Computers and Concrete

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Influences of porosity distributions on bending and buckling behaviour of functionally graded carbon nanotube-reinforced composite beam

  • Abdulmajeed M. Alsubaie (Department of Civil and Environmental Engineering, King Fahd University of Petroleum & Minerals) ;
  • Mohammed A. Al-Osta (Department of Civil and Environmental Engineering, King Fahd University of Petroleum & Minerals) ;
  • Ibrahim Alfaqih (Department of Civil and Environmental Engineering, King Fahd University of Petroleum & Minerals) ;
  • Abdelouahed Tounsi (Department of Civil and Environmental Engineering, King Fahd University of Petroleum & Minerals) ;
  • Abdelbaki Chikh (Material and Hydrology Laboratory, University of Sidi Bel Abbes, Faculty of Technology, Civil Engineering Department) ;
  • Ismail M. Mudhaffar (Department of Civil and Environmental Engineering, King Fahd University of Petroleum & Minerals) ;
  • Salah U. Al-Dulaijan (Department of Civil and Environmental Engineering, King Fahd University of Petroleum & Minerals) ;
  • Saeed Tahir (Department of Civil and Environmental Engineering, King Fahd University of Petroleum & Minerals)
  • Received : 2022.12.19
  • Accepted : 2024.01.01
  • Published : 2024.08.25
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Abstract

The bending and buckling effect for carbon nanotube-reinforced composite (CNTRC) beams can be evaluated by developing the theory of third shear deformation (TSDT). This study examines beams supported by viscoelastic foundations, where single-walled carbon nanotubes (SWCNTs) are dispersed and oriented within a polymer matrix. Four patterns of reinforcement are used for the CNTRC beams. The rule of mixtures is assessed for the material properties of CNTRC beams. The effective functionally graded materials (FGM) properties are studied by considering three different uneven distribution types of porosity. The damping coefficient is considered to investigate the viscosity effect on the foundation in addition to Winkler's and Pasternak's parameters. The accuracy of the current theory is inspected with multiple comparison works. Moreover, the effects of different beam parameters on the CNTRC beam bending and buckling over a viscoelastic foundation are discussed. The results demonstrated that the O-beam is the weakest type of CNTRC beam to resist buckling and flexure loads, whereas the X-beam is the strongest. Moreover, it is indicated that the presence of porosity in the beams decreases the stiffness and increases deflection. In comparison, the deflection was reduced in the presence of a viscoelastic foundation.

Keywords

Acknowledgement

The authors would like to acknowledge the support provided by the Interdisciplinary Research Center for Construction & Building Materials (IRC-CBM) at King Fahd University of Petroleum & Minerals (KFUPM), Saudi Arabia, for funding this work through Project No. INCB2209. The support provided by the Department of Civil & Environmental Engineering, KFUPM, Saudi Arabia, is also greatly acknowledged.

References

  1. Almitani, K.H., Eltaher, M.A., Abdelrahman, A.A. and Abd-El-Mottaleb, H.E. (2021), "Finite element based stress and vibration analysis of axially functionally graded rotating beams", Struct. Eng. Mech., 79(1), 23-33. https://doi.org/10.12989/sem.2021.79.1.023.
  2. AlSaid-Alwan, H.H.S. and Avcar, M. (2020), "Analytical solution of free vibration of FG beam utilizing different types of beam theories: A comparative study", Comput. Concrete, 26(3), 285-292. http://doi.org/10.12989/cac.2020.26.3.285.
  3. Alsubaie, A.M., Alfaqih, I., Al-Osta, M.A., Tounsi, A., Chikh, A., Mudhaffar, I.M. and Tahir, S. (2023), "Porosity-dependent vibration investigation of functionally graded carbon nanotube-reinforced composite beam", Comput. Concrete, 32(1), 75-85. https://doi.org/10.12989/cac.2023.32.1.075.
  4. Behdinan, K. and Moradi-Dastjerdi, R. (2022), "Thermal buckling resistance of a lightweight lead-free piezoelectric nanocomposite sandwich plate", Adv. Nano Res., 12(6), 593-603. https://doi.org/10.12989/anr.2022.12.6.593.
