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Static deflections and stress distribution of functionally graded sandwich plates with porosity

  • Hadji, Lazreg (Laboratory of Geomatics and Sustainable Development, Ibn Khaldoun University of Tiaret) ;
  • Tounsi, Abdelouahed (Material and Hydrology Laboratory, Faculty of Technology, Civil Engineering Department, University of Sidi Bel Abbes)
  • Received : 2020.09.03
  • Accepted : 2021.01.28
  • Published : 2021.09.25
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Abstract

In this paper a higher-order shear deformation plate theory is presented to investigate the stress distribution and static deflections of functionally graded sandwich plates with porosity effects. The displacement field of the present theory is chosen based on nonlinear variations in the in-plane displacements through the thickness of the plate. By dividing the transverse displacement into the bending and shear parts and making further assumptions, the number of unknowns and equations of motion of the present theory is reduced a and hence makes them simple to use. The functionally graded materials (FGM) used in plates contain probably a porosity volume fraction which needs taking into account this aspect of imperfection in the mechanical bahavior of such structures. The present work aims to study the effect of the distribution forms of porosity on the bending of simply supported FG sandwich plate. The governing equations of the problem are derived by using the principle of virtual work. In the solution of the governing equations, the Navier procedure is used for the simply supported plate. In the porosity effect, four different porosity types are used for functionally graded sandwich plates. In the numerical results, the effects of the porosity parameters, porosity types and aspect ratio of plates on the normal stress, shear stress and static deflections of the functionally graded sandwich plates are presented and discussed. Also, some comparison studies are performed in order to validate the present formulations.

