The incorporation of carbon nanotubes (CNT) into a polymer matrix has opened up exciting possibilities for creating Nano-composite materials with exceptional mechanical properties. In this study, the buckling behavior of a reinforced polymer plate mixed with CNTs is investigated. Various factors, such as the plate’s shape and the elastic base, are examined for their effects on behavior. The investigation is grounded in scientific rigor, drawing upon several theories that address plate behavior. Specifically, the high-order theory, which accounts for transverse shear effects and the parabolic distribution of transverse shear stresses across the plate thickness, is employed. By analyzing the critical buckling load, the interaction between different types of carbon nanotubes within the polymer matrix and the elastic medium is explored. The model’s governing equations, derived from Hamilton’s principle, allow for the prediction of the critical loads associated with axial compression buckling. Notably, it is found that the parabolic distribution, coupled with the Winkler—Pasternak elastic foundation, renders the plate less flexible compared to scenarios without an elastic foundation. This insight leads to a crucial enhancement in the critical buckling load. The significance of incorporating carbon nanotubes in polymer matrices to achieve nanocomposite materials with exceptional properties is underscored. The scientific foundation upon which this study rests provides valuable insights for designing robust and efficient structures.
BozlarM. Modification de surface des nanotubes de carbone par un polymère conducteur électrogénéré pour la réalisation de nanocomposites multifonctionnels2009. https://theses.hal.science/tel-00458677, Doctoral dissertation, Châtenay-Malabry, Ecole centrale de Paris.
2.
MoitaJSAraújoALMota SoaresCM, et al.Vibration analysis of functionally graded material sandwich structures with passive damping. Compos Struct2018; 183: 407–415.
3.
ChikerYBacheneMGuemanaM, et al.Free vibration analysis of multilayer functionally graded polymer nanocomposite plates reinforced with nonlinearly distributed carbon-based nanofillers using a layer-wise formulation model. Aero Sci Technol2020; 104: 105913. DOI: 10.1016/j.ast.2020.105913.
4.
AnumandlaVGibsonRF. A comprehensive closed form micromechanics model for estimating the elastic modulus of nanotube-reinforced composites. Compos Appl Sci Manuf2006; 37(12): 2178–2185. DOI: 10.1016/j.compositesa.2005.09.016.
5.
HuangHGuoMZhangW, et al.Numerical investigation on the bearing capacity of RC columns strengthened by HPFL-BSP under combined loadings. J Build Eng2021; 39: 102266. DOI: 10.1016/j.jobe.2021.102266.
6.
ZhangWLiuXHuangY, et al.Reliability-based analysis of the flexural strength of concrete beams reinforced with hybrid BFRP and steel rebars. Arch Civ Mech Eng2022; 22(4): 171. DOI: 10.1007/s43452-022-00493-7.
7.
HuangHHuangMZhangW, et al.Progressive collapse of multistory 3D reinforced concrete frame structures after the loss of an edge column. Struct. Infrastruct. Eng2022; 18(2): 249–265. DOI: 10.1080/15732479.2020.1841245.
8.
SongXWangWDengY, et al.Data-driven modeling for residual velocity of projectile penetrating reinforced concrete slabs. Eng Struct2024; 306: 117761. DOI: 10.1016/j.engstruct.2024.117761.
9.
CaoJDuJFanQ, et al.Reinforcement for earthquake-damaged glued-laminated timber knee-braced frames with self-tapping screws and CFRP fabric. Eng Struct2024; 306: 117787. DOI: 10.1016/j.engstruct.2024.117787.
10.
ZhanPLouJChenT, et al.Dynamic hysteresis compensation and iterative learning control for underwater flexible structures actuated by macro fiber composites. Ocean Eng2024; 298: 117242. DOI: 10.1016/j.oceaneng.2024.117242.
11.
DongJLiuYYuanS, et al.Mechanical behavior and impact resistance of rubberized concrete enhanced by basalt fiber-epoxy resin composite. Construct Build Mater2024; 435: 136836. DOI: 10.1016/j.conbuildmat.2024.136836.
12.
DongJFGuanZWChaiHK, et al.High temperature behaviour of basalt fibre-steel tube reinforced concrete columns with recycled aggregates under monotonous and fatigue loading. Construct Build Mater2023; 389: 131737. DOI: 10.1016/j.conbuildmat.2023.131737.
13.
