Finite Element Model and Size Dependent Stability Analysis of Boron Nitride and Silicon Carbide Nanowires/Nanotubes

Document Type : Article


1 Akdeniz University, Faculty of Engineering, Civil Engineering Department, Division of Mechanics ‎ Antalya-TURKIYE

2 Akdeniz University, Civil Eng.Dept.

3 Akdeniz University Civil Eng.


In present paper, the stability analysis of boron nitride and silicon carbide nanotubes/nanowires is investigated using different size effective theories, finite element method, and computer software. Size effective theories used in paper are modified couple stress theory (MCST), modified strain gradient theory (MSGT), nonlocal elasticity theory (NET), surface elasticity theory (SET), nonlocal surface elasticity theory (NSET). As computer software, ANSYS and COMSOL multiphysics are used. Comparative results between theories and software and literature are given in result section. Comparative results are in good harmony. As results, it is clearly seen that nonlocal elasticity theory gives lowest results for every modes and structures while modified strain gradient theory gives the highest.


Main Subjects

1. Lin, H.R., Zhou, C.K., Tian, Y., et al. Bulk assembly of organic metal halide nanotubes", Chem Sci, 8(12), pp. 8400-8404 (2017). 2. Moaseri, E., Karimi, M., Bazubandi, B., et al. Alignment of carbon nanotubes in bulk epoxy matrix using a magnetic-assisted method: Solenoid magnetic _eld", Polym Sci Ser a+, 59(5), pp. 726-733 (2017). 3. Zhao, X.L., Zhang, S.C., Zhu, Z.X., et al. Catalysts for single-wall carbon nanotube synthesis From surface growth to bulk preparation", MRS Bull, 42(11), pp. 809-818 (2017). 4. Mishra, R.K., Mishra, P., Verma, K., et al. Manipulation of thermo-mechanical, morphological and electrical properties of PP/PET polymer blend using MWCNT as nano compatibilizer: A comprehensive study of hybrid nanocomposites", Vacuum, 157, pp. 433-441 (2018). 5. Li, Q., Rottmair, C.A., and Singer, R.F. CNT reinforced light metal composites produced by melt stirring and by high pressure die casting", Compos Sci Technol, 70(16), pp. 2242-2247 (2010). 6. Calbi, M.M., Toigo, F., and Cole, M.W. Dilationinduced phases of gases absorbed within a bundle of carbon nanotubes", Phys Rev Lett, 86(22), pp. 5062- 5065 (2001). 7. Lalwani, G., Kwaczala, A.T., Kanakia, S., et al. Fab2096 H.M. Numano_glu et al./Scientia Iranica, Transactions A: Civil Engineering 26 (2019) 2079{2099 rication and characterization of three-dimensional macroscopic all-carbon sca_olds", Carbon, 53, pp. 90- 100 (2013). 8. Valenti, G., Boni, A., Melchionna, M., et al. Co-axial heterostructures integrating palladium/ titanium dioxide with carbon nanotubes for e_cient electrocatalytic hydrogen evolution", Nat Commun, 7, pp. 1-8 (2016). 9. Iijima, S. Helical microtubules of graphitic carbon", Nature, 354(6348), pp. 56-58 (1991). 10. Watson, J.H. and Kaufmann, K. Electron microscope examination of the microphysical properties of the polymer cuprene", Journal of Applied Physics, 17(12), pp. 996-1005 (1946). 11. Radushkevich, L. and Lukyanovich, V. About the structure of carbon formed by thermal decomposition of carbon monoxide on iron substrate", J. Phys. Chem.(Moscow), 26, pp. 88-95 (1952). 12. Bacon, R. Growth, structure, and properties of graphite whiskers", Journal of Applied Physics, 31(2), pp. 283-290 (1960). 