Advances in aircraft and spacecraft science

Techno-Press (테크노프레스)
권호 표지
DOI QR코드

DOI QR Code

Isogeometric analysis of FG polymer nanocomposite plates reinforced with reduced graphene oxide using MCST

  • Farzam, Amir (Department of Civil Engineering, Ferdowsi University of Mashhad) ;
  • Hassani, Behrooz (Department of Mechanical Engineering, Ferdowsi University of Mashhad)
  • Received : 2021.08.06
  • Accepted : 2022.01.27
  • Published : 2022.01.25
⟨ Previous Next ⟩

Abstract

Reduced graphene oxide (rGO) is one of the derivatives of graphene, which has drawn some experimental research interests in recent years however, numerical research studying the mechanical behaviors of composites made of rGO has not been taken into consideration yet. The objective of this research is to investigate the buckling, and free vibration of functionally graded reduced graphene oxide reinforced nanocomposite (FG rGORC) plates employing isogeometric analysis (IGA). The effective Young's modulus of rGORC is determined based onthe Halpin-Tsai model. Four different FG distribution types of rGO are considered varying across plate thickness. Besides, the refined plate theory is used based on Reddy's third-order function. To capture the size effect, modified couple stress theory (MCST) is employed. A comprehensive study is provided examining the effect of various parameters including rGO weight fraction, FG distribution types, boundary conditions, material length scale parameter, etc. Our obtained results show that the addition of only 1% of uniformly distributed rGO into epoxy plates leads to the fundamental frequency and critical buckling load 18% and 39% higher than those of pure epoxy plates, respectively.

Keywords

References

  1. Abazid, M.A., Zenkour, A.M. and Sobhy, M. (2020), "Wave propagation in FG porous GPLs-reinforced nanoplates under in-plane mechanical load and Lorentz magnetic force via a new quasi 3D plate theory", Mech. Bas. Des. Struct. Mach., 1-20. https://doi.org/10.1080/15397734.2020.1769651.
  2. Akgoz, B. and Civalek, O. (2017), "A size-dependent beam model for stability of axially loaded carbon nanotubes surrounded by Pasternak elastic foundation", Compos. Struct., 176, 1028-1038. https://doi.org/10.1016/j.compstruct.2017.06.039.
  3. An, Y., Han, J., Zhang, X., Han, W., Cheng, Y., Hu, P. and Zhao, G. (2016), "Bioinspired high toughness graphene/ZrB2 hybrid composites with hierarchical architectures spanning several length scales", Carbon, 107, 209-216. https://doi.org/10.1016/j.carbon.2016.05.074.
  4. Arefi, M., Bidgoli, E.M. and Rabczuk, T. (2019), "Effect of various characteristics of graphene nanoplatelets on thermal buckling behavior of FGRC micro plate based on MCST", Eur. J. Mech. A-Solid., 77, 103802. https://doi.org/10.1016/j.euromechsol.2019.103802.
  5. Belmahi, S., Zidour, M. and Meradjah, M. (2019), "Small-scale effect on the forced vibration of a nano beam embedded an elastic medium using nonlocal elasticity theory", Adv. Aircraft Spacecraft Sci., 6(1), 1. http://doi.org/10.12989/aas.2019.6.1.001.
  6. Belmonte, M., Nistal, A., Boutbien, P., Roman-Manso, B., Osendi, M.I. and Miranzo, P. (2016), "Toughened and strengthened silicon carbide ceramics by adding graphene-based fillers", Scripta Mater., 113, 127-130. https://doi.org/10.1016/j.scriptamat.2015.10.023.
  7. Carrera, E., de Miguel, A.G. and Pagani, A. (2017), "Extension of MITC to higher-order beam models and shear locking analysis for compact, thin-walled, and composite structures", Int. J. Numer. Meth. Eng., 112(13), 1889-1908. https://doi.org/10.1002/nme.5588.
  8. Carrera, E., Pagani, A., Petrolo, M. and Zappino, E. (2015), "Recent developments on refined theories for beams with applications", Mech. Eng. Rev., 2(2), 14-00298. https://doi.org/10.1299/mer.14-00298.
