Advances in nano research

  • 제7권1호
  • /
  • Pages.51-61
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  • 2019
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  • 2287-237X(pISSN)
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  • 2287-2388(eISSN)
테크노프레스 (Techno-Press)
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DOI QR코드

DOI QR Code

Buckling analysis of nanoplate-type temperature-dependent heterogeneous materials

  • Karami, Behrouz (Department of Mechanical Engineering, Marvdasht Branch, Islamic Azad University) ;
  • Karami, Sara (Department of Geology, Shiraz Branch, Islamic Azad University)
  • 투고 : 2018.08.24
  • 심사 : 2019.01.15
  • 발행 : 2019.01.25
⟨ 이전 논문 다음 논문 ⟩

초록

This paper develops a four-unknown refined plate theory and the Galerkin method to investigate the size-dependent stability behavior of functionally graded material (FGM) under the thermal environment and the FGM having temperature-dependent material properties. In the current study two scale coefficients are considered to examine buckling behavior much accurately. Reuss micromechanical scheme is utilized to estimate the material properties of inhomogeneous nano-size plates. Governing differential equations, classical and non-classical boundary conditions are obtained by utilizing Hamiltonian principles. The results showed the high importance of considering temperature-dependent material properties for buckling analysis. Different influencing parametric on the buckling is studied which may help in design guidelines of such complex structures.

키워드

참고문헌

  1. Aissani, K., Bouiadjra, M.B., Ahouel, M. and Tounsi, A. (2015), "A new nonlocal hyperbolic shear deformation theory for nanobeams embedded in an elastic medium", Struct. Eng. Mech., Int. J., 55(4), 743-763. https://doi.org/10.12989/sem.2015.55.4.743
  2. Apuzzo, A., Barretta, R., Luciano, R., de Sciarra, F.M. and Penna, R. (2017), "Free vibrations of Bernoulli-Euler nano-beams by the stress-driven nonlocal integral model", Compos. Part B: Eng., 123, 105-111. https://doi.org/10.1016/j.compositesb.2017.03.057
  3. Arani, A.G., Pourjamshidian, M. and Arefi, M. (2017), "Influence of electro-magneto-thermal environment on the wave propagation analysis of sandwich nano-beam based on nonlocal strain gradient theory and shear deformation theories", Smart Struct. Syst., Int. J., 20(3), 329-342.
  4. Askes, H. and Aifantis, E.C. (2009), "Gradient elasticity and flexural wave dispersion in carbon nanotubes", Phys. Rev. B, 80(19), 195412. https://doi.org/10.1103/PhysRevB.80.195412
  5. Aydogdu, M. and Arda, M. (2016), "Forced vibration of nanorods using nonlocal elasticity", Adv. Nano Res., Int. J., 4(4), 265-279. https://doi.org/10.12989/anr.2016.4.4.265
  6. Barati, M.R. (2017), "Nonlocal-strain gradient forced vibration analysis of metal foam nanoplates with uniform and graded porosities", Adv. Nano Res., Int. J., 5(4), 393-414. https://doi.org/10.21474/IJAR01/4731
  7. Barati, M.R. (2018), "A general nonlocal stress-strain gradient theory for forced vibration analysis of heterogeneous porous nanoplates", Eur. J. Mech.-A/Solids, 67, 215-230. https://doi.org/10.1016/j.euromechsol.2017.09.001
  8. Barretta, R. and de Sciarra, F.M. (2018), "Constitutive boundary conditions for nonlocal strain gradient elastic nano-beams", Int. J. Eng. Sci., 130, 187-198. https://doi.org/10.1016/j.ijengsci.2018.05.009
  9. Barretta, R., Faghidian, S.A., Luciano, R., Medaglia, C. and Penna, R. (2018a), "Free vibrations of FG elastic Timoshenko nano-beams by strain gradient and stress-driven nonlocal models", Compos. Part B: Eng., 154, 20-32. https://doi.org/10.1016/j.compositesb.2018.07.036
  10. Barretta, R., Luciano, R., de Sciarra, F.M. and Ruta, G. (2018b), "Stress-driven nonlocal integral model for Timoshenko elastic nano-beams", Eur. J. Mech.-A/Solids.
