DOI QR코드

DOI QR Code

An efficient and simple higher order shear deformation theory for bending analysis of composite plates under various boundary conditions

  • Adim, Belkacem (Departement de Genie Civil, Universite Ibn Khaldoun Tiaret) ;
  • Daouadji, Tahar Hassaine (Departement de Genie Civil, Universite Ibn Khaldoun Tiaret) ;
  • Rabia, Benferhat (Laboratoire de Geomateriaux, Departement de Genie Civil, Universite de Chlef) ;
  • Hadji, Lazreg (Departement de Genie Civil, Universite Ibn Khaldoun Tiaret)
  • Received : 2015.11.08
  • Accepted : 2016.06.15
  • Published : 2016.07.25

Abstract

In this study, the bending and dynamic behaviors of laminated composite plates is examined by using a refined shear deformation theory and developed for a bending analysis of orthotropic laminated composite plates under various boundary conditions. The displacement field of the present theory is chosen based on nonlinear variations in the in-plane displacements through the thickness of the plate. By dividing the transverse displacement into the bending and shear parts and making further assumptions, the number of unknowns and equations of motion of the present theory is reduced and hence makes them simple to use. In the analysis, the equation of motion for simply supported thick laminated rectangular plates is obtained through the use of Hamilton's principle. Numerical results for the bending and dynamic behaviors of antisymmetric cross-ply laminated plate under various boundary conditions are presented. The validity of the present solution is demonstrated by comparison with solutions available in the literature. Numerical results show that the present theory can archive accuracy comparable to the existing higher order shear deformation theories that contain more number of unknowns.

Keywords

References

  1. Abdelhak, Z., L. Hadji, Hassaine Daouadji T. and Adda bedia E.A. (2015), "Thermal buckling of functionally graded plates using a n-order four variable refined theory", Adv. Mater. Res., 4(1), 31-44. https://doi.org/10.12989/amr.2015.4.1.31
  2. 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. Sandwich Struct. Mater., 16(3), 293-318. https://doi.org/10.1177/1099636214526852
  3. Aydogdu, M. (2009), "A new shear deformation theory for laminated composite plates", Compos. Struct., 89(1), 94-101. https://doi.org/10.1016/j.compstruct.2008.07.008
  4. Benferhat, R., Hassaine Daouadji, T. and M. Said Mansour (2014), "A higher order shear deformation model for bending analysis of functionally graded plates", Transactions of the Indian Institute of Metals, 68(1), 7-16. https://doi.org/10.1007/s12666-014-0428-1
  5. Bouazza, M., K. Amara, M. Zidour, A. Tounsi and El A. Adda Bedia (2015), "Postbuckling analysis of functionally graded beams using hyperbolic shear deformation theory", Rev. Inform. Eng. Appl., 2(1), 1-14. https://doi.org/10.1186/s40535-014-0004-0
  6. Bouazza, M., K. Amara, M. Zidour, A. Tounsi and El A. Adda Bedia (2015), "Postbuckling analysis of nanobeams using trigonometric Shear deformation theory", Appl. Sci. Reports, 10(2), 112-121.
  7. Carrera, E. (2002), "Theories and finite elements for multilayered, anisotropic, composite plates and shells", Archiv. Comput. Meth. Eng., 9(2), 87-140. https://doi.org/10.1007/BF02736649
  8. Carrera, E. and Miglioretti, F. (2012), "Selection of appropriate multilayered plate theories by using a genetic like algorithm", Compos. Struct., 94(3), 1175-1186 https://doi.org/10.1016/j.compstruct.2011.10.013
  9. Hassaine Daouadji, T., Tounsi, A. and Adda bedia, E.A. (2013), "Analytical solution for bending analysis of functionally graded plates", Scientia Iranica, Trans. B: Mech. Eng., 20(3), 516-523.
  10. Hebali, H., A. Tounsi, S. Houari, A. Bessaim and E.A. Adda Bedia (2014), "A new quasi-3D hyperbolic shear deformation theory for the static and free vibration analysis of functionally graded plates", J. Eng. Mech., ASCE, 140(2), 374-383. https://doi.org/10.1061/(ASCE)EM.1943-7889.0000665
  11. Karama, M., K.S. Afaq, and S. Mistou (2003), "Mechanical behavior of laminated composite beam by the new multi-layered laminated composite structures model with transverse shear stress continuity", Int. J. Solid. Struct., 40(6), 15251546.
  12. Karama, M., Afaq, K.S. and Mistou, S. (2009), "A new theory for laminated composite plates", Proceeding of the IMechE, vol. 223 (Part L: Journal of Materials: Design and Applications).
  13. Mahi, A., E. Adda Bedia and A. Tounsi (2015), "A new hyperbolic shear deformation theory for bending and free vibration analysis of isotropic, functionally graded, sandwich and laminated composite plate", Appl. Math. Model., Appl. Math. Model., 39(9), 2489-2508.
  14. Mantari, J.L., A.S. Oktem and C. Guedes Soares (2012), "A new trigonometric shear deformation theory for isotropic, laminated composite and sandwich plates", Int. J. Solid. Struct., 49(1), 43-53. https://doi.org/10.1016/j.ijsolstr.2011.09.008
  15. Meiche, N.E., Tounsi, A., Ziane, N., Mechab, I. and Bedia, E.A. (2011), "A new hyperbolic shear deformation theory for buckling and vibration of functionally graded sandwich plate", Int. J. Mech. Sci., 53(4), 237-247. https://doi.org/10.1016/j.ijmecsci.2011.01.004
  16. Mindlin, R.D. (1951), "Influence of rotary inertia and shear on flexural motions of isotropic, elastic plates", J. Appl. Mech., 18, 31-38.
  17. Nedri, K., N. El Meiche and A. Tounsi (2014), "Free vibration analysis of laminated composite plates resting on elastic foundation by using a refined hyperbolic shear deformation theory", Mech. Compos. Mater., 49(6), 629-640. https://doi.org/10.1007/s11029-013-9379-6
  18. Noor, A.K. (1975), "Stability of multilayered composite plate", Fibre Sci. Technol., 8(2), 81-89. https://doi.org/10.1016/0015-0568(75)90005-6
  19. Noor, K. (1973), "Free vibrations of multilayered composite plates", AIAA J., 11(7), 1038-1039. https://doi.org/10.2514/3.6868
  20. Pagano, N.J. (1970), "Exact solutions for rectangular bidirectional composites and sandwich plates", J. Compos. Mater., 4(1), 20-34. https://doi.org/10.1177/002199837000400102
  21. Reddy, J.N. (1984), "A simple higher-order theory for laminated composite plates", J. Appl. Mech., ASME, 51(4), 745-752. https://doi.org/10.1115/1.3167719
  22. Reddy, J.N. (1986), "A refined shear deformation theory for the analysis of laminated plates", NASA Report3955.
  23. Reissner, E. (1945), "The effect of transverse shear deformation on the bending of elastic plates", J. Appl. Mech., Trans., ASME, 12(2), 69-77.
  24. Ren, J.G. (1986), "A new theory of laminated plate", Compos. Sci. Technol., 26(3), 225-239. https://doi.org/10.1016/0266-3538(86)90087-4
  25. Ren, J.G. (1990), "Bending, vibration and buckling of laminated plates", Ed., Cheremisinoff, N.P., Handbook of ceramics and composites, 1, 413-450.
  26. Shimpi, R.P. and Patel, H.G. (2006), "A two variable refined plate theory for orthotropic plate analysis", Int. J. Solid. Struct., 43(22), 6783-6799. https://doi.org/10.1016/j.ijsolstr.2006.02.007
  27. 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
  28. Tlidji, Y., Hassaine Daouadji, T., Hadji, L., Tounsi, A. and Adda bedia, E.A. (2014), "Elasticity solution for bending response of functionally graded sandwich plates under thermo mechanical loading", J. Therm. Stress, 37(7), 852-869. https://doi.org/10.1080/01495739.2014.912917
  29. Tounsi, A., Sid Ahmed, H., Benyoucef, S. and Adda Bedia, E.A. (2013), "A refined trigonometric shear deformation theory for thermoelastic bending of functionally graded sandwich plates", Aero. Sci. Technol., 24(1), 209-220. https://doi.org/10.1016/j.ast.2011.11.009
  30. Zenkour, A.M. (2006), "Generalized shear deformation theory for bending analysis of functionally graded plates", Appl. Math. Model., 30(1), 67-84. https://doi.org/10.1016/j.apm.2005.03.009

