Advances in nano research

  • 제10권1호
  • /
  • Pages.15-24
  • /
  • 2021
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  • 2287-237X(pISSN)
  • /
  • 2287-2388(eISSN)
테크노프레스 (Techno-Press)
권호 표지
DOI QR코드

DOI QR Code

The nano scale buckling properties of isolated protein microtubules based on modified strain gradient theory and a new single variable trigonometric beam theory

  • Alwabli, Afaf S. (Department of Biological Sciences, Rabigh College of Science and Arts, King Abdulaziz University) ;
  • Kaci, Abdelhakim (Material and Hydrology Laboratory, University of Sidi Bel Abbes, Faculty of Technology, Civil Engineering Department) ;
  • Bellifa, Hichem (Material and Hydrology Laboratory, University of Sidi Bel Abbes, Faculty of Technology, Civil Engineering Department) ;
  • Bousahla, Abdelmoumen Anis (Laboratoire de Modelisation et Simulation Multi-echelle, Departement de Physique, Faculte des Sciences Exactes, Departement de Physique, Universite de Sidi Bel Abbes) ;
  • Tounsi, Abdelouahed (Department of Civil and Environmental Engineering, King Fahd University of Petroleum & Minerals) ;
  • Alzahrani, Dhafer A. (Department of Biological Sciences, Rabigh College of Science and Arts, King Abdulaziz University) ;
  • Abulfaraj, Aala A. (Department of Biological Sciences, Rabigh College of Science and Arts, King Abdulaziz University) ;
  • Bourada, Fouad (Material and Hydrology Laboratory, University of Sidi Bel Abbes, Faculty of Technology, Civil Engineering Department) ;
  • Benrahou, Kouider Halim (Material and Hydrology Laboratory, University of Sidi Bel Abbes, Faculty of Technology, Civil Engineering Department) ;
  • Tounsi, Abdeldjebbar (Department of Civil and Environmental Engineering, King Fahd University of Petroleum & Minerals) ;
  • Mahmoud, S.R. (King Abdulaziz University, Faculty of Applied Studies, GRC Department) ;
  • Hussain, Muzamal (Department of Mathematics, Govt. College University Faisalabad)
  • 투고 : 2019.11.05
  • 심사 : 2020.10.11
  • 발행 : 2021.01.25
⟨ 이전 논문 다음 논문 ⟩

초록

Microtubules (MTs) are the main part of the cytoskeleton in living eukaryotic cells. In this article, a mechanical model of MT buckling, considering the modified strain gradient theory, is analytically examined. The MT is assumed as a cylindrical beam and a new single variable trigonometric beam theory is developed in conjunction with a modified strain gradient model. The main benefit of the present formulation is shown in its new kinematic where we found only one unknown as the Euler-Bernoulli beam model, which is even less than the Timoshenko beam model. The governing equations are deduced by considering virtual work principle. The effectiveness of the present method is checked by comparing the obtained results with those reported by other higher shear deformation beam theory involving a higher number of unknowns. It is shown that microstructure-dependent response is more important when material length scale parameters are closer to the outer diameter of MTs. Also, it can be confirmed that influences of shear deformation become more considerable for smaller shear modulus and aspect ratios.

키워드

참고문헌

  1. Aifantis, E.C. (1999), "Gradient deformation models at nano, micro and macro scales", J. Eng. Mater. Technol., 121, 189-202. https://doi.org/10.1115/1.2812366.
  2. Akbas, S.D. (2017), "Free vibration of edge cracked functionally graded microscale beams based on the modified couple stress theory", Int. J. Struct. Stabil. Dyn., 17(03), 1750033. https://doi.org/10.1142/S021945541750033X
  3. Akbas, S.D. (2018), "Bending of a cracked functionally graded nanobeam", Adv. Nano Res., Int. J., 6(3), 219-243. https://doi.org/10.12989/anr.2018.6.3.219.
  4. kgoz, B. and Civalek, O. (2011a), "Strain gradient elasticity and modified couple stress models for buckling analysis of axially loaded micro-scaled beams", Int. J. Eng. Sci., 49, 1268-1280. https://doi.org/10.1016/j.ijengsci.2010.12.009.
  5. Akgoz, B. and Civalek, O. (2011b), "Application of strain gradient elasticity theory for buckling analysis of protein microtubules", Curr. Appl. Phys., 11, 1133-1138. https://doi.org/10.1016/j.cap.2011.02.006.
