Steel and Composite Structures

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On the stability of isotropic and composite thick plates

  • Mahmoud, S.R. (GRC Department, Jeddah Community College, King Abdulaziz University) ;
  • Tounsi, Abdelouahed (Civil and Environmental Engineering Department, King Fahd University of Petroleum & Minerals)
  • Received : 2019.06.30
  • Accepted : 2019.10.27
  • Published : 2019.11.25
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Abstract

This proposed project presents the bi-axial and uni-axial stability behavior of laminated composite plates based on an original three variable "refined" plate theory. The important "novelty" of this theory is that besides the inclusion of a cubic distribution of transverse shear deformations across the thickness of the structure, it treats only three variables such as conventional plate theory (CPT) instead five as in the well-known theory of "first shear deformation" (FSDT) and theory of "higher order shear deformation" (HSDT). A "shear correction coefficient" is therefore not employed in the current formulation. The computed results are compared with those of the CPT, FSDT and exact 3D elasticity theory. Good agreement is demonstrated and proved for the present results with those of "HSDT" and elasticity theory.

Keywords

Acknowledgement

Supported by : Deanship of Scientific Research (DSR)

References

  1. Abualnour, M., Chikh, A., Hebali, H., Kaci, A., Tounsi, A., Bousahla, A.A. and Tounsi, A. (2019), "Thermomechanical analysis of antisymmetric laminated reinforced composite plates using a new four variable trigonometric refined plate theory", Comput. Concrete, Int. J., 24(6), December 2019. [In press]
  2. Akavci, S.S. (2007), "Buckling and free vibration analysis of symmetric and antisymmetric laminated composite plates on an elastic foundation", J. Reinf. Plast. Compos., 26(18), 1907-1919. https://doi.org/10.1177/0731684407081766
  3. Akbas, Ş.D. (2019), "Forced vibration analysis of functionally graded sandwich deep beams", Coupl. Syst. Mech., Int. J., 8(3), 259-271. https://doi.org/10.12989/csm.2019.8.3.259
  4. Akhavan, H., Hashemi, S.H., Damavanditaher, H.R., Alibeigloo, A. and Vahabi, S. (2009), "Exact solutions for rectangular Mindlin plates under in-plane loads resting on Pasternak elastic foundation. Part I: Buckling analysis", Comput. Mat. Sci., 44, 968-978. https://doi.org/10.1016/j.commatsci.2008.07.004
  5. Alimirzaei, S., Mohammadimehr, M. and Tounsi, A. (2019), "Nonlinear analysis of viscoelastic micro-composite beam with geometrical imperfection using FEM: MSGT electro-magnetoelastic bending, buckling and vibration solutions", Struct. Eng. Mech., Int. J., 71(5), 485-502. https://doi.org/10.12989/sem.2019.71.5.485
  6. Arya, H., Shimpi, R.P. and Naik, N.K. (2002), "A zig-zag model for laminated composite beams", Compos. Struct., 56, 21-24. https://doi.org/10.1016/S0263-8223(01)00178-7
  7. Avcar, M. (2019), "Free vibration of imperfect sigmoid and power law functionally graded beams", Steel Compos. Struct., Int. J., 30(6), 603-615. https://doi.org/10.12989/scs.2019.30.6.603
  8. Azhari, M. and Kassaei, K. (2004), "Local buckling analysis of thick anisotropic plates using complex finite strip method", Iran. J. Sci. Tech. Trans. B., 28, 21-30.