  11. Barzoki, A.A.M., Loghman, A. and Arani, A.G. (2015), "Temperature-dependent nonlocal nonlinear buckling analysis of functionally graded SWCNT-reinforced microplates embedded in an orthotropic elastomeric medium", Struct. Eng. Mech., Int. J., 53(3), 497-517. https://doi.org/10.12989/sem.2015.53.3.497
  12. Bensaid, I. (2017), "Arefined nonlocal hyperbolic shear deformation beam model for bending and dynamic analysis of nanoscale beams", Adv. Nano Res., Int. J., 5(2), 113-126. https://doi.org/10.21474/IJAR01/3121
  13. Bensaid, I. and Bekhadda, A. (2018), "Thermal stability analysis of temperature dependent inhomogeneous size-dependent nanoscale beams", Adv. Mater. Res., Int. J., 7(1), 363-378.
  14. Bensaid, I. and Guenanou, A. (2017), "Bending and stability analysis of size-dependent compositionally graded Timoshenko nanobeams with porosities", Adv. Mater., Res., Int. J., 6(1), 45-63.
  15. Bensaid, I. and Kerboua, B. (2017), "Interfacial stress analysis of functionally graded beams strengthened with a bonded hygrothermal aged composite plate", Compos. Interf., 24(2), 149-169. https://doi.org/10.1080/09276440.2016.1196333
  16. Bensaid, I., Cheikh, A., Mangouchi, A. and Kerboua, B. (2017), "Static deflection and dynamic behavior of higher-order hyperbolic shear deformable compositionally graded beams", Adv. Mater Res., Int. J., 6(1), 13-26.
  17. Bensaid, I., Bekhadda, A. and Kerboua, B. (2018a), "Dynamic analysis of higher order shear-deformable nanobeams resting on elastic foundation based on nonlocal strain gradient theory", Adv. Nano Res., Int. J., 6(3), 279-298.
  18. Bensaid, I., bekhadda, A., Kerboua, B. and Abdelmadjid, C. (2018b), "Investigating nonlinear thermal stability response of functionally graded plates using a new and simple HSDT", Wind Struct., Int. J., 27(6), 369.380.
  19. Chamkha, A.J., Molana, M., Rahnama, A. and Ghadami, F. (2018), "On the nanofluids applications in microchannels: a comprehensive review", Powder Technology.
  20. Damadam, M., Moheimani, R. and Dalir, H. (2018), "Bree's diagram of a functionally graded thick-walled cylinder under thermo-mechanical loading considering nonlinear kinematic hardening", Case Studies Thermal Eng., 12, 644-654. https://doi.org/10.1016/j.csite.2018.08.004
  21. Ebrahimi, F., Barati, M.R. and Dabbagh, A. (2016), "A nonlocal strain gradient theory for wave propagation analysis in temperature-dependent inhomogeneous nanoplates", Int. J. Eng. Sci., 107, 169-182. https://doi.org/10.1016/j.ijengsci.2016.07.008
  22. El-Borgi, S., Rajendran, P., Friswell, M., Trabelssi, M. and Reddy, J. (2018), "Torsional vibration of size-dependent viscoelastic rods using nonlocal strain and velocity gradient theory", Compos. Struct., 186, 274-292. https://doi.org/10.1016/j.compstruct.2017.12.002
  23. Eltaher, M., Khater, M., Park, S., Abdel-Rahman, E. and Yavuz, M. (2016), "On the static stability of nonlocal nanobeams using higher-order beam theories", Adv. Nano. Res., Int. J., 4(1), 51-64.
