1. 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. Multiscale carbon nanotubecarbon _ber reinforcement for advanced epoxy composites", Langmuir, 23, pp. 3970{3974 (2007). 2. Kepple, K.L., Sanborn, G.P., Lacasse, P.A., Gruenberg, K.M., and Ready, W.J. Improved fracture toughness of carbon _ber composite functionalized with multi walled carbon nanotubes", Carbon, 46, pp. 2026{2033 (2008). 3. Sawi, I.E., Olivier, P.A., Demont, P., and Bougherara, H. Processing and electrical characterization of a unidirectional CFRP composite_lled with double walled carbon nano-tubes", Compos. Sci. Technol., 73, pp. 19{26 (2012). 4. Tehrani, M., Safdari, M., Boroujeni, A.Y., Razavi, Z., Case, S.W., Dahmen, K., Garmestani, H., and Al-Haik, M.S. Hybrid carbon _ber/carbon nanotube composites for structural damping applications", Nanotechnology, 24, p. 155704 (2013). 5. Alipour Skandani, A. and Al-Haik, M. Viscoplastic characterization and modeling of hybrid carbon _ber/carbon nanotubes reinforced composites", Compos. Part B, 99, pp. 63{74 (2016). 6. Pal, G. and Kumar, S. Multiscale modeling of e_ective electrical conductivity of short carbon _ber-carbon nanotube-polymer matrix hybrid composites", Mater. Des., 89, pp. 129{136 (2016). 7. Zhou, H.W., Mishnaevsky Jr., L., Yi, H.Y., Liu, Y.Q., Hua, X., Warrier, A., and Dai, G.M. Carbon _ber/carbon nanotube reinforced hierarchical composites: E_ect of CNT distribution on shearing strength", Compos. Part B, 88, pp. 201{211 (2016). 8. Mittal, G., Dhand, V., Rhee, K.Y., Park, S.-J., and Lee, W.R. A review on carbon nanotubes and graphene as _llers in reinforced polymer nanocomposites", J. Indust. Eng. Chem., 21, pp. 11{25 (2015). 9. Seidel, G.D. and Lagoudas, D.C. Micromechanical analysis of the e_ective elastic properties of carbon nanotube reinforced composites", Mech. Mater., 38, pp. 884{907 (2006). 10. Giannopoulos, G.I., Georgantzinos, S.K., and Anifantis, N.K. A semi-continuum _nite element approach to evaluate the young's modulus of single-walled carbon nanotube reinforced composites", Compos. Part B, 41, pp. 594{601 (2010). 11. Loos, M.R. and Manas-Zloczower, I. Micromechanical models for carbon nanotube and cellulose nanowhisker reinforced composites", Polymer Eng. Sci., 53, pp. 882{887 (2013). 12. Ansari, R. and Hassanzadeh Aghdam, M.K. Micromechanics-based viscoelastic analysis of carbon nanotube-reinforced composites subjected to uniaxial and biaxial loading", Compos. Part B, 90, pp. 512{522 (2016). 13. Ansari, R. and Hassanzadeh Aghdam, M.K. Micromechanical characterizing elastic, thermoelastic and viscoelastic properties of functionally graded carbon nanotube reinforced polymer nanocomposites", Meccanica, 52, pp. 1625{1640 (2017). 14. Alva, A., Bhagat, A., and Raja, S. E_ective moduli evaluation of carbon nanotube reinforced polymers using micromechanics", Mech. Adv. Mater. Struct., 22, pp. 819{828 (2015). 15. Ansari, R., Hassanzadeh Aghdam, M.K., and Mahmoodi, M.J. Three-dimensional micromechanical analysis of the CNT waviness inuence on the mechanical properties of polymer nanocomposites", Acta Mech., 227, pp. 3475{3495 (2016). 16. Wattanasakulpong, N. and Ungbhakorn, V. Analytical solutions for bending, buckling and vibration responses of carbon nanotube-reinforced composite 260 M. Ahmadi et al./Scientia Iranica, Transactions B: Mechanical Engineering 27 (2020) 252{261 beams resting on elastic foundation", Comput. Mater. Sci., 71, pp. 201{208 (2013). 17. Lin, F. and Xiang, Y. Vibration analysis of carbon nanotube reinforced composite plates", Appl. Mech. Mater., 553, pp. 681{686 (2014). 18. Abdollahzadeh Shahrbabaki, E. and Alibeigloo, A. Three-dimensional free vibration of carbon nanotubereinforced composite plates with various boundary conditions using Ritz method", Compos. Struct., 111, pp. 362{370 (2014). 19. Ansari, R., Faghih Shojaei, M., Mohammadi, V., and Sadeghi, F. Nonlinear forced vibration analysis of functionally graded carbon nanotube-reinforced composite Timoshenko beams", Compos. Struct., 113, pp. 316{327 (2014). 