DOI QR코드

DOI QR Code

Assessment of negative Poisson's ratio effect on thermal post-buckling of FG-GRMMC laminated cylindrical panels

  • Shen, Hui-Shen (School of Aeronautics and Astronautics, Shanghai Jiao Tong University) ;
  • Xiang, Y. (School of Engineering, Design and Built Environment, Western Sydney University)
  • 투고 : 2020.12.23
  • 심사 : 2021.01.10
  • 발행 : 2021.05.25

초록

This paper examines the thermal post-buckling behaviors of graphene-reinforced metal matrix composite (GRMMC) laminated cylindrical panels which possess in-plane negative Poisson's ratio (NPR) and rest on an elastic foundation. A panel consists of GRMMC layers of piece-wise varying graphene volume fractions to obtain functionally graded (FG) patterns. Based on the MD simulation results, the GRMMCs exhibit in-plane NPR as well as temperature-dependent material properties. The governing equations for the thermal post-buckling of panels are based on the Reddy's third order shear deformation shell theory. The von Karman nonlinear strain-displacement relationship and the elastic foundation are also included. The nonlinear partial differential equations for GRMMC laminated cylindrical panels are solved by means of a singular perturbation technique in associate with a two-step perturbation approach and in the solution process the boundary layer effect is considered. The results of numerical investigations reveal that the thermal post-buckling strength for (0/90)5T GRMMC laminated cylindrical panels can be enhanced with an FG-X pattern. The thermal post-buckling load-deflection curve of 6-layer (0/90/0)S and (0/90)3T panels of FG-X pattern are higher than those of 10-layer (0/90/0/90/0)S and (0/90)5T panels of FG-X pattern.

키워드

과제정보

The supports for this work, provided by the National Natural Science Foundation of China (NSFC) under Grant 51779138, are gratefully acknowledged.

참고문헌

  1. Alderson, K.L. and Coenen, V.L. (2008), "The low velocity impact response of auxetic carbon fibre laminates", Phys. Stat. Sol. B, 245, 489-496. https://doi.org/10.1002/pssb.200777701.
  2. Ansari, R., Torabi, J. and Hassani, R. (2019), "Thermal buckling analysis of temperature-dependent FG-CNTRC quadrilateral plates", Comput. Math. Appl., 77, 1294-1311. https://doi.org/10.1016/j.camwa.2018.11.009
  3. Azoti, W.L., Koutsawa, Y., Bonfoh, N., Lipinski, P. and Belouettar, S. (2013), "Analytical modeling of multilayered dynamic sandwich composites embedded with auxetic layers", Eng. Struct., 57, 248-253. https://doi.org/10.1016/j.engstruct.2013.09.030
  4. Babaei, H., Kiani, Y. and Eslami, M.R. (2018), "Application of two-steps perturbation technique to geometrically nonlinear analysis of long FGM cylindrical panels on elastic foundation under thermal load", J. Thermal Stress., 41, 847-865. https://doi.org/ 10.1080/01495739.2017.1421054.
  5. Babaei, H., Kiani, Y. and Eslami, M.R. (2019), "Large amplitude free vibrations of long FGM cylindrical panels on nonlinear elastic foundation based on physical neutral surface", Compos. Struct., 220, 888-898. https://doi.org/10.1016/j.compstruct.2019.03.064.
  6. Bayat, M.R. and Mashhadi, M.M. (2018), "Low-velocity impact response of sandwich cylindrical panels with nanotube-reinforced and metal face sheet in thermal environment", Aeronaut. J., 122, 1943-1966. https://doi.org/10.1017/aer.2018.104.
  7. Chen, X. and Feng, Z. (2017), "Dynamic behaviour of a thin laminated plate embedded with auxetic layers subject to inplane excitation", Mech. Res. Commun., 85, 45-52. https://doi.org/10.1016/j.mechrescom.2017.07.013.
  8. Clarke, J.F., Duckett, R.A., Hine, P.J., Hutchinson, I.J. and Ward, I.M. (1994), "Negative Poisson's ratios in angle-ply laminates: theory and experiment", Compos., 25, 863-868. https://doi.org/10.1016/0010-4361(94)90027-2.
