DOI QR코드

DOI QR Code

Robust quasi 3D computational model for mechanical response of FG thick sandwich plate

  • Achouri, Fatima (Department of Civil Engineering, University Mustapha Stambouli of Mascara) ;
  • Benyoucef, Samir (Material and Hydrology Laboratory, University of SidiBel Abbes, Faculty of Technology) ;
  • Bourada, Fouad (Material and Hydrology Laboratory, University of SidiBel Abbes, Faculty of Technology) ;
  • Bouiadjra, Rabbab Bachir (Department of Civil Engineering, University Mustapha Stambouli of Mascara) ;
  • Tounsi, Abdelouahed (Material and Hydrology Laboratory, University of SidiBel Abbes, Faculty of Technology)
  • Received : 2019.01.21
  • Accepted : 2019.03.08
  • Published : 2019.06.10

Abstract

This paper aims to develop a quasi-3D shear deformation theory for the study of bending, buckling and free vibration responses of functionally graded (FG) sandwich thick plates. For that, in the present theory, both the components of normal deformation and shear strain are included. The displacement field of the proposed model contains undetermined integral terms and involves only four unknown functions with including stretching effect. Using Navier's technique the solution of the problem is derived for simply supported sandwich plate. Numerical results have been reported, and compared with those available in the open literature were excellent agreement was observed. Finally, a detailed parametric study is presented to demonstrate the effect of the different parameters on the flexural responses, free vibration and buckling of a simply supported sandwich plates.

Keywords

References

  1. 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., 25(6), 693-704. https://doi.org/10.12989/SCS.2017.25.6.693
  2. Abdelaziz, H.H., Atmane, H.A., Mechab I., Boumia L, Tounsi, A. and AddaBedia E.A. (2011), "Static analysis of functionally graded sandwich plates using an efficient and simple refined theory", Chin. J. Aeronaut., 24, 434-448. https://doi.org/10.1016/S1000-9361(11)60051-4.
  3. Ahmed, A. (2014), "Post buckling analysis of sandwich beams with functionally graded faces using a consistent higher order theory", Int. J. Civil, Struct., Environ., 4(2), 59-64.
  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. Ait Sidhoum, I., Boutchicha, D., Benyoucef , S. and Tounsi, A. (2017), "An original HSDT for free vibration analysis of functionally graded plates", Steel Compos. Struct., Int. J., 25(6), 735-745. https://doi.org/10.12989/scs.2017.25.6.735.
  6. Ait Sidhoum, I., Boutchicha, D., Benyoucef , S. and Tounsi, A., (2018), "A novel quasi-3D hyperbolic shear deformation theory for vibration analysis of simply supported functionally graded plates" . Smart Structures and Systems, 22(3), 303-314. https://doi.org/10.12989/sss.2018.22.3.303
  7. Akavci, S.S. (2016), "Mechanical behavior of functionally graded sandwich plates on elastic foundation", Compos. Part B., 96, 136-152. https://doi.org/10.1016/j.compositesb.2016.04.035.
  8. Alipour, M.M. and Shariyat, M. (2014), "Analytical stress analysis of annular FGM sandwich plates with non-uniform shear and normal tractions, employing a zigzag elasticity plate theory", Aerosp. Sci. Technol., 32(1), 235-259. https://doi.org/10.1016/j.ast.2013.10.007.
  9. Al-shujairi. M, and Cagri, Mollamahmutoglu (2018), "Buckling and free vibration analysis of functionally graded sandwich micro-beams resting on elastic foundation by using nonlocal strain gradient theory in conjunction with higher order shear theories under thermal effect", Composites Part B, 154, 292-312. https://doi.org/10.1016/j.compositesb.2018.08.103.