  9. Barton, O. (2008), "Buckling of simply supported rectangular plates under combined bending and compression using eigen sensitivity analysis", Thin-Wall. Struct., 46, 435-441. https://doi.org/10.1016/j.tws.2007.07.021
  10. Batou, B., Nebab, M., Bennai, R., Ait Atmane, H., Tounsi, A. and Bouremana, M. (2019), "Wave dispersion properties in imperfect sigmoid plates using various HSDTs", Steel Compos. Struct., Int. J., 33(5). [In press]
  11. Belkacem, A., Tahar, H.D., Abderrezak, R., Amine, B.M., Mohamed, Z. and Boussad, A. (2018), "Mechanical buckling analysis of hybrid laminated composite plates under different boundary conditions", Struct. Eng. Mech., Int. J., 66(6), 761-769. https://doi.org/10.12989/sem.2018.66.6.761
  12. Benferhat, R., Hassaine Daouadji, T., Hadji, L. and Said Mansour, M. (2016), "Static analysis of the FGM plate with porosities", Steel Compos. Struct., Int. J., 21(1), 123-136. https://doi.org/10.12989/scs.2016.21.1.123
  13. Bensattalah, T., Bouakkaz, K., Zidour, M. and Daouadji, T.H. (2018), "Critical buckling loads of carbon nanotube embedded in Kerr's medium", Adv. Nano Res., Int. J., 6(4), 339-356. https://doi.org/10.12989/anr.2018.6.4.339
  14. Bourada, F., Amara, K. and Tounsi, A. (2016), "Buckling analysis of isotropic and orthotropic plates using a novel four variable refined plate theory", Steel Compos. Struct., Int. J., 21(6),1287-1306. https://doi.org/10.12989/scs.2016.21.6.1287
  15. Carrera, E. (2003), "Historical review of zig-zag theories for multilayered plates and shells", App. Mech. Rev., 56(3), 287-308. https://doi.org/10.1115/1.1557614
  16. Darvizeh, M., Darvizeh, A., Ansari, R. and Sharma, C.B. (2004), "Buckling analysis of generally laminated composite plates (generalized differential quadrature rules versus Rayleigh-Ritz method", Compos. Struct., 63, 69-74. https://doi.org/10.1016/S0263-8223(03)00133-8
  17. Demasi, L. (2008), "${\infty}3$ Hierarchy plate theories for thick and thin composite plates: The generalized unified formulation", Compos. Struct., 84, 256-270. https://doi.org/10.1016/j.compstruct.2007.08.004
  18. Demasi, L. (2009a), "${\infty}6$ mixed plate theories based on the generalized unified formulation. Part I: Governing equations", Compos. Struct., 87, 1-11. https://doi.org/10.1016/j.compstruct.2008.07.013
  19. Demasi, L. (2009b), "${\infty}6$ mixed plate theories based on the generalized unified formulation. Part II: Layerwise theories", Compos. Struct., 87, 12-22. https://doi.org/10.1016/j.compstruct.2008.07.012
  20. Demasi, L. (2009c), "${\infty}6$ mixed plate theories based on the generalized unified formulation. Part III: Advanced mixed high order shear deformation theories", Compos. Struct., 87, 183-194. https://doi.org/10.1016/j.compstruct.2008.07.011
  21. Demasi, L. (2009d), "${\infty}6$ Mixed plate theories based on the generalized unified formulation. Part IV: Zig-zag theories", Compos. Struct., 87, 195-205. https://doi.org/10.1016/j.compstruct.2008.07.010
  22. Demasi, L. (2009e), "${\infty}6$ mixed plate theories based on the generalized unified formulation. Part V: Results", Compos. Struct., 87, 1-16. https://doi.org/10.1016/j.compstruct.2008.07.009
