journal article·2025-04Open access

New analytical buckling solutions for non-Lévy-type graphene-reinforced composite laminated plates

Zixuan Wang, Dian Xu, Jinbao Li, Zhaoyang Hu, Guangping Gong, Rui Li

Abstract

This study explores the buckling behavior for non-Lévy-type graphene-reinforced composite (GRC) laminated thin and moderately thick plates, with novel analytical solutions derived. The material properties for GRC laminated plates are assessed through an extended Halpin-Tsai model, while the governing buckling equations are derived within a Hamiltonian framework. The difficulty of analytical solution caused by the non-Lévy-type boundary conditions (BCs) is addressed by using the symplectic superposition method . Three different graphene distributions along the thickness direction are considered. The analytical solutions in this study are well verified by the literature results or the finite element numerical results. Based on the solutions, a detailed discussion is performed on the quantitative relationships between the critical buckling loads and the modulus ratios, number of layers, aspect ratios, laying angles, graphene distribution forms, temperatures, width-to-thickness ratios, graphene volume fractions, and BCs.
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Research context

OpenAlex topics: Composite Structure Analysis and Optimization · Structural Analysis and Optimization · Aeroelasticity and Vibration Control

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References (66)

Show source-provided references
1. An accurate, simple theory of the statics and dynamics of elastic plates10.1016/0093-6413(80)90049-X ↗
2. Stability and natural vibration analysis of laminated plates by using a mixed element based on a refined plate theory10.1016/0022-460X(86)90269-5 ↗
3. An efficient standard plate theory
4. Mechanical behaviour of laminated composite beam by the new multi-layered laminated composite structures model with transverse shear stress continuity10.1016/S0020-7683(02)00647-9 ↗
5. Buckling analysis of isotropic and laminated plates by radial basis functions according to a higher-order shear deformation theory10.1016/j.tws.2011.02.005 ↗
6. A new higher order shear deformation theory for sandwich and composite laminated plates10.1016/j.compositesb.2011.07.017 ↗
7. Electric field in atomically thin carbon films10.1126/science.1102896 ↗
8. A molecular mechanics approach for the vibration of single-walled carbon nanotubes10.1016/j.commatsci.2010.03.020 ↗
9. Measurement of the elastic properties and intrinsic strength of monolayer graphene10.1126/science.1157996 ↗
10. Elastic properties and frequencies of free vibrations of single-layer graphene sheets10.1166/jctn.2010.1598 ↗
11. Prediction of Young’s modulus of graphene sheets and carbon nanotubes using nanoscale continuum mechanics approach10.1016/j.matdes.2009.07.058 ↗
12. Buckling resistant graphene nanocomposites
13. Fracture and fatigue in graphene nanocomposites10.1002/smll.200901480 ↗
14. Enhanced mechanical properties of nanocomposites at low graphene content10.1021/nn9010472 ↗
15. Buckling and free vibration analyses of functionally graded graphene reinforced porous nanocomposite plates based on Chebyshev-Ritz method10.1016/j.compstruct.2018.03.090 ↗
16. Parametric studies on buckling behavior of functionally graded graphene-reinforced composites laminated plates in thermal environment10.1016/j.compstruct.2018.03.079 ↗
17. Multi-scale buckling and post-buckling analysis of functionally graded laminated composite plates reinforced by defective graphene sheets
18. Buckling and free vibration analysis of shear deformable graphene-reinforced composite laminated plates10.1016/j.compstruct.2021.114854 ↗
19. Buckling of spinning functionally graded graphene reinforced porous nanocomposite cylindrical shells: An analytical study10.1016/j.ast.2018.09.037 ↗
20. Nonlinear Thermo-Electro-Mechanical Buckling of Higher-Order Shear Deformable Stiffened FG-GRC Laminated Plates
21. A new analytical approach to the nonlinear buckling and postbuckling behavior of functionally graded graphene reinforced composite laminated cylindrical, parabolic, and half-sinusoid shallow imperfect panels10.1002/pc.27748 ↗
22. Nonlinear buckling of higher-order shear deformable stiffened FG-GRC laminated plates with nonlinear elastic foundation subjected to combined loads
23. Nonlinear buckling of stiffened FG-GRCL cylindrical panels under axial compression with the uniformly distributed temperature variation10.1140/epjp/s13360-023-03841-5 ↗
24. Nonlinear vibration and dynamic buckling responses of stiffened functionally graded graphene-reinforced cylindrical, parabolic, and sinusoid panels using the higher-order shear deformation theory
25. Isogeometric thermal buckling analysis of temperature dependent FG graphene reinforced laminated plates using NURBS formulation10.1016/j.compstruct.2017.08.057 ↗
26. Isogeometric thermal postbuckling of FG-GPLRC laminated plates
27. Vibration frequency of graphene based composites: A multiscale approach10.1016/j.mseb.2011.12.024 ↗
28. Free vibration, buckling and bending analyses of multilayer functionally graded graphene nanoplatelets reinforced composite plates using the NURBS formulation10.1016/j.compstruct.2019.03.100 ↗