  10. Amnieh, H.B., Zamzam, M.S. and Kolahchi, R. (2018), "Dynamic analysis of non-homogeneous concrete blocks mixed by $SiO_2$ nanoparticles subjected to blast load experimentally and theoretically", Construct. Build. Mater., 174, 633-644. https://doi.org/10.1016/j.conbuildmat.2018.04.140
  11. Attia, A., Bousahla, A.A., Tounsi, A., Mahmoud, S.R., Alwabli, A.S. (2018), "A refined four variable plate theory for thermoelastic analysis of FGM plates resting on variable elastic foundations", Struct. Eng. Mech., 65(4), 453-464. https://doi.org/10.12989/SEM.2018.65.4.453
  12. BachirBouiadjra, R., Mahmoudi, A., Benyoucef, S., Tounsi, A. and Bernard, F., (2018), "Analytical investigation of bending response of FGM plate using a new quasi 3D shear deformation theory: Effect of the micromechanical models", Struct. Eng. Mech, 66(3), 317-328. https://doi.org/10.12989/sem.2018.66.3.317.
  13. Bellifa, H., Benrahou, K.H., Bousahla, A.A., Tounsi, A. and Mahmoud, S.R. (2017), "A nonlocal zeroth-order shear deformation theory for nonlinear postbuckling of nanobeams", Struct. Mech. Eng., 62(6), 695-702. https://doi.org/10.12989/sem.2017.62.6.695.
  14. Bessaim, A., Houari, M.S.A., Tounsi, A., Mahmoud, S.R. and AddaBedia, 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", Sandw. Struct. Mater., 15(6), 671-703. https://doi.org/10.1177/1099636213498888.
  15. Bilouei, B.S., Kolahchi, R. and Bidgoli, M.R., (2016), "Buckling of concrete columns retrofitted with Nano-Fiber Reinforced Polymer (NFRP)", Comput. Concrete, 18(5), 1053-1063. https://doi.org/10.12989/cac.2016.18.5.1053
  16. Bouadi, A., Bousahla, A.A., Houari, M.S.A., Heireche, H. and Tounsi, A. (2018), "A new nonlocal HSDT for analysis of stability of single layer graphene sheet", Adv. Nano Res., 6(2), 147-162. https://doi.org/10.12989/ANR.2018.6.2.147
  17. Bouhadra A,.Tounsi A,.Bousahla A.A,.Benyoucef, S. and S.R. Mahmoud, (2018), "Improved HSDT accounting for effect of thickness stretching in advanced composite plates", Struct. Eng. Mech., 66(1), 61-73. https://doi.org/10.12989/SEM.2018.66.1.061
  18. Bourada, F., Amara, K., Bousahla, A.A., Tounsi, A. and Mahmoud, S.R. (2018), "A novel refined plate theory for stability analysis of hybrid and symmetric S-FGM plates", Struct. Eng. Mech., 68(6), 661-675. https://doi.org/10.12989/sem.2018.68.6.661
  19. 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.., 28(1), 19-30.
  20. Bourada, M., Tounsi, A., Houari, M.S.A. and AddaBedia, E.A. (2012), "A new four-variable refined plate theory for thermal buckling analysis of functionally graded sandwich plates", J. Sandw. Struct. Mater.,14(1), 5-33. https://doi.org/10.1177/1099636211426386.
  21. Bourada. F., Amara. K. and Tounsi, A. (2016), "Buckling analysis of isotropic and orthotropic plates using a novel four variable refined plate theory", Steel Compos. Struct., 21(6), 1287-1306. https://doi.org/10.12989/scs.2016.21.6.1287
  22. Bousahla, A.A., Benyoucef, S., Tounsi, A. and Mahmoud, S.R. (2016), "On thermal stability of plates with functionally graded coefficient of thermal expansion", Struct. Eng. Mech., 60(2), 313-335. https://doi.org/10.12989/sem.2016.60.2.313
  23. Carrera E, Brischetto S. and Robaldo, A. (2008), "Variable kinematic model for the analysis of functionally graded material plates", AIAA J, 46(1), 194-203. https://doi.org/10.2514/1.32490.
  24. Ebrahimi, F. and Reza, B.M. (2017), "Hygrothermal effects on vibration characteristics of viscoelastic FG nanobeams based on nonlocal strain gradient theory", Compos. Struct., 159, 433-444. https://doi.org/10.1016/j.compstruct.2016.09.092.