MotezakerMKolahchiRRajakDK, et al.Influences of fiber reinforced polymer layer on the dynamic deflection of concrete pipes containing nanoparticle subjected to earthquake load. Polym Compos2021; 42(8): 4073–4081. DOI: 10.1002/pc.26118.
14.
KolahchiRKeshtegarBTrungNT. Optimization of dynamic properties for laminated multiphase nanocomposite sandwich conical shell in thermal and magnetic conditions. J Sandw Struct Mater2022; 24(1): 643–662. DOI: 10.1177/10996362211020388.
15.
HajmohammadMHFarrokhianAKolahchiR. Dynamic analysis in beam element of wave-piercing Catamarans undergoing slamming load based on mathematical modelling. Ocean Eng2021; 234: 109269. DOI: 10.1016/j.oceaneng.2021.109269.
16.
Al-FurjanMSHHajmohammadMHShenX, et al.Evaluation of tensile strength and elastic modulus of 7075-T6 aluminum alloy by adding SiC reinforcing particles using vortex casting method. J Alloys Compd2021; 886: 161261. DOI: 10.1016/j.jallcom.2021.161261.
17.
Al-FurjanMSHXuMXFarrokhianA, et al.On wave propagation in piezoelectric-auxetic honeycomb-2D-FGM micro-sandwich beams based on modified couple stress and refined zigzag theories. Waves Random Complex Media2022; 1-25: 1–25. DOI: 10.1080/17455030.2022.2030499.
18.
Al-FurjanMSHYangYFarrokhianA, et al.Dynamic instability of nanocomposite piezoelectric-leptadenia pyrotechnica rheological elastomer-porous functionally graded materials micro viscoelastic beams at various strain gradient higher-order theories. Polym Compos2022; 43(1): 282–298. DOI: 10.1002/pc.26373.
19.
Al-FurjanMSHYinCShenX, et al.Energy absorption and vibration of smart auxetic FG porous curved conical panels resting on the frictional viscoelastic torsional substrate. Mech Syst Signal Process2022; 178: 109269. DOI: 10.1016/j.ymssp.2022.109269.
20.
Al-FurjanMSHShanLShenX, et al.Combination of FEM-DQM for nonlinear mechanics of porous GPL-reinforced sandwich nanoplates based on various theories. Thin-Walled Struct2022; 178: 109495. DOI: 10.1016/j.tws.2022.109495.
21.
Al-FurjanMSHShanLShenX, et al.A review on fabrication techniques and tensile properties of glass, carbon, and Kevlar fiber reinforced rolymer composites. J Mater Res Technol2022; 19: 2930–2959. DOI: 10.1016/j.jmrt.2022.06.008.
22.
Al-FurjanMSHKolahchiRShanL, et al.Slamming impact induced hydrodynamic response in wave-piercing catamaran beam elements with controller. Ocean Eng2022; 266: 112908. DOI: 10.1016/j.oceaneng.2022.112908.
23.
ChuCAl-FurjanMSHKolahchiR, et al.A nonlinear Chebyshev-based collocation technique to frequency analysis of thermally pre/post-buckled third-order circular sandwich plates. Commun Nonlinear Sci Numer Simul2023; 118: 107056. DOI: 10.1016/j.cnsns.2022.107056.
24.
Al-FurjanMSHQiZHShanL, et al.Nano supercapacitors with practical application in aerospace technology: vibration and wave propagation analysis. Aero Sci Technol2023; 133: 108082. DOI: 10.1016/j.ast.2022.108082.
25.
WanPHAl-FurjanMSHKolahchiR, et al.Application of DQHFEM for free and forced vibration, energy absorption, and post-buckling analysis of a hybrid nanocomposite viscoelastic rhombic plate assuming CNTs’ waviness and agglomeration. Mech Syst Signal Process2023; 189: 110064. DOI: 10.1016/j.ymssp.2022.110064.
26.
Al-FurjanMSHFanSShanL, et al.Wave propagation analysis of micro air vehicle wings with honeycomb core covered by porous FGM and nanocomposite magnetostrictive layers. Waves Random Complex Media2023; 1-30: 1–30. DOI: 10.1080/17455030.2022.2164378.
27.
AmoushahiHLajevardiMM. Buckling of functionally graded plates under thermal, axial, and shear in-plane loading using complex finite strip formulation. J Therm Stresses2018; 41(2): 182–203. DOI: 10.1080/01495739.2017.1389326.
28.
SaberiEAmoushahiHTanzadehH. Mechanical and thermal buckling of thick nanoplate with a new functionally graded porous pattern. Arch Civ Mech Eng2024; 24(2): 56. DOI: 10.1007/s43452-023-00856-8.
