Geomechanics and Engineering

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Visco-elastic foundation effect on buckling response of exponentially graded sandwich plates under various boundary conditions

  • Mimoun, Bennedjadi (Material and Hydrology Laboratory, University of Sidi Bel Abbes, Faculty of Technology, Civil Engineering Department) ;
  • Salem Mohammed, Aldosari (Enhanced Composite and Structures Centre, School of Aerospace, Transport, and Manufacturing, Cranfield University) ;
  • Abdelbaki, Chikh (Material and Hydrology Laboratory, University of Sidi Bel Abbes, Faculty of Technology, Civil Engineering Department) ;
  • Abdelhakim, Kaci (Material and Hydrology Laboratory, University of Sidi Bel Abbes, Faculty of Technology, Civil Engineering Department) ;
  • Abdelmoumen Anis, Bousahla (Laboratoire de Modelisation et Simulation Multi-echelle, Universite de Sidi Bel Abbes) ;
  • Fouad, Bourada (Material and Hydrology Laboratory, University of Sidi Bel Abbes, Faculty of Technology, Civil Engineering Department) ;
  • Abdeldjebbar, Tounsi (Industrial Engineering and Sustainable Development Laboratory, University of Relizane, Faculty of Science & Technology, Mechanical Engineering Department) ;
  • Kouider Halim, Benrahou (Material and Hydrology Laboratory, University of Sidi Bel Abbes, Faculty of Technology, Civil Engineering Department) ;
  • Abdelouahed, Tounsi (Material and Hydrology Laboratory, University of Sidi Bel Abbes, Faculty of Technology, Civil Engineering Department)
  • Received : 2021.04.21
  • Accepted : 2023.01.03
  • Published : 2023.01.25
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Abstract

In the present work, a simple and refined shear deformation theory is used to analyze the effect of visco-elastic foundation on the buckling response of exponentially-gradient sandwich plates under various boundary conditions. The proposed theory includes indeterminate integral variables kinematic with only four generalized parameters, in which no shear correction factor is used. The visco-Pasternak's foundation is taken into account by adding the influence of damping to the usual foundation model which characterized by the linear Winkler's modulus and Pasternak's foundation modulus. The four governing equations for FGM sandwich plates are derived by employing principle of virtual work. To solve the buckling problem, Galerkin's approach is utilized for FGM sandwich plates for various boundary conditions. The analytical solutions for critical buckling loads of several types of powerly graded sandwich plates resting on visco-Pasternak foundations under various boundary conditions are presented. Some numerical results are presented to indicate the effects of inhomogeneity parameter, elastic foundation type, and damping coefficient of the foundation, on the critical buckling loads.

Keywords

References

  1. Abdelrahman, W.G. (2020), "Effect of material transverse distribution profile on buckling of thick functionally graded material plates according to TSDT", Struct. Eng. Mech., 74(1), 83-90. http://dx.doi.org/10.12989/sem.2020.74.1.083.
  2. Adiyaman, G., Yaylaci, M. and Birinci, A. (2015), "Analytical and finite element solution of a receding contact problem", Struct. Eng. Mech., 54(1), 69-85. https://doi.org/10.12989/sem.2015.54.1.069.
  3. 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.
  4. Ait Amar Meziane, M., Abdelaziz, H.H. 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. Sandw. Struct. Mater., 16(3), 293-318. https://doi.org/10.1177/1099636214526852.
  5. 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.
  6. Akbas, S.D. (2015), "Wave propagation of a functionally graded beam in thermal environments", Steel Compos. Struct., 19(6), 1421-1447. http://dx.doi.org/10.12989/scs.2015.19.6.1421.
  7. Akgoz, B. and Civalek, O. (2013), "Buckling analysis of functionally graded microbeams based on the strain gradient theory", Acta Mechanica, 224(9), 2185-2201. https://doi.org/10.1007/s00707-013-0883-5.
