Analytical solution for hygro-thermo-elastic dynamic performance of Quasi-3D logarithmic shear-deformable lightweight plate positioned between GPL-reinforced skins

1. Al-Furjan, M.S., Safarpour, H., Habibi, M., Safarpour, M., Tounsi, A.: A comprehensive computational approach for nonlinear thermal instability of the electrically FG-GPLRC disk based on GDQ method. Eng. Computers. 38(1), 801–818 (2022)10.1007/s00366-020-01088-7 ↗

2. Arshid, E.: Computational analysis of thermal buckling in doubly-curved shells reinforced with origami-inspired auxetic graphene metamaterials. Comput. Model. Eng. Sci. 0, 1–10 (2025a). https://doi.org/10.32604/CMES.2025.07489810.32604/CMES.2025.074898 ↗

3. Arshid, E.: Thermomechanical stability of hyperbolic shells incorporating graphene origami auxetic metamaterials on elastic foundation: applications in lightweight structures. J. Compos. Sci. 9, 594 (2025b). https://doi.org/10.3390/jcs911059410.3390/jcs9110594 ↗

4. Arshid, E., Civalek, Ö.: Analytical vibration analysis of thermally loaded doubly curved shells reinforced with graphene origami metamaterials on Kerr foundation. Compos. Strut. 7, 119847 (2025)

5. Arshid, E., Khoddami, M.Z.: Dynamic analysis of prismatic auxetic trigonometric rotating blades integrated by GNPs-reinforced layers. Mech. Based Desi. Struct. Mach. 3, 1–28 (2025)

6. Arshid, E., Amir, S., Dadoo, I., Civalek, Ö.: Thermo-dependent dynamic analysis of imperfect shear-deformable nanocomposite conical micro shells. Arch. Civ. Mech. Eng. 25, 1–27 (2025a). https://doi.org/10.1007/S43452-025-01328-X10.1007/S43452-025-01328-X ↗

7. Arshid, E., Maraghi, Z.K., Civalek, Ö.: Variable-thickness higher-order sandwich beams with FG cellular core and CNT-RC patches: vibrational analysis in thermal environment. Arch. Appl. Mech. 95(2), 2 (2025b). https://doi.org/10.1007/s00419-024-02716-010.1007/s00419-024-02716-0 ↗

8. Atmane, V.P.H.A.: An n-order refined plate theory for bending and buckling of functionally graded polymer composite plates reinforced with graphene nanoplatelets. Adv. Nano Res. 19, 41–51 (2025). https://doi.org/10.12989/ANR.2025.19.1.04110.12989/ANR.2025.19.1.041 ↗

9. Babaei, M., Kiarasi, F., Asemi, K., Dimitri, R., Tornabene, F.: Transient thermal stresses in FG porous rotating truncated cones reinforced by Graphene platelets. Appl. Sci. 12, 3932 (2022). https://doi.org/10.3390/app1208393210.3390/app12083932 ↗

10. Babaei, H., Zavari, S., Kaveh, A., Arshid, E., Civalek, O.: Dynamic response of advanced lightweight porous plates integrated with nanocomposite face sheets resting on elastic substrate. Int. J. Struct. Stab. Dyn. (2024). https://doi.org/10.1142/S021945542550132910.1142/S0219455425501329 ↗

11. Boukhlif, Z., Bouremana, M., Bourada, F., Bousahla, A.A., Bourada, M., Tounsi, A., Al-Osta, M.A.: A simple quasi-3D HSDT for the dynamics analysis of FG thick plate on elastic foundation. Steel Compos. Struct. 31, 503–516 (2019). https://doi.org/10.12989/scs.2019.31.5.50310.12989/scs.2019.31.5.503 ↗

12. Dadoo, I., Amir, S., Arshid, E.: Free vibration analysis of porous variable-thickness rotating annular plates with randomly distributed agglomerated CNT-RC facesheets. Acta Mech. 2025, 1–32 (2025). https://doi.org/10.1007/S00707-025-04473-910.1007/S00707-025-04473-9 ↗

13. Daikh, A.A.: Thermal buckling analysis of functionally graded sandwich cylindrical shells. Adv. Aircr. Spacecr. Sci. 7, 351 (2020). https://doi.org/10.12989/AAS.2020.7.4.33510.12989/AAS.2020.7.4.335 ↗

14. Djebbour, K.D., Atmane, H.A., Nebab, M., Bennai, R., Hadji, L., Dahmane, M.: Effect of porosity distribution on free vibration of functionally graded plates: an accurate application of HSDT theory. Stud. Eng. Exact Sci. 5, e6915 (2024). https://doi.org/10.54021/seesv5n2-11410.54021/seesv5n2-114 ↗

