Steel and Composite Structures

  • 제41권2호
  • /
  • Pages.167-191
  • /
  • 2021
  • /
  • 1229-9367(pISSN)
  • /
  • 1598-6233(eISSN)
테크노프레스 (Techno-Press)
권호 표지
DOI QR코드

DOI QR Code

An original four-variable quasi-3D shear deformation theory for the static and free vibration analysis of new type of sandwich plates with both FG face sheets and FGM hard core

  • Kouider, Djilali (Material and Hydrology Laboratory, University of Sidi Bel Abbes, Faculty of Technology, Department of Civil Engineering) ;
  • Kaci, Abdelhakim (Universite Dr Tahar Moulay, Faculte de Technologie, Departement de Genie Civil et Hydraulique) ;
  • Selim, Mahmoud M. (Department of Mathematics, Al-Aflaj College of Science and Humanities, Prince Sattam bin Abdulaziz University) ;
  • Bousahla, Abdelmoumen Anis (Laboratoire de Modelisation et Simulation Multi-echelle, Universite de Sidi Bel Abbes) ;
  • Bourada, Fouad (Material and Hydrology Laboratory, University of Sidi Bel Abbes, Faculty of Technology, Department of Civil Engineering) ;
  • Tounsi, Abdeldjebbar (Material and Hydrology Laboratory, University of Sidi Bel Abbes, Faculty of Technology, Department of Civil Engineering) ;
  • Tounsi, Abdelouahed (Material and Hydrology Laboratory, University of Sidi Bel Abbes, Faculty of Technology, Department of Civil Engineering) ;
  • Hussain, Muzamal (Department of Mathematics, Govt. College University Faisalabad)
  • 투고 : 2020.12.25
  • 심사 : 2021.09.08
  • 발행 : 2021.10.25
⟨ 이전 논문 다음 논문 ⟩

초록

This paper presents an original high-order shear and normal deformation theory for the static and free vibration of sandwich plates. The number of unknowns and governing equations of the present theory is reduced, and hence makes it simple to use. Unlike any other theory, the number of unknown functions involved in displacement field is only four, as against five or more in the case of other shear and normal deformation theories. New types of functionally graded materials (FGMs) sandwich plates are considered, namely, both FG face sheets which the properties vary according to power-law function and exponentially graded hard core. The equations of motion for the present problem are derived from Hamilton's principle. For simply-supported boundary conditions, Navier's approach is utilized to solve the motion equations. The accuracy of the present theory is verified by comparing the obtained results with three-dimensional elasticity solutions and other quasi-3D higher-order theories reported in the literature. Other numerical examples are also presented to show the influences of the volume fraction distribution, geometrical parameters and power law index on the bending and free vibration responses of the FGM sandwich plates are studied. It can be concluded that present formulation which takes into account both the transverse shear and normal deformation, predicts the natural frequencies with the same degree of accuracy as that of 3D elasticity solutions and gives a good results of displacements and stress compared with others Quasi-3D theories. It can be also deduced that the central deflection is in direct correlation relation with inhomogeneity parameter and the natural frequency is in inverse relation with this parameter.

