Structural Engineering and Mechanics

Techno-Press (테크노프레스)
권호 표지
DOI QR코드

DOI QR Code

An efficient shear deformation theory with stretching effect for bending stress analysis of laminated composite plates

  • Abbas, Soufiane (Laboratory of Materials and Reactive Systems (LMRS), University of Sidi Bel Abbes, Faculty of Technology, Mechanical Engineering Department) ;
  • Benguediab, Soumia (Material and Hydrology Laboratory, University of Sidi Bel Abbes, Faculty of Technology, Civil Engineering Department) ;
  • Draiche, Kada (Material and Hydrology Laboratory, University of Sidi Bel Abbes, Faculty of Technology, Civil Engineering Department) ;
  • Bakora, Ahmed (Material and Hydrology Laboratory, University of Sidi Bel Abbes, Faculty of Technology, Civil Engineering Department) ;
  • Benguediab, Mohamed (Laboratory of Materials and Reactive Systems (LMRS), University of Sidi Bel Abbes, Faculty of Technology, Mechanical Engineering Department)
  • Received : 2019.03.14
  • Accepted : 2019.12.12
  • Published : 2020.05.10
⟨ Previous Next ⟩

Abstract

The focus of this paper is to develop an analytical approach based on an efficient shear deformation theory with stretching effect for bending stress analysis of cross-ply laminated composite plates subjected to transverse parabolic load and line load by using a new kinematic model, in which the axial displacements involve an undetermined integral component in order to reduce the number of unknowns and a sinusoidal function in terms of the thickness coordinate to include the effect of transverse shear deformation. The present theory contains only five unknowns and satisfies the zero shear stress conditions on the top and bottom surfaces of the plate without using any shear correction factors. The governing differential equations and its boundary conditions are derived by employing the static version of principle of virtual work. Closed-form solutions for simply supported cross-ply laminated plates are obtained applying Navier's solution technique, and the numerical case studies are compared with the theoretical results to verify the utility of the proposed model. Lastly, it can be seen that the present outlined theory is more accurate and useful than some higher-order shear deformation theories developed previously to study the static flexure of laminated composite plates.

Keywords

References

  1. Ahmed, A. (2014), "Post buckling analysis of sandwich beams with functionally graded faces using a consistent higher order theory", Int. J. Civil Struct. Environ., 4(2), 59-64.
  2. 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, 24(6), 489-498. https://doi.org/10.12989/cac.2019.24.06.489.
  3. Addou, F.Y., Meradjah, M., Bousahla, A.A, Benachour, A., Bourada, F., Tounsi, A., Mahmoud, S.R. (2019), "Influences of porosity on dynamic response of FG plates resting on Winkler/Pasternak/Kerr foundation using quasi 3D HSDT", Comput. Concrete, 24(4), 347-367. https://doi.org/10.12989/cac.2019.24.4.347.
  4. Akavci, S. S. (2007), "Buckling and free vibration analysis of symmetric and antisymmetric laminated composite plates on an elastic foundation", J. Reinf. Plastics Compos., 26(18), 1907-1919. https://doi.org/10.1177/0731684407081766.
  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., 71(5), 485-502. https://doi.org/10.12989/sem.2019.71.5.485.
  6. Avcar, M. (2015), "Effects of rotary inertia shear deformation and non-homogeneity on frequencies of beam", Struct. Eng. Mech., 55(4), 871-884. https://doi.org/10.12989/sem.2015.55.4.871.
  7. Avcar, M. (2016), "Effects of material non-homogeneity and two parameter elastic foundation on fundamental frequency parameters of Timoshenko beams", Acta Physica Polonica A, 130(1), 375-378. https://doi.org/10.12693/APhysPolA.130.375
  8. Avcar, M. and Mohammed, W.K.M. (2018), "Free vibration of functionally graded beams resting on Winkler-Pasternak foundation", Arab. J. Geosci., 11, 232. https://doi.org/10.1007/s12517-018-3579-2.
