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A mechanical behavior of composite plates using a simple three variable refined plate theory

  • Bakoura, Ahmed (Departement de Genie Civil, Faculte d'Architecture et de Genie Civil, Universite des Sciences et de la Technologie d'Oran) ;
  • Djedid, Ibrahim Klouche (Laboratoire Materiaux et Structures (LMS), Departement de Genie Civil, Faculte des Sciences Appliquees, University of Tiaret) ;
  • Bourada, Fouad (Material and Hydrology Laboratory, Civil Engineering Department, Faculty of Technology, University of Sidi Bel Abbes) ;
  • Bousahla, Abdelmoumen Anis (Laboratoire de Modelisation et Simulation Multi-echelle, Universite de Sidi Bel Abbes) ;
  • Mahmoud, S.R. (GRC Department, Jeddah Community College, King Abdulaziz University) ;
  • Tounsi, Abdelouahed (Material and Hydrology Laboratory, Civil Engineering Department, Faculty of Technology, University of Sidi Bel Abbes) ;
  • Ghazwani, Mofareh Hassan (Department of Mechanical Engineering, Faculty of Engineering, Jazan University) ;
  • Alnujaie, Ali (Department of Mechanical Engineering, Faculty of Engineering, Jazan University)
  • Received : 2021.01.28
  • Accepted : 2022.07.04
  • Published : 2022.09.10

Abstract

A novel three variable refined plate theory (TVRPT) is developed in this article for laminated composite plates for the first time. The theory takes into account the nonlinear variation of transverse shear deformations, and satisfies the boundary conditions of zero traction on the plate surfaces without considering the "shear correction factor". The important characteristic of this new kinematic is that the unknowns numbers is only 3 as is employed in "classical plate theory" (CPT). The numerical results of the current theory are compared with 3D-elasticity solutions and the calculations of "first order theories" and other higher order models found in the literature.

Keywords

References

  1. Abed, Z.A.K. and Majeed, W.I. (2020), "Effect of boundary conditions on harmonic response of laminated plates", Compos. Mater. Eng., 2(2), 125-140. https://doi.org/10.12989/cme.2020.2.2.125.
  2. Adhikari, B. and Singh, B.N. (2019), "Dynamic response of functionally graded plates resting on two-parameter-based elastic foundation model using a quasi-3D theory", Mech. Bas. Des. Struct. Mach., 47(4), 399-429. https://doi.org/10.1080/15397734.2018.1555965.
  3. Ahmed, R.A., Fenjan, R.M. and Faleh, N.M. (2019), "Analyzing post-buckling behavior of continuously graded FG nanobeams with geometrical imperfections", Geomech. Eng., 17(2), 175-180. https://doi.org/10.12989/gae.2019.17.2.175.
  4. Akavci, S. (2010), "Two new hyperbolic shear displacement models for orthotropic laminated composite plates", Mech. Compos. Mater., 46(2), 215-226. https://doi.org/10.1007/s11029-010-9140-3.
  5. Akavci, S. (2016), "Mechanical behavior of functionally graded sandwich plates on elastic foundation", Compos. Part B, 96, 136-152. https://doi.org/10.1016/j.compositesb.2016.04.035.
  6. Akbas, S.D. (2015), "Wave propagation of a functionally graded beam in thermal environments", Steel Compos. Struct., 19(6), 1421-1447. https://doi.org/10.12989/scs.2015.19.6.1421.
  7. Akbas, S.D. (2021), "Dynamic analysis of axially functionally graded porous beams under a moving load", Steel Compos. Struct., 39(6), 811-821. https://doi.org/10.12989/scs.2021.39.6.811.
  8. Al-Basyouni, K.S., Ghandourah, E., Mostafa, H.M. and Algarni, A. (2020), "Effect of the rotation on the thermal stress wave propagation in non-homogeneous viscoelastic body", Geomech. Eng., 21(1), 1-9. https://doi.org/10.12989/gae.2020.21.1.001.
  9. Arani, A.G., Navi, B.R. and Mohammadimehr, M. (2021), "Buckling and vibration of porous sandwich microactuatormicrosensor with three-phase carbon nanotubes/fiber/polymer piezoelectric polymeric nanocomposite face sheets", Steel Compos. Struct., 41(6), 805-820. https://doi.org/10.12989/scs.2021.41.6.805.
  10. Attia, M.A. (2017), "On the mechanics of functionally graded nanobeams with the account of surface elasticity", Int. J. Eng. Sci., 115, 73-101. https://doi.org/10.1016/j.ijengsci.2017.03.011.
