DOI QR코드

DOI QR Code

Effect of distribution shape of the porosity on the interfacial stresses of the FGM beam strengthened with FRP plate

  • Received : 2018.08.20
  • Accepted : 2019.04.01
  • Published : 2019.05.25

Abstract

The effect of the porosity and its distribution shape on the normal and shear interfacial stresses of the FGM beam strengthened with FRP plate subjected to a uniformly distributed load are investigated analytically in the present paper. Basically, the governing equations of FGM beams with porosity strengthened with composite plates are identical to the ones without porosity. Nonetheless, when the effect of the porosity and its distribution shape are taken into account, the rule of mixture was reformulated to assess the material characteristics with the porosity phases and its distribution shape. This work discusses the influence of the gradient index, the porosity and its distribution shape on the interfacial stresses.

Acknowledgement

Supported by : Ministry of Higher Education and Scientific Research (MESRS)

References

  1. Abualnour, M., Houari, M.S.A., Tounsi, A. and Mahmoud, S.R. (2018), "A novel quasi-3D trigonometric plate theory for free vibration analysis of advanced composite plates", Compos. Struct., 184, 688-697. https://doi.org/10.1016/j.compstruct.2017.10.047. https://doi.org/10.1016/j.compstruct.2017.10.047
  2. 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), 223-244. https://doi.org/10.12989/amr.2016.5.4.223. https://doi.org/10.12989/amr.2016.5.4.223
  3. Adim, B., Daouadji, T.H. and Rabahi, A. (2016c), "A simple higher order shear deformation theory for mechanical behavior of laminated composite plates", Int. J. Adv. Struct. Eng. (IJASE), 8, 103-117. https://doi.org/10.1007/s40091-016-0109-x. https://doi.org/10.1007/s40091-016-0109-x
  4. Adim, B., Daouadji, T.H., Abbes, B. and Rabahi, A. (2016b), "Buckling and free vibration analysis of laminated composite plates using an efficient and simple higher order shear deformation theory", Mech. Indus., 17, 512. https://doi.org/10.1051/meca/2015112. https://doi.org/10.1051/meca/2015112
  5. Adim, B., Daouadji, T.H., Rabia, B. and Hadji, L. (2016a), "An efficient and simple higher order shear deformation theory for bending analysis of composite plates under various boundary conditions", Earthq. Struct., 11(1), 63-82. https://doi.org/10.12989/eas.2016.11.1.063. https://doi.org/10.12989/eas.2016.11.1.063
  6. Alam, M.A. and Al Riyami, K. (2018), "Shear strengthening of reinforced concrete beam using natural fibre reinforced polymer laminates", Constr. Build. Mater., 162(20), 683-696. https://doi.org/10.1016/j.conbuildmat.2017.12.011. https://doi.org/10.1016/j.conbuildmat.2017.12.011
  7. Attia, A., Bousahla, A.A., Tounsi, A., Mahmoud, S.R. and Alwabli, A.S. (2018), "A refined four variable plate theory for thermoelastic analysis of FGM plates resting on variable elastic foundations", Struct. Eng. Mech., 65(4), 453-464. https://doi.org/10.12989/sem.2018.65.4.453. https://doi.org/10.12989/SEM.2018.65.4.453
  8. Belabed, Z., Bousahla, A.A., Houari, M.S.A., Tounsi, A. and Mahmoud, S.R. (2018), "A new 3- unknown hyperbolic shear deformation theory for vibration of functionally graded sandwich plate", Earthq. Struct., 14(2), 103-115. https://doi.org/10.12989/eas.2018.14.2.103. https://doi.org/10.12989/EAS.2018.14.2.103
  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. https://doi.org/10.12989/SEM.2018.66.6.761