  9. Avcar, M. (2019), "Free vibration of imperfect sigmoid and power law functionally graded beams", Steel Compos. Struct., 30(6), 603-615. https://doi.org/10.12989/scs.2019.30.6.603.
  10. Ayat, H., Kellouche, Y., Ghrici, M., Boukhatem, B. (2018), "Compressive strength prediction of limestone filler concrete using artificial neural networks", Adv. Comput. Design, 3(3), 289-302. https://doi.org/10.12989/acd.2018.3.3.289.
  11. Aydogdu, M. (2006), "Comparison of various shear deformation theories for bending, buckling and vibration of rectangular symmetric cross-ply plate with simply supported edges", J. Compos. Mater., 40(23), 2143-2155. https://doi.org/10.1177/0021998306062313.
  12. Baltac, A.K. (2018), "Numerical approaches for vibration response of annular and circular composite plates", Steel Compos. Struct., 29(6), 755-766. https://doi.org/10.12989/scs.2018.29.6.759.
  13. Balubaid, M., Tounsi, A., Dakhel, B., Mahmoud, S.R. (2019), "Free vibration investigation of FG nanoscale plate using nonlocal two variables integral refined plate theory", Comput. Concrete., 24(6), 579-586. https://doi.org/10.12989/cac.2019.24.6.579.
  14. Batou, B., Nebab, M., Bennai, R., Ait Atmane, H., Tounsi, A., Bouremana, M. (2019), "Wave dispersion properties in imperfect sigmoid plates using various HSDTs", Steel Compos. Struct., 33(5), 699-716. https://doi.org/10.12989/scs.2019.33.5.699.
  15. Behera, S., Kumari, P. (2018), "Free vibration of Levy-type rectangular laminated plates using efficient zig-zag theory", Adv. Comput. Design, 3(3), 213-232. https://doi.org/10.12989/acd.2018.3.3.213.
  16. Belbachir, N., Draich, K., Bousahla, A.A., Bourada, M., Tounsi, A., Mohammadimehr, M. (2019), "Bending analysis of antisymmetric cross-ply laminated plates under nonlinear thermal and mechanical loadings", Steel Compos. Struct., 33(1), 913-924. https://doi.org/10.12989/scs.2019.33.1.081.
  17. Belkacem, A., Tahar, H.D., Abderrezak, R., Amine, B.M., Mohamed, Z., Boussad, A. (2018), "Mechanical buckling analysis of hybrid laminated composite plates under different boundary conditions", Struct. Eng. Mech., 66(6), 761-769. https://doi.org/10.12989/sem.2018.66.6.761.
  18. Belmahi, S., Zidour, M., Meradjah, M., Bensattalah, T., &Dihaj, A. (2018), "Analysis of boundary conditions effects on vibration of nanobeam in a polymeric matrix", Struct. Eng. Mech., 67(5), 517-525. https://doi.org/10.12989/sem.2018.67.5.517.
  19. Berghouti, H., AddaBedia, E.A. Benkhedda, A., Tounsi, A. (2019), "Vibration analysis of nonlocal porous nanobeams made of functionally graded material", Adv. Nano Res., 7(5), 351-364. https://doi.org/10.12989/anr.2019.7.5.351.
  20. Bouanati, S., Benrahou, K.H., AitAtmane, H., AitYahia, S., Bernard, F., Tounsi, A., AddaBedia, E.A. (2019), "Investigation of wave propagation in anisotropic plates via quasi 3D HSDT", Geomech. Eng., 18(1), 85-96. https://doi.org/10.12989/gae.2019.18.1.085.
  21. Bouazza, M., Kenouza, Y., Benseddiq, N., Zenkour, A. M. (2017), "A two-variable simplified nth-higher-order theory for free vibration behavior of laminated plates", Compos. Struc.,182, 533-541. https://doi.org/10.1016/j.compstruct.2017.09.041.