15. Fazzolari, F.A.: Generalized exponential, polynomial and trigonometric theories for vibration and stability analysis of porous FG sandwich beams resting on elastic foundations. Compos. Part B Eng. 136, 254–271 (2018). https://doi.org/10.1016/J.COMPOSITESB.2017.10.02210.1016/J.COMPOSITESB.2017.10.022 ↗

16. Ferdowsi, S.B., Doranga, S., Li, Y.: Comparison of the reliability of SAC305 and Innolot-based solder alloy in a board-level BGA package considering harmonic and random vibration environment. Electronics 14(2), 292 (2025). https://doi.org/10.3390/ELECTRONICS1402029210.3390/ELECTRONICS14020292 ↗

17. Fu, T., Hu, X., Yang, C.: Impact response analysis of stiffened sandwich functionally graded porous materials doubly-curved shell with re-entrant honeycomb auxetic core. Appl. Math. Model. 124, 553–575 (2023). https://doi.org/10.1016/j.apm.2023.08.02410.1016/j.apm.2023.08.024 ↗

18. Gao, K., Gao, W., Wu, B., Wu, D., Song, C.: Nonlinear primary resonance of functionally graded porous cylindrical shells using the method of multiple scales. Thin-Walled Struct. 125, 281–293 (2018). https://doi.org/10.1016/j.tws.2017.12.03910.1016/j.tws.2017.12.039 ↗

19. Hadji, M., Bouhadra, A., Mamen, B., Menasria, A., Bousahla, A.A., Bourada, F., Bourada, M., LastNameBenrahoul, K.H., Tounsi, A.: Combined influence of porosity and elastic foundation parameters on the bending behavior of advanced sandwich structures. Steel Compos. Struct. 46, 1 (2023). https://doi.org/10.12989/SCS.2023.46.1.00110.12989/SCS.2023.46.1.001 ↗

20. Hadji, L., Plevris, V., Madan, R., Ait Atmane, H.: Multi-directional functionally graded sandwich plates: buckling and free vibration analysis with refined plate models under various boundary conditions. Computation (2024). https://doi.org/10.3390/computation1204006510.3390/computation12040065 ↗

21. Hadji, L., Plevris, V., Madan, R.: Dynamic Behavior of Imperfect FGM Beams with Various Porosity Distribution Rates: Analysis and Modeling. Lect. Notes Civ. Eng. 237, 1515–1527 (2025). https://doi.org/10.1007/978-3-031-69626-8_12610.1007/978-3-031-69626-8_126 ↗

22. Han, S.-C., Park, W.-T., Jung, W.-Y.: 3D graphical dynamic responses of FGM plates on Pasternak elastic foundation based on quasi-3D shear and normal deformation theory. Compos. Part B Eng. 95, 324–334 (2016). https://doi.org/10.1016/j.compositesb.2016.04.01810.1016/j.compositesb.2016.04.018 ↗

23. Hasani Baferani, A., Saidi, A.R., Ehteshami, H.: Accurate solution for free vibration analysis of functionally graded thick rectangular plates resting on elastic foundation. Compos. Struct. 93, 1842–1853 (2011). https://doi.org/10.1016/j.compstruct.2011.01.02010.1016/j.compstruct.2011.01.020 ↗

24. Hebali, H., Boulefrakh, L., Chikh, A., Bousahla, A.A., Tounsi, A., Mahmoud, S.R.: The effect of parameters of visco-Pasternak foundation on the bending and vibration properties of a thick FG plate. Geomech. Eng. 18, 161–178 (2019). https://doi.org/10.12989/GAE.2019.18.2.16110.12989/GAE.2019.18.2.161 ↗

25. Heydari, M.M., Nabi, A.H., Heydari, M.: Nonlinear bending behavior of orthotropic Mindlin plate resting on orthotropic Pasternak foundation using GDQM. Nonlinear Dyn. 78, 1645–1657 (2014). https://doi.org/10.1007/s11071-014-1545-410.1007/s11071-014-1545-4 ↗

26. Hou, Y., Choi, K.R., Ghazouani, N., Kaveh, A., Babaei, Z., Kumar, A.: Static package design thorough thickness stretching and thermal environment effects for porous micro-scaled plates with piezoelectric nanocomposite patches. Acta Mech. 235, 1235–1254 (2023). https://doi.org/10.1007/S00707-023-03794-X/METRICS10.1007/S00707-023-03794-X/METRICS ↗

