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Size dependent effect on deflection and buckling analyses of porous nanocomposite plate based on nonlocal strain gradient theory

  • Khazaei, Pegah (Department of Solid Mechanics, Faculty of Mechanical Engineering, University of Kashan) ;
  • Mohammadimehr, Mehdi (Department of Solid Mechanics, Faculty of Mechanical Engineering, University of Kashan)
  • Received : 2019.08.19
  • Accepted : 2020.05.18
  • Published : 2020.10.10

Abstract

In this paper, the deflection and buckling analyses of porous nano-composite piezoelectric plate reinforced by carbon nanotube (CNT) are studied. The equations of equilibrium using energy method are derived from principle of minimum total potential energy. In the research, the non-local strain gradient theory is employed to consider size dependent effect for porous nanocomposite piezoelectric plate. The effects of material length scale parameter, Eringen's nonlocal parameter, porosity coefficient and aspect ratio on the deflection and critical buckling load are investigated. The results indicate that the effect of porosity coefficient on the increase of the deflection and critical buckling load is greatly higher than the other parameters effect, and size effect including nonlocal parameter and the material length scale parameter have a lower effect on the deflection increase with respect to the porosity coefficient, respectively and vice versa for critical buckling load. Porous nanocomposites are used in various engineering fields such as aerospace, medical industries and water refinery.

Keywords

Acknowledgement

The authors would like to thank the referees for their valuable comments. Also, they are thankful to the the Iranian Nanotechnology Development Committee for their financial support and the University of Kashan for supporting this work by Grant No. 682561/28.

References

  1. Aghababaei, R. and Reddy, JN. (2009), "Nonlocal third-order shear deformation plate theory with application to bending and vibration of plates", J. Sound Vib., 326(1-2), 277-289, https://doi.org/10.1016/j.jsv.2009.04.044.
  2. AkhavanAlavi S. M., Mohammadimehr M., Edjtahed SH. (2019) "Active control of micro Reddy beam integrated with functionally graded nanocomposite sensor and actuator based on linear quadratic regulator method", Euro. J. Mech. A/Solids, 74, 449-461. https://doi.org/10.1016/j.euromechsol.2018.12.008.
  3. Alavi, SH. and Eipakchi, H. (2019), "Geometry and load effects on transient response of a VFGM annular plate: An analytical approach", Struct. Eng. Mech., 70(2), 179-197, https://doi.org/10.12989/sem.2019.70.2.179.
  4. Alizada, A.N. and Sofiyev, A.H. (2011), "Modified Young's moduli of nano-materials taking into account the scale effects and vacancies", Meccanica, 46(5), 915-920, https://doi.org/10.1007/s11012-010-9349-1.
  5. Apuzzo, A., Barretta R., Faghidian, SA., Luciano, R. and De Sciarra, FM. (2018), "Free vibrations of elastic beams by modified nonlocal strain gradient theory", Int. J. Eng. Sci., 133, 99-108. https://doi.org/10.1016/j.ijengsci.2018.09.002.
  6. Arani, AG. and Jalaei, MH. (2017), "Investigation of the longitudinal magnetic field effect on dynamic response of viscoelastic graphene sheet based on sinusoidal shear deformation theory", Physica B Cond Matter, 506, 94-104, https://doi.org/10.1016/j.physb.2016.11.004.
  7. Arani, AG., Jamali, M., Mosayyebi, M. and Kolahchi, R. (2016), "Wave propagation in FG-CNT-reinforced piezoelectric composite micro plates using viscoelastic quasi-3D sinusoidal shear deformation theory", Compos. Part B Eng., 95, 209-224, https://doi.org/10.1016/j.compositesb.2016.03.077.
  8. Arani, AG., Kolahchi, R. and Vossough, H. (2012), "Buckling analysis and smart control of SLGS using elastically coupled PVDF nanoplate based on the nonlocal Mindlin plate theory", Physica B Cond. Matter, 407(22), 4458-4465, https://doi.org/10.1016/j.physb.2012.07.046.