  6. Akgoz, B. and Civalek, O. (2012), "Analysis of micro-sized beams for various boundary conditions based on the strain gradient elasticity theory", Arch. Appl. Mech., 82, 423-443. https://doi.org/10.1007/s00419-011-0565-5.
  7. Akgoz, B. and Civalek, O. (2013), "Longitudinal vibration analysis of strain gradient bars made of functionally graded materials (FGM)", Compos. Part B Eng., 55, 263-268. https://doi.org/10.1016/j.compositesb.2013.06.035.
  8. Akgoz, B. and Civalek, O. (2014a), "Longitudinal vibration analysis for microbars based on strain gradient elasticity theory", J. Vib. Control, 20, 606-616. https://doi.org/10.1177/1077546312463752.
  9. Akgoz, B. and Civalek, O. (2014b), "Mechanical analysis of isolated microtubules based on a higher-order shear deformation beam theory", Compos. Struct., 118, 9-18. https://doi.org/10.1016/j.compstruct.2014.07.029.
  10. Akil, A. (2014), "Post buckling analysis of sandwich beams with functionally graded faces using a consistent higher order theory", Int. J. Civ. Struct. Environ. Infrastruct. Eng. Res. Dev., 4(2), 59-64.
  11. Ansari, R., Gholami, R. and Sahmani, S. (2011), "Free vibration analysis of size-dependent functionally graded microbeams based on the strain gradient Timoshenko beam theory", Compos. Struct., 94, 221-228. https://doi.org/10.1016/j.compstruct.2011.06.024.
  12. Artan, R. and Toksoz, A. (2013), "Stability analysis of gradient elastic beams by the method of initial value", Arch. Appl. Mech., 83, 1129-1144. https://doi.org/10.1007/s00419-013-0739-4.
  13. Asghari, M., Kahrobaiyan, M.H., Nikfar, M. and Ahmadian, M.T. (2012), "A size-dependent nonlinear Timoshenko microbeam model based on the strain gradient theory", Acta. Mech., 223, 1233-1249. https://doi.org/10.1007/s00707-012-0625-0.
  14. Avcar, M. (2019), "Free vibration of imperfect sigmoid and power law functionally graded beams", Steel Compos. Struct., Int. J., 30(6), 603-615. https://doi.org/10.12989/scs.2019.30.6.603.
  15. Batou, B., Nebab, M., Bennai, R., Ait Atmane, H., Tounsi, A. and Bouremana, M. (2019), "Wave dispersion properties in imperfect sigmoid plates using various HSDTs", Steel Compos. Struct., Int. J., 33(5), 699-716. https://doi.org/10.12989/scs.2019.33.5.699.
  16. Bensattalah, T., Bouakkaz, K., Zidour, M. and Daouadji, T.H. (2018), "Critical buckling loads of carbon nanotube embedded in Kerr's medium", Adv. Nano Res., Int. J., 6(4), 339-356. https://doi.org/10.12989/anr.2018.6.4.339.
  17. Bensattalah, T., Zidour, M. and Daouadji, T.H. (2019), "A new nonlocal beam model for free vibration analysis of chiral single-walled carbon nanotubes", Compos. Mater. Eng., 1(1), 21-31. https://doi.org/10.12989/cme.2019.1.1.021.
  18. Bensattalah, T., Hamidi, A., Bouakkaz, K., Zidour, M. and Daouadji, T.H. (2020), "Critical buckling load of triple-walled carbon nanotube based on nonlocal elasticity theory", J. Nano Res., 62, 108-119. https://doi.org/10.4028/www.scientific.net/JNanoR.62.108.
  19. Boulal, A., Bensattalah, T., Karas, A., Zidour, M., Heireche, H. and Adda Bedia, E.A. (2020), "Buckling of carbon nanotube reinforced composite plates supported by Kerr foundation using Hamilton's energy principle", Struct. Eng. Mech., Int. J., 73(2), 209-223. https://doi.org/10.12989/sem.2020.73.2.209.
  20. Civalek, O ., Demir, Ç . and Akgoz, B. (2010), "Free vibration and bending analyses of cantilever microtubules based on nonlocal continuum model", Math Comput. Appl., 15, 289-298. https://doi.org/10.3390/mca15020289.