27. Kaddari, M., Kaci, A., Bousahla, A.A., Tounsi, A., Bourada, F., Tounsi, A., Bedia, E.A.A., Al-Osta, M.A.: Computers and Concrete. Comput. Concr. 25, 57 (2020). https://doi.org/10.12989/CAC.2020.25.1.03710.12989/CAC.2020.25.1.037 ↗

28. Karimiasl, M., Ebrahimi, F., Mahesh, V.: Nonlinear forced vibration of smart multiscale sandwich composite doubly curved porous shell. Thin-Walled Struct. 143, 106152 (2019). https://doi.org/10.1016/J.TWS.2019.04.04410.1016/J.TWS.2019.04.044 ↗

29. Khorasani, M., Eyvazian, A., Karbon, M., Tounsi, A., Lampani, L., Sebaey, T.A.: Magneto-electro-elastic vibration analysis of modified couple stress-based three-layered micro rectangular plates exposed to multi-physical fields considering the flexoelectricity effects. Smart Struct. Syst. 26, 331–343 (2020). https://doi.org/10.12989/sss.2020.26.3.33110.12989/sss.2020.26.3.331 ↗

30. Kiani, Y.: Free vibration of functionally graded carbon nanotube reinforced composite plates integrated with piezoelectric layers. Comput. Math. Appl. 72, 2433–2449 (2016). https://doi.org/10.1016/j.camwa.2016.09.00710.1016/j.camwa.2016.09.007 ↗

31. Kiani, Y., Akbarzadeh, A.H., Chen, Z.T., Eslami, M.R.: Static and dynamic analysis of an FGM doubly curved panel resting on the Pasternak-type elastic foundation. Compos. Struct. 94, 2474–2484 (2012). https://doi.org/10.1016/J.COMPSTRUCT.2012.02.02810.1016/J.COMPSTRUCT.2012.02.028 ↗

32. Lakel, A., Hadji, L., Avcar, M., Atmane, H.A., Madan, R.: The natural frequency analysis of FG-GNPR nanoplates under different boundary conditions. Adv. Nano Res. 17, 533–546 (2024). https://doi.org/10.12989/anr.2024.17.6.53310.12989/anr.2024.17.6.533 ↗

33. Ma, R., Jin, Q.: Stability of functionally graded graphene-reinforced composite laminated thick plates in thermal environment. Acta Mech. 233, 3977–3996 (2022). https://doi.org/10.1007/s00707-022-03300-910.1007/s00707-022-03300-9 ↗

34. Mao, J.J., Zhang, W.: Buckling and post-buckling analyses of functionally graded graphene reinforced piezoelectric plate subjected to electric potential and axial forces. Compos. Struct. 216, 392–405 (2019). https://doi.org/10.1016/J.COMPSTRUCT.2019.02.09510.1016/J.COMPSTRUCT.2019.02.095 ↗

35. Mellal, F., Bennai, R., Avcar, M., Nebab, M., Atmane, H.A.: On the vibration and buckling behaviors of porous FG beams resting on variable elastic foundation utilizing higher-order shear deformation theory. Acta Mech. 234, 3955–3977 (2023). https://doi.org/10.1007/s00707-023-03603-510.1007/s00707-023-03603-5 ↗

36. Mirjavadi, S.S., Forsat, M., Barati, M.R., Hamouda, A.M.S.: Post-buckling analysis of geometrically imperfect tapered curved micro-panels made of graphene oxide powder reinforced composite. Steel Compos. Struct. 36, 63–74 (2020). https://doi.org/10.12989/scs.2020.36.1.06310.12989/scs.2020.36.1.063 ↗

37. Mohammadimehr, M., Akhavan Alavi, S.M., Okhravi, S.V., Edjtahed, S.H.: Free vibration analysis of micro-magneto-electro-elastic cylindrical sandwich panel considering functionally graded carbon nanotube–reinforced nanocomposite face sheets, various circuit boundary conditions, and temperature-dependent material properties us. J. Intell. Mater. Syst. Struct. 29, 863–882 (2018). https://doi.org/10.1177/1045389X1772104810.1177/1045389X17721048 ↗

38. Ovesy, H.R., Ghannadpour, S.A.: Large deflection finite strip analysis of functionally graded plates under pressure loads. Int. J. Struct. Stability. Dynamics. 7(02), 193–211 (2007)10.1142/S0219455407002241 ↗