  9. Compton, O.C. and Nguyen, S.T. (2010), "Graphene oxide, highly reduced graphene oxide, and graphene: versatile building blocks for carbon-based materials", Small, 6(6), 711-723. https://doi.org/10.1002/smll.200901934.
  10. Dastjerdi, S., Akgoz, B. and Civalek, O. (2020), "On the effect of viscoelasticity on behavior of gyroscopes" Int. J. Eng. Sci., 149, 103236. https://doi.org/10.1016/j.ijengsci.2020.103236.
  11. Devarajan, B. and Kapania, R.K. (2020), "Thermal buckling of curvilinearly stiffened laminated composite plates with cutouts using isogeometric analysis", Compos. Struct., 238, 111881. https://doi.org/10.1016/j.compstruct.2020.111881.
  12. Devarajan, B. and Kapania, R.K. (2022), "Analyzing thermal buckling in curvilinearly stiffened composite plates with arbitrary shaped cutouts using isogeometric level set method", Aerosp. Sci. Technol., 107350. https://doi.org/10.1016/j.ast.2022.107350.
  13. Dindarloo, M.H. and Zenkour, A.M. (2020), "Nonlocal strain gradient shell theory for bending analysis of FG spherical nanoshells in thermal environment", Eur. Phys. J. Plus, 135(10), 1-18. https://doi.org/10.1140/epjp/s13360-020-00796-9.
  14. Eringen, A.C. and Edelen, D.G.B. (1972), "On nonlocal elasticity", Int. J. Eng. Sci., 10, 233-248. https://doi.org/10.1016/0020-7225(72)90039-0.
  15. Farzam-Rad, S.A., Hassani, B. and Karamodin, A. (2017), "Isogeometric analysis of functionally graded plates using a new quasi-3D shear deformation theory based on physical neutral surface", Compos. Part B, 108, 174-189. https://doi.org/10.1016/j.compositesb.2016.09.029.
  16. Farzam, A. and Hassani, B. (2018), "Thermal and mechanical buckling analysis of FG carbon nanotube reinforced composite plates using modified couple stress theory and isogeometric approach", Compos. Struct., 206, 774-790. https://doi.org/10.1016/j.compstruct.2018.08.030.
  17. Farzam, A. and Hassani, B. (2019a), "Size-dependent analysis of FG microplates with temperature-dependent material properties using modified strain gradient theory and isogeometric approach", Compos. Part B, 161, 150-168. https://doi.org/10.1016/j.compositesb.2018.10.028.
  18. Farzam, A. and Hassani, B. (2019b), "Isogeometric analysis of in-plane functionally graded porous microplates using modified couple stress theory", Aerosp. Sci. Technol., 91, 508-524. https://doi.org/10.1016/j.ast.2019.05.012.
  19. Farzam, A. and Hassani, B. (2019c), "A new efficient shear deformation theory for FG plates with in-plane and through-thickness stiffness variations using isogeometric approach", Mech. Adv. Mater. Struct., 26(6), 512-525. https://doi.org/10.1080/15376494.2017.1400623.
  20. Farzam, A. and Kapania, R. (2022), "Buckling analysis of functionally graded plates using Isogeometric Finite Element Method and ABAQUS", AIAA SCITECH 2022 Forum, San Diego. https://doi.org/10.2514/6.2022-1488.
  21. Fenjan, R.M., Hamad, L.B. and Faleh, N.M. (2020), "Mechanical-hygro-thermal vibrations of functionally graded porous plates with nonlocal and strain gradient effects", Adv. Aircraft Spacecraft Sci., 7(2), 169-86. http://doi.org/10.12989/aas.2020.7.2.169.
  22. Fleck, N.A. and Hutchinson, J.W. (1993), "A phenomenological theory for strain gradient effects in plasticity", J. Mech. Phys. Solid., 41, 1825-1857. https://doi.org/10.1016/0022-5096(93)90072-N.
  23. Fornes, T.D. and Paul, D.R. (2003), "Modeling properties of nylon 6/clay nanocomposites using composite theories", Polym., 44(17), 4993-5013. https://doi.org/10.1016/S0032-3861(03)00471-3.