키워드

참고문헌

  1. Abbas, S., Benguediab, S., Draiche, K., Bakora, A. and Benguediab, M. (2020), "An efficient shear deformation theory with stretching effect for bending stress analysis of laminated composite plates", Struct. Eng. Mech., 74(3), 365-380. https://doi.org/10.12989/sem.2020.74.3.365.
  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. 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.
  4. Akbas, S.D. (2020), "Dynamic responses of laminated beams under a moving load in thermal environment", Steel Compos. Struct., 35(6), 729-737. https://doi.org/10.12989/scs.2020.35.6.729.
  5. 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.
  6. Alibeigloo, A. and Liew, K.M. (2014), "Free vibration analysis of sandwich cylindrical panel with functionally graded core using three-dimensional theory of elasticity", Compos. Struct., 113, 23-30. https://doi.org/10.1016/j.compstruct.2014.03.004.
  7. 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.
  8. 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.
  9. 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.
  10. Belabed, Z., Ahmed Houari, M.S., Tounsi, A., Mahmoud, S.R. and Anwar Beg, O. (2014), "An efficient and simple higher order shear and normal deformation theory for functionally graded material (FGM) plates", Compos. Part B: Eng., 60, 274-283. https://doi.org/10.1016/j.compositesb.2013.12.057.
  11. Benachour, A., Tahar, H.D., Atmane, H.A., Tounsi, A. and Ahmed, M.S. (2011), "A four variable refined plate theory for free vibrations of functionally graded plates with arbitrary gradient", Compos. Part B: Eng., 42(6), 1386-1394. https://doi.org/10.1016/j.compositesb.2011.05.032.
  12. Benferhat, R., Daouadji, T.H. and Rabahi, A. (2021b), "Effect of air bubbles in concrete on the mechanical behavior of RC beams strengthened in flexion by externally bonded FRP plates under uniformly distributed loading", Compos. Mater. Eng., 3(1), 41-55. https://doi.org/10.12989/cme.2021.3.1.041.
  13. Bennoun, M., Houari, M.S.A. and Tounsi, A. (2015), "A novel five-variable refined plate theory for vibration analysis of functionally graded sandwich plates", Mech. Adv. Mater. Struct., 23(4), 423-431. https://doi.org/10.1080/15376494.2014.984088.
  14. Bessaim, A., Houari, M.S., Tounsi, A., Mahmoud, S. and Bedia, E. A.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", J. Sandw. Struct. Mater., 15(6), 671-703. https://doi.org/10.1177/1099636213498888.
  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 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.
  17. Carrera, E. and Brischetto, S. (2009), "A survey with numerical assessment of classical and refined theories for the analysis of sandwich plates", Appl. Mech. Rev., 62(1), 010803. https://doi.org/10.1115/1.3013824.
  18. Chen, C.S., Hsu, C.Y. and Tzou, G.J. (2009), "Vibration and stability of functionally graded plates based on a higher-order deformation theory", J. Reinf. Plast. Compos., 28(10), 1215-1234. https://doi.org/10.1177/0731684408088884.
  19. Civalek, O. and Avcar, M. (2020), "Free vibration and buckling analyses of CNT reinforced laminated non-rectangular plates by discrete singular convolution method", Eng. with Comput.. https://doi.org/10.1007/s00366-020-01168-8.
  20. 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.
  21. Dean, J., S-Fallah, A., Brown, P.M., Louca, L.A. and Clyne, T.W. (2011), "Energy absorption during projectile perforation of lightweight sandwich panels with metallic fibre cores", Compos. Struct., 93(3), 1089-1095. https://doi.org/10.1016/j.compstruct.2010.09.019.