  22. Boukhlif, Z., Bouremana, M., Bourada, F., Bousahla, A.A., Bourada, M., Tounsi, A., Al-Osta, M.A. (2019), "A simple quasi-3D HSDT for the dynamics analysis of FG thick plate on elastic foundation", Steel Compos. Struct., 31(5), 503-516. https://doi.org/10.12989/scs.2019.31.5.503.
  23. Boulefrakh, L., Hebali, H., Chikh, A., Bousahla, A.A., Tounsi, A., Mahmoud, S.R. (2019), "The effect of parameters of visco-Pasternak foundation on the bending and vibration properties of a thick FG plate", Geomech. Eng., 18(2), 161-178. https://doi.org/10.12989/gae.2019.18.2.161.
  24. Bourada, F., Bousahla, A.A., Bourada, M., Azzaz, A., Zinata, A., Tounsi, A. (2019), "Dynamic investigation of porous functionally graded beam using a sinusoidal shear deformation theory", Wind Struct., 28(1), 19-30. https://doi.org/10.12989/was.2019.28.1.019
  25. Boussoula, A., Boucham, B., Bourada, M., Bourada, F., Tounsi, A., Bousahla, A.A., Tounsi, A. (2020), "A simple nth-order shear deformation theory for thermomechanical bending analysis of different configurations of FG sandwich plates", Smart Struct. Syst., 25(2), 197-218. https://doi.org/10.12989/sss.2020.25.2.197.
  26. Boutaleb, S., Benrahou, K.H., Bakora, A., Algarni, A., Bousahla, A.A., Tounsi, A., Mahmoud, S.R., Tounsi, A. (2019), "Dynamic Analysis of nanosize FG rectangular plates based on simple nonlocal quasi 3D HSDT", Adv. Nano Res., 7(3), 189-206. https://doi.org/10.12989/anr.2019.7.3.191.
  27. Chaabane, L.A., Bourada, F., Sekkal, M., Zerouati, S., Zaoui, F.Z., Tounsi, A., Derras, A., Bousahla, A.A., Tounsi, A. (2019), "Analytical study of bending and free vibration responses of functionally graded beams resting on elastic foundation", Struct. Eng. Mech., 71(2), 185-196. https://doi.org/10.12989/sem.2019.71.2.185.
  28. Carlos M.M.S., Cristovao M.M.S., and Manuel J.M.F. (1999), Mechanics of Composite Materials and Structures, Springer Science+Business Media, 517.
  29. Cetkovic, M. and Vuksanovic, D. (2011), "Large deflection analysis of laminated composite plates using layerwise displacement model", Struct. Eng. Mech., 40(2), 257-277. https://doi.org/10.12989/sem.2011.40.2.257.
  30. Chemi, A., Zidour, M., Heireche, H., Rakrak, K. and Bousahla, A. A. (2018), "Critical buckling load of chiral double-walled carbon nanotubes embedded in an elastic medium", Mech. Compos. Mater., 53(6), 827-836. https://doi.org/10.1007/s11029-018-9708-x.
  31. Chikh, A., Tounsi, A., Hebali, H. and Mahmoud, S.R. (2017), "Thermal buckling analysis of cross-ply laminated plates using a simplified HSDT", Smart Struct. Syst., 19(3), 289-297. https://doi.org/10.12989/sss.2017.19.3.289.
  32. Civalek, O. (2008), "Analysis of thick rectangular plates with symmetric cross-ply laminates based on first-order shear deformation theory", J. Compos. Mater, 42, 2853-2867. https://doi.org/10.1177%2F0021998308096952. https://doi.org/10.1177/0021998308096952
  33. Daouadji, T.H. (2017), "Analytical and numerical modeling of interfacial stresses in beams bonded with a thin plate", Adv. Comput. Design, 2(1), 57-69. https://doi.org/10.12989/acd.2017.2.1.057.
