Steel and Composite Structures

Techno-Press (테크노프레스)
권호 표지
DOI QR코드

DOI QR Code

A novel four variable refined plate theory for laminated composite plates

  • Merdaci, Slimane (Material and Hydrology Laboratory, University of Sidi Bel Abbes, Faculty of Technology, Civil Engineering Department) ;
  • Tounsi, Abdelouahed (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)
  • Received : 2016.04.19
  • Accepted : 2016.10.12
  • Published : 2016.11.20
⟨ Previous Next ⟩

Abstract

A novel four variable refined plate theory is proposed in this work for laminated composite plates. The theory considers a parabolic distribution of the transverse shear strains, and respects the zero traction boundary conditions on the surfaces of the plate without employing shear correction coefficient. The displacement field is based on a novel kinematic in which the undetermined integral terms are used, and only four unknowns are involved. The analytical solutions of antisymmetric cross-ply and angle-ply laminates are determined via Navier technique. The obtained results from the present model are compared with three-dimensional elasticity solutions and results of the first-order and the other higher-order theories reported in the literature. It can be concluded that the developed theory is accurate and simple in investigating the bending and buckling responses of laminated composite plates.

Keywords

References

  1. Ait Amar Meziane, M., Abdelaziz, H.H. and Tounsi, A. (2014), "An efficient and simple refined theory for buckling and free vibration of exponentially graded sandwich plates under various boundary conditions", J. Sandw. Struct. Mater., 16(3), 293-318. https://doi.org/10.1177/1099636214526852
  2. Ait Atmane, H., Tounsi, A., Bernard, F. and Mahmoud, S.R. (2015), "A computational shear displacement model for vibrational analysis of functionally graded beams with porosities", Steel Compos. Struct., Int. J., 19(2), 369-384. https://doi.org/10.12989/scs.2015.19.2.369
  3. Ait Yahia, S., Ait Atmane, H., Houari, M.S.A. and Tounsi, A. (2015), "Wave propagation in functionally graded plates with porosities using various higher-order shear deformation plate theories", Struct. Eng. Mech., Int. J., 53(6), 1143-1165. https://doi.org/10.12989/sem.2015.53.6.1143
  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.S. (2014), "An efficient shear deformation theory for free vibration of functionally graded thick rectangular plates on elastic foundation", Compos. Struct., 108, 667-676. https://doi.org/10.1016/j.compstruct.2013.10.019
  6. Al-Basyouni, K.S., Tounsi, A. and Mahmoud, S.R. (2015), "Size dependent bending and vibration analysis of functionally graded micro beams based on modified couple stress theory and neutral surface position", Compos. Struct., 125, 621-630. https://doi.org/10.1016/j.compstruct.2014.12.070
  7. Attia, A., Tounsi, A., Adda Bedia, E.A. and Mahmoud, S.R. (2015), "Free vibration analysis of functionally graded plates with temperature-dependent properties using various four variable refined plate theories", Steel Compos. Struct., Int. J., 18(1), 187-212. https://doi.org/10.12989/scs.2015.18.1.187
  8. Belabed, Z., Houari, M.S.A., Tounsi, A., Mahmoud, S.R. and Anwar Beg, O. (2014), "An efficient and simple higher order shear and normal deformation theory for functionally graded material (FGM) plates", Compos.: Part B, 60, 274-283. https://doi.org/10.1016/j.compositesb.2013.12.057
  9. Beldjelili, Y., Tounsi, A. and Mahmoud, S.R. (2016), "Hygro-thermo-mechanical bending of S-FGM plates resting on variable elastic foundations using a four-variable trigonometric plate theory", Smart Struct. Syst., Int. J., 18(4), 755-786. https://doi.org/10.12989/sss.2016.18.4.755
