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Hygro-thermo-mechanical bending response of FG plates resting on elastic foundations

  • Merazka, Bouzid (Materials and Hydrology Laboratory, University of Sidi Bel Abbes, Faculty of Technology, Civil Engineering Department) ;
  • Bouhadra, Abdelhakim (Materials and Hydrology Laboratory, University of Sidi Bel Abbes, Faculty of Technology, Civil Engineering Department) ;
  • Menasria, Abderrahmane (Materials and Hydrology Laboratory, University of Sidi Bel Abbes, Faculty of Technology, Civil Engineering Department) ;
  • Selim, Mahmoud M. (Department of Mathematics, Al-Aflaj College of Science and Humanities, Prince Sattam bin Abdulaziz University) ;
  • Bousahla, Abdelmoumen Anis (Laboratoire de Modelisation et Simulation Multi-echelle, Universite de Sidi Bel Abbes) ;
  • Bourada, Fouad (Materials and Hydrology Laboratory, University of Sidi Bel Abbes, Faculty of Technology, Civil Engineering Department) ;
  • Tounsi, Abdeldjebbar (Materials and Hydrology Laboratory, University of Sidi Bel Abbes, Faculty of Technology, Civil Engineering Department) ;
  • Benrahou, Kouider Halim (Materials and Hydrology Laboratory, University of Sidi Bel Abbes, Faculty of Technology, Civil Engineering Department) ;
  • Tounsi, Abdelouahed (Materials and Hydrology Laboratory, University of Sidi Bel Abbes, Faculty of Technology, Civil Engineering Department) ;
  • Al-Zahrani, Mesfer Mohammad (Department of Civil and Environmental Engineering, King Fahd University of Petroleum & Minerals)
  • Received : 2019.12.12
  • Accepted : 2020.11.02
  • Published : 2021.06.10
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Abstract

The aim of this work is to study the hygro-thermo-mechanical bending responses of simply supported FG plate resting on a Winkler-Pasternak elastic foundation. The effect transverse shear strains is taken into account in which the zero transverse shear stress condition on the top and bottom surfaces of the plate is ensured without using any shear correction factors. The developed model contains only four unknowns variable which is reduced compared to other HSDTs models. The material properties of FG-plate are supposed to vary across the thickness of the plate according to power-law mixture. The differential governing equations are derived based on the virtual working principle. Numerical outcomes of bending analysis of FG plates under hygro-thermo-mechanical loads are performed and compared with those available in the literature. The effects of the temperature, moisture concentration, elastic foundation parameters, shear deformation, geometrical parameters, and power-law-index on the dimensionless deflections, axial and transverse shear stresses of the FG-plate are presented and discussed.

Keywords

References

  1. Abdulrazzaq, M.A., Fenjan, R.M., Ahmed, R.A. and Faleh, N.M. (2020), "Thermal buckling of nonlocal clamped exponentially graded plate according to a secant function based refined theory", Steel Compos. Struct., 35(1), 147-157. https://doi.org/10.12989/scs.2020.35.1.147.
  2. Ahmed, R.A., Fenjan, R.M. and Faleh, N.M. (2019), "Analyzing post-buckling behavior of continuously graded FG nanobeams with geometrical imperfections", Geomech. Eng., 17(2), 175-180. https://doi.org/10.12989/gae.2019.17.2.175.
  3. Akavci, S.S. (2016), "Mechanical behavior of functionally graded sandwich plates on elastic foundation", Compos. Part B: Eng., 96, 136-152. https://doi.org/10.1016/j.compositesb.2016.04.035.
  4. Akbas, S.D. (2015), "Wave propagation of a functionally graded beam in thermal environments", Steel Compos. Struct., 19(6), 1421-1447. https://doi.org/10.12989/SCS.2015.19.6.1421.
  5. Akbas, S.D. (2019a), "Nonlinear static analysis of laminated composite beams under hygro-thermal effect", Struct. Eng. Mech., 72(4), 433-441. https://doi.org/10.12989/sem.2019.72.4.433.
  6. Akbas, S.D. (2019b), "Nonlinear behavior of fiber reinforced cracked composite beams", Steel Compos. Struct., 30(4), 327-336. https://doi.org/10.12989/SCS.2019.30.4.327.
  7. Akbas, S.D. (2020), "Dynamic responses of laminated beams under a moving load in thermal environment", Steel Compos. Struct., 35(6), 729-737. https://doi.org/10.12989/SCS.2020.35.6.729.
