Structural Engineering and Mechanics

  • 제85권1호
  • /
  • Pages.1-14
  • /
  • 2023
  • /
  • 1225-4568(pISSN)
  • /
  • 1598-6217(eISSN)
테크노프레스 (Techno-Press)
권호 표지
DOI QR코드

DOI QR Code

Free vibration of various types of FGP sandwich plates with variation in porosity distribution

  • Aicha, Kablia (Civil Engineering Department, University of Tiaret) ;
  • Rabia, Benferhat (Civil Engineering Department, University of Tiaret) ;
  • Tahar Hassaine, Daouadji (Civil Engineering Department, University of Tiaret) ;
  • Rabahi, Abderezak (Civil Engineering Department, University of Tiaret)
  • 투고 : 2022.05.18
  • 심사 : 2022.11.30
  • 발행 : 2023.01.10
⟨ 이전 논문 다음 논문 ⟩

초록

The use of functionally graded materials in applications involving severe thermal gradients is quickly gaining acceptance in the composite mechanics community, the aerospace and aircraft industry. In the present study, a refined sandwich plate model is applied to study the free vibration analysis of porous functionally graded material (FGM) sandwich plates with various distribution rate of porosity. Two types of common FG sandwich plates are considered. The first sandwich plate is composed of two FG material (FGM) face sheets and a homogeneous ceramic or metal core. The second one consists of two homogeneous fully metal and ceramic face sheets at the top and bottom, respectively, and a FGM core. The displacement field of the present theory is chosen based on nonlinear variations in the in-plane displacements through the thickness of the sandwich plate. 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 sandwich plates is obtained using Hamilton's principle. In order to present the effect of the variation of the porosity distribution on the dynamic behavior of the FGM sandwich plates, new mixtures are proposed which take into account different rate of porosity distribution between the ceramic and the metal. The present method is applicable to study the dynamic behavior of FGM plates and sandwich plates. The frequencies of two kinds of FGM sandwich structures are analyzed and discussed. Several numerical results have been compared with the ones available in the literature.

키워드

과제정보

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.

