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Temperature dependent buckling analysis of graded porous plate reinforced with graphene platelets

  • Wei, Guohui (R & D department, Beijing Scistar Technology Co., Ltd.) ;
  • Tahouneh, Vahid (Young Researchers and Elite Club, Islamshahr Branch, Islamic Azad University)
  • Received : 2020.09.02
  • Accepted : 2021.04.09
  • Published : 2021.05.10
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Abstract

The main purpose of this research work is to investigate the critical buckling load of functionally graded (FG) porous plates with graphene platelets (GPLs) reinforcement using generalized differential quadrature (GDQ) method at thermal condition. It is supposed that the GPL nanofillers and the porosity coefficient vary continuously along the plate thickness direction. Generally, the thermal distribution is considered to be nonlinear and the temperature changing continuously through the thickness of the nanocomposite plates according to the power-law distribution. To model closed cell FG porous material reinforced with GPLs, Halpin-Tsai micromechanical modeling in conjunction with Gaussian-Random field scheme are used, through which mechanical properties of the structures can be extracted. Based on the third order shear deformation theory (TSDT) and the Hamilton's principle, the equations of motion are established and solved for various boundary conditions (B.Cs). The fast rate of convergence and accuracy of the method are investigated through the different solved examples and validity of the present study is evaluated by comparing its numerical results with those available in the literature. A special attention is drawn to the role of GPLs weight fraction, GPLs patterns through the thickness, porosity coefficient and distribution of porosity on critical buckling load. Results reveal that the importance of thermal condition on of the critical load of FGP-GPL reinforced nanocomposite plates.

Keywords

References

  1. Afrookhteh, S.S., Fathi, A., Naghdipour, M. and Alizadeh Sahraei, A. (2016), "An experimental investigation of the effects of weight fractions of reinforcement and timing of hardener addition on the strain sensitivity of carbon nanotube/polymer composites", U.P.B. Sci. Bull., Series B, 78(4), 121-130.
  2. Afrookhteh, S.S., Shakeri, M., Baniassadi, M. and Alizadeh Sahraei, A. (2018), "Microstructure Reconstruction and Characterization of the Porous GDLs for PEMFC Based on Fibers Orientation Distribution", Fuel Cells, 18(2), https://doi.org/10.1002/fuce.201700239.
  3. Aghababaei, R. and Reddy, J.N. (2009), "Nonlocal third-order shear deformation plate theory with application to bending and vibration of plates ", J. Sound Vib., 326(1-2), 277-289. https://doi.org/10.1016/j.jsv.2009.04.044.
  4. Ahmadi, S.M., Campoli, G., Yavari, S.A., Sajadi, B., Wauthle, R., Schrooten, J., Weinans, H. and Zadpoor, A.A. (2014), "Mechanical behavior of regular open-cell porous biomaterials made of diamond lattice unit cells", J. Mech. Behav. Biomed. Mater., 34, 106-115. https://doi.org/10.1016/j.jmbbm.2014.02.003.
  5. Ahmed Houari, M.S., Bessaim, A., Bernard, F., Tounsi, A. and Mahmoud, S.R. (2018), "Buckling analysis of new quasi-3D FG nanobeams based on nonlocal strain gradient elasticity theory and variable length scale parameter", Steel Compos. Struct., 28(1), 13-24. https://doi.org/10.12989/scs.2018.28.1.013.
  6. Alibeigloo, A. (2013), "Three-dimensional free vibration analysis of multi-layered graphene sheets embedded in elastic matrix", J.V.C., 19(16), 2357-2371. https://doi.org/10.1177/1077546312456056.
  7. Alizadeh Sahraei, A., Mokarizadeh, A.H., George, D., Rodrigue, D., Baniassadi, M. and Foroutan, M. (2019), "Insights into interphase thickness characterization for graphene/epoxy nanocomposites: A molecular dynamics simulation", Phys. Chem. Chem. Phys., 21(36), 19890-19903. https://doi.org/10.1039/C9CP04091A.