  10. Bellifa, H., Benrahou, K.H., Bousahla, A.A., Tounsi, A. and Mahmoud, S.R. (2017), "A nonlocal zeroth-order shear deformation theory for nonlinear postbuckling of nanobeams", Struct. Eng. Mech., 62(6), 695-702. https://doi.org/10.12989/sem.2017.62.6.695. https://doi.org/10.12989/SEM.2017.62.6.695
  11. Benachour, A., Benyoucef, S. and Tounsi, A. (2008), "Interfacial stress analysis of steel beams reinforced with bonded prestressed FRP plate", Eng. Struct., 30, 3305-3315. https://doi.org/10.1016/j.engstruct.2008.05.007. https://doi.org/10.1016/j.engstruct.2008.05.007
  12. Benadouda, M., Ait Atmane, H., Tounsi, A., Bernard, F. and Mahmoud, S.R. (2017), "An efficient shear deformation theory for wave propagation in functionally graded material beams with porosities", Earthq. Struct., 13(3), 255-265. https://doi.org/10.12989/sem.2016.57.5.837. https://doi.org/10.12989/EAS.2017.13.3.255
  13. Abdelhak, Z., Hadji, L., Daouadji, T.H. and Adda, B. (2016), "Thermal buckling response of functionally graded sandwich plates with clamped boundary conditions", Smart Struct. Syst., 18(2) 267-291. https://doi.org/10.12989/sss.2016.18.2.267. https://doi.org/10.12989/sss.2016.18.2.267
  14. Abdelhak, Z., Hadji, L., Khelifa, Z., Hassaine, D. and Adda, B. (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. https://doi.org/10.12989/was.2016.22.3.291
  15. Benchohra, M., Driz, H., Bakora, A., Tounsi, A., Adda Bedia, E. A. and Mahmoud, S.R. (2018), "A new quasi-3D sinusoidal shear deformation theory for functionally graded plates", Struct. Eng. Mech., 65(1), 19-31. https://doi.org/10.12989/sem.2018.65.1.019. https://doi.org/10.12989/SEM.2018.65.1.019
  16. Benferhat, R., Daouadji, T.H. and Mansour, M.S. (2016), "Free vibration analysis of FG plates resting on the elastic foundation and based on the neutral surface concept using higher order shear deformation theory", Comptes Rendus Mecanique, 344(9), 631-641. https://doi.org/10.1016/j.crme.2016.03.002. https://doi.org/10.1016/j.crme.2016.03.002
  17. Benferhat, R., Daouadji, T.H., Mansour, M.S. and Hadji, L. (2016a), "Effect of porosity on the bending and free vibration response of functionally graded plates resting on Winkler-Pasternak foundations", Earthq. Struct., 10(5), 1429-1449. https://doi.org/10.12989/eas.2016.10.6.1429. https://doi.org/10.12989/eas.2016.10.6.1429
  18. Benferhat, R., Hassaine Daouadji, T. and Said Mansour, M. (2015), "A higher order shear deformation model for bending analysis of functionally graded plates", Tran. Ind. Inst. Meter., 68(1), 7-16 https://doi.org/10.1007/s12666-014-0428-1
  19. Benferhat, R., Hassaine, D., Hadji, L. and Said, M. (2016b), "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. https://doi.org/10.12989/scs.2016.21.1.123
  20. Benferhat, R., Rabahi, A., Hassaine Daouadji, T., Abbes, B., Adim B. and Abbes, F. (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. https://doi.org/10.12989/amr.2018.7.1.029
  21. 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. https://doi.org/10.1080/15376494.2014.984088
  22. Bensattalah, T., Bouakkaz, K., Zidour, M. and Daouadji, T.H. (2018), "Critical buckling loads of carbon nanotube embedded in Kerr's medium", Adv. Nano Res., 6(4), 339-356. https://doi.org/10.12989/anr.2018.6.4.339. https://doi.org/10.12989/anr.2018.6.4.339
  23. Bensattalah, T., Zidour, M., Ait Amar Meziane, M., Hassaine Daouadji, T. and Tounsi, A. (2018), "Critical buckling load of carbon nanotube with non-local Timoshenko beam using the differential transform method", Int. J. Civil Environ. Eng., 12(6), 637-644. https://doi.org/10.5281/zenodo.1317114.
