DOI QR코드

DOI QR Code

A refined theory with stretching effect for the flexure analysis of laminated composite plates

  • Draiche, Kada (Departement de Genie Civil, Universite Ibn Khaldoun Tiaret) ;
  • Tounsi, Abdelouahed (Material and Hydrology Laboratory, University of Sidi Bel Abbes, Faculty of Technology, Civil Engineering Department) ;
  • Mahmoud, S.R. (Department of Mathematics, Faculty of Science, King Abdulaziz University)
  • Received : 2015.07.16
  • Accepted : 2016.07.03
  • Published : 2016.11.25

Abstract

This work presents a static flexure analysis of laminated composite plates by utilizing a higher order shear deformation theory in which the stretching effect is incorporated. The axial displacement field utilizes sinusoidal function in terms of thickness coordinate to consider the transverse shear deformation influence. The cosine function in thickness coordinate is employed in transverse displacement to introduce the influence of transverse normal strain. The highlight of the present method is that, in addition to incorporating the thickness stretching effect (${\varepsilon}_z{\neq}0$), the displacement field is constructed with only 5 unknowns, as against 6 or more in other higher order shear and normal deformation theory. Governing equations of the present theory are determined by employing the principle of virtual work. The closed-form solutions of simply supported cross-ply and angle-ply laminated composite plates have been obtained using Navier solution. The numerical results of present method are compared with those of the classical plate theory (CPT), first order shear deformation theory (FSDT), higher order shear deformation theory (HSDT) of Reddy, higher order shear and normal deformation theory (HSNDT) and exact three dimensional elasticity theory wherever applicable. The results predicted by present theory are in good agreement with those of higher order shear deformation theory and the elasticity theory. It can be concluded that the proposed method is accurate and simple in solving the static bending response of laminated composite plates.

