Steel and Composite Structures

  • 제44권3호
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  • Pages.353-369
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  • 2022
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  • 1229-9367(pISSN)
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  • 1598-6233(eISSN)
테크노프레스 (Techno-Press)
권호 표지
DOI QR코드

DOI QR Code

Coupled effect of variable Winkler-Pasternak foundations on bending behavior of FG plates exposed to several types of loading

  • Himeur, Nabil (Reactive Materials and Systems Laboratory (LMSR), Department of mechanical Engineering, University of Sidi Bel Abbes, Faculty of Technology) ;
  • Mamen, Belgacem (Material and Hydrology Laboratory, University of Sidi Bel Abbes, Faculty of Technology) ;
  • Benguediab, Soumia (Department of Civil Engineering and Hydraulic, University of Saida) ;
  • Bouhadra, Abdelhakim (Material and Hydrology Laboratory, University of Sidi Bel Abbes, Faculty of Technology) ;
  • Menasria, Abderrahmane (Material and Hydrology Laboratory, University of Sidi Bel Abbes, Faculty of Technology) ;
  • Bouchouicha, Benattou (Reactive Materials and Systems Laboratory (LMSR), Department of mechanical Engineering, University of Sidi Bel Abbes, Faculty of Technology) ;
  • Bourada, Fouad (Material and Hydrology Laboratory, University of Sidi Bel Abbes, Faculty of Technology) ;
  • Benguediab, Mohamed (Reactive Materials and Systems Laboratory (LMSR), Department of mechanical Engineering, University of Sidi Bel Abbes, Faculty of Technology) ;
  • Tounsi, Abdelouahed (Material and Hydrology Laboratory, University of Sidi Bel Abbes, Faculty of Technology)
  • 투고 : 2021.08.22
  • 심사 : 2022.07.15
  • 발행 : 2022.08.10
⟨ 이전 논문 다음 논문 ⟩

초록

This study attempts to shed light on the coupled impact of types of loading, thickness stretching, and types of variation of Winkler-Pasternak foundations on the flexural behavior of simply- supported FG plates according to the new quasi-3D high order shear deformation theory, including integral terms. A new function sheep is used in the present work. In particular, both Winkler and Pasternak layers are non-uniform and vary along the plate length direction. In addition, the interaction between the loading type and the variation of Winkler-Pasternak foundation parameters is considered and involved in the governing equilibrium equations. Using the virtual displacement principle and Navier's solution technique, the numerical results of non-dimensional stresses and displacements are computed. Finally, the non-dimensional formulas' results are validated with the existing literature, and excellent agreement is detected between the results. More importantly, several complementary parametric studies with the effect of various geometric and material factors are examined. The present analytical model is suitable for investigating the bending of simply-supported FGM plates for special technical engineering applications.

