Steel and Composite Structures

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Nonlinear low-velocity impact response of graphene platelets reinforced metal foams doubly curved shells

  • Hao-Xuan Ding (College of Mechanical and Vehicle Engineering, Chongqing University) ;
  • Yi-Wen Zhang (College of Mechanical and Vehicle Engineering, Chongqing University) ;
  • Yin-Ping Li (College of Mechanical and Vehicle Engineering, Chongqing University) ;
  • Gui-Lin She (College of Mechanical and Vehicle Engineering, Chongqing University)
  • Received : 2023.02.04
  • Accepted : 2023.10.31
  • Published : 2023.11.10
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Abstract

Due to the fact that the nonlinear low-velocity impact response of graphene platelets reinforced metal foams (GPLRMF) doubly curved shells have not been investigated in the existing works, this paper aims to solve this issue. Using Reddy's high-order shear deformation theory (HSDT), the nonlinear governing equations of GPLRMF doubly curved shells are obtained by Euler-Lagrange method, discretized by Galerkin principle, and solved by the fourth-order Runge-Kutta method to obtain the impact force and central deflection. The nonlinear Hertz contact law is applied to determine the contact force. Finally, the impacts of graphene platelets (GPLs) distribution pattern, porosity distribution form, porosity coefficient, damping coefficient, impact parameters (radius and initial velocity), GPLs weight fraction, pre-stressing force and different shell types on the low-velocity impact curves are analyzed. It can be found that, among the four shell structures, the impact resistance of spherical shell is the best, while that of cylindrical shell is the worst.

Keywords

Acknowledgement

The authors acknowledge this work is supported by the first-rate talent introduction project of Chongqing University (02090011044159).

References

  1. Abolfazl, N.K., Marcello I., Giuseppe L. and Nicola B. (2023a), "Increasing melting and solidification performances of a phase change material-based flat plate solar collector equipped with metal foams, nanoparticles, and wavy wall-Y-shaped surface", Energ. Convers. Manage., 291, 117268, https://doi.org/10.1016/j.enconman.2023.117268.
  2. Abolfazl, N.K., Marcello I., Giuseppe L. and Nicola B. (2023b), "Thermal enhancement techniques for a lobed-double pipe PCM thermal storage system", Appl. Therm. Eng., 233, 121139. https://doi.org/10.1016/j.applthermaleng.2023.121139.
  3. Affdl, J.H. and Kardos, J. (1976), "The Halpin-Tsai equations: a review", Polym. Eng. Sci., 16, 344-352. https://doi.org/10.1002/pen.760160512.
  4. Ahmadi, H., Bayat, A. and Duc, N.D. (2021), "Nonlinear forced vibrations analysis of imperfect stiffened FG doubly curved shallow shell in thermal environment using multiple scales method", Compos Struct., 256, 113090. https://doi.org/10.1016/j.compstruct.2020.113090.
  5. Al-Furjan, M.S.H., Farrokhian, A., Mahmoud, S.R. and Kolahchi, R. (2018), "Dynamic deflection and contact force histories of graphene platelets reinforced conical shell integrated with magnetostrictive layers subjected to low-velocity impact", Thin. Wall. Struct., 163, 554-565. https://doi.org/10.1016/j.tws.2021.107706.
  6. Chen, H.Y., Wang, A.W., Hao, Y.X. and Zhang, W. (2017), "Free vibration of FGM sandwich doubly-curved shallow shell based on a new shear deformation theory with stretching effects", Compos. Struct., 179, 50-60. https://doi.org/10.1016/j.compstruct.2017.07.032.
  7. Chen, X., Zhao, J.L., She, G.L., Jing, Y., Luo, J. and Pu, H.Y. (2022a), "On wave propagation of functionally graded CNT strengthened fluid-conveying pipe in thermal environment", Eur. Phys. J. Plus., 137(10), 1158. https://doi.org/10.1140/epjp/s13360-022-03234-0.
