Steel and Composite Structures

Techno-Press (테크노프레스)
권호 표지
DOI QR코드

DOI QR Code

Analysis of mechanical performance of continuous steel beams with variable section bonded by a prestressed composite plate

  • Tahar Hassaine Daouadji (Laboratory of Geomatics and sustainable development, University of Tiaret) ;
  • Rabahi Abderezak (Laboratory of Geomatics and sustainable development, University of Tiaret) ;
  • Benferhat Rabia (Laboratory of Geomatics and sustainable development, University of Tiaret)
  • Received : 2022.02.19
  • Accepted : 2023.11.17
  • Published : 2024.01.25
⟨ Previous Next ⟩

Abstract

In this paper, a closed-form rigorous solution for interfacial stress in continuous steel beam with variable section strengthened with bonded prestressed FRP plates and subjected to a uniformly distributed load is developed using linear elastic theory and including the variation of fiber volume fractions with a longitudinal orientation of the fibers of the FRP plates. The results show that there exists a high concentration of both shear and normal stress at the ends of the laminate, which might result in premature failure of the strengthening scheme at these locations. The theoretical predictions are compared with other existing solutions. Overall, the predictions of the different solutions agree closely with each other. A parametric study has been conducted to investigate the sensitivity of interface behavior to parameters such as laminate and adhesive stiffness, the thickness of the laminate and the fiber volume fractions where all were found to have a marked effect on the magnitude of maximum shear and normal stress in the composite member. This research gives a numerical precision in relating to the others studies which neglect the effect of prestressed plate and the shear lag impact. The physical and geometric properties of materials are taken into account, and that may play an important role in reducing the interfacial stresses magnitude.

Keywords

Acknowledgement

This research was supported by the Algerian Ministry of Higher Education and Scientific Research (MESRS) as part of the grant for the PRFU research project n° A01L02UN140120200002 and by the University of Tiaret, in Algeria.

