Advances in nano research

  • 제16권5호
  • /
  • Pages.509-519
  • /
  • 2024
  • /
  • 2287-237X(pISSN)
  • /
  • 2287-2388(eISSN)
테크노프레스 (Techno-Press)
권호 표지
DOI QR코드

DOI QR Code

Static analysis of nonlinear FG-CNT reinforced nano-composite beam resting on Winkler/Pasternak foundation

  • Mostefa Sekkak (Material and Hydrology Laboratory, University of Sidi Bel Abbes, Faculty of Technology, Civil Engineering Department) ;
  • Rachid Zerrouki (Laboratory of Geomatics and Sustainable Development, University of Tiaret) ;
  • Mohamed Zidour (Laboratory of Geomatics and Sustainable Development, University of Tiaret) ;
  • Abdelouahed Tounsi (Department of Civil and Environmental Engineering, Lebanese American University) ;
  • Mohamed Bourada (Material and Hydrology Laboratory, University of Sidi Bel Abbes, Faculty of Technology, Civil Engineering Department) ;
  • Mahmoud M Selim (Department of Mathematics, College of Science and Humanities, Prince Sattam bin Abdulaziz University) ;
  • Hosam A. Saad (Department of Chemistry, College of Science, Taif University)
  • 투고 : 2023.06.09
  • 심사 : 2024.03.02
  • 발행 : 2024.05.25
⟨ 이전 논문 다음 논문 ⟩

초록

In this study, the static analysis of carbon nanotube-reinforced composites (CNTRC) beams resting on a Winkler-Pasternak elastic foundation is presented. The developed theories account for higher-order variation of transverse shear strain through the depth of the beam and satisfy the stress-free boundary conditions on the top and bottom surfaces of the beam. To study the effect of carbon nanotubes distribution in functionally graded (FG-CNT), we introduce in the equation of CNT volume fraction a new exponent equation. The SWCNTs are assumed to be aligned and distributed in the polymeric matrix with different patterns of reinforcement. The rule of mixture is used to describe the material properties of the CNTRC beams. The governing equations were derived by employing Hamilton's principle. The models presented in this work are numerically provided to verify the accuracy of the present theory. The analytical solutions are presented, and the obtained results are compared with the existing solutions to verify the validity of the developed theories. Many parameters are investigated, such as the Pasternak shear modulus parameter, the Winkler modulus parameter, the volume fraction, and the order of the exponent in the volume fraction equation. New results obtained from bending and stresses are presented and discussed in detail. From the obtained results, it became clear the influence of the exponential CNTs distribution and Winkler-Pasternak model improved the mechanical properties of the CNTRC beams.

키워드

과제정보

The authors extend their appreciation to Taif University, Saudi Arabia, for supporting this work through project number (TU-DSPP-2024-104).