  23. Eltaher, M.A., Fouda, N., El-midany, T. and Sadoun, A.M. (2018), "Modified porosity model in analysis of functionally graded porous nanobeams", J. Brazil. Soc. Mech. Sci. Eng., 40,141. https://doi.org/10.1007/s40430-018-1065-0
  24. Fadoun, O.O., Borokinni, A.S., Layeni, O.P. and Akinola, A.P. (2017), "Dynamics analysis of a transversely isotropic nonclassical thin plate", Wind Struct., Int. J., 25(1), 25-38. https://doi.org/10.12989/was.2017.25.1.025
  25. Fenjan, R.M., Ahmed, R.A., Alasadi, A.A. and Faleh, N.M. (2019), "Nonlocal strain gradient thermal vibration analysis of double-coupled metal foam plate system with uniform and nonuniform porosities", Coupl. Syst. Mech., Int. J., 8(3), 247-257. https://doi.org/10.12989/csm.2019.8.3.247
  26. Ferreira, A.J.M., Roque, C.M.C. and Jorge, R.M.N. (2005), "Analysis of composite plates by trigonometric shear deformation theory and multiquadrics", Comput. Struct., 83, 2225-2237. https://doi.org/10.1016/j.compstruc.2005.04.002
  27. Ferreira, A.J.M., Roque, C.M.C., Neves, A.M.A., Jorge, R.M.N., Soares, C.M.M. and Liew, K.M. (2011), "Buckling and vibration analysis of isotropic and laminated plates by radial basis functions", Compos. Part B., 42, 592-606. https://doi.org/10.1016/j.compositesb.2010.08.001
  28. Fiedler, L., Lacarbonara, W. and Vestroni, F. (2010), "A generalized higher-order theory for buckling of thick multilayered composite plates with normal and transverse shear strains", Compos. Struct., 92, 3011-3019. https://doi.org/10.1016/j.compstruct.2010.05.017
  29. Ghugal, Y.M. and Shimpi, R.P. (2002), "A review of refined shear deformation theories for isotropic and anisotropic laminated plates", J. Reinf. Plast. Compos., 21, 775-813. https://doi.org/10.1177/073168402128988481
  30. Gilat, R., Williams, T.O. and Aboudi, J. (2001), "Buckling of composite plates by global-local plate theory", Compos. Part B., 32, 229-236. https://doi.org/10.1016/S1359-8368(00)00059-7
  31. Hadji, L. and Zouatnia, N. (2019), "Effect of the micromechanical models on the bending of FGM beam using a new hyperbolic shear deformation theory", Earthq. Struct., Int. J., 16(2),177-183. https://doi.org/10.12989/eas.2019.16.2.177
  32. Hashemia, A.S., Khorshidia, K. and Amabilib, M. (2008), "Exact solution for linear buckling of rectangular Mindlin plates", J. Sound Vib., 315, 318-342. https://doi.org/10.1016/j.jsv.2008.01.059
  33. Huang, Y.Q. and Li, Q.S. (2004), "Bending and buckling analysis of antisymmetric laminates using the moving least square differential quadrature method", Comput. Meth. App. Mech. Eng., 193, 3471-3492. https://doi.org/10.1016/j.cma.2003.12.039
  34. Hussain, M. and Naeem, M.N. (2019), "Rotating response on the vibrations of functionally graded zigzag and chiral single walled carbon nanotubes", Appl. Math. Model., 75, 506-520. https://doi.org/10.1016/j.apm.2019.05.039
  35. Jafari, A.A. and Eftekhari, S.A. (2011), "An efficient mixed methodology for free vibration and buckling analysis of orthotropic rectangular plates", App. Math. Comput., 218, 2670-2692. https://doi.org/10.1016/j.amc.2011.08.008
