Computers and Concrete

Techno-Press (테크노프레스)
권호 표지
DOI QR코드

DOI QR Code

Mechanical behavior analysis of FG-CNTRC porous beams resting on Winkler and Pasternak elastic foundations: A finite element approach

  • Zakaria Belabed (Artificial Intelligence Laboratory for Mechanical and Civil Structures, and Soil, Institute of Technology, University Center of Naama) ;
  • Abdeldjebbar Tounsi (Material and Hydrology Laboratory, University of Sidi Bel Abbes, Faculty of Technology, Civil Engineering Department) ;
  • Abdelmoumen Anis Bousahla (Laboratoire de Modelisation et Simulation Multi-echelle, Universite de Sidi Bel Abbes) ;
  • Abdelouahed Tounsi (Material and Hydrology Laboratory, University of Sidi Bel Abbes, Faculty of Technology, Civil Engineering Department) ;
  • Khaled Mohamed Khedher (Department of Civil Engineering, College of Engineering, King Khalid University) ;
  • Mohamed Abdelaziz Salem (Department of Mechanical Engineering, College of Engineering, King Khalid University)
  • Received : 2023.08.21
  • Accepted : 2024.03.04
  • Published : 2024.10.25
⟨ Previous Next ⟩

Abstract

The current research proposes an innovative finite element model established within the context of higher-order beam theory to examine the bending and buckling behaviors of functionally graded carbon nanotube-reinforced composite (FG-CNTRC) beams resting on Winkler-Pasternak elastic foundations. This two-node beam element includes four degrees of freedom per node and achieves inter-element continuity with both C1 and C0 continuities for kinematic variables. The isoparametric coordinate system is implemented to generate the elementary stiffness and geometric matrices as a way to enhance the existing model formulation. The weak variational equilibrium equations are derived from the principle of virtual work. The mechanical properties of FG-CNTRC beams are considered to vary gradually and smoothly over the beam thickness. The current investigation highlights the influence of porosity dispersions through the beam cross-section, which is frequently omitted in previous studies. For this reason, this analysis offers an enhanced comprehension of the mechanical behavior of FG-CNTRC beams under various boundary conditions. Through the comparison of the current results with those published previously, the proposed finite element model demonstrates a high rate of efficiency and accuracy. The estimated results not only refine the precision in the mechanical analysis of FG-CNTRC beams but also offer a comprehensive conceptual model for analyzing the performance of porous composite structures. Moreover, the current results are crucial in various sectors that depend on structural integrity in specific environments.

Keywords

Acknowledgement

The Authors extend their appreciation to the Deanship Scientific Research at King Khalid University for funding this work through large group Research Project under grant number: RGP2/388/45.

