DOI QR코드

DOI QR Code

A new quasi-3D theory for the study of the bending of thick FGM's plates on elastic foundation

  • Belarouci, Abdelghani (Faculty of Technology, Civil Engineering and Public Works Department, University of Sidi Bel Abbes) ;
  • Fekrar, Abdelkader (Faculty of Technology, Civil Engineering and Public Works Department, University of Sidi Bel Abbes)
  • 투고 : 2020.04.02
  • 심사 : 2021.01.27
  • 발행 : 2021.05.25

초록

In this work, a new theory quasi-3D shear deformation is presented to analyze the bending of thick FGM (functionally graded materials) plates resting on Pasternak elastic foundations, whose number of variables is limited to five. The mathematical model used presents a new range of displacement based on indeterminate integral variables where the stretching of thickness is taken into account according to the power laws P-FGM, E-FGM and S-FGM. The compositions and volume fractions of the constituents in the FGM are supposed to change through the thickness. The principle of virtual work, as well as the Naiver method, is used in this study to solve the governing equations of motion to study these types of plates. The equilibrium equations according to the FG plate resting on Pasternak foundations are presented. The results obtained are compared to those determined by the other authors. It was observed from the comparative studies that quasi-3D theories that take into account thickness stretching effects can predict bending behavior more accurately than other theories.

키워드

과제정보

Authors would like to acknowledge the support provided by the Directorate General for Scientific Research and Technological Development (DGRSDT).

