Structural Engineering and Mechanics

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A refined quasi-3D theory for stability and dynamic investigation of cross-ply laminated composite plates on Winkler-Pasternak foundation

  • Nasrine Belbachir (Civil Engineering Department, Faculty of Science and Technology, Abdelhamid Ibn Badis University) ;
  • Fouad Bourada (Material and Hydrology Laboratory, University of Sidi Bel Abbes, Faculty of Technology, Civil Engineering Department) ;
  • Abdelmoumen Anis Bousahla (Laboratoire de Modelisation et Simulation Multi-Echelle, Universite de Sidi Bel Abbes) ;
  • Abdelouahed Tounsi (Material and Hydrology Laboratory, University of Sidi Bel Abbes, Faculty of Technology, Civil Engineering Department) ;
  • Mohamed A. Al-Osta (Department of Civil and Environmental Engineering, King Fahd University of Petroleum & Minerals) ;
  • Mofareh Hassan Ghazwani (Department of Mechanical Engineering, Faculty of Engineering, Jazan University) ;
  • Ali Alnujaie (Department of Mechanical Engineering, Faculty of Engineering, Jazan University) ;
  • Abdeldjebbar Tounsi (Industrial Engineering and Sustainable Development Laboratory, Faculty of Science & Technology, Mechanical Engineering Department, University of Relizane)
  • Received : 2022.07.28
  • Accepted : 2023.01.10
  • Published : 2023.02.25
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Abstract

The current paper discusses the dynamic and stability responses of cross-ply composite laminated plates by employing a refined quasi-3D trigonometric shear deformation theory. The proposed theory takes into consideration shear deformation and thickness stretching by a trigonometric variation of in-plane and transverse displacements through the plate thickness and assures the vanished shear stresses conditions on the upper and lower surfaces of the plate. The strong point of the new formulation is that the displacements field contains only 4 unknowns, which is less than the other shear deformation theories. In addition, the present model considers the thickness extension effects (εz≠0). The presence of the Winkler-Pasternak elastic base is included in the mathematical formulation. The Hamilton's principle is utilized in order to derive the four differentials' equations of motion, which are solved via Navier's technique of simply supported structures. The accuracy of the present 3-D theory is demonstrated by comparing fundamental frequencies and critical buckling loads numerical results with those provided using other models available in the open literature.

Keywords

References

  1. Aagaah, M.R., Mahinfalah, M and Jazar, G.N. (2006), "Natural frequencies of laminated composite plates using third order shear deformation theory", Compos. Struct., 72(3), 273-279. https://doi.org/10.1016/j.compstruct.2004.11.012.
  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. Akavci, S.S. and Tanrikulu, A.H. (2008), "Buckling and free vibration analyses of laminated composite plates by using two new hyperbolic shear-deformation theories", Mech. Compos. Mater., 44, 145-154. https://doi.org/10.1007/s11029-008-9004-2.
  4. Alibakhchi, R. (2012), "The effect of Anisotropy on free vibration of rectangular composite plates with path mass", Int. J. Ing., 25(3), 223-232.
  5. 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.
  6. Bendada, A., Boutchicha, D., Khatir, S., Magagnini, E., Capozucca, R. and Wahab, M.A. (2020), "Mechanical characterization of an epoxy panel reinforced by date palm petiole particle", Steel Compos. Struct., 35(5), 627-634. https://doi.org/10.12989/scs.2020.35.5.627.
  7. Benhenni, M.A., Daouaji, T.H., Abbes, B., Adim, B., Li, Y. and Abbes, F. (2018a), "Dynamic analysis for anti-symmetric crossply and angle-ply laminates for simply supported thick hybrid rectangular plates", Adv. Mater. Res., 7(2), 119-136. https://doi.org/10.12989/amr.2018.7.2.119.
  8. Benhenni, M.A., Daouaji, T.H., Abbes, B., Li, Y. and Abbes, F. (2018b), "Analytical and numerical results for free vibration of laminated composites plates", Int. J. Chem. Molecul. Eng., 12(6), 300-304.
  9. Cuong-Le, T., Ferreira, A.J.M. and Abdel Wahab, M. (2019b), "A refined size-dependent couple stress theory for laminated composite micro-plates using isogeometric analysis", Thin Wall. Struct., 145, 106427. https://doi.org/10.1016/j.tws.2019.106427.
