References:
[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 Nanotube−Carbon Fiber 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 fiber 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 character-ization of a unidirectional CFRP compositefilled 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 fiber/carbon nanotube composites for structural damping applications,” Nanotechnology, 24, 155704 (2013).
[5] Alipour Skandani, A., and Al-Haik, M., “Viscoplastic characterization and modeling of hybrid carbon fiber/carbon nanotubes reinforced composites,” Compos. Part B, 99, pp. 63–74 (2016).
[6] Pal, G., and Kumar, S., “Multiscale modeling of effective electrical conductivity of short carbon fiber-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 fiber/carbon nanotube reinforced hierarchical composites: Effect 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 fillers 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 effective 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 Finite 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., “Effective 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 influence 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 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 Nanotube-Reinforced 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 effect 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 deflection 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/fiber/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/fiber/polymer multiscale laminated composite rectangular plates with different 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 nanotube-reinforced polymer composites,” Compos. Sci. Technol., 63, pp. 1671–87 (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 Rafiee, R., “Stochastic multi-scale 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 effects in carbon nanotube reinforced composites,” Physica E, 45, pp. 28–35 (2012).
[37] Vu-Bac, N., Rafiee, R., Zhuang, X., Lahmer, T., and Rabczuk, T., “Uncertainty quantification 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 fiber/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 fiber/carbon nanotube-polymer composite: A hierarchical finite element approach,” Mech. Adv. Mater. Struct., https://doi.org/10.1080/15376494.2018.1430276 (2018).
[40] Ahmadi, M., Ansari, R., and Rouhi, H., “Free and forced vibration analysis of rectangular/circular/annular plates made of carbon fiber-carbon nanotube-polymer hybrid composites,” Sci. Eng. Compos. Mater., https://doi.org/10.1515/secm-2017-0279 (2018).
[41] Ahmadi, M., Ansari, R., and Rouhi, H., “On the free vibrations of piezoelectric carbon nanotube-reinforced microbeams: a multiscale finite element approach,” Iranian J. Sci. Technol. Trans. Mech. Eng., https://doi.org/10.1007/s40997-018-0157-x (2018).
[42] Ahmadi, M., Ansari, R., and Rouhi, S., “Fracture behavior of the carbon nanotube/carbon fiber/polymer multiscale composites under bending test – A stochastic finite element method,” Mech. Adv. Mater. Struct., https://doi.org/10.1080/15376494.2018.1432790 (2018).
[43] Ahmadi, M., Ansari, R., and Rouhi, H., “Free vibration analysis of carbon fiber-carbon nanotube-polymer matrix composite plates by a finite element-based multi-scale modeling approach,” J. Multiscale Model., 9, 1850002 (2018).
[44] Civalek, Ö., and Demir, Ç., “A simple mathematical model of microtubules surrounded by an elastic matrix by nonlocal finite element method,” Appl. Math. Comput., 289, pp. 335-352 (2016).
[45] Mercan, K., and Civalek, Ö., “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 different 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 size-dependent theory,” Scientia Iranica F, 25, pp. 1864-1878 (2018).
[48] Akgöz, B., and Civalek, Ö., “Buckling analysis of cantilever carbon nanotubes using the strain gradient elasticity and modified 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 modified couple stress theory,” Arch. Appl. Mech., 83, pp. 431–444 (2013).
[50] Akgoz, B., and Civalek, Ö., “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, DOI: 10.24200/SCI.2018.20495 (2018).
[52] Jafari-Talookolaei, R. -A., Ebrahimzade, N., Rashidi-Juybari, S., and Teimoori, K., “Bending and vibration analysis of delaminated Bernoulli-Euler microbeams using the modified 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, 045414 (2004).
[54] Shen, L., and Li, J., “Transversely isotropic elastic properties of multiwalled carbon nanotubes,” Phys. Rev. B, 71, 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 fiber 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).