  36. Jones, R.M. (1975), Mechanics of Composite Materials, McGraw Hill Kogakusha, Ltd, Tokyo, Japan.
  37. Kar, V.R. and Panda, S.K. (2016), "Post-buckling behaviour of shear deformable functionally graded curved shell panel under edge compression", Int. J. Mech. Sci., 115, 318-324. https://doi.org/10.1016/j.ijmecsci.2016.07.014
  38. Kar, V.R. and Panda, S.K. (2017), "Postbuckling analysis of shear deformable FG shallow spherical shell panel under nonuniform thermal environment", J. Thermal Stress., 40(1), 25-39. https://doi.org/10.1080/01495739.2016.1207118
  39. Kar, V.R., Panda, S.K. and Mahapatra, T.R. (2016), "Thermal buckling behaviour of shear deformable functionally graded single/doubly curved shell panel with TD and TID properties", Adv. Mater. Res., Int. J., 5(4), 205-221. https://doi.org/10.12989/amr.2016.5.4.205
  40. Kar, V.R., Mahapatra, T.R. and Panda, S.K. (2017), "Effect of different temperature load on thermal postbucklingbehaviour of functionally graded shallow curved shell panels", Compos. Struct., 160, 1236-1247. https://doi.org/10.1016/j.compstruct.2016.10.125
  41. Karami, B., Shahsavari, D. and Janghorban, M. (2018), "Wave propagation analysis in functionally graded (FG) nanoplates under in-plane magnetic field based on nonlocal strain gradient theory and four variable refined plate theory", Mech. Adv. Mat. Struct., 25(12), 1047-1057. https://doi.org/10.1080/15376494.2017.1323143
  42. Katariya, P. and Panda, S.K. (2014), "Thermo-mechanical stability analysis of composite cylindrical panels", Proceedings of ASME 2013 Gas Turbine India Conference. https://doi.org/10.1115/GTINDIA2013-3651
  43. Katariya, P. and Panda, S. (2016), "Thermal buckling and vibration analysis of laminated composite curved shell panel", Aircr. Eng. Aerosp. Technol., 88(1), 97-107. https://doi.org/10.1108/AEAT-11-2013-0202
  44. Katariya, P.V., Panda, S.K., Hirwani, C.K., Mehar, K. and Thakare, O. (2017a), "Enhancement of thermal buckling strength of laminated sandwich composite panel structure embedded with shape memory alloy fibre", Smart Struct. Syst., Int. J., 20(5), 595-605. https://doi.org/10.12989/sss.2017.20.5.595
  45. Katariya, P.V., Panda, S.K. and Mahapatra, T.R. (2017b), "Nonlinear thermal bucklingbehaviour of laminated composite panel structure including the stretching effect and higher-order finite element", Adv. Mater. Res., Int. J., 6(4), 349-361. https://doi.org/10.12989/amr.2017.6.4.349
  46. Katariya, P.V., Das, A. and Panda, S.K. (2018), "Buckling analysis of SMA bonded sandwich structure - using FEM", IOP Conference Series: Materials Science and Engineering, 338(1), 012035. https://doi.org/10.1088/1757-899X/338/1/012035
  47. Kheirikhah, M.M., Khalili, S.M.R. and Fard, K.M. (2012), "Biaxial buckling analysis of soft-core composite sandwich plates using improved high-order theory", Eur. J. Mech. A/Solids, 31, 54-66. https://doi.org/10.1016/j.euromechsol.2011.07.003
  48. Kolahchi, R., Safari, M. and Esmailpour, M. (2016), "Dynamic stability analysis of temperature-dependent functionally graded CNT-reinforced visco-plates resting on orthotropic elastomeric medium", Compos. Struct., 150, 255-265. https://doi.org/10.1016/j.compstruct.2016.05.023
  49. Kreja, I. (2011), "A literature review on computational models for laminated composite and sandwich panels", Cent. Eur. J. Eng., 1(1), 59-80. https://doi.org/10.2478/s13531-011-0005-x
  50. Kuo, S.Y. and Shiau, L.C. (2009), "Buckling and vibration of composite laminated plates with variable fiber spacing", Compos. Struct., 90, 196-200. https://doi.org/10.1016/j.compstruct.2009.02.013
