Advances in materials Research

Techno-Press (테크노프레스)
권호 표지
DOI QR코드

DOI QR Code

Static and free vibration behavior of functionally graded sandwich plates using a simple higher order shear deformation theory

  • Zouatnia, Nafissa (Department of Mechanical Engineering, University of Tiaret) ;
  • Hadji, Lazreg (Laboratory of Geomatics and Sustainable Development, University of Tiaret)
  • Received : 2020.01.05
  • Accepted : 2020.02.01
  • Published : 2019.12.25
⟨ Previous Next ⟩

Abstract

The objective of the present paper is to investigate the bending and free vibration behavior of functionally graded material (FGM) sandwich rectangular plates using an efficient and simple higher order shear deformation theory. Unlike other theories, there are only four unknown functions involved, as compared to five in other shear deformation theories. The most interesting feature of this theory is that it does not require the shear correction factor. Two common types of FGM sandwich plates are considered, namely, the sandwich with the FGM facesheet and the homogeneous core and the sandwich with the homogeneous facesheet and the FGM core. The equation of motion for the FGM sandwich plates is obtained based on Hamilton's principle. The closed form solutions are obtained by using the Navier technique. A static and free vibration frequency is given for different material properties. The accuracy of the present solutions is verified by comparing the obtained results with the existing solutions.