  10. Cuong-Le, T., Nguyen, K.D., Hoang-Le, M., Sang-To, T., Phan-Vu, P. and Abdel Wahab, M. (2022a), "Nonlocal strain gradient IGA numerical solution for static bending, free vibration and buckling of sigmoid FG sandwich nanoplate", Physica B: Condens. Mat., 631, 413726. https://doi.org/10.1016/j.physb.2022.413726.
  11. Cuong-Le, T., Nguyen, K.D., Lee, J. Rabczuk, T. and Nguyen-Xuan, H. (2022b), "A 3D nano scale IGA for free vibration and buckling analyses of multi-directional FGM nanoshells", Nanotechnol., 33(6), 065703. https://doi.org/10.1088/1361-6528/ac32f9.
  12. Cuong-Le, T., Nguyen, K.D., Nguyen-Trong, N., Khatir, S., Nguyen-Xuan, H. and Abdel-Wahab, M. (2020a), "A three-dimensional solution for free vibration and buckling of annular plate, conical, cylinder and cylindrical shell of FG porous-cellular materials using IGA", Compos. Struct., 259, 113216. https://doi.org/10.1016/j.compstruct.2020.113216.
  13. Cuong-Le, T., Nguyen, T.N., Vu, T.H., Khatir, S. and Abdel Wahab, M. (2020b), "A geometrically nonlinear size-dependent hypothesis for porous functionally graded micro-plate", Eng. Comput., 38, 449-460. https://doi.org/10.1007/s00366-020-01154-0.
  14. Cuong-Le, T., Tran, L.V., Vu-Huu, T. and Abdel-Wahab, M. (2019a), "The size-dependent thermal bending and buckling analyses of composite laminate microplate based on new modified couple stress theory and isogeometric analysis", Comp. Meth. Appl. Mech. Eng., 350, 337-361. https://doi.org/10.1016/j.cma.2019.02.028.
  15. Fares, M.E. and Zenkour, A.M. (1999), "Buckling and free vibration of non-homogeneous composite cross-ply laminated plates with various plate theories", Compos. Struct., 44(4), 279-287. https://doi.org/10.1016/S0263-8223(98)00135-4.
  16. Ghugal, Y.M. and Pawar, M.D. (2011), "Buckling and vibration of plates by hyperbolic shear deformation theory", J. Aerosp. Eng. Technol., 1(1), 1-12.
  17. Grover, N., Maiti, D.K. and Singh, B.N. (2013), "A new inverse hyperbolic shear deformation theory for static and buckling analysis of laminated composite and sandwich plates", Compos. Struct., 95, 667-675. https://doi.org/10.1016/j.compstruct.2012.08.012.
  18. Hui-Shen, S., Zheng, J.J. and Huang, X.L. (2003), "Dynamic response of shear deformable laminated plates under thermomechanical loading and resting on elastic foundations", Compos. Struct., 60(1), 57-66. https://doi.org/10.1016/S0263-8223(02)00295-7.
  19. Javed, S., Viswanathan, K.K., Aziz, Z.A., Karthik, K. and Lee, J.H. (2016), "Vibration of antisymmetric angle-ply laminated plates under higher order shear theory", Steel Compos. Struct., 22(6), 1281-1299. https://doi.org/10.12989/scs.2016.22.6.1281.
  20. Javed, S., Viswanathan, K.K., Nurul Izyan, M.D., Aziz, Z.A. and Lee, J.H. (2018), "Free vibration of cross-ply laminated plates based on higher-order shear deformation theory", Steel Compos. Struct., 26(4), 473-484. https://doi.org/10.12989/scs.2018.26.4.473.
  21. Jung, W.Y., Han, S.C. and Park, W.T. (2016), "Four-variable refined plate theory for forced-vibration analysis of sigmoid functionally graded plates on elastic foundation", Int. J. Mech. Sci., 111-112, 73-87. https://doi.org/10.1016/j.ijmecsci.2016.03.001.
  22. Kant, T. and Swaminathan, K. (2001), "Analytical solution for free vibration of laminated composite and sandwich plates based on a higher refined theory", Compos. Struct., 53, 75-85. https://doi.org/10.1016/S0263-8223(00)00180-X.
