Steel and Composite Structures

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A new higher-order shear and normal deformation theory for functionally graded sandwich beams

  • Bennai, Riadh (Departement de genie civil, Faculte de genie civil et d'architecture, Univesite Hassiba Benbouali de Chlef) ;
  • Atmane, Hassen Ait (Departement de genie civil, Faculte de genie civil et d'architecture, Univesite Hassiba Benbouali de Chlef) ;
  • Tounsi, Abdelouahed (Material and Hydrology Laboratory, University of Sidi Bel Abbes, Faculty of Technology, Civil Engineering Department)
  • Received : 2014.10.31
  • Accepted : 2015.03.23
  • Published : 2015.09.25
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Abstract

A new refined hyperbolic shear and normal deformation beam theory is developed to study the free vibration and buckling of functionally graded (FG) sandwich beams under various boundary conditions. The effects of transverse shear strains as well as the transverse normal strain are taken into account. Material properties of the sandwich beam faces are assumed to be graded in the thickness direction according to a simple power-law distribution in terms of the volume fractions of the constituents. The core layer is still homogeneous and made of an isotropic material. Equations of motion are derived from Hamilton's principle. Analytical solutions for the bending, free vibration and buckling analyses are obtained for simply supported sandwich beams. Illustrative examples are given to show the effects of varying gradients, thickness stretching, boundary conditions, and thickness to length ratios on the bending, free vibration and buckling of functionally graded sandwich beams.