13. Oberlin, A., Endo, M., and Koyama, T. Filamentous growth of carbon through benzene decomposition", J Cryst Growth, 32(3), pp. 335-349 (1976). 14. Abrahamson, J., Wiles, P.G., and Rhoades, B.L. Structure of carbon _bers found on carbon arc anodes", Carbon, 37(11), pp. 1873-1874 (1999). 15. Kolesnik, N.F., Akhmatov, Y.S., and Shomlin, V.I. Metals", Izvestiya Akademii Nauk SSSR, 3, pp. 12- 17 (1982). 16. Reibold, M., Pauer, P., Levin, A.A., et al. Materials - carbon nanotubes in an ancient damascus sabre", Nature, 444(7117), p. 286 (2006). 17. Ding, C.Y., Wang, L.J., Zhou, W.W., et al. New design on Li-ion battery anode of ternary complex metal/metal oxide@CNT: A case study of hierarchical NiCo-NiCo2O4@CNTs", Chem Eng J, 353, pp. 340- 349 (2018). 18. Kazazi, M., Zafar, Z.A., Delshad, M., et al. TiO2/CNT nanocomposite as an improved anode material for aqueous rechargeable aluminum batteries", Solid State Ionics, 320, pp. 64-69 (2018). 19. Kesavan, T., Gunawardhana, N., Senthil, C., et al. Fabrication of hollow Co3O4 nanospheres and their nanocomposites of CNT and rGO as highperformance anodes for lithium-ion batteries", Chemistryselect, 3(20), pp. 5502-5511 (2018). 20. Lakshmi-Narayana, A., Dhananjaya, M., Guru- Prakash, N., et al. Li2TiO3/Graphene and Li2TiO3/CNT composites as anodes for high power Li-Ion batteries", Chemistryselect, 3(31), pp. 9150- 9158 (2018). 21. Park, B.H., Roh, H.K., Haghighat-Shishavan, S., et al. Silicon diphosphide-CNT composite anode material for high-performance Li-ion batteries", Abstr Pap Am Chem S, 256 (2018). 22. Peng, T., Guo, W., Zhang, Q., et al. Uniform coaxial CNT@Li2MnSiO4@C as advanced cathode material for lithium-ion battery", Electrochim Acta, 291, pp. 1-8 (2018). 23. Razaq, R., Sun, D., Xin, Y., et al. Enhanced kinetics of polysul_de redox reactions on Mo2C/CNT in lithium-sulfur batteries", Nanotechnology, 29(29) (2018). 24. Wang, D., Guo, J., Cui, C.Y., et al. Controllable synthesis of CNT@ZnO composites with enhanced electrochemical properties for lithium-ion battery", Mater Res Bull, 101, pp. 305-310 (2018). 25. Wang, D.X., Li, D., Muhammad, J., Zhou, Y.L., et al. Buildup of Sn@CNT nanorods by in-situ thermal plasma and the electronic transport behaviors", Sci China Mater, 61(12), pp. 1605-1613 (2018). 26. Wang, J.F., Li, H.R., Xu, N.N., et al. Optimization of rechargeable zinc-air battery with Co3O4/MnO2/CNT bifunctional catalyst: e_ects of catalyst loading, binder content, and spraying area", Ionics, 24(12), pp. 3877-3884 (2018). 27. Yuan, J.J., Zheng, X.K., Jiang, L., et al. CNTintercalated rGO/sulfur laminated structure for highrate and long-life lithium-sulfur batteries", Mater Lett, 219, pp. 68-71 (2018). 28. Zhang, X., Wang, C.Y., Li, H.H., et al. High performance Li-CO2 batteries with NiO-CNT cathodes", J Mater Chem A, 6(6), pp. 2792-2796 (2018). 29. Peng, S., Cho, K.J., Qi, P.F., et al. Ab initio study of CNT NO2 gas sensor", Chem Phys Lett, 387(4-6), pp. 271-276 (2004). 30. Kim, S. CNT sensors for detecting gases with low adsorption energy by ionization", Sensors-Basel, 6(5), pp. 503-513 (2006). 31. Kim, S.J. The e_ect on the gas selectivity of CNTbased gas sensors by binder in SWNT/Silane sol solution", IEEE Sens J, 10(1), pp. 173-177 (2010). 32. Srivastava, S., Sharma, S.S., Agrawal, S., et al. Study of chemiresistor type CNT doped polyaniline gas sensor", Synthetic Met, 160(5-6), pp. 529-534 (2010). 