Acknowledgement
This research is financially supported by the Ministry of Science and Technology of China (Grant No. 2019YFE0112400, 2018YFC1504303), the Key Research and Development Program of Liaoning Province (Grant No. 2017231010), the Taishan Scholar Priority Discipline Talent Group program funded by the Shandong Province, and the first-class discipline project funded by the Education Department of Shandong Province.
References
- Abdelhak, Z., Hadji, L., Daouadji, T.H. and Adda Bedia, E.A. (2016), "Thermal buckling response of functionally graded sandwich plates with clamped boundary conditions", Smart Struct. Syst., Int. J., 18(2), 267-291. https://doi.org/10.12989/sss.2016.18.2.267
- Affdl, J.H. and Kardos, J.L. (1976), "The Halpin-Tsai equations: a review", Polym. Eng. Sci., 16(5), 344-352 https://doi.org/10.1002/pen.760160512
- Alamusi, A., Hu, N., Qiu, J., Li, Y., Chang, C., Atobe, S., Fukunaga, H., Liu, Y., Ning, H., Wu, L. and Li, J. (2013), "Multi-scale numerical simulations of thermal expansion properties of CNT-reinforced nanocomposites", Nanoscale Res. Lett., 8(1), 15-15. https://doi.org/10.1186/1556-276X-8-15
- Bekyarova, E., Thostenson, E.T., Yu, A., Kim, H., Gao, J., Tang, J., Hahn, H.T., Chou, T.W., Itkis, M.E. and Haddon, R.C. (2007a), "Multiscale carbon nanotube- carbon fiber reinforcement for advanced epoxy composites", Langmuir, 23(7), 3970-3974. https://doi.org/10.1021/la062743p
- Bekyarova, E., Thostenson, E.T., Yu, A., Itkis, M.E., Fakhrutdinov, D., Chou, T.W. and Haddon, R.C. (2007b), "Functionalized single-walled carbon nanotubes for carbon fiber-epoxy composites", J. Phys. Chem. C, 111(48), 17865-17871. https://doi.org/10.1021/jp071329a
- Cao, Y., Musharavati, F., Baharom, S., Talebizadehsardari, P., Sebaey, T.A., Eyvazian, A. and Zain, A.M. (2020), "Vibration response of FG-CNT-reinforced plates covered by magnetic layer utilizing numerical solution", Steel Compos. Struct., Int. J., 37(2), 253-258. https://doi.org/10.12989/scs.2020.37.2.253
- Chamis, C.C. (1983), "Simplified composite micromechanics equations for hygral, thermal and mechanical properties".
- Chamis, C.C. and Sendeckyj, G.P. (1968), "Critique on theories predicting thermoelastic properties of fibrous composites", J. Compos. Mater., 2(3), 332-358. https://doi.org/10.1177/002199836800200305
- Chikh, A., Tounsi, A., Hebali, H. and Mahmoud, S.R. (2017), "Thermal buckling analysis of cross-ply laminated plates using a simplified HSDT", Smart Struct. Syst., Int. J., 19(3), 289-297. https://doi.org/10.12989/sss.2017.19.3.289
- Dabbagh, A., Rastgoo, A. and Ebrahimi, F. (2020), "Thermal buckling analysis of agglomerated multiscale hybrid nanocomposites via a refined beam theory", Mech. Based. Des. Struc., pp. 1-27. https://doi.org/10.1080/15397734.2019.1692666
- Dat, N.D., Quan, T.Q. and Duc, N.D. (2019), "Nonlinear thermal vibration of carbon nanotube polymer composite elliptical cylindrical shells", Int. J. Mech. Mater. Des., 1-20. https://doi.org/ 10.1007/s10999-019-09464-y
- Dat, N.D., Quan, T.Q., Mahesh, V. and Duc, N.D. (2020a), "Analytical solutions for nonlinear magneto-electro-elastic vibration of smart sandwich plate with carbon nanotube reinforced nanocomposite core in hygrothermal environment", Int. J. Mech. Sci., 186, p. 105906. https://doi.org/10.1016/j.ijmecsci.2020.105906
- Dat, N.D., Khoa, N.D., Nguyen, P.D. and Duc, N.D. (2020b), "An analytical solution for nonlinear dynamic response and vibration of FG-CNT reinforced nanocomposite elliptical cylindrical shells resting on elastic foundations", ZAMM-Z ANGEW MATH ME, 100(1), p. e201800238. https://dx.doi.org/10.1002/zamm.201800238
- Do, Q.C., Pham, D.N., Vu, D.Q., Vu, T.T.A. and Nguyen, D.D. (2019), "Nonlinear buckling and post-buckling of functionally graded CNTs reinforced composite truncated conical shells subjected to axial load", Steel Compos. Struct., Int. J., 31(3), 243-259. http://dx.doi.org/10.12989/scs.2019.31.3.243
- Duc, N.D. (2014), "Nonlinear static and dynamic stability of functionally graded plates and shells", Vietnam National University Press, Hanoi, Vietnam.