  11. 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.
  12. 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.
  13. Benferhat, R., Hassaine Daouadji, T., Hadji, L. and Said Mansour, M. (2016), "Static analysis of the FGM plate with porosities", Steel Compos. Struct., 21(1), 123-136. https://doi.org/10.12989/scs.2016.21.1.123.
  14. Bharath, H.S., Waddar, S., Bekinal, S.I., Jeyaraj, P. and Doddamani, M. (2020), "Effect of axial compression on dynamic response of concurrently printed sandwich", Compo. Struct., 259, 113223. https://doi.org/10.1016/j.compstruct.2020.113223.
  15. Bi, R., Gao, J. and Allahyari, S. (2021), "Higher order plate theory for buckling analysis of plates based on exact solution", Steel Compos. Struct., 40(3), 451-459. https://doi.org/10.12989/scs.2021.40.3.451.
  16. Daouadji, T.H. and Hadji, L. (2015), "Analytical solution of nonlinear cylindrical bending for functionally graded plates", Geomech. Eng., 9(5), 631-644. https://doi.org/10.12989/gae.2015.9.5.631.
  17. Dergachova, N.V. and Zou, G. (2021), "Dynamic response of functionally graded plates with a porous middle layer under time-dependent load", Comput. Concrete, 27(3), 269-282. https://doi.org/10.12989/cac.2021.27.3.269.
  18. 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., 25(1), 25-38. https://doi.org/10.12989/was.2017.25.1.025.
  19. Ferreira, A.J.M., Roque, C.M.C., Neves, A.M.A., Jorge, R.M.N., Coares, C.M.M. and Reddy, J.N. (2011), "Buckling analysis of isotropic and laminated plates by radial basis functions according to a higher-order shear deformation theory", Thin Wall. Struct., 49(7), 804-811. https://doi.org/10.1016/j.tws.2011.02.005.
  20. Ghandourah, E.E., Ahmed, H.M., Eltaher, M.A., Attia, M.A. and Abdraboh, A.M. (2021), "Free vibration of porous FG nonlocal modified couple nanobeams via a modified porosity model", Adv. Nano Res., 11(4), 405-422. https://doi.org/10.12989/anr.2021.11.4.405.
  21. Grover, N., Maiti, D.K. and Singh, B.N. (2013), "New non polynomial shear-deformation theories for structural behavior of laminated composite and sandwich plates", AIAA J., 51(8), 1861-1871. https://doi.org/10.2514/1.J052399.
  22. Hadji, L. (2020), "Influence of the distribution shape of porosity on the bending of FGM beam using a new higher order shear deformation model", Smart Struct. Syst., 26(2), 253-262. https://doi.org/10.12989/sss.2020.26.2.253.
  23. He, J. and Sun, Y. (2021), "Numerical and computational modeling for nonlinear dynamic simulation of curved shells under multi-physical fields", Adv. Nano Res., 11(5), 467-477. https://doi.org/10.12989/anr.2021.11.5.467.
  24. Hendi, A.A., Eltaher, M.A., Mohamed, S.A., Attia, M.A. and Abdalla, A.W. (2021), "Nonlinear thermal vibration of pre/postbuckled two-dimensional FGM tapered microbeams based on a higher order shear deformation theory", Steel Compos. Struct., 41(6), 787-803. https://doi.org/10.12989/scs.2021.41.6.787.
  25. 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.
  26. Jrad, H., Mars, J., Wali, M. and Dammak, F. (2018), "An extended finite element method for modeling elastoplastic FGM plateshell type structures", Struct. Eng. Mech., 68(3), 299-312. https://doi.org/10.12989/sem.2018.68.3.299.
  27. Kant, T. and Pandya, B.N. (1988), "A simple finite element formulation of a higher order theory for unsymetrically laminated composite plates", Compos. Struct., 9, 215-246. https://doi.org/10.1016/0263-8223(88)90015-3.
  28. Kant, T. and Swaminathan, K. (2002), "Analytical solution for the static analysis of laminated composite and sandwich plates based on a higher order refined theory", Compos. Struct., 56, 329-344. https://doi.org/10.1016/S0263-8223(02)00017-X.
  29. 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., 5(4), 205-221. https://doi.org/10.12989/amr.2016.5.4.205.
  30. Karakoti, A., Pandey, S. and Kar, V.R. (2021), "Dynamic responses analysis of P and S-FGM sandwich cylindrical shell panels using a new layerwise method", Struct. Eng. Mech., 80(4), 417-432. https://doi.org/10.12989/sem.2021.80.4.417.