  9. Cong, P.H., Khanh, N.D., Khoa, N.D. and Duc, N.D. (2018), "New approach to investigate nonlinear dynamic response of sandwich auxetic double curves shallow shells using TSDT", Compos. Struct., 185, 455-465. https://doi.org/10.1016/j.compstruct.2017.11.047.
  10. Dadkhah, M., Saboori, A. and Fino, P. (2019), "An overview of the recent developments in metal matrix nanocomposites reinforced by graphene", Materials, 12, 2823. https://doi.org/10.3390/ma12172823.
  11. Dehrouyeh-Semnani, A.M. and Jafarpour, S. (2019), "Nonlinear thermal stability of temperature-dependent metal matrix composite shallow arches with functionally graded fiber reinforcements", Int. J. Mech. Sci., 161, 105075. https://doi.org/10.1016/ j.ijmecsci.2019.105075.
  12. Duc, N.D., Kim, S.-E., Tuan, N.D., Tran, P. and Khoa, N.D. (2017), "New approach to study nonlinear dynamic response and vibration of sandwich composite cylindrical panels with auxetic honeycomb core layer", Aero. Sci. Tech., 70, 396-404. https://doi.org/10.1016/j.ast.2017.08.023.
  13. Duc, N.D. and Cong, P.H. (2018), "Nonlinear dynamic response and vibration of sandwich composite plates with negative Poisson's ratio in auxetic honeycombs", J. Sandw. Struct. Mater., 20, 692-717. https://doi.org/10.1177/1099636216674729.
  14. Ebrahimi, F., Nouraei, M., Dabbagh, A. and Rabczuk, T. (2019), "Thermal buckling analysis of embedded graphene-oxide powder-reinforced nanocomposite plates", Adv. Nano Res., Int. J., 7(5), 293-310. https://doi.org/10.12989/anr.2019.7.5.293.
  15. Evans, K.E., Donoghue, J.P. and Alderson, K.L. (2004), "The design, matching and manufacture of auxetic carbon fibre laminates", J. Compos. Mater., 38, 95-105. https://doi.org/10.1177/0021998304038645.
  16. Fan, Y. and Wang, Y. (2021), "The effect of negative Poisson's ratio on the low-velocity impact response of an auxetic nanocomposite laminate beam", Int. J. Mech. Mater. Des., 17(1), 153-169. https://doi.org/ 10.1007/s10999-020-09521-x.
  17. Fan, Y., Xiang, Y. and Shen, H.-S. (2019), "Temperature-dependent negative Poisson's ratio of monolayer graphene: Prediction from molecular dynamics simulations", Nanotechnol. Rev., 8, 415-421. https://doi.org/10.1515/ntrev-2019-0037.
  18. Fan, Y., Xiang, Y. and Shen, H.-S. (2020), "Temperature-dependent mechanical properties of graphene/Cu nanocomposites with in-plane negative Poisson's ratios", Research, 2020, 5618021. https://doi.org/10.34133/2020/5618021l.
  19. Fattahi, A.M. and Sahmani, S. (2017), "Size dependency in the axial postbuckling behavior of nanopanels made of functionally graded material considering surface elasticity", Arab. J. Sci. Eng., 42, 4617-4633. https://doi.org/10.1007/s13369-017-2600-5.
  20. Feldman, E. (1996), "The effect of temperature-dependent material properties on elasto-viscoplastic buckling behaviour of non-uniformly heated MMC plates", Compos. Struct., 35, 65-74. https://doi.org/10.1016/0263-8223(96)00024-4.
  21. Feldman, E. and Aboudi, J. (1995), "Thermal postbuckling of metal matrix laminated plates", J. Thermal Stress., 18, 197-218. https://doi.org/10.1080/01495739508946299.
  22. Harkati, E.H., Bezazi, A., Scarpa, F., Alderson, K. and Alderson, A. (2007), "Modelling the influence of the orientation and fibre reinforcement on the Negative Poisson's ratio in composite laminates", Phys. Status Solidi B, 244, 883-892. https://doi.org/10.1002/ pssb.200572707.