  8. Chen, X., Zhao, J.L., She, G.L., Jing, Y., Pu, H.Y. and Luo, J. (2022b), "Nonlinear free vibration analysis of functionally graded carbon nanotube reinforced fluid-conveying pipe in thermal environment", Steel. Compos. Struct., 45(5), 641-652. https://doi.org/10.12989/scs.2022.45.5.641.
  9. Cui, S. and Ni, X. (2021), "Propagation of combined longitudinal and torsional stress waves in a functionally graded thin-walled tube", Appl. Math. Mech.-Engl., 42, 1717-1732. https://doi.org/10.1007/s10483-021-2805-6.
  10. Ding, H.X. and She, G.L. (2021), "A higher-order beam model for the snap-buckling analysis of FG pipes conveying fluid", Struct. Eng. Mech., 80(1), 63-72. https://doi.org/10.12989/sem.2021.80.1.063.
  11. Ding, H.X. and She, G.L. (2023a), "Nonlinear resonance of axially moving graphene platelet-reinforced metal foam cylindrical shells with geometric imperfection", Archiv. Civil Mech. Eng., 23, 97. https://doi.org/10.1007/s43452-023-00634-6.
  12. Ding, H.X. and She, G.L. (2023b), "Nonlinear primary resonance behavior of graphene platelets reinforced metal foams conical shells under axial motion", Nonlinear Dyn., 111(15), 13723-13752. https://doi.org/10.1007/s11071-023-08564-x.
  13. Ding, H.X. and She, G.L. (2024), "Nonlinear transient response of graphene platelets reinforced metal foams annular plate considering rotating motion and initial geometric imperfection", Aeros. Sci. Technol.
  14. Ding, H.X., Eltaher, M.A. and She, G.L. (2023a), "Nonlinear low-velocity impact of graphene platelets reinforced metal foams cylindrical shell: Effect of spinning motion and initial geometric imperfections", Aeros. Sci. Technol., 140, 108435. https://doi.org/10.1016/j.ast.2023.108435.
  15. Ding, H.X., Liu, H.B., She, G.L. and Wu, F. (2023c), "Wave propagation of FG-CNTRC plates in thermal environment using the high-order shear deformation plate theory", Comput. Concrete, 32(2), 207-215. https://doi.org/10.12989/cac.2023.32.2.207.
  16. Ding, H.X., She, G.L. and Zhang, Y.W. (2022a), "Nonlinear buckling and resonances of functionally graded fluid-conveying pipes with initial geometric imperfection", Eur. Phys. J. Plus, 137, 1329. https://doi.org/10.1140/epjp/s13360-022-03570-1.
  17. Ding, H.X., Zhang, Y.W. and She, G.L. (2022b), "On the resonance problems in FG-GPLRC beams with different boundary conditions resting on elastic foundations", Comput. Concrete, 30(6),433-443. https://doi.org/10.12989/cac.2022.30.6.433.
  18. Ding, H.X., Zhang, Y.W. and She, G.L. (2023b), "Propagation characteristics of guided waves in CNTRCs plates resting on elastic foundations in a thermal environment", Waves Random Complex Media. https://doi.org/10.1080/17455030.2023.2235611.
  19. Dong, M. (2020), "Scattering of Tollmien-Schlichting waves by localized roughness in transonic boundary layers", Appl. Math. Mech.-Engl., 41, 1105-1124. https://doi.org/10.1007/s10483-020-2622-6.
  20. Gan, L.L. and She, G.L. (2023), "Nonlinear snap-buckling and resonance of FG-GPLRC curved beams with different boundary conditions", Geomech. Eng., 32(5), 541-551. https://doi.org/10.12989/gae.2023.32.5.541.
  21. Gan, L.L. and She, G.L. (2024), "Nonlinear low-velocity impact of magneto-electro-elastic plates with initial geometric imperfection", Acta Astronautica, 214, 11-29. https://doi.org/10.1016/j.actaastro.2023.10.016.