- Duc, N.D., Hadavinia, H., Quan, T.Q. and Khoa, N.D. (2019a), "Free vibration and nonlinear dynamic response of imperfect nanocomposite FG-CNTRC double curved shallow shells in thermal environment", Eur. J. Mech. A Solids., 75, 355-366. https://doi.org/10.1016/j.euromechsol.2019.01.024
- Duc, N.D., Nguyen, P.D., Cuong, N.H., Van Sy, N. and Khoa, N.D. (2019b), "An analytical approach on nonlinear mechanical and thermal post-buckling of nanocomposite double-curved shallow shells reinforced by carbon nanotubes", Proc. Inst. Mech. Eng., Part C, 233(11), 3888-3903. https://doi.org/10.1177/0954406218802921
- Duong, T.M., Vu, T.T.A., Pham, D.N. and Nguyen, D.D. (2020), "Nonlinear post-buckling of CNTs reinforced sandwich-structured composite annular spherical shells", Int. J. Struct. Stab. Dyn., 20(2). https://dx.doi.org/10.1142/S0219455420500182
- Ebrahimi, F. and Dabbagh, A. (2019), "On thermo-mechanical vibration analysis of multi-scale hybrid composite beams", J. Vib. Control, 25(4), 933-945. https://doi.org/10.1177/1077546318806800
- Eslami, M.R. (2018), "Buckling and Postbuckling of Beams, Plates, and Shells". Cham, Switzerland: Springer International Publishing.
- Eyvazian, A., Musharavati, F., Tarlochan, F., Pasharavesh, A., Rajak, D.K., Husain, M.B. and Tran, T.N. (2020a), "Free vibration of FG-GPLRC conical panel on elastic foundation", Struct. Eng. Mech., Int. J., 75(1), 1-18. https://doi.org/10.12989/sem.2020.75.1.001
- Eyvazian, A., Musharavati, F., Talebizadehsardari, P. and Sebaey, T.A. (2020b), "Free vibration of FG-GPLRC spherical shell on two parameter elastic foundation", Steel Compos. Struct., Int. J., 36(6), 711-727. https://doi.org/10.12989/scs.2020.36.6.711
- Eyvazian, A., Shahsavari, D. and Karami, B. (2020c), "On the dynamic of graphene reinforced nanocomposite cylindrical shells subjected to a moving harmonic load", Int. J. Eng. Sci., 154, p.103339. https://doi.org/10.1016/j.ijengsci.2020.103339
- Fattahi, A.M., Safaei, B. and Ahmed, N.A. (2019a), "A comparison for the non-classical plate model based on axial buckling of single-layered graphene sheets", Eur. Phys. J. Plus., 134(11), p. 555. https://doi.org/10.1140/epjp/i2019-12912-7
- Fattahi, A.M., Safaei, B. and Moaddab, E. (2019b), "The application of nonlocal elasticity to determine vibrational behavior of FG nanoplates", Steel Compos. Struct., Int. J., 32(2), 281-292. https://doi.org/10.12989/scs.2019.32.2.281
- Ghanati, P. and Safaei, B. (2019), "Elastic buckling analysis of polygonal thin sheets under compression", Indian J. Phys., 93(1), 47-52. https://doi.org/10.1007/s12648-018-1254-9
- Ghasemi, A.R., Mohammadi, M.M. and Mohandes, M. (2015), "The role of carbon nanofibers on thermo-mechanical properties of polymer matrix composites and their effect on reduction of residual stresses", Compos. B. Eng., 77, 519-527. https://doi.org/10.1016/j.compositesb.2015.03.065
