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An accurate analytical model for the buckling analysis of FG-CNT reinforced composite beams resting on an elastic foundation with arbitrary boundary conditions

  • Aicha Remil (Laboratoire d'Etude des Structures et de Mecanique des Materiaux, Departement de Genie Civil, Faculte des Sciences et de la Technologie, Universite Mustapha Stambouli) ;
  • Mohamed-Ouejdi Belarbi (Laboratoire de Recherche en Genie Civil, LRGC, Universite de Biskra) ;
  • Aicha Bessaim (Laboratoire d'Etude des Structures et de Mecanique des Materiaux, Departement de Genie Civil, Faculte des Sciences et de la Technologie, Universite Mustapha Stambouli) ;
  • Mohammed Sid Ahmed Houari (Laboratoire d'Etude des Structures et de Mecanique des Materiaux, Departement de Genie Civil, Faculte des Sciences et de la Technologie, Universite Mustapha Stambouli) ;
  • Ahmed Bouamoud (Laboratory of Mechanics of Structures and Solids (LMSS), Faculty of Technology, Department of Mechanical Engineering, University Djilali Liabes of Sidi Bel Abbes) ;
  • Ahmed Amine Daikh (Laboratoire d'Etude des Structures et de Mecanique des Materiaux, Departement de Genie Civil, Faculte des Sciences et de la Technologie, Universite Mustapha Stambouli) ;
  • Abderrahmane Mouffoki (Laboratoire d'Etude des Structures et de Mecanique des Materiaux, Departement de Genie Civil, Faculte des Sciences et de la Technologie, Universite Mustapha Stambouli) ;
  • Abdelouahed Tounsi (YFL (Yonsei Frontier Lab), Yonsei University) ;
  • Amin Hamdi (Department of Civil Engineering, Faculty of Engineering, King Abdulaziz University) ;
  • Mohamed A. Eltaher (Faculty of Engineering, Mechanical Design and Production Department, Zagazig University)
  • 투고 : 2022.07.29
  • 심사 : 2023.01.26
  • 발행 : 2023.03.25

초록

The main purpose of the current research is to develop an efficient two variables trigonometric shear deformation beam theory to investigate the buckling behavior of symmetric and non-symmetric functionally graded carbon nanotubes reinforced composite (FG-CNTRC) beam resting on an elastic foundation with various boundary conditions. The proposed theory obviates the use to shear correction factors as it satisfies the parabolic variation of through-thickness shear stress distribution. The composite beam is made of a polymeric matrix reinforced by aligned and distributed single-walled carbon nanotubes (SWCNTs) with different patterns of reinforcement. The material properties of the FG-CNTRC beam are estimated by using the rule of mixture. The governing equilibrium equations are solved by using new analytical solutions based on the Galerkin method. The robustness and accuracy of the proposed analytical model are demonstrated by comparing its results with those available by other researchers in the existing literature. Moreover, a comprehensive parametric study is presented and discussed in detail to show the effects of CNTs volume fraction, distribution patterns of CNTs, boundary conditions, length-to-thickness ratio, and spring constant factors on the buckling response of FG-CNTRC beam. Some new referential results are reported for the first time, which will serve as a benchmark for future research.

키워드

참고문헌

  1. Abo-Bakr, R.M., Eltaher, M.A. and Attia, M.A. (2022), "Pull-in and freestanding instability of actuated functionally graded nanobeams including surface and stiffening effects", Eng. Comput., 38(1), 255-276. https://doi.org/10.1007/s00366-020-01146-0.
  2. Abdelrahman, A.A., Esen, I., Daikh, A.A. and Eltaher, M.A. (2021), "Dynamic analysis of FG nanobeam reinforced by carbon nanotubes and resting on elastic foundation under moving load", Mech. Based Des. Struct. Mach., 2021, 1-24. https://doi.org/10.1080/15397734.2021.1999263.