  24. Garcia-Macias, E., Rodriguez-Tembleque, L. and Saez, A. (2018), "Bending and free vibration analysis of functionally graded graphene vs. carbon nanotube reinforced composite plates", Compos. Struct., 186, 123-138. https://doi.org/10.1016/j.compstruct.2017.11.076.
  25. Gomez-Navarro, C., Burghard, M. and Kern, K. (2008), "Elastic properties of chemically derived single graphene sheets", Nano Lett., 8(7), 2045-2049. https://doi.org/10.1021/nl801384y.
  26. Gong, L.X., Pei, Y.B., Han, Q.Y., Zhao, L., Wu, L.B., Jiang, J.X. and Tang, L.C. (2016), "Polymer grafted reduced graphene oxide sheets for improving stress transfer in polymer composites", Compos. Sci. Technol., 134, 144-152. https://doi.org/10.1016/j.compscitech.2016.08.014.
  27. Hanzel, O., Sedlak, R., Sedlacek, J., Bizovska, V., Bystricky, R., Girman, V., Kovalcikova, A., Dusza, J. and Sajgalik, P. (2017), "Anisotropy of functional properties of SiC composites with GNPs, GO and in-situ formed graphene", J. Eur. Ceram. Soc., 37(12), 3731-3739. https://doi.org/10.1016/j.jeurceramsoc.2017.03.060.
  28. Hosseini, S.A., Moghaddam, M.H. and Rahmani, O. (2020)," Exact solution for axial vibration of the power, exponential and sigmoid FG nonlocal nanobeam", Adv. Aircraft Spacecraft Sci., 7(6), 517-36. http://doi.org/10.12989/aas.2020.7.6.517.
  29. Huang, Y., Jiang, D., Zhang, X., Liao, Z. and Huang, Z. (2018), "Enhancing toughness and strength of SiC ceramics with reduced graphene oxide by HP sintering", J. Eur. Ceram. Soc., 38(13), 4329-4337. https://doi.org/10.1016/j.jeurceramsoc.2018.05.033.
  30. Hughes, T.J.R., Cottrell, J.A. and Bazilevs, Y. (2005), "Isogeometric analysis: CAD, finite elements, NURBS, exact geometry and mesh refinement", Comput. Meth. Appl. Mech. Eng., 194, 4135-4195. https://doi.org/10.1016/j.cma.2004.10.008.
  31. Iqbal, M.Z., Abdala, A.A., Mittal, V., Seifert, S., Herring, A.M. and Liberatore, M.W. (2016), "Processable conductive graphene/polyethylene nanocomposites: Effects of graphene dispersion and polyethylene blending with oxidized polyethylene on rheology and microstructure", Polym., 98, 143-155. https://doi.org/10.1016/j.polymer.2016.06.021.
  32. Ji, W.F., Chang, K.C., Lai, M.C., Li, C.W., Hsu, S.C., Chuang, T.L., Yeh, J.M. and Liu, W.R. (2014), "Preparation and comparison of the physical properties of PMMA/thermally reduced graphene oxides composites with different carboxylic group content of thermally reduced graphene oxides", Compos. Part A, 65, 108-114. https://doi.org/10.1016/j.compositesa.2014.05.017.
  33. Kapoor, H. and Kapania, R.K. (2012), "Geometrically nonlinear NURBS isogeometric finite element analysis of laminated composite plates", Compos. Struct., 94(12), 3434-3447. https://doi.org/10.1016/j.compstruct.2012.04.028.
  34. Kapoor, H., Kapania, R.K. and Soni, S.R. (2013), "Interlaminar stress calculation in composite and sandwich plates in NURBS Isogeometric Finite Element Analysis", Compos. Struct., 106, 537-548. https://doi.org/10.1016/j.compstruct.2013.05.028.
  35. Karami, B., Shahsavari, D., Janghorban, M. and Tounsi, A. (2019), "Resonance behavior of functionally graded polymer composite nanoplates reinforced with graphene nanoplatelets", Int. J. Mech. Sci., 156, 94-105. https://doi.org/10.1016/j.ijmecsci.2019.03.036.
