Structural Engineering and Mechanics

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Impact of viscoelastic foundation on bending behavior of FG plate subjected to hygro-thermo-mechanical loads

  • Ismail M. Mudhaffar (Department of Civil and Environmental Engineering, King Fahd University of Petroleum & Minerals) ;
  • Abdelbaki Chikh (Material and Hydrology Laboratory, Faculty of Technology, Civil Engineering Department, University of Sidi Bel Abbes) ;
  • Abdelouahed Tounsi (Department of Civil and Environmental Engineering, King Fahd University of Petroleum & Minerals) ;
  • Mohammed A. Al-Osta (Department of Civil and Environmental Engineering, King Fahd University of Petroleum & Minerals) ;
  • Mesfer M. Al-Zahrani (Department of Civil and Environmental Engineering, King Fahd University of Petroleum & Minerals) ;
  • Salah U. Al-Dulaijan (Department of Civil and Environmental Engineering, King Fahd University of Petroleum & Minerals)
  • Received : 2022.09.02
  • Accepted : 2023.02.21
  • Published : 2023.04.25
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Abstract

This work applies a four-known quasi-3D shear deformation theory to investigate the bending behavior of a functionally graded plate resting on a viscoelastic foundation and subjected to hygro-thermo-mechanical loading. The theory utilizes a hyperbolic shape function to predict the transverse shear stress, and the transverse stretching effect of the plate is considered. The principle of virtual displacement is applied to obtain the governing differential equations, and the Navier method, which comprises an exponential term, is used to obtain the solution. Novel to the current study, the impact of the viscoelastic foundation model, which includes a time-dependent viscosity parameter in addition to Winkler's and Pasternak parameters, is carefully investigated. Numerical examples are presented to validate the theory. A parametric study is conducted to study the effect of the damping coefficient, the linear and nonlinear loadings, the power-law index, and the plate width-tothickness ratio on the plate bending response. The results show that the presence of the viscoelastic foundation causes an 18% decrease in the plate deflection and about a 10% increase in transverse shear stresses under both linear and nonlinear loading conditions. Additionally, nonlinear loading causes a one-and-a-half times increase in horizontal stresses and a nearly two-times increase in normal transverse stresses compared to linear loading. Based on the article's findings, it can be concluded that the viscosity effect plays a significant role in the bending response of plates in hygrothermal environments. Hence it shall be considered in the design.

Keywords

Acknowledgement

This work is supported by the deanship of graduate studies (DSR) at King Fahd University of Petroleum and Minerals through project No. DF181032. The Civil and Environment Engineering department's support is also acknowledged.