  10. Bellifa, H., Benrahou, K.H., Hadji, L., Houari, M.S.A. and Tounsi, A. (2016), "Bending and free vibration analysis of functionally graded plates using a simple shear deformation theory and the concept the neutral surface position", J. Braz. Soc. Mech. Sci. Eng., 38, 265-275. https://doi.org/10.1007/s40430-015-0354-0
  11. Belkorissat, I., Houari, M.S.A., Tounsi, A., Adda Bedia, E.A. and Mahmoud, S.R. (2015), "On vibration properties of functionally graded nano-plate using a new nonlocal refined four variable model", Steel Compos. Struct., Int. J., 18(4), 1063-1081. https://doi.org/10.12989/scs.2015.18.4.1063
  12. Bennoun, M., Houari, M.S.A. and Tounsi, A. (2016), "A novel five variable refined plate theory for vibration analysis of functionally graded sandwich plates", Mech. Adv. Mater. Struct., 23(4), 423-431. https://doi.org/10.1080/15376494.2014.984088
  13. Bouchafa, A., Bachir Bouiadjra, M., Houari, M.S.A. and Tounsi, A. (2015), "Thermal stresses and deflections of functionally graded sandwich plates using a new refined hyperbolic shear deformation theory", Steel Compos. Struct., Int. J., 18(6), 1493-1515. https://doi.org/10.12989/scs.2015.18.6.1493
  14. Bouderba, B., Houari, M.S.A. and Tounsi, A. (2013), "Thermomechanical bending response of FGM thick plates resting on Winkler-Pasternak elastic foundations", Steel Compos. Struct., Int. J., 14(1), 85-104. https://doi.org/10.12989/scs.2013.14.1.085
  15. Bouderba, B., Houari, M.S.A. and Tounsi, A. and Mahmoud, S.R. (2016), "Thermal stability of functionally graded sandwich plates using a simple shear deformation theory", Struct. Eng. Mech., Int. J., 58(3), 397-422. https://doi.org/10.12989/sem.2016.58.3.397
  16. Boukhari, A., Ait Atmane, H., Tounsi, A., Adda Bedia, E.A. and Mahmoud, S.R. (2016), "An efficient shear deformation theory for wave propagation of functionally graded material plates", Struct. Eng. Mech., Int. J., 57(5), 837-859. https://doi.org/10.12989/sem.2016.57.5.837
  17. Bounouara, F., Benrahou, K.H., Belkorissat, I. and Tounsi, A. (2016), "A nonlocal zeroth-order shear deformation theory for free vibration of functionally graded nanoscale plates resting on elastic foundation", Steel Compos. Struct., Int. J., 20(2), 227-249. https://doi.org/10.12989/scs.2016.20.2.227
  18. Bourada, M., Kaci, A., Houari, M.S.A. and Tounsi, A. (2015), "A new simple shear and normal deformations theory for functionally graded beams", Steel Compos. Struct., Int. J., 18(2), 409-423. https://doi.org/10.12989/scs.2015.18.2.409
  19. 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
  20. Bousahla, A.A., Houari, M.S.A., Tounsi, A. and Adda Bedia, E.A. (2014), "A novel higher order shear and normal deformation theory based on neutral surface position for bending analysis of advanced composite plates", Int. J. Computat. Method., 11(6), 1350082. https://doi.org/10.1142/S0219876213500825
  21. Bousahla, A.A., Benyoucef, S., Tounsi, A. and Mahmoud, S.R. (2016), "On thermal stability of plates with functionally graded coefficient of thermal expansion", Struct. Eng. Mech., Int. J., 60(2), 313-335. https://doi.org/10.12989/sem.2016.60.2.313
  22. Chakraborty, A., Gopalakrishnan, S. and Reddy, J.N. (2003), "A new beam finite element for the analysis of functionally graded materials", Int. J. Mech. Sci., 45(3), 519-539. https://doi.org/10.1016/S0020-7403(03)00058-4
  23. 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(27), 2225-2237. https://doi.org/10.1016/j.compstruc.2005.04.002
  24. Ghugal, Y.M. and Shimpi, R.P. (2002), "A review of refined shear deformation theories of isotropic and anisotropic laminated plates", J. Reinf. Plast Compos., 21(9), 775-813. https://doi.org/10.1177/073168402128988481
  25. 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
  26. Hamidi, A., Houari, M.S.A., Mahmoud, S.R. and Tounsi, A. (2015), "A sinusoidal plate theory with 5-unknowns and stretching effect for thermomechanical bending of functionally graded sandwich plates", Steel Compos. Struct., Int. J., 18(1), 235-253. https://doi.org/10.12989/scs.2015.18.1.235
