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Assessment of the effect of the materials composition on the bending response of FG plates lying on two models of elastic foundations in thermo-hygro-mechanical environments

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Abstract

This study fulfils a thermo-hygro-mechanical analysis of the bending behavior of FG plates resting on different elastic foundation models. A quasi-3D high-order shear deformation theory with five unknowns is used herein to perform this analysis. The impact of shear deformation and stretching effect are included in the formulation of the used approach. The result of the change in material characteristics and the volumetric fraction of components on the bending response of FG plates in a thermo-hygro-mechanical environment is analyzed and discussed. The principle of virtual displacements is used to obtain the equilibrium equations, and the Navier-type solution is applied to solve the resulting equations. The results show that the increase in thermal load and moisture concentration causes a rapid deflection increase. Furthermore, the Winkler parameter influences the shear stresses more than the deflections.

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References

  1. Zenkour, A.M., Allam, M.N.M., Radwan, A.F.: Effects of hygrothermal conditions on cross-ply laminated plates resting on elastic foundations. Arch. Civ. Mech. Eng. 14, 144–159 (2014). https://doi.org/10.1016/j.acme.2013.07.008

    Article  Google Scholar 

  2. Ahmed, R.A., Fenjan, R.M., Faleh, N.M.: Analyzing post-buckling behavior of continuously graded FG nanobeams with geometrical imperfections. Geomech. Eng. 17(2), 175–180 (2019). https://doi.org/10.12989/gae.2019.17.2.175

    Article  Google Scholar 

  3. Al-Maliki, A.F., Faleh, N.M., Alasadi, A.A.: Finite element formulation and vibration of nonlocal refined metal foam beams with symmetric and non-symmetric porosities. Struct. Monit. Maint. 6(2), 147–159 (2019). https://doi.org/10.12989/smm.2019.6.2.147

    Article  Google Scholar 

  4. Gafour, Y., Hamidi, A., Benahmed, A., Zidour, M., Bensattalah, T.: Porosity-dependent free vibration analysis of FG nanobeam using non-local shear deformation and energy principle. Adv. Nano Res. 8(1), 49–58 (2020). https://doi.org/10.12989/anr.2020.8.1.049

    Article  Google Scholar 

  5. Kar, V.R., Panda, S.K.: Nonlinear flexural vibration of shear deformable functionally graded spherical shell panel. Steel Compos. Struct. 18(3), 693–709 (2020). https://doi.org/10.12989/scs.2015.18.3.693

    Article  Google Scholar 

  6. Mashat, D., Zenkour, A., Radwan, A.: A quasi 3-D higher-order plate theory for bending of FG plates resting on elastic foundations under thermo-hygro-mechanical loads with porosity. Eur. J. Mech. A/Solids 82, 103985 (2020). https://doi.org/10.1016/j.euromechsol.2020.103985

    Article  MathSciNet  MATH  Google Scholar 

  7. Winkler, E.: Die Lehre von der Elastizit¨at and Festigkeit, Prague Dominicus. (1867).

  8. Zenkour, A.M., Allam, M.N.M., Shaker, M.O., Radwan, A.F.: On the simple and mixed first-order theories for plates resting on elastic foundations. Acta. Mech. 220, 33–46 (2011). https://doi.org/10.1007/s00707-011-0453-7

    Article  MATH  Google Scholar 

  9. Zenkour, A.M., Allam, M.N.M., Radwan, A.F.: Bending of cross-ply laminated plates resting on elastic foundations under thermo-mechanical loading. Int. J. Mech. Mater. Des. 9, 239–251 (2013). https://doi.org/10.1007/s10999-012-9212-8

    Article  Google Scholar 

  10. Thai, H.-T., Choi, D.-H.: A refined plate theory for functionally graded plates resting on elastic foundation. Compos. Sci. Technol. 71, 1850–1858 (2011). https://doi.org/10.1016/j.compscitech.2011.08.016

    Article  Google Scholar 

  11. Thai, H.-T., Choi, D.-H.: A simple refined theory for bending, buckling, and vibration of thick plates resting on elastic foundation. Int. J. Mech. Sci. 73, 40–52 (2013). https://doi.org/10.1016/j.ijmecsci.2013.03.017

    Article  Google Scholar 

  12. Yas, M.H., Tahouneh, V.: 3-D Free vibration analysis of thick functionally graded annular plates on Pasternak elastic foundation via differential quadrature method (DQM). Acta Mech. 223, 43–62 (2012). https://doi.org/10.1007/s00707-011-0543-6