  5. Carrera, E. (2003), "Theories and finite elements for multilayered plates and shells: A unified compact formulation with numerical assessment and benchmarking", Arch. Comput. Method. Eng., 10(3), 215-296. https://doi.org/10.1007/BF02736224.
  6. Chai, Q. and Wang, Y.Q. (2022), "Traveling wave vibration of graphene platelet reinforced porous joined conical-cylindrical shells in a spinning motion", Eng. Struct., 252, 113718. https://doi.org/10.1016/j.engstruct.2021.113718.
  7. Chikh, A. (2019), "Analysis of static behavior of a P-FGM Beam", J. Mater. Eng. Struct., 6(4), 513-524.
  8. Cui, Z., Cai, X., Ali, H.E. and Muhsen, S. (2022), "Investigating nonlinear vibration behavior of sandwich panels with multiscale skins based on a numerical method", Struct. Eng. Mech., 83(3), 283-292. https://doi.org/10.12989/sem.2022.83.3.283.
  9. Cuong-Le, T., Hoang-Le, M., Ferreira, A.J.M. and Wahab, M.A. (2022), "Small size-effect isogeometric analysis for linear and nonlinear responses of porous metal foam microplate", Compos. Struct., 285, 115189. https://doi.org/10.1016/j.compstruct.2022.115189.
  10. Daouadji, T.H., Adim, B. and Benferhat, R. (2016), "Bending analysis of an imperfect FGM plates under hygro-thermomechanical loading with analytical validation", Adv. Mater. Res., 5(1), 35-53. https://doi.org/10.12989/amr.2016.5.1.035.
  11. Ding, H.X., Zhang, Y.W. and She, G.L. (2022), "On the resonance problems in FG-GPLRC beams with different boundary conditions resting on elastic foundations", Comput. Concrete, 30(6), 433-443. https://doi.org/10.12989/cac.2022.30.6.433.
  12. Eyvazian, A., Zhang, C., Musharavati, F., Khan, A. and Mohamed, A. M. (2021), "Elastic wave phenomenon of nanobeams including thickness stretching effect", Adv. Nano Res., 10(3), 271-280. https://doi.org/10.12989/anr.2021.10.3.271.
  13. Farokhian, A. and Kolahchi, R., (2020), "Frequency and instability responses in nanocomposite plate assuming different distribution of CNTs", Struct. Eng. Mech., 73(5), 555-563. https://doi.org/10.12989/sem.2020.73.5.555.
  14. Filippi, M., Carrera, E. and Zenkour, A.M. (2015), "Static analyses of FGM beams by various theories and finite elements", Compos. Part B: Eng., 72, 1-9. https://doi.org/10.1016/j.compositesb.2014.12.004.
  15. Ghandourah, E., Hussain, M., Al Thobiani, F., Hefni, M. and Alghamdi, S. (2022), "Direct strength measurement of Timoshenko-beam model: Vibration analysis of double walled carbon nanotubes", Struct. Eng. Mech., 84(1), 77-83. https://doi.org/10.12989/sem.2022.84.1.077.
  16. Ghorbani Shenas, A., Ziaee, S. and Malekzadeh, P. (2019), "A unified higher-order beam theory for free vibration and buckling of FGCNT-reinforced microbeams embedded in elastic medium based on unifying stress-strain gradient framework", Iran. J. Sci. Technol. Trans. Mech. Eng., 43(s1), 469-492. https://doi.org/10.1007/s40997-018-0171-z.
  17. Hadji, L. (2019), "An analytical solution for bending and free vibration responses of functionally graded beams with porosities: Effect of the micromechanical models", Struct. Eng. Mech., 69(2), 231-241. https://doi.org/10.12989/sem.2019.69.2.231.
  18. Hadji, L., Zouatnia, N. and Kassoul, A. (2016), "Bending analysis of FGM plates using a sinusoidal shear deformation theory", Wind Struct., 23(6), 543. https://doi.org/10.12989/was.2016.23.6.543.