  9. Arefi, M., Kiani, M. and Rabczuk, T. (2019), "Application of nonlocal strain gradient theory to size dependent bending analysis of a sandwich porous nanoplate integrated with piezomagnetic face-sheets", Compos. Part B Eng., 168, 320-333, https://doi.org/10.1016/j.compositesb.2019.02.057.
  10. Barretta, R., and Sciarra, F.M.D. (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.
  11. Barretta, R., Faghidian, S.A. and Sciarra, F.M. D. )2019(, "Stress-driven nonlocal integral elasticity for axisymmetric nano-plates", Int. J. Eng. Sci., 136, 38-52, https://doi.org/10.1016/j.ijengsci.2019.01.003.
  12. Batra, RC. (2007), "Higher-order shear and normal deformable theory for functionally graded incompressible linear elastic plates", Thin-Walled Struct., 45(12), 974-982, https://doi.org/10.1016/j.tws.2007.07.008.
  13. Batra, RC. and Aimmanee, S. (2005), "Vibrations of thick isotropic plates with higher order shear and normal deformable plate theories", Comput. Struct., 83(12-13), 934-955, https://doi.org/10.1016/j.compstruc.2004.11.023.
  14. Batra, RC. and Aimmanee, S. (2007), "Vibration of an incompressible isotropic linear elastic rectangular plate with a higher-order shear and normal deformable theory", J. Sound Vib., 307(3-5), 961-971, https://doi.org/110.1016/j.jsv.2007.06.064.
  15. Batra, RC., Vidoli, S. and Vestroni, F. (2002), "Plane wave solutions and modal analysis in higher order shear and normal deformable plate theories", J. Sound Vib., 257(1), 63-88, https://doi.org/10.1006/jsvi.2002.5029.
  16. Ebrahimi, F. and Barati, MR. (2018), "Damping vibration analysis of graphene sheets on viscoelastic medium incorporating hygro-thermal effects employing nonlocal strain gradient theory", Compos. Struct., 185, 241-253, https://doi.org/10.1016/j.compstruct.2017.10.021.
  17. Ebrahimi, F., Seyfi, A. and Tornabene, F. (2019), "Wave dispersion characteristics of porous graphene platelet-reinforced composite shells", Struct. Eng. Mech., 71(1), 99-107, https://doi.org/10.12989/sem.2019.71.1.099.
  18. Gholami, R. and Ansari, R. (2017), "A unified nonlocal nonlinear higher-order shear deformable plate model for postbuckling analysis of piezoelectric-piezomagnetic rectangular nanoplates with various edge supports", Compos. Struct., 166, 202-218, https://doi.org/10.1016/j.compstruct.2017.01.045.
  19. Ghorbanpour Arani A., Rousta Navi B., Mohammadimehr M. (2016) "Surface stress and agglomeration effects on nonlocal biaxial buckling polymeric nanocomposite plate reinforced by CNT using various approaches", Adv. Compos. Mater., 25(5), 423-441. https://doi.org/10.1080/09243046.2015.1052189
  20. Jomehzadeh, E., Noori, HR. and Saidi, AR. (2011), "The size-dependent vibration analysis of micro-plates based on a modified couple stress theory", Physica E: Low-dimens. Sys. Nanostruct., 43(4), 877-883, https://doi.org/10.1016/j.physe.2010.11.005.
  21. Kim, J., Zur, KK. and Reddy, JN. (2019), "Bending, free vibration, and buckling of modified couples stress-based functionally graded porous micro-plates", Compos. Struct., 209, 879-888, https://doi.org/10.1016/j.compstruct.2018.11.023.
  22. Li, L., Hu, Y. and Ling, L. (2016), "Wave propagation in viscoelastic single-walled carbon nanotubes with surface effect under magnetic field based on nonlocal strain gradient theory", Physica E: Low-dimens. Sys. Nanostruct., 75, 118-124, https://doi.org/10.1016/j.physe.2015.09.028.