    Article  MathSciNet  MATH  Google Scholar 

  13. Shen, H.-S.: Nonlinear analysis of simply-supported Reissner-Mindlin plates subjected to lateral pressure and thermal loading and resting on two-parameter elastic foundations. Eng. Struct. 23, 1481–1493 (2000). https://doi.org/10.1016/S0141-0296(99)00086-3

    Article  Google Scholar 

  14. Pradhan, S.C., Murmu, T.: Thermo-mechanical vibration of FGM sandwich beam under variable elastic foundations using differential quadrature method. J. Sound Vib. 321, 342–362 (2009). https://doi.org/10.1016/j.jsv.2008.09.018

    Article  Google Scholar 

  15. Sobhy, M.: Thermoelastic response of FGM plates with temperature-dependent properties resting on variable elastic foundations. J. Appl. Mech. 7(6), 1550082 (2015). https://doi.org/10.1142/S1758825115500829

    Article  MathSciNet  Google Scholar 

  16. Attia, A., Bousahla, A.A., Tounsi, A., Mahmoud, S.R., Alwabli, A.S.: A refined four variable plate theory for thermoelastic analysis of FGM plates resting on variable elastic foundations. Struct. Eng. Mech. An Int. J. 65(4), 453–464 (2018)

    Google Scholar 

  17. Zidi, M., Tounsi, A., Houari, M., Bedia, E., Bég, O.: Bending analysis of FGM plates under thermo-hygro-mechanical loading using a four variable refined plate theory. Aerosp. Sci. Technol. (2014). https://doi.org/10.1016/j.ast.2014.02.001

    Article  Google Scholar 

  18. Daouadji, T.H., Benferhat, R.: Bending analysis of an imperfect FGM plates under hygro-thermo-mechanical loading with analytical validation. Adv. Mater. Res. 5(1), 035 (2016). https://doi.org/10.12989/AMR.2016.5.1.035

    Article  Google Scholar 

  19. Moleiro, F., Carrera, E., Li, G., Cinefra, M., Reddy, J.N.: Thermo-hygro-mechanical modelling of multilayered plates: hybrid composite laminates, fibre metal laminates and sandwich plates. Compos. Part B: Eng. (2019). https://doi.org/10.1016/j.compositesb.2019.107388

    Article  Google Scholar 

  20. Refrafi, S., Bousahla, A.A., Bouhadra, A., Menasria, A., Bourada, F., Tounsi, A., Adda Bedia, E.A., Mahmoud, S.R., Benrahou, K.H., Tounsi, A.: Effects of hygro-thermo- mechanical conditions on the buckling of FG sandwich plates resting on elastic foundations. Comput. Concrete 25(4), 311–325 (2020). https://doi.org/10.12989/cac.2020.25.4.311

    Article  Google Scholar 

  21. Merazka, B., Bouhadra, A., Menasria, A., Selim, M.M., Bousahla, A.A., Bourada, F., Al-Zahrani, M.: Thermo-hygro-mechanical bending response of FG plates resting on elastic foundations. Steel Compos. Struct. 39(5), 631–643 (2021). https://doi.org/10.12989/SCS.2021.39.5.631

    Article  Google Scholar 

  22. Hirwani, C.K., Panda, S.K., Patle, B.K.: Theoretical and experimental validation of nonlinear deflection and stress responses of an internally debonded layer structure using different higher-order theories. Acta Mech. 229, 3453–3473 (2018). https://doi.org/10.1007/s00707-018-2173-8

    Article  MathSciNet  Google Scholar 

  23. Ramteke, P.M., Panda, S.K., Sharma, N.: Effect of grading pattern and porosity on the eigen characteristics of porous functionally graded structure. Steel Compos. Struct. 33(6), 865–874 (2019). https://doi.org/10.12989/scs.2019.33.6.865

    Article  Google Scholar 

  24. Mehar, K., Panda, S.K.: Nonlinear deformation and stress responses of a graded carbon nanotube sandwich plate structure under thermoelastic loading. Acta Mech. 231, 1105–1123 (2020). https://doi.org/10.1007/s00707-019-02579-5

    Article  MathSciNet  Google Scholar 

  25. Ramteke, P.M., Patel, B., Panda, S.K.: Time-dependent deflection responses of porous FGM structure including pattern and porosity. Int. J. Appl. Mech. 12(09), 2050102 (2020). https://doi.org/10.1142/S1758825120501021