20. Ansari, R., Hasrati, E., Faghih Shojaei, M., Gholami, R., and Shahabodini, A. Forced vibration analysis of functionally graded carbon nanotube-reinforced composite plates using a numerical strategy", Physica E, 69, pp. 294{305 (2015). 21. Wu, H.L., Yang, J., and Kitipornchai, S. Imperfection sensitivity of postbuckling behaviour of functionally graded carbon nanotube-reinforced composite beams", Thin-Walled Struct., 108, pp. 225{233 (2016). 22. Ansari, R., Shahabodini, A., and Faghih Shojaei, M. Vibrational analysis of carbon nanotube-reinforced composite quadrilateral plates subjected to thermal environments using a weak formulation of elasticity", Compos. Struct., 139, pp. 167{187 (2016). 23. Mirzaei, M. and Kiani, Y. Free vibration of functionally graded carbon-nanotube-reinforced composite plates with cutout", Beilstein J. Nanotechnol., 7, pp. 511{523 (2016). 24. Ansari, R., Pourashraf, T., Gholami, R., and Shahabodini, A. Analytical solution for nonlinear postbuckling of functionally graded carbon nanotube-reinforced composite shells with piezoelectric layers", Compos. Part B, 90, pp. 267{277 (2016). 25. Ghorbani Shenas, A., Malekzadeh, P., and Ziaee, S. Vibration analysis of pre-twisted functionally graded carbon nanotube reinforced composite beams in thermal environment", Compos. Struct., 162, pp. 325{340 (2017). 26. Gholami, R., Ansari, R., and Gholami, Y. Nonlinear resonant dynamics of geometrically imperfect higher-order shear deformable functionally graded carbon-nanotube reinforced composite beams", Compos. Struct., 174, pp. 45{58 (2017). 27. Gholami, R. and Ansari, R. The e_ect of initial geometric imperfection on the nonlinear resonance of functionally graded carbon nanotube-reinforced composite rectangular plates", Appl. Math. Mech., 39, pp. 1219{1238 (2018). 28. Gholami, R. and Ansari, R. Nonlinear harmonically excited vibration of third-order shear deformable functionally graded graphene platelet-reinforced composite rectangular plates", Eng. Struct., 156, pp. 197{209 (2018). 29. Gholami, R. and Ansari, R. Large deection geometrically nonlinear analysis of functionally graded multilayer graphene platelet-reinforced polymer composite rectangular plates", Compos. Struct., 180, pp. 760{ 771 (2018). 30. Gholami, R., Ansari, R., and Gholami, Y. Numerical study on the nonlinear resonant dynamics of carbon nanotube/_ber/polymer multiscale laminated composite rectangular plates with various boundary conditions", Aerosp. Sci. Technol., 78, pp. 118{129 (2018). 31. Gholami, R. and Ansari, R. Nonlinear bending of third-order shear deformable carbon nanotube/ _ber/polymer multiscale laminated composite rectangular plates with di_erent edge supports", Eur. Phys. J. Plus, 133, p. 282 (2018). 32. Gholami, R. and Ansari, R. Geometrically nonlinear resonance of higher-order shear deformable functionally graded carbon-nanotube-reinforced composite annular sector plates excited by harmonic transverse loading", Eur. Phys. J. Plus, 133, p. 56 (2018). 33. Odegard, G.M., Gates, T.S., Wise, K.E., Park, C., and Siochi, E.J. Constitutive modeling of nanotubereinforced polymer composites", Compos. Sci. Technol., 63, pp. 1671{1687 (2003). 34. Tsai, J.L., Tzeng, S.H., and Chiu, Y.T. Characterizing elastic properties of carbon nanotubes/polyimide nanocomposites using multi-scale simulation", Compos. Part B, 41, pp. 106{115 (2010). 35. Shokrieh, M.M. and Ra_ee, R. Stochastic multiscale modeling of CNT/polymer composites", Comput. Mater. Sci., 50, pp. 437{446 (2010). 36. Joshi, U.A., Sharma, S.C., and Harsha, S.P. A multiscale approach for estimating the chirality e_ects in carbon nanotube reinforced composites", Physica E, 45, pp. 28{35 (2012). 37. Vu-Bac, N., Ra_ee, R., Zhuang, X., Lahmer, T., and Rabczuk, T. Uncertainty quanti_cation for multiscale modeling of polymer nanocomposites with correlated parameters", Compos. Part B, 68, pp. 446{464 (2015). 38. Ahmadi, M., Ansari, R., and Rouhi, H. Multi-scale bending, buckling and vibration analyses of carbon _ber/carbon nanotube-reinforced polymer nanocomposite plates with various shapes", Physica E, 93, pp. 17{25 (2017). 