  51. Levy, M. (1877), "Memoire sur la theorie des plaques elastique planes", J. Pure Appl. Math., 30, 219-306.
  52. Liew, K.M. and Chen, X.L. (2004), "Buckling of rectangular Mindlin plates subjected to partial in-plane edge loads using the radial point interpolation method", Int. J. Solids Struct., 41, 1677-1695. https://doi.org/10.1016/j.ijsolstr.2003.10.022
  53. Liew, K.M. and Huang, Y.Q. (2003), "Bending and buckling of thick symmetric rectangular laminates using the moving leastsquares differential quadrature method", Int. J. Mech. Sci., 45, 95-114. https://doi.org/10.1016/S0020-7403(03)00037-7
  54. Liew, K.M., Wang, J., Ng, T.Y. and Tan, M.J. (2004), "Free vibration and buckling analyses of shear-deformable plates based on FSDT meshfree method", J. Sound Vib., 276, 997-1017. https://doi.org/10.1016/j.jsv.2003.08.026
  55. Liu, F.L. (2001), "Differential quadrature element method for the buckling analysis of rectangular Mindlin plates having discontinuous", Int. J. Solids Struct., 38, 2305-2321. https://doi.org/10.1016/S0020-7683(00)00120-7
  56. Liu, Y.G. and Pavlovic, M.N. (2008), "A generalized analytical approach to the buckling of simply-supported rectangular plates under arbitrary loads", Eng. Struct., 30, 1346-1359. https://doi.org/10.1016/j.engstruct.2007.07.025
  57. Liu, J., Cheng, Y.S. and Li, R.F. (2010), "A semi-analytical method for bending, buckling and free vibration analyses of sandwich panels with square-honeycomb cores", Int. J. Struct. Stab. Dyn., 10(1), 127-151. https://doi.org/10.1142/S0219455410003361
  58. 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), 179-188. https://doi.org/10.12989/anr.2019.7.3.179
  59. Mehar, K., Panda, S.K., Devarajan, Y. and Choubey, G. (2019), "Numerical buckling analysis of graded CNT-reinforced composite sandwich shell structure under thermal loading", Compos. Struct., 216, 406-414. https://doi.org/10.1016/j.compstruct.2019.03.002
  60. Mindlin, R.D. (1951), "Influence of rotatory inertia and shear on flexural motions of isotropic, elastic plates", ASME J. Appl. Mech., 18, 31-38. https://doi.org/10.1115/1.4010217
  61. Nali, P., Carrera, E. and Lecca, S. (2011), "Assessments of refined theories for buckling analysis of laminated plates", Compos. Struct., 93, 456-464. https://doi.org/10.1016/j.compstruct.2010.08.035
  62. Noor, A.K. (1975), "Stability of multilayered composite plates", Fib. Sci. Tech., 8(2), 81-89. https://doi.org/10.1016/0015-0568(75)90005-6
  63. Noor, A.K. and Burton, W.S. (1989), "Assessment of shear deformation theories for multilayered composite plates", Appl. Mech. Rev., 42, 1-13. https://doi.org/10.1115/1.3152418
  64. Panda, S.K. and Katariya, P.V. (2015), "Stability and free vibration behaviour of laminated composite panels under thermomechanical loading", Int. J. Appl. Computat. Math., 1(3), 475-490. https://doi.org/10.1007/s40819-015-0035-9
  65. Panda, S.K. and Ramachandra, L.S. (2010), "Buckling of rectangular plates with various boundary conditions loaded by non-uniform in-plane loads", Int. J. Mech. Sci., 52, 819-828. https://doi.org/10.1016/j.ijmecsci.2010.01.009
  66. 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(3), 366-374. https://doi.org/10.1016/j.compstruct.2009.06.004
  67. Panda, S.K. and Singh, B.N. (2010a), "Nonlinear free vibration analysis of thermally post-buckled composite spherical shell panel", Int. J. Mech. Mater. Des., 6(2), 175-188. https://doi.org/10.1007/s10999-010-9127-1
  68. Panda, S.K. and Singh, B.N. (2010b), "Thermal post-buckling analysis of a laminated composite spherical shell panel embedded with shape memory alloy fibres using non-linear finite element method", Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science, 224(4), 757-769. https://doi.org/10.1243/09544062JMES1809