  19. Hajmohammad, M.H., Zarei, M.S., Farrokhian, A. and Kolahchi, R. (2018), "A layerwise theory for buckling analysis of truncated conical shells reinforced by CNTs and carbon fibers integrated with piezoelectric layers in hygrothermal environment", Adv. Nano Res., 6(4), 299-3321. https://doi.org/10.12989/anr.2018.6.4.299.
  20. Hussain, M., Asghar, S., Khadimallah, M.A., Ayed, H., Alghamdi, S., Bhutto, J.K., ... and Tounsi, A. (2022), "No title effect of dimensionless nonlocal parameter: Vibration of double-walled CNTs", Comput. Concrete, 30(4), 269-276. https://doi.org/10.12989/cac.2022.30.4.269.
  21. Iijima, S. (1991), "Helical microtubules of graphitic carbon", Nat., 354(6348), 56-58. https://doi.org/10.1038/354056a0.
  22. Iijima, S. and Ichihashi, T. (1993), "Single-shell carbon nanotubes of 1-nm diameter", Nat., 363(6430), 603-605. https://doi.org/10.1038/363603a0.
  23. Kallannavar, V. and Kattimani, S. (2023), "Effect of temperature and porosity on free vibration characteristics of a doubly-curved skew laminated sandwich composite structures with 3D printed PLA core", Thin Wall. Struct., 182, 110263. https://doi.org/10.1016/j.tws.2022.110263.
  24. Khazaei, P. and Mohammadimehr, M. (2020), "Vibration analysis of porous nanocomposite viscoelastic plate reinforced by FG-SWCNTs based on a nonlocal strain gradient theory", Comput. Concrete, 26(1), 31-52. https://doi.org/10.12989/cac.2020.26.1.031.
  25. Khelifa, Z., Hadji, L., Daouadji, T.H. and Bourada, M. (2018), "Buckling response with stretching effect of carbon nanotube-reinforced composite beams resting on elastic foundation", Struct. Eng. Mech., 67(2), 125-130. https://doi.org/10.12989/sem.2018.67.2.125.
  26. Li, X.F. (2008), "A unified approach for analyzing static and dynamic behaviors of functionally graded Timoshenko and Euler-Bernoulli beams", J. Sound Vib., 318(4-5), 1210-1229. https://doi.org/10.1016/j.jsv.2008.04.056.
  27. Nguyen, K.D., Thanh, C.L., Nguyen-Xuan, H. and Abdel-Wahab, M. (2023), "A hybrid phase-field isogeometric analysis to crack propagation in porous functionally graded structures", Eng. Comput., 39, 1-21. https://doi.org/10.1007/s00366-021-01518-0.
  28. Nguyen, T.K., Truong-Phong Nguyen, T., Vo, T.P. and Thai, H.T. (2015), "Vibration and buckling analysis of functionally graded sandwich beams by a new higher-order shear deformation theory", Compos. Part B: Eng., 76, 273-285. https://doi.org/10.1016/j.compositesb.2015.02.032.
  29. Nguyen, V.X., Lieu, Q.X., Le, T.A., Nguyen, T.D., Suzuki, T. and Luong, V.H. (2022), "A novel coupled finite element method for hydroelastic analysis of FG-CNTRC floating plates under moving loads", Steel Compos. Struct., 42(2), 243. https://doi.org/10.12989/scs.2022.42.2.243.
  30. Pham, Q., Tran, V.K. and Nguyen, P. (2022), "Case studies in thermal engineering hygro-thermal vibration of bidirectional functionally graded porous curved beams on variable elastic foundation using generalized finite element method", Case Stud. Therm. Eng., 40, 102478. https://doi.org/10.1016/j.csite.2022.102478.
  31. Polit, O., Anant, C., Anirudh, B. and Ganapathi, M. (2019), "Functionally graded graphene reinforced porous nanocomposite curved beams : Bending and elastic stability using a higher-order model with thickness stretch effect", Compos. Part B: Eng., 166, 310-327. https://doi.org/10.1016/j.compositesb.2018.11.074.