  36. Kashyap, S., Pratihar, S.K. and Behera, S.K. (2016), "Strong and ductile graphene oxide reinforced PVA nanocomposites", J. Alloy Compound., 684, 254-260. https://doi.org/10.1016/j.jallcom.2016.05.162.
  37. Kiani, Y. (2018), "Isogeometric large amplitude free vibration of grapheme reinforced laminated plates in thermal environment using NURBS formulation", Comput. Meth. Appl. Mech. Eng., 332, 86-101. https://doi.org/10.1016/j.cma.2017.12.015.
  38. Kiani, Y. (2018), "NURBS-based isogeometric thermal postbuckling analysis of temperature dependent graphene reinforced composite laminated plates", Thin Wall Struct., 125, 211-219. https://doi.org/10.1016/j.tws.2018.01.024.
  39. Kim, T.A., Pyo, J.B., Lee, S.S. and Park, M. (2019), "Highly aligned and porous reduced graphene oxide structures and their application for stretchable conductors", J. Ind. Eng. Chem., 80, 385-391. https://doi.org/10.1016/j.jiec.2019.08.018.
  40. Kong, J.Y., Choi, M.C., Kim, G.Y., Park, J.J., Selvaraj, M., Han, M. and Ha, C.S. (2012), "Preparation and properties of polyimide/graphene oxide nanocomposite films with Mg ion crosslinker", Eur. Polym. J., 48(8), 1394-1405. https://doi.org/10.1016/j.eurpolymj.2012.05.015.
  41. Lam, D.C.C., Yang, F., Chong, A.C.M., Wang, J. and Tong, P. (2003), "Experiments and theory in strain gradient elasticity", J. Mech. Phys. Solid., 51, 1477-1508. https://doi.org/10.1016/S0022-5096(03)00053-X.
  42. Lee, B., Koo, M.Y., Jin, S.H., Kim, K.T. and Hong, S.H. (2014), "Simultaneous strengthening and toughening of reduced graphene oxide/alumina composites fabricated by molecular-level mixing process", Carbon, 78, 212-219. https://doi.org/10.1016/j.carbon.2014.06.074.
  43. Li, K., Wu, D., Chen, X., Cheng, J., Liu, Z., Gao, W. and Liu, M. (2018), "Isogeometric Analysis of functionally graded porous plates reinforced by graphene platelets", Compos. Struct., 204, 114-130. https://doi.org/10.1016/j.compstruct.2018.07.059.
  44. Li, Y., Tang, J., Huang, L., Wang, Y., Liu, J., Ge, X., Tjong, S.C., Li, R.K. and Belfiore, L.A. (2015a), "Facile preparation, characterization and performance of noncovalently functionalized graphene/epoxy nanocomposites with poly (sodium 4-styrenesulfonate)", Compos. Part A, 68, 1-9. https://doi.org/10.1016/j.compositesa.2014.09.016.
  45. Li, Z., Fan, G., Tan, Z., Guo, Q., Xiong, D., Su, Y., Li, Z. and Zhang, D. (2014), "Uniform dispersion of graphene oxide in aluminum powder by direct electrostatic adsorption for fabrication of graphene/aluminum composites", Nanotechnol., 25(32), 325601. https://doi.org/10.1088/0957-4484/25/32/325601.
  46. Li, Z., Guo, Q., Li, Z., Fan, G., Xiong, D.B., Su, Y., Zhang, J. and Zhang, D. (2015b), "Enhanced mechanical properties of graphene (reduced graphene oxide)/aluminum composites with a bioinspired nanolaminated structure", Nano Lett., 15(12), 8077-8083. https://doi.org/10.1021/acs.nanolett.5b03492.
  47. Liu, J., Khan, U., Coleman, J., Fernandez, B., Rodriguez, P., Naher, S. and Brabazon, D. (2016), "Graphene oxide and graphene nanosheet reinforced aluminium matrix composites: Powder synthesis and prepared composite characteristics", Mater. Des., 94, 87-94. https://doi.org/10.1016/j.matdes.2016.01.031.