  24. Benyoucef, S., Tounsi, A., Meftah, S.A. and Adda Bedia, E.A. (2006), "Approximate analysis of the interfacial stress concentrations in FRP-RC hybrid beams", Compos. Interf., 13(7), 561-71. https://doi.org/10.1163/156855406778440758. https://doi.org/10.1163/156855406778440758
  25. Bouadi, A., Bousahla, A.A., Houari, M.S.A., Heireche, H. and Tounsi, A. (2018), "A new nonlocal HSDT for analysis of stability of single layer graphene sheet", Adv. Nano Res., 6(2), 147-162. https://doi.org/10.12989/anr.2018.6.2.147. https://doi.org/10.12989/ANR.2018.6.2.147
  26. Bouafia, K., Kaci, A., Houari, M.S.A., Benzair, A. and Tounsi, A. (2017), "A nonlocal quasi-3D theory for bending and free flexural vibration behaviors of functionally graded nanobeams", Smart Struct. Syst., 19(2), 115-126. https://doi.org/10.12989/sss.2017.19.2.115. https://doi.org/10.12989/sss.2017.19.2.115
  27. Bouakaz, K., Hassaine Daouadji, T., Meftah, S.A., Ameur, M. and Adda Bedia, E.A. (2014), "A numerical analysis of steel beams strengthened with composite materials", Mechanics of Composite Materials, 50(4), 685-696.
  28. Bouhadra, A., Tounsi, A., Bousahla, A.A., Benyoucef, S. and Mahmoud, S.R. (2018), "Improved HSDT accounting for effect of thickness stretching inadvanced composite plates", Struct. Eng. Mech., 66(1), 61-73. https://doi.org/10.12989/sem.2018.66.1.061. https://doi.org/10.12989/SEM.2018.66.1.061
  29. Boukhari, A., Atmane, H.A., Tounsi, A., Adda, B. and Mahmoud, S.R. (2016), "An efficient shear deformation theory for wave propagation of functionally graded material plates", Struct. Eng. Mech., 57(5), 837-859. https://doi.org/10.12989/sem.2016.57.5.837. https://doi.org/10.12989/sem.2016.57.5.837
  30. 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., 20(2), 227-249. https://doi.org/10.12989/scs.2016.20.2.227. https://doi.org/10.12989/scs.2016.20.2.227
  31. 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., 60(2), 313-335. https://doi.org/10.12989/sem.2016.60.2.313. https://doi.org/10.12989/sem.2016.60.2.313
  32. Chedad, A., Daouadji, T. H., Abderezak, R., Belkacem, A., Abbes, B., Rabia, B. and Abbes, F. (2018), "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. https://doi.org/10.12989/AMR.2017.6.4.317
  33. Chen, W., Pham, T.M., Sichembe, H., Chen, L. and Hao, H. (2018), "Experimental study of flexural behaviour of RC beams strengthened by longitudinal and U-shaped basalt FRP sheet", Compos. Part B: Eng., 134, 114-126. https://doi.org/10.1016/j.compositesb.2017.09.053. https://doi.org/10.1016/j.compositesb.2017.09.053
  34. Daouadji, H.T., Benyoucef, S., Tounsi, A., Benrahou, K.H. and Bedia, A.E. (2008), "Interfacial stresses concentrations in FRPDamaged RC hybrid beams", Compos. Interf., 15(4), 425-440. https://doi.org/10.1163/156855408784514702. https://doi.org/10.1163/156855408784514702
  35. Daouadji, T.H. and Adim, B. (2016a), "Theoretical analysis of composite beams under uniformly distributed load", Adv. Mater. Res., 5(1), 1-9. https://doi.org/10.12989/amr.2016.5.1.001. https://doi.org/10.12989/amr.2016.5.1.001
  36. Daouadji, T.H. and Adim, B. (2016e), "An analytical approach for buckling of functionally graded plates", Adv. Mater. Res., 5(3), 141-169. https://doi.org/10.12989/amr.2016.5.3.141. https://doi.org/10.12989/amr.2016.5.3.141