  23. Lu, L., Guo, X. and Zhao, J. (2017), "Size-dependent vibration analysis of nanobeams based on the nonlocal strain gradient theory", Int. J. Eng. Sci., 116, 12-24, https://doi.org/10.1016/j.ijengsci.2017.03.006.
  24. Lu, L., Guo, X. and Zhao, J. (2019), "A unified size-dependent plate model based on nonlocal strain gradient theory including surface effects", Appl. Math. Model., 68, 583-602, https://doi.org/10.1016/j.apm.2018.11.023.
  25. Mahinzare, M., Alipour, MJ., Sadatsakkak, SA. and Ghadiri, M. (2019), "A nonlocal strain gradient theory for dynamic modeling of a rotary thermo piezo electrically actuated nano FG circular plate", Mech. Sys. Signal Proces., 115, 323-337, https://doi.org/10.1016/j.ymssp.2018.05.043.
  26. Magnucka-Blandzi, E. (2008), "Axi-symmetrical deflection and buckling of circular porous-cellular plate", Thin-Walled Struct., 46(3), 333-337, https://doi.org/10.1016/j.tws.2007.06.006.
  27. Malikan, M., Nguyen, VB. and Tornabene, F. (2018), "Damped forced vibration analysis of single-walled carbon nanotubes resting on viscoelastic foundation in thermal environment using nonlocal strain gradient theory", Eng. Sci. Technol., 21(4), 778-786, https://doi.org/10.1016/j.jestch.2018.06.001.
  28. Mao, JJ. and Zhang, W. (2019), "Buckling and post-buckling Analyses of Functionally Graded Graphene Reinforced Piezoelectric Plate Subjected to Electric Potential and Axial Forces", Compos. Struct., 216, 392-405, https://doi.org/10.1016/j.jestch.2018.06.001.
  29. Mohammadimehr, M., Navi, BR. and Arani AG. (2015), "Free vibration of viscoelastic double-bonded polymeric nanocomposite plates reinforced by FG-SWCNTs using MSGT, sinusoidal shear deformation theory and meshless method", Compos. Struct., 131, 654-671, https://doi.org/10.1016/j.compstruct.2015.05.077.
  30. Mohammadimehr, M., Mohammadi Najafabadi, MM., Nasiri, H. and Rousta Navi, B. (2016a), "Surface stress effects on the free vibration and bending analysis of the nonlocal single-layer graphene sheet embedded in an elastic medium using energy method", Proc. Ins. Mech. Eng. Part N: J. Nanomater, Nanoeng and Nanosys, 230(3), 148-160, https://doi.org/10.1177/1740349914559042.
  31. Mohammadimehr, M., Navi, BR. and Arani, AG. (2016b), "Modified strain gradient Reddy rectangular plate model for biaxial buckling and bending analysis of double-coupled piezoelectric polymeric nanocomposite reinforced by FG-SWNT", Compos. Part B Eng., 87, 132-148, https://doi.org/10.1016/j.compositesb.2015.10.007.
  32. Mohammadimehr, M., Salemi, M. and Navi, BR. (2016c), "Bending, buckling, and free vibration analysis of MSGT microcomposite Reddy plate reinforced by FG-SWCNTs with temperature-dependent material properties under hydro-thermo-mechanical loadings using DQM", Compos. Struct., 138, 361-380, https://doi.org/10.1016/j.compstruct.2015.11.055.
  33. Mohammadimehr, M., Nejad, ES. and Mehrabi M. (2018), "Buckling and vibration analyses of MGSGT double-bonded micro composite sandwich SSDT plates reinforced by CNTs and BNNTs with isotropic foam & flexible transversely orthotropic cores", Struct. Eng. Mech., 65(4), 491-504, https://doi.org/10.12989/sem.2018.65.4.491.