  69. Panda, S.K. and Singh, B.N. (2011), "Large amplitude free vibration analysis of thermally post-buckled composite doubly curved panel using nonlinear FEM", Finite Elem. Anal. Des., 47(4), 378-386. https://doi.org/10.1016/j.finel.2010.12.008
  70. Panda, S.K. and Singh, B.N. (2013a), "Nonlinear finite element analysis of thermal post-buckling vibration of laminated composite shell panel embedded with SMA fibre", Aerosp. Sci. Technol., 29(1), 47-57. https://doi.org/10.1016/j.ast.2013.01.007
  71. Panda, S.K. and Singh, B.N. (2013b), "Post-buckling analysis of laminated composite doubly curved panel embedded with SMA fibers subjected to thermal environment", Mech. Adv. Mater. Struct., 20(10), 842-853. https://doi.org/10.1080/15376494.2012.677097
  72. Panda, S.K. and Singh, B.N. (2013c), "Thermal postbuckling behavior of laminated composite spherical shell panel using NFEM", Mech. Based Des. Struct. Mach., 41(4), 468-488. https://doi.org/10.1080/15397734.2013.797330
  73. Panda, S.K. and Singh, B.N. (2013d), "Large amplitude free vibration analysis of thermally post-buckled composite doubly curved panel embedded with SMA fibers", Nonlinear Dyn., 74(1-2), 395-418. https://doi.org/10.1007/s11071-013-0978-5
  74. Panda, S.K., Mahapatra, T.R. and Kar, V.R. (2017), "Nonlinear finite element solution of post-buckling responses of FGM panel structure under elevated thermal load and TD and TID properties", MATEC Web of Conferences, 109, 05005. http://hdl.handle.net/2080/2625
  75. Panjehpour, M., Loh, E.W.K. and Deepak, T.J. (2018), "Structural Insulated Panels: State-of-the-Art", Trends Civil Eng. Architect., 3(1) 336-340. https://doi.org/10.32474/TCEIA.2018.03.000151
  76. Reddy, J.N. (1984), "A simple higher order theory for laminated composite plates", ASME J. App. Mech., 51, 745-752. https://doi.org/10.1115/1.3167719
  77. Reddy, J.N. and Arciniega, R.A. (2004), "Shear deformation plate and shell theories: From Stavsky to present", Mech. Adv. Mater. Struct., 11(6), 535-582. https://doi.org/10.1080/15376490490452777
  78. Reissner, E. (1945), "The effect of transverse shear deformation on the bending of elastic plates", J. Appl. Mech., 12, 69-77.
  79. Ruocco, E. and Fraldi, M. (2012), "An analytical model for the buckling of plates under mixed boundary conditions", Eng. Struct., 38, 78-88. https://doi.org/10.1016/j.engstruct.2011.12.049
  80. Ruocco, E., Minutolo, V. and Ciaramella, S. (2011), "A generalized analytical approach for the buckling analysis of thin rectangular plates with arbitrary boundary conditions", Int. J. Struct. Stab. Dyn., 11(1), 1-21. https://doi.org/10.1142/S0219455411003963
  81. Salah, F., Boucham, B., Bourada, F., Benzair, A., Bousahla, A.A. and Tounsi, A. (2019), "Investigation of thermal buckling properties of ceramic-metal FGM sandwich plates using 2D integral plate model", Steel Compos. Struct., Int. J., 35(5), December10 2019. [In press]
  82. Sayyad, A.S. and Ghugal, Y.M. (2013), "Effect of stress concentration on laminated plates", J. Mech., 29, 241-252. https://doi.org/10.1017/jmech.2012.131
  83. Sayyad, A.A. and Ghugal, Y.M. (2014), "On the buckling of isotropic, transversely isotropic and laminated composite rectangular plates", Int. J. Struct. Stabil. Dyn., 14(7), 1450020. https://doi.org/10.1142/S0219455414500205
  84. Selmi, A. and Bisharat, A. (2018), "Free vibration of functionally graded SWNT reinforced aluminum alloy beam", J. Vibroeng., 20(5), 2151-2164. https://doi.org/10.21595/jve.2018.19445
  85. Shahadat, M.R.B., Alam, M.F., Mandal, M.N.A. and Ali, M.M. (2018), "Thermal transportation behaviour prediction of defective graphene sheet at various temperature: A Molecular Dynamics Study", Am. J. Nanomater., 6(1), 34-40.