  23. Herakovich, C.T. (1984), "Composite laminates with Negative through-the-thickness Poisson's ratios", J. Compos. Mater., 18, 447-455. https://doi.org/10.1177/ 002199838401800504.
  24. Hine, P.J., Duckett, R.A. and Ward, I.M. (1997), "Negative Poisson's ratios in angle-ply laminates", J. Mater. Sci. Lett., 16, 541-544. https://doi.org/10.1023/A:1018505503088.
  25. Hu, Z., Tong, G., Lin, D., Chen, C., Guo, H., Xu, J. and Zhou, L. (2016), "Graphene-reinforced metal matrix nanocomposites-A review", Mater. Sci. Technol., 32, 930-953. https://doi.org/10.1080/02670836.2015.1104018.
  26. Huang, C. and Chen, L. (2016), "Negative Poisson's ratio in modern functional materials", Adv. Mater., 28, 8079-8096. https://doi.org/10.1002/adma.201601363.
  27. Huang, X.-H., Yang, J., Bai, L., Wang, X. and Ren, X. (2020a), "Theoretical solutions for auxetic laminated beam subjected to a sudden load", Structures, 28, 57-68. https://doi.org/10.1016/j.istruc.2020.08.030.
  28. Huang, X.-H., Yang, J., Wang, X. and Azim, I. (2020b), "Combined analytical and numerical approach for auxetic FG-CNTRC plate subjected to a sudden load", Eng. with Comput. https://doi.org/10.1007/s00366-020-01106-8.
  29. Karami, B. and Karami, S. (2019), "Buckling analysis of nanoplate-type temperature-dependent heterogeneous materials", Adv. Nano Res., Int. J., 7(1), 51-61. https://doi.org/10.12989/ anr.2019.7.1.051.
  30. Kiani, Y. (2018), "NURBS-based isogeometric thermal postbuckling analysis of temperature dependent graphene reinforced composite laminated plates", Thin-Walled Struct., 125, 211-219. https://doi.org/10.1016/j.tws.2018.01.024.
  31. Kiani, Y. and Mirzaei, M. (2018), "Enhancement of non-linear thermal stability of temperature dependent laminated beams with graphene reinforcements", Compos. Struct., 186, 114-122. https://doi.org/10.1016/j.compstruct.2017.11.086.
  32. Lakes, R.S. (2017), "Negative-Poisson's-ratio materials: Auxetic solids", Annu. Rev. Mater. Res., 47, 63-81. https://doi.org/10.1146/annurev-matsci-070616-124118.
  33. Lal, A., Singh, B.N. and Kale, S., (2012), "Stochastic thermal post-buckling response of laminated composite cylindrical shell panel with system randomness", Int. J. Appl. Mech., 4, 1250009. https://doi.org/10.1142/S1758825112001385.
  34. Lee, J.J., Oh, I.-K., Lee, I. and Yeom, C.H. (2002), "Thermal post-buckling behavior of patched laminated panels under uniform and non-uniform temperature distributions", Compos. Struct., 55, 137-145. https://doi.org/10.1016/S0263-8223(01)00139-8.
  35. Li, C., Shen, H.-S. and Wang, H. (2019a), "Thermal post-buckling of sandwich beams with functionally graded negative Poisson's ratio honeycomb core", Int. J. Mech. Sci., 152, 289-297. https://doi.org/10.1016/j.ijmecsci.2019.01.002.
  36. Li, C., Shen, H.-S. and Wang, H. (2019b), "Nonlinear bending of sandwich beams with functionally graded negative Poisson's ratio honeycomb core", Compos. Struct., 212, 317-325. https://doi.org/10.1016/j.compstruct.2019.01.020.
  37. Li, C., Shen, H.-S. and Wang, H. (2019c), "Nonlinear dynamic response of sandwich beams with functionally graded negative Poisson's ratio honeycomb core", Euro. Phys. J. Plus, 134, 79. https://doi.org/10.1140/epjp/i2019-12572-7.