  34. Mohammadimehr M., Shahedi S., Rousta Navi B. (2017a) "Nonlinear vibration analysis of FG-CNTRC sandwich Timoshenko beam based on modified couple stress theory subjected to longitudinal magnetic field using generalized differential quadrature method", Proc Inst Mech Eng, Part C: J. Mech. Eng. Sci., 231(20), 3866-3885. https://doi.org/10.1177/0954406216653622
  35. Mohammadimehr M., Navi BR., Ghorbanpour Arani A. (2017b) "Dynamic stability of modified strain gradient theory sinusoidal viscoelastic piezoelectric polymeric functionally graded single-walled carbon nanotubes reinforced nanocomposite plate considering surface stress and agglomeration effects under hydro-thermo-electro-magneto-mechanical loadings", Mech. Adv. Mater. Struct., 24(16), 1325-1342. https://doi.org/10.1080/15376494.2016.1227507
  36. Mohammadimehr M., Alimirzaei S. (2016) "Nonlinear static and vibration analysis of Euler-Bernoulli composite beam model reinforced by FG-SWCNT with initial geometrical imperfection using FEM", Struct. Eng. Mech., 59(3), 431-454. https://doi.org/10.12989/sem.2016.59.3.431
  37. Mohammadimehr M., Mohammadimehr MA., Dashti P. (2016d) "Size-dependent effect on biaxial and shear nonlinear buckling analysis of nonlocal isotropic and orthotropic micro-plate based on surface stress and modified couple stress theories using differential quadrature method", Appl. Math. Mech., 37(4), 529-554. https://doi.org/10.1007/s10483-016-2045-9
  38. Mohammadzadeh, B., Choi, E. and Kim, D. (2019), "Vibration of sandwich plates considering elastic foundation, temperature change and FGM faces", Struct. Eng. Mech., 70(5), 591-600, https://doi.org/10.12989/sem.2019.70.5.591.
  39. Reddy, JN. (2010), "Nonlocal nonlinear formulations for bending of classical and shear deformation theories of beams and plates", Int. J. Eng. Sci., 48(11), 1507-1518, https://doi.org/10.1016/j.ijengsci.2010.09.020.
  40. Reddy, J.N. (2017), "Energy principles and variational methods in applied mechanics", J. W. S.
  41. Reddy, JN. and Kim J. (2012), "A nonlinear modified couple stress-based third-order theory of functionally graded plates", Compos. Struct., 94(3), 1128-1143, https://doi.org/10.1016/j.compstruct.2011.10.006.
  42. Rezaei, AS. and Saidi, AR. (2015), "Exact solution for free vibration of thick rectangular plates made of porous materials", Compos. Struct., 134, 1051-1060, https://doi.org/10.1016/j.compstruct.2015.08.125.
  43. Rezaei, AS., Saidi, AR., Abrishamdari, M. and Mohammadi MP. (2017), "Natural frequencies of functionally graded plates with porosities via a simple four variable plate theory: an analytical approach", Thin-Walled Struct., 120, 366-377, https://doi.org/10.1016/j.tws.2017.08.003.
  44. Rajabi, J., Mohammadimehr, M. (2019) "Bending analysis of a micro sandwich skew plate using extended Kantorovich method based on Eshelby-Mori-Tanaka approach", Comput.Concrete, 23(5), pp. 361-376, https://doi.org/10.12989/cac.2019.23.5.361
  45. Saidi, AR., Rasouli, A. and Sahraee, S. (2009), "Axisymmetric bending and buckling analysis of thick functionally graded circular plates using unconstrained third-order shear deformation plate theory", Compos. Struct., 89(1), 110-119, https://doi.org/10.1016/j.compstruct.2008.07.003.
  46. She, GL., Yuan, FG., Ren, YR., Liu, HB. and Xiao, WS. (2018), "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.
  47. Shen, H.S. (2009), "Nonlinear bending of functionally graded carbon nanotube-reinforced composite plates in thermal environments", Compos. Struct., 91(1), 9-19, https://doi.org/10.1016/j.compstruct.2009.04.026.
