Structural Engineering and Mechanics

Techno-Press (테크노프레스)
권호 표지
DOI QR코드

DOI QR Code

Analysis on the buckling of imperfect functionally graded sandwich plates using new modified power-law formulations

  • Received : 2020.10.06
  • Accepted : 2021.02.04
  • Published : 2021.03.25
⟨ Previous Next ⟩

Abstract

A new simple solution for critical buckling of FG sandwich plates under axial and biaxial loads is presented using new modified power-law formulations. Both even and uneven distributions of porosity are taken into account in this study. Material properties of the sandwich plate faces are assumed to be graded in the thickness direction according to a modified power-law distribution in terms of the volume fractions of the constituents. Equilibrium and stability equations of FG sandwich plate with various boundary conditions are derived using the higher-order shear deformation plate theory. The results reveal that the distribution shape of the porosity, the gradient index, loading type and functionally graded layers thickness have significant influence on the buckling response of functionally graded sandwich plates.

Keywords

References

  1. Abdederak, R., Hassaine Daouadji, T., Benferhat, R. and Adim, B. (2018), "Nonlinear analysis of damaged RC beams strengthened with glass fiber reinforced polymer plate under symmetric loads", Earthq. Struct., 15(2), 113-122. https://doi.org/10.12989/eas.2018.15.2.113.
  2. Abdelhak, Z., Hadji, L., Khelifa, Z., Hassaine Daouadji, T. and Adda Bedia, E.A. (2016), "Analysis of buckling response of functionally graded sandwich plates using a refined shear deformation theory", Wind Struct., 22(3), 291-305. https://doi.org/10.12989/was.2016.22.3.291.
  3. Abderezak, R., Daouadji, T.H. and Rabia, B. (2020), "Analysis of interfacial stresses of the reinforced concrete foundation beams repairing with composite materials plate", Coupl. Syst. Mech., 9(5), 473-498. http://dx.doi.org/10.12989/csm.2020.9.5.473.
  4. Abderezak, R., Rabia, B., Daouadji, T.H., Abbes, B., Belkacem, A. and Abbes, F. (2018), "Elastic analysis of interfacial stresses in prestressed PFGM-RC hybrid beams", Adv. Mater. Res., 7(2), 83. https://doi.org/10.12989/amr.2018.7.2.083.
  5. Adim, B. and Daouadji, T.H. (2016), "Effects of thickness stretching in FGM plates using a quasi-3D higher order shear deformation theory", Adv. Mater. Res., 5(4), 223. https://doi.org/10.12989/amr.2016.5.4.223.
  6. Ait Atmane, H., Tounsi, A. and Bernard, F. (2015), "Effect of thickness stretching and porosity on mechanical response of a functionally graded beams resting on elastic foundations", Int. J. Mech. Mater., 1-14. https://doi.org/10.1007/s10999-015-9318-x.
  7. Batou, B., Mokhtar, N., Bennai, R., Ait Atmane, H., Tounsi, A. and Bouremana, M. (2019), "Wave dispersion properties in imperfect sigmoid plates using various HSDTs", Steel Compos. Struct., 33(5), 699-716. https://doi.org/10.12989/scs.2019.33.5.699.
  8. Bekki, H., Benferhat, R. and Hassaine Daouadji, T. (2019), "Influence of the distribution shape of porosity on the bending FGM new plate model resting on elastic foundations", Struct. Eng. Mech., 72(1), 823-832. https://doi.org/10.12989/sem.2019.72.1.061.
  9. Belkacem, A., Tahar, H.D., Abderrezak, R., Amine, B.M., Mohamed, Z. and Boussad, A. (2018), "Mechanical buckling analysis of hybrid laminated composite plates under different boundary conditions", Struct. Eng. Mech., 66(6), 761-769. https://doi.org/10.12989/sem.2018.66.6.761.
  10. Benferhat, R., Hassaine Daouadji, T., Hadji, L. amd 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.
  11. Benferhat, R., Hassaine Daouadji, T., Said Mansour, M. and Hadji, L. (2016), "Effect of porosity on the bending and free vibration response of functionally graded plates resting on Winkler-Pasternak foundations", Earthq. Struct, 10(6), 1429-1449. https://doi.org/10.12989/eas.2016.10.6.1429.