References

  1. Abderezak, R., Daouadji, T.H. and Tayeb, B. (2023), "Composite aluminum-slab RC beam bonded by a prestressed hybrid carbon-glass composite material", Struct. Eng. Mech., 85(5), 573. https://doi.org/10.12989/sem.2023.85.5.573.
  2. AbouEl-Hamd, O.R., Sweedan, A.M., El-Ariss, B. and El-Sawy, K.M. (2023), "Experimental and numerical investigation of the behavior of steel beams strengthened by bolted hybrid FRP composites", Buildings, 13(3), 824. https://doi.org/10.3390/buildings13030824.
  3. Abualnour, M., Chikh, A., Hebali, H., Kaci, A., Tounsi, A., Bousahla, A.A. and Tounsi, A. (2019), "Thermomechanical analysis of antisymmetric laminated reinforced composite plates using a new four variable trigonometric refined plate theory", Comput. Concrete, 24(6), 489-498. https://doi.org/10.12989/cac.2019.24.6.489.
  4. Addou, F.Y., Meradjah, M., Bousahla, A.A., Benachour, A., Bourada, F., Tounsi, A. and Mahmoud, S.R. (2019), "Influences of porosity on dynamic response of FG plates resting on Winkler/Pasternak/Kerr foundation using quasi 3D HSDT", Comput. Concrete, 24(4), 347-367. https://doi.org/10.12989/cac.2019.24.4.347.
  5. Aissa, B., Rabia, B. and Tahar, H.D. (2023), "Predicting and analysis of interfacial stress distribution in RC beams strengthened with composite sheet using artificial neural network", Struct. Eng. Mech., 87(6), 517-527. https://doi.org/10.12989/sem.2023.87.6.517.
  6. Amara K., Antar, K. and Benyoucef, S. (2019), "Hygrothermal effects on the behavior of reinforced-concrete beams strengthened by bonded composite laminate plates", Struct. Eng. Mech., 69(3), 327-334. https://doi.org/10.12989/sem.2019.69.3.327.
  7. Ameur M., Tounsi A., Benyoucef S., Bouiadjra B.B. and Adda, B. (2008), "Stress analysis of steel beams strengthened with a bonded hygrothermal aged composite plate", Int. J. Mech. Mater. Des., 5(2), 143-156. https://doi.org/10.1007/s10999-008-9090-2.
  8. Benachour, A., Benyoucef, S., Tounsi, A. and Adda bedia, E.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.
  9. 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, 491-500. https://doi.org/10.1007/s11029-014-9435-x.
  10. Boussoula, A., Boucham, B., Bourada, M., Bourada, F., Tounsi, A., Bousahla, A.A. and Tounsi, A. (2020), "A simple nth-order shear deformation theory for thermomechanical bending analysis of different configurations of FG sandwich plates", Smart Struct. Syst., 25(2), 197-218. https://doi.org/10.12989/sss.2020.25.2.197.
  11. Bouzid, H., Rabia, B. and Daouadji, T.H. (2022), "Curvature ductility of confined HSC columns", In International Conference on Innovative Solutions in Hydropower Engineering and Civil Engineering, pp. 253-262. https://doi.org/10.1007/978-981-99-1748-8_21.
  12. Bouzid, H., Rabia, B. and Daouadji, T.H. (2023), "Ultimate behavior of RC beams strengthened in flexure using FRP material", Eng. Struct., 289, 116300. https://doi.org/10.1016/j.engstruct.2023.116300.
  13. 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. https://doi.org/10.12989/amr.2019.8.3.197.
  14. Chikr, S.C., Kaci, A., Bousahla, A.A., Bourada, F., Tounsi, A., Bedia, E.A. and Tounsi, A. (2020), « A novel four-unknown integral model for buckling response of FG sandwich plates resting on elastic foundations under various boundary conditions using Galerkin's approach", Geomech. Eng., 21(5), 471-487. https://doi.org/10.12989/gae.2020.21.5.471.
  15. David, H., Rodrigo, G., Carlos, S. and Dinar, C. (2020) "GBTbased time-dependent analysis of steel-concrete composite beams including shear lag and concrete cracking effects" , Thin-Wall. Struct., 150(May, 2020), 106706. https://doi.org/10.1016/j.tws.2020.106706.