  24. Farokhi, H. and Ghayesh, M.H. (2015), "Thermo-mechanical dynamics of perfect and imperfect Timoshenko microbeams", Int. J. Eng. Sci., 91, 12-33. https://doi.org/10.1016/j.ijengsci.2015.02.005
  25. Farokhi, H., Ghayesh, M.H. and Amabili, M. (2013), "Nonlinear dynamics of a geometrically imperfect microbeam based on the modified couple stress theory", Int. J. Eng. Sci., 68, 11-23. https://doi.org/10.1016/j.ijengsci.2013.03.001
  26. Ghayesh, M.H. and Farajpour, A. (2018), "Nonlinear mechanics of nanoscale tubes via nonlocal strain gradient theory", Int. J. Eng. Sci., 129, 84-95. https://doi.org/10.1016/j.ijengsci.2018.04.003
  27. Ghayesh, M.H. and Farokhi, H. (2015), "Nonlinear dynamics of microplates", Int. J. Eng. Sci., 86, 60-73. https://doi.org/10.1016/j.ijengsci.2014.10.004
  28. Ghayesh, M.H., Amabili, M. and Farokhi, H. (2013a), "Threedimensional nonlinear size-dependent behaviour of Timoshenko microbeams", Int. J. Eng. Sci., 71, 1-14. https://doi.org/10.1016/j.ijengsci.2013.04.003
  29. Ghayesh, M.H., Farokhi, H. and Amabili, M. (2013b), "Nonlinear dynamics of a microscale beam based on the modified couple stress theory", Compos. Part B: Eng., 50, 318-324. https://doi.org/10.1016/j.compositesb.2013.02.021
  30. Ghayesh, M.H., Farokhi, H. and Amabili, M. (2014), "In-plane and out-of-plane motion characteristics of microbeams with modal interactions", Compos. Part B: Eng., 60, 423-439. https://doi.org/10.1016/j.compositesb.2013.12.074
  31. Gupta, A. and Talha, M. (2017), "Influence of Porosity on the Flexural and Free Vibration Responses of Functionally Graded Plates in Thermal Environment", Int. J. Struct. Stabil. Dyn., 1850013. https://doi.org/10.1142/S021945541850013X
  32. Heydari, A. and Shariati, M. (2018), "Buckling analysis of tapered BDFGM nano-beam under variable axial compression resting on elastic medium", Struct. Eng. Mech., Int. J., 66(6), 737-748.
  33. Houari, M.S.A., Bessaim, A., Bernard, F., Tounsi, A. and Mahmoud, S. (2018), "Buckling analysis of new quasi-3D FG nanobeams based on nonlocal strain gradient elasticity theory and variable length scale parameter", Steel Compos. Struct., Int. J., 28(1), 13-24.
  34. Huang, X.-L. and Shen, H.-S. (2004), "Nonlinear vibration and dynamic response of functionally graded plates in thermal environments", Int. J. Solids Struct., 41(9-10), 2403-2427. https://doi.org/10.1016/j.ijsolstr.2003.11.012
  35. Kant, T. and Swaminathan, K. (2001), "Free vibration of isotropic, orthotropic, and multilayer plates based on higher order refined theories", J. Sound Vib., 241(2), 319-327. https://doi.org/10.1006/jsvi.2000.3232
  36. Kar, V.R. and Panda, S.K. (2015a), "Large deformation bending analysis of functionally graded spherical shell using FEM", Struct. Eng. Mech., Int. J., 53(4), 661-679. https://doi.org/10.12989/sem.2015.53.4.661
  37. Kar, V.R. and Panda, S.K. (2015b), "Nonlinear flexural vibration of shear deformable functionally graded spherical shell panel", Steel Compos. Struct., Int. J., 18(3), 693-709. https://doi.org/10.12989/scs.2015.18.3.693
  38. Karami, B. and Janghorban, M. (2016), "Effect of magnetic field on the wave propagation in nanoplates based on strain gradient theory with one parameter and two-variable refined plate theory", Modern Phys. Lett. B, 30(36), 1650421. https://doi.org/10.1142/S0217984916504212
  39. Karami, B., Janghorban, M. and Tounsi, A. (2017), "Effects of triaxial magnetic field on the anisotropic nanoplates", Steel Compos. Struct., Int. J., 25 (3), 361-374.
  40. Karami, B., Janghorban, M. and Li, L. (2018a), "On guided wave propagation in fully clamped porous functionally graded nanoplates", Acta Astronautica, 143, 380-390. https://doi.org/10.1016/j.actaastro.2017.12.011
  41. Karami, B., Janghorban, M., Shahsavari, D. and Tounsi, A. (2018b), "A size-dependent quasi-3D model for wave dispersion analysis of FG nanoplates", Steel Compos. Struct., Int. J., 28(1), 99-110.
  42. Karami, B., Janghorban, M. and Tounsi, A. (2018c), "Galerkin's approach for buckling analysis of functionally graded anisotropic nanoplates/different boundary conditions", Engineering with Computers.