  3. Abualnour, M., Houari, M.S.A., Tounsi, A. and Mahmoud, S.R. (2018), "A novel quasi-3D trigonometric plate theory for free vibration analysis of advanced composite plates", Compos. Struct., 184, 688-697. https://doi.org/10.1016/j.compstruct.2017.10.047.
  4. Akbas, S.D. (2019), "Nonlinear behavior of fiber reinforced cracked composite beams", Steel Compos. Struct., 30(4), 327-336. http://doi.org/10.12989/scs.2019.30.4.327.
  5. Akbas, S.D. (2021), "Forced vibration analysis of a fiber reinforced composite beam", Adv. Mater. Res., 10(1), 57-66. https://doi.org/10.12989/amr.2021.10.1.057.
  6. Alazwari, M.A., Daikh, A.A., Houari, M.S.A., Tounsi, A. and Eltaher, M.A. (2021), "On static buckling of multilayered carbon nanotubes reinforced composite nanobeams supported on non-linear elastic foundations", Steel Compos. Struct., 40(3), 389-404. http://doi.org/10.12989/scs.2021.40.3.389.
  7. Arani, A.G., Haghparast, E. and Zarei, H.B.A. (2016), "Vibration of axially moving 3-phase CNTFPC plate resting on orthotropic foundation", Struct. Eng. Mech., 57(1), 105-126. http://doi.org/10.12989/sem.2016.57.1.105.
  8. Belarbi, M.O., Daikh, A.A., Garg, A. Hirane, H., Houari, M.S.A., Civalak, O. and Chalak, H.D. (2023), "Bending and free vibration analysis of porous functionally graded sandwich plate with various porosity distributions using an extended layerwise theory", Arch. Civil Mech. Eng., 23(1), 15. https://doi.org/10.1007/s43452-022-00551-0.
  9. Belarbi, M.O., Li, L., Houari, M.S.A, Garg, A., Chalak, H.D., Dimitri, R. and Tornabene, F. (2022a), "Nonlocal vibration of functionally graded nanoplates using a layerwise theory", Math. Mech. Solid., 27(12), 2634-2661. https://doi.org/10.1177/10812865221078571.
  10. Belarbi, M.O., Garg, A., Houari, M.S.A., Hirane, H., Tounsi, A. and Chalak, H.D. (2021), "A three-unknown refined shear beam element model for buckling analysis of functionally graded curved sandwich beams", Eng. Comput., 38, 4273-4300. https://doi.org/10.1007/s00366-021-01452-1.
  11. Belarbi, M.O., Houari, M.S.A., Hirane, H., Daikh, A.A. and Bordas, S.P.A. (2022b), "On the finite element analysis of functionally graded sandwich curved beams via a new refined higher order shear deformation theory", Compos. Struct., 279, 114715. https://doi.org/10.1016/j.compstruct.2021.114715.
  12. Belarbi, M.O., Salami, S.J., Garg, A., Hirane, H., Daikh, A.A., Houari, M.S.A. (2022c), "Finite element bending and buckling analysis of functionally graded carbon nanotubes-reinforced composite beam under arbitrary boundary conditions", Steel Compos. Struct., 44(4), 451-471. https://doi.org/10.12989/scs.2022.44.4.451.
  13. Belarbi, M.O., Houari, M.S.A., Daikh, A.A., Garg, A., Merzouki, T., Chalak, H.D. and Hirane, H. (2022d), "Nonlocal finite element model for the bending and buckling analysis of functionally graded nanobeams using a novel shear deformation theory", Compos. Struct., 264, 113712. https://doi.org/10.1016/j.compstruct.2021.113712.
  14. Daikh, A.A., Houari, M.S.A., Belarbi, M.O., Chakraverty, S. and Eltaher, M.A. (2022a), "Analysis of axially temperature-dependent functionally graded carbon nanotube reinforced composite plates", Eng. Comput., 38, 2533-2554. https://doi.org/10.1007/s00366-021-01413-8.