  34. Draoui, A., Zidour, M., Tounsi, A., Adim, B. (2019), "Static and dynamic behavior of nanotubes-reinforced sandwich plates using (FSDT)", J. Nano Res., 57, 117-135. https://doi.org/10.4028/www.scientific.net/JNanoR.57.117.
  35. Ferreira, A.J.M., Castro, L.M.S., Bertoluzza, S. (2009), "A high order collocation method for the static and vibration analysis of composite plates using a first-order theory", Compos. Struct, 89, 424-432. https://doi.org/10.1016/j.compstruct.2008.09.006.
  36. Ghugal, Y.M. and Sayyad, A.S. (2013), "Stress analysis of thick laminated plates using trigonometric shear deformation theory", Int. J. Appl. Mec., 5(1), 23. https://doi.org/10.1142/S1758825113500038.
  37. Hadji, L., Zouatnia, N., Bernard, F. (2019), "An analytical solution for bending and free vibration responses of functionally graded beams with porosities: Effect of the micromechanical models", Struct. Eng. Mech., 69(2), 231-241. https://doi.org/10.12989/sem.2019.69.2.231.
  38. Hellal, H., Bourada, M., Hebali, H., Bourada, F., Tounsi, A., Bousahla, A.A., Mahmoud, S.R. (2019), "Dynamic and stability analysis of functionally graded material sandwich plates in hygro-thermal environment using a simple higher shear deformation theory", J. Sandwich Struct. Mater., https://doi.org/10.1177/1099636219845841.
  39. Hirwani, C.K., Panda, S.K., Patle, B.K. (2018a), "Theoretical and experimental validation of nonlinear deflection and stress responses of an internally debonded layer structure using different higher-order theories", Acta Mechanica, 229(8), 3453-3473. https://doi.org/10.1007/s00707-018-2173-8.
  40. Hirwani, C.K., Panda, S.K., Mahapatra, T.R., Mandal, S.K., Mahapatra, S.S. and De, A.K. (2018b), "Delamination effect on flexural responses of layered curved shallow shell panel-experimental and numerical analysis", J. Comput. Methods, 15(4), 1850027. https://doi.org/10.1142/S0219876218500275.
  41. Hirwani, C.K., Panda, S.K. (2018), "Numerical and experimental validation of nonlinear deflection and stress responses of pre-damaged glass-fibre reinforced composite structure", Ocean Eng., 159, 237-252. https://doi.org/10.1016/j.oceaneng.2018.04.035.
  42. Hirwani, C.K., Panda, S.K. (2019), "Nonlinear finite element solutions of thermoelastic deflection and stress responses of internally damaged curved panel structure", Appl. Math. Modelling, 65, 303-317. https://doi.org/10.1016/j.apm.2018.08.014.
  43. Hussain, M., Naeem, M.N., Tounsi, A., Taj, M. (2019a), "Nonlocal effect on the vibration of armchair and zigzag SWCNTs with bending rigidity", Adv. Nano Res., 7(6), 431-442. https://doi.org/10.12989/anr.2019.7.6.431.
  44. Hussain et al. (2019b), "Nonlocal vibration of DWCNTs based on Flugge shell model using wave propagation approach", Steel Compos. Struct., 34(4), 599. https://doi.org/10.12989/scs.2020.34.4.599.
  45. Joshan, Y.S., Grover, N., Singh, B.N. (2018), "Assessment of non-polynomial shear deformation theories for thermo-mechanical analysis of laminated composite plates", Steel Compos. Struct., 27(6), 761-775. https://doi.org/10.12989/scs.2018.27.6.761.
  46. Karami, B., Janghorban, M., Tounsi, A. (2019a), "Wave propagation of functionally graded anisotropic nanoplates resting on Winkler-Pasternak foundation", Struct. Eng. Mech., 7(1), 55-66. https://doi.org/10.12989/sem.2019.70.1.055.
  47. Karami, B., Shahsavari, D., Janghorban, M., Tounsi, A. (2019b), "Resonance behavior of functionally graded polymer composite nanoplates reinforced with grapheme nanoplatelets", J. Mech. Sci., 156, 94-105. https://doi.org/10.1016/j.ijmecsci.2019.03.036.
