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A quasi 3D solution for thermodynamic response of FG sandwich plates lying on variable elastic foundation with arbitrary boundary conditions

  • Bouiadjra, Rabbab Bachir (Department of Civil Engineering, University Mustapha Stambouli of Mascara) ;
  • Mahmoudi, Abdelkader (Material and Hydrology Laboratory, University of Sidi Bel Abbes, Faculty of Technology, Civil Engineering Department) ;
  • Sekkal, Mohamed (Material and Hydrology Laboratory, University of Sidi Bel Abbes, Faculty of Technology, Civil Engineering Department) ;
  • Benyoucef, Samir (Material 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) ;
  • Tounsi, Abdelouahed (Material and Hydrology Laboratory, University of Sidi Bel Abbes, Faculty of Technology, Civil Engineering Department) ;
  • Hussain, Muzamal (Department of Mathematics, Govt. College University Faisalabad)
  • Received : 2021.05.31
  • Accepted : 2021.11.17
  • Published : 2021.12.25
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Abstract

In this paper, an analytical solution for thermodynamic response of functionally graded (FG) sandwich plates resting on variable elastic foundation is performed by using a quasi 3D shear deformation plate theory. The displacement field used in the present study contains undetermined integral terms and involves only four unknown functions with including stretching effect. The FG sandwich plate is considered to be subject to a time harmonic sinusoidal temperature field across its thickness with any combined boundary conditions. Equations of motion are derived from Hamilton's principle. The numerical results are compared with the existing results of quasi-3D shear deformation theories and an excellent agreement is observed. Several numerical examples for fundamental frequency, deflection, stress and variable elastic foundation parameter's analysis of FG sandwich plates are presented and discussed considering different material gradients, layer thickness ratios, thickness-to-length ratios and boundary conditions. The results of the present study reveal that the nature of the elastic foundation, the boundary conditions and the thermodynamic loading affect the response of the FG plate especially in the case of a thick plate.

Keywords

References

  1. Abazid, M.A., Al otebi, MS. and Sobhy, M. (2018), "A novel shear and normal deformation theory for hygrothermal bending response of FGM sandwich plates on Pasternak elastic foundation", Struct. Eng. Mech., 67(3), 219-232. https://doi.org/10.12989/sem.2018.67.3.219.
  2. Abdul Kareem Abed, Z. and Ibraheem Majeed, W. (2020), "Effect of boundary conditions on harmonic response of laminated plates", Compos. Mater. Eng., 2(2), 125-140. https://doi.org/10.12989/cme.2020.2.2.125.
  3. Abouelregal, A.A., Mohammed, W.W. and Sedighi, H.M. (2021), "Vibration analysis of functionally graded microbeam under initial stress via a generalized thermoelastic model with dual-phase lags", Arch. Appl. Mech. 91(5), 2127-2142. https://doi.org/10.1007/s00419-020-01873-2
  4. Achouri, F., Benyoucef, S., Bourada, F, Bachir Bouiadjra, R. and Tounsi, A. (2019), "Robust quasi 3D computational model for mechanical response of FG thick sandwich plate", Struct. Eng. Mech., 70(5), 571-589. https://doi.org/10.12989/sem.2019.70.5.571.
  5. Adiyaman, G., Yaylaci, M., Birinci, A., (2015), "Analytical and finite element solution of a receding contact problem", Structural Engineering and Mechanics, 54(1), 69-85., Doi: 10.12989/sem.2015.54.1.069.
  6. Ait Amar M.M., Hadj Henni, A. and Tounsi, A. (2014), "An efficient and simple refined theory for buckling and free vibration of exponentially graded sandwich plates under various boundary conditions", J. Sand. Struct. Mat., 16, 293-318. https://doi.org/10.1177/1099636214526852.
  7. Akavci, S.S. (2016), "Mechanical behavior of functionally graded sandwich plates on elastic foundation", Compos. Part B, 96, 136-152. http://dx.doi.org/10.1016/j.compositesb.2016.04.035.
  8. 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, 83, 203-215.http://dx.doi.org/10.1016/j.compositesb.2015.08.043.
  9. 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.
  10. Alibeigloo, A. and Alizadeh, M. (2015), "Static and free vibration analyses of functionally graded sandwich plates using state space differential quadrature method", Eur. J. Mech. A-Solids, 54, 252-266. https://doi.org/10.1016/j.euromechsol.2015.06.011.