  38. Li, C., Shen, H.-S. and Wang, H. (2019d), "Nonlinear vibration of sandwich beams with functionally graded negative Poisson's ratio honeycomb core", Int. J. Struct. Stabil. Dyn., 19, 1950034. https://doi.org/10.1142/S0219455419500342.
  39. Li, C., Shen, H.-S. and Wang, H. (2020a), "Postbuckling behavior of sandwich plates with functionally graded auxetic 3D lattice core", Compos. Struct., 237, 111894. https://doi.org/10.1016/j.compstruct.2020.111894.
  40. Li, C., Shen, H.-S., Wang, H. and Yu, Z. (2020b), "Large amplitude vibration of sandwich plates with functionally graded auxetic 3D lattice core", Int. J. Mech. Sci., 174, 105472. https://doi.org/10.1016/j.ijmecsci.2020.105472.
  41. Li, C., Shen, H.-S. and Wang, H. (2020c), "Nonlinear dynamic response of sandwich plates with functionally graded auxetic 3D lattice core", Nonlinear Dyn., 100, 3235-3252. https://doi.org/10.1007/s11071-020-05686-4.
  42. Li, C., Shen, H.-S. and Wang, H. (2020d), "Full-scale finite element modeling and nonlinear bending analysis of sandwich plates with functionally graded auxetic 3D lattice core", J. Sandw. Struct. Mater. https://doi.org/10.1177/1099636220924657.
  43. Liang, Q., Yao, X., Wang, W., Liu, Y. and Wong, C.P. (2011), "A three-dimensional vertically aligned functionalized multilayer graphene architecture: an approach for graphene-based thermal interfacial materials", ACS Nano, 5, 2392-2401. https://doi.org/10.1021/nn200181e.
  44. Lin, F., Xiang, Y. and Shen, H.-S. (2017), "Temperature dependent mechanical properties of graphene reinforced polymer nanocomposites - a molecular dynamics simulation", Compos. Part B-Eng., 111, 261-269. https://doi.org/10.1016/j.compositesb.2016.12.004.
  45. Liu, Q. (2006), "Literature review: Materials with negative Poisson's ratios and potential applications to aerospace and defence", Report no. dsto-gd-0472, Defence Science and Technology Organisation, Department of Defence, Australian Government.
  46. Ma, W., Yang, C., Ma, D. and Zhong, J.L. (2019), "Low-velocity impact response of nanotube-reinforced composite sandwich curved panels", SADHANA-Academy Proc. Eng. Sci., 44, 227. https://doi.org/10.1007/s12046-019-1214-x.
  47. 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. https://doi.org/10.12989/anr.2019.7.3.179.
  48. Milton, G.W. (1992), "Composite materials with Poisson's ratios close to - 1", J. Mech. Phys. Solids., 40, 1105-1137. https://doi.org/10.1016/0022-5096(92)90063-8.
  49. Mir, M., Ali, M.N., Sami, J. and Ansari, U. (2014), "Review of mechanics and applications of auxetic structures", Adv. Mater. Sci. Eng., 2014, 753496. https://doi.org/10.1155/2014/753496.
  50. Mirzaei, M. and Kiani, Y. (2016), "Thermal buckling of temperature dependent FG-CNT reinforced composite plates", Meccanica, 51, 2185-2201. https://doi.org/10.1007/s11012-015-0348-0.
  51. Mirzaei, M. and Kiani, Y. (2017), "Isogeometric thermal buckling analysis of temperature dependent FG graphene reinforced laminated plates using NURBS formulation", Compos. Struct., 180, 606-616. https://doi.org/10.1016/j.compstruct.2017.08.057.
  52. Naseer, A., Ahmad, F., Aslam, M., Guan, B.H., Wan Harund, W.S., Muhamade, N., Razaf, M.R. and German, R.M. (2019), "A review of processing techniques for graphene-reinforced metal matrix composites", Mater. Manufact. Process., 34, 957-985. https://doi.org/ 10.1080/10426914.2019.1615080.
  53. Ni, Z., Bu, H., Zou, M., Yi, H., Bi, K. and Chen, Y. (2010), "Anisotropic mechanical properties of graphene sheets from molecular dynamics", Physica B, 405, 1301-1306. https://doi.org/ 10.1016/j.physb.2009.11.071.