References

  1. Akbas, S.D. (2021), "Dynamic analysis of axially functionally graded porous beams under a moving load", Steel Compos. Struct., 39(6), 811-821. https://doi.org/10.12989/scs.2021.39.6.811.
  2. Al-Gahtani, H.J. and Mukhtar, F.M. (2014), "RBF-based meshless method for the free vibration of beams on elastic foundations", Appl. Math. Mech., 249, 198-208. https://doi.org/10.1016/j.amc.2014.09.097.
  3. Alibar, M.Y., Safaei, B., Asmael, M. and Zeeshan, Q. (2022), "Effect of carbon nanotubes and porosity on vibrational behavior of nanocomposite structures: A review", Arch. Comput. Methods Eng., 29, 2621-2657. https://doi.org/10.1007/s11831-021-09669-5.
  4. Alimoradzade M. and Akbas S.D. (2022), "Nonlinear thermal vibration of FGM beams resting on nonlinear viscoelastic foundation", Steel Compos. Struct., 44(4), 543-553. https://doi.org/10.12989/scs.2022.44.4.543.
  5. 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.
  6. Arefi, M. and Najafitabar, F. (2021), "Buckling and free vibration analyses of a sandwich beam made of a soft core with FG-GNPs reinforced composite face-sheets using Ritz Method", Thin Wall. Struct., 158, 107200. https://doi.org/10.1016/j.tws.2020.107200.
  7. Asgari, GH., Payganeh, GH. and Malekzadeh Fard, K. (2019), "Dynamic instability and free vibration behavior of three-layered soft-cored sandwich beams on nonlinear elastic foundations", Struct. Eng. Mech., 72(4), 525-540. https://doi.org/10.12989/sem.2019.72.4.525.
  8. Avcar, M. and Mohammed, W.K.M. (2018), "Free vibration of functionally graded beams resting on Winkler-Pasternak foundation", Arab. J. Geosci., 11(10), 232. https://doi.org/10.1007/s12517-018-3579-2.
  9. Belabed, Z., Selim, M.M., Slimani, O., Taibi, N., Tounsi, A. and Hussain, M. (2021), "An efficient higher order shear deformation theory for free vibration analysis of functionally graded shells", Steel Compos. Struct., 40(2), 307-321. https://doi.org/10.12989/scs.2021.40.2.307.
  10. Biswas, S. and Datta, P. (2021), "Finite element model for free vibration analyses of FG-CNT reinforced composite beams using refined shear deformation theories", IOP Conf. Ser.: Mater. Scie. Eng., 1206(1), 012019. https://doi.org/10.1088/1757-899x/1206/1/012019.
  11. Boudaa, S., Khalfallah, S. and Bilotta, E. (2019), "Static interaction analysis between beam and layered soil using a two-parameter elastic foundation", Int. J. Adv. Struct. Eng., 11(1), 21-30. https://doi.org/10.1007/s40091-019-0213-9.
  12. Chen, D., Rezaei, S., Rosendahl, P.L., Xu, B.X. and Schneider, J. (2022), "Multiscale modelling of functionally graded porous beams: Buckling and vibration analyses", Eng. Struct., 266, 114568. https://doi.org/10.1016/j.engstruct.2022.114568.
  13. Dabbagh, A., Rastgoo, A. and Ebrahimi, F. (2019), "Finite element vibration analysis of multi-scale hybrid nanocomposite beams via a refined beam theory", Thin Wall. Struct., 140, 304-317. https://doi.org/10.1016/j.tws.2019.03.031.
  14. Damghanian, R., Asemi, K. and Babaei, M. (2020), "A new beam element for static, free and forced vibration responses of microbeams resting on viscoelastic foundation based on modified couple stress and third-order beam theories", Iran. J. Mater. Sci., 46(1), 131-147. https://doi.org/10.1007/s40997-020-00407-z.
  15. Deng, H., Chen, K., Cheng, W. and Zhao, S. (2017), "Vibration and buckling analysis of double-functionally graded Timoshenko beam system on Winkler-Pasternak elastic foundation", Compos. Struct., 160, 152-168. https://doi.org/10.1016/j.compstruct.2016.10.027.
  16. Dhatt, G., Lefrancois, E. and Touzot, G. (2012), Finite Element Method, ISTE Ltd., London, UK.
  17. 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), 433-43. https://doi.org/10.12989/cac.2022.30.6.433.
  18. Doeva, O., Masjedi, P.K. and Weaver, P.M. (2021), "Closed form solutions for an anisotropic composite beam on a two-parameter elastic foundation", Eur. J. Mech. A Solids, 88, 104245. https://doi.org/10.1016/j.euromechsol.2021.104245.
