Advances in nano research

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Novel four-unknowns quasi 3D theory for bending, buckling and free vibration of functionally graded carbon nanotubes reinforced composite laminated nanoplates

  • Khadir, Adnan I. (Faculty of Engineering, Mechanical Engineering Department, King Abdulaziz University) ;
  • Daikh, Ahmed Amine (Laboratoire d'Etude des Structures et de Mecanique des Materiaux, Departement de Genie Civil, Faculte des Sciences et de la Technologie) ;
  • Eltaher, Mohamed A. (Faculty of Engineering, Mechanical Engineering Department, King Abdulaziz University)
  • Received : 2021.05.25
  • Accepted : 2021.09.14
  • Published : 2021.12.25
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Abstract

Effect of thickness stretching on mechanical behavior of functionally graded (FG) carbon nanotubes reinforced composite (CNTRC) laminated nanoplates resting on elastic foundation is analyzed in this paper using a novel quasi 3D higher-order shear deformation theory. The key feature of this theoretical formulation is that, in addition to considering the thickness stretching effect, the number of unknowns of the displacement field is reduced to four, and which is more than five in the other models. Single-walled carbon nanotubes (SWCNTs) are the reinforced elements and are distributed with four power-law functions which are, uniform distribution, V-distribution, O-distribution and X-distribution. To cover various boundary conditions, an analytical solution is developed based on Galerkin method to solve the governing equilibrium equations by considering the nonlocal strain gradient theory. A modified two-dimensional variable Winkler elastic foundation is proposed in this study for the first time. A parametric study is executed to determine the influence of the reinforcement patterns, power-law index, nonlocal parameter, length scale parameter, thickness and aspect ratios, elastic foundation, thermal environments, and various boundary conditions on stresses, displacements, buckling loads and frequencies of the CNTRC laminated nanoplate.

Keywords

Acknowledgement

This project was funded by the Deanship of Scientific Research (DSR) at King Abdulaziz University, Jeddah, under Grant no. G-111-135-1442. The authors, therefore, acknowledge with thanks DSR for technical and financial support.

References

  1. Al-Furjan, M.S.H., Habibi, M., rahimi, A., Chen, G., Safarpour, H. and Tounsi, A. (2020), "Chaotic simulation of the multi-phase reinforced thermo-elastic disk using GDQM", Eng. Comput., 1-24. https://doi.org/10.1007/s00366-020-01144-2.
  2. Askes, H. and Aifantis, E.C. (2009), "Gradient elasticity and flexural wave dispersion in carbon nanotubes", Phys. Rev. B, 80(19), 195412. https://doi.org/10.1103/PhysRevB.80.195412.
  3. Bekhadda, A., Cheikh, A., Bensaid, I., Hadjoui, A. and Daikh, A.A. (2019), "A novel first order refined shear-deformation beam theory for vibration and buckling analysis of continuously graded beams", Adv. Aircr. Spacecr. Sci., 6(3), 189-206. https://doi.org/10.12989/aas.2019.6.3.189.
  4. Belarbi, M.O., Houari, M.S.A., Daikh, A.A., Garg, A., Merzouki, T., Chalak, H.D. and Hirane, H. (2021), "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.
  5. Belarbi, O.M., Houari, M.S.A., Hirane, H. and Daikh, A.A. (2020). "An efficient nonlocal finite element model for the bending and buckling analysis of functionally graded nanobeams using a novel parabolic shear deformation theory", Compos. Struct., 264, 113712. https://doi.org/10.1016/j.compstruct.2021.113712.
  6. Bensaid, I. (2017), "A refined nonlocal hyperbolic shear deformation beam model for bending and dynamic analysis of nanoscale beams", Adv. Nano Res., 5(2), 113-126. http://doi.org/10.12989/anr.2017.5.2.113.
  7. Bensaid, I., Daikh, A.A. and Drai, A. (2020), "Size-dependent free vibration and buckling analysis of sigmoid and power law functionally graded sandwich nanobeams with microstructural defects", Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science, 234(18), 3667-3688. https://doi.org/10.1177/0954406220916481.
  8. Cao, Y., Khorami, M., Baharom, S., Assilzadeh, H. and Dindarloo, M.H. (2021), "The effects of multi-directional functionally graded materials on the natural frequency of the doubly-curved nanoshells", Compos. Struct., 258, 113403. https://doi.org/10.1016/j.compstruct.2020.113403.