  22. Gan, L.L., Xu, J.Q., and She, G.L. (2023), "Wave propagation of graphene platelets reinforced metal foams circular plates", Struct. Eng. Mech., 85(5), 645-654. https://doi.org/10.12989/sem.2023.85.5.645.
  23. Gao, W.L., Qin, Z.Y. and Chu, F.L. (2020), "Wave propagation in functionally graded porous plates reinforced with graphene platelets", Aerosp. Sci, Technol., 102, 105860. https://doi.org/10.1016/j.ast.2020.105860.
  24. Ghavanloo, E. and Fazelzadeh, S.A. (2013), "Free vibration analysis of orthotropic doubly-curved shallow shells based on the gradient elasticity", Compos. Part B-Eng., 45(1), 1448-1457. https://doi.org/10.1016/j.compositesb.2012.09.054.
  25. Gibson, I. and Ashby, M.F. (1982), "The mechanics of three-dimensional cellular materials", Proc. R. Soc. Lond. Ser. A, Math. Phys. Sci., 382, 43-59. https://doi.org/10.1098/rspa.1982.0088.
  26. Gu, X.J., Hao, Y.X., Zhang, W. and Chen, J. (2019), "Dynamic stability of rotating cantilever composite thin walled twisted plate with initial geometric imperfection under in-plane load", Thin. Wall. Struct., 144, 106267. https://doi.org/10.1016/j.tws.2019.106267.
  27. Guo, Y., Mi, H.L. and Habibi, M. (2021), "Electromechanical energy absorption, resonance frequency, and low-velocity impact analysis of the piezoelectric doubly curved system", Mech. Syst. Signal Pr., 157, 107723. https://doi.org/10.1016/j.ymssp.2021.107723.
  28. Hao, Y., Li, Z., Zhang, W., Li, S.B. and Yao, M.H. (2018), "Vibration of functionally graded sandwich doubly curved shells using improved shear deformation theory", Sci. China Technol. Sci., 61, 791-808. https://doi.org/10.1007/s11431-016-9097-7.
  29. He, Q., Dai, H.L., Zhang, Z. and Tang, H. (2022), "Hygro-thermo-elastic behavior for stiffened metal doubly-curved shallow shells with porous microcapsule coating under low-velocity impact considering in-plane initial load", Compos. Struct., 284, 115213. https://doi.org/10.1016/j.compstruct.2022.115213.
  30. Hu, W.P., Xi, X.J. Song, Z.B., Zhang, C.Z., Deng, Z.C. (2023a) "Coupling dynamic behaviors of axially moving cracked cantilevered beam subjected to transverse harmonic load", Mech. Syst. Signal Pr., 204, 110757. https://doi.org/10.1016/j.ymssp.2023.110757.
  31. Hu, W.P., Han, Z.Q, Bridges, T.J. Qiao, Z.J. (2023b), "Multisymplectic simulations of W/M-Shape-Peaks Solitons and Cuspons for Forq Equation", Appl. Math. Lett., 145, 108772. https://doi.org/10.1016/j.aml.2023.108772.
  32. Hu, W.P., Wang, Z., Zhao, Y.P., Deng, Z.C. (2020a), "Symmetry breaking of infinite-dimensional dynamic system", Appl. Math. Lett., 103, 106207. https://doi.org/10.1016/j.aml.2019.106207.
  33. Hu, W.P., Ye, J., Deng, Z.C. (2020b) "Internal resonance of a flexible beam in a spatial tethered system", J. Sound Vib., 475, 115286, https://doi.org/10.1016/j.jsv.2020.115286.
  34. Huai, Y.L., Hu, W.P., Song, W.Q., Zheng, Y.P., Deng, Z.C. (2023), "Magnetic-field-responsive property of Fe3O4/polyaniline solvent-free nanofluid", Phys. Fluids, https://doi.org/10.1063/5.0130588.