Keywords

References

  1. Abazid, A., Alotebi, M.S. 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., Int. J., 67(3), 219-232. https://doi.org/10.12989/sem.2018.67.3.219
  2. Abdelaziz, H.H., Ait Amar Meziane M., Bousahla, A.A., Tounsi, A., Mahmoud, S.R. and Alwabli, A.S. (2017), "An efficient hyperbolic shear deformation theory for bending, buckling and free vibration of FGM sandwich plates with various boundary conditions", Steel Compos. Struct., Int. J., 25(6), 693-704. https://doi.org/10.12989/scs.2017.25.6.693
  3. Abualnour, M., Chikh, A., Hebali, H., Kaci, A., Tounsi, A., Bousahla, A.A. and Tounsi, A. (2019), "Thermomechanical analysis of antisymmetric laminated reinforced composite plates using a new four variable trigonometric refined plate theory", Comput. Concrete, Int. J., 24(6), 489-498. https://doi.org/10.12989/cac.2019.24.6.489
  4. Adda Bedia, W., Houari, M.S.A., Bessaim, A., Bousahla, A.A., Tounsi, A., Saeed, T. and Alhodaly, M.S. (2019), "A new hyperbolic two-unknown beam model for bending and buckling analysis of a nonlocal strain gradient nanobeams", J. Nano Res., 57, 175-191. https://doi.org/10.4028/www.scientific.net/JNanoR.57.175
  5. Addou, F.Y., Meradjah, M., Bousahla, A.A., Benachour, A., Bourada, F., Tounsi, A. and Mahmoud, S.R. (2019), "Influences of porosity on dynamic response of FG plates resting on Winkler/Pasternak/Kerr foundation using quasi 3D HSDT", Comput. Concrete, Int. J., 24(4), 347-367. https://doi.org/10.12989/cac.2019.24.4.347
  6. Ahmadi, I. (2018), "Three-dimensional and free-edge hygrothermal stresses in general long Sandwich plates", Struct. Eng. Mech., Int. J., 65(3), 275-290. https://doi.org/10.12989/sem.2018.65.3.275
  7. Akbas, S.D. (2015a), "Wave propagation of a functionally graded beam in thermal environments", Steel Compos. Struct., Int. J., 19(6), 1421-1447. https://doi.org/10.12989/scs.2015.19.6.1421
  8. Akbas, S.D. (2015b), "Free vibration and bending of functionally graded beams resting on elastic foundation", Res. Eng. Struct. Mater., 1(1), 25-37. http://dx.doi.org/10.17515/resm2015.03st0107
  9. Akbas, S.D. (2015c), "Post-buckling analysis of axially functionally graded three-dimensional beams", Int. J. Appl. Mech., 7(3), 1550047. https://doi.org/10.1142/S1758825115500477
  10. Akbas, S.D. (2017a), "Vibration and static analysis of functionally graded porous plates", J. Appl. Computat. Mech., 3(3), 199-207. https://doi.org/10.22055/JACM.2017.21540.1107
  11. Akbas, S.D. (2017b), "Stability of a non-homogenous porous plate by using generalized differantial quadrature method", Int. J. Eng. Appl. Sci., 9, 147-155. https://doi.org/10.24107/ijeas.322375
  12. Akbas, S.D. (2017c), "Nonlinear static analysis of functionally graded porous beams under thermal effect", Coupl. Syst. Mech., Int. J., 6(4), 399-415. https://doi.org/10.12989/csm.2017.6.4.399
  13. Akbas, S.D. (2017d), "Forced vibration analysis of functionally graded nanobeams", Int. J. Appl. Mech., 9(7), 1750100. https://doi.org/10.1142/S1758825117501009
  14. Akbas, S.D. (2018), "Geometrically nonlinear analysis of functionally graded porous beams", Wind Struct., Int. J., 27(1), 59-70. https://doi.org/10.12989/was.2018.27.1.059
  15. Akbas, S.D. (2019), "Forced vibration analysis of functionally graded sandwich deep beams", Coupl. Syst. Mech., Int. J., 8(3), 259-271. https://doi.org/10.12989/csm.2019.8.3.259
  16. Alimirzaei, S., Mohammadimehr, M. and Tounsi, A. (2019), "Nonlinear analysis of viscoelastic microcomposite beam with geometrical imperfection using FEM: MSGT electro-magneto-elastic bending, buckling and vibration solutions", Struct. Eng. Mech., Int. J., 71(5), 485-502. https://doi.org/10.12989/sem.2019.71.5.485
  17. Amirani, M.C., Khalili, S.M.R. and Nemati, N. (2009), "Free vibration analysis of sandwich beam with FG core using the element free Galerkin method", Compos. Struct., 90(3), 373-379. https://doi.org/10.1016/j.compstruct.2009.03.023