- Ghasemi, A.R., Mohammadi Fesharaki, M. and Mohandes, M. (2017), "Three-phase micromechanical analysis of residual stresses in reinforced fiber by carbon nanotubes", J. Compos. Mater., 51(12), 1783-1794. https://doi.org/10.1177/0021998316669854
- Gholami, R. and Ansari, R. (2018), "Nonlinear bending of third-order shear deformable carbon nanotube/fiber/polymer multiscale laminated composite rectangular plates with different edge supports", Eur. Phys. J. Plus, 133(7), 282. https://doi.org/10.1140/epjp/i2018-12103-2
- Gholami, R., Ansari, R. and Gholami, Y. (2018), "Numerical study on the nonlinear resonant dynamics of carbon nanotube/fiber/polymer multiscale laminated composite rectangular plates with various boundary conditions", Aerosp. Sci. Technol., 78, 118-129. https://doi.org/10.1016/j.ast.2018.03.043
- Hajmohammad, M.H., Azizkhani, M.B. and Kolahchi, R. (2018), "Multiphase nanocomposite viscoelastic laminated conical shells subjected to magneto-hygrothermal loads: Dynamic buckling analysis", Int. J. Mech. Sci., 137, 205-213. https://doi.org/10.1016/j.ijmecsci.2018.01.026
- Han, S., Meng, Q., Araby, S., Liu, T. and Demiral, M. (2019), "Mechanical and electrical properties of graphene and carbon nanotube reinforced epoxy adhesives: experimental and numerical analysis", Compos. Part A. Appl., 120, 116-126. https://doi.org/10.1016/j.compositesa.2019.02.027
- He, X.Q., Rafiee, M., Mareishi, S. and Liew, K.M. (2015), "Large amplitude vibration of fractionally damped viscoelastic CNTs/fiber/polymer multiscale composite beams", Compos. Struct., 131, 1111-1123. https://doi.org/10.1016/j.compstruct.2015.06.038
- Javani, M., Kiani, Y. and Eslami, M.R. (2019), "Geometrically nonlinear rapid surface heating of temperature-dependent FGM arches", Aerosp. Sci. Technol., 90, 264-274. https://doi.org/10.1016/j.ast.2019.04.049
- Kamarian, S., Shakeri, M. and Yas, M.H. (2018), "Natural frequency analysis and optimal design of CNT/fiber/polymer hybrid composites plates using mori-tanaka approach, GDQ technique, and firefly algorithm", Polym. Compos., 39(5), 1433-1446. https://doi.org/10.1002/pc.24083
- Karami, B., Shahsavari, D., Ordookhani, A., Gheisari, P., Li, L. and Eyvazian, A. (2020), "Dynamics of graphene-nanoplatelets reinforced composite nanoplates including different boundary conditions", Steel Compos. Struct., Int. J., 36(6), 689-702. https://doi.org/10.12989/scs.2020.36.6.689
- Katariya, P., Panda, S.K., Hirwani, C.K., Mehar, K. and Thakare, O. (2017), "Enhancement of thermal buckling strength of laminated sandwich composite panel structure embedded with shape memory alloy fibre", Smart Struct. Syst., Int. J., 20(5), 595-605. https://doi.org/10.12989/sss.2017.20.5.595
- Khorasani, M., Eyvazian, A., Karbon, M., Tounsi, A., Lampani, L. and Sebaey, T.A. (2020), "Magneto-electro-elastic vibration analysis of modified couple stress-based three-layered micro rectangular plates exposed to multi-physical fields considering the flexoelectricity effects", Smart Struct. Syst., Int. J., 26(3), 331-343. https://doi.org/10.12989/sss.2020.26.3.331
