective boundary conditions", Heat Mass Transf., 43(12), 1227-1232. https://doi.org/10.1007/s00231-006-0135-5.
  51. Zhao, L., Chen, W.Q. and Lu, C.F. (2012), "Symplectic elasticity for bi-directional functionally graded materials", Mech. Mater., 54, 32-42. https://doi.org/10.1016/j.mechmat.2012.06.001.
  52. Zhou, H.M., Zhang, X.M. and Wang, Z.Y. (2019), "Thermal analysis of 2D FGM beam subjected to thermal loading using meshless weighted least-square method", Math. Probl. Eng., 2019. https://doi.org/10.1155/2019/2541707.
  53. Zhou, H., Li, S., Zhang, C. and Naser, M.Z. (2021), "Modeling fire performance of externally prestressed steel-concrete composite beams", Steel Compos. Struct., 41(5), 625-636. https://doi.org/10.12989/scs.2021.41.5.625.