  48. Karami, B., Janghorban, M. and Tounsi, A. (2019c), "Galerkin's approach for buckling analysis of functionally graded anisotropic nanoplates/different boundary conditions", Eng. Comput., 35, 1297-1316. https://doi.org/10.1007/s00366-018-0664-9.
  49. Karami, B., Janghorban, M., Tounsi, A. (2019d), "On exact wave propagation analysis of triclinic material using three dimensional bi-Helmholtz gradient plate model", Struct. Eng. Mech., 69(5), 487-497. https://doi.org/10.12989/sem.2019.69.5.487.
  50. Karami, B.,Janghorban, M., Tounsi, A. (2019e), "On pre-stressed functionally graded anisotropic nanoshell in magnetic field", J. Brazilian Soc. Mech. Sci. Eng., 41, 495. https://doi.org/10.1007/s40430-019-1996-0.
  51. Kar, V.R., Mahapatra, T.R., Panda, S.K. (2015), "Nonlinear flexural analysis of laminated composite flat panel under hygro-thermo-mechanical loading", Steel Compos. Struct.,19(4), 1011-1033. https://doi.org/10.1142/S0219876216500158.
  52. Katariya, P., Panda, S. and Mahapatra, T. (2018), "Bending and vibration analysis of skew sandwich plate", Aircraft Eng. Aerosp. Technol., 90(6), 885-895. https://doi.org/10.1108/AEAT-05-2016-0087.
  53. Katariya, P.V., Panda, S.K. (2019a), "Numerical frequency analysis of skew sandwich layered composite shell structures under thermal environment including shear deformation effects", Struct. Eng. Mech., 71(6), 657-668. https://doi.org/10.12989/sem.2019.71.6.657.
  54. Katariya, P.V., Panda, S.K. (2019b), "Numerical evaluation of transient deflection and frequency responses of sandwich shell structure using higher order theory and different mechanical loadings", Eng. Comput., 35(3), 1009-1026. https://doi.org/10.1007/s00366-018-0646-y.
  55. Katariya, P.V., Panda, S.K. (2019c), "Frequency and deflection responses of shear deformable skew sandwich curved shell panel: a finite element approach", Arabian J. Sci. Eng., 44(2), 1631-1648. https://doi.org/10.1007/s13369-018-3633-0.
  56. Khiloun, M., Bousahla, A.A., Kaci, A., Bessaim, A., Tounsi, A., Mahmoud, S.R. (2019), "Analytical modeling of bending and vibration of thick advanced composite plates using a four-variable quasi 3D HSDT", Eng. Comput.., https://doi.org/10.1007/s00366-019-00732-1.
  57. Kim, S. E., Thai, H. T. and Lee, J. (2009), "A two variable refined plate theory for laminated composite plates", Compos.Struct.,89, 197-205. https://doi.org/10.1016/j.compstruct.2008.07.017.
  58. Kirchhoff, G.R. (1850), "Uber das gleichgewicht und die bewegung einer elastischen scheibe", J. Pure and App. Math., 40, 51-88. https://doi.org/10.1515/crll.1850.40.51.
  59. Love, A. E. H., (1944), A Treatise on the Mathematical Theory of Elasticity, 4th ed., Dover Publ., New York, U.S.A.
  60. Mahi, A., Adda Bedia, E.A, Tounsi, A. (2015), "A new hyperbolic shear deformation theory for bending and free vibration analysis of isotropic, functionally graded, sandwich and laminated composite plates", Appl. Math. Model, 39, 2489-2508. https://doi.org/10.1016/j.apm.2014.10.045.
  61. Mahmoud, S.R., Tounsi, A. (2019), "On the stability of isotropic and composite thick plates", Steel Compos. Struct., 33(4), 551-568. https://doi.org/10.12989/scs.2019.33.4.551.