  19. Doeva, O., Masjedi, P.K. and Weaver, P.M. (2022), "Exact analytical solution for static deflection of Timoshenko composite beams on two-parameter elastic foundations", Thin Wall. Struct., 172, 108812. https://doi.org/10.1016/j.tws.2021.108812.
  20. Duc, N.D. and Minh, P.P. (2021), "Free vibration analysis of cracked FG CNTRC plates using phase field theory", Aerosp. Sci. Technol., 112. http://doi.org/10.1016/j.ast.2021.106654.
  21. Fallah, A. and Aghdam, M.M. (2023), "Physics-informed neural network for bending and free vibration analysis of three-dimensional functionally graded porous beam resting on elastic foundation", Eng. Comput., 40, 437-454. https://doi.org/10.1007/s00366-023-01799-7. 
  22. Fang, W., Yu, T., Van Lich, L. and Bui, T.Q. (2019), "Analysis of thick porous beams by a quasi-3D theory and isogeometric analysis", Compos. Struct., 221, 110890. https://doi.org/10.1016/j.compstruct.2019.04.062.
  23. Fazzolari, F.A. (2018), "Generalized exponential, polynomial and trigonometric theories for vibration and stability analysis of porous FG sandwich beams resting on elastic foundations", Compos. Part B: Eng., 136, 254-271. https://doi.org/10.1016/j.compositesb.2017.10.022.
  24. Fouaidi, M., Jamal, M., Zaite, A. and Belouaggadia, N. (2021), "Bending analysis of functionally graded graphene oxide powder-reinforced composite beams using a meshfree method", Aerosp. Sci. Technol., 110, 106479. https://doi.org/10.1016/j.ast.2020.106479.
  25. Ha, N.H., Tan, N.C., Ninh, D.G., Hung, N.C. and Dao, D.V. (2023), "Dynamical and chaotic analyses of single-variable-edge cylindrical panels made of sandwich auxetic honeycomb core layer in thermal environment", Thin Wall. Struct., 183, 110300. https://doi.org/10.1016/j.tws.2022.110300.
  26. Hao, N., Song, Y., Chen, J., He, C. and Li, Y. (2023), "Compressive performance of a foam-filled fiber-reinforced grid beetle elytron plate", Sci. Chin. Technol. Sci., 66, 830-840. https://doi.org/10.1007/s11431-022-2171-0.
  27. Hasrati, E., Ansari, R. and Torabi, J. (2017), "Nonlinear forced vibration analysis of FG-CNTRC cylindrical shells under thermal loading using a numerical strategy", Int. J. Appl. Mech., 9(8), 1750108. https://doi.org/10.1142/S1758825117501083.
  28. Hoang, V.N.V., Ninh, D.G., Truong, D.V., Bao, H.V. and Huy, V.L. (2021), "Behaviors of dynamics and stability standard of graphene nanoplatelet reinforced polymer corrugated plates resting on the nonlinear elastic foundations", Compos. Struct., 260, 113253. https://doi.org/10.1016/j.compstruct.2020.113253.
  29. Huang, W. and Tahouneh, V. (2021), "Frequency study of porous FGPM beam on two-parameter elastic foundations via Timoshenko theory", Steel Compos. Struct., 40(1), 139-156. https://doi.org/10.12989/scs.2021.40.1.139.
  30. Jena, S.K., Chakraverty, S. and Malikan, M. (2020), "Application of shifted Chebyshev polynomial-based Rayleigh-Ritz method and Navier's technique for vibration analysis of a functionally graded porous beam embedded in Kerr foundation", Eng. Comput., 37(4), 3569-3589. https://doi.org/10.1007/s00366-020-01018-7.
  31. Karamanli, A. and Vo, T.P. (2021), "Finite element model for carbon nanotube-reinforced and graphene nanoplatelet-reinforced composite beams", Compos. Struct., 264, 113739. https://doi.org/10.1016/j.compstruct.2021.113739.
  32. Keshtegar, B., Motezaker, M., Kolahchi, R. and Trung, N.T. (2020), "Wave propagation and vibration responses in porous smart nanocomposite sandwich beam resting on Kerr foundation considering structural damping", Thin Wall. Struct., 154, 106820. https://doi.org/10.1016/j.tws.2020.106820.
  33. Khazaei, P., 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.
  34. Kitipornchai, S., Chen, D. and Yang, J. (2017), "Free vibration and elastic buckling of functionally graded porous beams reinforced by graphene platelets", Mater. Des., 116, 656-665. https://doi.org/10.1016/j.matdes.2016.12.061.
  35. 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. Multidisc", Model. Mater. Struct., 13, 590-611. https://doi.org/10.1108/MMMS-05-2017-0032.
  36. Kumar, S. (2022), "Vibration analysis of non-uniform axially functionally graded beam resting on Pasternak foundation", Mater. Today Proc., 62, 619-623. https://doi.org/10.1016/j.matpr.2022.03.622.