  23. Khatir, S., Tiachacht, S., Cuong-Le, T, Quoc Bui, T. and Abdel Wahab, M. (2019), "Damage assessment in composite laminates using ANN-PSO-IGA and Cornwell indicator", Compos. Struct., 230, 111509. https://doi.org/10.1016/j.compstruct.2019.111509.
  24. Khatir, S., Tiachacht, S., Cuong-Le, T., Ghandourah, E., Mirjalili, S. and Abdel Wahab, M. (2021), "An improved Artificial Neural Network using Arithmetic Optimization Algorithm for damage assessment in FGM composite plates", Compos. Struct., 273, 114287. https://doi.org/10.1016/j.compstruct.2021.114.
  25. Khdeir, A.A. (1989), "Free vibration and buckling of unsymmetric cross-ply laminated plates using a refined theory", J. Sound Vib., 128(3), 377-395. https://doi.org/10.1016/0022-460X(89)90781-5
  26. Khdeir, A.A. and Librescu, L. (1988), "Analysis of symmetric cross-ply laminated elastic plates using a higher-order theory: Part II-Buckling and free vibration", Compos. Struct., 9(4), 259-277. https://doi.org/10.1016/0263-8223(88)90048-7.
  27. Kim, S.E., Thai, H.T. and Lee, J. (2009a), "Buckling analysis of plates using the two variable refined plate theory", Thin Wall Struct., 47(4), 455-462. https://doi.org/10.1016/j.tws.2008.08.002.
  28. Kim, S.E., Thai, H.T. and Lee, J. (2009b), "A two variable refined plate theory for laminated composite plates", Compos. Struct., 89(2), 197-205. https://doi.org/10.1016/j.compstruct.2008.07.017.
  29. Mansouri, L., Djebbar, A., Khatir, S. and Abdel Wahab, M. (2018), "Effect of hygrothermal aging in distilled and saline water on the mechanical behaviour of mixed short fibre/woven composites", Compos. Struct., 207, 816-825. https://doi.org/10.1016/j.compstruct.2018.09.067.
  30. Matsunaga, H. (2000), "Free vibration and stability of angle-ply laminated composite and sandwich plates under thermal loading", J. Eng. Mech., 77(2), 249-262. https://doi.org/10.1016/j.compstruct.2005.07.002.
  31. Matsunaga, H. (2001), "Vibration and stability of thick plates on elastic foundations", J. Eng. Mech., 126(1), 27-34. https://doi.org/10.1061/(ASCE)0733-9399(2000)126:1(27).
  32. Noor, A.K. (1973), "Free vibration of multilayered composite plates", AIAA J., 11(7), 1038-1039. https://doi.org/10.2514/3.6868
  33. Nosier, A. and Reddy, J.N. (1992), "On vibration and buckling of symmetric laminated plates according to shear deformation theories", Acta Mechanica, 94, 123-144. https://doi.org/10.1007/BF01176647.
  34. Rahmani, A., Faroughi, S. and Friswell, M.I. (2021), "Vibration analysis for antisymmetric laminated composite plates resting on visco-elastic foundation with temperature effects", Appl. Math. Model., 94, 421-445. https://doi.org/10.1016/j.apm.2021.01.026.
  35. Reddy, J.N. (1984), "A simple higher order theory for laminated composite plates". J. Appl. Mech., 51(4), 745-752. https://doi.org/10.1115/1.3167719.
  36. Reddy, J.N. (1997), Mechanics of Laminated Composite Plates, CRC Press, Boca Raton, New York, London, Tokyo.
  37. Reddy, J.N. and Khdeir, A.A. (1989), "Buckling and vibration of laminated composite plates using various plate theories", AIAA J., 27(12), 1808-1817. https://doi.org/10.2514/3.10338.
  38. Reissner, E. (1945), "The effect of transverse shear deformation on the bending of elastic plates", J. Appl. Mech., 12(2), 69-72. https://doi.org/10.1115/1.4009435.
  39. Reissner, E. (1972), "A consistent treatment of transverse shear deformations in laminated anisotropic plates", AIAA J., 10(5), 716-718. https://doi.org/10.2514/3.50194.
  40. Reissner, E. and Stavsky, Y. (1961), "Bending and stretching of certain types of heterogeneous aelotropic elastic plates", J. Appl. Mech., 28(3), 402-408. https://doi.org/10.1115/1.3641719.