  48. Maity, N., Mandal, A. and Nandi, A.K. (2016), "Synergistic interfacial effect of polymer stabilized graphene via non-covalent functionalization in poly (vinylidene fluoride) matrix yielding superior mechanical and electronic properties", Polym., 88, 79-93. https://doi.org/10.1016/j.polymer.2016.02.028.
  49. Miglani, J., Devarajan, B. and Kapania, R.K., (2021), "Isogeometric thermal buckling and sensitivity analysis of periodically supported laminated composite beams", AIAA J., 1-10. https://doi.org/10.2514/1.J060814.
  50. Mishra, S.K., Tripathi, S.N., Choudhary, V. and Gupta, B.D. (2014), "SPR based fibre optic ammonia gas sensor utilizing nanocomposite film of PMMA/reduced graphene oxide prepared by in situ polymerization", Sensor Actuat. B, 199, 190-200. https://doi.org/10.1016/j.snb.2014.03.109.
  51. Nguyen, L.B., Nguyen, N.V., Thai, C.H., Ferreira, A.M.J. and Nguyen-Xuan, H. (2019), "An isogeometric Bezier finite element analysis for piezoelectric FG porous plates reinforced by graphene platelets", Compos. Struct., 214, 227-245. https://doi.org/10.1016/j.compstruct.2019.01.077.
  52. Olowojoba, G.B., Eslava, S., Gutierrez, E.S., Kinloch, A.J., Mattevi, C., Rocha, V.G. and Taylor, A.C. (2016), "In situ thermally reduced graphene oxide/epoxy composites: thermal and mechanical properties", Appl. Nanosci., 6(7), 1015-1022. https://doi.org/10.1007/s13204-016-0518-y.
  53. Pham, V.H., Dang, T.T., Hur, S.H., Kim, E.J. and Chung, J.S. (2012), "Highly conductive poly (methyl methacrylate)(PMMA)-reduced graphene oxide composite prepared by self-assembly of PMMA latex and graphene oxide through electrostatic interaction", ACS Appl. Mater. Int., 4(5), 2630-2636. https://doi.org/10.1021/am300297j.
  54. Phung-Van, P., Ferreira, A.J.M., Nguyen-Xuan, H. and Abdel Wahab, M. (2017), "An isogeometric approach for size-dependent geometrically nonlinear transient analysis of functionally graded nanoplates", Compos. Part B, 118, 125-134. https://doi.org/10.1016/j.compositesb.2017.03.012.
  55. Phung-Van, P., Thai, C.H., Nguyen-Xuan, H. and Abdel-Wahab, M. (2019), "Porosity-dependent nonlinear transient responses of functionally graded nanoplates using isogeometric analysis", Compos. Part B, 164, 215-255. https://doi.org/10.1016/j.compositesb.2018.11.036.
  56. Phung-Van, P., Thanh, C.L., Nguyen-Xuan, H. and Abdel-Wahab, M. (2018), "Nonlinear transient isogeometric analysis of FG-CNTRC nanoplates in thermal environments", Compos. Struct., 201, 882-892. https://doi.org/10.1016/j.compstruct.2018.06.087.
  57. Potts, J.R., Lee, S.H., Alam, T.M., An, J., Stoller, M.D., Piner, R.D. and Ruoff, R.S. (2011), "Thermomechanical properties of chemically modified graphene/poly (methyl methacrylate) composites made by in situ polymerization", Carbon, 49(8), 2615-2623. https://doi.org/10.1016/j.carbon.2011.02.023.
  58. Pourjabari, A., Hajilak, Z.E., Mohammadi, A., Habibi, M. and Safarpour, H. (2019), "Effect of Porosity on free and forced vibration characteristics of the GPL reinforcement composite nanostructures", Comput. Math. Appl., 77(10), 2608-2626. https://doi.org/10.1016/j.camwa.2018.12.041.
  59. Qureshi, T.S. and Panesar, D.K. (2019), "Impact of graphene oxide and highly reduced graphene oxide on cement based composites", Constr. Build. Mater., 206, 71-83. https://doi.org/10.1016/j.conbuildmat.2019.01.176.
