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http://dx.doi.org/10.12989/anr.2022.13.6.545

Conventional problem solving on the linear and nonlinear buckling of truncated conical functionally graded imperfect micro-tubes  

Linyun, Zhou (School of Transportation, Southeast University)
Publication Information
Advances in nano research / v.13, no.6, 2022 , pp. 545-559 More about this Journal
Abstract
This paper studies the buckling response of nonuniform functionally graded micro-sized tubes according to the high-order tube theory (HOTT) and classical beam theory (CBT) in addition to nonlocal strain gradient theory. The microtube is made of axially functionally graded material (AFGM). Both inner and outer tube radiuses are changed along the tube length; the microtube is the truncated conical type of tube. The nonlinear partial differential (PD) the formulations are obtained on the basis of the energy conservation method. Then, the linear and nonlinear results are computed via a powerful numerical approach. Finally, the impact of various parameters on the stability of axially functionally graded (AFG) microtube regarding the buckling analysis is discussed.
Keywords
buckling analysis; functionally graded materials; microstructure; nonuniform tubes; stability analysis;
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Times Cited By KSCI : 15  (Citation Analysis)
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84 Habibi, M., Mohammadi, A., Safarpour, H., Shavalipour, A. and Ghadiri, M. (2019d), "Wave propagation analysis of the laminated cylindrical nanoshell coupled with a piezoelectric actuator", Mech. Based Des. Struct., 1-19. https://doi.org/10.1080/15397734.2019.1697932.   DOI
85 Habibi, M., Safarpour, M. and Safarpour, H. (2020), "Vibrational characteristics of a FG-GPLRC viscoelastic thick annular plate using fourth-order Runge-Kutta and GDQ methods", Mech. Based Des. Struct., 1-22. https://doi.org/10.1080/15397734.2020.1779086.   DOI
86 Al-Furjan, M., Fereidouni, M., Sedghiyan, D., Habibi, M. and won Jung, D. (2020c), "Three-dimensional frequency response of the CNT-Carbon-Fiber reinforced laminated circular/annular plates under initially stresses", Compos. Struct., 113146. https://doi.org/10.1016/j.compstruct.2020.113146.   DOI
87 Adamian, A., Safari, K.H., Sheikholeslami, M., Habibi, M., AlFurjan, M. and Chen, G. (2020), "Critical temperature and frequency characteristics of GPLs-reinforced composite doubly curved panel", Appl. Sci., 10(9), 3251. https://doi.org/10.3390/app10093251.   DOI
88 Al-Furjan, M., Dehini, R., Khorami, M., Habibi, M. and won Jung, D. (2020a), "On the dynamics of the ultra-fast rotating cantilever orthotropic piezoelectric nanodisk based on nonlocal strain gradient theory", Compos. Struct., 112990. https://doi.org/10.1016/j.compstruct.2020.112990.   DOI
89 Al-Furjan, M., Fereidouni, M., Habibi, M., Abd Ali, R., Ni, J. and Safarpour, M. (2020b), "Influence of in-plane loading on the vibrations of the fully symmetric mechanical systems via dynamic simulation and generalized differential quadrature framework", Eng. Comput., 1-23. https://doi.org/10.1007/s00366-020-01177-7.   DOI
90 Liu, H., Shen, S., Oslub, K., Habibi, M. and Safarpour, H. (2021b), "Amplitude motion and frequency simulation of a composite viscoelastic microsystem within modified couple stress elasticity", Eng. Comput., 1-15. https://doi.org/10.1007/s00366-021-01316-8.   DOI
91 Liu, S., Sai, Q., Wang, S. and Williams, J. (2022), "Effects of laser surface texturing and lubrication on the vibrational and tribological performance of sliding contact", Lubricants, 10(1). https://doi.org/10.3390/lubricants10010010.   DOI