  16. 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. https://doi.org/10.12989/cac.2019.24.4.369.
  17. 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 fiberreinforced polymer", Construct. Build. Mater., 249, 118745. https://doi.org/10.1016/j.conbuildmat.2020.118745.
  18. 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.
  19. 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.
  20. Hassaine Daouadji, T., Rabahi, A. and Benferhat, R. (2020), "Flexural performance of wooden beams strengthened by composite plate", Struct. Monit. Maint., 7(3), 233-259. http://dx.doi.org/10.12989/smm.2020.7.3.233.
  21. Hassaine Daouadji, T., Rabahi, A. and Benferhat, R. (2021a), "Hyperstatic steel structure strengthened with prestressed carbon/glass hybrid laminated plate", Coup. Syst. Mech., 10(5), 393-414. https://doi.org/10.12989/csm.2021.10.5.393.
  22. Hassaine Daouadji, T., Rabahi, A. and Benferhat, R. (2021d), "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", Struct. Eng. Mech., 79(5), 531-540. http://dx.doi.org/10.12989/sem.2021.79.5.531.
  23. Hassaine Daouadji, T., Rabahi, A. and Benferhat, R. (2022), "New technique for repairing circular steel beams by FRP plate", Adv. Mater. Res., 11(3), 171-190. https://doi.org/10.12989/amr.2022.11.3.171.
  24. Hassaine Daouadji, T., Rabahi, A., Benferhat, R. and Adim, B. (2019), "Flexural behaviour of steel beams reinforced by carbon fibre reinforced polymer: Experimental and numerical study", Struct. Eng. Mech., 72(4) 409-419. https://doi.org/10.12989/sem.2019.72.4.409.
  25. Hassaine Daouadji, T., Rabahi, A., Benferhat, R. and Tounsi, A. (2021b), "Performance of damaged RC continuous beams strengthened by prestressed laminates plate: Impact of mechanical and thermal properties on interfacial stresses", Coup. Syst. Mech., 10(2), 161-184. http://dx.doi.org/10.12989/csm.2021.10.2.161.
  26. Hassaine Daouadji, T., Rabahi, A., Benferhat, R. and Tounsi, A. (2021c), "Impact of thermal effects in FRP-RC hybrid cantilever beams", Struct. Eng. Mech., 78(5), 573-583. http://dx.doi.org/10.12989/sem.2021.78.5.573.
  27. He, X.J., Zhou, C.Y. and Wang, Y. (2020), "Interfacial stresses in reinforced concrete cantilever members strengthened with fibrereinforced polymer laminates", Adv. Struct. Eng., 23(2), 277-288. https://doi.org/10.1177/1369433219868933.
  28. Henni, M.A.B., Abbes, B., Daouadji, T.H., Abbes, F. and Adim, B. (2021), "Numerical modeling of hygrothermal effect on the dynamic behavior of hybrid composite plates", Steel Compos. Struct., 39(6), 751-763. http://dx.doi.org/10.12989/scs.2021.39.6.751.
  29. Huang, Z., Huang, X., Li, W., Chen, C., Li, Y., Lin, Z. and Liao, W.I. (2021), "Bond-slip behaviour of H-shaped steel embedded in UHPFRC", Steel Compos. Struct., 38(5), 563-582. https://doi.org/10.12989/scs.2021.38.5.563.
  30. 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", Coup. Syst. Mech., 9(6), 575-597. http://dx.doi.org/10.12989/csm.2020.9.6.575.
  31. Kablia, A., Benferhat, R., Daouadji, T.H. and Abderezak, R. (2023), "Free vibration of various types of FGP sandwich plates with variation in porosity distribution", Struct. Eng. Mech., 85(1), 1-14. https://doi.org/10.12989/sem.2023.85.1.001.
  32. Kablia, A., Rabia, B. and Hassaine Daouadji, T. (20022), "Dynamic of behavior for imperfect FGM plates resting on elastic foundation containing various distribution rates of porosity: Analysis and modeling", Coup. Syst. Mech., 11(5), 389-409. https://doi.org/10.12989/csm.2022.11.5.389.