  31. Karama, M., Afaq, K.S. and Mistou, S. (2003), "Mechanical behavior of laminated composite beam by the new multilayered laminated composite structures model with transverse shear stress continuity", Int. J. Solid. Struct., 40, 1525-1546. https://doi.org/10.1016/S0020-7683(02)00647-9.
  32. 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. Mater. Struct., 25(12), 1047-1057. https://doi.org/10.1080/15376494.2017.1323143.
  33. Kasiviswanathan, M. and Anbarasu, M. (2021), "Simplified approach to estimate the lateral torsional buckling of GFRP channel beams", Struct. Eng. Mech., 77(4), 523-533. https://doi.org/10.12989/sem.2021.77.4.523.
  34. Kiani, Y. (2019), "NURBS-based thermal buckling analysis of graphene platelet reinforced composite laminated skew plates", J. Therm. Stress., 43(1), 90-108. https://doi.org/10.1080/01495739.2019.1673687.
  35. 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.
  36. Kindova-Petrova, D.D. (2021), "A new crack size prediction method using damaged beam mode shape", Struct. Eng. Mech., 80(4), 391-399. https://doi.org/10.12989/sem.2021.80.4.391.
  37. Lata, P. and Kaur, H. (2021), "Deformation in a homogeneous isotropic thermoelastic solid with multi-dual-phase-lag heat & two temperature using modified couple stress theory", Compos. Mater. Eng., 3(2), 89-106. https://doi.org/10.12989/cme.2021.3.2.089.
  38. Lata, P., and Singh, S. (2021), "Stoneley wave propagation in nonlocal isotropic magneto-thermoelastic solid with multi-dualphase lag heat transfer", Steel Compos. Struct., 38(2), 141-150. http://doi.org/10.12989/scs.2021.38.2.141.
  39. Liu, J., Wang, H. and Yin, H. (2021), "Nonlinear vibration behavior of hybrid multi-scale cylindrical panels via semi numerical method", Comput. Concrete, 28(3), 233-242. https://doi.org/10.12989/cac.2021.28.3.233.
  40. Madenci, E. (2019), "A refined functional and mixed formulation to static analyses of fgm beams", Struct. Eng. Mech., 69(4), 427-437. https://doi.org/10.12989/sem.2019.69.4.427.
  41. Madenci, E. and Ozkilic, Y.O. (2021), "Cyclic response of selfcentering SRC walls with frame beams as boundary", Steel Compos. Struct., 40(2), 157-173. https://doi.org/10.12989/scs.2021.40.2.157.
  42. Maiti, D.K. and Sinha, P.K. (1994), "Bending, free vibration and impact response of thick laminated composite plates", Compos Struct., 49, 115-129. https://doi.org/10.1016/0045-7949(95)00232-4.
  43. Mehar, K. and Panda, S.K. (2019), "Multiscale modeling approach for thermal buckling analysis of nanocomposite curved structure", Adv. Nano Res., 7(3), 181-190. https://doi.org/10.12989/anr.2019.7.3.181.
  44. Mehar, K., Panda, S.K. and Mahapatra, T.R. (2017), "Theoretical and experimental investigation of vibration characteristic of carbon nanotube reinforced polymer composite structure", Int. J. Mech. Sci., 133, 319-329. https://doi.org/10.1016/j.ijmecsci.2017.08.057.
  45. Merzoug, M., Bourada, M., Sekkal, M., Ali Chaibdra, A., Belmokhtar, C., Benyoucef, S. and Benachour, A. (2020), "2D and quasi 3D computational models for thermoelastic bending of FG beams on variable elastic foundation: Effect of the micromechanical models", Geomech. Eng., 22(4), 361-374. https://doi.org/10.12989/gae.2020.22.4.361.
  46. Mindlin, R.D. (1951), "Influence of rotary inertia and shear on flexural motions of isotropic, elastic plates", J. Appl. Mech,. Trans., ASME, 18(1), 31-38. https://doi.org/10.1115/1.4010217.
  47. Mohamed, N., Mohamed, S.A. and Eltaher, M.A. (2021), "Buckling and post-buckling behaviors of higher order carbon nanotubes using energy-equivalent model", Eng. Comput., 37, 2823-2836. https://doi.org/10.1007/s00366-020-00976-2.