- Kiani, Y. and Eslami, M.R. (2010), Thermal buckling analysis of functionally graded material beams", Int. J. Mech. Mater. Des., 6(3), 229-238. https://doi.org/10.1007/s10999-010-9132-4
- Kiani, Y. and Mirzaei, M. (2018), "Enhancement of non-linear thermal stability of temperature dependent laminated beams with graphene reinforcements", Compos. Struct., 186, 114-122. https://doi.org/10.1016/j.compstruct.2017.11.086
- Kim, M., Park, Y.B., Okoli, O.I. and Zhang, C. (2009), "Processing, characterization, and modeling of carbon nanotube-reinforced multiscale composites", Compos. Sci. Technol., 69(3-4), 335-342. https://doi.org/10.1016/j.compscitech.2008.10.019
- Lee, S.Y. (2019), "Dynamic instability of carbon nanotubes/fiber/polymer multiscale composite spherical shells with delamination around a cutout", Int. J. Struct. Stab. Dy., 19(11), 1950132. https://doi.org/10.1142/S0219455419501323
- Lee, S.Y. (2020), "Dynamic stability and nonlinear transient behaviors of CNT-reinforced fiber/polymer composite cylindrical panels with delamination around a cutout", Nonlinear Dyn., 1-19. https://doi.org/10.1007/s11071-020-05477-x.
- Lee, S.Y. and Hwang, J.G. (2019), "Finite element nonlinear transient modelling of carbon nanotubes reinforced fiber/polymer composite spherical shells with a cutout", Nanotechnol. Rev., 8(1), 444-451. https://doi.org/10.1515/ntrev-2019-0039
- Mohammadimehr, M. and Alimirzaei, S. (2017), "Buckling and free vibration analysis of tapered FG-CNTRC micro Reddy beam under longitudinal magnetic field using FEM", Smart Struct. Syst., Int. J., 19(3), 309-322. https://doi.org/10.12989/sss.2017.19.3.309
- Motezaker, M. and Eyvazian, A. (2020), "Buckling load optimization of beam reinforced by nanoparticles", Struct. Eng. Mech., Int. J., 73(5), 481-486. https://doi.org/10.12989/sem.2020.73.5.481
- Nguyen, D.D. (2018), "Nonlinear thermo-electro-mechanical dynamic response of shear deformable piezoelectric sigmoid functionally graded sandwich circular cylindrical shells on elastic foundations", J. Sandw. Struct. Mater., 20(3), 351-378. https://doi.org/10.1177/1099636216653266
- Nguyen, D.D. and Pham, D.N. (2017), "The dynamic response and vibration of functionally graded carbon nanotubes reinforced composite (FG-CNTRC) truncated conical shells resting on elastic foundation", Materials, 10(10), p. 1194. https://doi.org/10.3390/ma10101194
- Nguyen, D.D., Tran, Q.Q. and Nguyen, D.K. (2017), "New approach to investigate nonlinear dynamic response and vibration of imperfect functionally graded carbon nanotube reinforced composite double curved shallow shells subjected to blast load and temperature", Aerosp. Sci. Technol., 71, 360-372. https://doi.org/10.1016/j.ast.2017.09.031
- Radue, M.S. and Odegard, G.M. (2018), "Multiscale modeling of carbon fiber/carbon nanotube/epoxy hybrid composites: Comparison of epoxy matrices", Compos. Sci. Technol., 166, 20-26. https://doi.org/10.1016/j.compscitech.2018.03.006.