참고문헌

  1. Abderezak, R., Daouadji, T.H. and Rabia, B. (2021), "Aluminum beam reinforced by externally bonded composite materials", Adv. Mater. Res., 10(1), 23-44. http://doi.org/10.12989/amr.2021.10.1.023.
  2. Abderezak, R., Daouadji, T.H. and Rabia, B. (2021), "Fiber reinforced polymer in civil engineering: Shear lag effect on damaged RC cantilever beams bonded by prestressed plate", Couple. Syst. Mech., 10(4), 299-316. http://doi.org/10.12989/csm.2021.10.4.299.
  3. Abderezak, R., Daouadji, T.H. and Rabia, B. (2021), "Modeling and analysis of the imperfect FGM-damaged RC hybrid beams", Adv. Comput. Des., 6(2), 117-133. http://doi.org/10.12989/acd.2021.6.2.117.
  4. Abderezak, R., Daouadji, T.H. and Rabia, B. (2021), "New solution for damaged porous RC cantilever beams strengthening by composite plate", Adv. Mater. Res., 10(3), 169-194. http://doi.org/10.12989/amr.2021.10.3.169.
  5. Abderezak, R., Daouadji, T.H. and Rabia, B. (2022), "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.
  6. Abderezak, R., Rabia, B. and Daouadji, T.H. (2022), "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.
  7. Ahmed, R.A., Khalaf, B.S., Raheef, K.M., Fenjan, R.M. and Faleh, N.M. (2021), "Investigating dynamic response of nonlocal functionally graded porous piezoelectric plates in thermal environment", Steel Compos. Struct, 40(2), 243-254. https://doi.org/10.12989/scs.2021.40.2.243.
  8. Aicha, K., Rabia, B. and Daouadji, T.H. (20022), "Dynamic of behavior for imperfect FGM plates resting on elastic foundation containing various distribution rates of porosity: Analysis and modeling", Couple. Syst. Mech., 11(5), 389-409. https://doi.org/10.12989/csm.2022.11.5.389.
  9. Aicha, K., Rabia, B., Daouadji, T.H. 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", Couple. Syst. Mech., 9(6), 575-597. http://doi.org/10.12989/csm.2020.9.6.575.
  10. Akbas, S.D. (2021), "Dynamic analysis of axially functionally graded porous beams under a moving load", Steel Compos. Struct., 39(6), 811-821. https://doi.org/10.12989/scs.2021.39.6.811.
  11. Alhaifi, K., Arshid, E. and Khorshidvand, A.R. (2021), "Large deflection analysis of functionally graded saturated porous rectangular plates on nonlinear elastic foundation via GDQM", Steel Compos. Struct., 39(6), 795-809. https://doi.org/10.12989/scs.2021.39.6.795.
  12. Alzahrani, F. and Abbas, I.A. (2021), "A study on thermo-elastic interactions in 2D porous media with-without energy dissipation", Steel Compos. Struct., 38(5), 523-531. https://doi.org/10.12989/scs.2021.38.5.523.
  13. Belbachir, N., Bourada, M., Draiche, K., Tounsi, A., Bourada, F., Bousahla, A.A. and Mahmoud, S.R. (2020), "Thermal flexural analysis of anti-symmetric cross-ply laminated plates using a four variable refined theory", Smart Struct. Syst., 25(4), 409-422. https://doi.org/10.12989/sss.2020.25.4.409.
  14. Benferhat, R., Daouadji, T.H. and Abderezak, R. (2021), "Effect of porosity on fundamental frequencies of FGM sandwich plates", Compos. Mater. Eng., 3(1), 25. http://doi.org/10.12989/cme.2021.3.1.025.
  15. Benferhat, R., Daouadji, T.H., Mansour, M.S. and Hadji, L. (2016), "Effect of porosity on the bending and free vibration response of functionally graded plates resting on WinklerPasternak foundations", Earthq. Struct., 10(6), 1429-1449. https://doi.org/10.12989/eas.2016.10.5.1033.
  16. Bouhadra, A., Menasria, A. and Rachedi, M.A. (2021), "Boundary conditions effect for buckling analysis of porous functionally graded nanobeam", Adv. Nano Res., 10(4), 313-325. https://doi.org/10.12989/anr.2021.10.4.313.
  17. Bourada, F., Bousahla, A.A., Tounsi, A., Bedia, E.A., Mahmoud, S.R., Benrahou, K.H. and Tounsi, A. (2020), "Stability and dynamic analyses of SW-CNT reinforced concrete beam resting on elastic-foundation", Comput. Concrete, 25(6), 485-495. https://doi.org/10.12989/cac.2020.25.6.485.