92 Liu, Y., Wang, W., He, T., Moradi, Z. and Larco Benitez, M.A. (2021c), "On the modelling of the vibration behaviors via discrete singular convolution method for a high-order sector annular system", Eng. Comput., 1-23. https://doi.org/10.1007/s00366-021-01454-z.   DOI
93 Ebrahimi, F., Hashemabadi, D., Habibi, M. and Safarpour, H. (2020a), "Thermal buckling and forced vibration characteristics of a porous GNP reinforced nanocomposite cylindrical shell", Microsyst. Technol., 26(2), 461-473. https://doi.org/10.1007/s00542-019-04542-9.   DOI
94 Roudbari, M.A. and Ansari, R. (2020), "Single-walled boron nitride nanotube as nano-sensor", Continuum Mech. Thermodyn., 32(3), 729-748. https://doi.org/10.1007/s00161-018-0719-6.   DOI
95 Roudbari, M.A. and Doroudgar Jorshari, T. (2018), "Vibrational control scrutiny of physically affected SWCNT acted upon by a moving nanoparticle in the framework of nonlocal-strain gradient theory", J. Brazil. Soc. Mech. Sci. Eng., 40(10), 499. https://doi.org/10.1007/s40430-018-1421-0.   DOI
96 Ebrahimi, F., Hajilak, Z.E., Habibi, M. and Safarpour, H. (2019b), "Buckling and vibration characteristics of a carbon nanotubereinforced spinning cantilever cylindrical 3D shell conveying viscous fluid flow and carrying spring-mass systems under various temperature distributions", Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science. 233(13), 4590-4605. https://doi.org/10.1177/0954406219832323.   DOI
97 Ebrahimi, F., Mohammadi, K., Barouti, M.M. and Habibi, M. (2019c), "Wave propagation analysis of a spinning porous graphene nanoplatelet-reinforced nanoshell", Waves Random Complex Med., 1-27. https://doi.org/10.1080/17455030.2019.1694729.   DOI
98 Ebrahimi, F. and Shafiei, N. (2016), "Application of Eringen's nonlocal elasticity theory for vibration analysis of rotating functionally graded nanobeams", Smart Struct. Syst., 17(5), 837-857. https://doi.org/10.12989/sss.2016.17.5.837.   DOI
99 Ebrahimi, F. and Shafiei, N. (2017), "Influence of initial shear stress on the vibration behavior of single-layered graphene sheets embedded in an elastic medium based on Reddy's higherorder shear deformation plate theory", Mech. Adv. Mater. Struct., 24(9), 761-772. https://doi.org/10.1080/15376494.2016.1196781.   DOI
100 Habibi, M., Hashemi, R., Sadeghi, E., Fazaeli, A., Ghazanfari, A. and Lashini, H. (2016), "Enhancing the mechanical properties and formability of low carbon steel with dual-phase microstructures", J. Mater. Eng. Perform., 25(2), 382-389. https://doi.org/10.1007/s11665-016-1882-1.   DOI
101 Habibi, M., Taghdir, A. and Safarpour, H. (2019e), "Stability analysis of an electrically cylindrical nanoshell reinforced with graphene nanoplatelets", Compos. Part B Eng., 175, 107125. https://doi.org/10.1016/j.compositesb.2019.107125.   DOI
102 Shafiei, N., Kazemi, M. and Ghadiri, M. (2016c), "Nonlinear vibration of axially functionally graded tapered microbeams", Int. J. Eng. Sci., 102, 12-26. https://doi.org/10.1016/j.ijengsci.2016.02.007.   DOI
103 Shafiei, N., Kazemi, M. and Ghadiri, M. (2016d), "On sizedependent vibration of rotary axially functionally graded microbeam", Int. J. Eng. Sci., 101, 29-44. https://doi.org/10.1016/j.ijengsci.2015.12.008.   DOI
104 Shafiei, N., Kazemi, M., Safi, M. and Ghadiri, M. (2016e), "Nonlinear vibration of axially functionally graded non-uniform nanobeams", Int. J. Eng. Sci., 106, 77-94. https://doi.org/10.1016/j.ijengsci.2016.05.009.   DOI