  15. Daikh, A.A., Belarbi, M.O., Ahmed, D., Houari, M.S.A., Avcar, M., Tounsi, A. and Eltaher, M.A. (2022b), "Static analysis of functionally graded plate structures resting on variable elastic foundation under various boundary conditions", Acta Mech., 234(2), 775-806. https://doi.org/10.1007/s00707-022-03405-1.
  16. Daikh, A.A., Houari, M.S.A., Belarbi, M.O., Mohamed, S.A. and Eltaher, M.A. (2021), "Static and dynamic stability responses of multilayer functionally graded carbon nanotubes reinforced composite nanoplates via quasi 3D nonlocal strain gradient theory", Defence Technol., 18(10), 1778-1809. https://doi.org/10.1016/j.dt.2021.09.011.
  17. Daikh, A.A., Bensaid, I., Bachiri, A., Houari, M.S.A., Tounsi, A. and Merzouki, T. (2020), "On static bending of multilayered carbon nanotube-reinforced composite plates", Comput. Concrete, 26(2), 137-150. http://doi.org/10.12989/cac.2020.26.2.137.
  18. De Borbon, F., Ambrosini, D. and Curadelli, O. (2014), "Damping response of composites beams with carbon nanotubes", Compos, Part B: Eng,, 60, 106-110. https://doi.org/10.1016/j.compositesb.2013.12.041.
  19. Dorduncu, M. (2020), "Stress analysis of sandwich plates with functionally graded cores using peridynamic differential operator and refined zigzag theory", Thin Wall. Struct., 146, 106468. https://doi.org/10.1016/j.tws.2019.106468.
  20. Ebrahimi, F. and Farazmandnia, N. (2018a), "Thermal buckling analysis of functionally graded carbon nanotube-reinforced composite sandwich beams", Steel Compos. Struct., 27(2), 149-159. http://doi.org/10.12989/scs.2018.27.2.149.
  21. Ebrahimi, F. and Farazmandnia, N. (2018b), "Vibration analysis of functionally graded carbon nanotube-reinforced composite sandwich beams in thermal environment", Adv. Aircraft Spacecraft Sci., 5(1), 107. http://doi.org/10.12989/aas.2018.5.1.107.
  22. Ebrahimi, F. and Rostami, P. (2018), "Propagation of elastic waves in thermally affected embedded carbon-nanotube-reinforced composite beams via various shear deformation plate theories", Struct. Eng. Mech., 66(4), 495-504. https://doi.org/10.12989/sem.2018.66.4.495.
  23. Eltaher, M.A. and Mohamed, N. (2020), "Nonlinear stability and vibration of imperfect CNTs by doublet mechanics", Appl. Math. Comput., 382, 125311. https://doi.org/10.1016/j.amc.2020.125311.
  24. Eltaher, M.A., Abdelrahman, A.A. and Esen, I. (2021), "Dynamic analysis of nanoscale Timoshenko CNTs based on doublet mechanics under moving load", Eur. Phys. J. Plus, 136(7), 1-21. https://doi.org/10.1140/epjp/s13360-021-01682-8.
  25. 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.
  26. Esen, I., Daikh, A.A. and Eltaher, M.A. (2021), "Dynamic response of nonlocal strain gradient FG nanobeam reinforced by carbon nanotubes under moving point load", Eur. Phys. J. Plus, 136(4), 1-22. https://doi.org/10.1140/epjp/s13360-021-01419-7.
  27. Feng, C., Kitipornchai, S. and Yang, J. (2017), "Nonlinear free vibration of functionally graded polymer composite beams reinforced with graphene nanoplatelets (GPLs)", Eng. Struct., 140, 110-119. http://doi.org/10.1016/j.engstruct.2017.02.052.