  25. Fakhar, A. and Kolahchi, R. (2018), "Dynamic buckling of magneto rheological fluid integrated by visco-piezo-GPL reinforced plates" , J. Mech. Sci., 144, 788-799. https://doi.org/10.1016/j.ijmecsci.2018.06.036
  26. Golabchi, H., Kolahchi, R. and RabaniBidgoli, M. (2018), "Vibration and instability analysis of pipes reinforced by SiO2 nanoparticles considering agglomeration effects", Comput. Concrete, 21(4), 431-440. https://doi.org/10.12989/CAC.2018.21.4.431
  27. Gupta, A. and Talha, M. (2017), "Nonlinear flexural and vibration response of geometrically imperfect gradient plates using hyperbolic higher-order shearand normal deformation theory", Compos. Part. B Eng.,123, 241-261. https://doi.org/10.1016/j.compositesb.2017.05.010.
  28. Hadji, L, Atmane, H.A., Tounsi, A., Mechab, I. and AddaBedia, E.A., (2011), "Free vibration of functionally graded sandwich plates using four variable refined plate theory", Appl. Math. Mech., 32, 925-942. https://doi.org/10.1007/s10483-011-1470-9.
  29. Hajmohammad, M.H., Farrokhian, A. and Kolahchi, R. (2018a), "Smart control and vibration of viscoelastic actuator-multiphase nanocomposite conical shells-sensor considering hygrothermal load based on layerwise theory", Aerosp.Sci. Technol., 78, 260-270. https://doi.org/10.1016/j.ast.2018.04.030.
  30. Hajmohammad, M.H., Maleki, M. and Kolahchi, R. (2018b), "Seismic response of underwater concrete pipes conveying fluid covered with nano-fiber reinforced polymer layer", Soil Dyn. Earthq. Eng., 110, 18-27. https://doi.org/10.1016/j.soildyn.2018.04.002.
  31. Hajmohammad, M.H., Zarei, M.S., Nouri, A. and Kolahchi, R. (2017), "Dynamic buckling of sensor/functionally gradedcarbon nanotube-reinforced laminated plates/actuator based on sinusoidal-visco-piezoelasticity theories", J. Sandw. Struct. Mater., https://doi.org/10.1177/1099636217720373.
  32. Hamidi, A., Houari, M.S.A., Mahmoud, S.R. and Tounsi, A., (2015), "A sinusoidal plate theory with 5-unknowns and stretching effect for thermomechanical bending of functionally graded sandwich plates", Steel Compos. Struct.,18(1), 235-253. https://doi.org/10.12989/scs.2015.18.1.235
  33. Hebali, H., Tounsi, A., Houari, M.S.A., Bessaim, A. and AddaBedia, E.A. (2014), "New quasi-3D hyperbolic shear deformation theory for the static and free vibration analysis of functionally graded plates", J. Eng. Mech., ASCE, 140, 374-383. https://doi.org/10.1061/(ASCE)EM.1943-7889.0000665
  34. Hosseini, H. and Kolahchi, R. (2018), "Seismic response of functionally graded-carbon nanotubes-reinforced submerged viscoelastic cylindrical shell in hygrothermal environment", Physica E, 102,101-109. https://doi.org/10.1016/j.physe.2018.04.037.
  35. Houari, M.S.A., Benyoucef, S., Mechab, I., Tounsi, A and Adda Bedia, E.A. (2011), "Two variable refined plate theory for thermoelastic bending analysis of functionally graded sandwich plates", J. Therm. Stresses, 34(4), 315-334. https://doi.org/10.1080/01495739.2010.550806.
  36. Karami, B. and Janghorban, M. (2019), "On the dynamics of porous nanotubes with variable material properties and variable thickness", J. Eng. Sci., 136(C), 53-66. https://doi.org/10.1016/j.ijengsci.2019.01.002.
  37. Karami, B., Janghorban, M. and Li, L. (2018a), "On guided wave propagation in fully clamped porous functionally graded nanoplates", Acta Astronaut., 143, 380-390. https://doi.org/10.1016/j.actaastro.2017.12.011.