  33. Kaddari, M., Kaci, A., Bousahla, A.A., Tounsi, A., Bourada, F., Bedia, E.A. and Al-Osta, M.A. (2020), "A study on the structural behaviour of functionally graded porous plates on elastic foundation using a new quasi-3D model: bending and free vibration analysis", Comput. Concrete, 25(1), 37-57. https://doi.org/10.12989/cac.2020.25.1.037.
  34. Krour, B., Bernard, F. and Tounsi, A. (2013), "Fibers orientation optimization for concrete beam strengthened with a CFRP bonded plate: A coupled analytical-numerical investigation", Eng. Struct., 56, 218-227. https://doi.org/10.1016/j.engstruct.2013.05.008.
  35. Liang, C., Liu, Y., Zhao, C., Lei, B. and Wu, J. (2021), "An investigation on the bearing capacity of steel girder-concrete abutment joints", Steel Compos. Struct., 38(3), 319-336. https://doi.org/10.12989/scs.2021.38.3.319.
  36. Liu, S., Yinzhi, Z., Qing Zheng, J.Z., Fengnian, J. and Hualin, F. (2019), "Blast responses of concrete beams reinforced with steel-GFRP composite bars", Structures, 200-212. https://doi.org/10.1016/j.istruc.2019.08.010.
  37. Liu, Y., Li, H.N., Li, C. and Dong, T.Z. (2021), "Lifetime seismic performance assessment of high-rise steel-concrete composite frame with buckling-restrained braces under wind-induced fatigue", Struct. Eng. Mech., 77(2), 197-215. https://doi.org/10.12989/sem.2021.77.2.197.
  38. Lou, T., Wu, S., Karavasilis, T.L. and Chen, B. (2021), "Long-term deflection prediction in steel-concrete composite beams", Steel Compos. Struct., 39(1), 21-33. https://doi.org/10.12989/scs.2021.39.1.021.
  39. Lyu, J., Zhou, S., Chen, Q. and Wang, Y. (2021), "The bearing capacity of monolithic composite beams with laminated slab throughout fire process", Steel Compos. Struct., 38(1), 87-102. https://doi.org/10.12989/scs.2021.38.1.087.
  40. Minos, K., Elias, B. and Nicholas, T. (2020), "Experimental and numerical study of CFRP reinforced steel beams", Proceedings of Mechanical Engineers Part M Journal of Engineering for the Maritime Environment, October 2020. https://doi.org/10.1177/1475090220960266.
  41. Mirambell, E., Bonilla, J., Bezerra, L.M. and Clero, B. (2021), "Numerical study on the deflections of steel-concrete composite beams with partial interaction", Steel Compos. Struct., 38(1), 67-78. https://doi.org/10.12989/scs.2021.38.1.067.
  42. Panjehpour, M., Ali, A.A.A., Voo, Y.L. and Aznieta, F.N. (2014), "Effective compressive strength of strut in CFRP-strengthened reinforced concrete deep beams following ACI 318-11", Comput. Concrete, 13(1), 135-165. https://doi.org/10.12989/cac.2014.13.1.135.
  43. Panjehpour, M., Farzadnia, N., Demirboga, R. and Ali, A.A.A. (2016), "Behavior of high-strength concrete cylinders repaired with CFRP sheets", J. Civil Eng. Manage, 22(1), 56-64. https://doi.org/10.3846/13923730.2014.897965.
  44. Parhi, A., Singh, B.N. and Panda, S.K. (2021), "Nonlinear free vibration analysis of composite conical shell panel with cluster of delamination in hygrothermal environment", Eng. Comput., 37, 1565-1577 (2021). https://doi.org/10.1007/s00366-019-00903-0.
  45. Pello, L., Leire, G., Ignacio, P. and Jose-Tomas, S.J. (2020), "Flexural strengthening of low-grade reinforced concrete beams with compatible composite material: Steel Reinforced Grout (SRG)", Construct. Build. Mater., 235, 117790. https://doi.org/10.1016/j.conbuildmat.2019.117790.
  46. Pierluigi, C. and Carlo, P. (2006), "An experimental, analytical and numerical study of the static behavior of steel beams reinforced by pultruded CFRP strips", Compos. Part B: Eng., 37(1), 64-73. https://doi.org/10.1016/j.compositesb.2005.03.002.
  47. Rabahi, A., Benferhat, R. and Hassaine Daouadji, Y. (2019), "Elastic analysis of interfacial stresses in prestressed PFGM-RC hybrid beams", Adv. Mater. Res., 7(2) 83-103. https://doi.org/10.12989/amr.2018.7.2.083.