  28. Ferreira, A.J.M., Castro, L.M. and Bertoluzza, S. (2009), "A high order collocation method for the static and vibration analysis of composite plates using a first-order theory", Compos. Struct., 89(3), 424-432. https://doi.org/10.1016/j.compstruct.2008.09.006.
  29. Fidelus, J.D., Wiesel, E., Gojny, F.H., Schulte, K. and Wagner, H.D. (2005), "Thermo-mechanical properties of randomly oriented carbon/epoxy nanocomposites", Compos. Part A: Appl. Sci. Manuf., 36(11), 1555-1561. https://doi.org/10.1016/j.compositesa.2005.02.006.
  30. Frikha, A., Zghal, S. and Dammak, F. (2018), "Finite rotation three and four nodes shell elements for functionally graded carbon nanotubes-reinforced thin composite shells analysis", Comput. Method. Appl. Mech. Eng., 329, 289-311. https://doi.org/10.1016/j.cma.2017.10.013.
  31. Garg, A., Chalak, H.D., Belarbi, M.O., Zenkour, A.M. and Sahoo, R. (2021), "Estimation of carbon nanotubes and their applications as reinforcing composite materials - An engineering review", Compos. Struct., 272, 114234. https://doi.org/10.1016/j.compstruct.2021.114234.
  32. Garg, A., Chalak, H.D., Zenkour, A.M., Belarbi, M.O. and Houari, M.S.A. (2022), "A review of available theories and methodologies for the analysis of nano isotropic, nano functionally graded, and CNT reinforced nanocomposite structures", Arch. Comput. Method. Eng., 29, 2237-2270 https://doi.org/10.1007/s11831-021-09652-0.
  33. Han, Y. and Elliott, J. (2007), "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.
  34. Heidari, M. and Arvin, H. (2019), "Nonlinear free vibration analysis of functionally graded rotating composite Timoshenko beams reinforced by carbon nanotubes", J. Vib. Control, 25(14), 2063-2078. https://doi.org/10.1177/1077546319847836.
  35. Hu, N., Fukunaga, H., Lu, C., Kameyama, M. and Yan, B. (2005), "Prediction of elastic properties of carbon nanotube reinforced composites", Proc. Royal Soc. A: Math. Phys. Eng. Sci., 461(2058), 1685-1710. https://doi.org/10.1098/rspa.2004.1422.
  36. Kamarian, S., Shakeri, M., Yas, M.H., Bodaghi, M. and Pourasghar, A. (2015), "Free vibration analysis of functionally graded nanocomposite sandwich beams resting on Pasternak foundation by considering the agglomeration effect of CNTs", J. Sandw. Struct. Mater., 17(6), 632-665. https://doi.org/10.1177/1099636215590280.
  37. Kumar, P. and Srinivas, J. (2017), "Free vibration, bending and buckling of a FG-CNT reinforced composite beam: Comparative analysis with hybrid laminated composite beam", Multidiscipl. Model. Mater. Struct., 13(4), 590-611. https://doi.org/10.1108/MMMS-05-2017-0032.
  38. Lal, A. and Markad, K. (2018), "Deflection and stress behaviour of multi-walled carbon nanotube reinforced laminated composite beams", Comput. Concrete, 22(6), 501-514. https://doi.org/10.12989/cac.2018.22.6.501.
  39. Lei, Z. and Zhang, Y. (2018), "Characterizing buckling behavior of matrix-cracked hybrid plates containing CNTR-FG layers", Steel Compos. Struct., 28(4), 495-508. http://doi.org/10.12989/scs.2018.28.4.495.
  40. Lin, F. and Xiang, Y. (2014), "Vibration of carbon nanotube reinforced composite beams based on the first and third order beam theories", Appl. Math. Model., 38(15-16), 3741-3754. https://doi.org/10.1016/j.apm.2014.02.008.