39. Ahmadi, M., Ansari, R., and Hassanzadeh-Aghdam, M.K. Low velocity impact analysis of beams made of short carbon _ber/carbon nanotube-polymer composite: A hierarchical _nite element approach", Mech. Adv. Mater. Struct., 26(13), pp. 1104{1114 (2019). https://doi.org/10.1080/15376494.2018.1430276 40. Ahmadi, M., Ansari, R., and Rouhi, H. Free and forced vibration analysis of rectangular/ circular/ annular plates made of carbon _ber-carbon nanotube-polymer hybrid composites", Sci. Eng. Compos. Mater., 26(1), pp. 70{76 (2019). https://doi.org/10.1515/secm-2017-0279 M. Ahmadi et al./Scientia Iranica, Transactions B: Mechanical Engineering 27 (2020) 252{261 261 41. Ahmadi, M., Ansari, R., and Rouhi, H. On the free vibrations of piezoelectric carbon nanotubereinforced microbeams: a multiscale _nite element approach", Iranian J. Sci. Technol. Trans. Mech. Eng., 43(Supplement 1), pp. 285{294 (2019). https://doi.org/10.1007/s40997-018-0157-x 42. Ahmadi, M., Ansari, R., and Rouhi, S. Fracture behavior of the carbon nanotube/carbon _ber/polymer multiscale composites under bending test - A stochastic _nite element method", Mech. Adv. Mater. Struct., 26(13), pp. 1169{1177 (2019). https://doi.org/10.1080/15376494.2018.1432790 43. Ahmadi, M., Ansari, R., and Rouhi, H. Free vibration analysis of carbon _ber-carbon nanotube-polymer matrix composite plates by a _nite element-based multiscale modeling approach", J. Multiscale Model., 9, p. 1850002 (2018). 44. Civalek, O. and Demir, C_ . A simple mathematical model of microtubules surrounded by an elastic matrix by nonlocal _nite element method", Appl. Math. Comput., 289, pp. 335{352 (2016). 45. Mercan, K. and Civalek, O. DSC method for buckling analysis of boron nitride nanotube (BNNT) surrounded by an elastic matrix", Compos. Struct., 143, pp. 300{309 (2016). 46. Refaeinejad, V., Rahmani, O., and Hosseini, S.A.H. An analytical solution for bending, buckling, and free vibration of FG nanobeam lying on Winkler-Pasternak elastic foundation using di_erent nonlocal higher order shear deformation beam theories", Scientia Iranica, F, 24, pp. 1635{1653 (2017). 47. Norouzzadeh, A., Ansari, R., and Rouhi, H. Isogeometric vibration analysis of small-scale Timoshenko beams based on the most comprehensive sizedependent theory", Scientia Iranica, F, 25, pp. 1864{ 1878 (2018). 48. Akgoz, B. and Civalek, O. Buckling analysis of cantilever carbon nanotubes using the strain gradient elasticity and modi_ed couple stress theories", J. Comput. Theor. Nanosci., 8, pp. 1821{1827 (2011). 49. Chen, W.J. and Li, X.P. Size-dependent free vibration analysis of composite laminated Timoshenko beam based on new modi_ed couple stress theory", Arch. Appl. Mech., 83, pp. 431{444 (2013). 50. Akgoz, B. and Civalek, O. Bending analysis of embedded carbon nanotubes resting on an elastic foundation using strain gradient theory", Acta Astronautica, 119, pp. 1{12 (2016). 51. Karimzadeh, A. and Ahmadian, M.T. Vibrational characteristics of size dependent vibrating ring gyroscope", Scientia Iranica, B (2018). DOI: 10.24200/SCI.2018.20495 52. Jafari-Talookolaei, R.-A., Ebrahimzade, N., Rashidi- Juybari, S., and Teimoori, K. Bending and vibration analysis of delaminated Bernoulli-Euler microbeams using the modi_ed couple stress", Scientia Iranica, B, 25, pp. 675{688 (2018). 53. Shen, L. and Li, J. Transversely isotropic elastic properties of single-walled carbon nanotubes", Phys. Rev. B, 69, p. 045414 (2004). 54. Shen, L. and Li, J. Transversely isotropic elastic properties of multiwalled carbon nanotubes", Phys. Rev. B, 71, p. 035412 (2005). 55. Selmi, A., Friebel, C., Doghri, I., and Hassis, H. Prediction of the elastic properties of single walled carbon nanotube reinforced polymers: A comparative study of several micromechanical models", Compos. Sci. Technol., 67, pp. 2071{2084 (2007). 56. Kulkarni, M., Carnahan, D., Kulkarni, K., Qian, D., and Abot, J.L. Elastic response of a carbon nanotube _ber reinforced polymeric composite: A numerical and experimental study", Compos. Part B, 41, pp. 414{421 (2010). 57. Odegard, G.M., Clancy, T.C., and Gates, T.S. Modeling of the mechanical properties of nanoparticle/polymer composites", Polymer, 46, pp. 553{562 (2005).
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