  18. Arani, A.G., Maraghi Z.K. and Ferasatmanesh, M. (2017), "Theoretical investigation on vibration frequency of sandwich plate with PFRC core and piezomagnetic face sheets under variable in-plane load", Struct. Eng. Mech., Int. J., 63(1), 65-76. https://doi.org/10.12989/sem.2017.63.1.065
  19. Balubaid, M., Tounsi, A., Dakhel, B. and Mahmoud, S.R. (2019), "Free vibration investigation of FG nanoscale plate using nonlocal two variables integral refined plate theory", Comput. Concrete, Int. J., 24(6), 579-586. https://doi.org/10.12989/cac.2019.24.6.579
  20. Belarbi, M.O., Tati, A., Ounis, H. and Benchabane, A. (2016), "Development of a 2D isoparametric finite element model based on the layerwise approach for the Bending analysis of sandwich plates", Struct. Eng. Mech., Int. J., 57(3), 473-506. https://doi.org/10.12989/sem.2016.57.3.473
  21. Belbachir, N., Draiche, K., Bousahla, A.A., Bourada, M., Tounsi, A. and Mahmoud, S.R. (2019), "Bending analysis of anti-symmetric cross-ply laminated plates under nonlinear thermal and mechanical loadings", Steel Compos. Struct., Int. J., 33(1), 913-924. https://doi.org/10.12989/scs.2019.33.1.081
  22. Berghouti, H., Adda Bedia, E.A., Benkhedda, A. and Tounsi, A. (2019), "Vibration analysis of nonlocal porous nanobeams made of functionally graded material", Adv. Nano Res., Int. J., 7(5), 351-364. https://doi.org/10.12989/anr.2019.7.5.351
  23. Boukhlif, Z., Bouremana, M., Bourada, F., Bousahla, A.A., Bourada, M., Tounsi, A. and Al-Osta, M.A. (2019), "A simple quasi-3D HSDT for the dynamics analysis of FG thick plate on elastic foundation", Steel Compos. Struct., Int. J., 31(5), 503-516. https://doi.org/10.12989/scs.2019.31.5.503
  24. Boulefrakh, L., Hebali, H., Chikh, A., Bousahla, A.A., Tounsi, A. and Mahmoud, S.R. (2019), "The effect of parameters of visco-Pasternak foundation on the bending and vibration properties of a thick FG plate", Geomech. Eng., Int. J., 18(2), 161-178. https://doi.org/10.12989/gae.2019.18.2.161
  25. Bourada, F., Bousahla, A.A., Bourada, M., Azzaz, A., Zinata, A. and Tounsi, A. (2019), "Dynamic investigation of porous functionally graded beam using a sinusoidal shear deformation theory", Wind Struct., Int. J., 28(1), 19-30. https://doi.org/10.12989/was.2019.28.1.019
  26. Boussoula, A., Boucham, B., Bourada, M., Bourada, F., Tounsi, A., Bousahla, A.A. and Tounsi, A. (2020), "A simple nth-order shear deformation theory for thermomechanical bending analysis of different configurations of FG sandwich plates", Smart Struct. Syst., Int. J., 25(2), 195-216. https://doi.org/10.12989/sss.2020.25.2.195
  27. Boutaleb, S., Benrahou, K.H., Bakora, A., Algarni, A., Bousahla, A.A., Tounsi, A., Tounsi, A. and Mahmoud, S.R. (2019), "Dynamic Analysis of nanosize FG rectangular plates based on simple nonlocal quasi 3D HSDT", Adv. Nano Res., Int. J., 7(3), 189-206. https://doi.org/10.12989/anr.2019.7.3.191
  28. Brischetto, S. (2009), "Classical and mixed advanced models for sandwich plates embedding functionally graded cores", J. Mech. Mater. Struct., 4(1), 13-33. https://doi.org/10.2140/jomms.2009.4.13
  29. Carrera, E., Brischetto, S., Cinefra, M. and Soave, M. (2011), "Effects of thickness stretching in functionally graded plates and shells", Compos. B Eng., 42(2), 123-133. https://doi.org/10.1016/j.compositesb.2010.10.005
  30. Chaabane, L.A., Bourada, F., Sekkal, M., Zerouati, S., Zaoui, F.Z., Tounsi, A., Derras, A., Bousahla, A.A. and Tounsi, A. (2019), "Analytical study of bending and free vibration responses of functionally graded beams resting on elastic foundation", Struct. Eng. Mech., Int. J., 71(2), 185-196. https://doi.org/10.12989/sem.2019.71.2.185
  31. Cunedioglu, Y. (2015), "Free vibration analysis of edge cracked symmetric functionally graded sandwich beams", Struct. Eng. Mech., Int. J., 56(6), 1003-1020. https://doi.org/10.12989/sem.2015.56.6.1003
  32. Dash, S., Mehar, K., Sharma, N., Mahapatra, T.R. and Panda, S.K. (2018), "Modal analysis of FG sandwich doubly curved shell structure", Struct. Eng. Mech., Int. J., 68(6), 721-733. https://doi.org/10.12989/sem.2018.68.6.721