Keywords

References

  1. Akavci, S.S. (2010), "Two new hyperbolic shear displacement models for orthotropic laminated composite plates", Mech. Compos. Mater., 46(2), 215-226. https://doi.org/10.1007/s11029-010-9140-3
  2. Akbas, S.D. (2017), "Vibration and static analysis of functionally graded porous plates", J. Appl. Computat. Mech., 3(3),199-207. https://doi.org/10.22055/JACM.2017.21540.1107
  3. Al Jahwari, F. and Naguib, H.E. (2016), "Analysis and homogenization of functionally graded viscoelastic porous structures with a higher order plate theory and statistical based model of cellular distribution", Appl. Mathe. Modell., 40(3), 2190-2205. https://doi.org/10.1016/j.apm.2015.09.038
  4. Avcar, M. (2019), "Free vibration of imperfect sigmoid and power law functionally graded beams", Steel Compos. Struct., Int. J., 30(6), 603-615. https://doi.org/10.12989/scs.2019.30.6.603
  5. Chen, D., Yang, J. and Kitipornchai, S. (2017), "Nonlinear vibration and postbuckling of functionally graded grapheme reinforced porous nanocomposite beams", Compos. Sci. Technol., 142, 235-245. https://doi.org/10.1016/j.compscitech.2017.02.008
  6. Ebrahimi, F. and Jafari, A. (2016a), "A higher-order thermomechanical vibration analysis of temperature-dependent FGM beams with porosities", J. Eng. http://dx.doi.org/10.1155/2016/9561504
  7. Ebrahimi, F., Ghasemi, F. and Salari, E. (2016b), "Investigating thermal effects on vibration behavior of temperaturedependent compositionally graded Euler beams with porosities", Meccanica, 51(1), 223-249. https://doi.org/10.1007/s11012-015-0208-y
  8. Ebrahimi, F., Dabbagh, A. and Rastgoo, A. (2019), "Vibration analysis of porous metal foam shells rested on an elastic substrate", J. Strain Anal. Eng. Des., 54(3), 199-208. https://doi.org/10.1177/0309324719852555
  9. Faghidian, S.A. (2014), "A smoothed inverse eigenstrain method for reconstruction of the regularized residual fields", Int. J. Solids Struct., 51(25-26). https://doi.org/10.1016/j.ijsolstr.2014.09.012
  10. 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
  11. Faghdian, S.A. (2020a), "Two phase local/nonlocal gradient mechanics of elastic torsion", Math. Meth. Appl. Sci. https://doi.org/10.1002/mma.6877
  12. Faghdian, S.A. (2020b), "Higher order mixture nonlocal gradient theory of wave propagation", Math. Meth. Appl. Sci. https://doi.org/10.1002/mma.6885
  13. Faghdian, S.A. (2020c), "Higher-order nonlocal gradient elasticity: A consistent variational theory", Int. J. Eng. Sci., 154, 103337. https://doi.org/10.1016/j.ijengsci.2020.103337
  14. Farrahi, G.H., Faghidian, S.A. and Smith, D.J. (2009), "An inverse approach to determination of residual stresses induced by shot peening in round bars", Int. J. Mech. Sci., 51(9-10), 726-731. https://doi.org/10.1016/j.ijmecsci.2009.08.004
  15. Fazzolari, F.A. (2018), "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. https://doi.org/10.1016/j.compositesb.2017.10.022
  16. Hadji, L. and Avcar, M. (2021), "Free Vibration Analysis of FG Porous Sandwich Plates under Various Boundary Conditions", J. Appl. Comput. Mech., 7(2), 505-519. https://doi.org/10.22055/JACM.2020.35328.2628
  17. Hadji, L., Zouatnia, N. and Bernard, F. (2019), "An analytical solution for bending and free vibration responses of functionally graded beams with porosities: Effect of the micromechanical models", Struct. Eng. Mech., Int. J., 69(2), 231-241. https://doi.org/10.12989/sem.2019.69.2.231
  18. Jouneghani, F.Z., Dimitri, R. and Tornabene, F. (2018), "Structural response of porous FG nanobeams under hygro-thermo-mechanical loadings", Compos. Part B: Eng., 152, 71-78. https://doi.org/10.1016/j.compositesb.2018.06.023
  19. Keddouri, A., Hadji, L. and Tounsi, A. (2019), "Static analysis of functionally graded sandwich plates with porosities", Adv. Mater. Res., Int. J., 8(3), 155-177. https://doi.org/10.12989/amr.2019.8.3.155
  20. Kitipornchai, S., Chen, D. and Yang, J. (2017), "Free vibration and elastic buckling of functionally graded porous beams reinforced by graphene platelets", Mater. Des., 116, 656-665. https://doi.org/10.1016/j.matdes.2016.12.061
  21. Merazi, M., Hadji, L., Hassaine Daouadji, T., Tounsi A. and Adda Bedia, E.A. (2015), "A new hyperbolic shear deformation plate theory for static analysis of FGM plate based on neutral surface position", Geomech. Eng., Int. J., 8(3), 305-321. https://doi.org/10.12989/gae.2015.8.3.305
  22. Nguyen, D.D., Quang, V.D., Nguyen, P.D. and Chien, T.M. (2018), "Nonlinear dynamic response of functionally graded porous plates on elastic foundation subjected to thermal and mechanical loads", J. Appl. Computat. Mech., 4(4), 245-259. https://doi.org/10.22055/JACM.2018.23219.1151
  23. Ramteke, P.M., Panda, S.K. and Sharma, N. (2019), "Effect of grading pattern and porosity on the eigen characteristics of porous functionally graded structure", Steel Compos. Struct., Int. J., 33(6), 865-875. https://doi.org/10.12989/scs.2019.33.6.865
  24. Simsek, M. and Aydin, M. (2017), "Size-dependent forced vibration of an imperfect functionally graded (FG) microplate with porosities subjected to a moving load using the modified couple stress theory", Compos. Struct., 160, 408-421. https://doi.org/10.1016/j.compstruct.2016.10.034
  25. Shahsavari, D., Shahsavari, M., Li, L. and Karami, B. (2018), "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. https://doi.org/10.1016/j.ast.2017.11.004
  26. Taati, E. and Fallah, F. (2019), "Exact solution for frequency response of sandwich microbeams with functionally graded cores", J. Vib. Control, 25(19-20), 2641-2655. https://doi.org/10.1177/1077546319864645
  27. Thai, H.T., Nguyen, T.K., Vo, T.P. and Lee, J. (2014), "Analysis of functionally graded sandwich plates using a new first-order shear deformation theory", Eur. J. Mech.-A/Solids, 45, 211-225. https://doi.org/10.1016/j.euromechsol.2013.12.008
  28. 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
  29. Wattanasakulpong, N., Prusty, B.G., Kelly, D.W. and Hoffman, M. (2012), "Free vibration analysis of layered functionally graded beams with experimental validation", Mater. Des., 36, 182-190. https://doi.org/10.1016/j.matdes.2011.10.049
  30. Wu, D., Liu, A., Huang, Y., Huang, Y., Pi, Y. and Gao, W. (2018), "Dynamic analysis of functionally graded porous structures through finite element analysis", Eng. Struct., 165, 287-301. https://doi.org/10.1016/j.engstruct.2018.03.023
  31. Xu, K., Yuan, Y. and Li, M. (2019), "Buckling behavior of functionally graded porous plates integrated with laminated composite faces sheets", Steel Compos. Struct., Int. J., 32(5), 633-642. https://doi.org/10.12989/scs.2019.32.5.633
  32. Yang, J., Chen, D. and Kitipornchai, S. (2018), "Buckling and free vibration analyses of functionally graded graphene reinforced porous nanocomposite plates based on Chebyshev-Ritz method", Compos. Struct., 193, 281-294. https://doi.org/10.1016/j.compstruct.2018.03.090
  33. Zenkour, A.M. (2005), "A comprehensive analysis of functionally graded sandwich plates: Part 1-Deflection and stresses", Int. J. Solids Struct., 42(18-19), 5224-5242. https://doi.org/10.1016/j.ijsolstr.2005.02.015
  34. Zhao, J., Xie, F., Wang, A., Shuai, C., Tang, J. and Wang, Q. (2019), "Vibration behavior of the functionally graded porous (FGP) doubly-curved panels and shells of revolution by using a semi-analytical method", Compos. Part B: Eng., 157, 219-238. https://doi.org/10.1016/j.compositesb.2018.08.087
  35. Zhu, J., Lai, Z., Yin, Z., Jeon, J. and Lee, S. (2001), "Fabrication of ZrO2-NiCr functionally graded material by powder metallurgy", Mater. Chem. Phys., 68, 130-135. https://doi.org/10.1016/j.prostr.2020.06.006