  21. Daikh, A.A., Drai, A., Houari, M.S.A. and Eltaher, M.A. (2020), "Static analysis of multilayer nonlocal strain gradient nanobeam reinforced by carbon nanotubes", Steel Compos. Struct., Int. J., 36(6), 643-656. http://dx.doi.org/10.12989/scs.2020.36.6.643.
  22. Dash, S., Mehar, K., Sharma, N., Mahapatra, T.R. and Panda, S.K. (2018), "Modal analysis of FG sandwich doubly curved shell structure", Struct. Eng. Mech., Int. J., 68(6), 721-733. http://dx.doi.org/10.12989/sem.2018.68.6.721.
  23. Dash, S., Mehar, K., Sharma, N., Mahapatra, T.R. and Panda, S.K. (2019), "Finite element solution of stress and flexural strength of functionally graded doubly curved sandwich shell panel", Earthq. Struct., Int. J., 16(1), 55-67. http://dx.doi.org/10.12989/eas.2019.16.1.055.
  24. Eltaher, M.A., Fouda, N., El-midany, T. and Sadoun, A.M. (2018), "Modified porosity model in analysis of functionally graded porous nanobeams", J. Braz. Soc. Mech. Sci. Eng., 40(3), 141. http://dx.doi.org/10.1007/s40430-018-1065-0.
  25. Enayat, S., Hashemian, M., Toghraie, D. and Jaberzadeh, E. (2020a), "A comprehensive study for mechanical behavior of functionally graded porous nanobeams resting on elastic foundation", J. Braz. Soc. Mech. Sci. Eng., 42, 420. https://doi.org/10.1007/s40430-020-02474-4.
  26. Enayat, S., Hashemian, M., Toghraie, D. and Jaberzadeh, E. (2020b), "Bending, buckling and vibration analyses of FG porous nanobeams resting on Pasternak foundation incorporating surface effects", ZAMM, 2020, e202000231. https://doi.org/10.1002/zamm.202000231.
  27. Eringen, A.C. (1967), "Theory of micropolar plates", Z. Angew. Math. Phys., 18, 12-30. https://doi.org/10.1007/BF01593891.
  28. Eringen, A.C. (1972), "Nonlocal polar elastic continua", Int. J. Eng. Sci., 10, 1-16. https://doi.org/10.1016/0020-7225(72)90070-5.
  29. Eringen, A.C. (1983), "On differential equations of nonlocal elasticity and solutions of screw dislocation and surface waves", J. Appl. Phys., 54, 4703-4710. https://doi.org/10.1063/1.332803.
  30. Fakhar, A. and Kolahchi, R. (2018), "Dynamic buckling of magneto rheological fluid integrated by visco-piezo-GPL reinforced plates", Int. J. Mech. Sci., 144, 788-799. https://doi.org/10.1016/j.ijmecsci.2018.06.036.
  31. Faleh, N.M., Ahmed, R.A. and Fenjan, R.M. (2018), "On vibrations of porous FG nanoshells", Int. J. Eng. Sci., 133, 1-14. https://doi.org/10.1016/j.ijengsci.2018.08.007.
  32. Fleck, N.A. and Hutchinson, J.W. (1993), "A phenomenological theory for strain gradient effects in plasticity", J. Mech. Phys. Solids, 41, 1825-1857. https://doi.org/10.1016/0022-5096(93)90072-n.
  33. Foroutan, S., Haghshenas, A., Hashemian, M., Eftekhari, S.A. and Toghraie, D. (2018), "Spatial buckling analysis of current-carrying nanowires in the presence of a longitudinal magnetic field accounting for both surface and nonlocal effects", Phys. E Low Dimens. Syst. Nanostruct., 97, 191-205. https://doi.org/10.1016/j.physe.2017.11.015.
  34. Fu, Y. and Zhang, J. (2010), "Modeling and analysis of microtubules based on a modified couple stress theory", Physica E, 42, 1741-1745. https://doi.org/10.1016/j.physe.2010.01.033.
  35. Fygenson, D.K., Marko, J.F. and Libchaber, A. (1997), "Mechanics of microtubule-based membrane extension", Phys. Rev. Lett., 79, 4497-4500. https://doi.org/10.1103/physrevlett.79.4497.
  36. Gafour, Y., Hamidi, A., Benahmed, A., Zidour, M. and Bensattalah, T. (2020), "Porosity-dependent free vibration analysis of FG nanobeam using non-local shear deformation and energy principle", Adv. Nano Res., Int. J., 8(1), 37-47. https://doi.org/10.12989/anr.2020.8.1.037.