  18. Chaabane, L.A. (2019), "Analytical study of bending and free vibration responses of functionally graded beams resting on elastic foundation", Struct. Eng. Mech., 71(2), 185-196. https://doi.org/10.12989/sem.2019.71.2.185.
  19. Chen, S., Zhang, Q. and Liu, H. (2022), "Dynamic response of double-FG porous beam system subjected to moving load", Eng. Comput., 38(3), 2309-2328. https://doi.org/10.1007/s00366-021-01376-w.
  20. Chikr, S.C., Kaci, A., Bousahla, A.A., Bourada, F., Tounsi, A., Bedia, E.A., ... & 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.
  21. Daouadji, T.H., Abderezak, R. and Rabia, B. (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.
  22. Dozio, L. (2013), "Natural frequencies of sandwich plates with FGM core via variable-kinematic 2-D Ritz models", Compos. Struct., 96, 561-568. https://doi.org/10.1016/j.compstruct.2012.08.016.
  23. 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.
  24. Gao, T., Zhang, Y., Li, C., Wang, Y., Chen, Y., An, Q., ... & Sharma, S. (2022), "Fiber-reinforced composites in milling and grinding: machining bottlenecks and advanced strategies", Front. Mech. Eng., 17(2), 1-35. https://doi.org/10.1007/s11465-022-0680-8.
  25. Gu, M., Mo, H., Qiu, J., Yuan, J. and Xia, Q. (2022), "Behavior of floating stone columns reinforced with geogrid encasement in model tests", Front. Mater., 9, 980851. https://doi.org/10.3389/fmats.2022.980851.
  26. Hadj, B., Rabia, B. and Daouadji, T.H. (2021), "Vibration analysis of porous FGM plate resting on elastic foundations: Effect of the distribution shape of porosity", Couple. Syst. Mech., 10(1), 61-77. http://doi.org/10.12989/csm.2021.10.1.061.
  27. Hadj, B., Rabia, B. and Daouadji, T.H. (2019), "Influence of the distribution shape of porosity on the bending FGM new plate model resting on elastic foundations", Struct. Eng. Mech., 72(1), 61-70. https://doi.org/10.12989/sem.2019.72.1.061.
  28. Hadji, L. and Avcar, M. (2021), "Nonlocal free vibration analysis of porous FG nanobeams using hyperbolic shear deformation beam theory", Adv. Nano Res., 10(3), 281-293. https://doi.org/10.12989/anr.2021.10.3.281.
  29. 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://doi.org/10.12989/scs.2021.39.6.751.
  30. Hosseini-Hashemi, S., Fadaee, M. and Atashipour, S.R. (2011), "Study on the free vibration of thick functionally graded rectangular plates according to a new exact closed-form procedure", Compos. Struct., 93(2), 722-735. https://doi.org/10.1016/j.compstruct.2010.08.007.
  31. Huang, B., Changhe, L.I., Zhang, Y., Wenfeng, D.I.N.G., Min, Y.A.N.G., Yuying, Y.A.N.G., ... & Zafar, S.A.I.D. (2021), "Advances in fabrication of ceramic corundum abrasives based on sol-gel process", Chin. J. Aeronaut., 34(6), 1-17. https://doi.org/10.1016/j.cja.2020.07.004.
  32. Huang, C.S., Yang, P.J. and Chang, M.J. (2012), "Three-dimensional vibration analyses of functionally graded material rectangular plates with through internal cracks", Compos. Struct., 94(9), 2764-2776. https://doi.org/10.1016/j.compstruct.2012.04.003.
  33. Huang, H., Yao, Y., Liang, C. and Ye, Y. (2022), "Experimental study on cyclic performance of steel-hollow core partially encased composite spliced frame beam", Soil Dyn. Earthq. Eng., 163, 107499. https://doi.org/10.1016/j.soildyn.2022.107499.
  34. Huang, W. and Tahouneh, V. (2021), "Frequency study of porous FGPM beam on two-parameter elastic foundations via Timoshenko theory", Steel Compos. Struct., 40(1), 139-156. https://doi.org/10.12989/scs.2021.40.1.139.
  35. 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.