  43. Karami, B., Janghorban, M. and Tounsi, A. (2018d), "Nonlocal strain gradient 3D elasticity theory for anisotropic spherical nanoparticles", Steel Compos. Struct., Int. J., 27(2), 201-216.
  44. Karami, B., Janghorban, M. and Tounsi, A. (2018e), "Variational approach for wave dispersion in anisotropic doubly-curved nanoshells based on a new nonlocal strain gradient higher order shell theory", Thin-Wall. Struct., 129, 251-264. https://doi.org/10.1016/j.tws.2018.02.025
  45. Karami, B., Shahsavari, D. and Janghorban, M. (2018f), "A comprehensive analytical study on functionally graded carbon nanotube-reinforced composite plates", Aerosp. Sci. Technol., 82, 499-512. https://doi.org/10.1016/j.ast.2018.10.001
  46. Karami, B., Shahsavari, D. and Janghorban, M. (2018g), "Wave propagation analysis in functionally graded (FG) nanoplates under in-plane magnetic field based on nonlocal strain gradient theory and four variable refined plate theory", Mech. Adv. Mater. Struct., 25(12), 1047-1057. https://doi.org/10.1080/15376494.2017.1323143
  47. Karami, B., Shahsavari, D., Janghorban, M. and Li, L. (2018h), "Wave dispersion of mounted graphene with initial stress", Thin-Wall. Struct., 122, 102-111. https://doi.org/10.1016/j.tws.2017.10.004
  48. Karami, B., Shahsavari, D., Karami, M. and Li, L. (2018i), "Hygrothermal wave characteristic of nanobeam-type inhomogeneous materials with porosity under magnetic field", Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science.
  49. Karami, B., Shahsavari, D. and Li, L. (2018j), "Hygrothermal wave propagation in viscoelastic graphene under in-plane magnetic field based on nonlocal strain gradient theory", Physica E: Low-dimensional Syst. Nanostruct., 97, 317-327. https://doi.org/10.1016/j.physe.2017.11.020
  50. Karami, B., Shahsavari, D. and Li, L. (2018k), "Temperaturedependent flexural wave propagation in nanoplate-type porous heterogenous material subjected to in-plane magnetic field", J. Therm. Stress., 41(4), 483-499. https://doi.org/10.1080/01495739.2017.1393781
  51. Karami, B., Shahsavari, D., Nazemosadat, S.M.R., Li, L. and Ebrahimi, A. (2018l), "Thermal buckling of smart porous functionally graded nanobeam rested on Kerr foundation", Steel Compos. Struct., Int. J., 29(3), 349-362.
  52. Karami, B., Shahsavari, D., Janghorban, M., Dimitri, R. and Tornabene, F. (2019a), "Wave Propagation of Porous Nanoshells", Nanomaterials, 9(1), 22. https://doi.org/10.3390/nano9010022
  53. Karami, B., Shahsavari, D., Li, L., Karami, M. and Janghorban, M. (2019b), "Thermal buckling of embedded sandwich piezoelectric nanoplates with functionally graded core by a nonlocal second-order shear deformation theory", Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science, 233(1), 287-301. https://doi.org/10.1177/0954406218756451
  54. Li, Q., Iu, V. and Kou, K. (2009), "Three-dimensional vibration analysis of functionally graded material plates in thermal environment", J. Sound Vib., 324(3), 733-750. https://doi.org/10.1016/j.jsv.2009.02.036
  55. Li, L., Hu, Y. and Ling, L. (2015), "Flexural wave propagation in small-scaled functionally graded beams via a nonlocal strain gradient theory", Compos. Struct.res, 133, 1079-1092. https://doi.org/10.1016/j.compstruct.2015.08.014
  56. Li, L., Tang, H. and Hu, Y. (2018), "The effect of thickness on the mechanics of nanobeams", Int. J. Eng. Sci., 123, 81-91. https://doi.org/10.1016/j.ijengsci.2017.11.021
  57. Lim, C., Zhang, G. and Reddy, J. (2015), "A higher-order nonlocal elasticity and strain gradient theory and its applications in wave propagation", J. Mech. Phys. Solids, 78, 298-313. https://doi.org/10.1016/j.jmps.2015.02.001