  37. Gao, Y. and Lei, F.M. (2009), "Small scale effects on the mechanical behaviors of protein microtubules based on the nonlocal elasticity theory", Biochem. Biophys. Res. Commun., 387, 467-471. https://doi.org/10.1016/j.bbrc.2009.07.042.
  38. Gao, Y. and An, L. (2010), "A nonlocal elastic anisotropic shell model for microtubule buckling behaviors in cytoplasm", Physica E, 42, 2406-2415. https://doi.org/10.1016/j.physe.2010.05.022
  39. Ghayesh, M.H., Amabili, M. and Farokhi, H. (2013), "Nonlinear forced vibrations of a microbeam based on the strain gradient elasticity theory", Int. J. Eng. Sci., 63, 52-60. https://doi.org/10.1016/j.ijengsci.2012.12.001.
  40. Guven, U. (2014), "Love-bishop rod solution based on strain gradient elasticity theory", C. R. Mecanique, 342, 8-16. https://doi.org/10.1016/j.crme.2013.10.011.
  41. Hadipeykani, M., Aghadavoudi, F. and Toghraie, D. (2020), "A molecular dynamics simulation of the glass transition temperature and volumetric thermal expansion coefficient of thermoset polymer based epoxy nanocomposite reinforced by CNT: A statistical study", Physica A, 546, 123995. https://doi.org/10.1016/j.physa.2019.123995.
  42. Hadji, L., Zouatnia, N. and Bernard, F. (2019), "An analytical solution for bending and free vibration responses of functionally graded beams with porosities: Effect of the micromechanical models", Struct. Eng. Mech., Int. J., 69(2), 231-241. https://doi.org/10.12989/sem.2019.69.2.231.
  43. Hashemian, M., Foroutan, S. and Toghraie, D. (2019b), "Comprehensive beam models for buckling and bending behavior of simple nanobeam based on nonlocal strain gradient theory and surface effects", Mech. Mater., 139, 103209. https://doi.org/10.1016/j.mechmat.2019.103209.
  44. Hashemian, M., Vaez, A.H. and Toghraie, D. (2019a), "Investigation of viscous fluid flow and dynamic stability of CNTs subjected to axial harmonic load coupled using Bolotin's method", Int. J. Num. Methods Heat Fluid Flow, 30(6), 3435-3462. https://doi.org/10.1108/HFF-12-2018-0739.
  45. Hashemian, M., Falsafioon, M., Pirmoradian, M. and Toghraie, D. (2020), "Nonlocal dynamic stability analysis of a Timoshenko nanobeam subjected to a sequence of moving nanoparticles considering surface effects", Mech. Mater., 148, 103452. https://doi.org/10.1016/j.mechmat.2020.103452.
  46. Heireche, H., Tounsi, A., Benhassaini, H., Benzair, A., Bendahmane, M., Missouri, M. and Mokadem, S. (2010), "Nonlocal elasticity effect on vibration characteristics of protein microtubules", Physica E, 42, 2375-2379. https://doi.org/10.1016/j.physe.2010.05.017.
  47. Hussain, M. and Naeem, M.N. (2019), "Effects of ring supports on vibration of armchair and zigzag FGM rotating carbon nanotubes using Galerkin's method", Compos. Part B Eng., 163, 548-561. https://doi.org/10.1016/j.compositesb.2018.12.144.
  48. Kahrobaiyan, M.H., Tajalli, S.A., Movahhedy, M.R., Akbari, J., Ahmadian, M.T. (2011a), "Torsion of strain gradient bars", Int. J. Eng. Sci., 49, 856-866. https://doi.org/10.1016/j.ijengsci.2011.04.008.
  49. Kahrobaiyan, M.H., Asghari, M., Rahaeifard, M. and Ahmadian, M.T. (2011b), "A nonlinear strain gradient beam formulation", Int. J. Eng. Sci., 49, 1256-1267. https://doi.org/10.1016/j.ijengsci.2011.01.006.
  50. Kahrobaiyan, M.H., Rahaeifard, M., Tajalli, S.A. and Ahmadian, M.T. (2012), "A strain gradient functionally graded Euler-Bernoulli beam formulation", Int. J. Eng. Sci., 52, 65-76. https://doi.org/10.1016/j.ijengsci.2011.11.010.