참고문헌

  1. Abdelmalek, A., Bouazza, M., Zidour, M. and Benseddiq, N. (2017), "Hygrothermal Effects on the Free Vibration Behavior of Composite Plate Using nth-Order Shear Deformation Theory: a Micromechanical Approach", Iran. J. Sci. Technol. Transact. Mech. Eng., 43(1), 61-73. https://doi.org/10.1007/s40997-017-0140-y
  2. Adim, B. and Hassaine Daouadji, T. (2016), "Effects of thickness stretching in FGM plates using a quasi-3D higher order shear deformation theory", Adv. Mater. Res., Int. J., 5(4), 223-244. https://doi.org/10.12989/amr.2016.5.4.223
  3. Amir, S., Arshid, E. and Arani, M.R.G. (2019), "Size-dependent magneto-electro-elastic vibration analysis of FG saturated porous annular/circular micro sandwich plates embedded with nano-composite face sheets subjected to multi-physical pre loads", Smart Struct. Syst., Int. J., 23(5), 429-447. https://doi.org/10.12989/sss.2019.23.5.429
  4. Arefi, M. (2015), "The effect of different functionalities of FGM and FGPM layers on free vibration analysis of the FG circular plates integrated with piezoelectric layers", Smart Struct. Syst., Int. J., 15(5), 1345-1362. https://doi.org/10.12989/sss.2015.15.5.1345
  5. 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
  6. Baferani, A.H. and Saidi, A.R. (2013), "Effects of in-plane loads on vibration of laminated thick rectangular plates resting on elastic foundation: An exact analytical approach", Eur. J. Mech.-A/Solids, 42, 299-314. https://doi.org/10.1016/j.euromechsol.2013.07.001
  7. Beldjelili, Y., Tounsi, A. and Mahmoud, S.R. (2016), "Hygrothermo-mechanical bending of S-FGM plates resting on variable elastic foundations using a four-variable trigonometric plate theory", Smart Struct. Syst., Int. J., 18(4), 755-786. https://doi.org/10.12989/sss.2016.18.4.755
  8. Belmahi, S., Zidour, M., Meradjah, M., Bensattalah, T. and Dihaj, A. (2018), "Analysis of boundary conditions effects on vibration of nanobeam in a polymeric matrix", Struct. Eng. Mech., Int. J., 67(5), 517-525. https://doi.org/10.12989/sem.2018.67.5.517
  9. Belmahi, S., Zidour, M. and Meradjah, M. (2019), "Small-scale effect on the forced vibration of a nano beam embedded an elastic medium using nonlocal elasticity theory", Adv. Aircr. Spacecr. Sci., Int. J., 6(1), 1-18. https://doi.org/10.12989/aas.2019.6.1.001
  10. Benahmed, A., Houari, M.S.A., Benyoucef, S., Belakhdar, K. and Tounsi, A. (2017), "A novel quasi-3D hyperbolic shear deformation theory for functionally graded thick rectangular plates on elastic foundation", Geomech. Eng., Int. J., 12(1), 9-34. https://doi.org/10.12989/gae.2017.12.1.009
  11. Benahmed, A., Fahsi, B., Benzair, A., Zidour, M., Bourada, F. and Tounsi, A. (2019), "Critical buckling of functionally graded nanoscale beam with porosities using nonlocal higher-order shear deformation", Struct. Eng. Mech., Int. J., 69(4), 457-466. https://doi.org/10.12989/sem.2019.69.4.457
  12. Bensattalah, T., Bouakkaz, K., Zidour, M. and Hassaine Daouadji, T. (2018a), "Critical buckling loads of carbon nanotube embedded in Kerr's medium", Adv. Nano Res., Int. J., 6(4), 339-356. https://doi.org/10.12989/anr.2018.6.4.339
  13. Bensattalah, T., Zidour, M. and Hassaine Daouadji, T. (2018b), "Analytical analysis for the forced vibration of CNT surrounding elastic medium including thermal effect using nonlocal Euler-Bernoulli theory", Adv. Mater. Res., Int. J., 7(3), 163-174. https://doi.org/10.12989/amr.2018.7.3.163
  14. Bensattalah, T., Zidour, M., Hassaine Daouadji, T. and Bouakaz, K. (2019a), "Theoretical analysis of chirality and scale effects on critical buckling load of zigzag triple walled carbon nanotubes under axial compression embedded in polymeric matrix", Struct. Eng. Mech., Int. J., 70(3), 269-277. https://doi.org/10.12989/sem.2019.70.3.269
  15. Bensattalah, T., Zidour, M. and Hassaine Daouadji, T. (2019b), "A new nonlocal beam model for free vibration analysis of chiral single-walled carbon nanotubes", Compos. Mater. Eng., Int. J., 1(1), 21-31. https://doi.org/10.12989/cme.2019.1.1.021
  16. Bensattalah, T., Hassaine Daouadji, T. and Zidour, M. (2019c), "Influences the Shape of the Floor on the Behavior of Buildings Under Seismic Effect", Proceedings of the 4th International Symposium on Materials and Sustainable Development, Benmounah A., Abadlia M.T., Saidi M., Zerizer A. (eds), Springer, Cham, pp. 26-42. https://doi.org/10.1007/978-3-030-43268-3_3
  17. Bouazza, M., Amara, K., Zidour, M., Tounsi, A. and Adda-Bedia, E.A. (2014a), "Hygrothermal effects on the postbuckling response of composite beams", Am. J. Mater. Res., 1(2), 35-43.