  9. Chi, S.H. and Chung, Y.L. (2006), "Mechanical behavior of functionally graded material plates under transverse load-Part I: Analysis", Int. J. Solid Struct., 43(13), 3657-74. https://doi.org/10.1016/j.ijsolstr.2005.04.011.
  10. Daikh, A.A. (2019), "Temperature dependent vibration analysis of functionally graded sandwich plates resting on Winkler/Pasternak/Kerr foundation", Mater. Res. Express., 6, 065702. https://doi.org/10.1088/2053-1591/ab097b.
  11. Daikh, A.A. (2020), "Thermal buckling analysis of functionally graded sandwich cylindrical shells", Adv. Aircr. Spacecr. Sci., 7(4), 335-351. http://doi.org/10.12989/aas.2020.7.4.335.
  12. Daikh, A.A. and Megueni, A. (2018), "Thermal buckling analysis of functionally graded sandwich plates", J. Therm. Stress, 41(2), 139-159. https://doi.org/10.1080/01495739.2017.1393644.
  13. Daikh, A.A. and Zenkour, A.M., (2019), "Free vibration and buckling of porous power-law and sigmoid functionally graded sandwich plates using a simple higher-order shear deformation theory", Mat. Res. Express., 6(11), 115707. https://doi.org/10.1088/2053-1591/ab48a9.
  14. Daikh, A.A. and Zenkour, A.M. (2020), "Bending of functionally graded sandwich nanoplates resting on pasternak foundation under different boundary conditions", J. Appl. Computat. Mech., 6, 1245-1259. https://doi.org/10.22055/JACM.2020.33136.2166.
  15. Daikh, A.A., Houari, M.S.A and Tounsi, A. (2019a), "Buckling analysis of porous FGM sandwich nanoplates due to heat conduction via nonlocal strain gradient theory", Eng. Res. Express., 1, 015022. https://doi.org/10.1088/2631-8695/ab38f9.
  16. Daikh, A.A., Guerroudj, M., Elajrami, M. and Megueni, A. (2019b), "Thermal buckling of functionally graded sandwich beams", Adv. Mater. Res., 1156, 43-59. https://doi.org/10.4028/www.scientific.net/AMR.1156.43.
  17. Daikh, A.A., Bachiri, A., Houari, M.S.A. and Tounsi. (2020a), "Size dependent free vibration and buckling of multilayered carbon nanotubes reinforced composite nanoplates in thermal environment", Mech. Based Des. Struct., 1-29. https://doi.org/10.1080/15397734.2020.1752232.
  18. Daikh, A.A., Houari, M.S.A. and Eltaher. M.A. (2020b), "A novel nonlocal strain gradient Quasi-3D bending analysis of sigmoid functionally graded sandwich nanoplates", Compos. Struct., 113347. https://doi.org/10.1016/j.compstruct.2020.113347.
  19. Daikh, A.A., Drai, A., Bensaid, I., Houari, M.S.A. and Tounsi A. (2020c), "On vibration of functionally graded sandwich nanoplates in the thermal environment", J. Sandw. Struct. Mater., 1-28. https://doi.org/10.12989/aas.2020.7.4.335.
  20. Daikh, A.A., Drai, A., Houari M.S.A. and Mohamed A. Eltaher. (2020d), "Static analysis of multilayer nonlocal strain gradient nanobeam reinforced by carbon nanotubes", Steel Compos. Struct., 36 (6), 643-656. https://doi.org/10.12989/scs.2020.36.6.643.
  21. Daikh, A.A., Bensaid, I., Bachiri, A., Houari, M.S.A. Tounsi, A. and Merzouki, T. (2020e), "On static bending of multilayered carbon nanotube-reinforced composite plates", Comput. Concrete., 26(2), 137-150. https://doi.org/10.12989/cac.2020.26.2.137.
  22. Daikh, A.A., Bensaid, I. and Zenkour, A.M. (2020f), "Temperature dependent thermomechanical bending response of functionally graded sandwich plates", Eng. Res. Express., 2, 015006. https://doi.org/10.1088/2631-8695/ab638c.
  23. Daikh, A.A., Houari, M.S.A., Belarbi, M.O. Chakraverty, S. and Eltaher, M.A. (2021), "Analysis of axially temperature-dependent functionally graded carbon nanotube reinforced composite plates", Eng. Comput., 1-22. https://doi.org/10.1007/s00366-021-01413-8.
  24. Duc, N.D., Lee, J., Nguyen-Thoi, T. and Pham, T.T. (2017), "Static response and free vibration of functionally graded carbon nanotube-reinforced composite rectangular plates resting on Winkler-Pasternak elastic foundations", Aerosp. Sci. Technol., 68, 391-402. https://doi.org/10.1016/j.ast.2017.05.032.