  37. Daouadji, T.H., Adim, B. and Benferhat, R. (2016c), "Bending analysis of an imperfect FGM plates under hygro-thermomechanical loading with analytical validation", Adv. Mater. Res., 5(1), 35-53. https://doi.org/10.12989/amr.2016.5.1.035. https://doi.org/10.12989/amr.2016.5.1.035
  38. Daouadji, T.H., Benferhat, R. and Adim, B. (2016b), "A novel higher order shear deformation theory based on the neutral surface concept of FGM plate under transverse load", Adv. Mater. Res., 5(2), 107-120. https://doi.org/10.12989/amr.2016.5.2.107. https://doi.org/10.12989/amr.2016.5.2.107
  39. Daouadji, T.H., Benferhat, R. and Adim, B. (2016d), "Bending analysis of an imperfect advanced composite plates resting on the elastic foundations", Coupl. Syst. Mech., 5(3), 269-285. https://doi.org/10.12989/csm.2017.5.3.269 https://doi.org/10.12989/csm.2016.5.3.269
  40. 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. https://doi.org/10.1080/01694243.2016.1140703
  41. El-Haina, F., Bakora, A., Bousahla, A.A., Tounsi, A. and Mahmoud, S.R. (2017), "A simple analytical approach for thermal buckling of thick functionally graded sandwich plates", Struct. Eng. Mech., 63(5), 585-595. https://doi.org/10.12989/sem.2017.63.5.585. https://doi.org/10.12989/SEM.2017.63.5.585
  42. Fourn, H., Atmane, H.A., Bourada, M., Bousahla, A.A., Tounsi, A. and Mahmoud, S.R. (2018), "A novel four variable refined plate theory for wave propagation in functionally graded material plates", Steel Compos. Struct., 27(1), 109-122. https://doi.org/10.12989/scs.2018.27.1.109. https://doi.org/10.12989/SCS.2018.27.1.109
  43. Fu, B., Teng, J.G., Chen, G.M., Chen, J.F. and Guo, Y.C. (2018), "Effect of load distribution on IC debonding in FRPstrengthened RC beams: Full-scale experiments", Compos. Struct., 188, 483-496. https://doi.org/10.1016/j.compstruct.2018.01.026. https://doi.org/10.1016/j.compstruct.2018.01.026
  44. Guenaneche B., Tounsi, A. and Adda Bedia, E.A. (2014), "Effect of shear deformation on interfacial stress analysis in plated beams under arbitrary loading", Adhes. Adhesiv., 48, 1-13. https://doi.org/10.1016/j.ijadhadh.2013.09.016. https://doi.org/10.1016/j.ijadhadh.2013.09.016
  45. Hachemi, H., Kaci, A., Houari, M.S.A., Bourada, M., Tounsi, A. and Mahmoud, S.R. (2017), "A new simple three-unknown shear deformation theory for bending analysis of FG plates resting on elastic foundations", Steel Compos. Struct., 25(6), 717-726. https://doi.org/10.12989/scs.2017.25.6.717. https://doi.org/10.12989/SCS.2017.25.6.717
  46. Hadji, L., Hassaine Daouadji, T. and Adda Bedia, E. (2015), "A refined exponential shear deformation theory for free vibration of FGM beam with porosities", Geomech. Eng., 9(3), 361-372. https://doi.org/10.12989/gae.2015.9.3.361. https://doi.org/10.12989/gae.2015.9.3.361
  47. 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. https://doi.org/10.1007/s11223-013-9496-4. https://doi.org/10.1007/s11223-013-9496-4
  48. Hassaine Daouadji, T. and Adim, B. (2017), "Mechanical behaviour of FGM sandwich plates using a quasi-3Dhigher order shear and normal deformation theory", Struct. Eng. Mech., 61(1), 49-63. https://doi.org/10.12989/sem.2017.61.1.049. https://doi.org/10.12989/sem.2017.61.1.049
  49. Hassaine Daouadji, T. 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. https://doi.org/10.12989/gae.2015.9.5.631
  50. Hassaine Daouadji, T., Tounsi, A. and Adda Bedia, E.A. (2012), "Analyse des contraintes d'interface dans les poutres en beton arme renforcees par collage des stratifiees composites", Revue de Genie Industriel, 8, 3-12.