39. Radwan, A.F.: Quasi-3D integral model for thermomechanical buckling and vibration of FG porous nanoplates embedded in an elastic medium. Int. J. Mech. Sci. 157–158, 320–335 (2019). https://doi.org/10.1016/j.ijmecsci.2019.04.03110.1016/j.ijmecsci.2019.04.031 ↗

40. Rasooli Jazi, F., Amir, S., Arshid, E.: Vibration analysis of asymmetric sandwich rotating FG porous discs coated with agglomerated nanocomposite facesheets. Arch. Civ. Mech. Eng. 24, 201 (2024). https://doi.org/10.1007/s43452-024-01009-110.1007/s43452-024-01009-1 ↗

41. Shahgholian, D., Safarpour, M., Rahimi, A.R., Alibeigloo, A.: Buckling analyses of functionally graded graphene-reinforced porous cylindrical shell using the Rayleigh–Ritz method. Acta Mech. 231, 1887–1902 (2020). https://doi.org/10.1007/s00707-020-02616-810.1007/s00707-020-02616-8 ↗

42. Shahsavari, D., Shahsavari, M., Li, L., Karami, B.: A novel quasi-3D hyperbolic theory for free vibration of FG plates with porosities resting on Winkler/Pasternak/Kerr foundation. Aerosp. Sci. Technol. 72, 134–149 (2018). https://doi.org/10.1016/j.ast.2017.11.00410.1016/j.ast.2017.11.004 ↗

43. Shen, H.S., Xiang, Y., Fan, Y.: Nonlinear vibration of functionally graded graphene-reinforced composite laminated cylindrical shells in thermal environments. Compos. Struct. 182, 447–456 (2017). https://doi.org/10.1016/j.compstruct.2017.09.01010.1016/j.compstruct.2017.09.010 ↗

44. Sobhy, M.: An accurate shear deformation theory for vibration and buckling of FGM sandwich plates in hygrothermal environment. Int. J. Mech. Sci. 110, 62–77 (2016). https://doi.org/10.1016/j.ijmecsci.2016.03.00310.1016/j.ijmecsci.2016.03.003 ↗

45. Sobhy, M., Zenkour, A.M.: A comprehensive study on the size-dependent hygrothermal analysis of exponentially graded microplates on elastic foundations. Mech. Adv. Mater. Struct. 27, 816–830 (2020). https://doi.org/10.1080/15376494.2018.149998610.1080/15376494.2018.1499986 ↗

46. Tao, C., Dai, T.: Isogeometric analysis for postbuckling of sandwich cylindrical shell panels with graphene platelet reinforced functionally graded porous core. Compos. Struct. 260, 113258 (2021). https://doi.org/10.1016/j.compstruct.2020.11325810.1016/j.compstruct.2020.113258 ↗

47. Tian, F., Cui, D., Schwarz, H., Estrada, G.G., Kobayashi, H.: Cytotoxicity of single-wall carbon nanotubes on human fibroblasts. Toxicol. in Vitro 20, 1202–1212 (2006). https://doi.org/10.1016/j.tiv.2006.03.00810.1016/j.tiv.2006.03.008 ↗

48. Uzun, B., Civalek, Ö., Yaylı, M.Ö.: A hardening nonlocal approach for vibration of axially loaded nanobeam with deformable boundaries. Acta Mech. 234, 2205–2222 (2023). https://doi.org/10.1007/s00707-023-03490-w10.1007/s00707-023-03490-w ↗

49. Vu, T.-V., Nguyen, H.T.T., Nguyen-Van, H., Nguyen, T.-P., Curiel-Sosa, J.L.: A refined quasi-3D logarithmic shear deformation theory-based effective meshfree method for analysis of functionally graded plates resting on the elastic foundation. Eng. Anal. Bound. Elem. 131, 174–193 (2021). https://doi.org/10.1016/j.enganabound.2021.06.02110.1016/j.enganabound.2021.06.021 ↗

50. Wang, Y., Zeng, R., Safarpour, M.: Vibration analysis of FG-GPLRC annular plate in a thermal environment. Mech. Based des. Struct. Mach. 50, 352–370 (2020a). https://doi.org/10.1080/15397734.2020.171950810.1080/15397734.2020.1719508 ↗

51. Wang, Y., Zhou, A., Fu, T., Zhang, W.: Transient response of a sandwich beam with functionally graded porous core traversed by a non-uniformly distributed moving mass. Int. J. Mech. Mater. des. 16, 519–540 (2020b). https://doi.org/10.1007/s10999-019-09483-910.1007/s10999-019-09483-9 ↗