참고문헌

  1. Adiyaman, G., O ner, E., Yaylaci, M. and Birinci, A. (2023). "A study on the contact problem of a layer consisting of functionally graded material (FGM) in the presence of body force", J. Mech. Mater. Struct., 18(1), 125-141. https://doi.org/10.2140/jomms.2023.18.125
  2. AkhavanAlavi, S.M., Mohammadimehr, M. and Ejtahed, S.H. (2021), "Vibration analysis and control of micro porousbeam integrated with FG-CNT distributed piezoelectric sensor and actuator", Steel Compos. Struct., 41(4), 595-608. https://doi.org/10.12989/scs.2021.41.4.595
  3. 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. Concr., 26(3), 285-292. https://doi.org/10.12989/cac.2020.26.3.285
  4. Ansari, M.I. and Kumar, A. (2019), "Bending analysis of functionally graded CNT reinforced doubly curved singly ruled truncated rhombic cone", Mech. Based Des. Struct., 47(1) ,67-86. https://doi.org/10.1080/15397734.2018.1519635
  5. Asadijafari, M.H., Zarastvand, M.R. and Talebitooti, R. (2021), "The effect of considering Pasternak elastic foundation on acoustic insulation of the finite doubly curved composite structures", Compos. Struct., 256, 113064. https://doi.org/10.1016/j.compstruct.2020.113064
  6. AsadiJafari, M. H., Zarastvand, M. and Zhou, J. (2023), "Doubly curved truss core composite shell system for broadband diffuse acoustic insulation", J. Vib. Control, 10775463231206229. https://doi.org/10.1177/10775463231206229
  7. Avcar, M., Hadji, and L., Civalek, O . (2023), "The influence of non-linear carbon nanotube reinforcement on the natural frequencies of composite beams", Adv. Nano Res., 14(5), 421-433. https://doi.org/10.12989/anr.2023.14.5.421
  8. Bao, T. and Liu, Z.L. (2020), "Evaluation of Winkler model and Pasternak model for dynamic soil-structure interaction analysis of structures partially embedded in soils", Int. J. Geomech., 20(2), 04019167. https://doi.org/10.1061/(ASCE)GM.1943-5622.0001519
  9. Coleman, J.N., Khan, U., Blau, W.J. and Gun'ko, Y.K. (2006), "Small but strong: a review of the mechanical properties of carbon nanotube-polymer composites", Carbon, 44(9), 1624-1652. https://doi.org/10.1016/j.carbon.2006.02.038
  10. Cui, X., Han, B., Zheng, Q., Yu, X., Dong, S., Zhang, L. and Ou, J. (2017), "Mechanical properties and reinforcing mechanisms of cementitious composites with different types of multiwalled carbon nanotubes, Composites Part A", Appl. Sci. Manuf., 103, 131-147. https://doi.org/10.1016/j.compositesa.2017.10.001
  11. Dat, N.D., Khoa, N.D., Nguyen, P.D. and Duc, N.D. (2020), "An analytical solution for nonlinear dynamic response and vibration of FG-CNT reinforced nanocomposite elliptical cylindrical shells resting on elastic foundations". ZAMM J. Appl. Math. Mech., 100(1), e201800238. https://doi.org/10.1002/zamm.201800238
  12. Draoui, A., Zidour, M., Tounsi, A. andAdim, B. (2019), "Static and dynamic behavior of nanotubes-reinforced sandwich plates using (FSDT)", J. Nano Res., 57, 117-135. https://doi.org/10.4028/www.scientific.net/JNanoR.57.117
  13. Gafour, Y., Hamidi, A., Benahmed, A., Zidour, M. and Bensattalah, T. (2020), "Porosity-dependent free vibration analysis of FG nanobeam using non-local shear deformation and energy principle", Adv. Nano Res., 8(1), 49. https://doi.org/10.12989/anr.2020.8.1.037
  14. Garg, A., Belarbi, M.O., Chalak, H.D. and Chakrabarti, A. (2021), "A review of the analysis of sandwich FGM", Compos. Struct., 258, 113427. https://doi.org/10.1016/j.compstruct.2020.113427
  15. Ghafouri, M., Ghassabi, M., Zarastvand, M.R. and Talebitooti, R. (2022), "Sound propagation of three-dimensional sandwich panels: influence of three-dimensional re-entrant auxetic core", AIAA J., 60(11), 6374-6384. https://doi.org/10.2514/1.J061219