  60. Rafiee, M.A., Rafiee, J., Srivastava, I., Wang, Z., Song, H., Yu, Z.Z. and Koratkar, N. (2010), "Fracture and fatigue in graphene nanocomposites", Small, 6, 179-183. https://doi.org/10.1002/smll.200901480.
  61. Ramirez, C., Miranzo, P., Belmonte, M., Osendi, M.I., Poza, P., Vega-Diaz, S.M. and Terrones, M. (2014), "Extraordinary toughening enhancement and flexural strength in Si3N4 composites using graphene sheets", J. Eur. Ceram. Soc., 34(2), 161-169. https://doi.org/10.1016/j.jeurceramsoc.2013.08.039.
  62. 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.
  63. Robinson, J.T., Zalalutdinov, M., Baldwin, J.W., Snow, E.S., Wei, Z., Sheehan, P. and Houston, B.H. (2008), "Wafer-scale reduced graphene oxide films for nanomechanical devices", Nano Lett., 8(10), 3441-3445. https://doi.org/10.1021/nl8023092.
  64. Saeedi, A., Hassani, B. and Farzam, A. (2020), "Simultaneous modeling and structural analysis of curvilinearly stiffened plates using an isogeometric approach", Acta Mechanica, 231(8), 3473-3498. https://doi.org/10.1007/s00707-020-02725-4.
  65. Sahmani, S., Aghdam, M.M. and Rabczuk, T. (2018), "Nonlocal strain gradient plate model for nonlinear large-amplitude vibrations of functionally graded porous micro/nano-plates reinforced with GPLs", Compos. Struct., 198, 51-62. https://doi.org/10.1016/j.compstruct.2018.05.031.
  66. Sandhya, P.K., Sreekala, M.S., Padmanabhan, M., Jesitha, K. and Thomas, S. (2019), "Effect of starch reduced graphene oxide on thermal and mechanical properties of phenol formaldehyde resin nanocomposites", Compos. Part B, 167, 83-92. https://doi.org/10.1016/j.compositesb.2018.12.009.
  67. She, X., He, C., Peng, Z. and Kong, L. (2014), "Molecular-level dispersion of graphene into epoxidized natural rubber: Morphology, interfacial interaction and mechanical reinforcement", Polym., 55(26), 6803-6810. https://doi.org/10.1016/j.polymer.2014.10.054.
  68. Shin, J.H. and Hong, S.H. (2014), "Fabrication and properties of reduced graphene oxide reinforced yttria-stabilized zirconia composite ceramics", J. Eur. Ceram. Soc., 34(5), 1297-1302. https://doi.org/10.1016/j.jeurceramsoc.2013.11.034.
  69. Sobhy, M. and Zenkour, A.M. (2019), "Porosity and inhomogeneity effects on the buckling and vibration of double-FGM nanoplates via a quasi-3D refined theory", Compos. Struct., 220, 289-303. https://doi.org/10.1016/j.compstruct.2019.03.096.
  70. Sobhy, M. and Zenkour, A.M. (2020), "The modified couple stress model for bending of normal deformable viscoelastic nanobeams resting on visco-Pasternak foundations", Mech. Adv. Mater. Struct., 27(7), 525-538. https://doi.org/10.1080/15376494.2018.1482579.
  71. Sobhy, M. and Zenkour, A.M., (2021), "Wave propagation in magneto-porosity FG bi-layer nanoplates based on a novel quasi-3D refined plate theory", Wav. Rand. Complex Media, 31(5), 921-941. https://doi.org/10.1080/17455030.2019.1634853.
  72. Song, M., Yang, J. and Kitipornchai, S. (2018), "Bending and buckling analyses of functionally graded polymer composite plates reinforced with graphene nanoplatelets", Compos. Part B, 134, 106-113. https://doi.org/10.1016/j.compositesb.2017.09.043.
  73. Starkova, O., Chandrasekaran, S., Prado, L.A., Tolle, F., Mulhaupt, R. and Schulte, K. (2013), "Hydrothermally resistant thermally reduced graphene oxide and multi-wall carbon nanotube based epoxy nanocomposites", Polym. Degrad. Stabil., 98(2), 519-526. https://doi.org/10.1016/j.polymdegradstab.2012.12.005.