29. Size dependent free vibration analysis of multilayer functionally graded GPLRC microplates based on modified strain gradient theory10.1016/j.compositesb.2019.02.048 ↗
30. Isogeometric analysis for buckling and postbuckling of graphene platelet reinforced composite plates in thermal environments10.1016/j.engstruct.2021.112746 ↗
31. Isogeometric analysis for postbuckling of sandwich cylindrical shell panels with graphene platelet reinforced functionally graded porous core10.1016/j.compstruct.2020.113258 ↗
32. Isogeometric analysis of functionally graded porous plates reinforced by graphene platelets10.1016/j.compstruct.2018.07.059 ↗
33. Buckling and post-buckling analyses of functionally graded graphene reinforced piezoelectric plate subjected to electric potential and axial forces10.1016/j.compstruct.2019.02.095 ↗
34. Parametric instability of thermo-mechanically loaded functionally graded graphene reinforced nanocomposite plates10.1016/j.ijmecsci.2017.11.039 ↗
35. Thermal buckling and postbuckling of functionally graded graphene nanocomposite plates10.1016/j.matdes.2017.07.025 ↗
36. Thermal and Mechanical Buckling and Vibration Analysis of FG-GPLRC Annular Plate Using Higher Order Shear Deformation Theory and Generalized Differential Quadrature Method10.1142/S1758825120500192 ↗
37. A computational framework for multi-stability analysis of laminated shells10.1016/j.jmps.2021.104317 ↗
38. A data-driven approach for instability analysis of thin composite structures10.1016/j.compstruc.2022.106898 ↗
39. Nonlinear bending of functionally graded graphene-reinforced composite laminated plates resting on elastic foundations in thermal environments10.1016/j.compstruct.2017.03.001 ↗
40. Thermal buckling and postbuckling of functionally graded graphene-reinforced composite laminated plates resting on elastic foundations10.1016/j.tws.2017.05.006 ↗
41. Thermal buckling and postbuckling behavior of FG-GRC laminated cylindrical shells with temperature-dependent material properties10.1007/s11012-019-00945-0 ↗
42. Buckling and postbuckling of functionally graded graphene-reinforced composite laminated plates in thermal environments10.1016/j.compositesb.2017.03.020 ↗
43. Tension buckling and postbuckling of nanocomposite laminated plates with in-plane negative Poisson’s ratio10.1515/ntrev-2023-0173 ↗
44. Effect of negative Poisson’s ratio on the post-buckling behavior of FG-GRMMC laminated plates in thermal environments10.1016/j.compstruct.2020.112731 ↗
45. Buckling and postbuckling of biaxially compressed functionally graded multilayer graphene nanoplatelet-reinforced polymer composite plates10.1016/j.ijmecsci.2017.07.017 ↗
46. Bending and buckling analyses of functionally graded polymer composite plates reinforced with graphene nanoplatelets10.1016/j.compositesb.2017.09.043 ↗
47. Analytical solution of cross- and angle-ply nano plates with strain gradient theory for linear vibrations and buckling10.1080/15376494.2019.1655613 ↗
48. Characterization of the vibration, stability and static responses of graphene-reinforced sandwich plates under mechanical and thermal loadings using the refined shear deformation plate theory10.1177/1099636221993865 ↗
49. Post-buckling behavior of rectangular multilayer FG-GPLRC plate with initial geometric defects subjected to non-uniform in-plane compression loads in thermal environment10.1080/15376494.2022.2119313 ↗
50. Stability analysis of embedded graphene platelets reinforced composite plates in thermal environment10.1140/epjp/i2019-12581-6 ↗
51. 3D thermo-mechanical bending solution of functionally graded graphene reinforced circular and annular plates10.1016/j.apm.2017.04.044 ↗
52. Exact solutions for functionally graded and laminated elastic materials10.1016/S0022-5096(98)00048-9 ↗
53. Benchmark symplectic solutions for bending of corner-supported rectangular thin plates
54. On new symplectic elasticity approach for exact bending solutions of rectangular thin plates with two opposite sides simply supported10.1016/j.ijsolstr.2007.01.007 ↗
55. A new symplectic approach for piezoelectric cantilever composite plates10.1016/j.compstruc.2008.04.005 ↗
56. Dynamic buckling of cylindrical shells subject to an axial impact in a symplectic system10.1016/j.ijsolstr.2005.03.005 ↗
57. Symplectic elasticity approach for free vibration of rectangular plates
58. Yao · 2009
59. New analytic bending, buckling, and free vibration solutions of rectangular nanoplates by the symplectic superposition method10.1038/s41598-021-82326-w ↗
60. New symplectic analytic solutions for buckling of CNT reinforced composite rectangular plates10.1016/j.compstruct.2022.116361 ↗
61. New analytical solutions for eastoplastic buckling of non-Lévy-type rectangular plates10.2514/1.J063147 ↗
62. Free vibration of non-Lévy-type rectangular line-hinged plates: Analytical solutions in the symplectic framework10.1016/j.tws.2024.111692 ↗
63. The Halpin-Tsai equations: A review10.1002/pen.760160512 ↗
64. Reddy · 2003
65. Analysis User's Guide V6. 13
66. Temperature dependent mechanical properties of graphene reinforced polymer nanocomposites – A molecular dynamics simulation10.1016/j.compositesb.2016.12.004 ↗