  8. Akgoz, B. andCivalek, O. (2016), "Bending analysis of embedded carbon nanotubes resting on an elastic foundation using strain gradient theory", Acta Astronautica, 119, 1-12. https://doi.org/10.1016/j.actaastro.2015.10.021.
  9. Al-Basyouni, K.S., Ghandourah, E., Mostafa, H.M. and Algarni, A. (2020), "Effect of the rotation on the thermal stress wave propagation in non-homogeneous viscoelastic body", Geomech. Eng., 21(1), 1-9. https://doi.org/10.12989/gae.2020.21.1.001.
  10. AlSaid-Alwan, H.H.S. and Avcar, M. (2020), "Analytical solution of free vibration of FG beam utilizing different types of beam theories: A comparative study", Comput. Concrete, 26(3), 285-292. http://dx.doi.org/10.12989/cac.2020.26.3.285.
  11. Ameur, M., Tounsi, A., Mechab, I. and El Bedia, A.A. (2011), "A new trigonometric shear deformation theory for bending analysis of functionally graded plates resting on elastic foundations", KSCE J. Civil Eng., 15(8), 1405-1414. http://dx.doi.org/10.1007/s12205-011-1361-z.
  12. Attia, M.A. (2017), "On the mechanics of functionally graded nanobeams with the account of surface elasticity", Int. J. Eng. Sci., 115, 73-101. https://doi.org/10.1016/j.ijengsci.2017.03.011.
  13. Avcar, M. (2019), "Free vibration of imperfect sigmoid and power law functionally graded beams", Steel Compos. Struct., 30(6), 603-615. https://doi.org/10.12989/SCS.2019.30.6.603.
  14. Bensattalah, T., Bouakkaz, K., Zidour, M. and Daouadji, T.H. (2019), "Critical buckling loads of carbon nanotube embedded in Kerr's medium", Adv. Nano Res., 6(4), 339. https://doi.org/10.12989/anr.2018.6.4.339.
  15. Bensattalah, T., Hamidi, A., Bouakkaz, K., Zidour, M. and Daouadji, T.H. (2020), "Critical Buckling Load of Triple-Walled Carbon Nanotube Based on Nonlocal Elasticity Theory", J. Nano Res., 62, 108-119. https://doi.org/10.4028/www.scientific.net/JNanoR.62.108.
  16. Bharath, H.S., Waddar, S., Bekinal, S.I., Jeyaraj, P. and Doddamani, M. (2020), "Effect of axial compression on dynamic response of concurrently printed sandwich", Compos. Struct. https://doi.org/10.1016/j.compstruct.2020.113223.
  17. Birman, V. and Byrd, L.W. (2007), "Modeling and Analysis of Functionally Graded Materials and Structures", Appl. Mech. Rev., 60(5), 195. https://doi.org/10.1115/1.2777164.
  18. Boulal, A., Bensattalah, T., Karas, A., Zidour, M., Heireche, H. and Adda Bedia, E.A. (2020), "Buckling of carbon nanotube reinforced composite plates supported by Kerr foundation using Hamilton's energy principle", Struct. Eng. Mech., 73(2), 209-223. https://doi.org/10.12989/sem.2020.73.2.209.
  19. Carrera, E., Brischetto, S., Cinefra, M. and Soave, M. (2011), "Effects of thickness stretching in functionally graded plates and shells", Compos. Part B: Eng., 42(2), 123-133. https://doi.org/10.1016/j.compositesb.2010.10.005.
  20. Carrera, E., Brischetto, S. and Robaldo, A. (2008), "Variable Kinematic Model for the Analysis of Functionally Graded Material plates", AIAA J., 46(1), 194-203. https://doi.org/10.2514/1.32490.
  21. Chandra, B.M., Ramji, K., Kar, V. R., Panda, S. K., Lalepalli, K.A. and Pandey, H.K. (2018), "Numerical study of temperature dependent eigenfrequency responses of tilted functionally graded shallow shell structures", Struct. Eng. Mech., 68(5), 527-536. https://doi.org/10.12989/sem.2018.68.5.527.
  22. Civalek, O. and Avcar, M. (2020), "Free vibration and buckling analyses of CNT reinforced laminated non-rectangular plates by discrete singular convolution method", Eng. with Comput., 1-33. https://doi.org/10.1007/s00366-020-01168-8.
  23. Civalek, O., Uzun, B., Yayli, M.O. and Akgoz, B. (2020), "Size-dependent transverse and longitudinal vibrations of embedded carbon and silica carbide nanotubes by nonlocal finite element method", Eur. Phys. J. Plus, 135(4). https://doi.org/10.1140/epjp/s13360-020-00385-w.