  27. Hebali, H., Tounsi, A., Houari, M.S.A., Bessaim, A. and Adda Bedia, E.A. (2014), "A new quasi-3D hyperbolic shear deformation theory for the static and free vibration analysis of functionally graded plates", ASCE J. Eng. Mech., 140, 374-383. https://doi.org/10.1061/(ASCE)EM.1943-7889.0000665
  28. Houari, M.S.A., Tounsi, A., Bessaim, A. and Mahmoud, S.R. (2016), "A new simple three -unknown sinusoidal shear deformation theory for functionally graded plates", Steel Compos. Struct., Int. J., (Accepted).
  29. Kant, T. and Khare, R.K. (1997), "A higher-order facet quadrilateral composite shell element", Int. J. Numer. Meth. Eng., 40(24), 4477-4499. https://doi.org/10.1002/(SICI)1097-0207(19971230)40:24<4477::AID-NME229>3.0.CO;2-3
  30. Kant, T. and Pandya, B.N. (1988), "A simple finite element formulation of a higher-order theory for unsymmetrically laminated composite plates", Compos. Struct., 9(3), 215-246. https://doi.org/10.1016/0263-8223(88)90015-3
  31. Kant, T., Ravichandran, R., Pandya, B. and Mallikarjuna, B. (1988), "Finite element transient dynamic analysis of isotropic and fibre reinforced composite plates using a higher-order theory", Compos. Struct., 9(4), 319-342. https://doi.org/10.1016/0263-8223(88)90051-7
  32. Karama, M., Afaq, K.S. and Mistou, S. (2003), "Mechanical behaviour of laminated composite beam by the new multi-layered laminated composite structures model with transverse shear stress continuity", Int. J. Solids Struct., 40(6), 1525-1546. https://doi.org/10.1016/S0020-7683(02)00647-9
  33. Khandan, R., Noroozi, S., Sewell, P. and Vinney, J. (2012), "The development of laminated composite plate theories: a review", J. Mater. Sci., 47(16), 5901-5910. https://doi.org/10.1007/s10853-012-6329-y
  34. Khdeir, A.A. (1989), "Comparison between shear deformable and Kirchhoff theories for bending, buckling and vibration of antisymmetric angle-ply laminated plates", Compos. Struct., 13(3), 159-172. https://doi.org/10.1016/0263-8223(89)90001-9
  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. Li, X.F. (2008), "A unified approach for analyzing static and dynamic behaviors of functionally graded Timoshenko and Euler-Bernoulli beams", J. Sound Vib., 318(4-5), 1210-1229. https://doi.org/10.1016/j.jsv.2008.04.056
  37. Lo, K.H., Christensen, R.M. and Wu, E.M. (1977), "A higher-order theory of plate deformation, part 2:laminated plates", J. Appl. Mech., 44(4), 669-676. https://doi.org/10.1115/1.3424155
  38. Mahi, A., Adda Bedia, E.A. and 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
  39. Mallikarjuna, M. and Kant, T. (1989), "A higher-order theory for free vibration of unsymmetrically laminated composite and sandwich plates-finite element evaluations", Comput. Struct., 32(5), 1125-1132. https://doi.org/10.1016/0045-7949(89)90414-8
  40. Mallikarjuna, M. and Kant, T. (1993), "A critical review and some results of recently developed refined theories of fiber-reinforced laminated composites and sandwiches", Compos. Struct., 23(4), 293-312. https://doi.org/10.1016/0263-8223(93)90230-N
  41. Mantari, J.L. and Ore, M. (2015), "Free vibration of single and sandwich laminated composite plates by using a simplified FSDT", Compos. Struct., 132, 952-959. https://doi.org/10.1016/j.compstruct.2015.06.035
  42. 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.
  43. Noor, A.K. (1990), "Stability of multilayered composite plate", Fibre. Sci. Technol., 8, 81-89.
  44. Noor, A.K. and Burton, W.S. (1989), "Stress and free vibration analyses of multilayered composite plates", Compos. Struct., 11(3), 183-204. https://doi.org/10.1016/0263-8223(89)90058-5
  45. 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
  46. 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
  47. Reddy, J.N. (1990), "A review of refined theories of laminated composite plates", Shock Vib. Dig., 22(7), 3-17. https://doi.org/10.1177/058310249002200703