키워드

참고문헌

  1. Abdulrazzaq, M.A., Fenjan, R.M., Ahmed, R.A. and Faleh, N.M. (2019), "Thermal buckling of nonlocal clamped exponentially graded plate according to a secant function based refined theory", 35(1), 147-157. http://dx.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. Ahmed, R.A., Khalaf, B.S., Raheef, K.M., Fenjan, R.M. and Faleh, N.M. (2021), "Investigating dynamic response of nonlocal functionally graded porous piezoelectric plates in thermal environment", 40(2), 243-254. https://doi.org/10.12989/scs.2021.40.2.243.
  4. 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.
  5. Akbas, S.D. (2015), "Wave propagation of a functionally graded beam in thermal environments", Steel Compost. Struct., 19(6), 1421-1447. https://doi.org/10.12989/SCS.2015.19.6.1421.
  6. Akbas, S.D. (2019), "Hygro-Thermal Nonlinear Analysis of a Functionally Graded Beam", J. Appl. Comput. Mech., 5(2), 477-485. https://doi.org/10.22055/jacm.2018.26819.1360.
  7. 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.
  8. Asrari, R., Ebrahimi, F. and Kheirikhah, M.M. (2020), "On postbuckling characteristics of functionally graded smart magnetoelectro-elastic nanoscale shells", 9(1), 33-45. http://dx.doi.org/10.12989/anr.2020.9.1.033.
  9. Attia, M.A. (2017), "On the mechanics of functionally graded nanobeams with the account of surface elasticity", J. Eng. Sci., 115,73-101. https://doi.org/10.1016/j.ijengsci.2017.03.011.
  10. Avcar, M. (2016), "Effects of material non-homogeneity and two parameters elastic foundation on fundamental frequency parameters of Timoshenko beams", Acta Phys. Pol. A, 130(1), 375-378. https://doi.org/10.12693/APhysPolA.130.375.
  11. Avcar, M. (2019), "Free vibration of imperfect sigmoid and power law functionally graded beams", Steel Compost. Struct., 30(6), 603-615. https://doi.org/10.12989/SCS.2019.30.6.603.
  12. Avcar, M. and Mohammed, W.K.M. (2018), "Free vibration of functionally graded beams resting on Winkler-Pasternak foundation", Arab. J. Geosci. 11(10), 232. https://doi.org/10.1007/s12517-018-3579-2.
  13. Behravan Rad, A. (2015), "Thermo-elastic analysis of functionally graded circular plates resting on a gradient hybrid foundation", Appl. Math. Comput., 256, 276-298. https://doi.org/10.1016/j.amc.2015.01.026.
  14. Beldjelili, Y., Merazi, M., Boutaleb, S. and Hellal, H. (2021), "Analytical solution for static bending analysis of functionally graded plates with porosities", Frattura ed Integrita Strutturale, 15(55), 65-75. https://doi.org/10.3221/IGF-ESIS.55.05.
  15. 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.
  16. Boulal, A., Bensattalah, T., Karas, A., Zidour, M., Heireche, H. and Bedia, E.A. (2020), "Buckling of carbon nanotube reinforced composite plates supported by Kerr foundation using Hamilton's energy principle", 73(2), 209-223. https://doi.org/10.12989/sem.2020.73.2.209.
  17. Cao, Y., Qian, X., Fan, Q. and Ebrahimi, F. (2020), "Mechanical analysis of functionally graded spherical panel resting on elastic foundation under external pressure", 74(2), 297-311. http://dx.doi.org/10.12989/sem.2020.74.2.297.
  18. Civalek, O. and Avcar, M. (2020), "Free vibration and buckling analyses of CNT reinforced laminated non-rectangular plates by discrete singular convolution method", Eng. Comput., 1-33. https://doi.org/10.1007/s00366-020-01168-8.
  19. 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.
  20. Daouadji, T.A., Belkacem, A. and Benferhat, R. (2016), "Bending analysis of an imperfect FGM plates under hygro-thermomechanical loading with analytical validation", Adv. Mater. Res., 5(1), 5-53. http://dx.doi.org/10.12989/amr.2016.5.1.035.
  21. 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.
  22. Dehshahri, K., Nejad, M. Z., Ziaee, S., Niknejad, A. and Hadi, A. (2020), "Free vibrations analysis of arbitrary threedimensionally FGM nanoplates", 8(1), 115-134. http://dx.doi.org/10.12989/anr.2020.8.2.115.
  23. Farshad Heidari, Ahmad Afsari and Maziar Janghorban (2020), "Several models for bending and buckling behaviors of FGCNTRCs with piezoelectric layers including size effects", 9(3), 193-210. http://dx.doi.org/10.12989/anr.2020.9.3.193.
  24. Fenjan, R.M., Ahmed, R.A., Faleh, N.M. and Hani, F.M. (2020), "Static stability analysis of smart nonlocal thermo-piezomagnetic plates via a quasi-3D formulation", 26(1), 77-87. http://dx.doi.org/10.12989/sss.2020.26.1.077.
  25. Fenjan, R.M., Moustafa, N.M. and Faleh, N.M. (2020), "Scaledependent thermal vibration analysis of FG beams having porosities based on DQM", 8(4), 283-292. http://dx.doi.org/10.12989/anr.2020.8.4.283.