105 Shafiei, N., Mirjavadi, S.S., Afshari, B.M., Rabby, S. and Hamouda, A.M.S. (2017c), "Nonlinear thermal buckling of axially functionally graded micro and nanobeams", Compos. Struct., 168, 428-439. https://doi.org/10.1016/j.compstruct.2017.02.048.   DOI
106 Shafiei, N., Mirjavadi, S.S., MohaselAfshari, B., Rabby, S. and Kazemi, M. (2017d), "Vibration of two-dimensional imperfect functionally graded (2D-FG) porous nano-/micro-beams", Comput. Meth. Appl. Mech. Eng., 322, 615-632. https://doi.org/10.1016/j.cma.2017.05.007.   DOI
107 Shafiei, N., Mousavi, A. and Ghadiri, M. (2016f), "On sizedependent nonlinear vibration of porous and imperfect functionally graded tapered microbeams", Int. J. Eng. Sci., 106, 42-56. https://doi.org/10.1016/j.ijengsci.2016.05.007.   DOI
108 Lori, E.S., Ebrahimi, F., Supeni, E.E.B., Habibi, M. and Safarpour, H. (2020), "The critical voltage of a GPL-reinforced composite microdisk covered with piezoelectric layer", Eng. Comput., 1-20. https://doi.org/10.1007/s00366-020-01004-z.   DOI
109 Abo-bakr, R.M., Abo-bakr, H.M., Mohamed, S.A. and Eltaher, M.A. (2021), "Optimal weight for buckling of FG beam under variable axial load using Pareto optimality", Compos. Struct., 258, 113193. https://doi.org/10.1016/j.compstruct.2020.113193.   DOI
110 Hashemi, H.R., Alizadeh, A.a., Oyarhossein, M.A., Shavalipour, A., Makkiabadi, M. and Habibi, M. (2019), "Influence of imperfection on amplitude and resonance frequency of a reinforcement compositionally graded nanostructure", Waves Random Complex Med., 1-27. https://doi.org/10.1080/17455030.2019.1662968.   DOI
111 Ma, L., Liu, X. and Moradi, Z. "On the chaotic behavior of graphene-reinforced annular systems under harmonic excitation", Eng. Comput., 1-25. https://doi.org/10.1007/s00366-020-01210-9.   DOI
112 Mallek, H., Jrad, H., Algahtani, A., Wali, M. and Dammak, F. (2019), "Geometrically non-linear analysis of FG-CNTRC shell structures with surface-bonded piezoelectric layers", Comput. Meth. Appl. Mech. Eng., 347, 679-699. https://doi.org/10.1016/j.cma.2019.01.001.   DOI
113 Mirjavadi, S.S., Afshari, B.M., Shafiei, N., Hamouda, A., Kazemi, M. and Structures, C. (2017a), "Thermal vibration of twodimensional functionally graded (2D-FG) porous Timoshenko nanobeams", Steel Compos. Struct., 25(4), 415-426. https://doi.org/10.12989/scs.2017.25.4.415.   DOI
114 Mirjavadi, S.S., Matin, A., Shafiei, N., Rabby, S. and Mohasel Afshari, B. (2017b), "Thermal buckling behavior of twodimensional imperfect functionally graded microscale-tapered porous beam", J. Therm. Stress., 40(10), 1201-1214. https://doi.org/10.1080/01495739.2017.1332962.   DOI
115 Zare, R., Najaafi, N., Habibi, M., Ebrahimi, F. and Safarpour, H. (2020), "Influence of imperfection on the smart control frequency characteristics of a cylindrical sensor-actuator GPLRC cylindrical shell using a proportional-derivative smart controller", Smart Struct. Syst., 26(4), 469-480. https://doi.org/10.12989/sss.2020.26.4.469.   DOI
116 Zhang, H., Liu, Y. and Deng, Y. (2020a), "Temperature gradient modeling of a steel box-girder suspension bridge using Copulas probabilistic method and field monitoring", Adv. Struct. Eng., 24(5), 947-961. https://doi.org/10.1177/1369433220971779.   DOI
117 Roudbari, M.A., Jorshari, T.D., Arani, A.G., Lu, C. and Rabczuk, T. (2020), "Transient responses of two mutually interacting single-walled boron nitride nanotubes induced by a moving nanoparticle", Eur. J. Mech. A Solids, 82, 103978. https://doi.org/10.1016/j.euromechsol.2020.103978.   DOI