  33. Draiche, K., Bousahla, A.A., Tounsi, A., Alwabli, A.S., Tounsi, A. and Mahmoud, S.R. (2019), "Static analysis of laminated reinforced composite plates using a simple first-order shear deformation theory", Comput. Concrete, Int. J., 24(4), 369-378. https://doi.org/10.12989/cac.2019.24.4.369
  34. Draoui, A., Zidour, M., Tounsi, A. and Adim, B. (2019), "Static and dynamic behavior of nanotubesreinforced sandwich plates using (FSDT)", J. Nano Res., 57, 117-135. https://doi.org/10.4028/www.scientific.net/JNanoR.57.117
  35. Hellal, H., Bourada, M., Hebali, H., Bourda, F., Tounsi, A., Bousahla, A.A. and Mahmour, S.R. (2019), "Dynamic and stability analysis of functionally graded material sandwich plates in hygro-thermal environment using a simple higher shear deformation theory", J. Sandw. Struct. Mater. https://doi.org/10.1177/1099636219845841
  36. Hussain, M., Naeem, M.N., Tounsi, A. and Taj, M. (2019), "Nonlocal effect on the vibration of armchair and zigzag SWCNTs with bending rigidity", Adv. Nano Res., Int. J., 7(6), 431-442. https://doi.org/10.12989/anr.2019.7.6.431
  37. Kaddari, M., Kaci, A., Bousahla, A.A., Tounsi, A., Bourada, F., Tounsi, A., Adda Bedia, E.A. and Al-Osta, M.A. (2020), "A study on the structural behaviour of functionally graded porous plates on elastic foundation using a new quasi-3D model: Bending and Free vibration analysis", Comput. Concrete, Int. J., 25(1), 37-57. https://doi.org/10.12989/cac.2020.25.1.037
  38. Karami, B., Janghorban, M. and Tounsi, A. (2019a), "Galerkin's approach for buckling analysis of functionally graded anisotropic nanoplates/different boundary conditions", Eng. Comput., 35, 1297-1316. https://doi.org/10.1007/s00366-018-0664-9
  39. Karami, B., Janghorban, M. and Tounsi, A. (2019b), "Wave propagation of functionally graded anisotropic nanoplates resting on Winkler-Pasternak foundation", Struct. Eng. Mech., Int. J., 7(1), 55-66. https://doi.org/10.12989/sem.2019.70.1.055
  40. Karami, B., Shahsavari, D., Janghorban, M. and Tounsi, A. (2019c), "Resonance behavior of functionally graded polymer composite nanoplates reinforced with grapheme nanoplatelets", Int. J. Mech. Sci., 156, 94-105. https://doi.org/10.1016/j.ijmecsci.2019.03.036
  41. Karami, B., Janghorban, M. and Tounsi, A. (2019d), "On exact wave propagation analysis of triclinic material using three dimensional bi-Helmholtz gradient plate model", Struct. Eng. Mech., Int. J., 69(5), 487-497. https://doi.org/10.12989/sem.2019.69.5.487
  42. Karami, B., Janghorban, M. and Tounsi, A. (2019e), "On pre-stressed functionally graded anisotropic nanoshell in magnetic field", J. Brazil. Soc. Mech. Sci. Eng., 41(11), 495. https://doi.org/10.1007/s40430-019-1996-0
  43. 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. https://doi.org/10.1007/s00366-019-00732-1
  44. Kolahdouzan, F., Arani, A.G. and Abdollahian, M. (2018), "Buckling and free vibration analysis of FGCNTRC-micro sandwich plate", Steel Compos. Struct., Int. J., 26(3), 273-287. https://doi.org/10.12989/scs.2018.26.3.273
  45. Li, Q., Iu, V.P. and Kou, K.P. (2008), "Three-dimensional vibration analysis of functionally graded material sandwich plates", J. Sound Vib., 311, 498-515. https://doi.org/10.1016/j.jsv.2007.09.018
  46. Mahmoudi, A., Benyoucef, S., Tounsi, A., Benacour, A., Adda Bedia, E.A. and Mahmoud, S.R. (2019), "A refined quasi-3D shear deformation theory for thermo-mechanical behavior of functionally graded sandwich plates on elastic foundations", J. Sandw. Struct. Mater., 21(6), 1906-1926. https://doi.org/10.1177/1099636217727577
  47. Medani, M., Benahmed, A., Zidour, M., Heireche, H., Tounsi, A., Bousahla, A.A., Tounsi, A. and Mahmoud, S.R. (2019), "Static and dynamic behavior of (FG-CNT) reinforced porous sandwich plate", Steel Compos. Struct., Int. J., 32(5), 595-610. https://doi.org/10.12989/scs.2019.32.5.595
  48. 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., 1-30. https://doi.org/10.1177/1099636219851281
  49. 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