  51. Kahrobaiyan, M.H., Asghari, M. and Ahmadian, M.T. (2013), "Longitudinal behavior of strain gradient bars", Int. J. Eng. Sci., 66, 44-59. https://doi.org/10.1016/j.ijengsci.2013.02.005.
  52. Kar, V.R., Panda, S.K. and Mahapatra, T.R. (2016), "Thermal buckling behaviour of shear deformable functionally graded single/doubly curved shell panel with TD and TID properties", Adv. Mater. Res., Int. J., 5(4), 205-221. http://dx.doi.org/10.12989/amr.2016.5.4.205.
  53. Kar, V.R., Mahapatra, T.R. and Panda, S.K. (2017), "Effect of different temperature load on thermal postbuckling behaviour of functionally graded shallow curved shell panels", Compos. Struct., 160, 1236-1247. https://doi.org/10.1016/j.compstruct.2016.10.125.
  54. Katariya, P.V. and Panda, S.K. (2016), "Thermal buckling and vibration analysis of laminated composite curved shell panel", Aircr. Eng. Aerosp. Technol., 88(1), 97-107. https://doi.org/10.1108/AEAT-11-2013-0202.
  55. Katariya, P.V., Panda, S.K., Hirwani, C.K., Mehar, K. and Thakare, O. (2017a), "Enhancement of thermal buckling strength of laminated sandwich composite panel structure embedded with shape memory alloy fibre", Smart Struct. Syst., Int. J., 20(5), 595-605. http://dx.doi.org/10.12989/sss.2017.20.5.595.
  56. Katariya, P.V., Panda, S.K. and Mahapatra, T.R. (2017b), "Nonlinear thermal buckling behaviour of laminated composite panel structure including the stretching effect and higher-order finite element", Adv. Mater. Res., Int. J., 6(4), 349-361. http://dx.doi.org/10.12989/amr.2017.6.4.349.
  57. Khabaz, M.K., Eftekhari, S.A., Hashemian, M. and Toghraie, D. (2020), "Optimal vibration control of multi-layer micro-beams actuated by piezoelectric layer based on modified couple stress and surface stress elasticity theories", Physica A, 546, 123998. https://doi.org/10.1016/j.physa.2019.123998.
  58. Kiani, F., Hekmatifar, M. and Toghraie, D. (2020), "Analysis of forced and free vibrations of composite porous core sandwich cylindrical shells and FG-CNTs reinforced face sheets resting on visco-Pasternak foundation under uniform thermal field", J. Braz. Soc. Mech. Sci. Eng., 42, 504. https://doi.org/10.1007/s40430-020-02591-0.
  59. Koiter, W.T. (1964), "Couple-stresses in the theory of elasticity: I and II", Proc. K Ned. Akad. Wet B, 67, 17-44.
  60. Kurachi, M., Hoshi, M. and Tashiro, H. (1995), "Buckling of a single microtubule by optical trapping forces - direct measurement of microtubule rigidity", Cell Motil. Cytoskeleton, 30, 221-228. https://doi.org/10.1002/cm.970300306.
  61. Lam, D.C.C., Yang, F., Chong, A.C.M., Wang, J. and Tong, P. (2003), "Experiments and theory in strain gradient elasticity", J. Mech. Phys. Solids, 51, 1477-1508. https://doi.org/10.1016/s0022-5096(03)00053-x.
  62. Lata, P. and Singh, S. (2019), "Effect of nonlocal parameter on nonlocal thermoelastic solid due to inclined load", Steel Compos. Struct., Int. J., 33(1), 123-131. https://doi.org/10.12989/scs.2019.33.1.123.
  63. Lei, J., He, Y., Zhang, B., Gan, Z. and Zeng, P. (2013), "Bending and vibration of functionally graded sinusoidal microbeams based on the strain gradient elasticity theory", Int. J Eng. Sci., 72, 36-52. https://doi.org/10.1016/j.ijengsci.2013.06.012.
  64. McFarland, A.W. and Colton, J.S. (2005), "Role of material microstructure in plate stiffness with relevance to microcantilever sensors", J. Micromech. Microeng., 15(5), 1060-1067. https://doi.org/10.1088/0960-1317/15/5/024.