  16. Ghassabi, M., Zarastvand, M.R. and Talebitooti, R. (2020), "Investigation of state vector computational solution on modeling of wave propagation through functionally graded nanocomposite doubly curved thick structures", Eng. Comput., 36, 1417-1433. https://doi.org/10.1007/s00366-019-00773-6
  17. Giunta, G., Belouettar, S. and Carrera, E. (2010), "Analysis of FGM beams by means of classical and advanced theories", Mech. Adv. Mater. Struct., 17(8), 622-635. https://doi.org/10.1080/15376494.2010.518930
  18. Heidari, F., Afsari, A. and Janghorban, M. (2020), "Several models for bending and buckling behaviors of FG-CNTRCs with piezoelectric layers including size effects", Adv. Nano Res., 9(3), 193-210. https://doi.org/10.12989/anr.2020.9.3.193
  19. Heidari-Rarani, M., Alimirzaei, S. and Torabi, K. (2015), "Analytical solution for free vibration of functionally graded carbon nanotubes (FG-CNT) reinforced double-layered nanoplates resting on elastic medium", J. Sci. Technol. Compos., 2(3), 55-66.
  20. Huang, J. and Rodrigue, D. (2013), "Equivalent continuum models of carbon nanotube reinforced polypropylene composites", Mater. Des., 50, 936-945. https://doi.org/10.1016/j.matdes.2013.03.095
  21. Iijima, S. (1991), "Helical microtubules of graphitic carbon", Nature, 354(6348), 56-58. https://doi.org/10.1038/354056a0
  22. Karimzadeh, F., Ziaei-Rad, S. and Adibi, S. (2007), "Modeling considerations and material properties evaluation in analysis of carbon nano-tubes composite", Metall. Mater. Transact. B, 38(4), 695-705. https://doi.org/10.1007/s11663-007-9065-y
  23. Khazaei, P. and Mohammadimehr, M. (2020), "Vibration analysis of porous nanocomposite viscoelastic plate reinforced by FGSWCNTs based on a nonlocal strain gradient theory", Comput. Concr., 26(1), 31-52, https://doi.org/10.12989/cac.2020.26.1.031
  24. Koppad, P.G., Ram, H.A., Ramesh, C.S., Kashyap, K.T. and Koppad, R.G. (2013), "On thermal and electrical properties of multiwalled carbon nanotubes/copper matrix nanocomposites", J. Alloys Compd., 580, 527-532. https://doi.org/10.1016/j.jallcom.2013.06.123
  25. 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
  26. Lei, Z.X., Zhang, L.W. and Liew, K. (2016), "Vibration of FG-CNT reinforced composite thick quadrilateral plates resting on Pasternak foundations", Eng. Anal. Bound. Elem., 64, 1-11. https://doi.org/10.1016/j.enganabound.2015.11.014
  27. Madani, H., Hosseini, H. and Shokravi, M. (2016), "Differential cubature method for vibration analysis of embedded FG-CNT-reinforced piezoelectric cylindrical shells subjected to uniform and non-uniform temperature distributions", Steel Compos. Struct, 22(4), 889-913. http://doi.org/10.12989/scs.2016.22.4.889
  28. Medani, M., Benahmed, A., Zidour, M., Heireche, H., Tounsi, A., Bousahla, A.A., Tounsi, A. and Mahmoud, S.R. (2019), "Static and dynamic behavior of (FG-CNT) reinforced porous sandwich plate using energy principle", Steel Compos. Struct., 32(5), 595-610. https://doi.org/10.12989/scs.2019.32.5.595
  29. Mayandi, K. and Jeyaraj, P. (2015), "Bending, buckling and free vibration characteristics of FG-CNT-reinforced polymer composite beam under non-uniform thermal load", Proceedings of the Institution of Mechanical Engineers, Part L, Journal of Materials: Design and Applications, 229(1), 13-28. https://doi.org/10.1177/1464420713493720
  30. Nguyen, P.D., Papazafeiropoulos, G., Vu, Q.V. and Duc, N.D. (2022), "Buckling response of laminated FG-CNT reinforced composite plates: Analytical and finite element approach", Aerosp. Sci. Technol., 121, 107368. https://doi.org/10.1016/j.ast.2022.107368