  58. Malikan, M., Nguyen, V.B. and Tornabene, F. (2018), "Electromagnetic forced vibrations of composite nanoplates using nonlocal strain gradient theory", Mater. Res. Express, 5(7), 075031. https://doi.org/10.1088/2053-1591/aad144
  59. Nami, M.R. and Janghorban, M. (2014a), "Resonance behavior of FG rectangular micro/nano plate based on nonlocal elasticity theory and strain gradient theory with one gradient constant", Compos. Struct., 111, 349-353. https://doi.org/10.1016/j.compstruct.2014.01.012
  60. Nami, M.R. and Janghorban, M. (2014b), "Wave propagation in rectangular nanoplates based on strain gradient theory with one gradient parameter with considering initial stress", Modern Phys. Lett. B, 28(3), 1450021. https://doi.org/10.1142/S0217984914500213
  61. Nami, M.R., Janghorban, M. and Damadam, M. (2015), "Thermal buckling analysis of functionally graded rectangular nanoplates based on nonlocal third-order shear deformation theory", Aerosp. Sci. Technol., 41, 7-15. https://doi.org/10.1016/j.ast.2014.12.001
  62. Nayebi, A., Tirmomenin, A. and Damadam, M. (2015), "Elasto-plastic analysis of a functionally graded rotating disk under cyclic thermo-mechanical loadings considering continuum damage mechanics", Int. J. Appl. Mech., 7(2), 1550026. https://doi.org/10.1142/S175882511550026X
  63. Phung-Van, P., Thanh, C.-L., Nguyen-Xuan, H. and Abdel-Wahab, M. (2018), "Nonlinear transient isogeometric analysis of FGCNTRC nanoplates in thermal environments", Compos. Struct., 201, 882-892. https://doi.org/10.1016/j.compstruct.2018.06.087
  64. Reddy, J. and Chin, C. (1998), "Thermomechanical analysis of functionally graded cylinders and plates", J. Therm. Stress., 21(6), 593-626. https://doi.org/10.1080/01495739808956165
  65. Romano, G. and Barretta, R. (2017), "Nonlocal elasticity in nanobeams: the stress-driven integral model", Int. J. Eng. Sci., 115, 14-27. https://doi.org/10.1016/j.ijengsci.2017.03.002
  66. Sahmani, S., Aghdam, M.M. and Rabczuk, T. (2018), "Nonlinear bending of functionally graded porous micro/nano-beams reinforced with graphene platelets based upon nonlocal strain gradient theory", Compos. Struct., 186, 68-78. https://doi.org/10.1016/j.compstruct.2017.11.082
  67. 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
  68. Shahrjerdi, A., Mustapha, F., Bayat, M. and Majid, D. (2011), "Free vibration analysis of solar functionally graded plates with temperature-dependent material properties using second order shear deformation theory", J. Mech. Sci. Technol., 25(9), 2195. https://doi.org/10.1007/s12206-011-0610-x
  69. Shahsavari, D. and Janghorban, M. (2017), "Bending and shearing responses for dynamic analysis of single-layer graphene sheets under moving load", J. Brazil. Soc. Mech. Sci. Eng., 39(10), 3849-3861. https://doi.org/10.1007/s40430-017-0863-0
  70. Shahsavari, D., Karami, B., Janghorban, M. and Li, L. (2017), "Dynamic characteristics of viscoelastic nanoplates under moving load embedded within visco-Pasternak substrate and hygrothermal environment", Mater. Res. Express, 4(8), 085013. https://doi.org/10.1088/2053-1591/aa7d89
  71. Shahsavari, D., Karami, B., Fahham, H.R. and Li, L. (2018a), "On the shear buckling of porous nanoplates using a new sizedependent quasi-3D shear deformation theory", Acta Mechanica, 229(11), 4549-4573. https://doi.org/10.1007/s00707-018-2247-7
  72. Shahsavari, D., Karami, B. and Li, L. (2018b), "Damped vibration of a graphene sheet using a higher-order nonlocal straingradient Kirchhoff plate model", Comptes Rendus Mecanique.
  73. Shahsavari, D., Karami, B. and Li, L. (2018c), "A high-order gradient model for wave propagation analysis of porous FG nanoplates", Steel Compos. Struct., Int. J., 29 (1), 53-66.