  38. Karami, B., Janghorban, M., Shahsavari, D. and Tounsi, A, (2018h), "A size-dependent quasi-3D model for wave dispersion analysis of FG nanoplates", Steel Compos. Struct., 28(1), 99-110. https://doi.org/10.12989/scs.2018.28.1.099.
  39. Karami, B., Janghorban, M. and Tounsi, A. (2018e), "Variational approach for wave dispersion in anisotropic doubly-curved nanoshells based on a new nonlocal strain gradient higher order shell theory", Thin-Walled Struct,129, 251-264. https://doi.org/10.1016/j.tws.2018.02.025.
  40. Karami, B., Janghorban, M. and Tounsi, A. (2018g), "Nonlocal strain gradient 3d elasticity theory for anisotropic spherical nanoparticles", Steel Compos. Struct, 27(2), 201-216. https://doi.org/10.12989/SCS.2018.27.2.201
  41. Karami, B., Shahsavari, D., Janghorban, M., Dimitri, R. and Tornabene, F. (2019), "Wave Propagation of Porous Nanoshells", Nanomaterials, 9(1), 1-19. https://doi.org/10.3390/nano9010022.
  42. Karami, B., Shahsavari, D., Li, L., Karami, M. and Janghorban, M. (2018c), "Thermal buckling of embedded sandwich piezoelectric nanoplates with functionally graded core by a nonlocal second-order shear deformation theory", Proceedings of the Institution of Mechanical Engineers, Part C, 233(1), 287-301. https://doi.org/10.1177/0954406218756451
  43. Karami, B., Shahsavari, D., Nazemosadat, S.M.R., Li, L. (2018d), "Thermal buckling of smart porous functionally graded nanobeam rested on kerr foundation", Steel Compos. Struct., 29(3), 349-362. https://doi.org/10.12989/scs.2018.29.3.349.
  44. Karami, B., Janghorban, M. and Tounsi. A. (2018f), "Galerkin's approach for buckling analysis of functionally graded anisotropic nanoplates/different boundary conditions", Eng. Comput., 1-20. https://doi.org/10.1007/s00366-018-0664-9.
  45. Karami, B., Shahsavari, D. and Li, L. (2018b), "Temperaturedependent flexural wave propagation in nanoplate-type porous heterogenous material subjected to in-plane magnetic field", J. Therm. Stresses, 41(4), 483-499. https://doi.org/10.1080/01495739.2017.1393781.
  46. Kolahchi, R. (2017), "A comparative study on the bending, vibration and buckling of viscoelastic sandwich nano-plates based on different nonlocal theories using DC, HDQ and DQ methods", Aerosp. Sci. Technol., 66, 235-248. https://doi.org/10.1016/j.ast.2017.03.016.
  47. Kolahchi, R. and Cheraghbak, A. (2017), "Agglomeration effects on the dynamic buckling of viscoelastic microplates reinforced with SWCNTs using Bolotin method", Nonlin.Dyn., 90(1), 479492. https://doi.org/10.1007/s11071-017-3676-x.
  48. Kolahchi, R. and Arani, A.J. (2016), "Buckling analysis of embedded concrete columns armed with carbon nanotubes", Comput. Concrete, 17(5), 567-578. https://doi.org/10.12989/cac.2016.17.5.567
  49. Kolahchi, R., Keshtegar, B. and Fakhar, M.H. (2017b), "Optimization of dynamic buckling for sandwich nanocomposite plates with sensor and actuator layer based on sinusoidal-visco-piezoelasticity theories using Grey Wolf algorithm", J. Sandw. Struct. Mater. https://doi.org/10.1177/1099636217731071.
  50. Kolahchi, R., Zarei, M.S., Hajmohammad, M.H. and Nouri, A. (2017a), "Wave propagation of embedded viscoelastic FGCNT-reinforced sandwich plates integrated with sensor and actuator based on refined zigzag theory", J. Mech. Sci., 130, 534-545. https://doi.org/10.1016/j.ijmecsci.2017.06.039.