  32. Sankar, B.V (2001), "An elasticity solution for functionally graded beams", Compos. Sci. Technol., 61(5), 689-696. https://doi.org/10.1016/S0266-3538(01)00007-0.
  33. Sayyad, A.S. and Ghugal, Y.M. (2017), "A unified shear deformation theory for the bending of isotropic, functionally graded, laminated and sandwich beams and plates", Int. J. Appl. Mech., 9(1), 1750007. https://doi.org/10.1142/S1758825117500077.
  34. She, G.L., Yan, K.M., Zhang, Y.L., Liu, H.B. and Ren, Y.R. (2018), "Wave propagation of functionally graded porous nanobeams based on non-local strain gradient theory", Eur. Phys. J. Plus, 133(9), 368. https://doi.org/10.1140/epjp/i2018-12196-5.
  35. Srikarun, B., Songsuwan, W. and Wattanasakulpong, N. (2021), "Linear and nonlinear static bending of sandwich beams with functionally graded porous core under different distributed loads", Compos. Struct., 276, 114538. https://doi.org/10.1016/j.compstruct.2021.114538.
  36. Tagrara, S.H., Benachour, A., Bouiadjra, M.B. and Tounsi, A. (2015a), "On bending, buckling and vibration responses of functionally graded carbon nanotube-reinforced composite beams", Steel Compos. Struct., 19(5), 1259-1277. https://doi.org/10.12989/scs.2015.19.5.1259.
  37. Tagrara, S.H., Benachour, A., Bouiadjra, M.B. and Tounsi, A. (2015b), "On bending, buckling and vibration responses of functionally graded carbon nanotube-reinforced composite beams", Steel Compos. Struct., 19(5), 1259-1277. https://doi.org/10.12989/scs.2015.19.5.1259.
  38. Thai, H.T. and Vo, T.P. (2012), "Bending and free vibration of functionally graded beams using various higher-order shear deformation beam theories", Int. J. Mech. Sci., 62(1), 57-66. https://doi.org/10.1016/j.ijmecsci.2012.05.014.
  39. Thanh, C.L., Nguyen, T.N., Vu, T.H., Khatir, S. and Abdel Wahab, M. (2020), "A geometrically nonlinear size-dependent hypothesis for porous functionally graded micro-plate", Eng. Comput., 2020, 1-12. https://doi.org/10.1007/s00366-020-01154-0.
  40. Timesli, A. (2020), "Prediction of the critical buckling load of SWCNT reinforced concrete cylindrical shell embedded in an elastic foundation", Comput. Concrete, 26(1), 53-62. https://doi.org/10.12989/cac.2020.26.1.053.
  41. Vo-Duy, T., Ho-Huu, V. and Nguyen-Thoi, T. (2019), "Free vibration analysis of laminated FG-CNT reinforced composite beams using finite element method", Front. Struct. Civil Eng., 13(2), 324-336. https://doi.org/10.1007/s11709-018-0466-6.
  42. Wang, Y.Q. (2018), "Electro-mechanical vibration analysis of functionally graded piezoelectric porous plates in the translation state", Acta Astronaut., 143, 263-271. https://doi.org/10.1016/j.actaastro.2017.12.004.
  43. Wang, Y.Q., Wan, Y.H. and Zhang, Y.F. (2017), "Vibrations of longitudinally traveling functionally graded material plates with porosities", Eur. J. Mech. A/Solids, 66, 55-68. https://doi.org/doi.org/10.1016/j.euromechsol.2017.06.006.
  44. Wang, Y.Q., Ye, C. and Zu, J. W. (2019), "Nonlinear vibration of metal foam cylindrical shells reinforced with graphene platelets", Aerosp. Sci. Technol., 85, 359-370. https://doi.org/doi.org/10.1016/j.ast.2018.12.022.
  45. Wang, Y., Ye, C. and Zu, J. (2018), "Identifying the temperature effect on the vibrations of functionally graded cylindrical shells with porosities", Appl. Math. Mech., 39(11), 1587-1604. https://doi.org/doi.org/10.1007/s10483-018-2388-6.