  36. Keleshteri, M.M. and Jelovica, J. (2022), "Nonlinear vibration analysis of bidirectional porous beams", Eng. Comput., 38(6), 5033-5049. https://doi.org/10.1007/s00366-021-01553-x
  37. Kerr, A.D. (1964) "Elastic and viscoelastic foundation models", ASME J. Appl. Mech., 31(3), 491-498. https://doi.org/10.1115/1.3629667.
  38. Lal, R. and Ahlawat, N. (2015), "Axisymmetric vibrations and buckling analysis of functionally graded circular plates via differential transform method", Eur. J. Mech.-A/Solid., 52, 85-94. https://doi.org/10.1016/j.euromechsol.2015.02.004.
  39. Li, L. and Zhang, D.G. (2016), "Free vibration analysis of rotating functionally graded rectangular plates", Compos. Struct., 136, 493-504. https://doi.org/10.1016/j.compstruct.2015.10.013.
  40. Li, Q., Iu, V.P. and Kou, K.P. (2008), "Three-dimensional vibration analysis of functionally graded material sandwich plates", J. Sound Vib., 311(1-2), 498-515. https://doi.org/10.1016/j.jsv.2007.09.018.
  41. Li, X., Wang, T., Liu, F. and Zhu, Z. (2021), "Computer simulation of the nonlinear static behavior of axially functionally graded microtube with porosity", Adv. Nano Res., 11(4), 437-451. https://doi.org/10.12989/anr.2021.11.4.437.
  42. Li, Y.S., Liu, B.L. and Zhang, J.J. (2021), "Hygro-thermal buckling of porous FG nanobeams considering surface effects", Struct. Eng. Mech., 79(3), 359-371. https://doi.org/10.12989/sem.2021.79.3.359.
  43. Lu, Z.Q., Liu, W.H., Ding, H. and Chen, L.Q. (2022), "Energy Transfer of an axially loaded beam with a parallel-coupled nonlinear vibration isolator", J. Vib. Acoust., 144(5), 051009. https://doi.org/10.1115/1.4054324.
  44. Madenci, E. and Ozkilic, Y.O. (2021), "Free vibration analysis of open-cell FG porous beams: analytical, numerical and ANN approaches", Steel Compos. Struct., 40(2), 157-173. https://doi.org/10.12989/scs.2021.40.2.157.
  45. Mekerbi, M., Benyoucef, S., Mahmoudi, A., Bourada, F. and Tounsi, A. (2019), "Investigation on thermal buckling of porous FG plate resting on elastic foundation via quasi 3D solution", Struct. Eng. Mech., 72(4), 513-524. https://doi.org/10.12989/sem.2019.72.4.513
  46. Mouaici, F., Benyoucef, S., Atmane, H.A. and Tounsi, A. (2016), "Effect of porosity on vibrational characteristics of nonhomogeneous plates using hyperbolic shear deformation theory", Wind Struct., 22(4), 429-454. http://doi.org/10.12989/was.2016.22.4.429.
  47. Natarajan, S. and Manickam, G. (2012), "Bending and vibration of functionally graded material sandwich plates using an accurate theory", Finite Elem. Anal. Des., 57, 32-42. https://doi.org/10.1016/j.finel.2012.03.006.
  48. Nebab, M., Atmane, H.A., Bennai, R., Tounsi, A. and Bedia, E.A. (2019), "Vibration response and wave propagation in FG plates resting on elastic foundations using HSDT", Struct. Eng. Mech., 69(5), 511-525. http://doi.org/10.12989/sem.2019.69.5.511.
  49. Pandey, S. and Pradyumna, S. (2015), "Free vibration of functionally graded sandwich plates in thermal environment using a layerwise theory", Eur. J. Mech.-A/Solid., 51, 55-66. https://doi.org/10.1016/j.euromechsol.2014.12.001.
  50. Parandvar, H. and Farid, M. (2015), "Nonlinear reduced order modeling of functionally graded plates subjected to random load in thermal environment", Compos. Struct., 126, 174-183. https://doi.org/10.1016/j.compstruct.2015.02.006.
  51. Praveen, G.N. and Reddy, J.N. (1998), "Nonlinear transient thermoelastic analysis of functionally graded ceramic-metal plates", Int. J. Solid. Struct., 35(33), 4457-4476. https://doi.org/10.1016/S0020-7683(97)00253-9.
  52. Priyanka, R., Twinkle, C.M. and Pitchaimani, J. (2022), "Stability and dynamic behavior of porous FGM beam: Influence of graded porosity, graphene platelets, and axially varying loads", Eng. Comput., 38(5), 4347-4366. https://doi.org/10.1007/s00366-021-01478-5.