  48. Reddy, J.N. (1997), Mechanics of Laminated Composite Plate: Theory and Analysis, CRC Press, New York, NY, USA.
  49. Reissner, E. (1945), "The effect of transverse shear deformation on the bending of elastic plates", J. Appl. Mech., Trans. ASME, 12(2), 69-77.
  50. Ren, J.G. (1990), "Bending, vibration and buckling of laminated plates", (Cheremisinoff N.P. Editor), Handbook of Ceramics and Composites, (Vol. 1), Marcel Dekker, New York, NY, USA, pp. 413-450.
  51. Sahoo, R. and Singh, B.N. (2013), "A new inverse hyperbolic zigzag theory for the static analysis of laminated composite and sandwich plates", Compos. Struct., 105, 385-397. https://doi.org/10.1016/j.compstruct.2013.05.043
  52. Sayyad, A.S. and Ghugal, Y.M. (2014), "Flexure of cross-ply laminated plates using equivalent single layer trigonometric shear deformation theory", Struct. Eng. Mech., Int. J., 51(5), 867-891. https://doi.org/10.12989/sem.2014.51.5.867
  53. Soldatos, K. (1992), "A transverse shear deformation theory for homogeneous monoclinic plates", Acta Mech., 94(3), 195-220. https://doi.org/10.1007/BF01176650
  54. Sina, S.A., Navazi, H.M. and Haddadpour, H. (2009), "An analytical method for free vibration analysis of functionally graded beams", Mater. Des., 30(3), 741-747. https://doi.org/10.1016/j.matdes.2008.05.015
  55. Soldatos, K.P. (1992), "A transverse shear deformation theory for homogeneous monoclinic plates", Acta Mech., 94(3), 195-220. https://doi.org/10.1007/BF01176650
  56. Tounsi, A., Houari, M.S.A., Benyoucef, S. and Adda Bedia, E.A. (2013), "A refined trigonometric shear deformation theory for thermoelastic bending of functionally graded sandwich plates", Aerosp. Sci. Technol., 24(1), 209-220. https://doi.org/10.1016/j.ast.2011.11.009
  57. Tounsi, A., Houari, M.S.A. and Bessaim, A. (2016), "A new 3-unknowns non-polynomial plate theory for buckling and vibration of functionally graded sandwich plate", Struct. Eng. Mech., Int. J., (Accepted).
  58. 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
  59. Wei, D., Liu, Y. and Xiang, Z. (2012), "An analytical method for free vibration analysis of functionally graded beams with edge cracks", J. Sound Vib., 331(7), 1686-1700. https://doi.org/10.1016/j.jsv.2011.11.020
  60. Whitney, J.M. and Pagano, N.J. (1970), "Shear deformation in heterogeneous anisotropic plates", J. Appl. Mech., Trans. ASME, 37(4), 1031-1036. https://doi.org/10.1115/1.3408654
  61. 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(1), 31-37. https://doi.org/10.1016/j.compstruct.2009.04.029
  62. Xiang, S., Jin, Y.X., Bi, Z.Y., Jiang, S.X. and Yang, M.S. (2011), "A n-order shear deformation theory for free vibration of functionally graded and composite sandwich plates", Compos. Struct., 93(11), 2826-2832. https://doi.org/10.1016/j.compstruct.2011.05.022
  63. Yesilce, Y. (2010), "Effect of axial force on the free vibration of Reddy-Bickford multi- span beam carrying multiple spring-mass systems", J. Vib. Control, 16(1), 11-32. https://doi.org/10.1177/1077546309102673
  64. Yesilce, Y. and Catal, S. (2009), "Free vibration of axially loaded Reddy-Bickford beam on elastic soil using the differential transform method", Struct. Eng. Mech., Int. J., 31(4), 453-476. https://doi.org/10.12989/sem.2009.31.4.453
  65. Yesilce, Y. and Catal, H.H. (2011), "Solution of free vibration equations of semi-rigid connected Reddy-Bickford beams resting on elastic soil using the differential transform method", Arch. Appl. Mech., 81(2), 199-213. https://doi.org/10.1007/s00419-010-0405-z
  66. Zidi, M., Tounsi, A., Houari, M.S.A., Adda Bedia, E.A. and Anwar Beg, O. (2014), "Bending analysis of FGM plates under hygro-thermo-mechanical loading using a four variable refined plate theory", Aerosp. Sci. Technol., 34, 24-34. https://doi.org/10.1016/j.ast.2014.02.001