  74. Suk, J.W., Piner, R.D., An, J. and Ruoff, R.S. (2010), "Mechanical properties of monolayer graphene oxide", ACS Nano, 4(11), 6557-6564. https://doi.org/10.1021/nn101781v.
  75. Thai, C.H., Ferreira, A.J., Tran, T.D. and Phung-Van, P. (2019b), "A size-dependent quasi-3D isogeometric model for functionally graded graphene platelet-reinforced composite microplates based on the modified couple stress theory", Compos. Struct., 234, 111695. https://doi.org/10.1016/j.compstruct.2019.111695.
  76. Thai, C.H., Ferreira, A.J.M. and Phung-Van, P. (2019a), "Size dependent free vibration analysis of multilayer functionally graded GPLRC microplates based on modified strain gradient theory", Compos. Part B, 169, 174-188. https://doi.org/10.1016/j.compositesb.2019.02.048.
  77. Thai, C.H., Ferreira, A.J.M., Rabczuk, T. and Nguyen-Xuan, H. (2017), "A naturally stabilized nodal integration meshfree formulation for carbon nanotube-reinforced composite plate analysis", Eng. Anal. Bound. Elem., 160, 689-705. https://doi.org/10.1016/j.enganabound.2017.10.018.
  78. Thai, C.H., Ferreira, A.J.M., Tran, T.D. and Phung-Van, P. (2019c), "Free vibration, buckling and bending analyses of multilayer functionally graded graphene nanoplatelets reinforced composite plates using the NURBS formulation", Compos. Struct., 220, 749-759. https://doi.org/10.1016/j.compstruct.2019.03.100.
  79. Thai, H.T. and Kim, S.E. (2013), "A size-dependent functionally graded Reddy plate model based on a modified couple stress theory", Compos. Part B, 45, 1636-1645. https://doi.org/10.1016/j.compositesb.2012.09.065.
  80. Thanh, C.L., Phung-Van, P., Thai, C.H., Nguyen-Xuan, H. and Abdel Wahab, M. (2018), "Isogeometric analysis of functionally graded carbon nanotube reinforced composite nanoplates using modified couple stress theory", Compos. Struct., 184, 633-649. https://doi.org/10.1016/j.compstruct.2017.10.025.
  81. TK, B.S., Nair, A.B., Abraham, B.T., Beegum, P.S. and Thachil, E.T. (2014), "Microwave exfoliated reduced graphene oxide epoxy nanocomposites for high performance applications", Polym., 55(16), 3614-3627. https://doi.org/10.1016/j.polymer.2014.05.032.
  82. Tripathi, S.N., Saini, P., Gupta, D. and Choudhary, V. (2013), "Electrical and mechanical properties of PMMA/reduced graphene oxide nanocomposites prepared via in situ polymerization", J. Mater. Sci., 48(18), 6223-6232. https://doi.org/10.1007/s10853-013-7420-8.
  83. Van Es, M.A. (2001), "Polymer-clay nanocomposites: the importance of particle dimensions", Ph.D. Thesis, Delft University of Technology, Delft, The Netherlands.
  84. Walker, L.S., Marotto, V.R., Rafiee, M.A., Koratkar, N. and Corral, E.L. (2011), "Toughening in graphene ceramic composites", ACS Nano, 5(4), 3182-3190. https://doi.org/10.1021/nn200319d.
  85. Wang, J., Shi, Z., Ge, Y., Wang, Y., Fan, J. and Yin, J. (2012), "Solvent exfoliated graphene for reinforcement of PMMA composites prepared by in situ polymerization", Mater. Chem. Phys., 136(1), 43-50. https://doi.org/10.1016/j.matchemphys.2012.06.017.
  86. Weon, J.I. (2009), "Mechanical and thermal behavior of polyamide-6/clay nanocomposite using continuumbased micromechanical modeling", Macromol. Res., 17(10), 797-806. https://doi.org/10.1007/BF03218617.