  51. Kolahchi, R., Safari, M. and Esmailpour, M. (2016), "Dynamic stability analysis of temperature-dependent functionally graded CNT-reinforced visco-plates resting on orthotropic elastomeric medium", Compos. Struct.,150, 255-265. https://doi.org/10.1016/j.compstruct.2016.05.023.
  52. Li, D., Deng, Z. and Xiao, H. (2016), "Thermomechanical bending analysis of functionally graded sandwich plates using fourvariable refined plate theory", Compos. Pt B., 106, 107-119. https://doi.org/10.1016/j.compositesb.2016.08.041.
  53. Li, X.F. (2008), "A unified approach for analyzing static and dynamic behaviors of functionally graded Timoshenko and Euler-Bernoulli beams", J. Sound Vib.., 318, 1210-1229. https://doi.org/10.1016/j.jsv.2008.04.056.
  54. Madani, H., Hosseini, H. and Shokravi, M. (2016), "Differential cubature method for vibration analysis of embedded FG-CNT reinforced piezoelectric cylindrical shells subjected to uniform and non-uniform temperature distributions", Steel Compos. Struct., 22(4), 889-913. https://doi.org/10.12989/scs.2016.22.4.889
  55. Mahmoudi, A., Benyoucef, S., Tounsi, A., Benachour, A., AddaBedia, E.A and Mahmoud, S.R. (2017), "A refined quasi-3D shear deformation theory for thermo-mechanical behaviour of functionally graded sandwich plates on elastic foundations", J. Sandw. Struct. Mater., https://doi.org/10.1177/1099636217727577.
  56. Mahmoudi, A., Benyoucef, S., Tounsi, A., Benachour, A and Adda Bedia, E.A. (2018), "On the effect of the micromechanical models on the free vibration of rectangular FGM plate resting on elastic foundation", Struct. Eng. Mech., 14(2), 117-128. https://doi.org/10.12989/eas.2018.14.2.117.
  57. Mantari, J.L., Oktem, A.S. and Soares, O.G. (2012), "Bending response of functionally graded plates by using a new higher order shear deformation theory", Compos Struct., 94, 714-723. https://doi.org/10.1016/j.compstruct.2011.09.007.
  58. Mantari, J.L. and Soares, C.G. (2014), "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.
  59. Meksi, A., Benyoucef, S., Houari, M.S.A. and Tounsi, A. (2015), "A simple shear deformation theory based on neutral surface position for functionally graded plates resting on Pasternak elastic foundations", Struct. Eng. Mech., 53(6), 1215-1240. https://doi.org/10.12989/sem.2015.53.6.1215
  60. 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.
  61. Menasria, A., Bouhadra, A., Tounsi, A., Bousahla, A.A. and S.R. Mahmoud (2017), "A new and simple HSDT for thermal stability analysis of FG sandwich plates". Steel Compos.Struct., 25(2), 157-175. https://doi.org/10.12989/scs.2017.25.2.157.
  62. Merdaci, S., Tounsi, A., Houari, M.S.A., Mechab, I., Hebali, H., Benyoucef, S. (2011), "Two new refined shear displacement models for functionally graded sandwich plates". Arch. Appl. Mech., 81, 1507-1522. https://doi.org/10.1007/s00419-010-0497-5.
  63. Mindlin, R.D. (1951), "Influence of rotary inertia and shear on flexural motions of isotropic elastic plates", J. Appl. Mech., 18, 31-38. https://doi.org/10.1115/1.4010217
  64. Natarajan, S. and Manickam, G. (2012), "Bending and vibration of functionally graded material sandwich plates using an accurate theory", Finite. Elem. Anal. Des., 57, 32-42. https://doi.org/10.1016/j.finel.2012.03.006.
  65. Neves, A., Ferreira, A., Carrera, E., Cinefra, M., Jorge, R. and Soares, C. (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", J. Appl. Math. Mech., 92(9), 749-766. https://doi.org/10.1002/zamm.201100186.