  35. Hu, W.P., Deng, Z.C., Han, S.M., Zhang, W.R. (2013), "Generalized multi-symplectic integrators for a class of hamiltonian nonlinear wave PDEs", J. Comput. Phys., 235, 394-406. https://doi.org/10.1016/j.jcp.2012.10.032.
  36. Karami, B. and Shahsavari, D. (2020), "On the forced resonant vibration analysis of functionally graded polymer composite doubly-curved nanoshells reinforced with graphene-nanoplatelets", Comput. Method. Appl. M., 259, 112767. https://doi.org/10.1016/j.cma.2019.112767.
  37. Kareem, M.G. and Majeed, W.I. (2019), "Transient dynamic analysis of laminated shallow spherical shell under low-velocity impact", J. Mater. Res. Technol., 8(6), 5283-5300. https://doi.org/10.1016/j.jmrt.2019.08.050.
  38. Lei, Z.X. and Tong, L.H. (2019), "Analytical solution of low-velocity impact of graphene-reinforced composite functionally graded cylindrical shells", J. Braz. Soc. Mech. Sci., 41(11), 486. https://doi.org/10.1007/s40430-019-1983-5.
  39. Li, Y.P., She, G.L., Gan, L.L. and Liu, H.B (2023), "Nonlinear thermal post-buckling analysis of graphene platelets reinforced metal foams plates with initial geometrical imperfection", Steel Compos Struct., 46(5), 649-658. https://doi.org/10.12989/scs.2023.46.5.649.
  40. Liu, Y., Hu, W. and Zhu, R. (2022), "Dynamic responses of corrugated cylindrical shells subjected to nonlinear low-velocity impact", Aerosp. Sci. Technol., 121, 107321. https://doi.org/10.1016/j.ast.2021.107321.
  41. Lu, L., She, G.L. and Guo, X. (2021), "Size-dependent postbuckling analysis of graphene reinforced composite microtubes with geometrical imperfection", Int. J. Mech. Sci., 199, 106428. https://doi.org/10.1016/j.ijmecsci.2021.106428.
  42. Qi, Y.N., Dai, H.L. and Deng, S.T. (2020), "Thermoelastic analysis of stiffened sandwich doubly curved plate with FGM core under low velocity impact", Compos Struct., 253, 112826. https://doi.org/10.1016/j.compstruct.2020.112826.
  43. Reddy, J.N. (1984), "Exact Solutions of Moderately Thick Laminated Shells", J. Eng. Mech., 110(5), 794-809. https://doi.org/10.1061/(ASCE)0733-9399(1984)110:5(794).
  44. She, G.L. (2021), "Guided wave propagation of porous functionally graded plates: The effect of thermal loadings", J. Therm. Stresses, 44(10)1289-1305. https://doi.org/10.1080/01495739.2021.1974323.
  45. She, G.L. and Ding, H.X. (2023), "Nonlinear primary resonance analysis of initially stressed graphene platelet reinforced metal foams doubly curved shells with geometric imperfection", Acta Mech. Sin., 39, 522392. https://doi.org/10.1007/s10409-022-22392-x.
  46. She, G.L. and Li, Y.P. (2022), "Wave propagation in an FG circular plate in thermal environment", Geomech. Eng., 31(6), 615-622. https://doi.org/10.12989/gae.2022.31.6.615.
  47. She, G.L., Ding, H.X. and Zhang, Y.W. (2022), "Wave propagation in a FG circular plate via the physical neutral surface concept", Struct. Eng. Mech., 82(2), 225-232. https://doi.org/10.12989/sem.2022.82.2.225.
  48. She, G.L., Liu, H.B. and Karami, B. (2021), "Resonance analysis of composite curved microbeams reinforced with graphene nanoplatelets", Thin Wall. Struct., 160, 107407. https://doi.org/10.1016/j.tws.2020.107407.
  49. Sobhy, M. and Zenkour, A.M. (2019), "Vibration analysis of functionally graded graphene platelet-reinforced composite doubly-curved shallow shells on elastic foundations", Steel Compos Struct., 33(2), 195-208. https://doi.org/10.12989/scs.2019.33.2.195.