  41. Melaibari, A., Daikh, A.A., Basha, M., Abdalla, A.W., Othman, R., Almitani, K.H. and Eltaher, M.A. (2022), "Free vibration of FG-CNTRCs nano-plates/shells with temperature-dependent properties", Math., 10(4), 583. https://doi.org/10.3390/math10040583.
  42. Melaibari, A., Mohamed, S.A., Assie, A.E., Shanab, R.A. and Eltaher, M.A. (2023), "Mathematical and physical analyses of middle/neutral surfaces formulations for static response of bidirectional FG plates with movable/immovable boundary conditions", Math., 11(1), 2. https://doi.org/10.3390/math11010002.
  43. Mohammadimehr, M. and Alimirzaei, S. (2016), "Nonlinear static and vibration analysis of Euler-Bernoulli composite beam model reinforced by FG-SWCNT with initial geometrical imperfection using FEM", Struct. Eng. Mech., 59(3), 431-454. https://doi.org/10.12989/sem.2016.59.3.431.
  44. Muralidharan, N., Teblum, E., Westover, A.S., Schauben, D., Itzhak, A., Muallem, M. and Pint, C.L. (2018), "Carbon nanotube reinforced structural composite supercapacitor", Sci. Rep., 8(1), 1-9. https://doi.org/10.1038/s41598-018-34963-x.
  45. Pai, P.F. (1995), "A new look at shear correction factors and warping functions of anisotropic laminates", Int. J. Solid. Struct., 32(16), 2295-2313. https://doi.org/10.1016/0020-7683(94)00258-X.
  46. Sharma, L.K., Bhardwaj, G. and Grover, N. (2021), "Finite element framework for static analysis of temperature dependent IHSDT based functionally graded CNT reinforced plates", Mech. Based Des. Struct. Mach., 2021, 1-22. https://doi.org/10.1080/15397734.2021.1999265.
  47. Sharma, L.K., Grover, N. and Bhardwaj, G. (2023), "Buckling and free vibration analysis of temperature-dependent functionally graded CNT-reinforced plates", J. Vib. Eng. Technol., 11(1), 175-192. https://doi.org/10.1007/s42417-022-00571-3.
  48. 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.
  49. Shen, H.S., Xiang, Y. and Lin, F. (2017), "Nonlinear bending of functionally graded graphene-reinforced composite laminated plates resting on elastic foundations in thermal environments", Compos. Struct., 170, 80-90. https://doi.org/10.1016/j.compositesb.2017.10.032.
  50. Shi, Z., Yao, X., Pang, F. and Wang, Q. (2017), "An exact solution for the free-vibration analysis of functionally graded carbonnanotube-reinforced composite beams with arbitrary boundary conditions", Sci. Rep., 7(1), 1-18. https://doi.org/10.1038/s41598-017-12596-w.
  51. Sobhy, M. (2013), "Buckling and free vibration of exponentially graded sandwich plates resting on elastic foundations under various boundary conditions", Compos. Struct., 99, 76-87. https://doi.org/10.1016/j.compstruct.2012.11.018.
  52. Sobhy, M. (2019), "Levy solution for bending response of FG carbon nanotube reinforced plates under uniform, linear, sinusoidal and exponential distributed loadings", Eng. Struct., 182, 198-212. https://doi.org/10.1016/j.engstruct.2018.12.071.
  53. Soni, A., Grover, N., Bhardwaj, G. and Singh, B.N. (2020), "Non-polynomial framework for static analysis of functionally graded carbon nano-tube reinforced plates", Compos. Struct., 233, 111569. https://doi.org/10.1016/j.compstruct.2019.111569.
  54. Tagrara, S.H., Benachour, A., Bouiadjra, M.B. and Tounsi, A. (2015), "On bending, buckling and vibration responses of functionally graded carbon nanotube-reinforced composite beams", Steel Compos. Struct., 19(5), 1259-1277. http://doi.org/10.12989/scs.2015.19.5.1259.