  62. Mahmoudi, A., Benyoucef, S., Tounsi, A., Benachour, A., Adda Bedia, E.A., Mahmoud, S.R. (2019), "A refined quasi-3D shear deformation theory for thermo-mechanical behavior of functionally graded sandwich plates on elastic foundations", J. Sandwich Struct. Mater., 21(6), 1906-1926. https://doi.org/10.1177%2F1099636217727577. https://doi.org/10.1177/1099636217727577
  63. Mantari, J.L., Oktem, A.S., GuedesSoares, C. (2012), "A new trigonometric layerwise shear deformation theory for the finite element analysis of laminated composite and sandwich plates", Comput. and Struct., 94-95, 45-53. https://doi.org/10.1016/j.compstruc.2011.12.003.
  64. Matsunaga, H. (2000), "Vibration and stability of cross-ply laminated composite plates according to a global higher-order plate theory", Compos.Struct.,48(4), 231-244. https://doi.org/10.1016/S0263-8223(99)00110-5.
  65. Medani, M., Benahmed, A., Zidour, M., Heireche, H., Tounsi, A., Bousahla, A.A., Tounsi, A., Mahmoud, S.R. (2019), "Static and dynamic behavior of (FG-CNT) reinforced porous sandwich plate", Steel Compos. Struct., 32(5), 595-610. https://doi.org/10.12989/scs.2019.32.5.595.
  66. Mehar, K., Panda, S.K. (2019), "Theoretical deflection analysis of multi-walled carbon nanotube reinforced sandwich panel and experimental verification", Compos. Part B Eng., 167, 317-328. https://doi.org/10.1016/j.compositesb.2018.12.058.
  67. Meksi, R, Benyoucef, S., Mahmoudi, A., Tounsi, A., Adda Bedia, E.A. and Mahmoud, SR. (2019), "An analytical solution for bending, buckling and vibration responses of FGM sandwich plates", J. Sandw. Struct. Mater.,21(2), 727-757. https://doi.org/10.1177/1099636217698443.
  68. Mindlin, R.D. (1951), "Influence of rotatory inertia and shear on flexural motions of isotropic, elastic plates", J. App. Mec., 18, 31-38. https://doi.org/10.1115/1.4010217
  69. Nedri, K., El Meiche, N. and Tounsi, A. (2014), "Free vibration analysis of laminated composite plates resting on elastic foundations by using a refined hyperbolic shear deformation theory", Mec. Compos. Mater.,49(6), 629-640. https://doi.org/10.1007/s11029-013-9379-6.
  70. Nor Hafizah, A.K., Lee, J.H., Aziz, Z.A. and Viswanatha, K.K. (2018), "Vibration of antisymmetric angle-ply laminated plates of higher-order theory with variable thickness", Math. Prob. in Eng., Article ID 7323628, 14. https://doi.org/10.1155/2018/7323628.
  71. Rezaiee-Pajand, M., Shahabian, F., Tavakoli, F.H. (2012), "A new higher-order triangular plate bending element for the analysis of laminated composite and sandwich plates", Struct. Eng. Mech., 43(2), 253-271. https://doi.org/10.12989/sem.2012.43.2.253.
  72. Reddy, J. N. (1984), "A simple high-order theory of laminated composite plate", J. App. Mec. (Trans. ASME), 51, 745-752. https://doi.org/10.1115/1.3167719
  73. Reissner, E. (1945), "The effect of transverse shear deformation on the bending of elastic plates", ASME J. App. Mec., 12, 69-77. https://doi.org/10.1177/002199836900300316.
  74. Sahla, M., Saidi, H., Draiche, K., Bousahla, A.A., Bourada, F., Tounsi, A. (2019), "Free vibration analysis of angle-ply laminated composite and soft core sandwich plates", Steel Compos. Struct., 33(5), 663-679. https://doi.org/10.12989/scs.2019.33.5.663.