  50. Song, J.P. and She, G.L. (2023), "Nonlinear resonance of axially moving GPLRMF plates with different boundary conditions", Struct. Eng. Sci., 86(3), 361-371. https://doi.org/10.12989/sem.2023.86.3.361.
  51. Song, M.T., Li, X. and Kitipornchai, S. (2019), "Low-velocity impact response of geometrically nonlinear functionally graded graphene platelet-reinforced nanocomposite plates", Nonlinear Dyn., 95, 2333-2352. https://doi.org/10.1007/s11071-018-4695-y.
  52. Tan, T.M. and Sun, C. (1985), "Use of statical indentation laws in the impact analysis of laminated composite plates", J. Appl. Mech-T. Asme., 52, 6-12. https://doi.org/10.1115/1.3169029.
  53. Teng, M.W. and Wang, Y.Q. (2021), "Nonlinear forced vibration of simply supported functionally graded porous nanocomposite thin plates reinforced with graphene platelets", Thin. Wall. Struct., 164, 107799. https://doi.org/10.1016/j.tws.2021.107799.
  54. Vinh, P.V. and Tounsi, A. (2022), "Free vibration analysis of functionally graded doubly curved nanoshells using nonlocal first-order shear deformation theory with variable nonlocal parameters", Thin. Wall. Struct., 174, 109084. https://doi.org/10.1016/j.tws.2022.109084.
  55. Wan, Z.M., Yan, H.Z., Sun, Y., Yang, C., Chen, X., Kong, X.Z., Chen, Y.Y., Tu, Z.K. and Wang, X.D. (2023) "Thermal management improvement of air-cooled proton exchange membrane fuel cell by using metal foam flow field", Appl. Energ., 333, 120642. https://doi.org/10.1016/j.apenergy.2023.120642.
  56. Wang, Y.Q., Ye, C. and Zu, J.W. (2019), "Nonlinear vibration of metal foam cylindrical shells reinforced with graphene platelets", Aerosp. Sci. Technol., 85, 359-370. https://doi.org/10.1016/j.ast.2018.12.022.
  57. Wang, Y.W. and Zhang, W. (2022), "On the thermal buckling and postbuckling responses of temperature-dependent graphene platelets reinforced porous nanocomposite beams", Compos Struct., 296, 115880. https://doi.org/10.1016/j.compstruct.2022.115880.
  58. Wang, Z.X., Xu, J.F. and Qiao, P.Z. (2014), "Nonlinear low-velocity impact analysis of temperature-dependent nanotube-reinforced composite plates", Compos. Struct., 108, 423-434. https://doi.org/10.1016/j.compstruct.2013.09.024.
  59. Wu, H.Y.T. and Springer, G.S. (1988), "Impact induced stresses, strains, and delaminations in composite plates", J. Compos. Mater., 22(6), 533-560. https://doi.org/10.1177/002199838802200603.
  60. Wu, F. and She, G.L. (2023), "Wave propagation in double nano-beams in thermal environments using the Reddy's high-order shear deformation theory", Adv. Nano Res., 14(6), 495-506. https://doi.org/10.12989/anr.2023.14.6.495.
  61. Xu, J.Q. and She, G.L. (2022), "Thermal post-buckling analysis of porous functionally graded pipes with initial geometric imperfection", Geomech. Eng., 31(3), 329-337. https://doi.org/10.12989/gae.2022.31.3.329.
  62. Xu, J.Q. and She, G.L. (2023a), "Thermal post-buckling of graphene platelet reinforced metal foams doubly curved shells with geometric imperfection", Struct. Eng. Mech., 87(1), 85-94. https://doi.org/10.12989/sem.2023.87.1.085.
  63. Xu, J.Q. and She, G.L. (2023b), "The effects of temperature and porosity on resonance behavior of graphene platelet reinforced metal foams doubly-curved shells with geometric imperfection", Geomech. Eng., 35(1), 81-93. https://doi.org/10.12989/gae.2023.35.1.081.