  65. Mehar, K. and Panda, S.K. (2019), "Multiscale modeling approach for thermal buckling analysis of nanocomposite curved structure", Adv. Nano Res., Int. J., 7(3), 181-190. http://dx.doi.org/10.12989/anr.2019.7.3.181.
  66. Mehar, K., Mahapatra, T.R., Panda, S.K., Katariya, P.V. and Tompe, U.K. (2018), "Finite-element solution to nonlocal elasticity and scale effect on frequency behavior of shear deformable nanoplate structure", J. Eng. Mech., 144(9), 04018094. https://doi.org/10.1061/(ASCE)EM.1943-7889.0001519.
  67. Mehar, K., Panda, S.K., Devarajan, Y. and Choubey, G. (2019), "Numerical buckling analysis of graded CNT-reinforced composite sandwich shell structure under thermal loading", Compos. Struct., 216, 406-414. https://doi.org/10.1016/j.compstruct.2019.03.002.
  68. Merzoug, M., Bourada, M., Sekkal, M., Ali Chaibdra, A., Belmokhtar, C., Benyoucef, S. and Benachour, A. (2020), "2D and quasi 3D computational models for thermoelastic bending of FG beams on variable elastic foundation: Effect of the micromechanical models", Geomech. Eng., Int. J., 22(4), 361-374. https://doi.org/10.12989/gae.2020.22.4.361.
  69. Merzouki, T., Houari, M.S.A., Haboussi, M., Bessaim, A. and Ganapathi, M. (2020), "Nonlocal strain gradient finite element analysis of nanobeams using two-variable trigonometric shear deformation theory", Eng. Comput., 2020, 1-19. https://doi.org/10.1007/s00366-020-01156-y.
  70. Mindlin, R.D. and Tiersten, H.F. (1962), "Effects of couplestresses in linear elasticit", Arch. Ration Mech. Anal., 11, 415-448. https://doi.org/10.1007/BF00253946
  71. Mirkalantari, S.A., Hashemian, M., Eftekhari, S.A. and Toghraie, D. (2017), "Pull-in instability analysis of rectangular nanoplate based on strain gradient theory considering surface stress effects", Physica B Condens. Matter, 519, 1-14. https://doi.org/10.1016/j.physb.2017.05.028.
  72. Narendar, S., Ravinder, S. and Gopalakrishnan, S. (2012), "Strain gradient torsional vibration analysis of micro/nano rods", Int. J. Nano Dimens., 3, 1-17. https://doi.org/10.7508/IJND.2012.01.001.
  73. Nebab, M., Ait Atmane, H., Bennai, R. and Tahar, B. (2019), "Effect of nonlinear elastic foundations on dynamic behavior of FG plates using four-unknown plate theory", Earthq. Struct., Int. J., 17(5), 447-462. https://doi.org/10.12989/eas.2019.17.5.447.
  74. Nebab, M., Benguediab, S., Ait Atmane, H. and Bernard, F. (2020), A simple quasi-3D HDST for dynamic behavior of advanced composite plates with the effect of variables elastic foundations, Geomech. Eng., Int. J., 22(5), 415-431. http://dx.doi.org/10.12989/gae.2020.22.5.415.
  75. Odde, D.J., Ma, L., Briggs, A.H., DeMarco, A. and Kirschner, M.W. (1999), "Microtubule bending and breaking in living fibroblast cells", J. Cell Sci., 112, 3283-3288. https://doi.org/10.1242/jcs.112.19.3283
  76. Oveissi, S., Toghraie, D. and Eftekhari, S.A. (2016a), "Longitudinal vibration and stability analysis of carbon nanotubes conveying viscous fluid", Physica E Low Dimens. Syst. Nanostruct., 83, 275-283. https://doi.org/10.1016/j.physe.2016.05.004.
  77. Oveissi, S., Eftekhari, S.A. and Toghraie, D. (2016b), "Longitudinal vibration and instabilities of carbon nanotubes conveying fluid considering size effects of nanoflow and nanostructure", Physica E Low Dimens. Syst. Nanostruct., 83, 164-173. https://doi.org/10.1016/j.physe.2016.05.010.
  78. Oveissi, S., Toghraie, D. and Eftekhari, S.A. (2017), "Analysis of transverse vibrational response and instabilities of axially moving cnt conveying fluid", Int. J. Fluid Mech. Res., 44(2), 115-129. https://doi.org/10.1615/InterJFluidMechRes.2017016740.