33. Leghrib, R., Felten, A., Pireaux, J.J., et al. Gas sensors based on doped-CNT/SnO2 composites for NO2 detection at room temperature", Thin Solid Films, 520(3), pp. 966-970 (2011). 34. Lee, H., Lee, S., Kim, D.H., et al. Integrating metaloxide- decorated CNT networks with a CMOS readout in a gas sensor", Sensors-Basel, 12(3), pp. 2582-2597 (2012). 35. Istadeh, K.H., Kalantarinejad, R., Aghaei, M.J., et al. Computational Investigation on H2S Adsorption on the CNT Channel of Conductometric Gas Sensor", J Comput Theor Nanos, 10(11), pp. 2708-2713 (2013). 36. Park, S.J., Kwon, O.S., and Jang, J. A highperformance hydrogen gas sensor using ultrathin polypyrrole-coated CNT nanohybrids", Chem Commun, 49(41), pp. 4673-4675 (2013). H.M. Numano_glu et al./Scientia Iranica, Transactions A: Civil Engineering 26 (2019) 2079{2099 2097 37. Majumdar, S., Nag, P., and Devi, P.S. Enhanced performance of CNT/SnO2 thick _lm gas sensors towards hydrogen", Mater Chem Phys, 147(1-2), pp. 79-85 (2014). 38. Mittal, M. and Kumar, A. Carbon nanotube (CNT) gas sensors for emissions from fossil fuel burning", Sensor Actuat B-Chem, 203, pp. 349-362 (2014). 39. Kamble, V. and Umarji, A. Analyzing the kinetic response of tin oxide-carbon and tin oxide-CNT composites gas sensors for alcohols detection", Aip Adv, 5(3), pp. 1-9 (2015). 40. Rahman, R. and Servati, P. E_cient analytical model of conductivity of CNT/polymer composites for wireless gas sensors", IEEE T Nanotechnol, 14(1), pp. 118-129 (2015). 41. Donaldson, L. CNT sensors that can detect toxic gases", Mater Today, 19(9), pp. 489-490 (2016). 42. Alshammari, A.S., Alenezi, M.R., Lai, K.T., et al. Inkjet printing of polymer functionalized CNT gas sensor with enhanced sensing properties", Mater Lett, 189, pp. 299-302 (2017). 43. Guo, T., Zhou, T.H., Tan, Q.L., et al. A roomtemperature CNT/Fe3O4 based passive wireless gas sensor", Sensors-Basel, 18(10), pp. 1-11 (2018). 44. Shen, S.M., Fan, Z.H., Deng, J.H., et al. An LC Passive Wireless Gas Sensor Based on PANI/CNT Composite", Sensors-Basel, 18(9), pp. 1-13 (2018). 45. Zanjani, S.M.A., Dousti, M., and Dolatshahi, M. High-precision, resistor less gas pressure sensor and instrumentation ampli_er in CNT technology", Aeu- Int J Electron C, 93, pp. 325-336 (2018). 46. Mercan, K. A Comparative buckling analysis of silicon carbide nanotube and boron nitride nanotube", International Journal of Engineering & Applied Sciences, 8(4), pp. 99-107 (2016). 47. Mercan, K. and Civalek,  O. DSC method for buckling analysis of boron nitride nanotube (BNNT) surrounded by an elastic matrix", Composite Structures, 143, pp. 300-309 (2016). 48. Mercan, K. and Civalek,  O. Buckling analysis of silicon carbide nanotubes (SiCNTs)", International Journal of Engineering & Applied Sciences, 8(2), pp. 101-108 (2016). 49. Li, T., Tang, Z.N., Huang, Z.X., et al. A comparison between the mechanical and thermal properties of single-walled carbon nanotubes and boron nitride nanotubes", Physica E, 85, pp. 137-142 (2017). 50. Petrushenko, I.K. and Petrushenko, K.B. Mechanical properties of carbon, silicon carbide, and boron nitride nanotubes: e_ect of ionization", Monatsh Chem, 146(10), pp. 1603-1608 (2015). 51. Darwish, A.A., Hassan, M.H., Abou Mandour, M.A., et al. Mechanical properties of defective doublewalled boron nitride nanotubes for radiation shielding applications: A computational study", Comp Mater Sci, 156, pp. 142-147 (2019). 