  51. Jadooe, A., Al-Mahaidi, R. and Abdouka, K. (2018), "Performance of heat-damaged partially-insulated RC beams strengthened with NSM CFRP strips and epoxy adhesive", Constr. Build. Mater., 159, 617-634. https://doi.org/10.1016/j.conbuildmat.2017.11.020. https://doi.org/10.1016/j.conbuildmat.2017.11.020
  52. Kaci, A., Houari, M.S.A., Bousahla, A.A., Tounsi, A. and Mahmoud, S.R. (2018), "Post-buckling analysis of sheardeformable composite beams using a novel simple twounknown beam theory", Struct. Eng. Mech., 65(5), 621-631. https://doi.org/10.12989/sem.2018.65.5.621. https://doi.org/10.12989/SEM.2018.65.5.621
  53. Karami, B., Janghorban, M., Shahsavari, D. and Tounsi, A. (2018), "A size-dependent quasi-3D model for wave dispersion analysis of FG nanoplates", Steel Compos. Struct., 28(1), 99-110. https://doi.org/10.12989/scs.2018.28.1.099. https://doi.org/10.12989/SCS.2018.28.1.099
  54. Khelifa, Z., Hadji, L., Daouadji, T.H. and Bourada, M. (2018), "Buckling response with stretching effect of carbon nanotubereinforced composite beams resting on elastic foundation", Struct. Eng. Mech., 67(2), 125-130. https://doi.org/10.12989/sem.2018.67.2.125. https://doi.org/10.12989/SEM.2018.67.2.125
  55. Khetir, H., Bouiadjra, M.B., Houari, M.S.A., Tounsi, A. and Mahmoud, S.R. (2017), "A new nonlocal trigonometric shear deformation theory for thermal buckling analys", Struct. Eng. Mech., 64(4), 391-402. https://doi.org/10.12989/sem.2017.64.4.391. https://doi.org/10.12989/SEM.2017.64.4.391
  56. Mahi, B.E., Benrahou, K.H., Belakhdar, K., Tounsi, A. and Bedia, E.A. (2014), "effect of the tapered of the end of a FRP plate on the interfacial stresses in a strengthened beam used in civil engineering applications", Mech. Compos. Mater., 50(4), 465-474. https://doi.org/10.1007/s11029-014-9433-z.
  57. Menasria, A., Bouhadra, A., Tounsi, A., Bousahla, A.A. and Mahmoud, S.R. (2017), "A new and simple HSDT for thermal stability analysis of FG sandwich plates", Steel Compos. Struct., 25(2), 157-175. https://doi.org/10.12989/scs.2017.25.2.157. https://doi.org/10.12989/SCS.2017.25.2.157
  58. Mohamed, B., Hassaine Daouadji, T., Abbes, B., Li, Y.M. and Abbes, F. (2018), "Analytical and numerical results for free vibration of laminated composites plates", World Acad. Sci., Eng. Technol. Int. J. Chem. Molec. Eng., 12(6), 300-304.
  59. Mokhtar, Y., Heireche, H., Bousahla, A.A., Houari, M.S.A., Tounsi, A. and Mahmoud, S.R. (2018), "A novel shear deformation theory for buckling analysis of single layer graphene sheet based on nonlocal elasticity theory", Smart Struct. Syst., 21(4), 397-405. https://doi.org/10.12989/sss.2018.21.4.397. https://doi.org/10.12989/SSS.2018.21.4.397
  60. Mouffoki, A., Bedia, E.A., Houari, M.S.A., Tounsi, A. and Mahmoud, S.R. (2017), "Vibration analysis of nonlocal advanced nanobeams in hygro-thermal environment using a new two-unknown trigonometric shear deformation beam theory", Smart Struct. Syst., 20(3), 369-383. https://doi.org/10.12989/sss.2017.20.3.369. https://doi.org/10.12989/SSS.2017.20.3.369
  61. Mustapha, M., Samir, B., Abdelouahed, T., Bedia, E.A.A. and Slimane, M. (2010), "Interfacial stresses in plated beams with exponentially-varying properties", J. Adhes. Sci. Technol., 24, 1063-1081. https://doi.org/10.1163/016942409X12584625925024. https://doi.org/10.1163/016942409X12584625925024
  62. 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. https://doi.org/10.1177/0731684415613633
  63. Rabahi, A., Hassaine Daouadji, T., Benferhat, R. and Adim, B. (2018), "Elastic analysis of interfacial stress concentrations in CFRP-RC hybrid beams: Effect of creep and shrinkage", Adv. Mater. Res., 6(3), 257-278. https://doi.org/10.12989/amr.2017.6.3.257. https://doi.org/10.12989/AMR.2017.6.3.257
  64. Reddy, J.N. (2000), "Analysis of functionally graded plates", Int. J. Numer. Meth. Eng., 47(1-3), 663-684. https://doi.org/10.1002/(SICI)1097-0207. https://doi.org/10.1002/(SICI)1097-0207(20000110/30)47:1/3<663::AID-NME787>3.0.CO;2-8
  65. Roberts, T.M. (1989), "Approximate analysis of shear and normal stress concentrations in the adhesive layer of plated RC beams", Struct. Eng., 67(12), 229-233.