  22. Do, V.N.V. and Lee, C.H. (2017), "Thermal buckling analyses of FGM sandwich plates using the improved radial point interpolation mesh-free method", Compos. Struct., 177, 171-186. https://doi.org/10.1016/j.compstruct.2017.06.054.
  23. 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.
  24. Fazzolari, F.A. (2015), "Natural frequencies and critical temperatures of functionally graded sandwich plates subjected to uniform and non-uniform temperature distributions", Compos. Struct., 121, 197-210. https://doi.org/10.1016/j.compstruct.2014.10.039.
  25. Fenjan, R.M., Moustafa, N.M. and Faleh, N.M. (2020a), "Scale-dependent thermal vibration analysis of FG beams having porosities based on DQM", Adv. Nano Res., 8(4), 283-292. http://dx.doi.org/10.12989/anr.2020.8.4.283.
  26. Ferreira, A.J.M., Carrera, E., Cinefra, M., Roque, C.M.C. and Polit, O. (2011), "Analysis of laminated shells by a sinusoidal shear deformation theory and radial basis functions collocation, accounting for through-the-thickness deformations", Compos. Part B: Eng., 42(5), 1276-1284. https://doi.org/10.1016/j.compositesb.2011.01.031.
  27. Forcellese, A. and Simoncini, M. (2020), "Mechanical properties and formability of metal-polymer-metal sandwich composites", Int. J. Adv. Manufact. Technol., 1-17. https://doi.org/10.1007/s00170-020-05245-6.
  28. Fu, T., Chen, Z., Yu, H., Wang, Z. and Liu, X. (2018), "An analytical study of sound transmission through corrugated core FGM sandwich plates filled with porous material", Compos. Part B: Eng., 151, 161-172. https://doi.org/10.1016/j.compositesb.2018.06.010.
  29. 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.
  30. Ghandourah, E.E. and Abdraboh, A.M. (2020), "Dynamic analysis of functionally graded nonlocal nanobeam with different porosity models", Steel Compos. Struct., 36(3), 293-305. http://doi.org/10.12989/scs.2020.36.3.293.
  31. Gomes, G.F., de Almeida, F.A., Ancelotti, A.C. and da Cunha, S.S. (2020), "Inverse structural damage identification problem in CFRP laminated plates using SFO algorithm based on strain fields", Eng. with Comput.. https://doi.org/10.1007/s00366-020-01027-6.
  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. Hadji, L., Atmane, H.A., Tounsi, A., Mechab, I. and Adda Bedia, E. A. (2011), "Free vibration of functionally graded sandwich plates using four-variable refined plate theory", Appl. Math. Mech., 32(7), 925-942. https://doi.org/10.1007/s10483-011-1470-9.
  34. Hashim, H.A. and Sadiq, I.A. (2021), "A five-variable refined plate theory for thermal buckling analysis of composite plates", Compos. Mater. Eng., 3(2), 135-155. http://dx.doi.org/10.12989/cme.2021.3.2.135.
  35. 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", Steel Compos. Struct., 34(2), 279-288. https://doi.org/10.12989/scs.2020.34.2.279.
  36. Jung, W.Y., Han, S.C. and Park, W.T. (2016), "Four-variable refined plate theory for forced-vibration analysis of sigmoid functionally graded plates on elastic foundation", Int. J. Mech. Sci., 111-112, 73-87. https://doi.org/10.1016/j.ijmecsci.2016.03.001.
  37. Kant, T. and Swaminathan, K. (2002), "Analytical solutions for the static analysis of laminated composite and sandwich plates based on a higher order refined theory", Compos. Struct., 56(4), 329-344. https://doi.org/10.1016/s0263-8223(02)00017-x.
  38. Karami, B., Shahsavari, D., Janghorban, M. and Li, L. (2020), "Free vibration analysis of FG nanoplate with poriferous imperfection in hygrothermal environment", Struct. Eng. Mech., 73(2), 191-207. https://doi.org/10.12989/sem.2020.73.2.191.
  39. Kashtalyan, M. and Menshykova, M. (2009), "Three-dimensional elasticity solution for sandwich panels with a functionally graded core", Compos. Struct., 87(1), 36-43. https://doi.org/10.1016/j.compstruct.2007.12.003.