  48. Mohammadian, H., Kolahchi, R. and Bidgoli, M.R. (2017), "Dynamic response of concrete beams reinforced by Fe2O3 nanoparticles subjected to magnetic field and earthquake load", Earthq. Struct., 13(6), 589-598. https://doi.org/10.12989/eas.2017.13.6.589.
  49. Motaharifar, F., Ghassabi, M. and Talebitooti, R. (2021), "A variational iteration method (VIM) for nonlinear dynamic response of a cracked plate interacting with a fluid media", Eng. Comput., 37, 3299-3318. https://doi.org/10.1007/s00366-020-00998-w.
  50. Nejadi, M.M., Mohammadimehr, M. and Mehrabi, M. (2021), "Free vibration and buckling of functionally graded carbon nanotubes/graphene platelets Timoshenko sandwich beam resting on variable elastic foundation", Adv. Nano Res., 10(6), 539-548. https://doi.org/10.12989/anr.2021.10.6.539.
  51. Noor, A.K. (1975), "Stability of multilayered composite plate", Fibre Sci. Technol., 8, 81-89. https://doi.org/10.1016/0015-0568(75)90005-6.
  52. Oner, E., Yaylaci, M. and Birinci, A. (2015), "Analytical solution of a contact problem and comparison with the results from FEM", Struct. Eng. Mech., 54(4), 607-622. https://doi.org/10.12989/sem.2015.54.4.607.
  53. Pagano, N.J. (1970), "Exact solution for rectangular bidirectional composites and sandwich plates", J. Compos. Mater., 4(1), 20-34. https://doi.org/10.1177/002199837000400102.
  54. Panjehpour, M., Loh, E.W.K. and Deepak, T.J. (2018), "Structural insulated panels: State-of-the-art", Trend. Civil Eng. Its Arch., 3(1), 336-340. https://doi.org/10.32474/TCEIA.2018.03.000151.
  55. Pour, M.M.H. and Ovesy, H.R. (2021), "Nonlinear dynamic buckling analysis of imperfect viscoelastic composite laminated plates", Struct. Eng. Mech., 79(5), 653-663. https://doi.org/10.12989/sem.2021.79.5.653.
  56. Rachedi, M.A., Benyoucef, S., Bouhadra, A., Bachir Bouiadjra, R., Sekkal, M. and Benachour, A. (2020), "Impact of the homogenization models on the thermoelastic response of FG plates on variable elastic foundation", Geomech. Eng., 22(1), 65-80. https://doi.org/10.12989/gae.2020.22.1.065.
  57. Reddy, J.N. (1984), "A simple higher order shear deformation theory for laminated composite plates", J. Appl. Mech., 51, 752- 754. https://doi.org/10.1115/1.3167719.
  58. Reissner, E. (1945), "The effect of transverse shear deformation on the bending of elastic plates", J. Appl. Mech., Trans., ASME, 12(2), 69-77. https://doi.org/10.1115/1.4009435.
  59. Ren, J.G. (1990), "Bending, vibration and buckling of laminated plates", Handbook of Ceramics and Composites, Marcel Dekker, New York.
  60. Salami, S.J., Boroujerdy, M.S. and Bazzaz, E. (2021), "Geometrically nonlinear thermo-mechanical bending analysis of deep cylindrical composite panels reinforced by functionally graded CNTs", Adv. Nano Res., 10(4), 385-395. https://doi.org/10.12989/anr.2021.10.4.385.
  61. Sayyad, A.S. and Ghugal, Y.M. (2014), "A new shear and normal deformation theory for isotropic, transversely isotropic, laminated composite and sandwich plates", Int. J. Mech. Mater. Des., 10(3), 247-267. https://doi.org/10.1007/s10999-014-9244-3.
  62. Selmi, A. (2019), "Effectiveness of SWNT in reducing the crack effect on the dynamic behavior of aluminium alloy", Adv. Nano Res., 7(5), 365-377. https://doi.org/10.12989/anr.2019.7.5.365.
  63. Selmi, A. (2020), "Exact solution for nonlinear vibration of clamped-clamped functionally graded buckled beam", Smart Struct. Syst., 26(3), 361-371. https://doi.org/10.12989/sss.2020.26.3.361.
  64. 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. https://doi.org/10.12691/ajn-6-1-4.
  65. Shahsavari, D., Karami, B. and Li, L. (2018), "A high-order gradient model for wave propagation analysis of porous FG nanoplates", Steel Compos. Struct., 29(1), 53-66. https://doi.org/10.12989/scs.2018.29.1.053.