  54. Novoselov, K.S., Geim, A.K., Morozov, S.V., Jiang, D., Zhang, Y., Dubonos, S.V., Grigorieva, I.V. and Firsov, A. (2004), "Electric filed effect in atomically thin carbon films", Science, 306, 666-669. https://doi.org/10.1126/science.1102896.
  55. Oh, I.K. and Lee, I. (2001), "Thermal snapping and vibration characteristics of cylindrical composite panels using layerwise theory", Compos. Struct., 51, 49-61. https://doi.org/10.1016/S0263-8223(00)00123-9.
  56. Panda, S.K. and Singh, B.N. (2009), "Thermal post-buckling behaviour of laminated composite cylindrical/hyperboloid shallow shell panel using nonlinear finite element method", Compos. Struct., 91, 366-374. https://doi.org/10.1016/j.compstruct.2009.06.004.
  57. Panda, S.K. and Singh, B.N. (2013), "Post-buckling analysis of laminated composite doubly curved panel embedded with SMA fibers subjected to thermal environment", Mech. Adv. Mater. Struct., 20, 842-853. https://doi.org/10.1080/15376494.2012.677097.
  58. Paley, M. and Aboudi, J. (1991), "Inelastic thermal buckling of metal matrix laminated plates", J. Thermal Stress., 14, 479-497. https://doi.org/10.1080/01495739108927081.
  59. Prawoto, Y. (2012), "Seeing auxetic materials from the mechanics point of view: A structural review on the negative Poisson's ratio", Comput. Mater. Sci., 58, 140-153. https://doi.org/10.1016/j.commatsci.2012.02.012.
  60. Reddy, J.N. and Liu, C.F. (1985), "A higher-order shear deformation theory of laminated elastic shells", Int. J. Eng. Sci., 23, 319-330. https://doi.org/10.1016/0020-7225(85)90051-5.
  61. Ren, X., Das, R., Tran, P., Ngo, T.D. and Xie, Y.M. (2018), "Auxetic metamaterials and structures: a review", Smart Mater. Struct., 27, 023001. https://doi.org/10.1088/1361-665X/aaa61c.
  62. Roh, J.H., Oh, I.K., Yang, S.M., Han, J.H. and Lee, I. (2004), "Thermal post-buckling analysis of shape memory alloy hybrid composite shell panels", Smart Mater. Struct., 13, 1337-1344. https://doi.org/10.1088/0964-1726/13/6/006.
  63. Sahmani, S. and Fattahi, A.M. (2017), "Imperfection sensitivity of the size-dependent nonlinear instability of axially loaded FGM nanopanels in thermal environments", Acta Mech., 228, 3789-3810. https://doi.org/10.1007/s00707-017-1912-6.
  64. Saxena, K.K., Das, R. and Calius, E.P. (2016), "Three decades of auxetics research-materials with negative Poisson's ratio: A review", Adv. Eng. Mater., 18, 1847-1870. https://doi.org/10.1002/adem.201600053
  65. Sharma, S., Kumar, P. and Chandra, R. (2017), "Mechanical and thermal properties of graphene-carbon nanotube-reinforced metal matrix composites: A molecular dynamics study", J. Compos. Mater., 51, 3299-3313. https://doi.org/10.1177/0021998316682363.
  66. She, G.L., Yuan, F.G. and Ren, Y.R. (2017), "Research on nonlinear bending behaviors of FGM infinite cylindrical shallow shells resting on elastic foundations in thermal environments", Compos. Struct., 170, 111-121. https://doi.org/10.1016/j.compstruct.2017.03.010.
  67. Shen, H.-S. (2009a), Functionally Graded Materials Nonlinear Analysis of Plates and Shells, CRC Press, Boca Raton.
  68. Shen, H.-S. (2009b), "Nonlinear bending of functionally graded carbon nanotube-reinforced composite plates in thermal environments", Compos, Struct., 91, 9-19. https://doi.org/10.1016/ j.compstruct.2009.04.026.
  69. Shen, H.-S. (2013), A Two-Step Perturbation Method in Nonlinear Analysis of Beams, Plates and Shells, John Wiley & Sons Inc.