  40. Kiani, Y. (2019), "NURBS-based thermal buckling analysis of graphene platelet reinforced composite laminated skew plates", J. Therm. Stresses, 1-19. https://doi.org/10.1080/01495739.2019.1673687.
  41. Koizumi, M. (1997), "FGM activities in Japan", Compos. Part B: Eng., 28(1-2), 1-4. https://doi.org/10.1016/s1359-8368(96)00016-9.
  42. Li, D., Deng, Z., Chen, G., Xiao, H. and Zhu, L. (2017), "Thermomechanical bending analysis of sandwich plates with both functionally graded face sheets and functionally graded core", Compos. Struct., 169, 29-41. https://doi.org/10.1016/j.compstruct.2017.01.026.
  43. Li, Q., Iu, V.P. and Kou, K.P. (2008), "Three-dimensional vibration analysis of functionally graded material sandwich plates", J. Sound Vib., 311(1-2), 498-515. https://doi.org/10.1016/j.jsv.2007.09.018.
  44. Lindstrom, A. and Hallstrom, S. (2010), "Energy absorption of SMC/balsa sandwich panels with geometrical triggering features", Compos. Struct., 92(11), 2676-2684. https://doi.org/10.1016/j.compstruct.2010.03.018.
  45. Love, A.E.H. (1888), "On the small free vibrations and deformations of elastic shells", Philos. T. Roy. Soc.(London), 17. 491-549.
  46. 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.
  47. Mantari, J.L. and Guedes Soares, C. (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.
  48. Mantari, J.L., Oktem, A.S. and Guedes Soares, C. (2012a), "A new trigonometric layerwise shear deformation theory for the finite element analysis of laminated composite and sandwich plates", Comput. Struct., 94-95, 45-53. https://doi.org/10.1016/j.compstruc.2011.12.003.
  49. Mantari, J.L., Oktem, A.S. and Guedes Soares, C. (2012b), "A new higher order shear deformation theory for sandwich and composite laminated plates", Compos. Part B: Eng., 43(3), 1489-1499. https://doi.org/10.1016/j.compositesb.2011.07.017.
  50. Marshall, A. (1982), "Sandwich construction", Handbook of composites., Boston, MA, 557-601.
  51. 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.
  52. Mehar, K., Panda, S.K. and Mahapatra, T.R. (2017), "Thermoelastic nonlinear frequency analysis of CNT reinforced functionally graded sandwich structure", Eur. J. Mech. - A/Solids, 65, 384-396. https://doi.org/10.1016/j.euromechsol.2017.05.005.
  53. Mercan, K., Ebrahimi, F. and Civalek, O. (2020), "Vibration of angle-ply laminated composite circular and annular plates", Steel Compos. Struct., 34(1), 141-154. https://doi.org/10.12989/scs.2020.34.1.141.
  54. 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.
  55. 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
  56. Mirjavadi, S.S., Forsat, M., Nia, A.F., Badnava, S. and Hamouda, A.M.S. (2020), "Nonlocal strain gradient effects on forced vibrations of porous FG cylindrical nanoshells", Adv. Nano Res., 8(2), 149-156. https://doi.org/10.12989/anr.2020.8.2.149.
  57. Miyamoto, Y. (1999), "Functionally graded materials: design, processing and applications", Boston, MA: Kluwer Academic Publishers.
  58. Moayedi, H., Ebrahimi, F., Habibi, M., Safarpour, H., & Foong, L. K. (2020), "Application of nonlocal strain-stress gradient theory and GDQEM for thermo-vibration responses of a laminated composite nanoshell", Eng. with Comput., https://doi.org/10.1007/s00366-020-01002-1.
  59. Neves, A.M.A., Ferreira, A.J.M., Carrera, E., Cinefra, M., Jorge, R. M.N. and Soares, C.M.M. (2012c), "Static analysis of functionally graded sandwich plates according to a hyperbolic theory considering Zig-Zag and warping effects", Adv. Eng. Softw., 52, 30-43. https://doi.org/10.1016/j.advengsoft.2012.05.005.