  66. Shen, H.S., Teng, J.G. and Yang, J. (2001), "Interfacial stresses in beams and slabs bonded with thin plate", J. Eng. Mech., ASCE, 127(4), 399-406. https://doi.org/10.1061/(ASCE)0733-9399(2001)127:4(399). https://doi.org/10.1061/(ASCE)0733-9399(2001)127:4(399)
  67. Shen, K., Wan, S., Mo, Y.L. and Jiang, Z. (2018), "Theoretical analysis on full torsional behavior of RC beams strengthened with FRP materials", Compos. Struct., 183, 347-357. https://doi.org/10.1016/j.compstruct.2017.03.084. https://doi.org/10.1016/j.compstruct.2017.03.084
  68. Smith, S.T. and Teng, J.G. (2001), "Interfacial stresses in plated beams", Eng. Struct., 23(7), 857-871. https://doi.org/10.1016/S0141-0296(00)00090-0. https://doi.org/10.1016/S0141-0296(00)00090-0
  69. Tounsi, A. (2006), "Improved theoretical solution for interfacial stresses in concrete beams strengthened with FRP plate", Int. J. Solid. Struct., 43, 4154-74. https://doi.org/10.1016/j.ijsolstr.2005.03.074. https://doi.org/10.1016/j.ijsolstr.2005.03.074
  70. Tounsi, A. and Benyoucef, S. (2007), "Interfacial stresses in externally FRP-plated concrete beams", Int. J. Adhes. Adhesiv., 27, 207-215. https://doi.org/10.1016/j.ijadhadh.2006.01.009. https://doi.org/10.1016/j.ijadhadh.2006.01.009
  71. Tounsi, A., Daouadji, T.H. and Benyoucef, S. (2008), "Interfacial stresses in FRP-plated RC beams: Effect of adherend shear deformations", Int. J. Adhes. Adhesiv., 29(4), 343-351. https://doi.org/10.1016/j.ijadhadh.2008.06.008.