  53. Rabia, B., Tahar, H.D. and Abderezak, R. (2020), "Thermomechanical behavior of porous FG plate resting on the WinklerPasternak foundation", Couple. Syst. Mech., 9(6), 499-519. http://doi.org/10.12989/csm.2020.9.6.499
  54. Rahmani, M. and Mohammadi, Y. (2021), "Vibration of two types of porous FG sandwich conical shell with different boundary conditions", Struct. Eng. Mech., 79(4), 401-413. https://doi.org/10.12989/sem.2021.79.4.401.
  55. Rahmani, M.C., Kaci, A., Bousahla, A.A., Bourada, F., Tounsi, A., Bedia, E.A., ... & Tounsi, A. (2019), "Influence of boundary conditions on the bending and free vibration behavior of FGM sandwich plates using a four-unknown refined integral plate theory", Comput. Concrete, 27(2), 225-244. https://doi.org/10.12989/cac.2020.25.3.225.
  56. Ramady, A., Atia, H.A. and Mahmoud, S.R. (2021), "An analytical solution for equations and the dynamical behavior of the orthotropic elastic material", Adv. Concrete Constr., 11(4), 315-321. https://doi.org/10.12989/acc.2021.11.4.315.
  57. Safari, M., Mohammadimehr, M. and Ashrafi, H. (2021), "Free vibration of electro-magneto-thermo sandwich Timoshenko beam made of porous core and GPLRC", Adv. Nano Res., 10(2), 115-128. https://doi.org/10.12989/anr.2021.10.2.115.
  58. Salari, E. and Sadough Vanini, S.A. (2022), "Small/large amplitude vibration, snap-through and nonlinear thermomechanical instability of temperature-dependent FG porous circular nanoplates", Eng. Comput., 1-32. https://doi.org/10.1007/s00366-022-01629-2.
  59. Song, J., Wu, D. and Arefi, M. (2022), "Modified couple stress and thickness-stretching included formulation of a sandwich micro shell subjected to electro-magnetic load resting on elastic foundation", Defen. Technol., 18(11), 1935-1944. https://doi.org/10.1016/j.dt.2022.04.015.
  60. Ta, H.D. and Noh, H.C. (2015), "Analytical solution for the dynamic response of functionally graded rectangular plates resting on elastic foundation using a refined plate theory", Appl. Math. Model., 39(20), 6243-6257. https://doi.org/10.1016/j.apm.2015.01.062.
  61. Tahar, H.D., Abderezak, R. and Rabia, B. (2021), "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://doi.org/10.12989/sem.2021.79.5.531.
  62. Tahar, H.D., Abderezak, R. and Rabia, B. (2021), "Hyperstatic steel structure strengthened with prestressed carbon/glass hybrid laminated plate", Couple. Syst. Mech., 10(5), 393-414. https://doi.org/10.12989/csm.2021.10.5.393.
  63. Tahar, H.D., Abderezak, R., Rabia, B. and Tounsi, A. (2021), "Impact of thermal effects in FRP-RC hybrid cantilever beams", Struct. Eng. Mech., 78(5), 573-583. http://doi.org/10.12989/sem.2021.78.5.573.
  64. Tahar, H.D., Abderezak, R., Rabia, B. and Tounsi, A. (2021), "Performance of damaged RC continuous beams strengthened by prestressed laminates plate: Impact of mechanical and thermal properties on interfacial stresses", Couple. Syst. Mech., 10(2), 161-184. http://doi.org/10.12989/csm.2021.10.2.161.
  65. Tang, X., Li, Q., Liu, Q., Xue, Y., Liu, Y., He, X., ... & Tao, B. (2020), "Design and research of power grid equipment supply chain based on blockchain technology", IOP Conf. Ser.: Earth Environ. Sci., 446(4), 042003. https://doi.org/10.1088/1755-1315/446/4/042003.
  66. Taskin, V. and Demirhan, P.A. (2021), "Static analysis of simply supported porous sandwich plates", Struct. Eng. Mech., 77(4), 549-557. https://doi.org/10.12989/sem.2021.77.4.549.
  67. Tayeb, B., Daouadji, T.H., Abderezak, R. and Tounsi, A. (2021), "Structural bonding for civil engineering structures: New model of composite I-steel-concrete beam strengthened with CFRP plate", Steel Compos. Struct., 41(3), 417-435. https://doi.org/10.12989/scs.2021.41.3.417.