  64. Xu, J.Q., She, G.L., Li. Y.P., and Gan, L.L. (2023), "Nonlinear resonances of nonlocal strain gradient nanoplates made of functionally graded materials considering geometric imperfection", Steel Compos. Struct., 47(6), 795-811. https://doi.org/10.12989/scs.2023.47.6.795.
  65. Xu, M.N., Li, X.P., Luo, Y., Wang, G., Guo, Y.H., Liu, T.T., Huang, J.H. and Yan, G. (2020), "Thermal buckling of graphene platelets toughening sandwich functionally graded porous plate with temperature-dependent properties", Int. J. Appl. Mech., 12(8), 2050089. https://doi.org/10.1142/S1758825120500891.
  66. Yang, C. and Ma, W. (2022), "Low-velocity impact response of FG-CNTRC laminated plates with negative Poisson's ratios and clamped boundary conditions", J. Braz. Soc. Mech. Sci. Eng., 44, 337. https://doi.org/10.1007/s40430-022-03627-3.
  67. Yang, C.H., Ma, W.N. and Ma, D.W. (2018a), "Analysis of the low velocity impact response of functionally graded carbon nanotubes reinforced composite spherical shells", J. Mech. Sci. Technol., 32, 2681-2691. https://doi.org/10.1007/s12206-018-0525-x.
  68. Yang, C.H., Ma, W.N., Ma, D.W., He, Q. and Zhong, J.L. (2018b), "Analysis of the low velocity impact response of functionally graded carbon nanotubes reinforced composite spherical shells", J. Mech. Sci. Technol., 32, 2681-2691. https://doi.org/10.1007/s12206-018-0525-x.
  69. Yang, J.S., Zhang, W.M., Yang, F., Chen, S.Y., Schmidt, R., Schroder, K.U., Ma, L. and Wu, L.Z. (2020), "Low velocity impact behavior of carbon fibre composite curved corrugated sandwich shells", Compos Struct., 238, 112027. https://doi.org/10.1016/j.compstruct.2020.112027.
  70. Yang, J., Chen, D. and Kitipornchai, S. (2018c), "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.
  71. Yee, K., Kankanamalage, U.M., Ghayesh, M.H., Yan, J., Hussain, S. and Amabili, M. (2022), "Coupled dynamics of axially functionally graded graphene nanoplatelets-reinforced viscoelastic shear deformable beams with material and geometric imperfections", Eng. Anal. Bound. Elem., 136, 4-36. https://doi.org/10.1016/j.enganabound.2021.12.017.
  72. Zhang, H.W., Zheng, X.Y., Jiang, R.J., Liu, Z.H., Li, W.Y., Zhou, X. (2023) "Research progress of functional composite electromagnetic shielding materials", Eur. Polym. J., 185, 111825. https://doi.org/10.1016/j.eurpolymj.2023.111825.
  73. Zhang, J., Qin, Q. and Chen, S. (2020), "Low-velocity impact of multilayer sandwich beams with metal foam cores: Analytical, experimental, and numerical investigations", J. Sandw. Struct. Mater., 22(3), 626-657. https://doi.org/10.1177/1099636218759827.
  74. Zhang, L., Chen, Z., Habibi, M., Ghabussi, A. and Alyousef, R. (2021a), "Low-velocity impact, resonance, and frequency responses of FG-GPLRC viscoelastic doubly curved panel", Compos. Struct., 269, 114000. https://doi.org/10.1016/j.compstruct.2021.114000.
  75. Zhang, Y.W. and She, G.L. (2022), "Wave propagation and vibration of FG pipes conveying hot fluid", Steel. Compos, Struct., 42(3) 397-405. https://doi.org/10.12989/scs.2022.42.3.397.
  76. Zhang, Y.W. and She, G.L. (2023a), "Nonlinear low-velocity impact response of graphene platelet-reinforced metal foam cylindrical shells under axial motion with geometrical imperfection", Nonlinear Dyn., 111(7), 6317-6334. https://doi.org/10.1007/s11071-022-08186-9.