  24. Civalek, O ., Dastjerdi, S., Akbas, S.D. and Akgoz, B. (2021), "Vibration analysis of carbon nanotube-reinforced composite microbeams", Math. Method. Appl. Sci., https://doi.org/10.1002/mma.7069.
  25. Cuong-Le, T., Nguyen, K.D., Nguyen-Trong, N., Khatir, S., Nguyen-Xuan, H. and Abdel-Wahab, M. (2020), "A three-dimensional solution for free vibration and buckling of annular plate, conical, cylinder and cylindrical shell of FG porouscellular materials using IGA", Compos. Struct., 113216. https://doi.org/10.1016/j.compstruct.2020.113216.
  26. Daouadji, T.H. (2017), "Analytical and numerical modeling of interfacial stresses in beams bonded with a thin plate", Adv. Comput. Design, 2(1), 57-69. https://doi.org/10.12989/acd.2017.2.1.057.
  27. Daouadji, T.H. and Hadji, L. (2015), "Analytical solution of nonlinear cylindrical bending for functionally graded plates", Geomech. Eng., 9(5), 631-644. https://doi.org/10.12989/gae.2015.9.5.631.
  28. Demir, C. and Civalek, O. (2017), "On the analysis of microbeams", Int. J. Eng. Sci., 121, 14-33. https://doi.org/10.1016/j.ijengsci.2017.08.016.
  29. Duc, N.D. and Tung, H.V. (2011), "Mechanical and thermal postbuckling of higher order shear deformable functionally graded plates on elastic foundations", Compos. Struct., 93(11), 2874-2881. doi:10.1016/j.compstruct.2011.05.017.
  30. Gafour, Y., Hamidi, A., Benahmed, A., Zidour, M. and Bensattalah, T. (2020), "Porosity-dependent free vibration analysis of FG nanobeam using non-local shear deformation and energy principle", Adv. Nano Res., 8(1), 37-47. https://doi.org/10.12989/anr.2020.8.1.037.
  31. Ghandourah, E.E. and Abdraboh, A.M. (2020), "Dynamic analysis of functionally graded nonlocal nanobeam with different porosity models", Steel Compos. Struct., 36(3), 293-305. http://dx.doi.org/10.12989/scs.2020.36.3.293.
  32. 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.
  33. Hadji, L. (2020), "Influence of the distribution shape of porosity on the bending of FGM beam using a new higher order shear deformation model", Smart Struct. Syst., 26(2), 253-262. https://doi.org/10.12989/sss.2020.26.2.253.
  34. Han, J.B. and Liew, K.M. (1997), "Numerical differential quadrature method for Reissner/Mindlin plates on two-parameter foundations", Int. J. Mech. Sci., 39(9), 977-989. https://doi.org/10.1016/s0020-7403(97)00001-5.
  35. Jalaei, M.H. and Civalek, O. (2019), "On dynamic instability of magnetically embedded viscoelastic porous FG nanobeam", Int. J. Eng. Sci., 143, 14-32. https://doi.org/10.1016/j.ijengsci.2019.06.013.
  36. Kar, V.R. and Panda, S.K. (2015), "Large deformation bending analysis of functionally graded spherical shell using FEM", Struct. Eng. Mech., 53(4), 661-679. https://doi.org/10.12989/sem.2015.53.4.661.
  37. Karami, B. and Janghorban, M. (2020), "On the mechanics of functionally graded nanoshells", Int. J. Eng. Sci., 153, 103309. https://doi.org/10.1016/j.ijengsci.2020.103309.
  38. Kasaeian, A.B., Vatan, S.N. and Daneshmand, S. (2011), "FGM Materials and Finding an Appropriate Model for the Thermal Conductivity", Procedia Eng., 14, 3199-3204. https://doi.org/10.1016/j.proeng.2011.07.404.
  39. Kiani, Y. (2019), "NURBS-based thermal buckling analysis of graphene platelet reinforced composite laminated skew plates", J. Therm. Stresses, 1-19. https://doi.org/10.1080/01495739.2019.1673687.
  40. Kiani, Y. and Mirzaei, M. (2019), "Isogeometric thermal postbuckling of FG-GPLRC laminated plates", Steel Compos. Struct., 32(6), 821-832. https://doi.org/10.12989/scs.2019.32.6.821.
  41. Li, D., Deng, Z. and Xiao, H. (2016), "Thermomechanical bending analysis of functionally graded sandwich plates using four variable refined plate theory", Compos. B Eng., 106, 107-119. http://doi.org/10.1016/j.compositesb.2016.08.041.