118 Ebrahimi, F., Shafiei, N., Kazemi, M. and Mousavi Abdollahi, S.M. (2017), "Thermo-mechanical vibration analysis of rotating nonlocal nanoplates applying generalized differential quadrature method", Mech. Adv. Mater. Struct., 24(15), 1257-1273. https://doi.org/10.1080/15376494.2016.1227499.   DOI
119 Ebrahimi, F., Supeni, E.E.B., Habibi, M. and Safarpour, H. (2020b), "Frequency characteristics of a GPL-reinforced composite microdisk coupled with a piezoelectric layer", Eur. Phys. J. Plus, 135(2), 144. https://doi.org/10.1140/epjp/s13360-020-00217-x.   DOI
120 Ghazanfari, A., Soleimani, S.S., Keshavarzzadeh, M., Habibi, M., Assempuor, A. and Hashemi, R. (2020), "Prediction of FLD for sheet metal by considering through-thickness shear stresses", Mech. Based Des. Struct., 48(6), 755-772. https://doi.org/10.1080/15397734.2019.1662310.   DOI
121 Roudbari, M.A., Jorshari, T.D., Lu, C., Ansari, R., Kouzani, A.Z. and Amabili, M. (2022), "A review of size-dependent continuum mechanics models for micro- and nano-structures", Thin Wall. Struct., 170, 108562. https://doi.org/10.1016/j.tws.2021.108562.   DOI
122 Rouzegar, J. and Abad, F. (2015), "Free vibration analysis of FG plate with piezoelectric layers using four-variable refined plate theory", Thin Wall. Struct., 89, 76-83. https://doi.org/10.1016/j.tws.2014.12.010.   DOI
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124 Zhao, Y., Moradi, Z., Davoudi, M. and Zhuang, J. "Bending and stress responses of the hybrid axisymmetric system via statespace method and 3D-elasticity theory", Eng. Comput., 1-23. https://doi.org/10.1007/s00366-020-01242-1.   DOI
125 Shafiei, N., Mousavi, A. and Ghadiri, M. (2016g), "Vibration behavior of a rotating non-uniform FG microbeam based on the modified couple stress theory and GDQEM", Compos. Struct., 149, 157-169. https://doi.org/10.1016/j.compstruct.2016.04.024.   DOI
126 Shafiei, N. and She, G.L. (2018), "On vibration of functionally graded nano-tubes in the thermal environment", Int. J. Eng. Sci., 133, 84-98. https://doi.org/10.1016/j.ijengsci.2018.08.004.   DOI
127 Shahverdi, H. and Khalafi, V. (2016), "Bifurcation analysis of FG curved panels under simultaneous aerodynamic and thermal loads in hypersonic flow", Compos. Struct., 146, 84-94. https://doi.org/10.1016/j.compstruct.2016.03.011.   DOI
128 Zhang, X., Shamsodin, M., Wang, H., NoormohammadiArani, O., Khan, A.M., Habibi, M. and Al-Furjan, M. (2020b), "Dynamic information of the time-dependent tobullian biomolecular structure using a high-accuracy size-dependent theory", J. Biomol. Struct. Dyn., 1-16. https://doi.org/10.1080/07391102.2020.1760939.   DOI
129 Zhao, J. and Yu, Z. (2021), "On the modeling and simulation of the nonlinear dynamic response of NEMS via a couple of nonlocal strain gradient theory and classical beam theory", Adv. Nano Res., 11(5), 547-563. https://doi.org/10.12989/anr.2021.11.5.547.   DOI
130 Zhong, Y. and Liang, X. (2022), "Using CNN-VGG 16 to detect the tennis motion tracking by information entropy and unascertained measurement theory", Adv. Nano Res., 12(2), 223-229. https://doi.org/10.12989/anr.2022.12.2.223.   DOI
131 Zhou, J., Bai, J. and Liu, Y. (2022), "Fabrication and modeling of matching system for air-coupled transducer", Micromachines, 13(5). https://doi.org/10.3390/mi13050781.   DOI
132 Al-Furjan, M., Habibi, M., won Jung, D. and Safarpour, H. (2020d), "Vibrational characteristics of a higher-order laminated composite viscoelastic annular microplate via modified couple stress theory", Compos. Struct., 113152. https://doi.org/10.1016/j.compstruct.2020.113152.   DOI