  8. Allahkarami, F., Satouri, S. and Najafizadeh, M.M. (2016), "Mechanical buckling of two-dimensional functionally graded cylindrical shells surrounded by Winkler-Pasternak elastic foundation", Mech. Adv. Mater. Struct., 23(8), 873-87. http://dx.doi.org/10.1080/15376494.2015.1036181.
  9. Alnujaie, A., Akbas, S.D., Eltaher, M.A. and Assie, A. (2021), "Forced vibration of a functionally graded porous beam resting on viscoelastic foundation", Geomech. Eng., 24(1), 91-103. https://doi.org/10.12989/gae.2021.24.1.091.
  10. Anderson, T.A. (2003), "A 3-D elasticity solution for a sandwich composite with functionally graded core subjected to transverse loading by a rigid sphere", Compos. Struct., 60(3), 265-274. https://doi.org/10.1016/s0263-8223(03)00013-8.
  11. Arefi, M. and Zur, K.K. (2020), "Free vibration analysis of functionally graded cylindrical nanoshells resting on Pasternak foundation based on two-dimensional analysis", Steel Compos. Struct., 34(4), 615-623. https://doi.org/10.12989/scs.2020.34.4.615.
  12. Asiri, S.A., Akbas, S.D. and Eltaher, M.A. (2020), "Damped dynamic responses of a layered functionally graded thick beam under a pulse load", Struct. Eng. Mech., 75(6), 713-722. https://doi.org/10.12989/sem.2020.75.6.713.
  13. 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.
  14. 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.
  15. Balubaid, M., Abdo, H., Ghandourah, E. and Mahmoud, S.R. (2021), "Dynamical behavior of the orthotropic elastic material using an analytical solution", Geomech. Eng., 25(4), 331-339. https://doi.org/10.12989/gae.2021.25.4.331.
  16. Bashiri, A.H., Akbas, S.D., Abdelrahman, A.A., Assie, A., Eltaher, M.A. and Mohamed, E.F. (2021), "Vibration of multilayered functionally graded deep beams under thermal load", Geomech. Eng., 24(6), 545-557. https://doi.org/10.12989/gae.2021.24.6.545.
  17. Bhangale, R.K. andGanesan, N. (2006), "Thermoelastic buckling and vibration behavior of a functionally graded sandwich beam with constrained viscoelastic core", J. Sound Vib., 295(1-2), 294-316. https://doi.org/10.1016/j.jsv.2006.01.026.
  18. 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., 113223. https://doi.org/10.1016/j.compstruct.2020.113223.
  19. Bouiadjra, R.B., Bachiri, A., Benyoucef, S., Fahsi, B. and Bernard, F. (2020), "An investigation of the thermodynamic effect on the response of FG beam on elastic foundation", Struct. Eng. Mech., 76(1), 115-127. https://doi.org/10.12989/sem.2020.76.1.115.
  20. 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.
  21. Chami, K, Messafer, T. and Hadji, L. (2020), "Analytical modeling of bending and free vibration of thick advanced composite beams resting on Winkler-Pasternak elastic foundation", Earthq. Struct., 19(2), 91-101. https://doi.org/10.12989/eas.2020.19.2.091.
  22. Cuong-Le, T., Nguyen, K.D., Nguyen-Trong, N., Khatir, S., Nguyen-Xuan, H. and Abdel-Wahab, M. (2020a), "A threedimensional solution for free vibration and buckling of annular plate, conical, cylinder and cylindrical shell of FG porouscellular materials using IGA", Compos. Struct., 259, 113216. https://doi.org/10.1016/j.compstruct.2020.113216.
  23. Cuong-Le, T., Nguyen, K.D., Hoang-Le, M., Sang-To, T., Phan-Vu, P. and Abdel Wahab, M. (2022a), "Nonlocal strain gradient IGA numerical solution for static bending, free vibration and buckling of sigmoid FG sandwich nanoplate", Physica B: Condensed Matter, 631, 413726. https://doi.org/10.1016/j.physb.2022.413726.