  11. Ali Rachedi, M., Benyoucef, S., Bouhadra, A. Sekkal, M., Bachir Bouiadjra, R. and Benachour, A., (2020), "Impact of the homogenization models on the thermoelastic response of FG plates on variable elastic foundation", Geomech. Eng. Int. J., 22(1), 65-80. https://doi.org/10.12989/gae.2020.22.1.065.
  12. 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.
  13. Bessaim, A., Houari, M.S.A., Tounsi, A., Mahmoud, S.R. and Adda Bedia, E.A. (2013), "A new higher-order shear and normal deformation theory for the static and free vibration analysis of sandwich plates with functionally graded isotropic face sheets", J. Sand. Struct. Mat., 15(6), 671-703. https://doi.org/10.1177/1099636213498888.
  14. Daikh., A.A. and Zenkour., A.M. (2020), "Bending of functionally graded sandwich nanoplates resting on pasternak foundation under different boundary conditions", J. Appl. Comput. Mech., 6, 1245-1259. https://doi.org/10.22055/JACM.2020.33136.2166.
  15. Daouadji, T.H., and Adim, B. (2017), "Mechanical behaviour of FGM sandwich plates using a quasi 3D higher order shear and normal deformation theory", Struct. Eng. Mech. J. 61(1), 49-43. https://doi.org/10.12989/sem.2017.61.1.049.
  16. Demirhan, P.A. and Taskin, V. (2017), "Levy solution for bending analysis of functionally graded sandwich plates based on four variable plate theory", Compos. Struct., 177, 80-95. https://doi.org/10.1016/j.compstruct.2017.06.048.
  17. Eltaher, M.A. and Mohamed, S.A. (2020), "Buckling and stability analysis of sandwich beams subjected to varying axial loads", Steel Compos. Struct., 34(2), 241-260. https://doi.org/10.12989/scs.2020.34.2.241.
  18. Fu, T., Chen, Z., Yu, H., Wang, Z. and Liu, X., (2020), "Free vibration of functionally graded sandwich plates based on nth-order shear deformation theory via differential quadrature method", J. Sandwich Struct. Mater., 22(5), 1660-1680. https://doi.org/10.1177/1099636218809451.
  19. Ibrahim Majeed, W. and Abdul Kareem Abed, Z. (2019), "Buckling and pre stressed dynamics analysis of laminated composite plate with different boundary conditions", Al-Khwarizmi Eng. J., 15(1), 46-55. https://doi.org/10.22153/kej.2019.07.002.
  20. Ibrahim Majeed, W and Assad Ghani, R. (2017), "Free vibration analysis of laminated composite plates with general elastic boundary supports", J. Eng., 23(4),100-124.
  21. Hamed, M.A., Mohamed, S.A. and Eltaher, M.A. (2020), "Buckling analysis of sandwich beam rested on elastic foundation and subjected to varying axial in-plane loads", Steel Compos. Struct., 34(1), 75-89. https://doi.org/10.12989/scs.2020.34.1.075.
  22. Hammed, M.B., and Ibrahim Majeed, W. (2019), "Free vibration analysis of laminated composite plates with general boundary elastic supports under initial thermal load", Al-Khwarizmi Eng. J., 15(4), 23- 32. https://doi.org/10.22153/kej.2019.09.004.
  23. Hammed, M.B., and Ibrahim Majeed, W. (2020), "Thermal buckling analysis of laminated plates with general elastic boundary conditions", J. Eng., 26(3), 1-17. https://doi.org/10.31026/j.eng.2020.03.01.
  24. Kamarian, S., Yas, M.H. and Pourasghar, A. (2013), "Free vibration analysis of three-parameter functionally graded material sandwich plates resting on Pasternak foundations", J. Sand. Struct. Mat. 15(3), 292-308. https://doi.org/10.1177/1099636213487363.
  25. Katariya, P. V. and Panda, S.K. (2020), "Numerical analysis of thermal post-buckling strength of laminated skew sandwich composite shell panel structure including stretching effect", Steel Compos. Struct., 34(2), 279-288. https://doi.org/10.12989/SCS.2020.34.2.279.
  26. Kaur, H. and Lata, P. (2020), "Effect of thermal conductivity on isotropic modified couple stress thermoelastic medium with two temperatures", Steel Compos. Struct., 34(2), 309-319. http://dx.doi.org/10.12989/scs.2020.34.2.309.