  12. Benferhat, R., Rabahi, A., Hassaine Daouadji, T., Boussad, A. and Adim, B. (2018), "Analytical analysis of the interfacial shear stress in RC beams strengthened with prestressed exponentially-varying properties plate", Adv. Mater. Res., 7(1), 29-44. https://doi.org/10.12989/amr.2018.7.1.029.
  13. Benhenni, M.A., Adim, B., Daouadji, T.H., Abbes, B., Abbes, F., Li, Y. and Bouzidane, A. (2019), "A comparison of closed-form and finite-element solutions for the free vibration of hybrid cross-ply laminated plates", Mech. Compos. Mater., 55(2), 181-194. https://doi.org/10.1007/s11029-019-09803-2
  14. Benhenni, M.A., Daouadji, T.H., Abbes, B., Abbes, F., Li, Y. and Adim, B. (2019), "Numerical analysis for free vibration of hybrid laminated composite plates for different boundary conditions", Struct. Eng. Mech., 70(5), 535-549. https://doi.org/10.12989/sem.2019.70.5.535.
  15. Benhenni, M.A., Daouadji, T.H., Abbes, B., Adim, B., Li, Y. and Abbes, F. (2018), "Dynamic analysis for anti-symmetric cross-ply and angle-ply laminates for simply supported thick hybrid rectangular plates", Adv. Mater. Res., 7(2), 119. https://doi.org/10.12989/amr.2018.7.2.119.
  16. Bensattalah, T., Daouadji, T.H., Zidour, M., Tounsi, A. and Bedia, E.A. (2016), "Investigation of thermal and chirality effects on vibration of single-walled carbon nanotubes embedded in a polymeric matrix using nonlocal elasticity theories", Mech. Compos. Mater., 52(4), 555-568. https://doi.org/10.1007/s11029-016-9606-z.
  17. Bensattalah, T., Zidour, M. and Daouadji, T.H. (2018), "Analytical analysis for the forced vibration of CNT surrounding elastic medium including thermal effect using nonlocal Euler-Bernoulli theory", Adv. Mater. Res., 7(3), 163-174. https://doi.org/10.12989/amr.2018.7.3.163.
  18. Bouakaz, K., Daouadji, T.H., Meftah, S.A., Ameur, M., Tounsi, A. and Bedia, E.A. (2014), "A numerical analysis of steel beams strengthened with composite materials", Mech. Compos. Mater., 50(4), 491-500. https://doi.org/10.1007/s11029-014-9435-x.
  19. Carrera, E., Brischetto, S., Cinefra, M. and Soave M. (2011). "Effects of thickness stretching in functionally graded plates and shells", Compos. Part B, 42, 123-133. http://dx.doi.org/10.1016/j.compositesb.2010.10.005.
  20. Chedad, A., Daouadji, T.H., Abderezak, R., Adim, B., Abbes, B., Rabia, B. and Abbes, F. (2017), "A high-order closed-form solution for interfacial stresses in externally sandwich FGM plated RC beams", Adv. Mater. Res., 6(4), 317-328. https://doi.org/10.12989/amr.2017.6.4.317.
  21. Chergui, S., Daouadji, T.H., Hamrat, M., Boulekbache, B., Bougara, A., Abbes, B. and Amziane, S. (2019), "Interfacial stresses in damaged RC beams strengthened by externally bonded prestressed GFRP laminate plate: Analytical and numerical study", Adv. Mater. Res., 8(3), 197-217. https://doi.org/10.12989/amr.2019.8.3.197.
  22. Cooke, D.W. and Levinson, M. (1983), "Thick rectangular plates-II, the generalized Levy solution", Int. J. Mech. Sci., 25, 207-215. https://doi.org/10.1016/0020-7403(83)90094-2.
  23. Daouadji, T.H. (2016), "Theoretical analysis of composite beams under uniformly distributed load", Adv. Mater. Res., 5(1), 1. https://doi.org/10.12989/amr.2016.5.1.001.
  24. Daouadji, T.H. and Adim, B. (2016), "An analytical approach for buckling of functionally graded plates", Adv. Mater. Res., 5(3), 141. https://doi.org/10.12989/amr.2016.5.3.141.
  25. Daouadji, T.H. and Benferhat, R. (2016), "Bending analysis of an imperfect FGM plates under hygro-thermo-mechanical loading with analytical validation", Adv. Mater. Res., 5(1), 035. https://doi.org/10.12989/amr.2016.5.1.035.