  77. Zhang, Y.W. and She, G.L. (2023b), "Nonlinear primary resonance of axially moving functionally graded cylindrical shells in thermal environment", Mech. Adv. Mater. Strcut., https://doi.org/10.1080/15376494.2023.2180556.
  78. Zhang, Y.W., Ding, H.X. and She, G.L. (2022), "Snap-buckling and resonance of functionally graded graphene reinforced composites curved beams resting on elastic foundations in thermal environment", J. Therm. Stresses, 45(12), 1029-1042. https://doi.org/10.1080/01495739.2022.2125137.
  79. Zhang, Y.W., Ding, H.X. and She, G.L. (2023a), "Wave propagation in spherical and cylindrical panels reinforced with carbon nanotubes", Steel Compos. Struct., 46(1), 133-141. https://doi.org/10.12989/scs.2023.46.1.133.
  80. Zhang, Y.W., Ding, H.X., She, G.L. and Tounsi, A. (2023d), "Wave propagation of CNTRC beams resting on elastic foundation based on various higher-order beam theories", Geomech. Eng., 33(4), 381-391. https://doi.org/10.12989/gae.2023.33.4.381.
  81. Zhang, Y.W., She, G.L. and Ding, H.X. (2023b), "Nonlinear resonance of graphene platelets reinforced metal foams plates under axial motion with geometric imperfections", Eur. J. Mech. A-Solid., 98, 104887. https://doi.org/10.1016/j.euromechsol.2022.104887.
  82. Zhang, Y.W., She, G.L., Gan, L.L., and Li, Y.P. (2023c), "Thermal post-buckling behavior of GPLRMF cylindrical shells with initial geometrical imperfection", Geomech. Eng., 32(6), 615-625. https://doi.org/10.12989/gae.2023.32.6.615.
  83. Zhang, Y.W., She, G.L. and Eltaher, M.A. (2023d), "Nonlinear transient response of graphene platelets reinforced metal foams annular plate considering rotating motion and initial geometric imperfection", Aeros. Sci. Technol., https://doi.org/10.1016/j.ast.2023.108693.
  84. Zhang, Y.Y., Wang, X.Y., Zhang, X., Shen, H.M. and She, G.L. (2021), "On snap-buckling of FG-CNTRC curved nanobeams considering surface effects", Steel Compos. Struct., 38(3), 293-304. https://doi.org/10.12989/scs.2021.38.3.293.
  85. Zhang, W., Guo, L.J., Wang, Y.W., Mao, J.J. and Yan, J.W. (2022), "Nonlinear low velocity impact response of GRC beam with geometric imperfection under thermo-electro-mechanical loads", Nonlinear. Dyn., 110(4) 3255-3272. https://doi.org/10.1007/s11071-022-07809-5.
  86. Zhao, J.L., Chen, X., She, G.L., Jing, Y., Bai, R.Q., Yi, J., Pu, H.Y., and Luo, J. (2022a), "Vibration characteristics of functionally graded carbon nanotube-reinforced composite double-beams in thermal environments", Steel. Compos. Struct., 43(6), 797-808. https://doi.org/10.12989/scs.2022.43.6.797.
  87. Zhao, J.L., She, G.L., Wu, F., Yuan, S.J., Bai, R.Q., Pu, H.Y., Wang, S.L., and Luo, J. (2022b), "Guided waves of porous FG nanoplates with four edges clamped", Adv. Nano. Res., 13(5), 465-474. https://doi.org/10.12989/anr.2022.13.5.465.
  88. Zheng, G., Zhang, X. W., Li, S. F., Pang, T., Li, Q. and Sun, G.Y. (2022), "Correlation between kinematics and biomechanics of helmeted head under different impact conditions", Compos Struct., 291, 115514. https://doi.org/10.1016/j.compstruct.2022.115514.