  25. Ebrahimi, F. and Barati, A.F. (2016), "Analytical solution for nonlocal buckling characteristics of higher-order inhomogeneous nanosize beams embedded in elastic medium", Adv. Nano Res., 4(3), 229-249. http://doi.org/10.12989/anr.2016.4.3.229.
  26. Ehyaei, J., Akbarshahi, A., and Shafiei, N. (2017), "Influence of porosity and axial preload on vibration behavior of rotating FG nanobeam", Adv. Nano Res., 5(2), 141-169. http://doi.org/10.12989/anr.2017.5.2.141.
  27. Ekinci, K. and Roukes, M. (2005), "Nanoelectromechanical systems", Rev. Sci. Instrum., 76(6), 061101. https://doi.org/10.1063/1.1927327.
  28. Eltaher, M.A., Khater, M.E., Park, S., Abdel-Rahman, E. and Yavuz M. (2016), "On the static stability of nonlocal nanobeams using higher-order beam theories", Adv. Nano Res., 4(1), 51-64. http://doi.org/10.12989/anr.2016.4.1.051.
  29. Eringen, A.C. (1972), "Nonlocal polar elastic continua", Int. J. Eng. Sci., 10(1), 1-16. https://doi.org/10.1016/0020-7225(72)90070-5.
  30. Eringen, A.C. (1983), "On differential equations of nonlocal elasticity and solutions of screw dislocation and surface waves", J. Appl. Phys., 54(9), 4703-10 . https://doi.org/10.1063/1.332803.
  31. Esawi, A.M. and Farag, M.M. (2007), "Carbon nanotube reinforced composites: Potential and current challenges", Mater. Des., 28(9), 2394-401. https://doi.org/10.1016/j.matdes.2006.09.022.
  32. Esen, I., Abdelrahman, A.A. and Eltaher, Mohamed A. (2020), "Dynamics analysis of timoshenko perforated microbeams under moving loads", Eng. Comput., 1-17. https://doi.org/10.1007/s00366-020-01212-7.
  33. Esen, I., Abdelrahman, A.A. and Eltaher, M.A. (2021), "Free vibration of a cracked FG microbeam embedded in an elastic matrix and exposed to magnetic field in a thermal environment", Compos. Struct., 261, 113552/ https://doi.org/10.1016/j.compstruct.2021.113552.
  34. 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, 458. https://doi.org/10.1140/epjp/s13360-021-01419-7.
  35. Ferreira, A., Castro, L.M. and Bertoluzza, S. (2008), "A high order collocation method for the static and vibration analysis of composite plates using a first-order theory", Compos. Struct., 89(3), 424-32. https://doi.org/10.1016/j.compstruct.2008.09.006.
  36. Gurtin, M.E. and Murdoch, A.I. (1978), "Surface stress in solids", Int. J. Solid Struct., 197(14), 431-440. https://doi.org/10.1016/0020-7683(78)90008-2.
  37. Hamed, M.A. Abo-bakr, R.M. Mohamed, S.A. and Eltaher, M.A. (2020), "Influence of axial load function and optimization on static stability of sandwich functionally graded beams with porous core", Eng. Comput., 6, 1929-1946. https://doi.org/10.1007/s00366-020-01023-w.
  38. Han, Y. and Elliott, J. (2007) , "Molecular dynamics simulations of the elastic properties of polymer/carbon nanotube composites", Computat. Mater. Sci., 39(2), 315-323. https://doi.org/10.1016/j.commatsci.2006.06.011.
  39. Harris, P.J. (2004), "Carbon nanotubes and related structures: new materials for the twenty-first century", Am. Assoc. Phys. Teach., 72(3), 415. https://doi.org/10.1017/CBO9780511605819.
  40. Houari M.S.A, Tounsi, A. Bessaim, A. and Mahmoud, S.R. (2016), "A new simple three-unknown sinusoidal shear deformation theory for functionally graded plates", Steel Compos. Struct., 22(2), 257-276. http://doi.org/10.12989/scs.2016.22.2.257.
  41. Houari, M.S.A., Tounsi, A. and Beg, O.A. (2013), "Thermoelastic bending analysis of functionally graded sandwich plates using a new higher order shear and normal deformation theory", Int. J. Mech. Sci., 76, 102-11. https://doi.org/10.1016/j.ijmecsci.2013.09.004.