  70. Shen, H.-S. (2017), Postbuckling Behavior of Plates and Shells, World Scientific Publishing Co. Pte. Ltd., Singapore.
  71. Shen, H.-S. and Wang, H. (2013), "Thermal postbuckling of functionally graded fiber reinforced composite cylindrical shells surrounded by an elastic medium", Compos. Struct., 102, 250-260. https://doi.org/10.1016/j.compstruct.2013.03.011.
  72. Shen, H.-S. and Xiang, Y. (2015), "Thermal postbuckling of nanotube-reinforced composite cylindrical panels resting on elastic foundations", Compos. Struct., 123, 383-392. https://doi.org/ 10.1016/j.compstruct.2014.12.059.
  73. Shen, H.-S., and Xiang, Y. (2019), "Thermal buckling and postbuckling behavior of FG-GRC laminated cylindrical shells with temperature-dependent material properties", Meccanica, 54, 283-297. https://doi.org/10.1007/s11012-019-00945-0.
  74. Shen, H.-S. and Xiang, Y. (2020), "Effect of negative Poisson's ratio on the axially compressed postbuckling behavior of FG-GRMMC laminated cylindrical panels on elastic foundations", Thin-Walled Struct., 157, 107090. https://doi.org/10.1016/j.tws.2020.107090.
  75. Shen, H.-S., Lin, F. and Xiang, Y. (2017a), "Nonlinear bending and thermal postbuckling of functionally graded graphene-reinforced composite laminated beams resting on elastic foundations", Eng. Struct., 140, 89-97. https://doi.org/10.1016/j.engstruct.2017.02.069.
  76. Shen, H.-S., Xiang, Y. and Lin, F. (2017b), "Thermal buckling and postbuckling of functionally graded graphene-reinforced composite laminated plates resting on elastic foundations", Thin-Walled Struct., 118, 229-237. https://doi.org/10.1016/j.tws.2017.05.006.
  77. Shen, H.-S., Xiang, Y. and Fan, Y. (2019a), "Large amplitude vibration of doubly curved FG-GRC laminated panels in thermal environments", Nanotechnol. Rev., 8, 467-483. https://doi.org/ 10.1515/ntrev-2019-0042.
  78. Shen, H.-S., Xiang, Y. and Reddy, J.N. (2019b), "Thermal postbuckling behavior of FG-GRC laminated cylindrical panels with temperature-dependent properties", Compos. Struct., 211, 433-442. https://doi.org/10.1016/j.compstruct.2018.12.023.
  79. Shen, H.-S., Li, C. and Reddy, J.N. (2020a), "Large amplitude vibration of FG-CNTRC laminated cylindrical shells with negative Poisson's ratio", Comput. Methods Appl. Mech. Eng., 360, 112727. https://doi.org/10.1016/j.cma.2019.112727.
  80. Shen, H.-S., Huang, X.-H. and Yang, J. (2020b), "Nonlinear bending of temperature-dependent FG-CNTRC laminated plates with negative Poisson's ratio", Mech. Adv. Mater. Struct., 27, 1141-1153. https://doi.org/10.1080/15376494.2020.1716412.
  81. Shen, H.-S., Xiang, Y. and Reddy, J.N. (2020c), "Effect of negative Poisson's ratio on the post-buckling behavior of FG-GRMMC laminated plates in thermal environments", Compos. Struct., 253, 112731. https://doi.org/10.1016/j.compstruct.2020.112731.
  82. Shen, L., Shen, H.-S. and Zhang, C.L. (2010), "Temperature-dependent elastic properties of single layer graphene sheets", Mater. Des., 31, 4445-4449. https://doi.org/10.1016/j.matdes.2010.04.016.
  83. Sun, C.T. and Li, S.J. (1988), "Three-dimensional effective elastic constants for thick laminates", J. Compos. Mater., 22, 629-639. https://doi.org/10.1177/002199838802200703.
  84. Tabandeh-Khorshid, M., Kumar, A., Omrani, E., Kim, C. and Rohatgi, P. (2020), "Synthesis, characterization, and properties of graphene reinforced metal-matrix nanocomposites", Compos. Part B-Eng., 183, 107664. https://doi.org/10.1016/j.compositesb.2019.107664.