  24. Cuong-Le, T., Nguyen, K.D., Lee, J., Rabczuk, T. and NguyenXuan, H. (2022b), "A 3D nano scale IGA for free vibration and buckling analyses of multi-directional FGM nanoshells", Nanotechnology, 33(6), 065703. https://doi.org/10.1088/1361-6528/ac32f9.
  25. Cuong-Le, T., Nguyen, T.N., Vu, T.H., Khatir, S. and Abdel Wahab, M. (2020b), "A geometrically nonlinear size-dependent hypothesis for porous functionally graded micro-plate", Eng. with Comput., 38(2022), 449-460. https://doi.org/10.1007/s00366-020-01154-0.
  26. 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.
  27. Dehsaraji, M.L., Arefi, M. and Loghman, A. (2020), "Three dimensional free vibration analysis of functionally graded nano cylindrical shell considering thickness stretching effect", Steel Compos. Struct., 34(5), 657-670. https://doi.org/10.12989/scs.2020.34.5.657.
  28. Ebrahimi, F. And Barati, M.R. (2016), "A nonlocal higher-order refined magneto-electro-viscoelastic beam model for dynamic analysis of smart nanostructures", Int. J. Eng. Sci., 107, 183-196. https://doi.org/10.1016/j.ijengsci.2016.08.001.
  29. Ebrahimi, F. and Barati, M.R. (2016), "Vibration analysis of viscoelastic inhomogeneous nanobeams resting on a viscoelastic foundation based on nonlocal strain gradient theory incorporating surface and thermal effects", Acta Mechanica, 228(3), 1197-1210. https://doi.org/10.1007/s00707-016-1755-6.
  30. Eltaher, M.A. and Akbas, S.D. (2020), "Transient response of 2D functionally graded beam structure", Struct. Eng. Mech., 75(3), 357-367. https://doi.org/10.12989/SEM.2020.75.3.357.
  31. Etemadi, E., AfaghiKhatibi, A. and Takaffoli, M. (2009), "3D finite element simulation of sandwich panels with a functionally graded core subjected to low velocity impact", Compos. Struct., 89(1), 28-34. https://doi.org/10.1016/j.compstruct.2008.06.01.
  32. Fan, Y., Xiang, Y. and Shen, H.S. (2018), "Nonlinear forced vibration of FG-GRC laminated plates resting on viscoPasternak foundations", Compos. Struct., https://doi.org/10.1016/j.compstruct.2018.10.084.
  33. Fan, Y., Xiang, Y., Shen, H.S. and Hui, D. (2018), "Nonlinear lowvelocity impact response of FG-GRC laminated plates resting on visco-elastic foundations", Compos. Part B: Eng., 144, 184-194. https://doi.org/10.1016/j.compositesb.2018.02.016.
  34. Feng, H., Shen, D. and Tahouneh, V. (2020), "Vibration analysis of sandwich sector plate with porous core and functionally graded wavy carbon nanotube-reinforced layers", Steel Compos. Struct. 37(6), 711-731. http://dx.doi.org/10.12989/scs.2020.37.6.711.
  35. Ghannadpour, S.A.M., Mohammadi, B. and Fazilati, J. (2013), "Bending, buckling and vibration problems of nonlocal Euler beams using Ritz method", Compos. Struct., 96, 584-589. https://doi.org/ 10. 1016/j. compstruct. 2012. 08. 024. https://doi.org/10.1016/j.compstruct.2012.08.024
  36. Ghasemabadian, M.A. and Kadkhodayan, M. (2016), "Investigation of buckling behavior of functionally graded piezoelectric (FGP) rectangular plates under open and closed circuit conditions", Struct. Eng. Mech., 60(2), 271-299. https://doi.org/10.12989/sem.2016.60.2.271.
  37. 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.
  38. 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.
  39. Hosseini, M., Jamalpoor, A. and Bahreman, M. (2016), "Smallscale effects on the free vibrational behavior of embedded viscoelastic double-nanoplate-systems under thermal environment", Acta Astronautica, 129, 400-409. https://doi.org/10.1016/j.actaastro.2016.10.001.