  74. Shahsavari, D., Karami, B. and Mansouri, S. (2018d), "Shear buckling of single layer graphene sheets in hygrothermal environment resting on elastic foundation based on different nonlocal strain gradient theories", Eur. J. Mech.-A/Solids, 67, 200-214. https://doi.org/10.1016/j.euromechsol.2017.09.004
  75. Shahsavari, D., Shahsavari, M., Li, L. and Karami, B. (2018e), "A novel quasi-3D hyperbolic theory for free vibration of FG plates with porosities resting on Winkler/Pasternak/Kerr foundation", Aerosp. Sci. Technol., 72, 134-149. https://doi.org/10.1016/j.ast.2017.11.004
  76. She, G.-L., Ren, Y.-R., Yuan, F.-G. and Xiao, W.-S. (2018a), "On vibrations of porous nanotubes", Int. J. Eng. Sci., 125, 23-35. https://doi.org/10.1016/j.ijengsci.2017.12.009
  77. She, G.-L., Yan, K.-M., Zhang, Y.-L., Liu, H.-B. and Ren, Y.-R. (2018b), "Wave propagation of functionally graded porous nanobeams based on non-local strain gradient theory", Eur. Phys. J. Plus, 133(9), 368. https://doi.org/10.1140/epjp/i2018-12196-5
  78. She, G.-L., Yuan, F.-G. and Ren, Y.-R. (2018c), "On wave propagation of porous nanotubes", Int. J. Eng. Sci., 130, 62-74. https://doi.org/10.1016/j.ijengsci.2018.05.002
  79. She, G.-L., Yuan, F.-G., Ren, Y.-R., Liu, H.-B. and Xiao, W.-S. (2018d), "Nonlinear bending and vibration analysis of functionally graded porous tubes via a nonlocal strain gradient theory", Compos. Struct., 203, 614-623. https://doi.org/10.1016/j.compstruct.2018.07.063
  80. She, G.-L., Yuan, F.-G., Karami, B., Ren, Y.-R. and Xiao, W.-S. (2019), "On nonlinear bending behavior of FG porous curved nanotubes", Int. J. Eng. Sci., 135, 58-74. https://doi.org/10.1016/j.ijengsci.2018.11.005
  81. Shimpi, R. and Patel, H. (2006), "A two variable refined plate theory for orthotropic plate analysis", Int. J. Solids Struct., 43(22-23), 6783-6799. https://doi.org/10.1016/j.ijsolstr.2006.02.007
  82. Taghizadeh, M., Ovesy, H. and Ghannadpour, S. (2015), "Nonlocal integral elasticity analysis of beam bending by using finite element method", Struct. Eng. Mech., Int. J., 54(4), 755-769. https://doi.org/10.12989/sem.2015.54.4.755
  83. Touloukian, Y.S. and Ho, C. (1970), "Thermal expansion. Nonmetallic solids", In: Thermophysical Properties of Matter-The TPRC Data Series, New York: IFI/Plenum, 1970-, (Edited by Touloukian), YSI e (series ed.); Ho, CYI e (series tech. ed.).
  84. Tounsi, A., Benguediab, S., Adda, B., Semmah, A. and Zidour, M. (2013), "Nonlocal effects on thermal buckling properties of double-walled carbon nanotubes", Adv. Nano Res., Int. J., 1(1), 1-11. https://doi.org/10.12989/anr.2013.1.1.001
  85. Tufekci, E., Aya, S.A. and Oldac, O. (2016), "A unified formulation for static behavior of nonlocal curved beams", Struct. Eng. Mech., Int. J., 59(3), 475-502. https://doi.org/10.12989/sem.2016.59.3.475
  86. Wu, Z., Cheung, Y., Lo, S. and Chen, W. (2008), "Effects of higher-order global-local shear deformations on bending, vibration and buckling of multilayered plates", Compos. Struct., 82(2), 277-289. https://doi.org/10.1016/j.compstruct.2007.01.017
  87. Zenkour, A.M. (2016), "Buckling of a single-layered graphene sheet embedded in visco-Pasternak's medium via nonlocal firstorder theory", Adv. Nano Res., Int. J., 4(4), 309-326. https://doi.org/10.12989/anr.2016.4.4.309

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