  41. Sayyad, A.S. and Ghugal, M.Y. (2014), "On the buckling of isotropic, transversely isotropic and laminated composite rectangular plates", Int. J. Struct. Stab. Dyn., 14(6), 1-32. https://doi.org/10.1142/S0219455414500205.
  42. Sayyad, A.S. and Ghugal, M.Y. (2015), "On the free vibration analysis of laminated composite and sandwich plates: A review of recent literature with some numerical results", Compos. Struct., 129, 177-201. https://doi.org/10.1016/j.compstruct.2015.04.007.
  43. Sayyad, A.S., Shinde, B.M. and Ghugal, Y.M. (2016), "Bending, vibration and buckling of laminated composite plates using a simple four variable plate theory", Lat. J. Am. Sol. Struct., 13(3), 516-535. http://doi.org/10.1590/1679-78252241.
  44. Setoodeh, A.R. and Azizi. A. (2015), "Bending and free vibration analyses of rectangular laminated composite plates resting on elastic foundation using a refined shear deformation theory", Iran. J. Mater. Form., 2(2), 1-13. https://doi.org/10.22099/IJMF.2015.3236.
  45. Setoodeh, A.R. and Karami, G. (2004), "Static, free vibration and buckling analysis of anisotropic thick laminated composite plates on distributed and point elastic supports using a 3-D layer-wise FEM", Eng. Struct., 26, 211-220. https://doi.org/10.1016/j.engstruct.2003.09.009.
  46. Shen, H.S., Zheng, J.J. and Huang, X.L. (2003), "Dynamic response of shear deformable laminated plates under thermomechanical loading and resting on elastic foundations", Compos. Struct., 60(1), 57-66. https://doi.org/10.1016/S0263-8223(02)00295-7.
  47. Shi, P., Dong, C., Sun, F., Liu, W. and Hu, Q. (2018), "A new higher order shear deformation theory for static, vibration and buckling responses of laminated plates with the isogeometric analysis", Compos. Struct., 204, 342-358. https://doi.org/10.1016/j.compstruct.2018.07.080.
  48. Shimpi, R.P. (2002), "Refined plate theory and its variants", AIAA J., 40(1), 137-146. https://doi.org/10.2514/2.1622.
  49. Shimpi, R.P. and Patel, H.G. (2006), "Free vibrations of plate using two variable refined plate theory", J. Sound Vib., 296(4-5), 979-999. https://doi.org/10.1016/j.jsv.2006.03.030.
  50. Thai, H.T. and Kim, S.E. (2010), "Free vibration of laminated composite plates using two variable refined plate theory", Int. J. Mech. Sci., 52(4), 626-633. https://doi.org/10.1016/j.ijmecsci.2010.01.002.
  51. Timarci, T. and Aydogdu, M. (2005), "Buckling of symmetric cross-ply square plates with various boundary conditions", Compos. Struct., 68(4), 381-389. https://doi.org/10.1016/j.compstruct.2004.04.003.
  52. 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.
  53. Tran, T.M. and Cuong-Le, T. (2022), "A nonlocal IGA numerical solution for free vibration and buckling analysis of Porous Sigmoid Functionally Graded (P-SFGM) nanoplate", Int. J. Struct. Stab. Dyn., 22(16), 2250193. https://doi.org/10.1142/S0219455422501930.
  54. Xiang, Y., Kitipornchai, S. and Liew, K.M. (1996), "Buckling and vibration of thick laminates on pasternak foundation", J. Eng. Mech., ASCE, 122(1), 54-63. https://doi.org/10.1061/(ASCE)0733-9399(1996)122:1(54).
  55. Zenkour, A.M. and Radwan, A.F. (2018), "Free vibration analysis of multilayered composite and soft core sandwich plates resting on Winkler-Pasternak foundations", J. Sandw. Struct. Mater., 20(2), 169-190. https://doi.org/10.1177/1099636216644863.
  56. Zenzen, R., Khatir, S., Belaidi, I., Cuong-Le, T. and Abdel Wahab, M. (2020), "A modified transmissibility indicator and Artificial Neural Network for damage identification and quantification in laminated composite structures", Compos. Struct., 248, 112497. https://doi.org/10.1016/j.compstruct.2020.112497.