  42. Li, D., Deng, Z., Chen, G., Xiao, H. and Zhu, L. (2017), "Thermomechanical bending analysis of sandwich plates with both functionally graded face sheets and functionally graded core", Compos Struct., 169, 29-41. http://doi.org/10.1016/j.compstruct.2017.01.026.
  43. Madenci, E. (2019), "A refined functional and mixed formulation to static analyses of fgm beams", Struct. Eng. Mech., 69(4), 427-437. https://doi.org/10.12989/sem.2019.69.4.427.
  44. Mantari, J.L. and Guedes Soares, C. (2013), "A novel higher-order shear deformation theory with stretching effect for functionally graded plates", Compos. Part B: Eng., 45(1), 268-281. https://doi.org/10.1016/j.compositesb.2012.05.036.
  45. Mantari, J.L., Oktem, A.S. and Guedes Soares, C. (2012), "Bending response of functionally graded plates by using a new higher order shear deformation theory", Compos. Struct., 94(2), 714-723. https://doi.org/10.1016/j.compstruct.2011.09.007.
  46. Mehar, K. and Panda, S.K. (2019), "Multiscale modeling approach for thermal buckling analysis of nanocomposite curved structure", Adv. Nano Res., 7(3), 181-190. https://doi.org/10.12989/anr.2019.7.3.181.
  47. Mehar, K., Panda, S.K. and Mahapatra, T.R. (2017), "Thermoelastic nonlinear frequency analysis of CNT reinforced functionally graded sandwich structure", Eur. J. Mech. - A/Solids, 65, 384-396. https://doi.org/10.1016/j.euromechsol.2017.05.005.
  48. Merzoug, M., Bourada, M., Sekkal, M., Ali Chaibdra, A., Belmokhtar, C., Benyoucef, S. and Benachour, A. (2020), "2D and quasi 3D computational models for thermoelastic bending of FG beams on variable elastic foundation: Effect of the micromechanical models", Geomech. Eng., 22(4), 361-374. https://doi.org/10.12989/gae.2020.22.4.361.
  49. Mohammadimehr, M., Afshari, H., Salemi, M., Torabi, K. and Mehrabi, M. (2019), "Free vibration and buckling analyses of functionally graded annular thin sector plate in-plane loads using GDQM", Struct. Eng. Mech., 71(5), 525-544. https://doi.org/10.12989/sem.2019.71.5.525.
  50. Neves, A.M.A., Ferreira, A.J.M., Carrera, E., Roque, C.M.C., Cinefra, M., Jorge, R.M.N. and Soares, C.M.M. (2011), "Bending of FGM plates by a sinusoidal plate formulation and collocation with radial basis functions", Mech. Res. Commun., 38(5), 368-371. https://doi.org/10.1016/j.mechrescom.2011.04.011.
  51. Nguyen, D.D., Nguyen, D.K. and Hoang, T.T. (2018) "Nonlinear thermo-mechanical response of eccentrically stiffened Sigmoid FGM circular cylindrical shells subjected to compressive and uniform radial loads using the Reddy deformation shell theory", Mech. Adv. Mater. Struct., 25(13), 1156-1167. http://doi.org/10.1080/15376494.2017.1341581.
  52. Rachedi, M.A., Benyoucef, S., Bouhadra, A., Bachir Bouiadjra, R., Sekkal, M. and Benachour, A. (2020), "Impact of the homogenization models on the thermoelastic response of FG plates on variable elastic foundation", Geomech. En., 22(1), 65-80. https://doi.org/10.12989/gae.2020.22.1.065.
  53. Sahoo, B., Mehar, K., Sahoo, B., Sharma, N. and Panda, S.K. (2021), "Thermal frequency analysis of FG sandwich structure under variable temperature loading", Struct. Eng. Mech., 77(1), 57-74. http://dx.doi.org/10.12989/sem.2021.77.1.057.
  54. Sayyad, A.S. and Ghugal, Y.M. (2018), "Effects of nonlinear hygrothermomechanical loading on bending of FGM rectangular plates resting on two-parameter elastic foundation using four-unknown plate theory", J. Therm. Stresses, 1-20. https://doi.org/10.1080/01495739.2018.1469962.
  55. Selmi, A. (2020), "Exact solution for nonlinear vibration of clamped-clamped functionally graded buckled beam", Smart Struct. Syst., 26(3), 361-371. https://doi.org/10.12989/SSS.2020.26.3.361.
  56. Sepahi, O., Forouzan, M.R. and Malekzadeh, P. (2010), "Large deflection analysis of thermomechanical loaded annular FGM plates on nonlinear elastic foundation via DQM", Compos. Struct. 92, 2369-2378. https://doi.org/10.1016/j.compstruct.2010.03.011.