  26. Froio, D. and Rizzi, E. (2015), "Analytical solution for the elastic bending of beams lying on a variable Winkler support", Acta Mechanica, 227(4), 1157-1179. https://doi.org/10.1007/s00707-015-1508-y.
  27. 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
  28. Ghandourah, E.E. and Abdraboh, A.M. (2020), "Dynamic analysis of functionally graded nonlocal nanobeam with different porosity models", Steel Compost. Struct., 36(3), 293-305. https://doi.org/10.12989/SCS.2020.36.3.293.
  29. Ghandourh, E.E. and Abdraboh, A.M. (2020), "Dynamic analysis of functionally graded nonlocal nanobeam with different porosity models", 36(3), 293-305. http://dx.doi.org/10.12989/scs.2020.36.3.293.
  30. Ghannadpour, S.A.M. and Mehrparvar, M. (2020), "Nonlinear and post-buckling responses of FGM plates with oblique elliptical cutouts using plate assembly technique", 34(2), 227-239. http://dx.doi.org/10.12989/scs.2020.34.2.227.
  31. Ghumare, S.M. and Sayyad, A.S. (2019), "Nonlinear hygrothermo-mechanical analysis of functionally graded plates using a fifth-order plate theory", Arabian J. Sci. Eng., 44(10), 8727-8745. https://doi.org/10.1007/s13369-019-03894-8.
  32. 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.
  33. 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.
  34. Jena, S.K., Chakraverty, S., Malikan, M. and Sedighi, H. (2020), "Implementation of Hermite-Ritz method and Navier's technique for vibration of functionally graded porous nanobeam embedded in Winkler-Pasternak elastic foundation using biHelmholtz nonlocal elasticity", J. Mech. Mater. Struct., 15(3), 405-434. https://doi.org/10.2140/jomms.2020.15.405.
  35. Jung, W.Y. and Han, S.C. (2015), "Static and eigenvalue problems of sigmoid functionally graded materials (S-FGM) micro-scale plates using the modified couple stress theory", Appl. Math. Model., 39(12), 3506-3524. https://doi.org/10.1016/j.apm.2014.11.056.
  36. Kar, V.R. and Panda, S.K. (2016), "Nonlinear thermomechanical deformation behaviour of P-FGM shallow spherical shell panel", Chinese J. Aeronautics, 29(1), 173-183. https://doi.org/10.1016/j.cja.2015.12.007.
  37. Kar, V.R., Mahapatra, T.R. and Panda, S.K. (2015), "Nonlinear flexural analysis of laminated composite flat panel under hygrothermo-mechanical loading", Steel Compos. Struct., 19 (4), 1011-1033. https://doi.org/10.12989/scs.2015.19.4.1011.
  38. Karami, B., Shahsavari, D., Janghorban, M. and Li, L. (2020), "Free vibration analysis of FG nanoplate with poriferous imperfection in hygrothermal environment", 73(2), 191-207. http://dx.doi.org/10.12989/sem.2020.73.2.191.
  39. Khalaf, B.S., Fenjan, R.M. and Faleh, N.M. (2019), "Analyzing nonlinear mechanical-thermal buckling of imperfect micro-scale beam made of graded graphene reinforced composites", 8(3), 219-235. https://doi.org/10.12989/amr.2019.8.3.219.
  40. Kiani, Y. (2019), "NURBS-based thermal buckling analysis of graphene platelet reinforced composite laminated skew plates", J. Thermal Stresses, 43(1), 1-19. https://doi.org/10.1080/01495739.2019.1673687.
  41. Li, D., Deng, Z., Xiao, H. and Jin, P. (2018), "Bending analysis of sandwich plates with different face sheet materials and functionally graded soft core", Thin-Walled Struct., 122, 8-16. https://doi.org/10.1016/j.tws.2017.09.033.
  42. Liu, W.Q., Liu, S.J., Fan, M.Y., Tian, W., Wang, J.P. and Tahouneh, V. (2020), "Influence of internal pores and graphene platelets on vibration of non-uniform functionally graded columns", 35(2), 295-303. http://dx.doi.org/10.12989/scs.2020.35.2.295.
  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. Mahapatra, T.R., Kar, V.R. and Panda, S.K. (2016), "Large amplitude vibration analysis of laminated composite spherical panels under hygrothermal environment", J. Struct. Stability Dynam., 16(3), 1450105. https://doi.org/10.1142/s0219455414501053.
  45. 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.
  46. Mehar, K., Panda, S.K. and Mahapatra, T.R. (2017), "Thermoelastic nonlinear frequency analysis of CNT reinforced functionally graded sandwich structure", European J. Mech. A/Solids, 65, 384-396. https://doi.org/10.1016/j.euromechsol.2017.05.005.
  47. 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.
  48. Moraveji Tabasi, H., Eskandari Jam, J., Malekzadeh Fard, K. and Heydari Beni, M. (2020), "Buckling and free vibration analysis of fiber metal-laminated plates resting on partial elastic foundation", J. Appl. Comput. Mech., 6(1), 37-51. https://doi.org/10.22055/jacm.2019.28156.1489.
  49. Nebab, M., Ait Atmane, H., Bennai, R. and Tounsi, A. (2019), "Effect of variable elastic foundations on static behavior of functionally graded plates using sinusoidal shear deformation", Arab. J. Geosci., 12(24), 809. https://doi.org/10.1007/s12517-019-4871-5.