  50. Mirza, S.B., Hussain Khan, A. and Yasin, Y. (2018), "Effect of boundary conditions on the non-linear forced vibration response of isotropic plates", IOP Conference Series: Mater. Sci. Eng., 377, 012089. https://doi.org/10.1088/1757-899X/377/1/012089
  51. Nazargah, M.L. and Meshkani, Z. (2018), "An efficient partial mixed finite element model for static and free vibration analyses of FGM plates rested on two-parameter elastic foundations", Struct. Eng. Mech., Int. J., 66(5), 665-676. https://doi.org/10.12989/sem.2018.66.5.665
  52. Neves, A.M.A., Ferreira, A.J.M., Carrera, E., Cinefra, M., Jorge, R.M.N. and Soares, C.M.M. (2012), "Static analysis of functionally graded sandwich plates according to a hyperbolic theory considering Zig-Zag and warping effects", Adv. Eng. Software, 52, 30-43. https://doi.org/10.1016/j.advengsoft.2012.05.005
  53. Sahla, M., Saidi, H., Draiche, K., Bousahla, A.A., Bourada, F. and Tounsi, A. (2019), "Free vibration analysis of angle-ply laminated composite and soft core sandwich plates", Steel Compos. Struct., Int. J., 33(5), 663-679. https://doi.org/10.12989/scs.2019.33.5.663
  54. Semmah, A., Heireche, H., Bousahla, A.A. and Tounsi, A. (2019), "Thermal buckling analysis of SWBNNT on Winkler foundation by non local FSDT", Adv. Nano Res., Int. J., 7(2), 89-98. https://doi.org/10.12989/anr.2019.7.2.089
  55. Shashank, P. and Pradyumna, S. (2018), "Analysis of functionally graded sandwich plates using a higherorder layerwise theory", Compos. Part B, 153, 325-336. https://doi.org/10.1016/j.compositesb.2018.08.121
  56. Sudhakar, V., Gopalkrishnan, S. and Vijayaraju, K. (2018), "Development of super convergent euler finite elements for the analysis of sandwich beams with soft core", Struct. Eng. Mech., Int. J., 65(6), 657-678. https://doi.org/10.12989/sem.2018.65.6.657
  57. Thai, C.H., Zenkour, A.M., Wahab, M.A. and Nguyen-Xuan, H. (2016), "A simple four-unknown shear and normal deformations theory for functionally graded isotropic and sandwich plates based on isogeometric analysis", Compos. Struct., 139, 77-95. https://doi.org/10.1016/j.compstruct.2015.11.066
  58. Tlidji, Y., Zidour, M., Draiche, K., Safa, A., Bourada, M., Tounsi, A., Bousahla, A.A. and Mahmoud, S.R. (2019), "Vibration analysis of different material distributions of functionally graded microbeam", Struct. Eng. Mech., Int. J., 69(6), 637-649. https://doi.org/10.12989/sem.2019.69.6.637
  59. Zaoui, F.Z., Ouinas, D. and Tounsi, A. (2019), "New 2D and quasi-3D shear deformation theories for free vibration of functionally graded plates on elastic foundations", Compos. Part B, 159, 231-247. https://doi.org/10.1016/j.compositesb.2018.09.051
  60. Zarga, D., Tounsi, A., Bousahla, A.A., Bourada, F. and Mahmoud, S.R. (2019), "Thermomechanical bending study for functionally graded sandwich plates using a simple quasi-3D shear deformation theory", Steel Compos. Struct., Int. J., 32(3), 389-410. https://doi.org/10.12989/scs.2019.32.3.389
  61. Zenkour, A.M. (2005), "A comprehensive analysis of functionally graded sandwich plates: Part 1-deflection and stresses", Int. J. Solid Struct., 42(18-19), 5224-5242. https://doi.org/10.1016/j.ijsolstr.2005.02.015
  62. Zenkour, A.M. and Alghamdi, N.A. (2008), "Thermoelastic bending analysis of functionally graded sandwich plates", J. Mater. Sci., 43(8), 2574-2589. https://doi.org/10.1007/s10853-008-2476-6

Cited by

  1. A four-unknown refined plate theory for dynamic analysis of FG-sandwich plates under various boundary conditions vol.36, pp.3, 2020, https://doi.org/10.12989/scs.2020.36.3.355
  2. Porosity-dependent mechanical behaviors of FG plate using refined trigonometric shear deformation theory vol.26, pp.5, 2020, https://doi.org/10.12989/cac.2020.26.5.439
  3. The nano scale buckling properties of isolated protein microtubules based on modified strain gradient theory and a new single variable trigonometric beam theory vol.10, pp.1, 2019, https://doi.org/10.12989/anr.2021.10.1.015
  4. Investigation on the dynamic response of porous FGM beams resting on variable foundation using a new higher order shear deformation theory vol.39, pp.1, 2019, https://doi.org/10.12989/scs.2021.39.1.095