Thermo-electro-mechanical size-dependent buckling response for functionally graded graphene platelet reinforced piezoelectric cylindrical nanoshells. (English) Zbl 1535.74157
Summary: An accurate buckling response analysis for functionally graded graphene platelet (GPL) reinforced piezoelectric cylindrical nanoshells subject to thermo-electro-mechanical loadings is presented by a rigorous symplectic expansion approach. Three types of GPL reinforced patterns are considered, and the modified Halpin-Tsai model is employed to determine their effective material properties. By using Eringen’s nonlocal stress theory and Reissner’s shell theory, new governing equations are established in the Hamiltonian form. Exact solutions are expanded into symplectic series and three possible forms are derived. A comparison with the existing study is presented to validate the solution and very good agreement is observed. The effects of material and geometrical properties of GPLs, electric voltage and temperature rise on critical buckling stresses are investigated and discussed in detail.
Keywords:
analytical solution; buckling; functionally graded; graphene reinforced piezoelectric composite; nanoshell; symplecticReferences:
| [1] | Wei, J., Vo, T. and Inam, F., Epoxy/graphene nanocomposites – processing and properties: A review, RSC Adv.5(90) (2015) 73510-73524. |
| [2] | Liu, P., Zhong, J., Georgios, K., Lee, D., Steven, S., Chih-Jen, S., Eric, W., Joshua, T., Bo, Q., Krystyn, V. V., Richard, L., Brian, W. and Michael, S., Layered and scrolled nanocomposites with aligned semi-infinite graphene inclusions at the platelet limit, Science353(6297) (2016) 364. |
| [3] | Ren, Y., Zhang, Y., Fang, H., Ding, T., Li, J. and Bai, S., Simultaneous enhancement on thermal and mechanical properties of polypropylene composites filled with graphite platelets and graphene sheets, Compos. A Appl. Sci. Manuf.112 (2018) 57-63. |
| [4] | Zhang, Y. and Li, X., Bioinspired, graphene/Al_2O_3 doubly reinforced aluminum composites with high strength and toughness, Nano Lett.17(11) (2017) 6907-6915. |
| [5] | Nieto, Bisht, A., Lahiri, D., Zhang, C. and Agarwal, A., Graphene reinforced metal and ceramic matrix composites: A review, Int. Mater. Rev.62(5) (2017) 241-302. |
| [6] | Baughman, R. H., Zakhidov, A. A. and de Heer, W. A., Carbon nanotubes — the route toward applications, Science297(5582) (2002) 787. |
| [7] | Sandler, J. K. W., Kirk, J. E., Kinloch, I. A., Shaffer, M. S. P. and Windle, A. H., Ultra-low electrical percolation threshold in carbon-nanotube-epoxy composites, Polymer44(19) (2003) 5893-5899. |
| [8] | Moniruzzaman, M. and Winey, K. I., Polymer nanocomposites containing carbon nanotubes, Macromolecules39(16) (2006) 5194-5205. |
| [9] | Jiao, P. and Alavi, A. H., Buckling analysis of graphene-reinforced mechanical metamaterial beams with periodic webbing patterns, Int. J. Eng. Sci.131 (2018) 1-18. · Zbl 1423.74340 |
| [10] | Reza Barati, M. and Zenkour, A. M., Post-buckling analysis of refined shear deformable graphene platelet reinforced beams with porosities and geometrical imperfection, Compos. Struct.181 (2017) 194-202. |
| [11] | Chen, D., Yang, J. and Kitipornchai, S., Nonlinear vibration and postbuckling of functionally graded graphene reinforced porous nanocomposite beams, Compos. Sci. Technol.142 (2017) 235-245. |
| [12] | Kitipornchai, S., Chen, D. and Yang, J., Free vibration and elastic buckling of functionally graded porous beams reinforced by graphene platelets, Mater. Des.116 (2017) 656-665. |
| [13] | Mirzaei, M. and Kiani, Y., Isogeometric thermal buckling analysis of temperature dependent FG graphene reinforced laminated plates using NURBS formulation, Compos. Struct.180 (2017) 606-616. |
| [14] | Song, M., Yang, J. and Kitipornchai, S., Bending and buckling analyses of functionally graded polymer composite plates reinforced with graphene nanoplatelets, Compos. B Eng.134 (2018) 106-113. |