  40. Hosseini, M., Jamalpoor, A. and Fath, A. (2016), "Surface effect on the biaxial buckling and free vibration of FGM nanoplate embedded in visco-Pasternak standard linear solid-type of foundation", Meccanica, 52(6), 1381-1396. https://doi.org/10.1007/s11012-016-0469-0.
  41. Huang, Z.Y., Lu, C.F. and Chen, W.Q. (2008), "Benchmark solutions for functionally graded thick plates resting on Winkler-Pasternak elastic foundations", Compos. Struct., 85(2), 95-104. https://doi.org/10.1016/j.compstruct.2007.10.010.
  42. Karami, B. and Janghorban, M. (2020), "On the mechanics of functionally graded nanoshells", Int. J. Eng. Sci., 153, 103309. https://doi.org/10.16/j.ijengsci.2020.103309
  43. 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", Stee Compos. Struct., 34(2), 279-288. https://doi.org/10.12989/SCS.2020.34.2.279.
  44. Kertesz, S., Szerencses, S.G., Vereb, G., Csanadi, J., Laszlo, Z., Hodur, C. (2020), "Single- and multi-stage dairy wastewater treatment by vibratory membrane separation processes", Membrane Water Treatment, 11(6), 383-389. https://doi.org/10.12989/mwt.2020.11.6.383.
  45. Khatir, S., Tiachacht, S., Le Thanh, C., Ghandourah, E., Mirjalili, S. and Wahab, M.A. (2021), "An improved Artificial Neural Network using Arithmetic Optimization Algorithm for damage assessment in FGM composite plates", Compos. Struct., 273, 114287. https://doi.org/10.1016/j.compstruct.2021.114287.
  46. Khatir, S., Tiachacht, S., Thanh, C.L., Bui, T.Q. and Wahab, M.A. (2019), "Damage assessment in composite laminates using ANN-PSO-IGA and Cornwell indicator", Compos. Struct., 230, 111509. https://doi.org/10.1016/j.compstruct.2019.111509
  47. Kim, Y.W. (2015), "Free vibration analysis of FGM cylindrical shell partially resting on Pasternak elastic foundation with an oblique edge", Compos. Part B: Eng., 70, 263-276. https://doi.org/10.1016/j.compositesb.2014.11.024.
  48. Koizumi, M. (1993), "The concept of FGM", Ceramic Transactions, Functionally Gradient Materials., 34, 3-10.
  49. Kunbar, L.A.H., Hamad, L.B., Ahmed, R.A. and Faleh, N.M. (2020), "Nonlinear vibration of smart nonlocal magneto-electroelastic beams resting on nonlinear elastic substrate with geometrical imperfection and various piezoelectric effects", Smart Struct. Syst., 25(5), 619-630. https://doi.org/10.12989/SSS.2020.25.5.619.
  50. Li, J. and Zhang, Y. (2021), "Multiscale calculation results of the flow behavior in micro/nano porous filtration membrane with the adsorbed layer-fluid interfacial slippage", Membrane Water Treatment, 12(3), 107-114. https://doi.org/10.12989/mwt.2021.12.3.107.
  51. Li, M., GuedesSoares, C. and Yan, R. (2021), "Free vibration analysis of FGM plates on Winkler/Pasternak/Kerr foundation by using a simple quasi-3D HSDT", Compos. Struct., 264, 113643. https://doi.org/10.1016/j.compstruct.2021.113643.
  52. Li, Z.M. and Yang, D.Q.(2016), "Thermal postbuckling analysis of anisotropic laminated beams with tubular cross-section based on higher-order theory", Ocean Eng., 115, 93-106. https://doi.org/10.1016/j.oceaneng.2016.02.017.
  53. 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.
  54. 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.
  55. Mantari, J.L. and Granados, E.V. (2015a), "Dynamic analysis of functionally graded plates using a novel FSDT", Compos. Part B: Eng., 75, 148-155. https://doi.org/10.1016/j.compositesb.2015.01.028.