52. Mercan, K. and Civalek,  O. Buckling analysis of Silicon carbide nanotubes (SiCNTs) with surface e_ect and nonlocal elasticity using the method of HDQ", Composites Part B: Engineering, 114, pp. 34- 45 (2017). 53. Mercan, K., Numanoglu, H., Akgoz, B., et al. Higher-order continuum theories for buckling response of silicon carbide nanowires (SiCNWs) on elastic matrix", Archive of Applied Mechanics, 87(11), pp. 1797-1814 (2017). 54. Xu, H., Wang, Q., Fan, G.H., et al. Theoretical study of boron nitride nanotubes as drug delivery vehicles of some anticancer drugs", Theor Chem Acc, 137(7), pp. 1-15 (2018). 55. Niskanen, J., Zhang, I., Xue, Y.M., et al. Boron nitride nanotubes as vehicles for intracellular delivery of uorescent drugs and probes", Nanomedicine-Uk, 11(5), pp. 447-463 (2016). 56. Ferreira, T.H., Faria, J.A.Q.A., Gonzalez, I.J., et al. BNNT/Fe3O4 system as an e_cient tool for magnetohyperthermia therapy", J Nanosci Nanotechno, 18(10), pp. 6746-6755 (2018). 57. Srivastava, P., Sharma, V., and Jaiswal, N.K. Adsorption of COCl2 gas molecule on armchair boron nitride nanoribbons for nano sensor applications", Microelectron Eng, 146, pp. 62-67 (2015). 58. Song, J.X., Liu, H.X., and Shen, W.J. Dependence of electronic structures of multi-walled boron nitride nanotubes on layer numbers", Eur Phys J D, 72(10), pp. 1-8 (2018). 59. Schulz, M., Shanov, V., and Yin, Z., Nanotube Super_ber Materials: Changing Engineering Design, William Andrew (2013). 60. Zhou, M., Lu, Y.-H., Cai, Y.-Q., et al. Adsorption of gas molecules on transition metal embedded graphene: a search for high-performance graphene-based catalysts and gas sensors", Nanotechnol, 22(38), p. 385502 (2011). 61. Feng, J.-W., Liu, Y.-J., Wang, H.-X., et al. Gas adsorption on silicene: a theoretical study", Comp Mater Sci, 87, pp. 218-226 (2014). 62. Wu, R., Yang, M., Lu, Y., et al. Silicon carbide nanotubes as potential gas sensors for CO and HCN detection", J Phys Chem C, 112(41), pp. 15985- 15988 (2008). 63. Huang, J. and Wan, Q. Gas sensors based on semiconducting metal oxide one-dimensional nanostructures", Sensors, 9(12), pp. 9903-9924 (2009). 64. Akgoz, B. and Civalek, O. A new trigonometric beam model for buckling of strain gradient microbeams", Int J Mech Sci, 81, pp. 88-94 (2014). 65. Gurses, M., Akgoz, B., and Civalek, O. Mathematical modeling of vibration problem of nano-sized annular sector plates using the nonlocal continuum theory via eight-node discrete singular convolution transformation", Appl Math Comput, 219(6), pp. 3226-3240 (2012). 2098 H.M. Numano_glu et al./Scientia Iranica, Transactions A: Civil Engineering 26 (2019) 2079{2099 66. Civalek, O. and Akgoz, B. Free vibration analysis of microtubules as cytoskeleton components: non local Euler-Bernoulli beam modeling", Sci Iran Trans B, 17(5), pp. 367-375 (2010). 67. Mercan, K. A comparative buckling analysis of silicon carbide nanotube and boron nitride nanotube", Int J Eng Appl Sci, 8(4), pp. 99-107 (2016). 68. Mercan, K. and Civalek, O. Buckling analysis of Silicon carbide nanotubes (SiCNTs) with surface e_ect and nonlocal elasticity using the method of HDQ", Compos Part B-Eng, 114, pp. 35-45 (2017). 69. 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). 70. Kiani, K. Nonlocal Timoshenko beam for vibrations of magnetically a_ected inclined single-walled carbon nanotubes as nanouidic conveyors", Acta Phys Pol A, 131(6), pp. 1439-1444 (2017). 