  85. Thanh, C.L., Tran, L.V., Vu-Huu, T. and Abdel-Wahab, M. (2019), "The size-dependent thermal bending and buckling analyses of composite laminate microplate based on new modified couple stress theory and isogeometric analysis", Comput. Methods Appl. Mech. Eng., 350, 337-361. https://doi.org/10.1016/j.cma.2019.02.028.
  86. Tran, L.V., Wahab, M.A. and Kim, S.E. (2017), "An isogeometric finite element approach for thermal bending and buckling analyses of laminated composite plates", Compos. Struct., 179, 35-49. https://doi.org/10.1016/j.compstruct.2017.07.056.
  87. Trang, L.T.N. and Tung, H.V. (2020), "Thermally induced postbuckling of higher order shear deformable CNT-reinforced composite flat and cylindrical panels resting on elastic foundations with elastically restrained edges", Mech. Based Des. Struct. Machin., 1-24. https://doi.org/10.1080/15397734.2020.1785312.
  88. Tung, H.V. and Trang, L.T.N. (2020), "Thermal post-buckling of shear deformable CNT-reinforced composite plates with tangentially restrained edges and temperature-dependent properties", J. Thermoplastic Compos. Mater., 33, 97-124. https://doi.org/10.1177/ 0892705718804588.
  89. Yang, J., Huang, X.-H. and Shen, H.-S. (2020a), "Nonlinear vibration of temperature-dependent FG-CNTRC laminated plates with negative Poisson's ratio", Thin-Walled Struct., 148, 106514. https://doi.org/10.1016/j.tws.2019.106514.
  90. Yang, J., Huang, X.-H. and Shen, H.-S. (2020b), "Nonlinear flexural behavior of temperature-dependent FG-CNTRC laminated beams with negative Poisson's ratio resting on the Pasternak foundation", Eng. Struct., 207, 110250. https://doi.org/10.1016/ j.engstruct.2020.110250.
  91. Yang, J., Huang, X.-H. and Shen, H.-S. (2020c), "Nonlinear vibration of temperature-dependent FG-CNTRC laminated beams with negative Poisson's Ratio", Int. J. Struct. Stabil. Dyn., 20, 2050043. https://doi.org/10.1142/S0219455420500431.
  92. Yeh, H.L. amd Yeh, H.Y. (1999), "A discussion of negative poisson's ratio design for composites", J. Reinf. Plastics Compos., 18, 1546-1556. https://doi.org/10.1177/073168449901801701.
  93. Yu, Y. and Shen, H.-S. (2020a), "A comparison of nonlinear vibration and bending of hybrid CNTRC/metal laminated plates with positive and negative Poisson's ratios", Int. J. Mech. Sci., 183, 105790. https://doi.org/10.1016/j.ijmecsci.2020.105790.
  94. Yu, Y. and Shen, H.-S. (2020b), "A comparison of nonlinear bending and vibration of hybrid metal/CNTRC laminated beams with positive and negative Poisson's ratios", Int. J. Struct. Stabil. Dyn., 20, 2043007. https://doi.org/10.1142/S021945542043007.5
  95. Zhang, J., Zhu, X., Yang, X. and Zhang, W. (2019), "Transient nonlinear responses of an auxetic honeycomb sandwich plate under impact loads", Int. J. Impact Eng., 134, 103383. https://doi.org/10.1016/j.ijimpeng.2019.103383.
  96. Zhang, R., Yeh, H.L. and Yeh, H.Y. (1998), "A preliminary study of negative Poisson's ratio of laminated fiber reinforced composites", J. Reinf. Plastics Compos., 17, 1651-1664. https://doi.org/10.1177/073168449801701806.
  97. Zhao, Y.X., Liu, T. and Li, Z.M. (2018), "Nonlinear bending analysis of a 3D braided composite cylindrical panel subjected to transverse loads in thermal environments", Chinese J. Aeron., 31, 1716-1727. https://doi.org/10.1016/j.cja.2018.03.022.