  56. Mantari, J.L. and Granados, E.V. (2015b), "A refined FSDT for the static analysis of functionally graded sandwich plates", ThinWalled Struct., 90, 150-158. https://doi.org/10.1016/j.tws.2015.01.015.
  57. 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.
  58. Mindlin, R.D. (1951), "Thickness-shear and flexural vibrations of crystal plates", J. Appl. Phys., 22(3), 316-323. https://doi.org/10.1063/1.1699948.
  59. Navale, K.U. and Pise, C.P. (2021), "A review on high order shear deformation theory for orthotropic composite laminates", Int. J. Eng. Res. Technol., 10, 477-481. https://doi.org/10.17577/IJERTV10IS010156.
  60. Naz, A., Masood, H., Ehsan, S. and Tahir, T. (2020), "Removal of acid black 1 by Acacia Concinna; adsorption kinetics, isotherm and thermodynamic study", Membrane Water Treatment, 11(6), 407-416. https://doi.org/10.12989/sem.2020.11.6.407.
  61. Nebab, M., AitAtmane, H., Bennai, R. and Tahar, B. (2019), "Effect of nonlinear elastic foundations on dynamic behavior of FG plates using four-unknown plate theory", Earthq. Struct., 17(5), 447-462. https://doi.org/10.12989/eas.2019.17.5.447.
  62. Nebab, M., Benguediab, S., AitAtmane, H and Bernard, F. (2020), "A simple quasi-3D HDST for dynamic behavior of advanced composite plates with the effect of variables elastic foundations", Geomech. Eng., 22(5), 415-431. https://doi.org/10.12989/gae.2020.22.5.415.
  63. Neves, A.M.A., Ferreira, A.J.M., Carrera, E., Cinefra, M., Jorge, R.M.N. and Soares, C.M.M. (2012), "Buckling analysis of sandwich plates with functionally graded skins using a new quasi-3D hyperbolic sine shear deformation theory and collocation with radial basis functions", ZAMM - J. Appl. Math. Mech. / Zeitschrift Fur Angewandte Mathematik Und Mechanik, 92(9), 749-766. https://doi.org/10.1002/zamm.201100186.
  64. 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.
  65. Onyeka, F.C. and Edozie, O. T. (2021), "Analytical solution of thick rectangular plate with clamped and free support boundary condition using polynomial shear deformation theory", Adv. Sci. Technol. Eng. Syst. J., 6(1), 1427-1439. https://doi.org/10.25046/aj0601161.
  66. Panjehpour, M., Loh, E.W.K. and Deepak, TJ. (2018), "Structural Insulated Panels: State-of-the-Art", Trends in civil Engineering and its Architecture, 3(1), 336-340. https://doi.org/10.32474/TCEIA.2018.03.000151.
  67. Pasternak (1954), "On a new method of analysis of an elastic foundation by means of two foundation constants", Gosudarstvennoe Izdatelstvo Literaturipo Stroitelstvui Arkhitekture, Moscow.
  68. Pasternak, P.L. (1954), "On a new method of analysis of an elastic foundation by means of two foundation constants", Gosudarstvennoe Izdatelstro Liberaturipo Stroitelstvui Arkhitekture, Moscow.
  69. Rachedi, M.A., Benyoucef, S., Bouhadra, A., BachirBouiadjra, R., Sekkal, M. and Benachour, A. (2020), "Impact of the homogenization models on the thermoelastic response of FG plates on variable elastic foundation", Geomech. Eng., 22(1), 65-80. https://doi.org/10.12989/gae.2020.22.1.065.
  70. Rahmani, M., Mohammadi, Y., Kakavand, F. and Raeisifard, H. (2020), "Vibration Analysis of Different Types of Porous FG Conical Sandwich Shells in Various Thermal Surroundings", J. Appl. Comput. Mech., 6(3), 416-432. https://doi.org/10.22055/jacm.2019.29442.1598.