  79. Oveissi, S., Toghraie, D. and Eftekhari, S.A. (2018), "Investigation on the effect of axially moving carbon nanotube, nanoflow, and knudsen number on the vibrational behavior of the system", Int. J. Fluid Mech. Res., 45(2), 171-186. https://doi.org/10.1615/InterJFluidMechRes.2018021036.
  80. Panda, S.K. and Singh, B.N. (2013), "Nonlinear finite element analysis of thermal post-buckling vibration of laminated composite shell panel embedded with SMA fibre", Aerosp. Sci. Technol., 29(1), 47-57. https://doi.org/10.1016/j.ast.2013.01.007.
  81. Panda, S.K. and Katariya, P.V. (2015), "Stability and free vibration behaviour of laminated composite panels under thermomechanical loading", Int. J. Appl. Comput. Math, 1, 475-490. https://doi.org/10.1007/s40819-015-0035-9
  82. Panjehpour, M., KeeLoh, E.W. and Deepak, T.J. (2018), "Structural insulated panels: State-of-the-art", Trends Civ. Eng. Archit., 3(1) 336-340. https://doi.org/10.32474/TCEIA.2018.03.000151.
  83. Pirmoradian, M., Torkan, E., Abdali, N., Hashemian, M. and Toghraie, D. (2020a), "Thermo-mechanical stability of singlelayered graphene sheets embedded in an elastic medium under action of a moving nanoparticle", Mech. Mater., 141, 103248. https://doi.org/10.1016/j.mechmat.2019.103248.
  84. Pirmoradian, M., Torkan, E. and Toghraie, D. (2020b), "Study on size-dependent vibration and stability of DWCNTs subjected to moving nanoparticles and embedded on two-parameter foundations", Mech. Mater., 142, 103279. https://doi.org/10.1016/j.mechmat.2019.103279.
  85. Pirmoradian, M., Torkan, E., Zali, H., Hashemian, M. and Toghraie, D. (2020c), "Statistical and parametric instability analysis for delivery of nanoparticles through embedded DWCNT", Physica A, 554, 123911. https://doi.org/10.1016/j.physa.2019.123911.
  86. Poole, W.J., Ashby, M.F. and Fleck, N.A. (1996), "Micro-hardness of annealed and work hardened copper polycrystals", Scripta Mater, 34, 559-564. https://doi.org/10.1016/1359-6462(95)00524-2.
  87. Rachedi, M.A., Benyoucef, S., Bouhadra, A. Sekkal, M., Bachir Bouiadjra, R. and Benachour, A. (2020), "Impact of the homogenization models on the thermoelastic response of FG plates on variable elastic foundation", Geomech. Eng., Int. J., 22(1), 65-80. https://doi.org/10.12989/gae.2020.22.1.065.
  88. Safa, A., Hadji, L., Bourada, M. and Zouatnia, N. (2019), "Thermal vibration analysis of FGM beams Using an efficient shear deformation beam theory", Earthq. Struct., Int. J., 17(3), 329-336. https://doi.org/10.12989/eas.2019.17.3.329.
  89. Saffari, S., Hashemian, M. and Toghraie, D. (2017), "Dynamic stability of functionally graded nanobeam based on nonlocal Timoshenko theory considering surface effects", Physica B Condens. Matter, 520, 97-105. https://doi.org/10.1016/j.physb.2017.06.029.
  90. Sahouane, A., Hadji, L. and Bourada, M. (2019), "Numerical analysis for free vibration of functionally graded beams using an original HSDBT", Earthq. Struct., Int. J., 17(1), 31-37. https://doi.org/10.12989/eas.2019.17.1.031.
  91. Selmi, A. and Bisharat, A. (2018), "Free vibration of functionally graded SWNT reinforced aluminum alloy beam", J. Vib. Eng., 20(5), 2151-2164. https://doi.org/10.21595/jve.2018.19445.
  92. Shen, H.S. (2010a), "Nonlocal shear deformable shell model for postbuckling of axially compressed microtubules embedded in an elastic medium", Biomech. Model Mechanobiol., 9, 345-357. https://doi.org/10.1007/s10237-009-0180-3.
  93. Shen, H.S. (2010b), "Buckling and postbuckling of radially loaded microtubules by nonlocal shear deformable shell model", J. Theor. Biol., 264, 386-394. https://doi.org/10.1016/j.jtbi.2010.02.014.