  68. Thai, C.H., Zenkour, A.M., Wahab, M.A. and Nguyen-Xuan, H. (2016), "A simple four-unknown shear and normal deformations theory for functionally graded isotropic and sandwich plates based on isogeometric analysis", Compos. Struct., 139, 77-95. https://doi.org/10.1016/j.compstruct.2015.11.066.
  69. 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), 217-229.http://doi.org/10.12989/sem.2021.77.2.217.
  70. 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), 453-463. https://doi.org/10.12989/anr.2022.13.5.453.
  71. Tlidji, Y., Benferhat, R., Trinh, L.C., Tahar, H.D. and Abdelouahed, T. (2021), "New state-space approach to dynamic analysis of porous FG beam under different boundary conditions", Adv. Nano Res., 11(4), 347-359. https://doi.org/10.12989/.2021.11.4.347.
  72. Tounsi, A., Al-Dulaijan, S.U., Al-Osta, M.A., Chikh, A., AlZahrani, M.M., Sharif, A. and Tounsi, A. (2020), "A four variable trigonometric integral plate theory for hygro-thermomechanical 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.
  73. 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. http://doi.org/10.1016/S0022-460X(03)00412-7.
  74. 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.
  75. Wei, D. (2021), "A numerical and computer simulation for dynamic stability analysis of 3-unknown graded porous nanoplates using a Chebyshev-Ritz-Bolotin method", Struct. Eng. Mech., 78(4), 379-386. https://doi.org/10.12989/sem.2021.78.4.379.
  76. Wei, G. and Tahouneh, V. (2021), "Temperature dependent buckling analysis of graded porous plate reinforced with graphene platelets", Steel Compos. Struct., 39(3), 275-290. https://doi.org/10.12989/scs.2021.39.3.275.
  77. Xiang, Y., Wang, C.M. and Kitipornchai, S. (1994), "Exact vibration solution for initially stressed Mindlin plates on Pasternak foundations", Int. J. Mech. Sci., 36(4), 311-316. https://doi.org/10.1016/0020-7403(94)90037-X.
  78. Yang, M., Li, C., Zhang, Y., Jia, D., Li, R., Hou, Y., ... & Wang, J. (2019), "Predictive model for minimum chip thickness and size effect in single diamond grain grinding of zirconia ceramics under different lubricating conditions", Ceram. Int., 45(12), 14908-14920. https://doi.org/10.1016/j.ceramint.2019.04.226.
  79. Zhang, C., Kordestani, H., Masri, S.F., Wang, J. and Sun, L. (2021), "Data-driven system parameter change detection for a chain-like uncertainties embedded structure", Struct. Control Hlth. Monit., 28(11), e2821. https://doi.org/10.1002/stc.2821.
  80. Zhang, D.G. and Zhou, Y.H. (2008), "A theoretical analysis of FGM thin plates based on physical neutral surface", Comput. Mater. Sci., 44(2), 716-720. https://doi.org/10.1016/j.commatsci.2008.05.016.
  81. Zhang, D.G. and Zhou, H.M. (2015), "Mechanical and thermal post-buckling analysis of FGM rectangular plates with various supported boundaries resting on nonlinear elastic foundations", Thin Wall. Struct., 89, 142-151. https://doi.org/10.1016/j.tws.2014.12.021.
  82. Zhang, H., Li, L., Ma, W., Luo, Y., Li, Z. and Kuai, H. (2022), "Effects of welding residual stresses on fatigue reliability assessment of a PC beam bridge with corrugated steel webs under dynamic vehicle loading", Struct., 45, 1561-1572. https://doi.org/10.1016/j.istruc.2022.09.094.
  83. Zhang, J., Li, C., Zhang, Y., Yang, M., Jia, D., Liu, G., ... & Cao, H. (2018), "Experimental assessment of an environmentally friendly grinding process using nanofluid minimum quantity lubrication with cryogenic air", J. Clean. Prod., 193, 236-248. https://doi.org/10.1186/s10033-021-00536-9.
  84. Zohra, A., Benferhat, R., Tahar, H.D. and Tounsi, A. (2021), "Analysis on the buckling of imperfect functionally graded sandwich plates using new modified power-law formulations", Struct. Eng. Mech., 77(6), 797-807. http://doi.org/10.12989/sem.2021.77.6.797.