  71. 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., 33(6), 865-875. https://doi.org/10.12989/scs.2019.33.6.865.
  72. Reissner, E. (1944), "On the theory of bending of elastic plates", J. Math. Phys., 23(1-4), 184-191. https://doi.org/10.1002/sapm1944231184.
  73. Reissner, E. (1945), "The effect of transverse shear deformation on the bending of elastic plates", J. Appl. Mech., 12(2), 69-77. https://doi.org/10.1115/1.4009435.
  74. Saadatmorad, M., Jafari-Talookolaei, R.A., Pashaei, M.H. and Khatir, S. (2021), "Damage detection on rectangular laminated composite plates using wavelet based convolutional neural network technique", Compos. Struct., 278, 114656. https://doi.org/10.1016/j.compstruct.2021.114656.
  75. Sadoughifar, A., Farhatnia, F., Izadinia, M. and Talaeetaba, S.B. (2020), "Size-dependentbuckling behaviour of FG annular/circular thick nanoplates with porosities resting on Kerr foundation based on new hyperbolic shear deformation theory", Struct. Eng. Mech., 73(3), 225-238.  https://doi.org/10.12989/sem.2020.73.3.225.
  76. 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.
  77. Shahmohammadi, M.A., Azhari, M. and Saadatpour, M.M. (2020), "Free vibration analysis of sandwich FGM shells using isogeometric B-spline finite strip method", Steel Compos. Struct., 34(3), 361-376. https://doi.org/10.12989/scs.2020.34.3.361.
  78. Shen, H.S. and Yang, D.Q. (2014), "Nonlinear vibration of anisotropic laminated cylindrical shells with piezoelectric fiber reinforced composite actuators", Ocean Eng., 80, 36-49. https://doi.org/10.1016/j.oceaneng.2014.01.016.
  79. Shodja, H., Haftbaradaran, H. and Asghari, M. (2007), "A thermoelasticity solution of sandwich structures with functionally graded coating", Compos. Sci. Technol., 67(6), 1073-1080. https://doi.org/10.1016/j.compscitech.2006.06.001.
  80. Sobamowo, G. (2020), "Finite element thermal analysis of a moving porous fin with temperature-variant thermal conductivity and internal heat generation", Reports in Mech. Eng., 1(1), 110-127. https://doi.org/10.31181/rme200101110s.
  81. 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.
  82. Sobhy, M. and Zenkour, A.M. (2018), "Nonlocal thermal and mechanical buckling of nonlinear orthotropic viscoelastic nanoplates embedded in a visco-pasternak medium", Int. J. Appl. Mech., 10(8), 1850086. https://doi.org/10.1142/S1758825118500862.
  83. 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.
  84. Tj, H.G., Mikami, T., Kanie, S. andSato, M. (2006), "Free vibration characteristics of cylindrical shells partially buried in elastic foundations", J. Sound Vib., 290(3-5), 785-793. https://doi.org/10.1016/j.jsv.2005.04.014.
  85. Tornabene, F., Fantuzzi, N., Viola, E. and Reddy, J.N. (2014), "Winkler-Pasternak foundation effect on the static and dynamic analyses of laminated doubly-curved and degenerate shells and panels", Compos. Part B: Eng., 57, 269-296. https://doi.org/10.1016/j.compositesb.2013.06.020.
  86. Trabelsi, S., Zghal, S. and Dammak, F. (2020), "Thermo-elastic buckling and post-buckling analysis of functionally graded thin plate and shell structures", J. Brazilian Soc. Mech. Sci. Eng., 42(5), 1-22. https://doi.org/10.1007/s40430-020-02314-5.
  87. Tran, T.M. and Cuong-Le, T. (2022), "A nonlocal IGA numerical solution for free vibration and buckling analysis of porous sigmoid functionally graded (P-SFGM) nanoplate", Int. J. Struct. Stab. Dyn., 22(16), 2250193. https://doi.org/10.1142/S0219455422501930.