  26. Daouadji, T.H., Rabahi, A., Abbes, B. and Adim, B. (2016), "Theoretical and finite element studies of interfacial stresses in reinforced concrete beams strengthened by externally FRP laminates plate", J. Adhes. Sci. Technol., 30(12), 1253-1280. https://doi.org/10.1080/01694243.2016.1140703.
  27. Demirhan, P.A. and Taskin, V. (2019), "Bending and free vibration analysis of Levy-type porous functionally graded plate using state space approach", Compos. Part B: Eng., 160, 661-676. https://doi.org/10.1016/j.compositesb.2018.12.020.
  28. Draiche, K., Bousahla, A.A., Tounsi, A., Alwabli, A.S., Tounsi, A. and Mahmoud, S.R. (2019), "Static analysis of laminated reinforced composite plates using a simple first-order shear deformation theory", Comput. Concrete, 24(4), 369-378. http://dx.doi.org/10.12989/cac.2019.24.4.369.
  29. Hamrat, M., Bouziadi, F., Boulekbache, B., Daouadji, T.H., Chergui, S., Labed, A. and Amziane, S. (2020), "Experimental and numerical investigation on the deflection behavior of precracked and repaired reinforced concrete beams with fiber-reinforced polymer", Constr. Build. Mater., 249, 118745. https://doi.org/10.1016/j.conbuildmat.2020.118745.
  30. Hassaine Daouadji, T. (2013), "Analytical analysis of the interfacial stress in damaged reinforced concrete beams strengthened by bonded composite plates", Strength Mater., 45(5), 587-597. htttps://doi.org/10.1007/s11223-013-9496-4.
  31. Hassaine Daouadji, T. (2017), "Analytical and numerical modeling of interfacial stresses in beams bonded with a thin plate", Adv. Comput. Des., 2(1), 57-69. https://doi.org/10.12989/acd.2017.2.1.057.
  32. Hassaine Daouadjim T., Rabahim A., Benferhatm R. and Adimm B. (2019), "Flexural behavior of steel beams reinforced by carbon fiber reinforced polymer: Experimental and numerical study", Struct. Eng. Mech., 72(4), 409-419. https://doi.org/10.12989/sem.2019.72.4.409.
  33. Kablia, A., Benferhat, R., Hassaine Daouadji, T. and Bouzidene, A. (2020), "Effect of porosity distribution rate for bending analysis of imperfect FGM plates resting on Winkler-Pasternak foundations under various boundary conditions", Coupl. Syst. Mech., 9(6), 575-597. http://dx.doi.org/10.12989/csm.2020.9.6.575.
  34. Khelifa, Z., Hadji, L., Daouadji, T.H. and Bourada, M. (2018), "Buckling response with stretching effect of carbon nanotube-reinforced composite beams resting on elastic foundation", Struct. Eng. Mech., 67(2), 125-130. https://doi.org/10.12989/sem.2018.67.2.125.
  35. Lee, K.H., Lim, G.T. and Wang, C.M. (2002), "Thick Levy plates re-visited", Int. J. Solid. Struct., 39, 127-144. https://doi.org/10.1016/S0020-7683(01)00205-0.
  36. Lu, C.F., Lim, C.W. and Chen, W.Q. (2009), "Exact solutions for free vibrations of functionally graded thick plates on elastic foundations", Mech. Adv. Mater. Struct., 16(8), 576-584. https://doi.org/0.1080/15376490903138888. https://doi.org/10.1080/15376490903138888
  37. Mantari, J.L., Oktem, A.S. and Guedes Soares, C. (2012), "A new trigonometric shear deformation theory for isotropic, laminated composite and sandwich plates", Int. J. Solid. Struct., 49, 43-53. https://doi.org/10.1016/j.ijsolstr.2011.09.008.
  38. Rabahi, A., Daouadji, T.H., Abbes, B. and Adim, B. (2016), "Analytical and numerical solution of the interfacial stress in reinforced-concrete beams reinforced with bonded prestressed composite plate", J. Reinf. Plast. Compos., 35(3), 258-272. https://doi.org/10.1177/0731684415613633.
  39. Rabia, B., Daouadji, T.H. and Abderezak, R. (2019), "Effect of distribution shape of the porosity on the interfacial stresses of the FGM beam strengthened with FRP plate", Earthq. Struct, 16(5), 601-609. https://doi.org/10.12989/eas.2019.16.5.601.
  40. Rabia, B., Daouadji, T.H. and Abderezak, R. (2020), "Predictions of the maximum plate end stresses of imperfect FRP strengthened RC beams: study and analysis", Adv. Mater. Res., 9(4), 265. http://dx.doi.org/10.12989/amr.2020.9.4.265.