  55. Taraghi, I., Fereidoon, A. and Taheri-Behrooz, F. (2014), "Low-velocity impact response of woven kevlar/epoxy laminated composites reinforced with multi-walled carbon nanotubes at ambient and low temperatures", Mater. Des., 53, 152-158. https://doi.org/10.1016/j.matdes.2013.06.051.
  56. Vinh, P.V., Belarbi, M.O. and Tounsi, A. (2022), "Wave propagation analysis of functionally graded nanoplates using nonlocal higher-order shear deformation theory with spatial variation of the nonlocal parameters", Waves Random Complex Media, 2022, 1-21. https://doi.org/10.1080/17455030.2022.2036387.
  57. Wattanasakulpong, N. and Ungbhakorn, V. (2013). "Analytical solutions for bending, buckling and vibration responses of carbon nanotube-reinforced composite beams resting on elastic foundation", Comput. Mater. Sci., 71, 201-208. https://doi.org/10.1016/j.commatsci.2013.01.028.
  58. Wuite, J. and Adali, S. (2005), "Deflection and stress behaviour of nanocomposite reinforced beams using a multiscale analysis", Compos. Struct., 71(3-4), 388-396. https://doi.org/10.1016/j.compstruct.2005.09.011.
  59. Xie, X.L., Mai, Y.W. and Zhou, X.P. (2005), "Dispersion and alignment of carbon nanotubes in polymer matrix: A review", Mater. Sci. Eng.: R: Rep., 49(4), 89-112. https://doi.org/10.1016/j.mser.2005.04.002.
  60. Yadav, A., Bhardwaj, G. and Godara, R.K. (2022a), "Thermally induced fracture analysis of CNT reinforced FG structures with multiple discontinuities using XIGA", Eng. Frac. Mech., 275, 108822. https://doi.org/10.1016/j.engfracmech.2022.108822.
  61. Yadav, A., Bhardwaj, G. and Godara, R.K. (2022b), "Influence of discontinuities on the fracture behaviour of CNT reinforced composites subjected to thermo-mechanical load using XIGA", J. Strain Anal. Eng. Des., 2022, 03093247221122052. https://doi.org/10.1177/03093247221122052.
  62. Yadav, A., Godara, R.K., Bhardwaj, G., Patil, R.U., Singh, S.K. and Khanna, K. (2021), "A review on fracture analysis of CNT/graphene reinforced composites for structural applications", Arch. Comput. Method. Eng., 29, 545-582. https://doi.org/10.1007/s11831-021-09650-2.
  63. Yang, J., Wu, H. and Kitipornchai, S. (2017), "Buckling and postbuckling of functionally graded multilayer graphene platelet-reinforced composite beams", Compos. Struct., 161, 111-118. https://doi.org/10.1016/j.compstruct.2016.11.048.
  64. Yas, M.H. and Samadi, N. (2012), "Free vibrations and buckling analysis of carbon nanotube-reinforced composite Timoshenko beams on elastic foundation", Int. J. Press. Vessel. Pip., 98, 119-128. https://doi.org/10.1016/j.ijpvp.2012.07.012.
  65. Zghal, S., Frikha, A. and Dammak, F. (2017), "Static analysis of functionally graded carbon nanotube-reinforced plate and shell structures", Compos. Struct., 176, 1107-1123. https://doi.org/10.1016/j.compstruct.2017.06.015.
  66. Zhang, L.W., Lei, Z.X., Liew, K.M. and Yu, J.L. (2014), "Static and dynamic of carbon nanotube reinforced functionally graded cylindrical panels", Compos. Struct., 111, 205-212. https://doi.org/10.1016/j.compstruct.2013.12.035.
  67. Zhu, R., Pan, E. and Roy, A.K. (2007), "Molecular dynamics study of the stress-strain behavior of carbon-nanotube reinforced Epon 862 composites", Mater. Sci. Eng.: A, 447(1-2), 51-57. https://doi.org/10.1016/j.msea.2006.10.054.