  88. Vinh, P.V. (2021), "Formulation of a new mixed four-node quadrilateral element for static bending analysis of variable thickness functionally graded material plates", Math. Probl. Eng., 2021, 23. https://doi.org/10.1155/2021/6653350.
  89. 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.
  90. Wang, Y.Q. and Zu, J.W. (2017), "Vibration behaviors of functionally graded rectangular plates with porosities and moving in thermal environment", Aerosp. Sci. Technol., 69, 550-562. https://doi.org/10.1016/j.ast.2017.07.023.
  91. Wang, Y.Q., Huang, X.B. and Li, J. (2016), "Hydroelastic dynamic analysis of axially moving plates in continuous hot-dip galvanizing process", Int. J. Mech. Sci., 110, 201-216. https://doi.org/10.1016/j.ijmecsci.2016.03.010.
  92. Wang, Z.X. andShen, 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.
  93. Winkler, E. (1867), "Die Lehre von Elastizitat und Festigkeit (on ElasticityandFixity)", Dominicus, Prague.
  94. Yaghoobi, H. and Yaghoobi, P. (2013), "Buckling analysis of sandwich plates with FGM face sheets resting on elastic foundation with various boundary conditions: an analytical approach", Meccanica, 48(8), 2019-2035. https://doi.org/10.1007/s11012-013-9720-0.
  95. Yamanoushi, M., Koizumi, M., Hiraii, T. and Shiota, I. (1990), "Proceedings of the first international symposium on functionally gradient materials", Japan.
  96. Yaylaci, E.U., Yaylaci, M., Olmez, H. and Birinci, A. (2020a), "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.
  97. Yaylaci, M. (2016), "The investigation crack problem through numerical analysis", Structural Engineering and Mechanics, An Int'l Journal, 57(6), 1143-1156. https://doi.org/10.12989/sem.2016.57.6.1143
  98. 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.
  99. Yaylaci, M., Adiyaman, G., Oner, E. and Birinci, A. (2020b), "Examination of analytical and finite element solutions regarding contact of a functionally graded layer", Struct. Eng. Mech., 76(3), 325-336. https://doi.org/10.12989/sem.2020.76.3.325.
  100. Yaylaci, M., Adiyaman, G., Oner, E. and Birinci, A. (2021c), "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. https://doi.org/10.12989/cac.2021.27.3.199.
  101. Yaylaci, M., Eyuboglu, A., Adiyaman, G., Yaylaci, E.U., Oner, E. and Birinci, A. (2021a), "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.
  102. Yaylaci, M., Yayli, M., Yaylaci, E.U., Olmez, H. and Birinci, A. (2021d), "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.
  103. Zamani, H.A., Aghdam, M.M. and Sadighi, M. (2017), "Free vibration analysis of thick viscoelastic composite plates on visco-Pasternak foundation using higher-order theory", Compos. Struct., 182, 25-35. https://doi.org/10.1016/j.compstruct.2017.08.101.
  104. Zamani, H.A., Aghdam, M.M. and Sadighi, M. (2017), "Free vibration analysis of thick viscoelastic composite plates on visco-Pasternak foundation using higher-order theory", Compos. Struct., 182, 25-35. https://doi.org/10.1016/j.compstruct.2017.08.101.
  105. Zenkour, A.M. (2018), "A quasi-3D refined theory for functionally graded single-layered and sandwich plates with porosities", Compos. Struct., 201, 38-48. https://doi.org/10.1016/j.compstruct.2018.05.147.
  106. Zenzen, R., Khatir, S., Belaidi, I., Le Thanh, C. and Wahab, M.A. (2020), "A modified transmissibility indicator and Artificial Neural Network for damage identification and quantification in laminated composite structures", Compos. Struct., 248, 112497. https://doi.org/10.1016/j.compstruct.2020.112497.
  107. Zhang, W. (2001), "Global and chaotic dynamics for a parametrically excited thin plate", J. Sound Vib., 239(5), 1013-1036. https://doi.org/10.1006/jsvi.2000.3182.
  108. 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.