71. Jiang, J.N. and Wang, L.F. Timoshenko beam model for vibrational analysis of double-walled carbon nanotubes bridged on substrate", Curr Appl Phys, 17(12), pp. 1670-1690 (2017). 72. Demir, C., Mercan, K., Numanoglu, H.M., et al. Bending response of nanobeams resting on elastic foundation", Journal of Applied and Computational Mechanics, 4(2), pp. 105-114 (2018). 73. Avcar, M. and Mohammed, W.K.M. Free vibration of functionally graded beams resting on Winkler- Pasternak foundation", Arab J Geosci, 11(10), pp. 1-8 (2018). 74. Civalek, O. The determination of frequencies of laminated conical shells via the discrete singular convolution method", J Mech Mater Struct, 1(1), pp. 163-182 (2006). 75. Civalek, O. and Akgoz, B. Vibration analysis of micro-scaled sector shaped graphene surrounded by an elastic matrix", Comp Mater Sci, 77, pp. 295-303 (2013). 76. Baltacioglu, A.K., Civalek, O., Akgoz, B., et al. Large deection analysis of laminated composite plates resting on nonlinear elastic foundations by the method of discrete singular convolution", Int J Pres Ves Pip, 88(8-9), pp. 290-300 (2011). 77. Baltacioglu, A.K., Akgoz, B., and Civalek, O. Nonlinear static response of laminated composite plates by discrete singular convolution method", Compos Struct, 93(1), pp. 153-161 (2010). 78. Avcar, M. E_ects of material non-homogeneity and two parameter elastic foundation on fundamental frequency parameters of Timoshenko beams", Acta Phys Pol A, 130(1), pp. 375-378 (2016). 79. Avcar, M. E_ects of rotary inertia shear deformation and non-homogeneity on frequencies of beam", Struct Eng Mech, 55(4), pp. 871-884 (2015). 80. Fleck, N. and Hutchinson, J. Strain gradient plasticity", Adv Appl Mech, 33, pp. 296-361 (1997). 81. Yang, F., Chong, A., Lam, D.C., et al. Couple stress based strain gradient theory for elasticity", Int J Solids Struct, 39(10), pp. 2731-2743 (2002). 82. Ma, H., Gao, X.-L., and Reddy, J. A microstructuredependent Timoshenko beam model based on a modi_ed couple stress theory", J Mech Phys Solids, 56(12), pp. 3379-3391 (2008). 83. Reddy, J. Microstructure-dependent couple stress theories of functionally graded beams", J Mech Phys Solids, 59(11), pp. 2382-2399 (2011). 84. Zhou, S. and Li, Z. Length scales in the static and dynamic torsion of a circular cylindrical micro-bar", J Shandong Univ Technol, 31(5), pp. 401-407 (2001). 85. 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 Nanos, 8(9), pp. 1821-1827 (2011). 86. Akgoz, B. and Civalek,  O. Longitudinal vibration analysis for microbars based on strain gradient elasticity theory", J Vib Control, 20(4), pp. 606-616 (2014). 87. Akgoz, B. and Civalek,  O. Shear deformation beam models for functionally graded microbeams with new shear correction factors", Compos Struct, 112, pp. 214-225 (2014). 88. Asghari, M., Kahrobaiyan, M., and Ahmadian, M. A nonlinear Timoshenko beam formulation based on the modi_ed couple stress theory", Int J Eng Sci, 48(12), pp. 1749-1761 (2010). 89. Eringen, A.C. On di_erential equations of nonlocal elasticity and solutions of screw dislocation and surface waves", J Appl Phys, 54(9), pp. 4703-4710 (1983). 90. Eringen, A.C., Nonlocal Continuum Field Theories, Springer Science & Business Media (2002). 91. Dingreville, R., Qu, J., and Cherkaoui, M. Surface free energy and its e_ect on the elastic behavior of nano-sized particles, wires and _lms", J Mech Phys Solids, 53(8), pp. 1827-1854 (2005). 