  75. Sahouane, A., Hadji, L., Bourada, M., (2019), "Numerical analysis for free vibration of functionally graded beams using an original HSDBT", Earthq. Struct., 17(1), 31-37. https://doi.org/10.12989/eas.2019.17.1.031.
  76. Sahoo, R. and Singh, B.N. (2014), "A new trigonometric zigzag theory for static analysis of laminated composite and sandwich plates", Aerospace Sci. Tech., 35, 15-28. https://doi.org/10.1016/j.ast.2014.03.001.
  77. Sahoo, S.S., Panda, S.K. and Mahapatra, T.R. (2016), "Static, free vibration and transient response of laminated composite curved shallow panel-an experimental approach", Eur. J. Mec.-A/Solids, 59, 95-113. https://doi.org/10.1016/j.euromechsol.2016.03.014.
  78. Sahoo, S.S., Panda, S.K. and Mahapatra, T.R., Hirwani, C.K. (2019), "Numerical analysis of transient responses of delaminated layered structure using different mid-plane theories and experimental validation", Iranian J. Sci. Technol. Transactions Mech. Eng., 43(1), 41-56. https://doi.org/10.1007/s40997-017-0111-3.
  79. Salah, F., Boucham, B., Bourada, F., Benzair, A., Bousahla, A.A., Tounsi, A. (2019), "Investigation of thermal buckling properties of ceramic-metal FGM sandwich plates using 2D integral plate model", Steel Compos. Struct., 33(6), 805-822. https://doi.org/10.12989/scs.2019.33.6.805.
  80. Salami, S.J., Dariushi, S. (2018), "Analytical, numerical and experimental investigation of low velocity impact response of laminated composite sandwich plates using extended high order sandwich panel theory", Struct. Eng. Mech., 68(3), 325-334. https://doi.org/10.12989/sem.2018.68.3.325.
  81. Sayyad, A. S. and Ghugal, Y. M. (2013), "Effect of Stress Concentration on Laminated Plates", J. Mech., 29(02), 241-252. https://doi.org/10.1017/jmech.2012.131.
  82. Sayyad, A. S., Ghugal, Y. M., Shinde, B. M. (2016), "Thermal stress analysis of laminated composite plates using exponential shear deformation theory", Int. J. Automotive Compos., 2(1), 23-40. https://doi.org/10.1504/IJAUTOC.2016.078100
  83. Sayyad, A.S. and Ghugal, Y.M. (2017), "A unified shear deformation theory for the bending of isotropic, functionally graded, laminated and sandwich beams and plates", Int. J. App. Mec., 9(1), 1- 36. https://doi.org/10.1142/S1758825117500077.
  84. Sehoul, M., Benguediab, M., Bakora, A. and Tounsi, A. (2017), "Free vibrations of laminated composite plates using a novel four variable refined plate theory", Steel Compos. Struct., 24(5), 603-613. https://doi.org/10.12989/scs.2017.24.5.603.
  85. Semmah, A., Heireche, H., Bousahla, A.A., Tounsi, A. (2019), "Thermal buckling analysis of SWBNNT on Winkler foundation by non local FSDT", Adv. Nano Res., 7(2), 89-98. https://doi.org/10.12989/anr.2019.7.2.089.
  86. Sherafat, M.H., Ghannadpour, S.A.M., Ovesy, H.R. (2013), "Pressure loading, end-shortening and through-thickness shearing effects on geometrically nonlinear response of composite laminated plates using higher order finite strip method", Struct. Eng. Mech., 45(5), 677-691. https://doi.org/10.12989/sem.2013.45.5.677.
  87. Singh D. B. and Singh, B. N. (2017), "New higher order shear deformation theories for free vibration and buckling analysis of laminated and braided composite plates", J. Mec. Sci., 131, 265-277. https://doi.org/10.1016/j.ijmecsci.2017.06.053.
  88. Soldatos, KP, Timarci, T. (1993), "A unified formulation of laminated composite, shear deformable, five-degrees-of-freedom cylindrical shell theories", Compos. Struct., 1993, 25, 165-171. https://doi.org/10.1016/0263-8223(93)90162-J.