  48. Shen, H.S., and Zhang, C.L. (2010), "Thermal buckling and postbuckling behavior of functionally graded carbon nanotube-reinforced composite plates", Mater. Design, 31, 3403-3411, https://doi.org/10.1016/j.matdes.2010.01.048
  49. Sofiyev, A.H., Turkaslan, B.E., Bayramov, R.P. and Salamci, M.U. (2019), "Analytical solution of stability of FG-CNTRC conical shells under external pressures", Thin-Walled Struct., 144, 106338, https://doi.org/10.1016/j.tws.2019.106338.
  50. Tanzadeh, H. and Amoushahi, H. (2019), "Buckling and free vibration analysis of piezoelectric laminated composite plates using various plate deformation theories", Europ. J. Mech.-A/Solids, 74, 242-256, https://doi.org/10.1016/j.euromechsol.2018.11.013.
  51. Thai, HT. and Choi, DH. (2013), "Size-dependent functionally graded Kirchhoff and Mindlin plate models based on a modified couple stress theory", Compos. Struct., 95, 142-153, https://doi.org/10.1016/j.compstruct.2012.08.023.
  52. Thai, H.T. and Kim, S.E. (2013), "A size-dependent functionally graded Reddy plate model based on a modified couple stress theory", Compos. Part B: Eng., 45(1), 1636-1645, https://doi.org/10.1016/j.compositesb.2012.09.065.
  53. Van, D.T., Nguyen, D.K., Duc, N.D., Doan, D.H. and Bui, T.Q. (2017), "Analysis of bi-directional functionally graded plates by FEM and a new third-order shear deformation plate theory", Thin-Walled Struct., 119, 687-699. https://doi.org/10.1016/j.tws.2017.07.022
  54. Wang, Q. (2002), "On buckling of column structures with a pair of piezoelectric layers", Eng. Struct., 24(2), 199-205, https://doi.org/10.1016/S0141-0296(01)00088-8.
  55. Wang, B., Zhou, S., Zhao, J. and Chen, X. (2011), "A size-dependent Kirchhoff micro-plate model based on strain gradient elasticity theory", Europ. J. Mech.-A/Solids, 30(4) 517-524, https://doi.org/10.1016/j.tws.2017.07.022.
  56. Yang, J., Chen, D. and Kitipornchai, S. (2018), "Buckling and free vibration analyses of functionally graded graphene reinforced porous nanocomposite plates based on Chebyshev-Ritz method", Compos. Struct., 193, 281-294, https://doi.org/10.1016/j.compstruct.2018.03.090.
  57. Yazdani, R., Mohammadimehr, M. and Rousta Navi, B. (2019), "Free vibration of Cooper-Naghdi micro saturated porous sandwich cylindrical shells with reinforced CNT face sheets under magneto-hydro-thermo-mechanical loadings", Struct. Eng. Mech., 70(3), 351-365, https://doi.org/10.12989/sem.2019.70.3.351.
  58. Yin, L., Qian, Q., Wang, L. and Xia, W. (2010), "Vibration analysis of microscale plates based on modified couple stress theory", Acta Mech. Solida Sinica, 23(5), 386-393, https://doi.org/10.1016/S0894-9166(10)60040-7.
  59. Zenkour, AM. and Alghanmi, RA. (2019), "Stress analysis of a functionally graded plate integrated with piezoelectric faces via a four-unknown shear deformation theory", Results Phys., 12, 268-277, https://doi.org/10.1016/j.rinp.2018.11.045.
  60. Zenkour, AM. and Radwan, AF. (2018), "Compressive study of functionally graded plates resting on Winkler-Pasternak foundations under various boundary conditions using hyperbolic shear deformation theory", Arch. Civil Mech. Eng., 18(2), 645-658, https://doi.org/10.1016/j.acme.2017.10.003.
  61. Zhu, P., Lei, Z.X. and Liew, K.M. (2012), "Static and free vibration analyses of carbon nanotube-reinforced composite plates using finite element method with first order shear deformation plate theory", Compos. Struct., 94(4), 1450-1460, https://doi.org/10.1016/j.compstruct.2011.11.010.