  46. 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.
  47. Wattanasakulpong, N. and Ungbhakorn, V. (2014), "Linear and nonlinear vibration analysis of elastically restrained ends FGM beams with porosities", Aerosp. Sci. Technol., 32(1), 111-120. https://doi.org/10.1016/j.ast.2013.12.002.
  48. Xu, X., Zhang, C., Musharavati, F., Sebaey, T.A. and Khan, A. (2021), "Wave propagation analysis of porous functionally graded curved beams in the thermal environment", Struct. Eng. Mech., 79(6), 665-675. https://doi.org/10.12989/sem.2021.79.6.665.
  49. Yang, J. and Chen, Y. (2008), "Free vibration and buckling analyses of functionally graded beams with edge cracks", Compos. Struct., 83, 48-60. https://doi.org/10.1016/j.compstruct.2007.03.006.
  50. Yaylaci, M., Adiyaman, G., Oner, E. and Birinci, A. (2021), "Investigation of continuous and discontinuous contact cases in the contact mechanics of graded materials using analytical method and FEM", Comput. Concrete, 27(3), 199-210. https://doi.org/10.12989/cac.2021.27.3.199.
  51. Ye, C. and Wang, Y.Q. (2021), "Nonlinear forced vibration of functionally graded graphene platelet-reinforced metal foam cylindrical shells: Internal resonances", Nonlin. Dyn., 104(3), 2051-2069. https://doi.org/10.1007/s11071-021-06401-7.
  52. Yuksel, Y.Z. and Akbas, S.D. (2019), "Buckling analysis of a fiber reinforced laminated composite plate with porosity", J. Comput. Appl. Mech., 50(2), 375-380. https://doi.org/10.22059/jcamech.2019.291967.448.
  53. Zerrouki, R., Karas, A., Zidour, M., Bousahla, A.A., Tounsi, A., Bourada, F., Tounsi, A., Benrahou, K.H. and Mahmoud, S.R. (2021), "Effect of nonlinear FG-CNT distribution on mechanical properties of functionally graded nano-composite beam", Struct. Eng. Mech., 78(2), 117-124. https://doi.org/10.12989/sem.2021.78.2.117.
  54. Zghal, S., Frikha, A. and Dammak, F. (2018), "Non-linear bending analysis of nanocomposites reinforced by graphene-nanotubes with finite shell element and membrane enhancement", Eng. Struct., 158, 95-109. https://doi.org/10.1016/j.engstruct.2017.12.017.
  55. Zghal, S., Ataoui, D. and Dammak, F. (2020), "Static bending analysis of beams made of functionally graded porous materials", Mech. Based Des. Struct. Mach., 50(3), 1012-1029. https://doi.org/10.1080/15397734.2020.1748053.
  56. Zghal, S., Trabelsi, S. and Dammak, F. (2020), "Post-buckling behavior of functionally graded and carbon-nanotubes based structures with different mechanical loadings", Mech. Based Des. Struct. Mach., 50(9), 2997-3039. https://doi.org/10.1080/15397734.2020.1790387.
  57. Zhang, Z., Yang, Q. and Jin, C. (2022), "Axisymmetric vibration analysis of a sandwich porous plate in thermal environment rested on Kerr foundation", Steel Compos. Struct., 43(5), 581. https://doi.org/10.12989/scs.2022.43.5.581.
  58. Zhao, J.L., Chen, X., She, G.L., Jing, Y., Bai, R.Q., Yi, J., Pu, H.Y. and Luo, J. (2022), "Vibration characteristics of functionally graded carbon nanotube-reinforced composite double-beams in thermal environments", Steel Compos. Struct., 43(6), 797-808. https://doi.org/10.12989/scs.2022.43.6.797.
  59. Zhou, L. and Najjari, Y. (2022), "Analytical solution of buckling problem in plates reinforced by Graphene platelet based on third order shear deformation theory", Steel Compos. Struct., 43(6), 725-734. https://doi.org/10.12989/scs.2022.43.6.725.