  66. Shakouri, M. (2021), "Analytical solution for stability analysis of joined cross-ply thin laminated conical shells under axial compression", Compos. Mater. Eng., 3(2), 117-134. https://doi.org/10.12989/cme.2021.3.2.117.
  67. Shimpi, R.P., Arya, H. and Naik, N.K. (2003), "A higher order displacement model for the plate analysis", Reinf. Plast. Compos., 22(18), 1667-1688. https://doi.org/10.1177/073168403027618.
  68. Shokravi, M. (2017), "Vibration analysis of silica nanoparticlesreinforced concrete beams considering agglomeration effects", Comput. Concrete, 19(3), 333-338. https://doi.org/10.12989/cac.2017.19.3.333.
  69. Talha, M. and Singh, B.N. (2010), "Static response and free vibration analysis of FGM plates using higher order shear deformation theory", Appl. Math. Model., 34(12), 3991-3991. https://doi.org/10.1016/j.apm.2010.03.034.
  70. Timesli, A. (2020), "Prediction of the critical buckling load of SWCNT reinforced concrete cylindrical shell embedded in an elastic foundation", Comput. Concrete, 26(1), 53-62. https://doi.org/10.12989/cac.2020.26.1.053.
  71. Timesli, A. (2021), "A cylindrical shell model for nonlocal buckling behavior of CNTs embedded in an elastic foundation under the simultaneous effects of magnetic field, temperature change, and number of walls", Adv. Nano Res., 11(6), 581-593. https://doi.org/10.12989/anr.2021.11.6.581.
  72. Touratier, M. (1991), "An efficient standard plate theory", Int. J. Eng. Sci., 29, 901-916. https://doi.org/10.1016/0020- 7225(91)90165-Y.
  73. Vinyas, M. (2020), "On frequency response of porous functionally graded magneto-electro-elastic circular and annular plates with different electro-magnetic conditions using HSDT", Compos. Struct., 240, 112044. https://doi.org/10.1016/j.compstruct.2020.112044.
  74. Yaghoobi, H. and Yaghoobi, P. (2013), "Buckling analysis of sandwich plates with FGM face sheets resting on elastic foundation with various boundary conditions: an analytical approach", Meccanica, 48, 2019-2035. https://doi.org/10.1007/s11012-013-9720-0.
  75. Yahea, H.T. and Majeed, W.I. (2021), "Free vibration of laminated composite plates in thermal environment using a simple four variable plate theory", Compos. Mater. Eng., 3(3), 179-199. https://doi.org/10.12989/cme.2021.3.3.179.
  76. Yaylaci, E.U., Yaylaci, M., Olmez, H. and Birinci, A., (2020), "Artificial Neural Network calculations for a receding contact problem", Comput. Concrete, 25(6), 551-563. https://doi.org/10.12989/cac.2020.25.6.551.
  77. Yaylaci, M. (2016), "The investigation crack problem through numerical analysis", Struct. Eng. Mech., 57(6), 1143-1156. https://doi.org/10.12989/sem.2016.57.6.1143.
  78. Yaylaci, M. and Avcar, M. (2020), "Finite element modeling of contact between an elastic layer and two elastic quarter planes", Comput. Concrete, 26(2), 107-114. https://doi.org/10.12989/cac.2020.26.2.107.
  79. Yaylaci, M. and Birinci, A. (2013), "The receding contact problem of two elastic layers supported by two elastic quarter planes", Struct. Eng. Mech., 48(2), 241-255. https://doi.org/10.12989/sem.2013.48.2.241.
  80. Yaylaci, M., Eyuboglu, A., Adiyaman, G., Uzun Yaylaci, E., Oner, E. and Birinci, A. (2021), "Assessment of different solution methods for receding contact problems in functionally graded layered mediums", Mech. Mater., 154, 103730 .https://doi.org/10.1016/j.mechmat.2020.103730.
  81. Yaylaci, M., Terzi, C. and Avcar, M. (2019), "Numerical analysis of the receding contact problem of two bonded layers resting on an elastic half plane", Struct. Eng. Mech., 72(6), 775-783. https://doi.org/10.12989/sem.2019.72.6.775.
  82. Zhen, Y.X., Wen, S.L. and Tang, Y. (2019), "Free vibration analysis of viscoelastic nanotubes under longitudinal magnetic field based on nonlocal strain gradient Timoshenko beam model", Physica E: Low Dimens. Syst. Nanostr., 105, 116-124. https://doi.org/10.1016/j.physe.2018.09.005.