  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. (2012), "A quasi-3D sinusoidal shear deformation theory for the static and free vibration analysis of functionally graded plates", Compos Part B, 43(2), 711-725. https://doi.org/10.1016/j.compositesb.2011.08.009.
  51. 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.
  52. Park, M. and Choi, D.H. (2018), "A simplified first-order shear deformation theory for bending, buckling and free vibration analyses of isotropic plates on elastic foundations", KSCE J. Civ. Eng., 22(4), 1235-1249. https://doi.org/10.1007/s12205-017-1517-6.
  53. 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(1-2), 342-362. https://doi.org/10.1016/j.jsv.2008.09.018.
  54. Rachedi, M.A., Benyoucef, S., Bouhadra, A., Bouiadjra, R.B., 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.
  55. Rad, A.B. and Shariyat, M. (2013), "A three-dimensional elasticity solution for two-directional FGM annular plates with nonuniform elastic foundations subjected to normal and shear tractions", Acta. Mech. Solida. Sin., 26(6), 671-690. https://doi.org/10.1016/s0894-9166(14)60010-0.
  56. 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.
  57. Si, H., Shen, D., Xia, J. and Tahouneh, V. (2020), "Vibration behavior of functionally graded sandwich beam with porous core and nanocomposite layers", 36(1), 1-16. http://dx.doi.org/10.12989/scs.2020.36.1.001.
  58. 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.
  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", 8(2), 135-1481. https://doi.org/10.12989/anr.2020.8.2.135.
  60. Thai, H.T. and Choi, D.H. (2013), "A simple first order shears deformation theory for the bending and free vibration analysis of functionally graded plates", Compos. Struct., 101, 332-340. https://doi.org/10.1016/j.compstruct.2013.02.019.
  61. Thai, H.T. and Choi, D.H. (2013), "Finite element formulation of various four unknown shear deformation theories for functionally graded plates", Finite Elements Analysis Design, 75, 50-61. https://doi.org/10.1016/j.finel.2013.07.003.
  62. 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.
  63. 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.
  64. Uzun Yaylaci, 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.
  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. Yaghoobi, H. and Fereidoon, A. (2014), "Mechanical and thermal buckling analysis of functionally graded plates resting on elastic foundations: an assessment of a simple refined nth-order shear deformation theory", Compos. Part B, 62, 54-64. https://doi.org/10.1016/j.compositesb.2014.02.014.
  67. Yaylaci, M. (2016), "The investigation crack problem through numerical analysis", Struct. Eng. Mech., 57(6), 1143-1156., https://doi.org/10.12989/sem.2016.57.6.1143.
  68. Yaylaci, M. and Avcar, M. (2020), "Finite element modelling of contact between an elastic layer and two elastic quarter planes", Comput. Concrete, 26(2), 107-114, https://doi.org/10.12989/cac.2020.26.2.107.
  69. 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. http://doi.org/10.12989/sem.2013.48.2.241.
  70. 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. https://doi.org/10.12989/sem.2020.76.3.325.
  71. Yaylaci, M., Adiyaman, E., Oner, E. and Birinci, A. (2021), "Investigation of continuous and discontinuous contact cases in the contact mechanics of graded materials using analytical method and FEM", Comput. Concrete. 27(3), 199-https://doi.org/10.12989/cac.2021.27.3.199.
  72. Yaylaci, M., Eyuboglu, A., Adiyaman, G., Uzun Yaylaci, E., Oner, E. and Birinci, A. (2021), "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.
  73. Yaylaci, M., Yayli, M., Uzun Yaylaci, E., Olmez, H. and Birinci, A. (2021), "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.
  74. Yu, Q., Xu, H. and Liao, S. (2018), "Nonlinear analysis for extreme large bending deflection of a rectangular plate on nonuniform elastic foundations", Appl. Math. Modelling, 61, 316- 340. https://doi.org/10.1016/j.apm.2018.04.022.
  75. Yuan, Y., Zhao, K., Zhao, Y. and Kiani, K. (2020), "Nonlocalintegro-vibro analysis of vertically aligned monolayered nonuniform FGM nanorods", 37(5), 551-569. http://dx.doi.org/10.12989/scs.2020.37.5.551.
  76. 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.
  77. Zhang, H., Jiang, J.Q. and Zhang, Z.C. (2014), "Threedimensional elasticity solutions for bending of generally supported thick functionally graded plates", Appl. Math. Mech., 35(11), 1467-1478. https://doi.org/10.1007/s10483-014-1871-7.