  60. 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. (2012b), "A quasi3D hyperbolic shear deformation theory for the static and free vibration analysis of functionally graded plates", Compos. Struct., 94(5), 1814-1825. https://doi.org/10.1016/j.compstruct.2011.12.005.
  61. 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(1), 657-674. https://doi.org/10.1016/j.compositesb.2012.01.089.
  62. 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. (2012a), "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.
  63. Nguyen, N.V., Nguyen-Xuan, H. and Lee, J. (2021), "A quasi-three-dimensional isogeometric model for porous sandwich functionally graded plates reinforced with graphene nanoplatelets", J. Sandw. Struct. Mater.. https://doi.org/10.1177/10996362211020451.
  64. Nguyen, N.V., Nguyen-Xuan, H., Lee, D. and Lee, J. (2020a), "Anovel computational approach to functionally graded porous plates with graphene platelets reinforcement", Thin-Wall. Struct., 150, 106684. https://doi.org/10.1016/j.tws.2020.106684.
  65. Nguyen, N.V., Nguyen-Xuan, H., Nguyen, T.N., Kang, J., Lee, J. (2020b), "A comprehensive analysis of auxetic honeycomb sandwich plates with graphene nanoplatelets reinforcement", Compos. Struct., https://doi.org/10.1016/j.compstruct.2020.113213.
  66. Nguyen, Q.H., Nguyen, L.B., Nguyen, H.B. and Nguyen-Xuan, H. (2020c), "A three-variable high order shear deformation theory for isogeometric free vibration, buckling and instability analysis of FG porous plates reinforced by graphene platelets", Compos. Struct., 245, 112321. https://doi.org/10.1016/j.compstruct.2020.112321.
  67. Pourmoayed, A., Fard, K.M. and Rousta, B. (2021), "Free vibration analysis of sandwich structures reinforced by functionally graded carbon nanotubes", Compos. Mater. Eng., 3(1), 1-23. http:// doi.org/10.12989/cme.2021.3.1.001.
  68. Rachedi, M.A., Benyoucef, S., Bouhadra, A., Bachir Bouiadjra, 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.
  69. Reddy, J.N. (2011), "A general nonlinear third-order theory of functionally graded plates", Int. J. Aerosp. Lightweight Struct. (IJALS), 1(1), 1-21. https://doi.org/10.3850/s201042861100002x.
  70. Reissner, E. (1945), "Reflection on the theory of elastic plates", J Appl. Mech., 38, 1453-1464. https://doi.org/10.1115/1.3143699
  71. Rezaiee-Pajand, M., Arabi, E. and Masoodi, A.R. (2019), "Nonlinear analysis of FG-sandwich plates and shells", Aerosp. Sci. Technol., 87, 178-189. https://doi.org/10.1016/j.ast.2019.02.017.
  72. Rezaiee-Pajand, M., Masoodi, A.R. and Arabi, E. (2018a), "Geometrically nonlinear analysis of FG doubly-curved and hyperbolical shells via laminated by new element", Steel Compos. Struct., 28(3), 389-401. https://doi.org/10.12989/scs.2018.28.3.389.
  73. Rezaiee-Pajand, M., Masoodi, A.R. and Arabi, E. (2018d), "On the shell thickness-stretching effects using seven-parameter triangular element", Eur. J. Comput. Mech., 27(2), 163-185. https://doi.org/10.1080/17797179.2018.1484208.
  74. Rezaiee-Pajand, M., Masoodi, A.R. and Mokhtari, M. (2018c), "Static analysis of functionally graded non-prismatic sandwich beams", Adv. Comput. Design, 3(2), 165-190. https://doi.org/10.12989/acd.2018.3.2.165.
  75. Rezaiee-Pajand, M., Mokhtari, M. and Masoodi, A.R. (2018b), "Stability and free vibration analysis of tapered sandwich columns with functionally graded core and flexible connections", CEAS Aeronaut. J., 9(4), 629-648. https://doi.org/10.1007/s13272-018-0311-6.
  76. Rezaiee-Pajand, M., Sobhani, E. and Masoodi, A.R. (2020), "Free vibration analysis of functionally graded hybrid matrix/fiber nanocomposite conical shells using multiscale method", Aerosp. Sci. Technol., 105, 105998. https://doi.org/10.1016/j.ast.2020.105998.