  8. Arefi, M. (2015), "Elastic solution of a curved beam made of functionally graded materials with different cross sections", Steel Compos. Struct., 18(3), 659-672. https://doi.org/10.12989/scs.2015.18.3.659.
  9. Asemi, K., Shariyat, M., Salehi, M. and Ashrafi, H. (2013), "A full compatible three-dimensional elasticity element for buckling analysis of FGM rectangular plates subjected to various combinations of biaxial normal and shear loads", Finite Elem. Anal. Des., 74, 9-21. https://doi.org/10.1016/j.finel.2013.05.011.
  10. Barka, M., Benrahou, K.H., Bakora, A. and Tounsi, A. (2016), "Thermal post-buckling behavior of imperfect temperature-dependent sandwich FGM plates resting on Pasternak elastic foundation", Steel Compos. Struct., 22(1), 91-112. https://doi.org/10.12989/scs.2016.22.1.091.
  11. Bennai, R., AitAtmane, H. and Tounsi, A. (2015), "A new higher-order shear and normal deformation theory for functionally graded sandwich beams", Steel Compos. Struct., 19(3), 521-546. https://doi.org/10.12989/scs.2015.19.3.521.
  12. Benveniste, Y. (1987), "A new approach to the application of Mori-Tanaka's theory in composite materials", Mech. Mater., 6(2), 147-157. https://doi.org/10.1016/0167-6636(87)90005-6.
  13. Bert, C.W. and Malik, M. (1996), "Differential quadrature method in computational mechanics: a review", Appl. Mech. Reviews, 49(1), 1-28. https://doi.org/10.1115/1.3101882.
  14. Bonnet, P., Sireude, D., Garnier, B. and Chauvet, O. (2007), "Thermal properties and percolation in carbon nanotube-polymer composites", J. Appl. Phys., 91(20), 2019-2030. https://doi.org/10.1063/1.2813625.
  15. Bouchafa, A., Bouiadjra, M.B., Houari, M.S.A. and Tounsi, A. (2015), "Thermal stresses and deflections of functionally graded sandwich plates using a new refined hyperbolic shear deformation theory", Steel Compos. Struct., 18(6), 1493-1515. https://doi.org/10.12989/scs.2015.18.6.1493.
  16. Bouguenina, O., Belakhdar, K., Tounsi, A. and Bedia, E.A.A. (2015), "Numerical analysis of FGM plates with variable thickness subjected to thermal buckling", Steel Compos. Struct., 19(3), 679-695. https://doi.org/10.12989/scs.2015.19.3.679.
  17. Chang, T. and Gao, H. (2003), "Size-dependent elastic properties of a single-walled carbon nanotube via a molecular mechanics model", J. Mech. Phys. Solids, 51(6), 1059-1074. https://doi.org/10.1016/S0022-5096(03)00006-1.
  18. Chen, C.H. and Cheng, C.H. (1996), "Effective elastic moduli of misoriented short-fiber composites", Int. J. Solids Struct., 33(17), 2519-2539. https://doi.org/10.1016/0020-7683(95)00160-3.
  19. Chen, C.S., Liu, F.H. and Chen, W.R. (2017), "vibration and stability of initially stressed sandwich plates with FGM face sheets in thermal environments", Steel Compos. Struct., 23(3), 251-261. https://doi.org/10.12989/scs.2017.23.3.251.
  20. Chen, D., Yang, J. and Kitipornchai, S. (2015), "Elastic buckling and static bending of shear deformable functionally graded porous beam", Compos. Struct., 133, 54-61. https://doi.org/10.1016/j.compstruct.2015.07.052.
  21. Cheng, Z.Q. and Batra, R. (2000), "Exact correspondence between eigenvalues of membranes and functionally graded simply supported polygonal plates", J. Sound Vib., 229(4), 879-895. https://doi.org/10.1006/jsvi.1999.2525.
  22. Dong, Y., Li, X., Gao, K., Li, Y. and Yang, J. (2019), "Harmonic resonances of graphene-reinforced nonlinear cylindrical shells: effects of spinning motion and thermal environment", Nonlinear Dyn., 99, 981-1000. https://doi.org/10.1007/s11071-019-05297-8.