133 Al-Furjan, M., Moghadam, S.A., Dehini, R., Shan, L., Habibi, M. and Safarpour, H. (2020e), "Vibration control of a smart shell reinforced by graphene nanoplatelets under external load: Seminumerical and finite element modeling", Thin Wall. Struct., 107242. https://doi.org/10.1016/j.tws.2020.107242.   DOI
134 Safarpour, M., Ebrahimi, F., Habibi, M. and Safarpour, H. (2020), "On the nonlinear dynamics of a multi-scale hybrid nanocomposite disk", Eng. Comput., 1-20. https://doi.org/10.1007/s00366-020-00949-5.   DOI
135 Safarpour, H., Ghanizadeh, S.A. and Habibi, M. (2018), "Wave propagation characteristics of a cylindrical laminated composite nanoshell in thermal environment based on the nonlocal strain gradient theory", Eur. Phys. J. Plus, 133(12), 532. https://doi.org/10.1140/epjp/i2018-12385-2.   DOI
136 Safarpour, H., Hajilak, Z.E. and Habibi, M. (2019a), "A sizedependent exact theory for thermal buckling, free and forced vibration analysis of temperature dependent FG multilayer GPLRC composite nanostructures restring on elastic foundation", Int. J. Mech. Mater. Des., 15(3), 569-583. https://doi.org/10.1007/s10999-018-9431-8.   DOI
137 Safarpour, H., Pourghader, J. and Habibi, M. (2019b), "Influence of spring-mass systems on frequency behavior and critical voltage of a high-speed rotating cantilever cylindrical threedimensional shell coupled with piezoelectric actuator", J. Vib. Control., 25(9), 1543-1557. https://doi.org/10.1177/1077546319828465.   DOI
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139 Esmailpoor Hajilak, Z., Pourghader, J., Hashemabadi, D., Sharifi Bagh, F., Habibi, M. and Safarpour, H. (2019), "Multilayer GPLRC composite cylindrical nanoshell using modified strain gradient theory", Mech. Based Des. Struct., 47(5), 521-545. https://doi.org/10.1080/15397734.2019.1566743.   DOI
140 Fakher, M., Behdad, S., Naderi, A. and Hosseini-Hashemi, S. (2020), "Thermal vibration and buckling analysis of two-phase nanobeams embedded in size dependent elastic medium", Int. Mech. Sci., 171, 105381. https://doi.org/10.1016/j.ijmecsci.2019.105381.   DOI
141 Ghadiri, M. and Shafiei, N. (2016a), "Nonlinear bending vibration of a rotating nanobeam based on nonlocal Eringen's theory using differential quadrature method", Microsyst. Technol., 22(12), 2853-2867. https://doi.org/10.1007/s00542-015-2662-9.   DOI
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143 Ghadiri, M., Hosseini, S.H.S. and Shafiei, N. (2016a), "A power series for vibration of a rotating nanobeam with considering thermal effect", Mech. Adv. Mater. Struct., 23(12), 1414-1420. https://doi.org/10.1080/15376494.2015.1091527.   DOI
144 Ghadiri, M., Mahinzare, M., Shafiei, N. and Ghorbani, K. (2017a), "On size-dependent thermal buckling and free vibration of circular FG Microplates in thermal environments", Microsyst. Technol., 23(10), 4989-5001. https://doi.org/10.1007/s00542-017-3308-x.   DOI
145 Ghadiri, M. and Shafiei, N. (2016b), "Vibration analysis of a nano-turbine blade based on Eringen nonlocal elasticity applying the differential quadrature method", J. Vib. Control., 23(19), 3247-3265. https://doi.org/10.1177/1077546315627723.   DOI
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147 Ghorbanpour Arani, A., Kolahchi, R. and Zarei, M.S. (2015b), "Visco-surface-nonlocal piezoelasticity effects on nonlinear dynamic stability of graphene sheets integrated with ZnO sensors and actuators using refined zigzag theory", Compos. Struct., 132, 506-526. https://doi.org/10.1016/j.compstruct.2015.05.065.   DOI