  48. Rabahi, A., Benferhat, R. and Tahar Hassaine, D. (2022a), "Rehabilitation of RC structural elements: Application for continuous beams bonded by composite plate under a prestressing force", Adv. Mater. Res., 11(2), 91-109. https://doi.org/10.12989/amr.2022.11.2.091.
  49. Rabahi, A., Hassaine Daouadji, T. and Benferhat R. (2021d), "New solution for damaged porous RC cantilever beamsstrengthening by composite plate", Adv. Mater. Res., 10(3), 169-194. http://dx.doi.org/10.12989/amr.2021.10.3.169.
  50. Rabahi, A., Hassaine Daouadji, T. and Benferhat, R. (2020), "Analysis of interfacial stresses of the reinforced concrete foundation beams repairing with composite materials plate", Coup. Syst. Mech., 9(5), 473-498. http://dx.doi.org/10.12989/csm.2020.9.5.473.
  51. Rabahi, A., Hassaine Daouadji, T. and Benferhat, R. (2021a), "Modeling and analysis of the imperfect FGM-damaged RC hybrid beams", Adv. Comput. Des., 6(2) 117-133. http://dx.doi.org/10.12989/acd.2021.6.2.117.
  52. Rabahi, A., Hassaine Daouadji, T. and Benferhat, R. (2021b), "Aluminum beam reinforced by externally bonded composite materials", Adv. Mater. Res., 10(1), 23-44. http://dx.doi.org/10.12989/amr.2021.10.1.023.
  53. Rabahi, A., Hassaine Daouadji, T. and Benferhat, R. (2021c), "Fiber reinforced polymer in civil engineering: Shear lag effect on damaged RC cantilever beams bonded by prestressed plate", Coup. Syst. Mech., 10(4), 299-316. http://dx.doi.org/10.12989/csm.2021.10.4.299.
  54. Rabahi, A., Tahar Hassaine, D. and Benferhat, R. (2022b), "Analysis and modeling of hyperstatic RC beam bonded by composite plate symmetrically loaded and supported", Steel Compos. Struct., 45(4) 591-603. https://doi.org/10.12989/scs.2022.45.4.591.
  55. Rabia, B., Abderezak, R., Daouadji, T.H., Abbes, B., Belkacem, A. 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. https://doi.org/10.12989/amr.2018.7.1.029.
  56. 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. https://doi.org/10.12989/eas.2019.16.5.601.
  57. Rabia, B., Daouadji, T.H. and Abderezak, R. (2021), "Analysis and sizing of RC beams reinforced by external bonding of imperfect functionally graded plate", Adv. Mater. Res., 10, 77-98. http://dx.doi.org/10.12989/amr.2021.10.2.077.
  58. Rabia, B., Daouadji, T.H. and Abderezak, R. (2021), "Effect of air bubbles in concrete on the mechanical behavior of RC beams strengthened in flexion by externally bonded FRP plates under uniformly distributed loading", 3(1), 41. http://dx.doi.org/10.12989/cme.2021.3.1.041.
  59. Rabia, B., Daouadji, T.H. and Abderezak, R. (2023), "Mechanical behavior of RC beams bonded with thin porous FGM plates: Case of fiber concretes based on local materials from the mountains of the Tiaret highlands", Coup. Syst. Mech., 12(3), 241-260. https://doi.org/10.12989/csm.2023.12.3.241.
  60. Rabia, B., Hassaine Daouadji, T. and Mohamed Said, M. (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.
  61. Rabia, B., Hassaine Daouadji, T. and Rabahi, A. (2019), "Effect of porosity in interfacial stress analysis of perfect FGM beams reinforced with a porous functionally graded materials plate", Struct. Eng. Mech., 72(3), 293-304. https://doi.org/10.12989/sem.2019.72.3.293.
  62. Rabia, B., Hassaine Daouadji, T. and Rabahi, A. (2020), "Predictions of the maximum plate end stresses of imperfect FRP strengthened RC beams: study and analysis", Adv. Mater. Res., 9(4), 265-287. http://dx.doi.org/10.12989/amr.2020.9.4.265.
  63. Sabouri-Ghomi, S., Nasri, A., Jahani, Y. and Bhowmick, A.K. (2021), "Improved analytical formulation for Steel-Concrete (SC) composite walls under out-of-plane loads", Steel Compos. Struct., 38(4), 463-476. https://doi.org/10.12989/scs.2021.38.4.463.