    Article  Google Scholar 

  26. Ramteke, P.M., Patel, B., Panda, S.K.: Nonlinear eigenfrequency prediction of functionally graded porous structure with different grading patterns. Waves Random Complex Med. (2021). https://doi.org/10.1080/17455030.2021.2005850

    Article  Google Scholar 

  27. Ramteke, P.M., Panda, S.K.: Free vibrational behaviour of multi-directional porous functionally graded structures. Arab. J. Sci. Eng. 46, 7741–7756 (2021). https://doi.org/10.1007/s13369-021-05461-6

    Article  Google Scholar 

  28. Ramteke, P.M., Mehar, K., Sharma, N., Panda, S.K.: Numerical prediction of deflection and stress responses of functionally graded structure for grading patterns (power-law, sigmoid, and exponential) and variable porosity (even/uneven). Sci. Iran. 28(2), 811–829 (2021). https://doi.org/10.24200/sci.2020.55581.4290

    Article  Google Scholar 

  29. Ramteke, P.M., Panda, S.K., Patel, B.: Nonlinear eigenfrequency characteristics of multi-directional functionally graded porous panels. Compos. Struct. 279, 114707 (2022). https://doi.org/10.1016/j.compstruct.2021.114707

    Article  Google Scholar 

  30. Hissaria, P., Ramteke, P.M., Hirwani, C.K., et al.: Numerical investigation of eigenvalue characteristics (vibration and buckling) of damaged porous bidirectional FG panels. J. Vib. Eng. Technol. (2022). https://doi.org/10.1007/s42417-022-00677-8

    Article  Google Scholar 

  31. Sahoo B, Sharma N, Sahoo B, Ramteke PM, Panda SK, Mahmoud SR. Nonlinear vibration analysis of FGM sandwich structure under thermal loadings. In Structures 2022 Oct 1 (Vol. 44, pp. 1392-1402). Elsevier. https://doi.org/10.1016/j.istruc.2022.08.081.

  32. Choudhary, J., Patle, B.K., Ramteke, P.M., Hirwani, C.K., Panda, S.K., Katariya, P.V.: Static and dynamic deflection characteristics of cracked porous FG panels. Int. J. Appl. Mech. 14(7), 2250076 (2022). https://doi.org/10.1142/S1758825122500764

    Article  Google Scholar 

  33. Ramteke, P.M., Kumar, V., Sharma, N., Panda, S.K.: Geometrical nonlinear numerical frequency prediction of porous functionally graded shell panel under thermal environment. Int. J. Non-Linear Mech. 143, 104041 (2022). https://doi.org/10.1016/j.ijnonlinmec.2022.104041

    Article  Google Scholar 

  34. Ramteke, P.M., Panda, S.K., Sharma, N.: Nonlinear vibration analysis of multidirectional porous functionally graded panel under thermal environment. AIAA J. 60(8), 4923–4933 (2022). https://doi.org/10.2514/1.J061635

    Article  Google Scholar 

  35. Ramteke, P.M., Panda, S.K.: Computational modelling and experimental challenges of linear and nonlinear analysis of porous graded structure: a comprehensive review. Arch. Comput. Methods Eng. (2023). https://doi.org/10.1007/s11831-023-09908-x

    Article  Google Scholar 

  36. Ramteke, P.M., Panda, S.K.: Nonlinear thermomechanical static and dynamic responses of bidirectional porous FG shell panels and experimental verifications. J. Press. Vessel Technol. (2023). https://doi.org/10.1115/1.4062154

    Article  Google Scholar 

  37. Ramteke, P. M., Panda, S. K. Nonlinear static and dynamic (deflection/stress) responses of porous functionally graded shell panel and experimental validation. Proceedings of the Institution of Mechanical Engineers, Part C: J. Mech. Eng. Sci. 2023; https://doi.org/10.1177/09544062231155099.

  38. Ramteke, P.M., Panda, S.K.: Nonlinear static and dynamic response prediction of bidirectional doubly-curved porous FG panel and experimental validation. Compos. Part A: Appl. Sci. Manufact. 166, 107388 (2023). https://doi.org/10.1016/j.compositesa.2022.107388

    Article  Google Scholar 

  39. Ebrahimi, F., Karimiasl, M., Mahesh, V.: Nonlocal and surface effects on the bending analysis of flexoelectrically actuated piezoelectric microbeams in hygrothermal environment. Sādhanā 46, 107 (2021). https://doi.org/10.1007/s12046-021-01625-0

    Article  MathSciNet  Google Scholar 

  40. Shariati, A., Ebrahimi, F., Karimiasl, M., Selvamani, R., Toghroli, A.: On bending characteristics of smart magneto-electro-piezoelectric nanobeams system. Adv. Nano Res. 9(3), 183–191 (2020)