  42. Hussain, M., Naeem, M. N. and Tounsi, A. (2020a), "Response of orthotropic Kelvin modeling for single-walled carbon nanotubes: Frequency analysis", Adv. Nano Res., 8(3), 229-244. https://doi.org/10.12989/anr.2020.8.3.229.
  43. Hussain, M., Naeem, M. N., Asghar, S., & Tounsi, A. (2020b), "Theoretical impact of Kelvin's theory for vibration of double walled carbon nanotubes", Adv. Nano Res., 8(4), 307-322. https://doi.org/10.12989/anr.2020.8.4.307.
  44. Jena, S.K., Chakraverty, S. and Tornabene, F. (2019), "Dynamical behavior of nanobeam embedded in constant, linear, parabolic and sinusoidal types of Winkler elastic foundation using first-Order nonlocal strain gradient model", Mater. Res. Express., 6, 0850f2. https://doi.org/10.1088/2053-1591/ab2779.
  45. Liew, K.M. and Alibeigloo, A. (2020) , "Predicting bucking and vibration behaviors of functionally graded carbon nanotube reinforced composite cylindrical panels with three-dimensional flexibilities", Compos. Struct., 113039. https://doi.org/10.1016/j.compstruct.2020.113039.
  46. Lim, C.W., Zhang, G. and Reddy, J.N. (2015), "A higher-order nonlocal elasticity and strain gradient theory and its applications in wave propagation", J. Mech. Phys. Solid, 78, 298-313. https://doi.org/10.1016/j.jmps.2015.02.001
  47. Lu, L., She, G.L. and Guo, X. (2021a), "Size-dependent postbuckling analysis of graphene reinforced composite microtubes with geometrical imperfection", Int. J. Mech. Sci., 199, 106428. https://doi.org/10.1016/j.ijmecsci.2021.106428.
  48. Lu, L., Wang, S., Li, M. and Guo, X. (2021b), "Free vibration and dynamic stability of functionally graded composite microtubes reinforced with graphene platelets", Compos. Struct., 272(15), 114231. https://doi.org/10.1016/j.compstruct.2021.114231.
  49. Mantari, J. and Ore, M. (2015), "Free vibration of single and sandwich laminated composite plates by using a simplified FSDT", Compos. Struct., 132, 952-959. https://doi.org/10.1016/j.compstruct.2015.06.035.
  50. Neves, A., Ferreira, A., Carrera, E., Cinefra, M., Roque, C.M.C., Jorge, R.M.N. and Soares, C.M.M. (2013), "Free vibration analysis of functionally graded shells by a higher-order shear deformation theory and radial basis functions collocation, accounting for through-the-thickness deformations", Eur. J. Mech. A Solid, 37, 24-34 . https://doi.org/10.1016/j.euromechsol.2012.05.005.
  51. Nguyena, T.N., Ngo, T.D. and Nguyen-Xuan, H. (2017), "A novel three-variable shear deformation plate formulation: Theory and Isogeometric implementation", Comput. Methods Appl. Mech. Eng., 326, 376-401. http://doi.org/10.1016/j.cma.2017.07.024.
  52. Nguyena, T.N., Thai, C.H., Luu, A.T., Nguyen-Xuan, H. and Lee, J. (2019), "NURBS-based postbuckling analysis of functionally graded carbon nanotube-reinforced composite shells", Comput. Method Appl. M., 347, 983-1003. https://doi.org/10.1016/j.cma.2019.01.011.
  53. Nguyen-Xuan, H., Thai, C.H. and Nguyen-Thoi T. (2013), "Isogeometric finite element analysis of composite sandwich plates using a higher order shear deformation theory", Compos. Part B Eng., 55, 558-74. https://doi.org/10.1016/j.compositesb.2013.06.044.
  54. Reddy, J.N. (1984), "A simple higher-order theory for laminated composite plates", J. Appl. Mech., 51, 745-752. https://doi.org/10.1115/1.3167719.
  55. Shahsavari, D., Karami, B. and Mansouri S. (2018), "Shear buckling of single layer graphene sheets in hygrothermal environment resting on elastic foundation based on different nonlocal strain gradient theories", Eur. J. Mech. A Solid, 67, 200-214. https://doi.org/10.1016/j.euromechsol.2017.09.004.
  56. She, G.L., Liu, H.B. and Karami, B. (2021), "Resonance analysis of composite curved microbeams reinforced with graphene nanoplatelets", Thin Wall. Struct., 160, 107407. https://doi.org/10.1016/j.tws.2020.107407.