  57. She, G.L. (2020), "Wave propagation of FG polymer composite nanoplates reinforced with GNPs", Steel Compos. Struct., 37(1), 27-35. https://doi.org/10.12989/scs.2020.37.1.027 27.
  58. Sofiyev, A.H. (2011), "Thermal buckling of FGM shells resting on a two-parameter elastic foundation", Thin-Wall. Struct., 49(10), 1304-1311. https://doi.org/10.1016/j.tws.2011.03.018.
  59. Tayeb, T.S., Zidour, M., Bensattalah, T., Heireche, H., Benahmed, A. and Bedia, E.A. (2020), "Mechanical buckling of FG-CNTs reinforced composite plate with parabolic distribution using Hamilton's energy principle". Adv. Nano Res., 8(2), 135-148. https://doi.org/10.12989/anr.2020.8.2.135.
  60. Thai, H.T. and Choi, D.H. (2011), "A refined plate theory for functionally graded plates resting on elastic foundation", Compos. Sci. Techno., 71(16), 1850-1858. https://doi.org/10.1016/j.compscitech.2011.08.016.
  61. Thai, H.T. and Choi, D.H. (2013b), "Finite element formulation of various four unknown shear deformation theories for functionally graded plates", Finite Elem. Anal. Des., 75, 50-61. https://doi.org/10.1016/j.finel.2013.07.003.
  62. Thai, H.T., Park, M. and Choi, D.H. (2013a), "A simple refined theory for bending, buckling, and vibration of thick plates resting on elastic foundation", Int. J. Mech. Sci., 73, 40-52. https://doi.org/10.1016/j.ijmecsci.2013.03.017.
  63. Thanh, C.L., Nguyen, T.N., Vu, T.H., Khatir, S. and Abdel Wahab, M. (2020), "A geometrically nonlinear size-dependent hypothesis for porous functionally graded micro-plate", Eng. with Comput. https://doi.org/10.1007/s00366-020-01154-0.
  64. Timesli, A. (2020), "Prediction of the critical buckling load of SWCNT reinforced concrete cylindrical shell embedded in an elastic foundation", Comput. Concrete., 26(1), 53-62. https://doi.org/10.12989/cac.2020.26.1.053.
  65. Vinyas, M. (2020), "On frequency response of porous functionally graded magneto-electro-elastic circular and annular plates with different electro-magnetic conditions using HSDT", Compos. Struct., 240, 112044. https://doi.org/10.1016/j.compstruct.2020.112044.
  66. Wang, Z.X. and Shen, H.S. (2013), "Nonlinear dynamic response of sandwich plates with FGM face sheets resting on elastic foundations in thermal environments", Ocean Eng., 57, 99-110. https://doi.org/10.1016/j.oceaneng.2012.09.004.
  67. Yang, B., Ding, H.J. and Chen, W.Q. (2012), "Elasticity solutions for functionally graded rectangular plates with two opposite edges simply supported", Appl. Math. Model., 36(1), 488-503. https://doi.org/10.1016/j.apm.2011.07.020.
  68. Yaylaci, M. and Avcar, M. (2020), "Finite element modeling of contact between an elastic layer and two elastic quarter planes", Comput. Concrete, 6(2), 107-114. https://doi.org/10.12989/cac.2020.26.2.107.
  69. Yoosefian, A.R., Golmakani, M.E. and Sadeghian, M. (2020), "Nonlinear bending of functionally graded sandwich plates under mechanical and thermal load", Commun. Nonlin. Sci. Numer. Simul., 84, 105161. https://doi.org/10.1016/j.cnsns.2019.105161.
  70. Zenkour, A.M., Allam, M.N.M. and Radwan, A.F. (2014), "effects of transverse shear and normal strains on FG plates resting on elastic foundations under hygro-thermo-mechanical loading", Int. J. Appl. Mech., 6(5), 1450063. https://doi.org/10.1142/S175882511450063X.
  71. Zhu, P., Zhang, L.W. and Liew, K.M. (2014), "Geometrically nonlinear thermomechanical analysis of moderately thick functionally graded plates using a local Petrov-Galerkin approach with moving Kriging interpolation", Compos. Struct., 107, 298-314. https://doi.org/10.1016/j.compstruct.2013.08.001.
  72. Zouatnia, N. and Hadji, L. (2019), "Static and free vibration behavior of functionally graded sandwich plates using a simple higher order shear deformation theory", Adv. Mater. Res., 8(4), 313-335. https://doi.org/10.12989/amr.2019.8.4.313.

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