| [15] | Song, M., Yang, J., Kitipornchai, S. and Zhu, W., Buckling and postbuckling of biaxially compressed functionally graded multilayer graphene nanoplatelet-reinforced polymer composite plates, Int. J. Mech. Sci.131-132 (2017) 345-355. |
| [16] | Wu, H., Kitipornchai, S. and Yang, J., Thermal buckling and postbuckling of functionally graded graphene nanocomposite plates, Mater. Des.132 (2017) 430-441. |
| [17] | Yang, J., Chen, D. and Kitipornchai, S., Buckling and free vibration analyses of functionally graded graphene reinforced porous nanocomposite plates based on Chebyshev-Ritz method, Compos. Struct.193 (2018) 281-294. |
| [18] | Shen, H. S., Xiang, Y., Lin, F. and Hui, D., Buckling and postbuckling of functionally graded graphene-reinforced composite laminated plates in thermal environments, Compos. B Eng.119 (2017) 67-78. · Zbl 1439.74140 |
| [19] | Shen, H. S., Xiang, Y. and Fan, Y., Postbuckling of functionally graded graphene-reinforced composite laminated cylindrical panels under axial compression in thermal environments, Int. J. Mech. Sci.135 (2018) 398-409. |
| [20] | Shen, H. S. and Xiang, Y., Postbuckling behavior of functionally graded graphene-reinforced composite laminated cylindrical shells under axial compression in thermal environments, Comput. Methods Appl. Mech. Eng.330 (2018) 64-82. · Zbl 1439.74179 |
| [21] | Shen, H. S. and Xiang, Y., Postbuckling of functionally graded graphene-reinforced composite laminated cylindrical shells subjected to external pressure in thermal environments, Thin-Walled Struct.124 (2018) 151-160. |
| [22] | Wang, Y., Feng, C., Zhao, Z. and Yang, J., Buckling of graphene platelet reinforced composite cylindrical shell with cutout, Int. J. Struct. Stab. Dyn.18(3) (2018) 1850040. |
| [23] | Wang, Y., Feng, C., Zhao, Z., Lu, F. and Yang, J., Torsional buckling of graphene platelets (GPLs) reinforced functionally graded cylindrical shell with cutout, Compos. Struct.197 (2018) 72-79. |
| [24] | Wang, Y., Feng, C., Zhao, Z. and Yang, J., Eigenvalue buckling of functionally graded cylindrical shells reinforced with graphene platelets (GPL), Compos. Struct.202 (2017) 38-46. |
| [25] | Liu, D., Kitipornchai, S., Chen, W. and Yang, J., Three-dimensional buckling and free vibration analyses of initially stressed functionally graded graphene reinforced composite cylindrical shell, Compos. Struct.189 (2018) 560-569. |
| [26] | Sahmani, S. and Aghdam, M. M., Axial postbuckling analysis of multilayer functionally graded composite nanoplates reinforced with GPLs based on nonlocal strain gradient theory, Eur. Phys. J. Plus132(11) (2017) 490. |
| [27] | Sahmani, S. and Aghdam, M. M., Nonlinear instability of axially loaded functionally graded multilayer graphene platelet-reinforced nanoshells based on nonlocal strain gradient elasticity theory, Int. J. Mech. Sci.131-132 (2017) 95-106. |
| [28] | Sahmani, S. and Aghdam, M. M., A nonlocal strain gradient hyperbolic shear deformable shell model for radial postbuckling analysis of functionally graded multilayer GPLRC nanoshells, Compos. Struct.178 (2017) 97-109. |
| [29] | Abolhasani, M. M., Shirvanimoghaddam, K. and Naebe, M., PVDF/graphene composite nanofibers with enhanced piezoelectric performance for development of robust nanogenerators, Compos. Sci. Technol.138 (2017) 49-56. |
| [30] | Xu, K., Wang, K., Zhao, W., Bao, W., Liu, E., Ren, Y., Wang, M., Fu, Y., Zeng, J., Li, Z., Zhou, W., Song, F., Wang, X., Shi, Y., Wan, X., Fuhrer, M., Wang, B., Qiao, Z., Miao, F. and Xing, D., The positive piezoconductive effect in graphene, Nat. Commun.6 (2015) 8119. |
| [31] | Layek, R. K., Samanta, S., Chatterjee, D. P. and Nandi, A. K., Physical and mechanical properties of poly (methyl methacrylate)-functionalized graphene/poly (vinylidine fluoride) nanocomposites: Piezoelectric \(\beta\) polymorph formation, Polymer51(24) (2010) 5846-5856. |