  27. Kiani, Y. (2019), "NURBS-based thermal buckling analysis of graphene platelet reinforced composite laminated skew plates", J. Thermal Stresses, 1-19. http://ddoi.org/10.1080/01495739.2019.1673687.
  28. 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://dx.doi.org/10.1016/j.compstruct.2017.01.026.
  29. Li, H., Pang, F., Wang, X. and Li, S. (2017), "Benhmark solution for free vibration of moderately thick functionally graded sandwich sector plates on two-parameter elastic foundation with general boundary conditions", Shock Vib., 2017, 4018629, https://doi.org/10.1155/2017/4018629.
  30. Liu, M., Cheng, Y., Liu, J., (2015), "High-order free vibration analysis of sandwich plates with both functionally graded face sheets and functionally graded flexible core", Compos. Part B, 72, 97-107. https://doi.org/10.1016/j.compositesb.2014.11.037.
  31. Lyashenko, I.A., Borysiuk, V.N. and Popov, V.L. (2020), "Dynamical model of the asymmetric actuator of directional motion based on power-law graded materials", Facta Universitatis, Series: Mech. Eng., 18(2), 245-254. http://dx.doi.org/10.22190/FUME200129020L.
  32. Madenci, E. (2019), "A refined functional and mixed formulation to static analyses of fgm beams", Struct. Eng. Mech., 69(4), 427-437. http://doi.org/10.12989/sem.2019.69.4.427.
  33. Madenci, E. and Ozutok, A. (2020), "Variational approximate for high order bending analysis of laminated composite plates", Struct. Eng. Mech., 73(1), 97-108. http://doi.org/10.12989/sem.2020.73.1.097.
  34. Madenci, E., (2021a), "Free vibration and static analyses of metal-ceramic FG beams via high-order variational MFEM", Steel Compos. Struct., 39(5), 493-509. https://doi.org/10.12989/scs.2021.39.5.493.
  35. Madenci, E. (2021b), "Free vibration analysis of carbon nanotube RC nanobeams with variational approaches", Adv. Nano Res., 11(2), 157-171. http://dx.doi.org/10.12989/anr.2021.11.2.157.
  36. 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.
  37. Mahmoudi, A., Benyoucef, S., Tounsi, A., Benachour, A., Adda Bedia, E.A. and Mahmoud, S.R. (2019), "A refined quasi-3D shear deformation theory for thermo-mechanical behaviour of functionally graded sandwich plates on elastic foundations", J. Sandw.Struct.Mater., 21(6), 1906-1929. https://doi.org/10.1177/1099636217727577.
  38. Mantari, J.L. and Soares, C.G. (2014a), "A trigonometric plate theory with 5-unknowns and stretching effect for advanced composite plates", Compos. Struct., 107, 396-405. https://doi.org/10.1016/j.compstruct.2013.07.046.
  39. Mantari, J.L. and Soares, C.G. (2014b), "Four-unknown quasi-3D shear deformation theory for advanced composite plates", Compos. Struct., 109, 231-239. https://doi.org/10.1016/j.compstruct.2013.10.047.
  40. Mantari, J.L. and Granados, E.V. (2015), "A refined FSDT for the static analysis of functionally graded sandwich plates", Thin-Walled Struct., 90, 150-158. https://doi.org/10.1016/j.tws.2015.01.015.
  41. Madeh, R.A. and Ibraheem Majeed, W. (2021), "Effect of boundary conditions on thermal buckling of laminated composite shallow shell", Mater. Today: Proc., 42, 2397-2404. https://doi.org/10.1016/j.matpr.2020.12.501.
  42. Mekerbi, M., Benyoucef, S., Mahmoudi, A., Tounsi, A., Bousahla, A.A. and Mahmoud, S.R. (2019), "Thermodynamic behavior of functionally graded sandwich plates resting on different elastic foundation and with various boundary conditions", J. Sandw. Struct. Mater., https://doi.org/10.1177/1099636219851281.
  43. Meksi, R, Benyoucef, S., Mahmoudi, A., Tounsi, A., Adda Bedia, E.A. and Mahmoud, S.R. (2019), "An analytical solution for bending, buckling and vibration responses of FGM sandwich plates", J. Sandw. Struct. Mater., 21(2), 727-757. https://doi.org/10.1177/1099636217698443.