  72. Tounsi, A., Houari, M.S.A. and Benyoucef, S. (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. https://doi.org/10.1016/j.ast.2011.11.009
  73. Wattanasakulpong, N. and Ungbhakorn, V. (2014) "Linear and nonlinear vibration analysis of elastically restrained ends FGM beams with porosities", Aerosp. Sci. Technol., 32(1), 111-120. https://doi.org/10.1016/j.ast.2013.12.002. https://doi.org/10.1016/j.ast.2013.12.002
  74. Wattanasakulpong, N., Prusty, B.G., Kelly, D.W. and Hoffman, M. (2012), "Free vibration analysis of layered functionally graded beams with experimental validation", Mater. Des., 36, 182-190. https://doi.org/10.1016/j.matdes.2011.10.049. https://doi.org/10.1016/j.matdes.2011.10.049
  75. Yang, J. and Wu, Y.F. (2007), "Interfacial stresses of FRP strengthened concrete beams: Effect of shear deformation", Compos. Struct., 80, 343-351. https://doi.org/10.1016/j.compstruct.2006.05.016. https://doi.org/10.1016/j.compstruct.2006.05.016
  76. Yang, J. and Ye, J. (2010), "An improved closed-form solution to interfacial stresses in plated beams using a two-stage approach", Int. J. Mech. Sci., 52, 13-30. https://doi.org/10.1016/j.ijmecsci.2009.09.041. https://doi.org/10.1016/j.ijmecsci.2009.09.041
  77. Yang, J., Chen, J.F. and Teng, J.G. (2009), "Interfacial stress analysis of plated beams under symmetric mechanical and thermal loading", Constr. Build. Mater., 23(9), 2973-2987. https://doi.org/10.1016/j.conbuildmat.2009.05.004. https://doi.org/10.1016/j.conbuildmat.2009.05.004
  78. Yang, J., Ye, J. and Niu, Z. (2007), "Interfacial shear stress in FRP-plated RC beams under symmetric loads", Cement Concrete Compos., 29, 421-432. https://doi.org/10.1016/j.cemconcomp.2006.11.011. https://doi.org/10.1016/j.cemconcomp.2006.11.011
  79. Yang, X., Gao, W.Y., Dai, J.G., Lu, Z.D. and Yu, K.Q. (2018), "Flexural strengthening of RC beams with CFRP gridreinforced ECC matrix", Compos. Struct., 189, 9-26. https://doi.org/10.1016/j.compstruct.2018.01.048. https://doi.org/10.1016/j.compstruct.2018.01.048
  80. Yazid, M., Heireche, H., Tounsi, A., Bousahla, A.A. and Houari, M.S.A. (2018), "A novel nonlocal refined plate theory for stability response of orthotropic single-layer graphene sheet resting on elastic medium", Smart Struct. Syst., 21(1), 15-25. https://doi.org/10.12989/sss.2018.21.1.015. https://doi.org/10.12989/SSS.2018.21.1.015
  81. Youcef, D.O., Kaci, A., Benzair, A., Bousahla, A.A. and Tounsi, A. (2018), "Dynamic analysis of nanoscale beams including surface stress effects", Smart Struct. Syst., 21(1), 65-74. https://doi.org/10.12989/sss.2018.21.1.065. https://doi.org/10.12989/SSS.2018.21.1.065
  82. Younsi, A., Tounsi, A., Zaoui, F.Z., Bousahla, A.A. and Mahmoud, S.R. (2018), "Novel quasi-3D and 2D shear deformation theories for bending and free vibration analysis of FGM plates", Geomech. Eng., 14(6), 519-532. https://doi.org/10.12989/gae.2018.14.6.519. https://doi.org/10.12989/GAE.2018.14.6.519
  83. Yuan, C., Chen, W., Pham, T.M. and Hao, H. (2018), "Bond behavior between basalt fibres reinforced polymer sheets and steel fibres reinforced concrete", Eng. Struct., 176, 812-824. https://doi.org/10.1016/j.engstruct.2018.09.052. https://doi.org/10.1016/j.engstruct.2018.09.052
  84. Yuan, C., Chen, W., Pham, T.M. and Hao, H. (2019), "Effect of aggregate size on bond behaviour between basalt fibre reinforced polymer sheets and concrete", Compos. Part B: Eng., 158(1), 459-474. https://doi.org/10.1016/j.compositesb.2018.09.089. https://doi.org/10.1016/j.compositesb.2018.09.089
  85. Zhu, J., Lai, Z., Yin, Z., Jeon, J. and Lee, S. (2001), "Fabrication of $ZrO_2$-NiCr functionally graded material by powder metallurgy", Mater. Chem. Phys., 68(1-3), 130-135. https://doi.org/10.1016/S0254-0584(00)00355-2. https://doi.org/10.1016/S0254-0584(00)00355-2
  86. Zine, A., Tounsi, A., Draiche, K., Sekkal, M. and Mahmoud, S.R. (2018), "A novel higher-order shear deformation theory for bending and free vibration analysis of isotropic and multilayered plates and shells", Steel Compos. Struct., 26(2), 125-137. https://doi.org/10.12989/scs.2018.26.2.125. https://doi.org/10.12989/SCS.2018.26.2.125