  18. Bouazza, M., Amara, K., Zidour, M., Tounsi, A. and El Addas, A.B. (2014b), "Thermal effect on buckling of multiwalled carbon nanotubes using different gradient elasticity theories", Nanosci. Nanotechnol., 4(2), 27-33.
  19. Bouazza, M., Amara, K., Zidour, M., Tounsi, A. and Adda-Bedia, E.A. (2015), "Postbuckling analysis of functionally graded beams using hyperbolic shear deformation theory", Rev. Inform. Eng. Applicat., 2(1), 1-14. https://doi.org/10.18488/journal.79/2015.2.1/79.1.1.14
  20. 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", Struct. Eng. Mech., Int. J., 73(2), 209-223. https://doi.org/10.12989/sem.2020.73.2.209
  21. Chen, Y.Z. (2018), "Transfer matrix method for solution of FGMs thick-walled cylinder with arbitrary inhomogeneous elastic response", Smart Struct. Syst., Int. J., 21(4), 469-477. https://doi.org/10.12989/sss.2018.21.4.469
  22. Dihaj, A., Zidour, M., Meradjah, M., Rakrak, K., Heireche, H. and Chemi, A. (2018), "Free vibration analysis of chiral double-walled carbon nanotube embedded in an elastic medium using non-local elasticity theory and Euler Bernoulli beam model", Struct. Eng. Mech., Int. J., 65(3), 335-342. https://doi.org/10.12989/sem.2018.65.3.335
  23. Dorduncu, M. (2019), "Flexure Analysis of Functionally Graded Plates Using {2, 2}-Refined Zigzag Theory", J. Aeronaut. Space Technol., 12(1), 19-30.
  24. Ebrahimi, F. and Barati, M.R. (2016), "A nonlocal higher-order shear deformation beam theory for vibration analysis of size-dependent functionally graded nanobeams", Arab. J. Sci. Eng., 41(5), 1679-1690. https://doi.org/10.1007/s13369-015-1930-4
  25. Ebrahimi, F. and Daman, M. (2017), "Nonlocal thermoelectromechanical vibration analysis of smart curved FG piezoelectric Timoshenko nanobeam", Smart Struct. Syst., Int. J., 20(3), 351-368. https://doi.org/10.12989/sss.2017.20.3.351
  26. Fekrar, A., Houari, M.S.A., Tounsi, A. and Mahmoud, S.R. (2014), "A new five-unknown refined theory based on neutral surface position for bending analysis of exponential graded plates", Meccanica, 49(4), 795-810. https://doi.org/10.1007/s11012-013-9827-3
  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., Int. J., 8(1), 37-47. https://doi.org/10.12989/anr.2020.8.1.037
  28. Ghazzawi, S.M. and Abdelrahman, W.G. (2020), "Static Analysis of Thick Functionally Graded Plates with Different Property Distribution Functions", Arab. J. Sci. Eng., 45, 5099-5108. https://doi.org/10.1007/s13369-020-04344-6
  29. Guessas, H., Zidour, M., Meradjah, M. and Tounsi, A. (2018), "The critical buckling load of reinforced nanocomposite porous plates", Struct. Eng. Mech., Int. J., 67(2), 115-123. https://doi.org/10.12989/sem.2018.67.2.115
  30. Hamidi, A., Zidour, M., Bouakkaz, K. and Bensattalah, T. (2018), "Thermal and small-scale effects on vibration of embedded armchair single-walled carbon nanotubes", J. Nano Res., 51, 24-38. https://doi.org/10.4028/www.scientific.net/JNanoR.51.24
  31. Hirwani, C.K. and Panda, S.K. (2019), "Nonlinear finite element solutions of thermoelastic deflection and stress responses of internally damaged curved panel structure", Appl. Mathe. Modell., 65, 303-317. https://doi.org/10.1016/j.apm.2018.08.014
  32. Hirwani, C.K., Panda, S.K., Mahapatra, T.R. and Mahapatra, S.S. (2017), "Numerical study and experimental validation of dynamic characteristics of delaminated composite flat and curved shallow shell structure", J. Aerosp. Eng., 30(5), 04017045. https://doi.org/10.1061/(ASCE)AS.1943-5525.0000756
  33. Hirwani, C.K., Panda, S.K. and Mahapatra, T.R. (2018a), "Thermomechanical deflection and stress responses of delaminated shallow shell structure using higher-order theories", Compos. Struct., 184, 135-145. https://doi.org/10.1016/j.compstruct.2017.09.071
  34. Hirwani, C.K., Panda, S.K. and Patle, B.K. (2018b), "Theoretical and experimental validation of nonlinear deflection and stress responses of an internally debonded layer structure using different higher-order theories", Acta Mechanica, 229(8), 3453-3473. https://doi.org/10.1007/s00707-018-2173-8
  35. Kar, V.R. and Panda, S.K. (2015), "Thermoelastic analysis of functionally graded doubly curved shell panels using nonlinear finite element method", Compos. Struct., 129, 202-212. https://doi.org/10.1016/j.compstruct.2015.04.006
  36. Kar, V.R. and Panda, S.K. (2016), "Nonlinear thermomechanical behavior of functionally graded material cylindrical / hyperbolic /elliptical shell panel with dependent and ndependent temperature properties", J. Press. Vessel Technol., 138(6). https://doi.org/10.1115/1.4033701