  37. Luat, D.T., Thom, D.V., Thanh, T.T., Phung, M. and Vinh, P.V. (2021), "Mechanical analysis of bi-functionally graded sandwich nanobeams", Adv. Nano Res., 11(1), 55-71. https://doi.org/10.12989/anr.2021.11.1.055.
  38. Marandi, S.M. and Karimipour, I. (2023), "Free vibration analysis of a nanoscale FG-CNTRCs sandwich beam with flexible core: Implementing an extended high order approach", Eng. Struct., 276, 115320. https://doi.org/10.1016/j.engstruct.2022.115320.
  39. Mellouli, H., Jrad, H., Wali, M. and Dammak, F. (2020), "Free vibration analysis of FG-CNTRC shell structures using the meshfree radial point interpolation method", Comput. Math. Appl., 79(11), 3160-3178. https://doi.org/10.1016/j.camwa.2020.01.015.
  40. Mohseni, A. and Shakouri, M. (2019), "Vibration and stability analysis of functionally graded CNT-reinforced composite beams with variable thickness on elastic foundation", Proc. Inst. Mech. Eng. Part L: J. Mater. Des. Appl., 233, 2478-2489. https://doi.org/10.1177/1464420719866222.
  41. Nejadi, M.M. and Mohammadimehr, M. (2020a), "Analysis of a functionally graded nanocomposite sandwich beam considering porosity distribution on variable elastic foundation using DQM: Buckling and vibration behaviors", Comput. Concrete, 25(3), 215-224. http://doi.org/10.12989/cac.2020.25.3.215.
  42. Nejadi, M.M. and Mohammadimehr, M. (2020b), "Buckling analysis of nano composite sandwich Euler-Bernoulli beam considering porosity distribution on elastic foundation using DQM", Adv. Nano Res., 8(1), 59-68. https://doi.org/10.12989/anr.2020.8.1.059.
  43. Nejadi, M.M., Mohammadimehr, M. and Mehrabi, M. (2021), "Free vibration and buckling of functionally graded carbon nanotubes/graphene platelets Timoshenko sandwich beam resting on variable elastic foundation", Adv. Nano Res., 10(6), 539-548. https://doi.org/10.12989/anr.2021.10.6.539.
  44. Nguyen, N.D., Nguyen, T.N., Nguyen, T.K. and Vo, T.P. (2022), "A new two-variable shear deformation theory for bending, free vibration and buckling analysis of functionally graded porous beams", Compos. Struct., 282, 115095. https://doi.org/10.1016/j.compstruct.2021.115095.
  45. Nguyen, N.D., Nguyen, T.N., Nguyen, T.K. and Vo, T.P. (2023), "A Legendre-Ritz solution for bending, buckling and free vibration behaviours of porous beams resting on the elastic foundation", Struct., 50, 1934-1950. https://doi.org/10.1016/j.istruc.2023.03.018.
  46. Ninh, D.G. and Bich, D.H. (2016), "Nonlinear torsional bucklin and postbuckling of eccentrically stiffened ceramic functionally graded material metal layer cylindrical shell surrounded by elastic foundation subjected to thermo-mechanical load", J. Sandw. Struct. Mater., 18(6), 712-738. https://doi.org/10.1177/1099636216644787.
  47. Ninh, D.G., Ha, N.H., Long, N.T., Tan, N.C., Tien, N.D. and Dao, D.V. (2023b), "Thermal vibrations of complex-generatrix shells made of sandwich CNTRC sheets on both sides and open/closed cellular functionally graded porous core", Thin Wall. Struct., 182, 110161. https://doi.org/10.1016/j.tws.2022.110161.
  48. Ninh, D.G., Long, N.T., Van Vang, T., Ha, N.H., Nguyen, C.T. and Dao, D.V. (2023a), "A new study for aeroplane wing shapes made of boron nitride nanotubes-reinforced aluminium, Part I: review, dynamical analyses and simulation", Compos. Struct., 303, 116239. https://doi.org/10.1016/j.compstruct.2022.116239.
  49. Ninh, D.G., Quan, N.M. and Hoang, V.N.V. (2022), "Thermally vibrational analyses of functionally graded graphene nanoplatelets reinforced funnel shells with different complex shapes surrounded by elastic foundation", Mech. Adv. Mater. Struct., 29, 4654-4676. https://doi.org/10.1080/15376494.2021.1934763.
  50. Nuhu, A.A. and Safaei, B. (2023), "On the advances of computational nonclassical continuum theories of elasticity for bending analyses of small-sized plate-based structures: A review", Arch. Comput. Method. Eng., 30, 2959-3029. https://doi.org/10.1007/s11831-023-09891-3.