    Google Scholar 

  41. Ebrahimi, F., Karimiasl, M., Selvamani, R.: Bending analysis of magneto-electro piezoelectric nanobeams system under hygro-thermal loading. Adv. Nano. Res. 8(3), 203–214 (2020). https://doi.org/10.12989/ANR.2020.8.3.203

    Article  Google Scholar 

  42. Ebrahimi, F., Ahari, M.F.: Magnetostriction-assisted active control of the multi-layered nanoplates: effect of the porous functionally graded facesheets on the system’s behavior. Eng. Comput. 39, 269–283 (2023). https://doi.org/10.1007/s00366-021-01539-9

    Article  Google Scholar 

  43. Ebrahimi, F., Seyfi, A.: On wave propagation characteristics of hygrothermally excited graphene foam plates. Waves Random Complex Med. 30, 1–20 (2022). https://doi.org/10.1080/17455030.2022.2105416

    Article  Google Scholar 

  44. Rachedi, M.A., Benyoucef, S., Bouhadra, A., Bouiadjra, R.B., Sekkal, M., Benachour, A.: Impact of the homogenization models on the thermoelastic response of FG plates on variable elastic foundation. Geomech. Eng. 22(1), 65–80 (2020). https://doi.org/10.12989/GAE.2020.22.1.065

    Article  Google Scholar 

  45. Bouazza, M., Zenkour, A.M., Benseddiq, N.: Effect of material composition on bending analysis of FG plates via a two-variable refined hyperbolic theory. Arch. Mech. 70(2), 107–129 (2018)

    MathSciNet  MATH  Google Scholar 

  46. Bakhti, K., Sekkal, M., Adda Bedia, E.A., Tounsi, A.: Influence of material composition on buckling response of FG plates using a simple plate integral model. Smart Struct. Syst. 25(4), 447–457 (2020). https://doi.org/10.12989/SSS.2020.25.4.447

    Article  Google Scholar 

  47. Bouhadra, A., Menasria, A., Rachedi, M.A.: Boundary conditions effect for buckling analysis of porous functionally graded nanobeam. Adv. Nano Res. 10(4), 313–325 (2021). https://doi.org/10.12989/ANR.2021.10.4.313

    Article  Google Scholar 

  48. Pitakthapanaphong, S., Busso, E.P.: Self-consistent elasto-plastic stress solutions for functionally graded material systems subjected to thermal transients. J. Mech. Phys. Solids. 50, 695–715 (2002). https://doi.org/10.1016/S0022-5096(01)00105-3

    Article  MATH  Google Scholar 

  49. Sofiyev, A.H., Deniz, A., Akçay, I.H., Yusufogçlu, E.: The vibration and stability of a three-layered conical shell containing an FGM layer subjected to axial compressive load. Acta Mech. 183, 129–144 (2006). https://doi.org/10.1007/s00707-006-0328-5

    Article  MATH  Google Scholar 

  50. Benyoucef, S., Achouri, F., Bourada, F., Bouiadjra, R.B., Tounsi, A.: Robust quasi 3D computational model for mechanical response of FG thick sandwich plate. Struct. Eng. Mech. An Int. J. 70(5), 571–589 (2019). https://doi.org/10.12989/sem.2019.70.5.571

    Article  Google Scholar 

  51. Refrafi, S., Bousahla, A.A., Bouhadra, A., Menasria, A., Bourada, F., Tounsi, A., Adda Bedia, A., Mahmoud, S., Benrahou, K.H., Tounsi, A.: Effects of hygro-thermo-mechanical conditions on the buckling of FG sandwich plates resting on elastic foundations. Comput. Concrete Int. J. 25(4), 311–325 (2020). https://doi.org/10.12989/cac.2020.25.4.311

    Article  Google Scholar 

  52. Zenkour, A.M.: The effect of transverse shear and normal deformations on the thermomechanical bending of functionally graded sandwich plates. J. Appl. Math. Mech. 4, 667–707 (2009). https://doi.org/10.1142/S1758825109000368

    Article  Google Scholar 

  53. Bouderba, B., Houari, M.S., Tounsi, A.: Thermomechanical bending response of FGM thick plates resting on Winkler–Pasternak elastic foundations. Steel Compos. Struct. Int. J. 14(1), 85–104 (2013)