References

  1. Akavci, S.S. and Tanrikulu, A.H. (2015), "Static and free vibration analysis of functionally graded plates based on a new quasi-3D and 2D shear deformation theories", Compos. Part B: Eng., 83, 203-215. https://doi.org/10.1016/j.compositesb.2015.08.043.
  2. Amir, S., Arshid, E., Rasti-Alhosseini, S.M.A. and Loghman, A. (2020), "Quasi-3D tangential shear deformation theory for sizedependent free vibration analysis of three-layered FG porous micro rectangular plate integrated by nano-composite faces in hygrothermal environment", J. Therm. Stress., 43(2), 133-156. https://doi.org/10.1080/01495739.2019.1660601.
  3. Benbakhti, A., Bachir Bouiadjra, M., Retiel, N. and Tounsi, A. (2016), "A new five unknown quasi-3D type HSDT for thermomechanical bending analysis of FGM sandwich plates. Steel Compos. Struct., 22(5), 975-999. https://doi.org/10.12989/scs.2016.22.5.975.
  4. Bisheh, H. and Civalek, O . (2020), "Vibration of smart laminated carbon nanotube-reinforced composite cylindrical panels on elastic foundations in hygrothermal environments", Thin Wall Struct., 155, 106945. https://doi.org/10.1016/j.tws.2020.106945.
  5. Faghidian, S.A. (2014), "A smoothed inverse eigenstrain method for reconstruction of the regularized residual fields", Int. J. Solid. Struct., 51(25-26), 4427-4434. https://doi.org/10.1016/j.ijsolstr.2014.09.012.
  6. Faghidian, S.A. (2015), "Inverse determination of the regularized residual stress and eigenstrain fields due to surface peening", J. Strain Anal. Eng. Des., 50(2), 84-91. https://doi.org/10.1177/0309324714558326.
  7. Faghidian, S.A. (2020), "Higher order mixture nonlocal gradient theory of wave propagation", Math. Meth. Appl. Sci., https://doi.org/10.1002/mma.6885.
  8. Faghidian, S.A. (2021a), "Contribution of nonlocal integral elasticity to modified strain gradient theory", Eur. Phys. J. Plus, 136(5), 559. https://doi.org/10.1140/epjp/s13360-021-01520-x.
  9. Faghidian, S.A. (2021b), "Flexure mechanics of nonlocal modified gradient nano-beams", J. Comput. Des. Eng., 8(3), 949-959. https://doi.org/10.1093/jcde/qwab027.
  10. Faghidian, S.A., Zur, K.K., Pan, E. and Kim, J. (2022), "On the analytical and meshless numerical approaches to mixture stress gradient functionally graded nano-bar in tension", Eng. Anal. Bound. Elem., 134, 571-580. https://doi.org/10.1016/j.enganabound.2021.11.010.
  11. Faghidian, S.A., Zur, K.K. and Reddy, J.N. (2022), "A mixed variational framework for higher-order unified gradient elasticity", Int. J. Eng. Sci., 170, 103603. https://doi.org/10.1016/j.ijengsci.2021.103603.
  12. Bouderba, B. (2018), "Bending of FGM rectangular plates resting on non-uniform elastic foundations in thermal environment using an accurate theory", Steel Compos. Struct., 27(3), 311-325. https://doi.org/10.12989/scs.2018.27.3.311.
  13. Garg, A. and Chalak, H.D. (2019), "A review on analysis of laminated composite and sandwich structures under hygrothermal conditions", Thin Wall. Struct., 142, 205-226. https://doi.org/10.1016/j.tws.2019.05.005.
  14. 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. https://doi.org/10.12989/csm.2021.10.1.061.
  15. Hasheminejad, S.M. and Gheshlaghi, B. (2012), "Threedimensional elastodynamic solution for an arbitrary thick FGM rectangular plate resting on a two parameter viscoelastic foundation", Compos Struct., 94(9), 2746-2755. https://doi.org/10.1016/j.compstruct.2012.04.010.
  16. Hassan, A., Hassan, A. and Kurgan, N. (2020), "Bending analysis of thin FGM skew plate resting on Winkler elastic foundation using multi-term extended Kantorovich method", Eng. Sci. Technol., 23(4), 788-800. https://doi.org/10.1016/j.jestch.2020.03.009.
  17. Jafari, P. and Kiani, Y. (2021), "Free vibration of functionally graded graphene platelet reinforced plates: A quasi 3D shear and normal deformable plate model", Compos. Struct., 275, 114409. https://doi.org/10.1016/j.compstruct.2021.114409.
  18. Joshi, P.V., Jain, N.K. and Ramtekkar, G.D. (2015), "Thin-Walled Structures Effect of thermal environment on free vibration of cracked rectangular plate : An analytical approach", Thin Wall. Struct., 91, 38-49. https://doi.org/10.1016/j.tws.2015.02.004.
  19. Kerr, A.D. (1964), "Elastic and viscoelastic foundation models", J. Appl. Mech., 31(3), 491-498. https://doi.org/10.1115/1.3629667.
  20. Koizumi, M. (1997), "FGM activities in Japan", Compos. Part B: Eng., 28(1-2), 1-4. https://doi.org/10.1016/S1359-8368(96)00016-9.