  66. Neves, A.M.A., Ferreira, A.J.M., Carrera, E., Cinefra, M., Roque, C.M.C., Jorge, R.M.N and Soares, C.M.M. (2013), "Static, free vibration and buckling analysis of isotropic and sandwich functionally graded plates using a quasi-3D higher-order shear deformation theory and a meshless technique", Compos Part B:Eng., 44, 657-674. https://doi.org/10.1016/j.compositesb.2012.01.089.
  67. 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. Pt. B Eng., 66, 233-246. https://doi.org/10.1016/j.compositesb.2014.05.012.
  68. Petrov, N.A., Gorbatikh, L. and Lomov, V.S. (2018), "A parametric study assessing performance of eXtended Finite Element Method in application to the cracking process in crossply composite laminates", Compos. Struct.,187, 498-508. https://doi.org/10.1016/j.compstruct.2017.12.014.
  69. Reissner, E. (1945), "The effect of transverse shear deformation on the bending of elastic plates", J. Appl. Mech., 12(2), 69-77.
  70. Sekkal, M., Fahsi, B., Tounsi, A. and Mahmoud, S.R. (2017), "A novel and simple higher order shear deformation theory for stability and vibration of functionally graded sandwich plate", Steel Compos. Struct., 25(4), 389-401. https://doi.org/10.12989/SCS.2017.25.4.389
  71. Shahsavari, D., Karami, B., Fahham, H.R. and Li, L. (2018c), "On the shear buckling of porous nanoplates using a new sizedependent quasi-3d shear deformation theory", Acta Mech.229(11), 4549-4573. https://doi.org/10.1007/s00707-018-2247-7.
  72. Shahsavari, D., Karami, B., Janghorban, M. and Li, L. (2017), "Dynamic characteristics of viscoelastic nanoplates under moving load embedded within visco-Pasternak substrate and hygrothermal environment", Mater. Res. Exp.,4(8), 085013. https://doi.org/10.1088/2053-1591/aa7d89
  73. Shahsavari, D., Karami, B., Janghorban, M. and Li, L. (2018a), "Damped vibration of a graphene sheet using a higher-order nonlocal strain-gradient Kirchhoff plate model", Comptes Rendus Mecanique, 346 (12), 1216-1232. https://doi.org/10.1016/j.crme.2018.08.011.
  74. Shahsavari, D., Shahsavari, M., Li, L. and Karami, B. (2018b), "A novel quasi-3D hyperbolic theory for free vibration of FG plates with porosities resting on Winkler/Pasternak/Kerr foundation", Aerospace Science and Technology, 72, 134-149. https://doi.org/10.1016/j.ast.2017.11.004.
  75. She, G.L., Yuan, F.G., Ren, R.Y. and Xiao, W.S. (2017), "On buckling and postbuckling behavior of nanotubes", J. Eng. Sci., 121, 130-142. https://doi.org/10.1016/j.ijengsci.2017.09.005.
  76. She, G.L., Yuan, F.G., Karami, B., Ren, Y.R. and Xiao, W.S. (2019), "On nonlinear bending behavior of fg porous curved nanotubes", Int. J. Eng. Sci., 135, 58-74. https://doi.org/10.1016/j.ijengsci.2018.11.005.
  77. She, G.L., Yuan, F.G. and Ren, Y.R. (2018), "On wave propagation of porous nanotubes", Int. J. Eng. Sci, 130, 62-74. https://doi.org/10.1016/j.ijengsci.2018.05.002.
  78. Taibi, F.Z, Benyoucef, S., Tounsi, A., BachirBouiadjra, R., AddaBedia, 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.
  79. Thai, H.T. and Kim, S.E. (2013), "A simple higher-order shear deformation theory for bending and free vibration analysis of functionally graded plates", Compos. Struct., 96, 165-173. https://doi.org/10.1016/j.compstruct.2012.08.025.