    Article  Google Scholar 

  54. Ebrahimi, F., Shafiei, M.S., Ahari, M.F.: Vibration analysis of single and multi-walled circular graphene sheets in thermal environment using GDQM. Waves Random Complex Med. 30, 1–40 (2022)

    Google Scholar 

  55. Ahari, M.F., Ghadiri, M.: Resonator vibration of a magneto-electro-elastic nano-plate integrated with FGM layer subjected to the nano mass-Spring-damper system and a moving load. Waves Random Complex Med. 25, 1–39 (2022)

    Google Scholar 

  56. Ebrahimi, F., Shafiee, M.S., Ahari, M.F.: Buckling analysis of single and double-layer annular graphene sheets in thermal environment. Eng. Comput. 39(1), 625–639 (2023). https://doi.org/10.1007/s00366-022-01634-5

    Article  Google Scholar 

  57. Hadji, M., Bouhadra, A., Mamen, B., Menasria, A., Bousahla, A.A., Bourada, F., Bourada, M., Benrahou, 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), 1 (2023). https://doi.org/10.12989/scs.2023.46.1.001

    Article  Google Scholar 

  58. Himeur, N., Mamen, B., Benguediab, S., Bouhadra, A., Menasria, A., Bouchouicha, B., Tounsi, A.: Coupled effect of variable Winkler–Pasternak foundations on bending behavior of FG plates exposed to several types of loading. Steel Compos. Struct. 44(3), 339–355 (2022)

    Google Scholar 

  59. Carrera, E., Brischetto, S., Cinefra, M., Soave, M.: Effects of thickness stretching in functionally graded plates and shells. Compos. B 42, 123–133 (2011). https://doi.org/10.1016/j.compositesb.2010.10.005

    Article  Google Scholar 

  60. Carrera, E., Brischetto, S., Robaldo, A.: Variable kinematic model for the analysis of functionally graded material plates. AIAA J. 46, 194–203 (2008). https://doi.org/10.2514/1.32490

    Article  Google Scholar 

  61. Neves, A.M.A., Ferreira, A.J.M., Carrera, E., Roque, C.M.C., Cinefra, M., Jorge, R.M.N., Soares, C.M.M.: Bending of FGM plates by a sinusoidal plate formulation and collocation with radial basis functions. Mech. Res. Commun. 38, 368–371 (2011). https://doi.org/10.1016/j.mechrescom.2011.04.011

    Article  MATH  Google Scholar 

  62. Han, J.B., Liew, K.M.: Numerical differential quadrature method for Reissner/Mindlin plates on two-parameter foundations. Int. J. Mech. Sci. 39, 977–989 (1997). https://doi.org/10.1016/S0020-7403(97)00001-5

    Article  MATH  Google Scholar 

  63. Ameur, M., Tounsi, A., Mechab, I., Bedia, E.A.: A new trigonometric shear deformation theory for bending analysis of functionally graded plates resting on elastic foundations. J. Civ. Eng. 15, 1405–1414 (2010). https://doi.org/10.1007/s12205-011-1361-z

    Article  Google Scholar 

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Authors and Affiliations

  1. Department of Civil Engineering, Faculty of Science and Technology, Abbès Laghrour University of Khenchela, Khenchela, Algeria

    Mohamed Ali Rachedi, Abdelhakim Bouhadra & Belgacem Mamen

  2. Material and Hydrology Laboratory, Civil Engineering Department, Faculty of Technology, University of Sidi Bel Abbes, Sidi Bel Abbès, Algeria

    Abdelhakim Bouhadra, Belgacem Mamen, Samir Benyoucef & Abdelouahed Tounsi

  3. YFL (Yonsei Frontier Lab), Yonsei University, Seoul, Korea

    Abdelouahed Tounsi

  4. Department of Civil and Environmental Engineering, King Fahd University of Petroleum and Minerals, Eastern Province, 31261, Dhahran, Saudi Arabia

    Abdelouahed Tounsi

  5. Interdisciplinary Research Center for Construction and Building Materials, KFUPM, Dhahran, Saudi Arabia

    Abdelouahed Tounsi

  6. Department of Mechanical Engineering, Faculty of Engineering, Jazan University, P.O Box 45124, Jazan, Saudi Arabia

    M. H. Ghazwani

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  1. Mohamed Ali Rachedi
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Ali Rachedi, M., Bouhadra, A., Mamen, B. et al. Assessment of the effect of the materials composition on the bending response of FG plates lying on two models of elastic foundations in thermo-hygro-mechanical environments. Acta Mech 234, 6315–6340 (2023). https://doi.org/10.1007/s00707-023-03696-y

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