  51. Pham, Q.H., Nguyen, P.C., Tran, V.K. and Nguyen-Thoi, T. (2021), "Finite element analysis for functionally graded porous nano-plates resting on elastic foundation", Steel Compos. Struct., 41, 149-166. https://doi.org/10.12989/scs.2021.41.2.149.
  52. Priyanka, R., Twinkle, C.M. and Pitchaimani, J. (2021), "Stability and dynamic behavior of porous FGM beam: Influence of graded porosity, graphene platelets, and axially varying loads", Eng. Comput., 38(S5), 4347-4366. https://doi.org/10.1007/s00366-021-01478-5.
  53. Reza Barati, M. and Zenkour, A.M. (2017), "Post-buckling analysis of refined shear deformable graphene platelet reinforced beams with porosities and geometrical imperfection", Compos. Struct., 181, 194-202. https://doi.org/10.1016/j.compstruct.2017.08.082.
  54. Rostami, R. and Mohammadimehr, M. (2021), "Nonlinear stability analysis of porous sandwich beam with nanocomposite face sheet on nonlinear viscoelastic foundation by using Homotopy perturbation method", Steel Compos. Struct., 41(6), 821-829. https://doi.org/10.12989/scs.2021.41.6.821.
  55. Shen, H. (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.
  56. Shen, H.S., He, X.Q. and Yang, D.Q. (2017), "Vibration of thermally postbuckled carbon nanotube-reinforced composite beams resting on elastic foundations", Int. J. Non-Lin. Mech., 91, 69-75. https://doi.org/10.1016/j.ijnonlinmec.2017.02.010.
  57. Soni, S.K., Thomas, B., Swain, A. Roy, T. (2022), "Functionally graded carbon nanotubes reinforced composite structures: An extensive review", Compos. Struct., 299, 116075. https://doi.org/10.1016/j.compstruct.2022.116075.
  58. 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, 1259-1277. https://doi.org/10.12989/scs.2015.19.5.1259.
  59. Tien, N.D., Hoang, V.N.V., Ninh, D.G., Huy, V.L. and Hung, N.C. (2020), "Nonlinear dynamics and chaos of a nanocomposite plate subjected to electro-thermo-mechanical loads using Flugge-Lur'e-Bryrne theory", J. Vib. Control, 27(9-10), 1184-1197. https://doi.org/10.1177/1077546320938185.
  60. 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.
  61. Vinh, P.V. and Son, L.T. (2022), "A new first-order mixed beam element for static bending analysis of functionally graded graphene oxide powder-reinforced composite beams", Struct., 36, 463-472. https://doi.org/10.1016/j.istruc.2021.12.032.
  62. Wang, M., Xu, Y.G., Qiao, P. and Li, Z.M. (2019), "A two-dimensional elasticity model for bending and free vibration analysis of laminated graphene-reinforced composite beams", Compos. Struct., 211, 364-375. https://doi.org/10.1016/j.compstruct.2018.12.033.
  63. Wang, Y. and Kiani, Y. (2022), "Effects of initial compression/tension, foundation damping and pasternak medium on the dynamics of shear and normal deformable GPLRC beams under moving load", Mater. Today Commun., 33, 104938. https://doi.org/10.1016/j.mtcomm.2022.104938.
  64. 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.
  65. 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.
  66. 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. Vessels Pip., 98, 119-128. https://doi.org/10.1016/j.ijpvp.2012.07.012.
  67. Yuksel, Y.Z. and Akbas, S.D. (2019), "Buckling analysis of a fiber reinforced laminated composite plate with porosity", J. Appl. Comput. Mech., 50(2), 375-380. https://doi.org/10.22059/jcamech.2019.291967.448.
  68. Zhang, D.P., Lei, Y.J., Wang, C.Y. and Shen, Z.B. (2017), "Vibration analysis of viscoelastic single-walled carbon nanotubes resting on a viscoelastic foundation", J. Mech. Sci. Technol., 31(1), 87-98. https://doi.org/10.1007/s12206-016-1007-7.
  69. Zhang, L.H., Lai, S.K., Wang, C. and Yang, J. (2021), "DSC regularized Dirac-delta method for dynamic analysis of FG graphene platelet-reinforced porous beams on elastic foundation under a moving load", Compos. Struct., 255, 112865. https://doi.org/10.1016/j.compstruct.2020.112865.
  70. Zhang, Z., Li, Y., Wu, H., Zhang, H., Wu, H., Jiang, S. and Chai, G. (2018), "Mechanical analysis of functionally graded graphene oxide-reinforced composite beams based on the first-order shear deformation theory", Mech. Adv. Mater. Struct., 27(1), 3-11. https://doi.org/10.1080/15376494.2018.1444216.