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Hygro-thermo-mechanical bending and vibration analysis of the CNTRC doubly curved nanoshells with thickness stretching based on nonlocal strain gradient theory

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An Erratum to this article was published on 06 April 2021

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Abstract

In the present study, the bending and free vibration analysis of the CNTRC doubly curved nanoshells subjected to hygro-thermo-mechanical loading using higher-order shear and normal deformation theory is investigated. Thickness stretching impact is considered based on higher-order shear and normal deformation theory. The transverse displacement is divided into bending and shear ingredients based on sinusoidal shear deformation theory. To consider the nonlocality, nonlocal strain gradient shell theory is applied. All of the effective material properties of the shell are considered as temperature dependent. The temperature variation and moisture expansion vary through the thickness of the shell nonlinearly. The impacts of the five different kinds of distributions of CNTRC including UD, FGV, FGX, FGA and FGO are studied on the bending and natural frequency of the nanoshell. To obtain the equations of motion, Hamilton’s principle is applied, where Navier’s method is utilized to derive the mechanical responses of the nanoshell with simply supported boundary conditions. The calculated result illustrates that the length scale parameter has remarkable impact on the deflection and natural frequency of the CNTRC doubly curved nanoshells.

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Data availability statement

This manuscript has associated data in a data repository. [Authors’ comment: The datasets generated during the current study are available from the corresponding author on reasonable request.]

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References

  1. Y. Heidari, M. Arefi, M.I. Rahaghi, Effect of distributed piezoelectric segments on the buckling load of FG cylindrical micro/nano shell. Eur. Phys. J. Plus 136(1), 1–20 (2021)

    Article  Google Scholar 

  2. M.H. Dindarloo, A.M. Zenkour, Nonlocal strain gradient shell theory for bending analysis of FG spherical nanoshells in thermal environment. Eur. Phys. J. Plus 135(10), 1–18 (2020)

    Article  Google Scholar 

  3. H.K. Sharaf, S. Salman, M.H. Dindarloo, V.I. Kondrashchenko, A.A. Davidyants, S.V. Kuznetsov, The effects of the viscosity and density on the natural frequency of the cylindrical nanoshells conveying viscous fluid. Eur. Phys. J. Plus 136(1), 1–19 (2021)

    Article  Google Scholar 

  4. M.R. Barati, A.M. Zenkour, H. Shahverdi, Thermo-mechanical buckling analysis of embedded nanosize FG plates in thermal environments via an inverse cotangential theory. Compos. Struct. 141, 203–212 (2016)

    Article  Google Scholar 

  5. C.W. Lim, G. Zhang, J.N. Reddy, A higher-order nonlocal elasticity and strain gradient theory and its applications in wave propagation. J. Mech. Phys. Solids 78, 298–313 (2015)

    Article  ADS  MathSciNet  Google Scholar 

  6. L. Li, Y. Hu, L. Ling, Wave propagation in viscoelastic single-walled carbon nanotubes with surface effect under magnetic field based on nonlocal strain gradient theory. Phys. E Low Dimens. Syst. Nanostruct. 75, 118–124 (2016)

    Article  ADS  Google Scholar 

  7. M.H. Ghayesh, Viscoelastic dynamics of axially FG microbeams. Int. J. Eng. Sci. 135, 75–85 (2019)

    Article  MathSciNet  Google Scholar 

  8. A.M. Zenkour, Z.S. Hafed, Bending analysis of functionally graded piezoelectric plates via quasi-3D trigonometric theory. Mech. Adv. Mater. Struct. 27(18), 1551–1562 (2020)

    Article  Google Scholar 

  9. M. Bouazza, A.M. Zenkour, Hygro-thermo-mechanical buckling of laminated beam using hyperbolic refined shear deformation theory. Compos. Struct. 252, 112689 (2020)

    Article  Google Scholar 

  10. M.H. Ghayesh, Nonlinear vibration analysis of axially functionally graded shear-deformable tapered beams. Appl. Math. Model. 59, 583–596 (2018)

    Article  MathSciNet  Google Scholar 

  11. M. Bouazza, A.M. Zenkour, Vibration of carbon nanotube-reinforced plates via refined nth-higher-order theory. Arch. Appl. Mech. 90, 1755–1769 (2020)

    Article  ADS  Google Scholar 

  12. L. Li, X. Li, Y. Hu, Nonlinear bending of a two-dimensionally functionally graded beam. Compos. Struct. 184, 1049–1061 (2018)

    Article  Google Scholar 

  13. M.Z. Nejad, A. Hadi, A. Rastgoo, Buckling analysis of arbitrary two-directional functionally graded Euler-Bernoulli nano-beams based on nonlocal elasticity theory. Int. J. Eng. Sci. 103, 1–10 (2016)

    Article  MathSciNet  Google Scholar 

  14. M.Z. Nejad, A. Hadi, Non-local analysis of free vibration of bi-directional functionally graded Euler-Bernoulli nano-beams. Int. J. Eng. Sci. 105, 1–11 (2016)

    Article  MathSciNet  Google Scholar 

  15. S. Sahmani, B. Safaei, Nonlocal strain gradient nonlinear resonance of bi-directional functionally graded composite micro/nano-beams under periodic soft excitation. Thin Wall. Struct. 143, 106226 (2019)