  89. Szilard, R. (1974), Theory and Analysis of Plates, Classical and Numerical Methods, Prentice-Hall Inc., Englewood Cliffs, New Jersey, U.S.A.
  90. Timoshenko, S. P. and Woinowsky-Krieger, S. (1959), Theory of Plates and Shells, McGraw-Hill Book Company, Inc., New York, U.S.A.
  91. Timoshenko, S. P. and Gere, J. (1961), Theory of Elastic Stability, McGraw-Hill Book Company, Inc., New York, U.S.A.
  92. Tounsi, A., Al-Dulaijan, S.U., Al-Osta, M.A., Chikh, A., Al-Zahrani, M.M., Sharif, A. and Tounsi, A. (2020), "A four variable trigonometric integral plate theory for hygro-thermo-mechanical bending analysis of AFG ceramic-metal plates resting on a two-parameter elastic foundation", Steel Compos. Struct., 34(4), 511-524. https://doi.org/10.12989/scs.2020.34.4.511
  93. 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.
  94. Ugural, A. C. (1981), Stresses in Plates and Shells, McGraw-Hill Book Company, Inc., New York, U.S.A.
  95. Vo, T. P., Thai, H.T., Nguyen, T. K., Lanc, D. and Karamanli, A. (2017), "Flexural analysis of laminated composite and sandwich beams using a four unknown shear and normal deformation theory", Compos. Struct., 176, 388-397. https://doi.org/10.1016/j.compstruct.2017.05.041.
  96. Wang, S. (1997), "Buckling analysis of skew fibre-reinforced composite laminates based on first-order shear deformation plate theory", Compos Struct, 37, 5-19. https://doi.org/10.1016/S0263-8223(97)00050-0.
  97. Whitney, J.M. (1969), "The effect of transverse shear deformation on the bending of laminated plates", J. Compos. Mater, 3, 534-547. https://doi.org/10.1177/002199836900300316.
  98. Whitney, J. M., and Pagano, N. J. (1970), "Shear deformation in heterogeneous anisotropic plates", ASME J. App. Mech., 37, 1031-1036. https://doi.org/10.1115/1.3408654
  99. Yang, P. C., Norris, C. H., and Stavsky, Y. (1966), "Elastic wave propogation in heterogeneous plates", Int. J. Solids Struct., 2, 665-684. https://doi.org/10.1016/0020-7683(66)90045-X.
  100. Zamani, H.A., Aghdam, M.M., Sadighi, M. (2017), "Free vibration analysis of thick viscoelastic composite plates on visco-Pasternak foundation using higher-order theory", Compos.Struct., 182, 25-35. https://doi.org/10.1016/j.compstruct.2017.08.101
  101. Zaoui, F.Z., Ouinas, D., Tounsi, A. (2019), "New 2D and quasi-3D shear deformation theories for free vibration of functionally graded plates on elastic foundations", Compos. Part B, 159, 231-247. https://doi.org/10.1016/j.compositesb.2018.09.051.
  102. Zarga, D., Tounsi, A., Bousahla, A.A., Bourada, F., Mahmoud, S.R. (2019), "Thermomechanical bending study for functionally graded sandwich plates using a simple quasi-3D shear deformation theory", Steel Compos. Struct., 32(3), 389-410. https://doi.org/10.12989/scs.2019.32.3.389.
  103. Zenkour, A.M. (2004), "Analytical solution for bending of cross-ply laminated plates under thermo-mechanical loading", Compos. Struct., 65, 367-379. https://doi.org/10.1016/j.compstruct.2003.11.012.
  104. Zine, A., Tounsi, A., Draiche, K., Sekkal, M., and Mahmoud, S.R. (2018), "A novel higher-order shear deformation theory for bending and free vibration analysis of isotropic and multilayered plates and shells", Steel Compos. Struct., 26(2), 125-137. https://doi.org/10.12989/scs.2018.26.2.125.