| [32] | Abbasipour, M., Khajavi, R., Yousefi, A. A., Yazdanshenas, M. E. and Razaghian, F., The piezoelectric response of electrospun PVDF nanofibers with graphene oxide, graphene, and halloysite nanofillers: A comparative study, J. Mater. Sci.-Mater. Electron.28(21) (2017) 15942-15952. |
| [33] | Hu, Y. C., Hsu, W. L., Wang, Y. T., Ho, C. T. and Chang, P. Z., Enhance the pyroelectricity of polyvinylidene fluoride by graphene-oxide doping, Sensors14(4) (2014) 6877-6890. |
| [34] | Maity, N., Mandal, A. and Nandi, A. K., Hierarchical nanostructured polyaniline functionalized graphene/poly (vinylidene fluoride) composites for improved dielectric performances, Polymer103 (2016) 83-97. |
| [35] | Chen, C. Q., Shi, Y., Zhang, Y. S., Zhu, J. and Yan, Y. J., Size dependence of Young’s modulus in ZnO nanowires, Phys. Rev. Lett., 96(7) (2006) 075505. |
| [36] | Stan, G., Ciobanu, C. V., Parthangal, P. M. and Cook, R. F., Diameter-dependent radial and tangential elastic moduli of ZnO nanowires, Nano Lett.7(12) (2007) 3691-3697. |
| [37] | Agrawal, R., Peng, B., Gdoutos, E. E. and Espinosa, H. D., Elasticity size effects in ZnO nanowires-A combined experimental-computational approach, Nano Lett.8(11) (2008) 3668-3674. |
| [38] | Papageorgiou, D. G., Kinloch, I. A. and Young, R. J., Mechanical properties of graphene and graphene-based nanocomposites, Prog. Mater. Sci.90 (2017) 75-127. |
| [39] | Yang, Q. and Lim, C. W., Thermal effects on buckling of shear deformable nanocolumns with von Kármán nonlinearity based on nonlocal stress theory, Nonlinear Anal.-Real World Appl.13(2) (2012) 905-922. · Zbl 1238.74015 |
| [40] | Sahmani, S. and Ansari, R., On the free vibration response of functionally graded higher-order shear deformable microplates based on the strain gradient elasticity theory, Compos. Struct.95 (2013) 430-442. |
| [41] | Ke, L. L. and Wang, Y. S., Free vibration of size-dependent magneto-electro-elastic nanobeams based on the nonlocal theory, Physica E63 (2014) 52-61. |
| [42] | Ma, L. H., Ke, L. L., Wang, Y. Z. and Wang, Y. S., Wave propagation in magneto-electro-elastic nanobeams via two nonlocal beam models, Physica E86 (2017) 253-261. |
| [43] | Zhou, Z., Li, Y., Fan, J., Rong, D., Sui, G. and Xu, C., Exact vibration analysis of a double-nanobeam-systems embedded in an elastic medium by a Hamiltonian-based method, Physica E99 (2018) 220-235. |
| [44] | Xu, C., Rong, D., Tong, Z., Zhou, Z., Hu, J. and Xu, X., Coupled effect of in-plane magnetic field and size effect on vibration properties of the completely free double-layered nanoplate system, Physica E108 (2019) 215-225. |
| [45] | Lim, C. W., Zhang, G. and Reddy, J. N., A higher-order nonlocal elasticity and strain gradient theory and its applications in wave propagation, J. Mech. Phys. Solids78 (2015) 298-313. · Zbl 1349.74016 |
| [46] | J. S. Wang and Q. H. Qin, Symplectic model for piezoelectric wedges and its application in analysis of electroelastic singularities, Philos. Mag.87(2) (2007) 225-251. |
| [47] | Chen, W. Q. and Zhao, L., The symplectic method for plane elasticity problem of functionally graded materials, Acta Mech. Sin.41(4) (2009) 588-594. |
| [48] | Yao, W. A., Zhong, W. X. and Lim, C. W., Symplectic Elasticity (World Scientific, Singapore, 2009). · Zbl 1170.74002 |
| [49] | Lim, C. W. and Xu, X. S., Symplectic elasticity: Theory and applications, Appl. Mech. Rev.63(5) (2010) 050802. |
| [50] | Sun, J. B., Xu, X. S. and Lim, C. W., Accurate symplectic space solutions for thermal buckling of functionally graded cylindrical shells, Compos. B Eng.55 (2013) 208-214. |
| [51] | Sun, J. B., Xu, X. S. and Lim, C. W., Buckling of functionally graded cylindrical shells under combined thermal and compressive loads, J. Therm. Stresses37(3) (2014) 340-362. |
| [52] | Sun, J. B., Xu, X. S. and Lim, C. W., Torsional buckling of functionally graded cylindrical shells with temperature-dependent properties, Int. J. Struct. Stab. Dyn.14(1) (2014) 1350048. · Zbl 1359.74107 |