  23. Endo, M., Hayashi, T., Kim, Y.A., Terrones, M. and Dresselhaus, M.S. (2004), "Applications of carbon nanotubes in the twenty-first century", P. T. Roy. Soc. Lond. Series A: Math Phys. Eng. Sci., 362, 2223-2238. https://doi.org/10.1098/rsta.2004.1437.
  24. Esawi, A.M. and Farag, M.M. (2007), "Carbon nanotube reinforced composites: potential and current challenges", Mater. Des., 28(9), 2394-2401. https://doi.org/10.1016/j.matdes.2006.09.022.
  25. Eshelby, J.D. (1957), "The determination of the elastic field of an ellipsoidal inclusion, and related problems", P. Roy. Soc. London, Ser. A., 241(1226), 376-396.
  26. Eshelby, J.D. (1959), "The elastic field outside an ellipsoidal inclusion", Proc. R. Soc. London, Ser. A., 252(1271), 561-569.
  27. Fidelus, J., Wiesel, E., Gojny, F., Schulte, K. and Wagner, H. (2005), "Thermo-mechanical properties of randomly oriented carbon/epoxy nanocomposites", Compos. Part A: Appl. Sci. Manufact., 36(11), 1555-1561. https://doi.org/10.1016/j.compositesa.2005.02.006
  28. Formica, G., Lacarbonara, W. and Alessi, R. (2010), "Vibrations of carbon nanotube-reinforced composites", J. Sound Vib., 329(10), 1875-1889. https://doi.org/10.1016/j.jsv.2009.11.020
  29. Fung, Y.C. and Tong, P. (2001), "Classical and computational solid mechanics", 5, World scientific Singapore.
  30. Giordano, S., Palla, P. and Colombo, L. (2009), "Nonlinear elasticity of composite materials", Eur. Phys. J. B. Condensed Matter Complex Syst., 68(89), 89-101. https://doi.org/10.1140/epjb/e2009-00063-1.
  31. Hadji, L. and Bernard, F. (2020), "Bending and free vibration analysis of functionally graded beams on elastic foundations with analytical validation", Adv. Mater. Res., 9(1), 63-98. https://doi.org/10.12989/amr.2020.9.1.063.
  32. Han, Y. and Elliott, J., "Molecular dynamics simulations of the elastic properties of polymer/carbon nanotube composites", Comput. Mater. Sci., 39(2), 315-323. https://doi.org/10.1016/j.commatsci.2006.06.011.
  33. Hosseini, S.M. and Zhang, C. (2018), "Elastodynamic and wave propagation analysis in a FG Graphene platelets-reinforced nanocomposite cylinder using a modified nonlinear micromechanical model", Steel Compos. Struct., 27(3), 255-271. https://doi.org/10.12989/scs.2018.27.3.255.
  34. Hosseini-Hashemi, S., Kermajani, M. and Nazemnezhad, R. (2015), "An analytical study on the buckling and free vibration of rectangular nanoplates using nonlocal third-order shear deformation plate theory", Eur. J. Mech. A/Solids, 51, 29-43. https://doi.org/10.1016/j.euromechsol.2014.11.005.
  35. Hu, N., Fukunaga, H., Lu, C., Kameyama, M. and Yan, B. (2005), "Prediction of elastic properties of carbon nanotube reinforced composites", P. Roy. Soc. London, Ser. A, 461(2058), 1685-1710.
  36. Jabbari, M., Hashemitaheri, M., Mojahedin, A. and Eslami, M.R. (2014), "Thermal buckling analysis of functionally graded thin circular plate made of saturated porous materials", J. Therm. Stresses, 37(2), 202-220. https://doi.org/10.1080/01495739.2013.839768.
  37. Jabbari, M., Mojahedin, A., Khorshidvand, A.R. and Eslami, M.R. (2013), "Buckling analysis of a functionally graded thin circular plate made of saturated porous materials", J. Eng. Mech., 140, 287-295. https://doi.org/10.1061/(ASCE)EM.1943-7889.0000663.