  41. Reddy, J.N. (2000), "Analysis of functionally graded plates", Int. J. Numer. Meth. Eng., 47, 663-684. http://dx.doi.org/10.10.1002/(SICI)1097- 0207(20000110/30)47:1/33.0.CO;2-8.
  42. Reddy, J.N., Wang, C.M., Lim, G.T. and Ng, K.H. (2001), "Bending solutions of Levinson beams and plates in terms of the classical theories", Int. J. Solid. Struct., 38, 4701-4720. https://doi.org/10.1016/S0020-7683(00)00298-5.
  43. Slimane, M. (2018), "Analysis of bending of ceramic-metal functionally graded plates with porosities using of high order shear theory", Adv. Eng. Forum, 30, 54-70. https://doi.org/10.4028/www.scientific.net/AEF.30.54.
  44. Tahar Hassaine, D., Adim, B. and Benferhat, R. (2016), "Bending analysis of an imperfect FGM plates under hygro-thermo-mechanical loading with analytical validation", Adv. Mater. Res., 5(1), 35-53. https://doi.org/10.12989/amr.2016.5.1.035.
  45. Tahar, H.D., Abderezak, R. and Rabia, B. (2020), "Flexural performance of wooden beams strengthened by composite plate", Struct. Monit. Mainten., 7(3), 233-259. http://dx.doi.org/10.12989/smm.2020.7.3.233.
  46. Tayeb, B. and Daouadji, T.H. (2020), "Improved analytical solution for slip and interfacial stress in composite steel-concrete beam bonded with an adhesive", Adv. Mater. Res., 9(2), 133-153. https://doi.org/10.12989/amr.2020.9.2.133.
  47. Thai, H.T. and Choi, D.H. (2013), "Finite element formulation of various four unknown shear deformation theories for functionally graded plates", Finite Elem. Anal. Des., 75, 50-61. https://doi.org/10.1016/j.finel.2013.07.003.
  48. Tlidji, Y., Benferhat, R. and Tahar, H.D. (2021), "Study and analysis of the free vibration for FGM microbeam containing various distribution shape of porosity", Struct. Eng. Mech., 77(2), 217. http://dx.doi.org/10.12989/sem.2021.77.2.217.
  49. Tounsi, A., Al-Dulaijan, S.U., Al-Osta, M.A., Chikh, A., Al-Zahrani, M.M., Sharif, A. and Tounsi, A. (2020), "A four variable trigonometric integral plate theory for hygro-thermo-mechanical bending analysis of AFG ceramic-metal plates resting on a two-parameter elastic foundation", Steel Compos. Struct., 34(4), 511-524. https://doi.org/10.12989/scs.2020.34.4.511.
  50. Vel, S.S. and Batra, R.C. (2004), "Three-dimensional exact solution for the vibration of functionally graded rectangular plates", J. Sound Vib., 272(3-5), 703-730. https://doi.org/10.1016/S0022-460X(03)00412-7.
  51. Wattanasakulponga, N. and Ungbhakornb, V. (2014), "Linear and non linear vibration analysis of elastically restrained ends FGM beams with porosities", Aero. Sci. Technol., 32(1), 111-120. https://doi.org/10.1016/j.ast.2013.12.002.
  52. Ying, J., Lu, C.F. and Lim, C.W. (2009), "3D thermoelasticity solutions for functionally graded thick plates", J. Zhejiang Univ.-Sci. A, 10(3), 327-336. https://doi.org/10.1631/jzus.A0820406.
  53. Zenkour, A M. (2005), "A comprehensive analysis of functionally graded sandwich plates: Part 2-Buckling and free vibration", Int. J. Solid. Struct., 42(18-19), 5243-5258. https://doi.org/10.1016/j.ijsolstr.2005.02.016.
  54. Zenkour, A.M. and Radwan, A.F. (2018), "Compressive study of functionally graded plates resting on Winkler-Pasternak foundations under various boundary conditions using hyperbolic shear deformation theory", Arch. Civil Mech. Eng., 18, 645-658. https://doi.org/10.1016/j.acme.2017.10.003.

Cited by

  1. A new model for adhesive shear stress in damaged RC cantilever beam strengthened by composite plate taking into account the effect of creep and shrinkage vol.79, pp.5, 2021, https://doi.org/10.12989/sem.2021.79.5.531
  2. New solution for damaged porous RC cantilever beams strengthening by composite plate vol.10, pp.3, 2021, https://doi.org/10.12989/amr.2021.10.3.169