Cited by

  1. Experimental observation and energy based analytical investigation of matrix cracking distribution pattern in angle-ply laminates vol.92, 2017, https://doi.org/10.1016/j.tafmec.2017.06.007
  2. A non-polynomial four variable refined plate theory for free vibration of functionally graded thick rectangular plates on elastic foundation vol.23, pp.3, 2016, https://doi.org/10.12989/scs.2017.23.3.317
  3. Thermal buckling analysis of cross-ply laminated plates using a simplified HSDT vol.19, pp.3, 2016, https://doi.org/10.12989/sss.2017.19.3.289
  4. Free vibration analysis of embedded nanosize FG plates using a new nonlocal trigonometric shear deformation theory vol.19, pp.6, 2016, https://doi.org/10.12989/sss.2017.19.6.601
  5. Free vibrations of laminated composite plates using a novel four variable refined plate theory vol.24, pp.5, 2017, https://doi.org/10.12989/scs.2017.24.5.603
  6. An original single variable shear deformation theory for buckling analysis of thick isotropic plates vol.63, pp.4, 2017, https://doi.org/10.12989/sem.2017.63.4.439
  7. A four variable refined nth-order shear deformation theory for mechanical and thermal buckling analysis of functionally graded plates vol.13, pp.3, 2016, https://doi.org/10.12989/gae.2017.13.3.385
  8. Vibration analysis of nonlocal advanced nanobeams in hygro-thermal environment using a new two-unknown trigonometric shear deformation beam theory vol.20, pp.3, 2016, https://doi.org/10.12989/sss.2017.20.3.369
  9. A new and simple HSDT for thermal stability analysis of FG sandwich plates vol.25, pp.2, 2016, https://doi.org/10.12989/scs.2017.25.2.157
  10. A novel simple two-unknown hyperbolic shear deformation theory for functionally graded beams vol.64, pp.2, 2016, https://doi.org/10.12989/sem.2017.64.2.145
  11. Free vibration of functionally graded plates resting on elastic foundations based on quasi-3D hybrid-type higher order shear deformation theory vol.20, pp.4, 2017, https://doi.org/10.12989/sss.2017.20.4.509
  12. An efficient and simple four variable refined plate theory for buckling analysis of functionally graded plates vol.25, pp.3, 2016, https://doi.org/10.12989/scs.2017.25.3.257
  13. A novel and simple higher order shear deformation theory for stability and vibration of functionally graded sandwich plate vol.25, pp.4, 2017, https://doi.org/10.12989/scs.2017.25.4.389
  14. A new nonlocal trigonometric shear deformation theory for thermal buckling analysis of embedded nanosize FG plates vol.64, pp.4, 2016, https://doi.org/10.12989/sem.2017.64.4.391
  15. An original HSDT for free vibration analysis of functionally graded plates vol.25, pp.6, 2016, https://doi.org/10.12989/scs.2017.25.6.735
  16. A high-order gradient model for wave propagation analysis of porous FG nanoplates vol.29, pp.1, 2018, https://doi.org/10.12989/scs.2018.29.1.053
  17. Improved HSDT accounting for effect of thickness stretching in advanced composite plates vol.66, pp.1, 2016, https://doi.org/10.12989/sem.2018.66.1.061
  18. A new nonlocal HSDT for analysis of stability of single layer graphene sheet vol.6, pp.2, 2016, https://doi.org/10.12989/anr.2018.6.2.147
  19. Nonlinear vibration of functionally graded nano-tubes using nonlocal strain gradient theory and a two-steps perturbation method vol.69, pp.2, 2016, https://doi.org/10.12989/sem.2019.69.2.205
  20. Free Vibration Analysis of Composite Material Plates "Case of a Typical Functionally Graded FG Plates Ceramic/Metal" with Porosities vol.25, pp.None, 2016, https://doi.org/10.4028/www.scientific.net/nhc.25.69
  21. Influences of porosity on dynamic response of FG plates resting on Winkler/Pasternak/Kerr foundation using quasi 3D HSDT vol.24, pp.4, 2016, https://doi.org/10.12989/cac.2019.24.4.347
  22. Dispersion of waves characteristics of laminated composite nanoplate vol.40, pp.3, 2016, https://doi.org/10.12989/scs.2021.40.3.355