    Article  Google Scholar 

  16. A.M. Zenkour, A two-unknown nonlocal shear and normal deformations theory for buckling analysis of nanorods. J. Braz. Soc. Mech. Sci. Eng. 42(358), 358 (2020)

    Article  Google Scholar 

  17. D.S. Mashat, A.M. Zenkour, A.F. Radwan, A quasi 3-D higher-order plate theory for bending of FG plates resting on elastic foundations under hygro-thermo-mechanical loads with porosity. Eur. J. Mech. A Solids 82, 103985 (2020)

    Article  ADS  MathSciNet  Google Scholar 

  18. A.M. Zenkour, Z.S. Hafed, Bending response of functionally graded piezoelectric plates using a two-variable shear deformation theory. Adv. Aircr. Spacecr. Sci. 7(2), 115–134 (2020)

    Google Scholar 

  19. A.M. Zenkour, Quasi-3D refined theory for functionally graded porous plates: displacements and stresses. Phys. Mesomech. 23(1), 39–53 (2020)

    Article  Google Scholar 

  20. A.A. Daikh, A.M. Zenkour, Free vibration and buckling of porous power-law and sigmoid functionally graded sandwich plates using a simple higher-order shear deformation theory. Mater. Res. Express 6(11), 115707 (2019)

    Article  ADS  Google Scholar 

  21. A. Hadi, M.Z. Nejad, M. Hosseini, Vibrations of three-dimensionally graded nanobeams. Int. J. Eng. Sci. 128, 12–23 (2018)

    Article  MathSciNet  Google Scholar 

  22. A.M. Zenkour, A.H. Al-Subhi, Thermal vibrations of a graphene sheet embedded in viscoelastic medium based on nonlocal shear deformation theory. Int. J. Acoust. Vib. 24(3), 485–493 (2019)

    Article  Google Scholar 

  23. M.R. Barati, N.M. Faleh, A.M. Zenkour, Dynamic response of nanobeams subjected to moving nanoparticles and hygro-thermal environments based on nonlocal strain gradient theory. Mech. Adv. Mater. Struct. 26(19), 1661–1669 (2019)

    Article  Google Scholar 

  24. M. Arefi, A.M. Zenkour, Influence of magneto-electric environments on size-dependent bending results of three-layer piezomagnetic curved nanobeam based on sinusoidal shear deformation theory. J. Sandwich Struct. Mater. 21(8), 2751–2778 (2019)

    Article  Google Scholar 

  25. M. Arefi, G.G. Talkhunche, Higher-order vibration analysis of FG cylindrical nano-shell. Eur. Phys. J. Plus 136(2), 1–21 (2021)

    Article  Google Scholar 

  26. M.H. Ghayesh, Viscoelastic mechanics of Timoshenko functionally graded imperfect microbeams. Compos. Struct. 225, 110974 (2019)

    Article  Google Scholar 

  27. M.H. Ghayesh, Mechanics of viscoelastic functionally graded microcantilevers. Eur. J. Mech. A Solids 73, 492–499 (2019)

    Article  ADS  MathSciNet  Google Scholar 

  28. Y. Kiani, Buckling of functionally graded graphene reinforced conical shells under external pressure in thermal environment. Compos. B Eng. 156, 128–137 (2019)

    Article  Google Scholar 

  29. J.N. Reddy, Mechanics of Laminated Composite Plates and Shells: Theory and Analysis (CRC Press, London, 2003).

    Book  Google Scholar 

  30. Zenkour AM, Hafed ZS (2019) Hygro-thermo-mechanical bending of FG piezoelectric plates using quasi-3D shear and normal deformations theory. Latin American Journal of Solids and Structures, 16(7).

  31. M.H. Dindarloo, L. Li, R. Dimitri, F. Tornabene, Nonlocal elasticity response of doubly-curved nanoshells. Symmetry 12(3), 466 (2020)

    Article  Google Scholar 

  32. A. Bhimaraddi, Three-dimensional elasticity solution for static response of orthotropic doubly curved shallow shells on rectangular planform. Compos. Struct. 24(1), 67–77 (1993)

    Article  ADS  Google Scholar 

  33. M.H. Dindarloo, L. Li, Vibration analysis of carbon nanotubes reinforced isotropic doubly-curved nanoshells using nonlocal elasticity theory based on a new higher order shear deformation theory. Compos. B Eng. 175, 107170 (2019)

    Article  Google Scholar 

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Authors and Affiliations

  1. Suzhou Zhongheng Tong Road and Bridge Co. Ltd., Suzhou, 215124, China

    Hao Wei

  2. Department of Mechanical Engineering, Tarbiat Modares University, Tehran, Iran

    Reza Mohammadi

Authors
  1. Hao Wei
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  2. Reza Mohammadi
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Correspondence to Hao Wei.

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The original online version of this article was revised: In the original publication of the article, unfortunately the corresponding author was wrong.

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Wei, H., Mohammadi, R. Hygro-thermo-mechanical bending and vibration analysis of the CNTRC doubly curved nanoshells with thickness stretching based on nonlocal strain gradient theory. Eur. Phys. J. Plus 136, 326 (2021). https://doi.org/10.1140/epjp/s13360-021-01296-0

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