Keywords

shear deformation;stretching effect;static flexure;laminated plate

References

  1. 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
  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. 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
  4. 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
  5. Bachir Bouiadjra, M., Houari, M.S.A. and Tounsi, A. (2012), "Thermal buckling of functionally graded plates according to a four-variable refined plate theory", J. Therm. Stresses, 35(8), 677-694. https://doi.org/10.1080/01495739.2012.688665
  6. Bachir Bouiadjra, R., Adda Bedia, E.A. and Tounsi, A. (2013), "Nonlinear thermal buckling behavior of functionally graded plates using an efficient sinusoidal shear deformation theory", Struct. Eng. Mech., Int. J., 48(4), 547-567. https://doi.org/10.12989/sem.2013.48.4.547
  7. Bakora, A. and Tounsi, A. (2015)," Thermo-mechanical post-buckling behavior of thick functionally graded plates resting on elastic foundations", Struct. Eng. Mech., Int. J., 56(1), 85-106. https://doi.org/10.12989/sem.2015.56.1.085
  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", Composites: Part B, 60, 274-283. https://doi.org/10.1016/j.compositesb.2013.12.057
  9. Bhimaradi A. and Stevens, L.K. (1984), "A higher order theory for free vibration of orthotropic, homogenous and laminated rectangular plates", J. Appl. Mech., 51(1),195-198. https://doi.org/10.1115/1.3167569
  10. 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
  11. 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
  12. 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
  13. 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(1), 265-275. https://doi.org/10.1007/s40430-015-0354-0
  14. Bennai, R., Ait Atmane, H. and Tounsi, A. (2015), "A new higher-order shear and normal deformation theory for functionally graded sandwich beams", Steel Compos. Struct., Int. J., 19(3), 521-546. https://doi.org/10.12989/scs.2015.19.3.521
  15. 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
  16. 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
  17. Bouderba, B., Houari, M.S.A., 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
  18. 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
  19. 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
  20. Bourada, M., Tounsi, A., Houari, M.S.A. and Adda Bedia, E.A. (2012), "A new four-variable refined plate theory for thermal buckling analysis of functionally graded sandwich plates", J. Sandw. Struct. Mater., 14(1), 5-33. https://doi.org/10.1177/1099636211426386
  21. 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
  22. 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
  23. Brischetto, S., Carrera, E. and Demasi, L. (2009), "Improved response of unsymmetrically laminated sandwich plates by using zig-zag functions", J. Sandw. Struct. Mater., 11(2-3), 257-267. https://doi.org/10.1177/1099636208099379
  24. Chalak, H.D., Chakrabarti, A., Iqbal M.A. and Sheikh, A.H. (2012), "An improved $C^{\circ}$ FE model for the analysis of laminated sandwich plate with soft core", Finite Elem. Anal. Des., 56, 20-31. https://doi.org/10.1016/j.finel.2012.02.005
  25. Chattibi, F., Benrahou, K.H., Benachour, A., Nedri, K. and Tounsi, A. (2015), "Thermomechanical effects on the bending of antisymmetric cross-ply composite plates using a four variable sinusoidal theory", Steel Compos. Struct., Int. J., 19(1), 93-110. https://doi.org/10.12989/scs.2015.19.1.093
  26. Draiche, K., Tounsi, A. and Khalfi, Y. (2014), "A trigonometric four variable plate theory for free vibration of rectangular composite plates with patch mass", Steel Compos. Struct., Int. J., 17(1), 69-81. https://doi.org/10.12989/scs.2014.17.1.069
  27. Fekrar, A., Houari, M.S.A., Tounsi, A. and Mahmoud, S.R. (2014), "A new five-unknown refined theory based on neutral surface position for bending analysis of exponential graded plates", Meccanica, 49(4), 795-810. https://doi.org/10.1007/s11012-013-9827-3
  28. 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
  29. 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
  30. 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(2), 374-383. https://doi.org/10.1061/(ASCE)EM.1943-7889.0000665
  31. Hidebrand, F.B., Reissner, E. and Thomas, G.B. (1949), "Note on the foundations of the theory of small displacements of orthotropic shells", NACA TN-1883.
  32. Kant, T. (1982), "Numerical analysis of thick plates", Comput. Method. Appl. Mech. Eng., 31(1), 1-18. https://doi.org/10.1016/0045-7825(82)90043-3
  33. Kant, T. and Swaminathan, K. (2002), "Analytical solutions for the static analysis of laminated composite and sandwich plates based on a higher order refined theory", Compos. Struct., 56(4), 329-344. https://doi.org/10.1016/S0263-8223(02)00017-X