  87. Xia, H., Zhang, X., Shi, Z., Zhao, C., Li, Y., Wang, J. and Qiao, G. (2015), "Mechanical and thermal properties of reduced graphene oxide reinforced aluminum nitride ceramic composites", Mater. Sci. Eng., 639, 29-36. https://doi.org/10.1016/j.msea.2015.04.091.
  88. Xu, C., Gao, J., Xiu, H., Li, X., Zhang, J., Luo, F., Zhang, Q., Chen, F. and Fu, Q. (2013), "Can in situ thermal reduction be a green and efficient way in the fabrication of electrically conductive polymer/reduced graphene oxide nanocomposites?", Compos. Part A, 53, 24-33. https://doi.org/10.1016/j.compositesa.2013.06.007.
  89. Yang, F., Chong, A.C.M., Lam, D.C.C. and Tong, P. (2002), "Couple stress based strain gradient theory for elasticity", Int. J. Solids Struct., 39, 2731-2743. https://doi.org/10.1016/S0020-7683(02)00152-X.
  90. Yousefi, N., Gudarzi, M.M., Zheng, Q., Lin, X., Shen, X., Jia, J., Sharif, F. and Kim, J.K. (2013b), "Highly aligned, ultralarge-size reduced graphene oxide/polyurethane nanocomposites: mechanical properties and moisture permeability", Compos. Part A, 49, 42-50. https://doi.org/10.1016/j.compositesa.2013.02.005.
  91. Yousefi, N., Lin, X., Zheng, Q., Shen, X., Pothnis, J.R., Jia, J., Zussman, E. and Kim, J.K. (2013a), "Simultaneous in situ reduction, self-alignment and covalent bonding in graphene oxide/epoxy composites", Carbon, 59, 406-417. https://doi.org/10.1016/j.carbon.2013.03.034.
  92. Zeng, X., Yang, J. and Yuan, W. (2012), "Preparation of a poly (methyl methacrylate)-reduced graphene oxide composite with enhanced properties by a solution blending method", Eur. Polym. J., 48(10), 1674-1682. https://doi.org/10.1016/j.eurpolymj.2012.07.011.
  93. Zenkour, A. M. (2018b), "Refined two-temperature multi-phase-lags theory for thermomechanical response of microbeams using the modified couple stress analysis", Acta Mechanica, 229(9), 3671-3692. https://doi.org/10.1007/s00707-018-2172-9.
  94. Zenkour, A.M. (2018a), "Modified couple stress theory for micro-machined beam resonators with linearly varying thickness and various boundary conditions", Arch. Mech. Eng., 65(1), 43-64. https://doi.org/10.24425/119409.
  95. Zhang, L.W., Liew, K.M. and Reddy, J.N. (2016), "Postbuckling of carbon nanotube reinforced functionally graded plates with edges elastically restrained against translation and rotation under axial compression", Comput. Meth. Appl. Mech. Eng., 298, 1-28. https://doi.org/10.1016/j.cma.2015.09.016.
  96. 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. Mat. Struct., 1-9. https://doi.org/10.1080/15376494.2018.1444216.
  97. Zhao, J., Wang, Q., Deng, X., Choe, K., Zhong, R. and Shuai, C. (2019), "Free vibrations of functionally graded porous rectangular plate with uniform elastic boundary conditions", Compos. Part B, 168, 106-120. https://doi.org/10.1016/j.compositesb.2018.12.044.
  98. Zhou, T., Chen, F., Tang, C., Bai, H., Zhang, Q., Deng, H. and Fu, Q. (2011), "The preparation of high performance and conductive poly (vinyl alcohol)/graphene nanocomposite via reducing graphite oxide with sodium hydrosulfite", Compos. Sci. Technol., 71(9), 1266-1270. https://doi.org/10.1016/j.compscitech.2011.04.016.
  99. Zhu, Y., Murali, S., Cai, W., Li, X., Suk, J.W., Potts, J.R. and Ruoff, R.S. (2010), "Graphene and graphene oxide: synthesis, properties, and applications", Adv. Mater., 22(35), 3906-3924. https://doi.org/10.1002/adma.201001068.