  21. Leissa, A.W. (1973), "The free vibration of rectangular plates", J. Sound Vib., 31(3), 257-293. https://doi.org/10.1016/S0022- 460X(73)80371-2.
  22. Madenci, E. and Gulcu, S. (2020), "Optimization of flexure stiffness of FGM beams via artificial neural networks by mixed FEM", Struct. Eng. Mech., 75(5), 633-642. https://doi.org/10.12989/sem.2020.75.5.633.
  23. Madenci, E. and O zutok, A. (2020), "Variational approximate for high order bending analysis of laminated composite plates", Struct. Eng. Mech., 73(1), 97-108. https://doi.org/10.12989/sem.2020.73.1.097
  24. Madenci, E. and Ozkili, 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.
  25. Madenci, E. (2021), "Free vibration and static analyses of metalceramic FG beams via high-order variational MFEM", Steel Compos. Struct., 39(5), 493-509. https://doi.org/10.12989/scs.2021.39.5.493.
  26. Matsunaga, H. (2009), "Stress analysis of functionally graded plates subjected to thermal and mechanical loadings", Compos. Struct., 87(4), 344-357. https://doi.org/10.1016/j.compstruct.2008.02.002.
  27. Mindlin, R.D. (1989), "Influence of rotatory inertia and shear on flexural motions of isotropic, elastic plates", J. Appl. Mech, 18(1), 31-38. https://doi.org/10.1115/1.4010217.
  28. Moleiro, F., Carrera, E., Ferreira, A.J.M. and Reddy, J.N. (2020), "Hygro-thermo-mechanical modelling and analysis of multilayered plates with embedded functionally graded material layers", Compos. Struct., 233, 111442. https://doi.org/10.1016/j.compstruct.2019.111442.
  29. Naghavi, M. (2021), "Bending analysis of functionally graded sandwich plates using the refined finite strip method", J. Sandw. Struct. Mater., 24(1), 448-483. https://doi.org/10.1177/10996362211020448.
  30. Njim, E.K., Al-Waily, M. and Bakhy, S.H. (2021), "A critical review of recent research of free vibration and stability of functionally graded materials of sandwich plate", IOP Conf. Ser.: Mater. Sci. Eng., 1094(1), 012081. https://doi.org/10.1088/1757-899x/1094/1/012081.
  31. Pasternak, P.L. (1954), "On a new method of an elastic foundation by means of two foundation constants", Gosudarstvennoe Izdatelstvo Literaturi Po Stroitelstuve i Arkhitekture.
  32. Rahmani, M.C., Kaci, A., Bousahla, A.A., Bourada, F., Tounsi, A., Bedia, E.A.A., Mahmoud, S.R., Benrahou, K.H. and 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.2019.27.2.225.
  33. Reddy, J.N. (1984), "A simple higher-order theory for laminated composite plates", J. Appl. Mech., Trans., ASME, 51(4), 745-752. https://doi.org/10.1115/1.3167719.
  34. 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(20000110/30)47:1/3%3C663::AID-NME787%3E3.0.CO,2-8.
  35. Reddy, J.N. and Chin, C.D. (1998), "Thermomechanical analysis of functionally graded cylinders and plates", J. Therm. Stress., 21(6), 593-626. https://doi.org/10.1080/01495739808956165.
  36. Sahraee, S. (2009), "Bending analysis of functionally graded sectorial plates using Levinson plate theory", Compos. Struct., 88(4), 548-557. https://doi.org/10.1016/j.compstruct.2008.05.014.
  37. Sayyad, A.S. and Ghumare, S.M. (2021), "Thermomechanical bending analysis of FG sandwich plates using a quasi-threedimensional theory", J. Aerosp. Eng., 34(3), 04021007. https://doi.org/10.1061/(ASCE)AS.1943-5525.0001249.
  38. Van Do, V.N. and Lee, C.H. (2018), "Nonlinear analyses of FGM plates in bending by using a modified radial point interpolation mesh-free method", Appl. Math. Model., 57, 1-20. https://doi.org/10.1016/j.apm.2017.12.035.
  39. Winkler, E. (1867), Die Lehre von der Elasticitat und Festigkeit mit besonderer Rucksicht auf ihre Anwendung in der Technik.
  40. Zenkour, A. M., & Aljadani, M. H. (2021). "Quasi-3D refined theory for functionally graded porous plates: Vibration analysis", Физическая мезомеханика, 24(2), 56-70. https://doi.org/10.24412/1683-805X-2021-2-56-70.
  41. Zenkour, A.M. and Radwan, A.F. (2019), "Hygrothermomechanical buckling of FGM plates resting on elastic foundations using a quasi-3D model", Int. J. Comput. Meth. Eng. Sci. Mech., 20(2), 85-98. https://doi.org/10.1080/15502287.2019.1568618.
  42. Zhang, Z., Liu, X. and Mohammadi, R. (2021), "Impacts of the hygro-thermo conditions on the vibration analysis of 2D - FG nanoplates based on a novel HSDT", Eng. Comput, 38(Suppl 4), 2995-3008. https://doi.org/10.1007/s00366-021-01443-2.
  43. Zur, K.K. and Faghidian, S.A. (2021), "Analytical and meshless numerical approaches to unified gradient elasticity theory", Eng. Anal. Bound. Elem., 130, 238-248. https://doi.org/10.1016/j.enganabound.2021.05.022.