  94. Shen, H.S. (2010c), "Nonlocal shear deformable shell model for bending buckling of microtubules embedded in an elastic medium", Phys. Lett. A, 374, 4030-4039. https://doi.org/10.1016/j.physleta.2010.08.006.
  95. Sourani, P., Hashemian, M., Pirmoradian, M. and Toghraie, D. (2020), "A comparison of the Bolotin and incremental harmonic balance methods in the dynamic stability analysis of an Euler-Bernoulli nanobeam based on the nonlocal strain gradient theory and surface effects", Mech. Mater., 145, 103403. https://doi.org/10.1016/j.mechmat.2020.103403.
  96. Suleiman, O.M.E., Osman, M.Y. and Hassan, T. (2019), "Effect of boundary conditions on buckling load for laminated composite plates", Int. J. Eng. Adv. Res. Technol., 5(1), 1-11.
  97. Tajalli, S.A., Rahaeifard, M., Kahrobaiyan, M.H., Movahhedy, M.R., Akbari, J. and Ahmadian, M.T. (2013), "Mechanical behavior analysis of size-dependent micro-scaled functionally graded Timoshenko beams by strain gradient elasticity theory", Compos. Struct., 102, 72-80. https://doi.org/10.1016/j.compstruct.2013.03.001.
  98. Tayeb, T.S., Zidour, M., Bensattalah, T., Heireche, H., Benahmed, A. and Bedia, E.A. (2020), "Mechanical buckling of FG-CNTs reinforced composite plate with parabolic distribution using Hamilton's energy principle", Adv. Nano Res., Int. J., 8(2), 135-148. https://doi.org/10.12989/anr.2020.8.2.135.
  99. Timesli, A., Braikat, B., Jamal, M. and Damil, N. (2017), "Prediction of the critical buckling load of multi-walled carbon nanotubes under axial compression", Comptes Rendus Mcanique, 345, 158-168. https://doi.org/10.1016/j.crme.2016.12.002.
  100. Toupin, R.A. (1964), "Theory of elasticity with couple stresses", Arch. Ration Mech. Anal., 17, 85-112. https://doi.org/10.1007/BF00253050.
  101. Vardoulakis, I. and Sulem, J. (1995), Bifurcation Analysis in Geomechanics, Blackie/Chapman & Hall, London, UK.
  102. Venier, P., Maggs, A.C., Carlier, M.F. and Pantaloni, D. (1994), "Analysis of microtubule rigidity using hydrodynamic flow and thermal fluctuations", J. Biol. Chem., 269, 13353-13360. https://doi.org/10.1016/S0021-9258(17)36840-0
  103. Wang, B., Zhao, J. and Zhou, S. (2010), "A micro scale Timoshenko beam model based on strain gradient elasticity theory", Eur. J. Mech. A Solids, 29, 591-599. https://doi.org/10.1016/j.euromechsol.2009.12.005.
  104. Yousefzadeh, S., Akbari, A., Najafi, M., Akbari, O.I. and Toghraie, D. (2020), "Analysis of buckling of a multi-layered nanocomposite rectangular plate reinforced by single-walled carbon nanotubes on elastic medium considering nonlocal theory of Eringen and variational approach", Indian J. Phys., 94, 1009-1023. https://doi.org/10.1007/s12648-019-01546-z.
  105. Zhao, J., Zhou, S., Wang, B. and Wang, X. (2012), "Nonlinear microbeam model based on strain gradient theory", Appl. Math Model, 36, 2674-2686. https://doi.org/10.1016/j.apm.2011.09.051.
  106. Zouatnia, N. and Hadji, L. (2019a), "Effect of the micromechanical models on the bending of FGM beam using a new hyperbolic shear deformation theory", Earthq. Struct., Int. J., 16(2), 177-183. https://doi.org/10.12989/eas.2019.16.2.177.
  107. Zouatnia, N. and Hadji, L. (2019b), "Static and free vibration behavior of functionally graded sandwich plates using a simple higher order shear deformation theory", Adv. Mater. Res., Int. J., 8(4), 313-335. https://doi.org/10.12989/amr.2019.8.4.313.

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  1. Mathematical approach for the effect of the rotation, the magnetic field and the initial stress in the non-homogeneous an elastic hollow cylinder vol.79, pp.5, 2021, https://doi.org/10.12989/sem.2021.79.5.593