29.
TanzadehHAmoushahiH. Analysis of laminated composite plates based on different shear deformation plate theories. Struct Eng Mech2020; 75(2): 247–269. DOI: 10.12989/sem.2020.75.2.247.
30.
EstiliMSakkaY. Recent advances in understanding the reinforcing ability and mechanism of carbon nanotubes in ceramic matrix composites. Sci Technol Adv Mater2014; 15(6): 064902. DOI: 10.1088/1468-6996/15/6/064902.
31.
ZhuPLeiZXLiewKM. Static and free vibration analyses of carbon nanotube-reinforced composite plates using finite element method with first order shear deformation plate theory. Compos Struct2012; 94(4): 1450–1460. DOI: 10.1016/j.compstruct.2011.11.010.
32.
AraghBSBaratiANHedayatiH. Eshelby–Mori–Tanaka approach for vibrational behavior of continuously graded carbon nanotube-reinforced cylindrical panels. Composites Part B2012; 43(4): 1943–1954. DOI: 10.1016/j.compositesb.2012.01.004.
MessaoudiABouhadraAMenasriaA, et al.Impact of the shear and thickness stretching effects on the free vibrations of advanced composite plates. Mech Compos Mater2023; 59(5): 1001–1018. DOI: 10.1007/s11029-023-10148-0.
35.
SobhyMAlsalehF. Nonlinear bending of FG metal/graphene sandwich microplates with metal foam core resting on nonlinear elastic foundations via a new plate theory. Mech Base Des Struct Mach2024; 52(7): 3842–3869. DOI: 10.1080/15397734.2023.2210214.
36.
Al-AliAHAl MukahalFHSobhyM. Magneto axisymmetric vibration of FG-GPLs reinforced annular sandwich plates with an FG porous core using DQM and a new shear deformation theory. Symmetry2024; 16(6): 696. DOI: 10.3390/sym16060696.
37.
SobhyM. Nonlinear deflection and traveling wave solution for FG-GPLs reinforced microtubes embedded in Kerr foundation and conveying magnetic fluid. Ocean Eng2024; 296: 117026. DOI: 10.1016/j.oceaneng.2024.117026.
38.
SobhyMRadwanAF. An axial magnetic field effect on frequency analysis of rotating sandwich cylindrical shells with FG graphene/AL face sheets and honeycomb core. Int J Appl Mech2022; 14(08): 2250074. DOI: 10.1142/S1758825122500740.
39.
BaseriVJafariGSKolahchiR. Analytical solution for buckling of embedded laminated plates based on higher order shear deformation plate theory. Steel Compos Struct2016; 21(4): 883–919. DOI: 10.12989/scs.2016.21.4.883.
40.
KolahchiRBidgoliAMMHeydariMM. Size-dependent bending analysis of FGM nano-sinusoidal plates resting on orthotropic elastic medium. Struct Eng Mech2015; 55(5): 1001–1014. DOI: 10.12989/sem.2015.55.5.1001.
41.
Al-FurjanMSHFarrokhianAKeshtegarB, et al.Higher order nonlocal viscoelastic strain gradient theory for dynamic buckling analysis of carbon nanocones. Aero Sci Technol2020; 107: 106259. DOI: 10.1016/j.ast.2020.106259.
42.
AmniehHBZamzamMSKolahchiR. Dynamic analysis of non-homogeneous concrete blocks mixed by SiO2 nanoparticles subjected to blast load experimentally and theoretically. Construct Build Mater2018; 174: 633–644. DOI: 10.1016/j.conbuildmat.2018.04.140.
43.
KolahchiRHosseiniHFakharMH, et al.A numerical method for magneto-hygro-thermal postbuckling analysis of defective quadrilateral graphene sheets using higher order nonlocal strain gradient theory with different movable boundary conditions. Comput Math Appl2019; 78(6): 2018–2034. DOI: 10.1016/j.camwa.2019.03.042.
44.
HanYElliottJ. Molecular dynamics simulations of the elastic properties of polymer/carbon nanotube composites. Comput Mater Sci2007; 39(2): 315–323. DOI: 10.1016/j.commatsci.2006.06.011.
45.
XieXLMaiYWZhouXP. Dispersion and alignment of carbon nanotubes in polymer matrix: a review. Mater Sci Eng R Rep2005; 49(4): 89–112. DOI: 10.1016/j.mser.2005.04.002.
46.