  57. She, G.L., Yuan, F.G., Ren, Y.R., Liu, H.B and Xiao, W.S. (2018), "Nonlinear bending and vibration analysis of functionally graded porous tubes via a nonlocal strain gradient theory", Compos. Struct., 203, 614-623. https://doi.org/10.1016/j.compstruct.2018.07.063.
  58. 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.
  59. Singh, D.B. and Singh, B.N. (2017), "New higher order shear deformation theories for free vibration and buckling analysis of laminated and braided composite plates", Int. J. Mech. Sci., 131, 265-277. https://doi.org/10.1016/j.ijmecsci.2017.06.053.
  60. Soldatos, K.P. (1992), "A transverse shear deformation theory for homogeneous monoclinic plates", Acta. Mech., 94(3-4), 195-220. https://doi.org/10.1007/BF01176650.
  61. Thai, C.H., Kulasegaram, S., Tran, L.V. and Nguyen-Xuan, H. (2014), "Generalized shear deformation theory for functionally graded isotropic and sandwich plates based on isogeometric approach", Comput. Struct., 141, 94-112. http://doi.org/10.1016/j.compstruc.2014.04.003.
  62. Thai, C.H., Ferreira, A., Bordas, S. and Rabczuk, T. (2013), "Nguyen-Xuan H. Isogeometric analysis of laminated composite and sandwich plates using a new inverse trigonometric shear deformation theory", Eur. J. Mech. A Solid, 43, 89-108. https://doi.org/10.1016/j.euromechsol.2013.09.001.
  63. Thai, C.H., Zenkour, A.M., Wahab, M.A. and Nguyen-Xuan, H. (2016), "A simple four-unknown shear and normal deformations theory for functionally graded isotropic and sandwich plates based on isogeometric analysis", Compos. Struct., 139, 77-95. https://doi.org/10.1016/j.compstruct.2015.11.066.
  64. Thai, H.T., Nguyen, T.K., Vo, T.P., Lee, J. (2014), "Analysis of functionally graded sandwich plates using a new first-order shear deformation theory", Eur. J. Mech. A Solid, 45, 211-25. https://doi.org/10.1016/j.euromechsol.2013.12.008.
  65. Thang, P.T., Tran, P. and Nguyen-Thoi, T. (2021), "Applying nonlocal strain gradient theory to size-dependent analysis of functionally graded carbon nanotube-reinforced composite nanoplates" Appl. Math. Modell., 93, 775-791. https://doi.org/10.1016/j.apm.2021.01.001.
  66. Touloukian, Y.S. (1967), Thermophysical Properties of High Temperature Solid Materials, MacMillan, New York, U.S.A.
  67. Touratier M. (1991), "An efficient standard plate theory", Int. J. Eng. Sci., 29(8), 901-916. https://doi.org/10.1016/0020-7225(91)90165-Y.
  68. Vaghefi, R. (2020), "Thermo-elastoplastic analysis of functionally graded sandwich plates using a three-dimensional meshless model", Compos. Struct., 242, 112144. https://doi.org/10.1016/j.compstruct.2020.112144.
  69. Vuong, P.M. and Duc, N.D. (2020), "Nonlinear buckling and post-buckling behavior of shear deformable sandwich toroidal shell segments with functionally graded core subjected to axial compression and thermal loads", Aerosp. Sci. Technol., 106, 106084. https://doi.org/10.1016/j.ast.2020.106084.
  70. Wattanasakulpong, N., Chaikittiratana, A. (2015, "Exact solutions for static and dynamic analyses of carbon nanotube-reinforced composite plates with Pasternak elastic foundation", Appl. Math. Modell., 39, 5459-5472. https://doi.org/10.1016/j.apm.2014.12.058
  71. Yang, F., Chong, A., Lam, D.C.C. and Tong, P. "Couple stress based strain gradient theory for elasticity", Int. J. Solid Struct., 39(10), 2731-2743. https://doi.org/10.1016/S0020-7683(02)00152-X.
  72. Zenkour, A.M. (2016), "Buckling of a single-layered graphene sheet embedded in visco-Pasternak", Adv. Nano Res., 4(4), 309-329. http://doi.org/10.12989/anr.2016.4.4.309.
  73. Zhang, Y.Y., Wang, X.Y., Zhang, X., Shen, H.M. and She, G.L. (2021), "On snapbuckling of FG-CNTR curved nanobeams considering surface effects", Steel Compos. Struct., 38(3), 293-304. https://doi.org/10.12989/scs.2021.38.3.293.