  38. Javaheri, R. and Eslami, M.R. (2002), "Buckling of Functionally Graded Plates under In-plane Compressive Loading", ZAMM-J. Appl. Math. Mech., 82(4), 277-283.
  39. Jin, Y. and Yuan, F. (2003), "Simulation of elastic properties of single-walled carbon nanotubes", Compos. Sci. Technol., 63(11), 1507-1515. https://doi.org/10.1016/S0266-3538(03)00074-5
  40. Jones, R.M. (2015), "Design of composite structures", Bull Ridge Publishing, Blacksburg, Virginia.
  41. Kitipornchai, S., Chen, D. and Yang, J. (2017), "Free vibration and elastic buckling of functionally graded porous beams reinforced by graphene platelets", Mater. Design, 116, 656-665. https://doi.org/10.1016/j.matdes.2016.12.061.
  42. Liew, K.M., Han, J.B., Xiao, Z. and Du, H. (1996), "Differential quadrature method for Mindlin plates on Winkler foundations", Int. J. Mech. Sci., 38(4), 405-421. https://doi.org/10.1016/0020-7403(95)00062-3.
  43. Liu, F., Ming, P. and Li, J., (2007), "Ab initio calculation of ideal strength and phonon instability of graphene under tension", Phys. Review B., 76, 064120. https://doi.org/10.1103/physrevb.76.064120
  44. Liu, R. and Wang, L.F. (2015), "Thermal vibration of a single-walled carbon nanotube predicted by semiquantum molecular dynamics", Phys. Chem. Chem. Phys., 7.
  45. Marin, M. (2010), "A domain of influence theorem for microstretch elastic materials, Nonlinear Anal. Real World Appl., 11(5), 3446-3452. https://doi.org/10.1016/j.nonrwa.2009.12.005.
  46. Marin, M. and Lupu, M. (1998), "On harmonic vibrations in thermoelasticity of micropolar bodies", J. Vib. Control, 4(5), 507-518. https://doi.org/10.1177/107754639800400501.
  47. Marin, M. and Marinescu, C. (1998), "Thermoelasticity of initially stressed bodies. Asymptotic equipartition of energies", Int. J. Eng. Sci., 36(1), 73-86. https://doi.org/10.1016/S0020-7225(97)00019-0.
  48. Matsunaga, H. (2000), "Vibration and stability of thick plates on elastic foundations", J. Eng. Mech. - ASCE, 126(1), 27-34. https://doi.org/10.1061/(ASCE)0733-9399(2000)126:1(27).
  49. Matsunaga, H. (2008), "Free vibration and stability of functionally graded plates according to a 2-D higher-order deformation theory", Compos. Struct., 82(4), 499-512. https://doi.org/10.1016/j.compstruct.2007.01.030.
  50. Mechab, I., Meiche, N.E., and Bernard, F. (2016), "Free Vibration Analysis of Higher-Order Shear Elasticity Nanocomposite Beams with Consideration of Nonlocal Elasticity and Poisson Effect", J. Nanomech. Micromech., 6(3), 1-13. https://doi.org/10.1061/(ASCE)NM.2153-5477.0000110.
  51. Moniruzzaman, M. and Winey, K.I. (2006), "Polymer nanocomposites containing carbon nanotubes", Macromolecules, 39(16), 5194-5205. https://doi.org/10.1021/ma060733p.
  52. Moradi-Dastjerdi, R. and Momeni-Khabisi, H. (2016), "Dynamic analysis of functionally graded nanocomposite plates reinforced by wavy carbon nanotube", Steel Compos. Struct., 22(2). https://doi.org/10.12989/scs.2016.22.2.277.
  53. Mori, T. and Tanaka, K. (1973), "Average stress in matrix and average elastic energy of materials with misfitting inclusions", Acta Metall., 21(5), 571-574. https://doi.org/10.1016/0001-6160(73)90064-3.