  34. Kapuria, S. and Nath, J.K. (2013), "On the accuracy of recent global-local theories for bending and vibration of laminated plates", Compos. Struct., 95, 163-172. https://doi.org/10.1016/j.compstruct.2012.06.018
  35. Kar, V.R., Mahapatra, T.R. and Panda, S.K. (2015), "Nonlinear flexural analysis of laminated composite flat panel under hygro-thermo-mechanical loading", Steel Compos. Struct., Int. J., 19(4), 1011-1033. https://doi.org/10.12989/scs.2015.19.4.1011
  36. Larbi Chaht, F., Kaci, A., Houari, M.S.A., Tounsi, A., Anwar Beg, O. and Mahmoud, S.R. (2015), "Bending and buckling analyses of functionally graded material (FGM) size-dependent nanoscale beams including the thickness stretching effect", Steel Compos. Struct., Int. J., 18(2), 425-442. https://doi.org/10.12989/scs.2015.18.2.425
  37. Levinson, M. (1980), "An accurate simple theory of statics and dynamics of elastic plates", Mech. Res. Commun., 7(6), 343-350. https://doi.org/10.1016/0093-6413(80)90049-X
  38. Librescu, L. (1975), "Elastostatics and kinematics of anisotropic and heterogenous shell type structures", The Netherlands: Noordhoff.
  39. Lo, K.H., Christensen, R.M. and Wu, E.M. (1977a), "A high-order theory of plate deformation, part-1: homogenous plates", J. Appl. Mech., 44(4), 663-668. https://doi.org/10.1115/1.3424154
  40. Lo, K.H., Christensen, R.M. and Wu, E.M. (1977b), "A high-order theory of plate deformation, part-2: homogenous plates", J. Appl. Mech., 44(4), 669-676. https://doi.org/10.1115/1.3424155
  41. 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(9), 2489-2508. https://doi.org/10.1016/j.apm.2014.10.045
  42. Mantari, J.L. and Granados, E.V. (2015), "Thermoelastic analysis of advanced sandwich plates based on a new quasi-3D hybrid type HSDT with 5 unknowns", Compos.: Part B, 69, 317-334. https://doi.org/10.1016/j.compositesb.2014.10.009
  43. Meksi, A., Benyoucef, S., Houari, M.S.A. and Tounsi, A. (2015), "A simple shear deformation theory based on neutral surface position for functionally graded plates resting on Pasternak elastic foundations", Struct. Eng. Mech., Int. J., 53(6), 1215-1240. https://doi.org/10.12989/sem.2015.53.6.1215
  44. Meradjah, M., Kaci, A., Houari, M.S.A., Tounsi, A. and Mahmoud, S.R. (2015), "A new higher order shear and normal deformation theory for functionally graded beams", Steel Compos. Struct., Int. J., 18(3), 793-809. https://doi.org/10.12989/scs.2015.18.3.793
  45. Mindlin, R.D. (1951), "Influence of rotatory inertia and shear on flexural motions of isotropic, elastic plates", ASME J. Appl. Mech., 18, 31-38.
  46. Murthy, M.V.V. (1981), "An improved transverse shear deformation theory for laminated anisotropic plates", NASA Technical Paper.
  47. 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", Mech. Compos. Mater., 49(6), 629-640. https://doi.org/10.1007/s11029-013-9379-6
  48. Nguyen, K.T., Thai, T.H. and Vo, T.P. (2015), "A refined higher-order shear deformation theory for bending, vibration and buckling analysis of functionally graded sandwich plates", Steel Compos. Struct., Int. J., 18(1), 91-120. https://doi.org/10.12989/scs.2015.18.1.091
  49. Nelson, R.B. and Lorch, D.R. (1974), "A refined theory for laminated orthotropic plates", ASME J. Appl. Mech., 41(1), 177-183. https://doi.org/10.1115/1.3423219
  50. Pagano, N.J. (1970), "Exact solutions for bidirectional composites and sandwich plates", J. Compos. Mater., 4, 20-34. https://doi.org/10.1177/002199837000400102
  51. Pandit, M.K., Sheikh, A.H. and Singh, B.N. (2010), "Analysis of laminated sandwich plates based on an improved higher order zigzag theory", J. Sandw. Struct. Mater., 12, 307-326. https://doi.org/10.1177/1099636209104517
  52. Reddy, J.N. (1984), "A simple higher order shear deformation theory for laminated composite plates", J. Appl. Mech., 51(4), 745-753. https://doi.org/10.1115/1.3167719
  53. Ren, J.G. (1990), "Bending, vibration and buckling of laminated plates", In: Cheremisinoff NP, editor. Handbook of ceramics and composites, vol. 1. New York: Marcel Dekker; pp. 413-450.
  54. Sadoune, M., Tounsi, A., Houari, M.S.A. and Adda Bedia, E.A. (2014), "A novel first-order shear deformation theory for laminated composite plates", Steel Compos. Struct., Int. J., 17(3), 321-338. https://doi.org/10.12989/scs.2014.17.3.321
  55. Sahoo, R. and Singh, B.N. (2013), "A new shear deformation theory for the static analysis of laminated composite and sandwich plates", Int. J. Mech. Sci., 75, 324-336. https://doi.org/10.1016/j.ijmecsci.2013.08.002
  56. Saidi, H., Houari, M.S.A., Tounsi, A. and Adda Bedia, E.A. (2013), "Thermo-mechanical bending response with stretching effect of functionally graded sandwich plates using a novel shear deformation theory", Steel Compos. Struct., Int. J., 15, 221-245. https://doi.org/10.12989/scs.2013.15.2.221