  31. Oner, E., SengulSabano, B., Uzun Yaylaci, E., Adiyaman, G., Yaylaci, M. and Birinci, A. (2022), "On the plane receding contact between two functionally graded layers using computational, finite element and artificial neural network methods", ZAMM J. Appl. Math. Mech., 102(2), e202100287. https://doi.org/10.1002/zamm.202100287
  32. Reissner, E. (1945), "The effect of transverse shears deformation on the bending of elastic plates", J. Appl. Mech., 12, 69-77. https://doi.org/10.1115/1.4009435
  33. Salami, S.J., Boroujerdy, M.S. and Bazzaz, E. (2021), "Geometrically nonlinear thermo-mechanical bending analysis of deep cylindrical composite panels reinforced by functionally graded CNTs", Adv. Nano Res., 10(4), 385, https://doi.org/10.12989/anr.2021.10.4.385
  34. Sankar, N., Reddy, M.N. and Prasad, R.K. (2016), "Carbon nanotubes dispersed polymer nanocomposites: mechanical, electrical, thermal properties and surface morphology", Bull. Mater. Sci., 39(1), 47-55. https://doi.org/10.1007/s12034-015-1117-3
  35. Sayyad, A.S. and Ghugal, Y.M. (2020), "Bending, buckling and free vibration analysis of size-dependent nanoscale FG beams using refined models and Eringen's nonlocal theory", Int. J. Appl. Mech., 12(1), 2050007. https://doi.org/10.1142/S1758825120500076
  36. Singh, Y.T., Patra, P.K., Obodo, K.O. and Rai, D.P. (2022), "Electronic and mechanical properties of (6, 1) single-walled carbon nanotubes with different tube diameters: a theoretical study", Carbon Lett., 32(2), 451-460. https://doi.org/10.1007/s42823-021-00274-x
  37. Talebitooti, R. and Zarastvand, M.R. (2018), "Vibroacoustic behavior of orthotropic aerospace composite structure in the subsonic flow considering the Third order Shear Deformation Theory", Aerosp. Sci. Technol., 75, 227-236. https://doi.org/10.1016/j.ast.2018.01.011
  38. 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, https://doi.org/10.12989/scs.2015.19.5.1259
  39. Tayeb, T.S., Zidour, M., Bensattalah, T., Heireche, H., Benahmed, A. and Bedia, E.A. (2020), "Mechanical buckling of FG-CNTs reinforced composite plate with parabolic distribution using Hamilton's energy principle", Adv. Nano Res., 8(2), 135, https://doi.org/10.12989/anr.2020.8.2.135
  40. Turan, M., Uzun Yaylaci, E. and Yaylaci, M. (2023), "Free vibration and buckling of functionally graded porous beams using analytical, finite element, and artificial neural network methods", Arch. Appl. Mech., 93(4), 1351-1372. https://doi.org/10.1007/s00419-022-02332-w
  41. Vakili-Nezhaad, G., Al-Wadhahi, M., Gujrathi, A.M., Al-Maamari, R. and Mohammadi, M. (2017), "Effect of temperature and diameter of narrow single-walled carbon nanotubes on the viscosity of nanofluid: A molecular dynamics study", Fluid Phase Equil., 434, 193-199. https://doi.org/10.1016/j.fluid.2016.11.032
  42. Wang, Y., Xie, K., Fu, T. and Shi, C. (2019), "Bending and elastic vibration of a novel functionally graded polymer nanocomposite beam reinforced by grapheme nanoplatelets", Nanomaterials, 9(12), 1690. https://doi.org/10.3390/nano9121690
  43. 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
  44. Wu, K., Li, Y., Huang, R., Chai, S., Chen, F. and Fu, Q. (2017), "Constructing conductive multi-walled carbon nanotubes network inside hexagonal boron nitride network in polymer composites for significantly improved dielectric property and thermal conductivity", Compos. Sci. Technol., 151, 193-201. https://doi.org/10.1016/j.compscitech.2017.07.014
  45. 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
  46. Yaylaci, E.U., O ner, E., Yaylaci, M., O zdemir, M.E., Abushattal, A. and Birinci, A. (2022c), "Application of artificial neural networks in the analysis of the continuous contact problem", Struct. Eng. Mech., 84(1), 35-48. https://doi.org/10.12989/sem.2022.84.1.035