  44. Nguyen, T.K., Vo, T.P. and Thai, H.T. (2014a), "Vibration and buckling analysis of functionally graded sandwich plates with improved transverse shear stiffness based on the first-order shear deformation theory", Proc. IMechE Part C: J. Mech. Eng. Sci., 228(12), 2110-2131. https://doi.org/10.1177/0954406213516088.
  45. Nguyen, V.H., Nguyen, T.K., Thai, H.T. and Vo, T.P. (2014), "A new inverse trigonometric shear deformation theory for isotropic and functionally graded sandwich plates", Compos. Part B, 66, 233-246. https://doi.org/10.1016/j.compositesb.2014.05.012.
  46. Oner, E., Yaylaci, M. and Birinci, A. (2015), "Analytical solution of a contact problem and comparison with the results from FEM", Struct. Eng. Mech., 54(4), 607-622. https://doi.org/10.12989/sem.2015.54.4.607.
  47. Ozutok, A. and Madenci, E. (2017), "Static analysis of laminated composite beams based on higher-order shear deformation theory by using mixed-type finite element method", Int. J. Mech. Sci., 130, 234-243. https://doi.org/10.1016/j.ijmecsci.2017.06.013.
  48. Pradhan, S.C. and Murmu, T. (2009), "Thermo-mechanical vibration of FGM sandwich beam under variable elastic foundations using differential quadrature method", J. Sound Vib., 321, 342-362. https://doi.org/10.1016/j.jsv.2008.09.018.
  49. Radwan, A.F. (2019), "Effects of non-linear hygrothermal conditions on the buckling of FG sandwich plates resting on elastic foundations using a hyperbolic shear deformation theory", J. Sandw. Struct. Mater., 21(1), 289-319. https://doi.org/10.1177/1099636217693557.
  50. 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.
  51. Sedighi, H.M. (2020), "Divergence and flutter instability of magneto thermo elastic C BN hetero nanotubes conveying fluid", Acta Mechanica Sinica, 36(2), 381-396. https://doi.org/10.1007/s10409-019-00924-4.
  52. Shahsavari, D., Karami, B. and Janghorban, M. (2019), "Size-dependent vibration analysis of laminated 1. composite plates", Adv. Nano Res., 7(5), 337-349. http://dx.doi.org/10.12989/anr.2019.7.5.337.
  53. Shariati, A., Jung, D., W., Sedighi, H.M., Zur, K., K. and Habibi, M. (2020), "On the vibrations and stability of moving viscoelastic axially functionally graded nanobeams", Mater, 13(7), 1707. http://.doi.org/10.3390/ma13071707.
  54. Singh, S.J. and Harsha, S.P. (2019), "Nonlinear dynamic analysis of sandwich S-FGM plate resting on pasternak foundation under thermal environment", Europ. J. Mech. - A/Solids, 76, 155-179. https://doi.org/10.1016/j.euromechsol.2019.04.005.
  55. Sobhy, M. and Alotebi, M.S. (2018), "Transient hygrothermal analysis of FG sandwich plates lying on a visco-pasternak foundation via a simple and accurate plate theory", Arab. J. Sci. Eng., 43, 5423-5437. https://doi.org/10.1007/s13369-018-3142-1.
  56. Sobhy, M. (2013), "Buckling and free vibration of exponentially graded sandwich plates resting on elastic foundations under various boundary conditions", Compos. Struct., 99, 76-87. https://doi.org/10.1016/j.compstruct.2012.11.018.
  57. Sobhy, M. (2015), "Thermoelastic response of FGM plates with temperature-dependent properties resting on variable elastic foundations", J. Appl. Mech., 7(6), 1550082. https://doi.org/10.1142/S1758825115500829.
  58. Sobhy, M. and Zenkour, A.M. (2015), "Thermodynamical bending of FGM sandwich plates resting on Pasternak's elastic foundations", Adv. Appl. Math. Mech., 7, 116-134. https://doi.org/10.4208/aamm.2013.m143.
  59. Taibi, F.Z, Benyoucef, S., Tounsi, A., Bachir Bouiadjra, R., Adda Bedia, E.A. and Mahmoud, S.R. (2015), "A simple shear deformation theory for thermo-mechanical behaviour of functionally graded sandwich plates on elastic foundations", J. Sandw. Struct. Mater., 17(2), 99-129. https://doi.org/10.1177/1099636214554904.