BousahlaAABouradaFMahmoudSR, et al.Buckling and dynamic behavior of the simply supported CNT-RC beams using an integral-first shear deformation theory. Computers and Concrete, An International Journal2020; 25(2): 155–166. DOI: 10.12989/cac.2020.25.2.155.
47.
DingHXLiuHBSheGL, et al.Wave propagation of FG-CNTRC plates in thermal environment using the high-order shear deformation plate theory. Comput Concr2023; 32(2): 207–215. DOI: 10.12989/cac.2023.32.2.207.
48.
ChavanSGLalA. Dynamic bending response of SWCNT reinforced composite plates subjected to hygro-thermo-mechanical loading. Comput Concr2017; 20(2): 229–246. DOI: 10.12989/cac.2017.20.2.229.
49.
FarokhianAKolahchiR. Frequency and instability responses in nanocomposite plate assuming different distribution of CNTs. Struct Eng Mech Int J2020; 73(5): 555–563. DOI: 10.12989/sem.2020.73.5.555.
50.
ChoJR. Investigation of nonlinear free vibration of FG-CNTRC cylindrical panels resting on elastic foundation. Structural Engineering and Mechanics, An Int'l Journal2023; 88(5): 439–449. DOI: 10.12989/sem.2023.88.5.439.
51.
ReddyJN, Mechanics of laminated composite plates and shells: theory and analysis. 2nd edition. Oxfordshire, UK: Taylor & Francis eBooks, CRC Press, 2004. DOI: 10.1201/b12409.
52.
TayebTSZidourMBensattalahT, et al.Mechanical buckling of FG-CNTs reinforced composite plate with parabolic distribution using Hamilton's energy principle. Adv Nano Res2020; 8(2): 135–148. DOI: 10.12989/anr.2020.8.2.135.
53.
AraniAJKolahchiR. Buckling analysis of embedded concrete columns armed with carbon nanotubes. Comput Concr2016; 17(5): 567–578. DOI: 10.12989/cac.2016.17.5.567.
54.
KumarRJanaP. Exact modal analysis of multilayered FG-CNT plate assemblies using the dynamic stiffness method. Mech Adv Mater Struct2023; 30(22): 4501–4520. DOI: 10.1080/15376494.2022.2097353.
55.
OnvaniDJafariADehkordiMB. Carrera unified formulation for bending and free vibration analysis of sandwich plate with FG-CNT faces considering the both soft and stiff cores. Mech Adv Mater Struct2022; 29(27): 6718–6732. DOI: 10.1080/15376494.2021.1983899.
56.
DasSJanaP. Buckling analysis of nonuniformly compressed rectangular FG-CNT reinforced laminated composite plate resting on elastic foundation: an analytical solution. Mech Adv Mater Struct2024; 1-22: 1–22. DOI: 10.1080/15376494.2024.2327645.
57.
MeradjahMBouakkazKZaouiFZ, et al.A refined quasi-3D hybrid-type higher order shear deformation theory for bending and free vibration analysis of advanced composites beams. Wind Struct2018; 27(4): 269–282. DOI: 10.12989/was.2018.27.4.269.
58.
BakhaddaBBouiadjraMBBouradaF, et al.Dynamic and bending analysis of carbon nanotube-reinforced composite plates with elastic foundation. Wind Struct2018; 27(5): 311–324. DOI: 10.12989/was.2018.27.5.311.
59.
DatNDThanhNVMinhAnhV, et al.Vibration and nonlinear dynamic analysis of sandwich FG-CNTRC plate with porous core layer. Mech Adv Mater Struct2022; 29(10): 1431–1448. DOI: 10.1080/15376494.2020.1822476.
60.
MedaniMBenahmedAZidourM, et al.Static and dynamic behavior of (FG-CNT) reinforced porous sandwich plate using energy principle. Steel Compos Struct2019; 32(5): 595–610. DOI: 10.12989/scs.2019.32.5.595.
61.
BenahmedAFahsiBBenzairA, et al.Critical buckling of functionally graded nanoscale beam with porosities using nonlocal higher-order shear deformation. Struct Eng Mech2019; 69(4): 457–466. DOI: 10.12989/sem.2019.69.4.457.
62.
WattanasakulpongNChaikittiratanaA. Exact solutions for static and dynamic analyses of carbon nanotube-reinforced composite plates with Pasternak elastic foundation. Appl Math Model2015; 39(18): 5459–5472. DOI: 10.1016/j.apm.2014.12.058.