  86. Shaikh, A.E.R. and Ganeshan, R. (2012), "Buckling analysis of tapered composite plates using Ritz method based on first-order shear deformation theory", Int. J. Struct. Stab. Dyn., 12(4), 1-21. https://doi.org/10.1142/S0219455412500307
  87. Shimpi, R.P. and Ghugal, Y.M. (2002), "A layerwise shear deformation theory for two layered cross-ply laminated plates", Mech. Adv. Mater. Struct., 7(4), 331-353. https://doi.org/10.1080/10759410050201690
  88. Shimpi, R.P., Arya, H. and Naik, N.K. (2003), "A higher order displacement model for the plate analysis", J. Reinf. Plast. Compos., 22(18), 1667-1688. https://doi.org/10.1177/073168403027618
  89. Shojaee, S., Valizadeh, N., Izadpanah, E., Bui, T. and Vu, T. (2012), "Free vibration and buckling analysis of laminated composite plates using the NURBS-based isogeometric finite element method", Compos. Struct., 94, 1677-1693. https://doi.org/10.1016/j.compstruct.2012.01.012
  90. Shufrin, I., Rabinovitch, O. and Eisenberger, M. (2008), "Buckling of symmetrically laminated rectangular plates with general boundary conditions-A semi analytical approach", Compos. Struct., 82, 521-531. https://doi.org/10.1016/j.compstruct.2007.02.003
  91. Shukla, K.K., Nath, Y., Kreuzer, E. and Kumar, K.V.S. (2005), "Buckling of laminated composite rectangular plates", ASCE J. Aero. Eng., 18(4), 215-223. https://doi.org/10.1061/(ASCE)0893-1321(2005)18:4(215)
  92. Soldatos, K.P. (1992), "A transverse shear deformation theory for homogeneous monoclinic plates", Acta Mech., 94, 195-220. https://doi.org/10.1007/BF01176650
  93. Stein, M. and Bains, N.J.C. (1990), "Post buckling behavior of longitudinally compressed orthotropic plates with transverse shearing flexibility", AIAA J., 28, 892-895. https://doi.org/10.2514/3.25135
  94. Touratier, M. (1991), "An efficient standard plate theory", Int. J. Eng. Sci., 29(8), 901-916. https://doi.org/10.1016/0020-7225(91)90165-Y
  95. Verma, V.K. and Singh, B.N. (2009), "Thermal buckling of laminated composite plates with random geometric and material properties", Int. J. Struct. Stab. Dyn., 9(2), 187-211. https://doi.org/10.1142/S0219455409002990
  96. Wang, C.M. and Lee, K.H. (1998), "Buckling load relationship between Reddy and Kirchhoff circular plates", J. Franklin Institute, 335B(6), 989-995. https://doi.org/10.1016/S0016-0032(97)00047-1
  97. Wang, C.M. and Reddy, J.N. (1997), "Buckling load relationship between Reddy and Kirchhoff plates of polygonal shape with simply supported edges", Mech. Res. Commun., 24(1), 103-108. https://doi.org/10.1016/S0093-6413(96)00084-5
  98. Wang, C.M., Reddy, J.N. and Lee, K.H. (2000), Shear Deformable Beams and Plates: Relationships with Classical Solutions, Elsevier, Oxford, UK.
  99. Wanji, C. and Zhen, W. (2008), "A selective review on recent development of displacement-based laminated plate theories", Rec. Pat. Mech. Eng., 1, 29-44. https://doi.org/10.2174/2212797610801010029
  100. Xiang, Y. and Wang, C.M. (2002), "Exact buckling and vibration solutions for stepped rectangular plates", J. Sound Vib., 250(3), 503-517. https://doi.org/10.1006/jsvi.2001.3922
  101. Xiang, S., Wang, K., Ai, Y., Sha, Y. and Shi, H. (2009), "Analysis of isotropic, sandwich and laminated plates by a meshless method and various shear deformation theories", Compos. Struct., 91, 31-37. https://doi.org/10.1016/j.compstruct.2009.04.029
  102. Zhong, H. and Gu, C. (2007), "Buckling of symmetrical cross-ply composite rectangular plates under a linearly varying in-plane load", Compos. Struct., 80, 42-48. https://doi.org/10.1016/j.compstruct.2006.02.030