  47. Yaylaci, M., Abanoz, M., Yaylaci, E.U., O lmez, H., Sekban, D.M. and Birinci, A. (2022b), "Evaluation of the contact problem of functionally graded layer resting on rigid foundation pressed via rigid punch by analytical and numerical (FEM and MLP) methods", Arch. Appl. Mech., 92(6), 1953-1971. https://doi.org/10.1007/s00419-022-02159-5
  48. Yaylaci, M., Abanoz, M., Yaylaci, E.U., Olmez, H., Sekban, D. M. and Birinci, A. (2022d), "The contact problem of the functionally graded layer resting on rigid foundation pressed via rigid punch", Steel Compos. Struct., 43(5), 661. https://doi.org/10.12989/SCS.2022.43.5.661
  49. Yaylaci, M., Sabano, B.S., O zdemir, M.E. andBirinci, A. (2022a), "Solving the contact problem of functionally graded layers resting on a HP and pressed with a uniformly distributed load by analytical and numerical methods", Struct. Eng. Mech., 82(3), 401-416. https://doi.org/10.12989/sem.2022.82.3.401
  50. Yaylaci, M., Uzun Yaylaci, E., O zdemir, M.E., Ay, S. and O zturk, S. (2022e), "Implementation of finite element and artificial neural network methods to analyze the contact problem of a functionally graded layer containing crack", Steel Compos. Struct., 45(4), 501. https://doi.org/10.12989/scs.2022.45.4.501
  51. Yaylaci, M, Yaylaci, E.U., O zdemir, M.E., O zturk, S. & Sesli, H. (2023), "Vibration and buckling analyses of FGM beam with edge crack: Finite element and multilayer perceptron methods", Steel Compos. Struct., 46(4), 565-575. https://doi.org/10.12989/scs.2023.46.4.565
  52. Yaylaci, M., Yayli, M., Yaylaci, E. U., Olmez, H. andBirinci, A. (2021), "Analyzing the contact problem of a functionally graded layer resting on an elastic half plane with theory of elasticity, finite element method and multilayer perceptron", Struct. Eng. Mech., 78(5), 585-597 https://doi.org/10.12989/sem.2021.78.5.585
  53. Yaylaci, M. (2016), "The investigation crack problem through numerical analysis", Struct. Eng. Mech., 57(6), 1143-1156. https://doi.org/10.12989/sem.2016.57.6.1143
  54. Zarastvand, M.R., Asadijafari, M.H. and Talebitooti, R. (2021a), "Improvement of the low-frequency sound insulation of the poro elastic aerospace constructions considering Pasternak elastic foundation", Aerosp. Sci. Technol., 112, 106620. https://doi.org/10.1016/j.ast.2021.106620
  55. Zarastvand, M.R., Asadijafari, M.H. and Talebitooti, R. (2022b), "Acoustic wave transmission characteristics of stiffened composite shell systems with double curvature", Compos. Struct., 292, 115688. https://doi.org/10.1016/j.compstruct.2022.115688
  56. Zarastvand, M.R., Ghassabi, M. and Talebitooti, R. (2021b), "A review approach for sound propagation prediction of plate constructions", Arch. Comput. Meth. Eng., 28, 2817-2843. https://doi.org/10.1007/s11831-020-09482-6
  57. Zarastvand, M.R., Ghassabi, M. and Talebitooti, R. (2022a), "Prediction of acoustic wave transmission features of the multilayered plate constructions: A review", J. Sandw. Struct. Mater., 24(1), 218-293. https://doi.org/10.1177/1099636221993891
  58. Zerrouki, R., Karas, A. and Zidour, M. (2020), "Critical buckling analyses of nonlinear FG-CNT reinforced nano-composite beam", Adv. Nano Res., 9(3), 211-220. https://doi.org/10.12989/anr.2020.9.3.211.
  59. Zhang, L.W., Song, Z.G. and Liew, K.M. (2015), "Nonlinear bending analysis of FG-CNT reinforced composite thick plates resting on Pasternak foundations using the element-free IMLS-Ritz method", Compos. Struct., 128, 165-175. https://doi.org/10.1016/j.compstruct.2015.03.011
  60. Zhu, P., Lei, Z.X. and Liew, K.M. (2012), "Static and free vibration analyses of carbon nanotube-reinforced composite plates using finite element method with first order shear deformation plate theory", Compos. Struct., 94(4), 1450-1460. https://doi.org/10.1016/j.compstruct.2011.11.010