  57. Sallai, B., Hadji, L., Hassaine Daouadji, T. and Adda Bedia, E.A. (2015), "Analytical solution for bending analysis of functionally graded beam", Steel Compos. Struct., Int. J., 19(4), 829-841. https://doi.org/10.12989/scs.2015.19.4.829
  58. Sayyad, A.S. and Ghugal, Y.M. (2014a), "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
  59. Sayyad, A.S. and Ghugal, Y.M. (2014b), "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
  60. Soldatos, K.P. (1988), "On certain refined theories for plate bending", ASME J. Appl. Mech., 55(4), 994-995. https://doi.org/10.1115/1.3173757
  61. Tagrara, S.H., Benachour, A., Bachir Bouiadjra, M. and Tounsi, A. (2015), "On bending, buckling and vibration responses of functionally graded carbon nanotube-reinforced composite beams", Steel Compos. Struct., Int. J., 19(5), 1259-1277. https://doi.org/10.12989/scs.2015.19.5.1259
  62. Tebboune, W., Benrahou, K.H., Houari, M.S.A. and Tounsi, A. (2015), "Thermal buckling analysis of FG plates resting on elastic foundation based on an efficient and simple trigonometric shear deformation theory", Steel Compos. Struct., Int. J., 18(2), 443-465. https://doi.org/10.12989/scs.2015.18.2.443
  63. 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
  64. Zenkour, A.M. (2007), "Three-dimensional elasticity solution for uniformly loaded cross-ply laminates and sandwich plates", J. Sandw. Struct. Mater., 9(3), 213-238. https://doi.org/10.1177/1099636207065675
  65. Zhen, W. and Wanji, C. (2010), "A $C^{\circ}$-type higher-order theory for bending analysis of laminated composite and sandwich plates", Compos. Struct., 92(3), 653-661. https://doi.org/10.1016/j.compstruct.2009.09.032
  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. Post-buckling analysis of refined shear deformable graphene platelet reinforced beams with porosities and geometrical imperfection vol.181, 2017, https://doi.org/10.1016/j.compstruct.2017.08.082
  3. Mesoscale Modelling of Bond Behavior at FRP-Concrete under Mode II Loading: Effect of Rayleigh Damping vol.2017, 2017, https://doi.org/10.1155/2017/6053181
  4. Bending, buckling and vibration analyses of MSGT microcomposite circular-annular sandwich plate under hydro-thermo-magneto-mechanical loadings using DQM 2017, https://doi.org/10.1080/19475411.2017.1377312
  5. Earthquake induced dynamic deflection of submerged viscoelastic cylindrical shell reinforced by agglomerated CNTs considering thermal and moisture effects vol.187, 2018, https://doi.org/10.1016/j.compstruct.2017.12.004
  6. Size-dependent electro-magneto-elastic bending analyses of the shear-deformable axisymmetric functionally graded circular nanoplates vol.132, pp.10, 2017, https://doi.org/10.1140/epjp/i2017-11666-6
  7. Dynamic modeling of porous heterogeneous micro/nanobeams vol.132, pp.12, 2017, https://doi.org/10.1140/epjp/i2017-11754-7
  8. Eigenvalue approach to two dimensional coupled magneto-thermoelasticity in a rotating isotropic medium vol.7, 2017, https://doi.org/10.1016/j.rinp.2017.07.053
  9. A general higher-order nonlocal couple stress based beam model for vibration analysis of porous nanocrystalline nanobeams vol.112, 2017, https://doi.org/10.1016/j.spmi.2017.09.010
  10. Eigenvalue approach to coupled thermoelasticity in a rotating isotropic medium vol.8, 2018, https://doi.org/10.1016/j.rinp.2017.09.021
  11. A novel quasi-3D hyperbolic theory for free vibration of FG plates with porosities resting on Winkler/Pasternak/Kerr foundation vol.72, 2018, https://doi.org/10.1016/j.ast.2017.11.004
  12. Numerical analysis of acoustic radiation properties of laminated composite flat panel in thermal environment: A higher-order finite-boundary element approach 2017, https://doi.org/10.1177/0954406217735866
  13. Size-dependent nonlinear vibration of beam-type porous materials with an initial geometrical curvature vol.184, 2018, https://doi.org/10.1016/j.compstruct.2017.10.052
  14. A new non-polynomial four variable shear deformation theory in axiomatic formulation for hygro-thermo-mechanical analysis of laminated composite plates vol.182, 2017, https://doi.org/10.1016/j.compstruct.2017.09.029
  15. Damping vibration behavior of visco-elastically coupled double-layered graphene sheets based on nonlocal strain gradient theory 2017, https://doi.org/10.1007/s00542-017-3529-z
  16. Vibration and buckling analysis of a rotary functionally graded piezomagnetic nanoshell embedded in viscoelastic media vol.29, pp.11, 2018, https://doi.org/10.1177/1045389X18770856
  17. A novel approach for nonlinear bending response of macro- and nanoplates with irregular variable thickness under nonuniform loading in thermal environment pp.1539-7742, 2019, https://doi.org/10.1080/15397734.2018.1557529