92. Mercan, K. and Civalek,  O. Buckling Analysis of Silicon Carbide Nanotubes (SiCNTs)", International Journal of Engineering & Applied Sciences (IJEAS), 8(2), pp. 101-108 (2016). 93. Rahmani, O., Asemani, S., and Hosseini, S. Study the surface e_ect on the buckling of nanowires embedded in Winkler-Pasternak elastic medium based on a nonlocal theory", J Nanostructures, 6(1), pp. 90-95 (2016). 94. Sharma, P. and Ganti, S. Size-dependent Eshelby's tensor for embedded nano-inclusions incorporating surface/interface energies", J Appl Mech, 71(5), pp. 663-671 (2004). H.M. Numano_glu et al./Scientia Iranica, Transactions A: Civil Engineering 26 (2019) 2079{2099 2099 95. Sharma, P., Ganti, S., and Bhate, N. E_ect of surfaces on the size-dependent elastic state of nanoinhomogeneities", Appl Phys Lett, 82(4), pp. 535-537 (2003). 96. Ansari, R., Rouhi, S., Aryayi, M., et al. On the buckling behavior of single-walled silicon carbide nanotubes", Sci Iran, 19(6), pp. 1984-1990 (2012). 97. Arani, A.G. and Hashemian, M. Surface stress e_ects on dynamic stability of double-walled boron nitride nanotubes conveying viscose uid based on nonlocal shell theory", Sci Iran, 20(6), pp. 2356-2374 (2013). 98. Saljooghi, R., Ahmadiana, M.T., and Farrahi, G.H. Vibration and buckling analysis of functionally graded beams using reproducing kernel particle method", Sci Iran, 21(6), pp. 1896-1906 (2014). 99. Darvizeh, M., Darvizeh, A., Ansari, R., et al. Preand post-buckling analysis of functionally graded beams subjected to statically mechanical and thermal loads", Sci Iran, 22(3), pp. 778-791 (2015). 100. Shooshtari, A. and Dalir, M.A. Nonlinear free vibration analysis of clamped circular _ber metal laminated plates", Sci Iran, 22(3), pp. 813-824 (2015). 101. Ansari, R. and Gholami, R. Nonlocal nonlinear _rst-order shear deformable beam model for postbuckling analysis of magneto-electro-thermo-elastic nanobeams", Sci Iran, 23(6), pp. 3099-3114 (2016). 102. Rouzegar, J. and Sharifpoor, R.A. Finite element formulations for free vibration analysis of isotropic and orthotropic plates using two-variable re_ned plate theory", Sci Iran, 23(4), pp. 1787-1799 (2016). 103. 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", Sci Iran, 24(3), pp. 1635-1653 (2017). 104. Jabbarian, S. and Ahmadian, M.T. Free vibration analysis of functionally graded sti_ened microcylinder based on the modi_ed couple stress theory", Sci Iran, 25(5), pp. 2598-2615 (2018). 105. Sahoo, S.S., Hirwani, C.K., Panda, S.K., et al. Numerical analysis of vibration and transient behaviour of laminated composite curved shallow shell structure: An experimental validation", Sci Iran, 25(4), pp. 2218-2232 (2018). 106. COMSOL Multiphysics® v. 5.2. COMSOL AB, Stockholm, Sweden. 107. ANSYS® Academic Research Mechanical. 108. Jalan, S.K., Rao, B.N., and Gopalakrishnan, S. Vibrational characteristics of zigzag, armchair and chiral cantilever single-walled carbon nanotubes", Adv Compos Lett, 22(6), pp. 131-142 (2013). 109. Gurtin, M.E. and Murdoch, A.I. A continuum theory of elastic material surfaces", Archive for Rational Mechanics and Analysis, 57(4), pp. 291-323 (1975). 110. Gurtin, M.E. and Murdoch, A.I. Surface Stress in Solids", Int J Solids Struct, 14(6), pp. 431-440 (1978). 111. 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). 112. Naidu, N. and Rao, G. Vibrations of initially stressed uniform beams on a two-parameter elastic foundation", Comp Struct, 57(5), pp. 941-943 (1995).