  54. Mura, T. (1987), Micromechanics of defects in solids, 3, Springer Science & Business Media.
  55. Odegard, G., Gates, T., Wise, K., Park, C. and Siochi, E. (2003), "Constitutive modeling of nanotube–reinforced polymer composites", Compos. Sci. Technol., 63(11), 1671-1687. https://doi.org/10.1016/S0266-3538(03)00063-0.
  56. Park, W.T., Han, S.C., Jung, W.Y. and Lee, W.H. (2016), "Dynamic instability analysis for S-FGM plates embedded in Pasternak elastic medium using the modified couple stress theory", Steel Compos. Struct., 22(6), 1239-1259. https://doi.org/10.12989/scs.2016.22.6.1239.
  57. Qian, D., Dickey, E.C., Andrews, R. and Rantell, T. (2000), "Load transfer and deformation mechanisms in carbon nanotube-polystyrene composites", Appl. Phys. Lett., 76, 2868-2870. https://doi.org/10.1063/1.126500.
  58. Rafiee, M. A., Rafiee, J., Wang, Z., Song, H., Yu, Z. Z., Koratkar, N. (2009), "Enhanced mechanical properties of nanocomposites at low graphene content", ACS Nano, 3(12), 3884-3890. https://doi.org/10.1021/nn9010472.
  59. Salvetat-Delmotte, J.P. and Rubio, A. (2002), "Mechanical properties of carbon nanotubes: a fiber digest for beginners", Carbon, 40(10), 1729-1734. https://doi.org/10.1016/S0008-6223(02)00012-X
  60. Shen, H.S. (2009), "Nonlinear bending of functionally graded carbon nanotube-reinforced composite plates in thermal environments", Compos. Struct., 91(1), 9-19. https://doi.org/10.1016/j.compstruct.2009.04.026.
  61. Shen, H.S. (2012), "Thermal buckling and postbuckling behavior of functionally graded carbon nanotube-reinforced composite cylindrical shells", Compos. Part B: Eng., 43(3), 1030-1038. https://doi.org/10.1016/j.compositesb.2011.10.004.
  62. Shen, H.S. and Zhang, C.L. (2010), "Thermal buckling and postbuckling behavior of functionally graded carbon nanotube-reinforced composite plates", Mater. Design, 31(7), 3403-3411. https://doi.org/10.1016/j.matdes.2010.01.048.
  63. Shen, H.S. and Zhu, Z.H. (2010), "Buckling and postbuckling behavior of functionally graded nanotube-reinforced composite plates in thermal environments", Comput. Mater. Continua (CMC), 18(2), 155-182. https://doi.org/10.3970/cmc.2010.018.155.
  64. Shu, C. and Wang, C. (1999), "Treatment of mixed and nonuniform boundary conditions in GDQ vibration analysis of rectangular plates", Eng. Struct., 21(2), 125-134. https://doi.org/10.1016/S0141-0296(97)00155-7.
  65. Tahouneh, V., Naei, M.H., Mosavi Mashhadi, M. (2019), "Using IGA and trimming approaches for vibrational analysis of L-shape graphene sheets via nonlocal elasticity theory", Steel Compos. Struct., 33(5), 717-727. https://doi.org/10.12989/scs.2019.33.5.717.
  66. Tahouneh, V., Naei, M.H., Mosavi Mashhadi, M. (2020), "Influence of vacancy defects on vibration analysis of graphene sheets applying isogeometric method: Molecular and continuum approaches", Steel Compos. Struct., 34(2), 261-277. https://doi.org/10.12989/scs.2020.34.2.261.
  67. Thostenson, E.T., Ren, Z. and Chou, T.W. (2001), "Advances in the science and technology of carbon nanotubes and their composites: a review", Compos. Sci. Technol., 61(13), 1899-1912. https://doi.org/10.1016/S0266-3538(01)00094-X.
  68. Tornabene, F., Bacciocchi, M., Fantuzzi, N. and Reddy, J.N. (2018), "Multiscale Approach for Three-Phase CNT/Polymer/Fiber Laminated Nanocomposite Structures", Polymer Composites, In Press, https://doi.org/10.1002/pc.24520.