52. Wu, M.J., Zhu, J., Azim, I., Chen, H., Huang, X.H.: Auxetic effects in the large deflection bending characteristics of FG GRMMC shallow arches. Appl. Math. Model. 119, 534–548 (2023). https://doi.org/10.1016/j.apm.2023.02.03410.1016/j.apm.2023.02.034 ↗

53. Wu, M.J., Azim, I., Huang, X.H.: A novel technique for low-velocity impact of shallow arches. Comput. Struct. 298, 107386 (2024). https://doi.org/10.1016/J.COMPSTRUC.2024.10738610.1016/J.COMPSTRUC.2024.107386 ↗

54. Xia, L., Wang, R., Chen, G., Asemi, K., Tounsi, A.: The finite element method for dynamics of FG porous truncated conical panels reinforced with graphene platelets based on the 3-D elasticity. Adv. Nano Res. 14, 375 (2023). https://doi.org/10.12989/.2023.14.4.37510.12989/.2023.14.4.375 ↗

55. Yaghoobi, M., Sedaghatjo, M., Karkon, M., Hadji, L.: Free vibration analysis of pores functionally graded plates using new element based on Hellinger-Reissner functional. Steel Compos. Struct. 49, 713–728 (2023). https://doi.org/10.12989/scs.2023.49.6.71310.12989/scs.2023.49.6.713 ↗

56. Yang, Z., Lu, H., Sahmani, S., Safaei, B.: Isogeometric couple stress continuum-based linear and nonlinear flexural responses of functionally graded composite microplates with variable thickness. Arch. Civ. Mech. Eng. 21(3), 1–19 (2021). https://doi.org/10.1007/S43452-021-00264-W10.1007/S43452-021-00264-W ↗

57. Yao, Y., Arshid, E.: Effects of folding degree and mass fraction on the static and natural frequency characteristics of functionally graded graphene origami-enabled auxetic metamaterials annular plates. Int. J. Struct. Stab. Dyn. (2024). https://doi.org/10.1142/S021945542650128210.1142/S0219455426501282 ↗

58. Yu, T., Hu, H., Zhang, J., Bui, T.Q.: Isogeometric analysis of size-dependent effects for functionally graded microbeams by a non-classical quasi-3D theory. Thin-Walled Struct. 138, 1–14 (2019). https://doi.org/10.1016/j.tws.2018.12.00610.1016/j.tws.2018.12.006 ↗

59. Zanjanchi, M., Ghadiri, M., Sabouri-Ghomi, S.: Dynamic stability and bifurcation point analysis of FG porous core sandwich plate reinforced with graphene platelet. Acta Mech. 234, 5015–5037 (2023). https://doi.org/10.1007/s00707-023-03638-810.1007/s00707-023-03638-8 ↗

60. Zenkour, A.M., Sobhy, M.: Nonlocal piezo-hygrothermal analysis for vibration characteristics of a piezoelectric Kelvin–Voigt viscoelastic nanoplate embedded in a viscoelastic medium. Acta Mech. 229, 3–19 (2018). https://doi.org/10.1007/s00707-017-1920-610.1007/s00707-017-1920-6 ↗

61. Zenkour, A.M., Arefi, M., Alshehri, N.A.: Size-dependent analysis of a sandwich curved nanobeam integrated with piezomagnetic face-sheets. Results Phys. 7, 2172–2182 (2017). https://doi.org/10.1016/j.rinp.2017.06.03210.1016/j.rinp.2017.06.032 ↗

62. Zhang, D., Ashraf, M.A., Liu, Z., Li, C., Peng, W.: Effect of graphene nanoplatelets addition on the elastic properties of short ceramic fiber-reinforced aluminum-based hybrid nanocomposites. Mech. Based des. Struct. Mach. 50, 1417–1433 (2020). https://doi.org/10.1080/15397734.2020.175353510.1080/15397734.2020.1753535 ↗

63. Zhang, W., Ma, H., Wang, Y.: Stability and vibration of nanocomposite microbeams reinforced by graphene oxides using an MCST-based improved shear deformable computational framework. Acta Mech. (2022). https://doi.org/10.1007/s00707-022-03467-110.1007/s00707-022-03467-1 ↗

64. Zhou, K., Huang, X., Tian, J., Hua, H.: Vibration and flutter analysis of supersonic porous functionally graded material plates with temperature gradient and resting on elastic foundation. Compos. Struct. 204, 63–79 (2018). https://doi.org/10.1016/j.compstruct.2018.07.05710.1016/j.compstruct.2018.07.057 ↗