  80. Thai, H.T. and Choi, D.H. (2013), "A simple first-order shear 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.
  81. Thai, H.T. and Choi, D.H. (2012), "An efficient and simple refined theory for buckling analysis of functionally graded plates", Appl. Math. Model., 36, 1008-1022. https://doi.org/10.1016/j.apm.2011.07.062
  82. Thai, H.T., Nguyen, T.K. and Vo, T. (2014), "Analysis of functionally graded sandwich plates using a new first- order shear deformation theory", Europ. J. Mech. A/Solids., 45, 211-225. https://doi.org/10.1016/j.euromechsol.2013.12.008.
  83. Tounsi, A., Houari, M.S.A. and Benyoucef, S. (2013), "A refined trigonometric shear deformation theory for thermoelastic bending of functionally graded sandwich plates", Aerosp. Sci. Technol., 24(1), 209-220. https://doi.org/10.1016/j.ast.2011.11.009.
  84. Uymaz, B. and Aydogdu, M. (2007), "Three-dimensional vibration analyses of functionally graded plates under various boundary conditions", J. Reinf. Plast. Compos., 26(18), 1847-1863. https://doi.org/10.1177/0731684407081351.
  85. Wu, C.P. and Chiu, K.H. (2011), "RMVT-based meshless collocation and element-free Galerkin methods for the quasi-3D free vibration analysis of multilayered composite and FGM plates", Compos. Struct. 93(5), 1433-1448. https://doi.org/10.1016/j.compstruct.2010.11.015.
  86. Xiang, S., Jin, Y., Bi, Z., Jiang, S. and Yang, M. (2011), "A n-order shear deformation theory for free vibration of functionally graded and composite sandwich plates", Compos. Struct., 93, 2826-2832. https://doi.org/10.1016/j.compstruct.2011.05.022.
  87. Xiang, S., Kang, G., Yang, M. and Zhao, Y. (2013), "Natural frequencies of sandwich plate with functionally graded face and homogeneous core", Compos. Struct., 96, 226-231. https://doi.org/10.1016/j.compstruct.2012.09.003.
  88. Zamanian, M., Kolahchi, R. and Bidgoli, M.R. (2017), "Agglomeration effects on the buckling behaviour of embedded concrete columns reinforced with SiO2 nano-particles", Wind Struct., 24(1), 43-57. https://doi.org/10.12989/was.2017.24.1.043.
  89. Zarei, M.S., Kolahchi, R., Hajmohammad, M.H. and Maleki, M. (2017), "Seismic response of underwater fluid-conveying concrete pipes reinforced with SiO nanoparticles and fiber reinforced polymer (FRP) layer", Soil Dyn. Earthq. Eng., 103, 76-85. https://doi.org/10.1016/j.soildyn.2017.09.009.
  90. Zenkour, A.M. (2006), "Generalized shear deformation theory for bending analysis of functionally graded materials", Appl Math Model, 30, 67-84. https://doi.org/10.1016/j.apm.2005.03.009.
  91. Zenkour, M. (2013), "Bending analysis of functionally graded sandwich plates using a simple four-unknown shear and normal deformations theory", J. Sandwich. Struct. Mater., 15, 629-656. https://doi.org/10.1177/1099636213498886.
  92. Zenkour, A.M. (2005a), "A comprehensive analysis of functionally graded sandwich plates: Part 1-Deflection and stresses", Inter. J. Sol. Struct., 42, 5224-5242. https://doi.org/10.1016/j.ijsolstr.2005.02.015.
  93. Zenkour, A.M. (2005b), "A Comprehensive Analysis of Functionally Graded Sandwich Plates: Part 2-Buckling and Free Vibration", Inter. J. of Sol. and Struct., 42, 5243-5258. https://doi.org/10.1016/j.ijsolstr.2005.02.016.
  94. Zenkour, A.M. and Alghamdi, N.A. (2010), "Bending analysis of functionally graded sandwich plates under the effect of mechanical and thermal loads", Mec. Ad. Mater. Struct., 17, 419-432. https://doi.org/10.1080/15376494.2010.483323.

Cited by

  1. Vibration behavior of bi-dimensional functionally graded beams vol.77, pp.5, 2019, https://doi.org/10.12989/sem.2021.77.5.587