  69. Tornabene, F., Fantuzzi, N., Ubertini, F. and Viola, E. (2015), "Strong Formulation Finite Element Method Based on Differential Quadrature: A Survey", Appl. Mech. Rev., 67(2), 1-55. https://doi.org/10.1115/1.4028859.
  70. Tornabene, F., Fantuzzi, N., Bacciocchi, M. (2019), "Refined shear deformation theories for laminated composite arches and beams with variable thickness: Natural frequency analysis", Eng. Anal. Bound. Elem., 100, 24-47. https://doi.org/10.1016/j.enganabound.2017.07.029.
  71. Tornabene, F., Fantuzzi, N., Bacciocchi, M. (2017), "Foam core composite sandwich plates and shells with variable stiffness: Effect of the curvilinear fiber path on the modal response", J. Sandw. Struct. Mater., 21(1), 320-365. https://doi.org/10.1177/1099636217693623.
  72. Valter, B., Ram, M.K. and Nicolini, C. (2002), "Synthesis of multiwalled carbon nanotubes and poly (o-anisidine) nanocomposite material: Fabrication and characterization of its Langmuir-Schaefer films", Langmuir, 18(5), 1535-1541. https://doi.org/10.1021/la0104673.
  73. Van Do, V.N. and Lee, C.H. (2019), "Mesh-free thermal buckling analysis of multilayered composite plates based on an nth-order shear deformation theory", Compos. Struct., 224. https://doi.org/10.1016/j.compstruct.2019.111042.
  74. Wang, L.F. and Hu, H. (2014a), "Thermal vibration of single-walled carbon nanotubes with quantum effects", Proc. R. Soc. A., 470. http://dx.doi.org/10.1098/rspa.2014.0087.
  75. Wang, L.F. and Hu, H. (2014b), "Thermal vibration of a rectangular single-layered graphene sheet with quantum effects", J. Appl. Phys., 115(23), https://doi.org/10.1063/1.4885015.
  76. Wang, L.F. and Hu, H. (2015), "Thermal vibration of a circular single-layered graphene sheet with simply supported or clamped boundary" J. Sound Vib., 349, 206-215. https://doi.org/10.1016/j.jsv.2015.03.045.
  77. Wang, Z.X. and Shen, H.S. (2011), "Nonlinear vibration of nanotube-reinforced composite plates in thermal environments", Comput. Mater. Sci., 50(8), 2319-2330. https://doi.org/10.1016/j.commatsci.2011.03.005.
  78. Wang, Y.Q., Ye, C. and Zu, J.W. (2019), "Vibration analysis of circular cylindrical shells made of metal foams under various boundary conditions", Int. J. Mech. Mater. Des., 15(2), 333-344. https://doi.org/10.1007/s10999-018-9415-8.
  79. Wernik, J. and Meguid, S. (2011), "Multiscale modeling of the nonlinear response of nano-reinforced polymers", Acta Mech., 217(1), 1-16. https://doi.org/10.1016/10.1007/s00707-010-0377-7.
  80. Wu, C.P. and Liu, Y.C. (2016), "A state space meshless method for the 3D analysis of FGM axisymmetric circular plates", Steel Compos. Struct., 22(1), 161-182. https://doi.org/10.12989/scs.2016.22.1.161.
  81. Yas, M.H. and Aragh, B.S. (2010), "Free vibration analysis of continuous grading fiber reinforced plates on elastic foundation", Int. J. Eng. Sci., 48(12), 1881-1895. https://doi.org/10.1016/j.ijengsci.2010.06.015.
  82. Yokozeki, T., Iwahori, Y. and Ishiwata, S. (2007), "Matrix cracking behaviors in carbon fiber/epoxy laminates filled with cup-stacked carbon nanotubes (CSCNTs)", Compos. Part A: Appl. Sci. Manufact., 38(3), 917-924. https://doi.org/10.1016/j.compositesa.2006.07.005.
  83. Zhang, Y. and Wang, L.F. (2018), "Thermally stimulated nonlinear vibration of rectangular single-layered black phosphorus", J. Appl. Phys., 124(13), https://doi.org/10.1063/1.5047584.