  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., Int. J., 19(4), 1011-1033. https://doi.org/10.12989/scs.2015.19.4.1011
  38. Katariya, P.V., Hirwani, C.K. and Panda, S.K. (2019), "Geometrically nonlinear deflection and stress analysis of skew sandwich shell panel using higher-order theory", Eng. Comput., 35(2), 467-485. https://doi.org/10.1007/s00366-018-0609-3
  39. Khiloun, M., Bousahla, A.A., Kaci, A., Bessaim, A., Tounsi, A. and Mahmoud, S.R. (2019), "Analytical modeling of bending and vibration of thick advanced composite plates using a four-variable quasi 3D HSDT", Eng. Comput., 1-15. https://doi.org/10.1007/s00366-019-00732-1
  40. Lee, W.H., Han, S.C. and Park, W.T. (2015), "A refined higher order shear and normal deformation theory for E-, P-, and S-FGM plates on Pasternak elastic foundation", Compos. Struct., 122, 330-342. https://doi.org/10.1016/j.compstruct.2014.11.047
  41. Mantari, J.L. and Soares, C.G. (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
  42. 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: Eng., 43(2), 711-725. https://doi.org/10.1016/j.compositesb.2011.08.009
  43. Nguyen, T.K. (2015), "A higher-order hyperbolic shear deformation plate model for analysis of functionally graded materials", Int. J. Mech. Mater. Des., 11(2), 203-219. https://doi.org/10.1007/s10999-014-9260-3
  44. Nguyen, H.N., Hong, T.T., Vinh, P.V., Quang, N.D. and Thom, D.V. (2019), "A refined simple first-order shear deformation theory for static bending and free vibration analysis of advanced composite plates", Materials, 12(15), 2385. https://doi.org/10.3390/ma12152385
  45. Panda, K.B. and Chandran, K.R. (2003), "Titanium-titanium boride (Ti-TiB) functionally graded materials through reaction sintering: Synthesis, microstructure, and properties", Metallurg. Mater. Transact. A, 34(9), 1993-2003. https://doi.org/10.1007/s11661-003-0164-3
  46. Panda, S.K. and Singh, B.N. (2013), "Thermal Postbuckling Behavior of Laminated Composite Spherical Shell Panel Using NFEM#", Mech. Based Des. Struct. Mach., 41(4), 468-488. https://doi.org/10.1080/15397734.2013.797330
  47. Radwan, A.F. and Zenkour, A.M. (2018), "Quasi 3-D trigonometric plate theory for bending analysis of EG plates resting on Pasternak foundations", Curv. Layer. Struct., 5(1), 146-155. https://doi.org/10.1515/cls-2018-0011
  48. 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
  49. Shokravi, M. (2017), "Vibration analysis of silica nanoparticles-reinforced concrete beams considering agglomeration effects", Comput. Concrete, Int. J., 19(3), 333-338. https://doi.org/10.12989/cac.2017.19.3.333
  50. 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., Int. J., 8(2), 135-148. https://doi.org/10.12989/anr.2020.8.2.135
  51. Thai, H.T. and Kim, S.E. (2013), "A simple quasi-3D sinusoidal shear deformation theory for functionally graded plates", Compos. Struct., Int. J., 99, 172-180. https://doi.org/10.1016/j.compstruct.2012.11.030
  52. Vel, S.S. and Batra, R.C. (2003), "Exact thermoelasticity solution for cylindrical bending deformations of functionally graded plates", In: IUTAM Symposium on Dynamics of Advanced Materials and Smart Structures, Watanabe K., Ziegler F. (eds), pp. 429-438. https://doi.org/10.1007/978-94-017-0371-0_42
  53. Wu, C.P. and Liu, W.L. (2014), "3D buckling analysis of FGM sandwich plates under bi-axial compressive loads", Smart Struct. Syst., Int. J., 13(1), 111-135. https://doi.org/10.12989/sss.2014.13.1.111
  54. Yi, S.C., Yao, L.Q. and Tang, B.J. (2017), "A novel higher-order shear and normal deformable plate theory for the static, free vibration and buckling analysis of functionally graded plates", Mathe. Problems Eng., Article ID 6879508, 20 p. https://doi.org/10.1155/2017/6879508
  55. Zenkour, A.M. (2009), "The refined sinusoidal theory for FGM plates on elastic foundations", Int. J. Mech. Sci., 51(11-12), 869-880. https://doi.org/10.1016/j.ijmecsci.2009.09.026
  56. Zenkour, A.M. and Alghanmi, R.A. (2018), "Bending of functionally graded plates via a refined quasi-3D shear and normal deformation theory", Curv. Layer. Struct., 5(1), 190-200. https://doi.org/10.1515/cls-2018-0014
  57. Zenkour, A.M. and Radwan, A.F. (2018), "Compressive study of functionally graded plates resting on Winkler-Pasternak foundations under various boundary conditions using hyperbolic shear deformation theory", Arch. Civil Mech. Eng., 18(2), 645-658. https://doi.org/10.1016/j.acme.2017.10.003
  58. Zerrouki, R., Karas, A. and Zidour, M. (2020), "Critical buckling analyses of nonlinear FG-CNT reinforced nano-composite beam", Adv. Nano Res., Int. J., 9(3), 211-220. https://doi.org/10.12989/anr.2020.9.3.211