- Rafiee, M., Yang, J. and Kitipornchai, S. (2013), "Thermal bifurcation buckling of piezoelectric carbon nanotube reinforced composite beams", Comput. Math. Appl., 66(7), 1147-1160. https://doi.org/10.1016/j.camwa.2013.04.031
- Rafiee, M., He, X.Q., Mareishi, S. and Liew, K.M. (2014a), "Modeling and stress analysis of smart CNTs/fiber/polymer multiscale composite plates", Int. J. Appl. Mech., 6(3), 1450025. https://doi.org/10.1142/S1758825114500252
- Rafiee, M., Liu, X.F., He, X.Q. and Kitipornchai, S. (2014b), "Geometrically nonlinear free vibration of shear deformable piezoelectric carbon nanotube/fiber/polymer multiscale laminated composite plates", J. Sound Vib., 333(14), 3236-3251. https://doi.org/10.1016/j.jsv.2014.02.033
- Rafiee, M., Nitzsche, F. and Labrosse, M.R. (2018), "Cross-sectional design and analysis of multiscale carbon nanotubes-reinforced composite beams and blades", Int. J. Appl. Mech., 10(3), 1850032. https://doi.org/10.1142/S1758825118500321
- Rahman, M.M., Zainuddin, S., Hosur, M.V., Malone, J.E., Salam, M.B.A., Kumar, A. and Jeelani, S. (2012), "Improvements in mechanical and thermo-mechanical properties of e-glass/epoxy composites using amino functionalized MWCNTs", Compos. Struct., 94(8), 2397-2406. https://doi.org/10.1016/j.compstruct.2012.03.014
- Rahmanian, S., Suraya, A.R., Shazed, M.A., Zahari, R. and Zainudin, E.S. (2014), "Mechanical characterization of epoxy composite with multiscale reinforcements: carbon nanotubes and short carbon fibers", Mater. Des., 60, 34-40. https://doi.org/10.1016/j.matdes.2014.03.039
- Reddy, J.N. (2006), Theory and Analysis of Elastic Plates and Shells, CRC press.
- Rodriguez, A.J., Guzman, M.E., Lim, C.S. and Minaie, B. (2011), "Mechanical properties of carbon nanofiber/fiber-reinforced hierarchical polymer composites manufactured with multiscale-reinforcement fabrics", Carbon, 49(3), 937-948. https://doi.org/10.1016/j.carbon.2010.10.057
- Safarpour, M., Rahimi, A., NoormohammadiArani, O. and Rabczuk, T. (2020), "Frequency characteristics of multiscale hybrid nanocomposite annular plate based on a Halpin-Tsai homogenization model with the aid of GDQM", Appl. Sci., 10(4), 1412. https://doi.org/10.3390/app10041412
- Safaei, B. (2020), "The effect of embedding a porous core on the free vibration behavior of laminated composite plates", Steel Compos. Struct., Int. J., 35(5), 659-670. https://doi.org/10.12989/SCS.2020.35.5.659
- Safaei, B., Khoda, F.H. and Fattahi, A.M. (2019), "Non-classical plate model for single-layered graphene sheet for axial buckling", Adv. Nano Res., Int. J., 7(4), 265-277. https://doi.org/10.12989/anr.2019.7.4.265
- Seidi, J. and Kamarian, S. (2017), "Free vibrations of non-uniform CNT/fiber/polymer nanocomposite beams", Curved Layer. Struct., 4(1), 21-30. https://doi.org/10.1515/cls-2017-0003
- Shahbazi, Y., Delavari, E. and Chenaghlou, M.R. (2014), "Predicting the buckling load of smart multilayer columns using soft computing tools", Smart Struct. Syst., Int. J., 13(1), 81-98. https://doi.org/10.12989/sss.2014.13.1.081
- Shokravi, M. (2018), "Dynamic buckling of smart sandwich beam subjected to electric field based on hyperbolic piezoelasticity theory", Smart Struct. Syst., Int. J., 22(3), 327-334. https://doi.org/10.12989/sss.2018.22.3.327