| [53] | Li, R., Wang, P. C., Tian, Y., Wang, B. and Li, G., A unified analytic solution approach to static bending and free vibration problems of rectangular thin plates, Sci. Rep.5 (2015) 17054. |
| [54] | Ni, Y. W., Tong, Z. Z., Rong, D. L., Zhou, Z. H. and Xu, X. S., A new Hamiltonian-based approach for free vibration of a functionally graded orthotropic circular cylindrical shell embedded in an elastic medium, Thin-Walled Struct.120 (2017) 236-248. |
| [55] | Ni, Y. W., Tong, Z. Z., Rong, D. L., Zhou, Z. H. and Xu, X. S., Accurate thermal buckling analysis of functionally graded orthotropic cylindrical shells under the symplectic framework, Thin-Walled Struct.129 (2018) 1-9. |
| [56] | Yu, Y. M. and Lim, C. W., A nonlinear constitutive model for axisymmetric bending of annular graphene-like nanoplate with gradient elasticity enhancement effects, ASCEJ. Eng. Mech.139(8) (2013) 1025-1035. |
| [57] | Leissa, W., Vibration of Shells (Acoustical Society of America, New York, 1993). |
| [58] | Wang, Q., On buckling of column structures with a pair of piezoelectric layers, Eng. Struct.24(2) (2002) 199-205. |
| [59] | Pietrzakowski, M., Piezoelectric control of composite plate vibration: Effect of electric potential distribution, Comput. Struct.86(9) (2008) 948-954. |
| [60] | Lang, Z. and Li, X., Buckling and vibration analysis of functionally graded magneto-electro-thermo-elastic circular cylindrical shells, Appl. Math. Model.37(4) (2013) 2279-2292. · Zbl 1349.74145 |
| [61] | Pour, H. R., Arani, A. G. and Sheikhzadeh, G., Pulsating fluid induced dynamic stability of embedded viscoelastic piezoelectric separators using different cylindrical shell theories, Steel Compos. Struct.24(4) (2017) 499-512. |
| [62] | Yang, B., Yang, J. and Kitipornchai, S., Thermoelastic analysis of functionally graded graphene reinforced rectangular plates based on 3D elasticity, Meccanica52(10) (2017) 2275-2292. · Zbl 1380.74028 |
| [63] | Affdl, J. C. H. and Kardos, J. L., The Halpin-Tsai equations: A review, Polym. Eng. Sci.16(5) (1976) 344-352. |
| [64] | Mao, J. J. and Zhang, W., Linear and nonlinear free and forced vibrations of graphene reinforced piezoelectric composite plate under external voltage excitation, Compos. Struct.203 (2018) 551-565. |
| [65] | Yang, B., Kitipornchai, S., Yang, Y. F. and Yang, J., 3D thermo-mechanical bending solution of functionally graded graphene reinforced circular and annular plates, Appl. Math. Model.49 (2017) 69-86. · Zbl 1480.74211 |
| [66] | Mosallaie Barzoki, A., Ghorbanpour Arani, A., Kolahchi, R. and Mozdianfard, M. R., Electro-thermo-mechanical torsional buckling of a piezoelectric polymeric cylindrical shell reinforced by DWBNNTs with an elastic core, Appl. Math. Model.36(7) (2012) 2983-2995. · Zbl 1252.74045 |
| [67] | Zhang, Y. Q., Liu, G. R. and Wang, J. S., Small-scale effects on buckling of multiwalled carbon nanotubes under axial compression, Phys. Rev. B70(20) (2004) 205430. |
| [68] | Ghorbanpour Arani, A., Amir, S., Shajari, A. R. and Mozdianfard, M. R., Electro-thermo-mechanical buckling of DWBNNTs embedded in bundle of CNTs using nonlocal piezoelasticity cylindrical shell theory, Compos. B Eng.43(2) (2012) 195-203. |
| [69] | Mehralian, F., Tadi Beni, Y. and Ansari, R., Size dependent buckling analysis of functionally graded piezoelectric cylindrical nanoshell, Compos. Struct.152 (2016) 45-61. |
| [70] | Mehralian, F. and Beni, Y. T., Thermo-electro-mechanical buckling analysis of cylindrical nanoshell on the basis of modified couple stress theory, J. Mech. Sci. Technol.31(4) (2017) 1773-1787. |
| [71] | Mehralian, F. and Tadi Beni, Y., Buckling of bimorph functionally graded piezoelectric cylindrical nanoshell, Proc. Inst. Mech. Eng. C J. Mech. Eng. Sci.232(19) (2017) 3538-3550. |
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