Cited by

  1. Dynamic analysis for anti-symmetric cross-ply and angle-ply laminates for simply supported thick hybrid rectangular plates vol.7, pp.2, 2016, https://doi.org/10.12989/amr.2018.7.2.119
  2. Dynamic analysis for anti-symmetric cross-ply and angle-ply laminates for simply supported thick hybrid rectangular plates vol.7, pp.2, 2016, https://doi.org/10.12989/amr.2018.7.2.119
  3. Effect of distribution shape of the porosity on the interfacial stresses of the FGM beam strengthened with FRP plate vol.16, pp.5, 2016, https://doi.org/10.12989/eas.2019.16.5.601
  4. Numerical analysis for free vibration of hybrid laminated composite plates for different boundary conditions vol.70, pp.5, 2019, https://doi.org/10.12989/sem.2019.70.5.535
  5. Influence of the distribution shape of porosity on the bending FGM new plate model resting on elastic foundations vol.72, pp.1, 2016, https://doi.org/10.12989/sem.2019.72.1.061
  6. Flexural behaviour of steel beams reinforced by carbon fibre reinforced polymer: Experimental and numerical study vol.72, pp.4, 2019, https://doi.org/10.12989/sem.2019.72.4.409
  7. Flexural behaviour of steel beams reinforced by carbon fibre reinforced polymer: Experimental and numerical study vol.72, pp.4, 2019, https://doi.org/10.12989/sem.2019.72.4.409
  8. Improved analytical solution for slip and interfacial stress in composite steel-concrete beam bonded with an adhesive vol.9, pp.2, 2016, https://doi.org/10.12989/amr.2020.9.2.133
  9. Optimization of flexure stiffness of FGM beams via artificial neural networks by mixed FEM vol.75, pp.5, 2020, https://doi.org/10.12989/sem.2020.75.5.633
  10. Analysis of interfacial stresses of the reinforced concrete foundation beams repairing with composite materials plate vol.9, pp.5, 2016, https://doi.org/10.12989/csm.2020.9.5.473
  11. Thermo-mechanical behavior of porous FG plate resting on the Winkler-Pasternak foundation vol.9, pp.6, 2016, https://doi.org/10.12989/csm.2020.9.6.499
  12. Study and analysis of the free vibration for FGM microbeam containing various distribution shape of porosity vol.77, pp.2, 2016, https://doi.org/10.12989/sem.2021.77.2.217
  13. Modeling and analysis of the imperfect FGM-damaged RC hybrid beams vol.6, pp.2, 2016, https://doi.org/10.12989/acd.2021.6.2.117
  14. New solution for damaged porous RC cantilever beams strengthening by composite plate vol.10, pp.3, 2016, https://doi.org/10.12989/amr.2021.10.3.169