- Shokrieh, M.M., Daneshvar, A., Akbari, S. and Chitsazzadeh, M. (2013), "The use of carbon nanofibers for thermal residual stress reduction in carbon fiber/epoxy laminated composites", Carbon, 59, 255-263. https://doi.org/10.1016/j.carbon.2013.03.016
- Song, Y.S. (2007), "Multiscale fiber-reinforced composites prepared by vacuum-assisted resin transfer molding", Polym. Compos., 28(4), 458-461. https://doi.org/10.1002/pc.20301
- Song, M., Chen, L., Yang, J., Zhu, W. and Kitipornchai, S. (2019), "Thermal buckling and postbuckling of edge-cracked functionally graded multilayer graphene nanocomposite beams on an elastic foundation", Int. J. Mech. Sci., 161, 105040. https://doi.org/10.1016/j.ijmecsci.2019.105040
- Sung, D.H., Kim, M. and Park, Y.B. (2018), "Prediction of thermal conductivities of carbon-containing fiber-reinforced and multiscale hybrid composites", Compos. Part B Eng., 133, 232-239. https://doi.org/10.1016/j.compositesb.2017.09.032
- Talebizadehsardari, P., Eyvazian, A., Musharavati, F., Mahani, R.B. and Sebaey, T.A. (2020a), "Elastic Wave Characteristics of Graphene Reinforced Polymer Nanocomposite Curved Beams Including Thickness Stretching Effect", Polymers, 12(10), p. 2194. https://doi.org/10.3390/polym12102194
- Talebizadehsardari, P., Eyvazian, A., Azandariani, M.G., Tran, T.N., Rajak, D.K. and Mahani, R.B. (2020b), "Buckling analysis of smart beams based on higher order shear deformation theory and numerical method", Steel Compos. Struct., Int. J., 35(5), 635-640. https://doi.org/10.12989/scs.2020.35.5.635
- Thanh, N.V., Khoa, N.D., Tuan, N.D., Tran, P. and Duc, N.D. (2017), "Nonlinear dynamic response and vibration of functionally graded carbon nanotube-reinforced composite (FG-CNTRC) shear deformable plates with temperature-dependent material properties and surrounded on elastic foundations", J. Therm. Stress., 40(10), 1254-1274. https://doi.org/10.1080/01495739.2017.1338928
- Thostenson, E.T., Li, W.Z., Wang, D.Z., Ren, Z.F. and Chou, T.W. (2002), "Carbon nanotube/carbon fiber hybrid multiscale composites", J. Appl. Phys., 91(9), 6034-6037. https://doi.org/10.1063/1.1466880.
- Tornabene, F., Bacciocchi, M., Fantuzzi, N. and Reddy, J.N. (2019), "Multiscale approach for three-phase CNT/polymer/fiber laminated nanocomposite structures", Polym. Compos., 40(S1), E102-E126. https://doi.org/10.1002/pc.24520
- Van Thanh, N., Dinh Quang, V., Dinh Khoa, N., Seung-Eock, K. and Dinh Duc, N. (2019), "Nonlinear dynamic response and vibration of FG CNTRC shear deformable circular cylindrical shell with temperature-dependent material properties and surrounded on elastic foundations", J. Sandw. Struct. Mater, 21(7), 2456-2483. https://doi.org/10.1177/1099636217752243
- Wu, H., Kitipornchai, S. and Yang, J. (2017), "Thermal buckling and postbuckling of functionally graded graphene nanocomposite plates", Mater. Des., 132, 430-441. https://doi.org/10.1016/j.matdes.2017.07.025
- Zarei, M.S., Azizkhani, M.B., Hajmohammad, M.H. and Kolahchi, R. (2017), "Dynamic buckling of polymer-carbon nanotube-fiber multiphase nanocomposite viscoelastic laminated conical shells in hygrothermal environments", J. Sandw. Struct. Mater., 1099636217743288. https://doi.org/10.1177/1099636217743288