  60. 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.
  61. Tran, T.T., Pham, Q.H., Nguyen-Thoi, T. and Tran, TV., (2020), "Dynamic analysis of sandwich auxetic honeycomb plates subjected to moving oscillator load on elastic foundation", Adv. Mater. Sci. Eng., 2020, 6309130. https://doi.org/10.1155/2020/6309130.
  62. Tossapanon, P. and Wattanasakulpong, N. (2020), "Flexural vibration analysis of functionally graded sandwich plates resting on elastic foundation with arbitrary boundary conditions: Chebyshev collocation technique", Sandw. Struct.Mater.,22(2), 156-189. https://doi.org/10.1177/1099636217736003.
  63. Tounsi, A., Ait Atmane, H., Khiloun, M., Sekkal, M., Taleb, O. and Bousahla, A.A. (2019), "On buckling behavior of thick advanced composite sandwich plates", Compos. Mater. Eng., 1(1), 1-19. https://doi.org/10.12989/cme.2019.1.1.001.
  64. Vinh, P.H. and Huy, L.Q. (2021), "Finite element analysis of functionally graded sandwich plates with porosity via a new hyperbolic shear deformation theory", Defence Technol. https://doi.org/10.1016/j.dt.2021.03.006.
  65. Vaghefi, R. (2020), "Thermo-elastoplastic analysis of functionally graded sandwich plates using a three-dimensional meshless model", Compos. Struct, 242, 112144. https://doi.org/10.1016/j.compstruct.2020.112144.
  66. Yaylaci, U.E., Yaylaci, M., Olmez, H. and Birinci, A., (2020). "Artificial neural network calculations for a receding contact problem", Comput. Concrete, 25(6), 551-563. https://doi.org/10.12989/cac.2020.25.6.551.
  67. Yaylaci M., Adiyaman E., Oner E. and Birinci A. (2021a). "Investigation of continuous and discontinuous contact cases in the contact mechanics of graded materials using analytical method and FEM", Comput. Concrete, 27(3), 199-210. http://dx.doi.org/10.12989/cac.2021.27.3.199.
  68. Yaylaci, M., Eyuboglu, A., Adiyaman, G., Uzun Yaylaci, E., Oner, E. and Birinci, A. (2021b), "Assessment of different solution methods for receding contact problems in functionally graded layered mediums", Mech. Mater., 154, 103730. https://doi.org/10.1016/j.mechmat.2020.103730.
  69. Yaylaci, M., Yayli, M., Yaylaci U.E., Olmez, H. and Birinci A. (2021c), "Analyzing the contact problem of a functionally graded layer resting on an elastic half plane with theory of elasticity, finite element method and multilayer perceptron", Struct. Eng. Mech., 78(5), 585-597. https://doi.org/10.12989/sem.2021.78.5.585.
  70. Yaylaci, M. and Birinci, A. (2013), "The receding contact problem of two elastic layers supported by two elastic quarter planes", Struct. Eng. Mech., 48(2), 241-255. https://doi.org/10.12989/sem.2013.48.2.241
  71. Yaylaci, M., Adiyaman, E., Oner, E. and Birinci, A. (2020), "Examination of analytical and finite element solutions regarding contact of a functionally graded layer", Struct. Eng. Mech., 76(3), 325-336. http://dx.doi.org/10.12989/sem.2020.76.3.325.
  72. Yaylaci, M. (2016), "The investigation crack problem through numerical analysis", Struct. Eng. Mech., 57(6), 1143-1156. http://doi.org/10.12989/sem.2016.57.6.1143.
  73. Yang, C., Jin, G., Ye, X., and Liu, Z. (2016), "A modified Fourier-Ritz solution for vibration and damping analysis of sandwich plates with viscoelastic and functionally graded materials", Int. J. Mech. Sci., 106, 1-18. https://doi.org/10.1016/j.ijmecsci.2015.11.031.
  74. Younesian, D., Hosseinkhani, A., Askari, H. and Esmailzadeh, E. (2019), "Elastic and viscoelastic foundations: a review on linear and nonlinear vibration modeling and applications", Nonlinear Dyn., 97, 853-895. https://doi.org/10.1007/s11071-019-04977-9.
  75. 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. Int. J., 8(4), 313-335. https://doi.org/10.12989/amr.2019.8.4.313.