  64. Shaheen, Y.B., Refat, H.M. and Mahmoud, A.M. (2021), "Structural behavior of concrete walls reinforced with ferrocement laminates", Struct. Eng. Mech., 78(4), 455-471. https://doi.org/10.12989/sem.2021.78.4.455.
  65. Sharma, N., Lalepalli, A.K., Hirwani, C.K., Das, A., Panda, S.K., Topal, U. and Dede, T. (2021), "Optimal deflection and stacking sequence prediction of curved composite structure using hybrid (FEM and soft computing) technique", Eng. Comput., 37, 477-487. https://doi.org/10.1007/s00366-019-00836-8.
  66. Siwowski, T.W. and Siwowska, P. (2018), "Experimental study on CFRP-strengthened steel beams", Compos. Part B: Eng., 149, 12-21. https://doi.org/10.1016/j.compositesb.2018.04.060.
  67. Smith, S.T. and Teng, J.G. (2002), "Interfacial stresses in plated beams", Eng. Struct., 23(7), 857-871. http://dx.doi.org/10.1016/S0141-0296(00)00090-0.
  68. Sun, K.Q., Zhang, N., Liu, X. and Tao, Y.X. (2021), "An equivalent single-layer theory for free vibration analysis of steelconcrete composite beams", Steel Compos. Struct., 38(3), 281-291. https://doi.org/10.12989/scs.2021.38.3.281.
  69. Tlidji, Y., Benferhat, R., Daouadji, T.H., Tounsi, A. and Trinh, L.C. (2022), "Free vibration analysis of FGP nanobeams with classical and non-classical boundary conditions using Statespace approach", Adv. Nano Res., 13(5), 453. https://doi.org/10.12989/anr.2022.13.5.453.
  70. Tlidji, Y., Benferhat, R., Draiche, K. and Tahar, H.D. (2023), "Assessing the effects of porosity on the buckling of functionally graded beams", In Functionally Graded Structures: Modelling and computation of static and dynamical problems, Bristol, UK: IOP Publishing. https://doi.org/10.1088/978-0-7503-5301-4ch6.
  71. Tounsi, A. (2006), "Improved theoretical solution for interfacial stresses in concrete beams strengthened with FRP plate", Int. J. Struct., 43(14-15), 4154-4174. https://doi.org/10.1016/j.ijsolstr.2005.03.074.
  72. 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 twoparameter elastic foundation", Steel Compos. Struct., 34(4), 511-524. https://doi.org/10.12989/scs.2020.34.4.511.
  73. Tounsi, A., Hassaine Daouadji, T., Benyoucef, S. and Adda bedia, E.A. (2008), "Interfacial stresses in FRP-plated RC beams: Effect of adherend shear deformations", Int. J. Adhesion Adhesives, 29, 313-351. https://doi.org/10.1016/j.ijadhadh.2008.06.008.
  74. Wang, Y.H., Yu, J., Liu, J.P., Zhou, B.X. and Chen, Y.F. (2020), "Experimental study on assembled monolithic steel-prestressed concrete composite beam in negative moment", J. Construct. Steel Res., 167, 105667. https://doi.org/10.1016/j.jcsr.2019.06.004
  75. Zarga, D. (2019), "Thermomechanical bending study for functionally graded sandwich plates using a simple quasi-3D shear deformation theory", Steel Compos. Struct., 32(3), 389-410. https://doi.org/10.12989/scs.2019.32.3.389.
  76. Zhang, F., Wu, M., Hou, X., Cheng, H., Xinhe, W. and Xiayu, X. (2022), "Post-buckling reliability analysis of stiffened composite panels based on adaptive iterative sampling", Eng. Comput., 38 (Suppl 4), 2651-2661. https://doi.org/10.1007/s00366-021-01424-5.
  77. Zhang, T., Gong, Y.Z., Ding, F.X., Liu, X.M. and Yu, Z.W. (2021), "Experimental and numerical investigation on the behavior of concrete-filled rectangular steel tubes under bending", Struct. Eng. Mech., 78(3), 231-253. https://doi.org/10.12989/sem.2021.78.3.231.
  78. Zohra, A., Rabia, B. and Tahar, H.D. (2023), "Critical thermal buckling analysis of porous FGP sandwich plates under various boundary conditions", Struct. Eng. Mech., 87(1), 29-46. https://doi.org/10.12989/sem.2023.87.1.029.