  77. Safaei, B. (2020), "The effect of embedding a porous core on the free vibration behavior of laminated composite plates", Steel Compos. Struct., 35(5), 659-670. https://doi.org/10.12989/scs.2020.35.5.659.
  78. 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.
  79. Seyfaddini, F., Nguyen-Xuan, H. and Nguyen, V.H. (2021), "A semi-analytical isogeometric analysis for wave dispersion in functionally graded plates immersed in fluids", Acta Mech., 232, 15-32. https://doi.org/10.1007/s00707-020-02818-0.
  80. 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/cs.2020.34.3.361.
  81. Shen, H.S. and Li, S.R. (2008), "Postbuckling of sandwich plates with FGM face sheets and temperature-dependent properties", Compos. Part B: Eng., 39(2), 332-344. https://doi.org/10.1016/j.compositesb.2007.01.004.
  82. Shimpi, R.P. (2002), "Refined plate theory and its variants", AIAA J., 40(1), 137-146. https://doi.org/10.2514/2.1622.
  83. Sobhani, E., Masoodi, A.R. and Ahmadi-Pari, A.R. (2021), "Vibration of FG-CNT and FG-GNP sandwich composite coupled Conical-Cylindrical-Conical shell", Compos. Struct., 273, 114281. https://doi.org/10.1016/j.compstruct.2021.114281.
  84. 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.
  85. Sobhy, M. (2016), "An accurate shear deformation theory for vibration and buckling of FGM sandwich plates in hygrothermal environment", Int. J. Mech. Sci., 110, 62-77. https://doi.org/10.1016/j.ijmecsci.2016.03.003.
  86. Suresh, S. and Mortensen, A. (1998), "Fundamentals of functionally graded materials", London: Maney Publishing.
  87. Talebizadehsardari, P., Eyvazian, A., Azandariani, M.G., Tran, T. N., Rajak, D.K. and Mahani, R.B. (2020), "Buckling analysis of smart beams based on higher order shear deformation theory and numerical method", Steel Compos. Struct., 35(5), 635-640. https://doi.org/10.12989/scs.2020.35.5.635.
  88. Talha, M. and Singh, B.N. (2010), "Static response and free vibration analysis of FGM plates using higher order shear deformation theory", Appl. Math. Model., 34(12), 3991-4011. https://doi.org/10.1016/j.apm.2010.03.034.
  89. Tanzadeh, H. and Amoushahi, H. (2021), "Analysis of laminated composite plates based on different shear deformation plate theories", Struct. Eng. Mech., 75(2), 247-269. https://doi.org/10.12989/sem.2020.75.2.247.
  90. 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., 8(2), 135-148. https://doi.org/10.12989/anr.2020.8.2.135.
  91. 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.
  92. Vinson J.R. (2005), "Sandwich Structures: Past, Present, and Future", In: Thomsen O., Bozhevolnaya E., Lyckegaard A. (eds) Sandwich Structures 7: Advancing with Sandwich Structures and Materials. Springer, Dordrecht. 3-12. https://doi.org/10.1007/1-4020-3848-8_1.
  93. Vinson, J.R. (2001), "Sandwich Structures", Appl. Mech. Rev., 54(3), 201-214. https://doi.org/10.1115/1.3097295.
  94. 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.
  95. Wang, H., Yan, W. and Li, C. (2020), "Response of angle-ply laminated cylindrical shells with surface-bonded piezoelectric layers", Struct. Eng. Mech., 76(5), 599-611. https://doi.org/10.12989/sem.2020.76.5.599.
  96. Wu, Z.P., Liu, G.R. and Han, X. (2002), "An inverse procedure for crack detection in anisotropic laminated plates using elastic waves", Eng. with Comput., 18(2), 116-123. https://doi.org/10.1007/s003660200010.
  97. Yaylaci, M. and Avcar, M. (2020), "Finite element modeling 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.
  98. Zenkert, D. (1997), "The handbook of sandwich construction", Engineering Materials Advisory Services,.

피인용 문헌

  1. Free Vibration of Composite Cylindrical Shells Based on Third-Order Shear Deformation Theory vol.2021, 2021, https://doi.org/10.1155/2021/3792164