Keywords

References

  1. Akavci, S.S. (2010), "Two new hyperbolic shear displacement models for orthotropic laminated composite plates", Mech. Compos. Mater., 46(2), 215-226. https://doi.org/10.1007/s11029-010-9140-3
  2. Akavci, S.S. (2014a), "An efficient shear deformation theory for free vibration of functionally graded thick rectangular plates on elastic foundation", Compos. Struct., 108, 667-676. https://doi.org/10.1016/j.compstruct.2013.10.019
  3. Akavci, S.S. (2014b), "Thermal buckling a nalysis of functionally graded plates on an elastic foundation according to a hyperbolic shear deformation theory", Mech. Compos. Mater., 50(2), 197-212. https://doi.org/10.1007/s11029-014-9407-1
  4. Akavci, S.S. and Tanrikulu, A.H. (2008), "Buckling and free vibration analyses of laminated composite plates by using two new hyperbolic shear deformation theories", Mech. Compos. Mater., 44(2), 145-154. https://doi.org/10.1007/s11029-008-9004-2
  5. 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
  6. Ait Yahia, S., Ait Atmane, H., Houari, M.S.A. and Tounsi, A. (2015), "Wave propagation in functionally graded plates with porosities using various higher-order shear deformation plate theories", Struct. Eng. Mech., Int. J., 53(6), 1143-1165. https://doi.org/10.12989/sem.2015.53.6.1143
  7. Al-Basyouni, K.S., Tounsi, A. and Mahmoud, S.R. (2015), "Size dependent bending and vibration analysis of functionally graded micro beams based on modified couple stress theory and neutral surface position", Compos. Struct., 125, 621-630. https://doi.org/10.1016/j.compstruct.2014.12.070
  8. 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
  9. Attia, A., Tounsi, A., Adda Bedia, E.A. and, Mahmoud, S.R. (2015), "Free vibration analysis of functionally graded plates with temperature-dependent properties using various four variable refined plate theories", Steel Compos. Struct., Int. J., 18(1), 187-212. https://doi.org/10.12989/scs.2015.18.1.187
  10. Bachir Bouiadjra, M., Houari, M.S.A. and Tounsi, A. (2012), "Thermal buckling of functionally graded plates according to a four-variable refined plate theory", J. Therm. Stress., 35(8), 677-694. https://doi.org/10.1080/01495739.2012.688665
  11. Bachir Bouiadjra, R., Adda Bedia, E.A. and Tounsi, A. (2013), "Nonlinear thermal buckling behavior of functionally graded plates using an efficient sinusoidal shear deformation theory", Struct. Eng. Mech., Int. J., 48(4), 547-567. https://doi.org/10.12989/sem.2013.48.4.547
  12. Belabed, Z., Houari, M.S.A., 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, 60, 274-283. https://doi.org/10.1016/j.compositesb.2013.12.057
  13. Belkorissat, I., Houari, M.S.A., Tounsi, A., Adda Bedia, E.A. and Mahmoud, S.R. (2015), "On vibration properties of functionally graded nano-plate using a new nonlocal refined four variable model", Steel Compos. Struct., Int. J., 18(4), 1063-1081. https://doi.org/10.12989/scs.2015.18.4.1063
  14. Benachour, A., Daouadji, H.T., Ait Atmane, H., Tounsi, A. and Meftah, S.A. (2011), "A four variable refined plate theory for free vibrations of functionally graded plates with arbitrary gradient", Compos. Part B, 42(6), 1386-1394. https://doi.org/10.1016/j.compositesb.2011.05.032
  15. Berrabah, H.M., Tounsi, A., Semmah, A. and Adda Bedia, E.A. (2013), "Comparison of various refined nonlocal beam theories for bending, vibration and buckling analysis of nanobeams", Struct. Eng. Mech., 48(3), 351-365. https://doi.org/10.12989/sem.2013.48.3.351
  16. Bessaim, A., Houari, M.S.A., Tounsi, A., Mahmoud, S.R. and Adda Bedia, 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", J. Sandw. Struct. Mater., 15(6), 671-703. https://doi.org/10.1177/1099636213498888
  17. Bhangale, R.K. and Ganesan, N. (2006), "Thermoelastic buckling and vibration behavior of a functionally graded sandwich beam with constrained viscoelastic core", J. Sound Vib., 295(12), 294-316. https://doi.org/10.1016/j.jsv.2006.01.026
  18. Bouderba, B., Houari, M.S.A. and Tounsi, A. (2013), "Thermomechanical bending response of FGM thick plates resting on Winkler-Pasternak elastic foundations", Steel Compos. Struct., Int. J., 14(1), 85-104. https://doi.org/10.12989/scs.2013.14.1.085
  19. Bourada, M., Tounsi, A., Houari, M.S.A. and Adda Bedia, 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
  20. Bourada, M., Kaci, A., Houari, M.S.A. and Tounsi, A. (2015), "A new simple shear and normal deformations theory for functionally graded beams", Steel Compos. Struct., Int. J., 18(2), 409-423. https://doi.org/10.12989/scs.2015.18.2.409
  21. Bousahla, A.A., Houari, M.S.A., Tounsi, A. and Adda Bedia, E.A. (2014), "A novel higher order shear and normal deformation theory based on neutral surface position for bending analysis of advanced composite plates", Int. J. Comput. Method., 11(6), 1350082. https://doi.org/10.1142/S0219876213500825
  22. Bui, T.Q., Khosravifard, A., Zhang, C., Hematiyan, M.R. and Golub, M.V. (2013), "Dynamic analysis of sandwich beams with functionally graded core using a truly meshfree radial point interpolation method", Eng. Struct., 47, 90-104. https://doi.org/10.1016/j.engstruct.2012.03.041
  23. Dellal, F. and Erdogan, F. (1983), "The crack problem for a non-homogeneous plane", J. Appl. Mech., 50(3), 609. https://doi.org/10.1115/1.3167098
  24. Draiche, K., Tounsi, A. and Khalfi, Y. (2014), "A trigonometric four variable plate theory for free vibration of rectangular composite plates with patch mass", Steel Compos. Struct., Int. J., 17(1), 69-81. https://doi.org/10.12989/scs.2014.17.1.069
  25. El Meiche, N., Tounsi, A., Ziane, N., Mechab, I. and Adda Bedia, E.A. (2011), "A new hyperbolic shear deformation theory for buckling and vibration of functionally graded sandwich plate", Int. J. Mech. Sci., 53(4), 237-247. https://doi.org/10.1016/j.ijmecsci.2011.01.004
  26. Etemadi, E., Khatibi, A.A. and Takaffoli, M. (2009), "3D finite element simulation of sandwich panels with a functionally graded core subjected to low velocity impact", Compos. Struct., 89(1), 28-34. https://doi.org/10.1016/j.compstruct.2008.06.013
  27. 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
  28. Ghugal, Y.M. (2011), "Buckling and vibration of plates by hyperbolic shear deformation theory", J. Aerosp. Eng. Technol., 1(1), 1-12.
  29. Ghugal, Y.M. and Sharma, R. (2009), "A hyperbolic shear deformation theory for flexure and vibration of thick isotropic beams", Int. J. Comput. Method., 6(4), 585-604. https://doi.org/10.1142/S0219876209002017
  30. Ghugal, Y.M. and Pawar, M. (2011), "Flexural analysis of thick plates by hyperbolic shear deformation theory", J. Exp. Appl. Mech., 2(1), 17-37.
  31. Grover, N., Maiti, D.K. and Singh, B.N. (2013), "A new inverse hyperbolic shear deformation theory for static and buckling analysis of laminated composite and sandwich plates", Compos. Struct., 95, 667-675. https://doi.org/10.1016/j.compstruct.2012.08.012
  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., Int. J., 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 Adda Bedia, E.A. (2014), "A new quasi-3D hyperbolic shear deformation theory for the static and free vibration analysis of functionally graded plates", ASCE J. Eng. Mech., 140(2), 374-383. https://doi.org/10.1061/(ASCE)EM.1943-7889.0000665
  34. Houari, M.S.A., Tounsi, A. and Anwar Beg, O. (2013), "Thermoelastic bending analysis of functionally graded sandwich plates using a new higher order shear and normal deformation theory", Int. J. Mech. Sci., 76, 467-479.
  35. Kettaf, F.Z., Houari, M.S.A., Benguediab, M. and Tounsi, A. (2013), "Thermal buckling of functionally graded sandwich plates using a new hyperbolic shear displacement model", Steel Compos. Struct., Int. J., 15(4), 399-423. https://doi.org/10.12989/scs.2013.15.4.399
  36. Khalfi, Y., Houari, M.S.A. and Tounsi, A. (2014), "A refined and simple shear deformation theory for thermal buckling of solar functionally graded plates on elastic foundation", Int. J. Comput. Method., 11(5), 135007.
  37. Larbi Chaht, F., Kaci, A., Houari, M.S.A., Tounsi, A., Anwar Bég, O. and Mahmoud, S.R. (2015), "Bending and buckling analyses of functionally graded material (FGM) size-dependent nanoscale beams including the thickness stretching effect", Steel Compos. Struct., Int. J., 36(5), 545-560.
  38. Li, J., Shi, C., Kong, X., Li, X. and Wu, W. (2013), "Free vibration of axially loaded composite beams with general boundary conditions using hyperbolic shear deformation theory", Compos. Struct., 97, 1-14. https://doi.org/10.1016/j.compstruct.2012.10.014
  39. Mahi, A., Adda Bedia, E.A. and Tounsi, A. (2015), "A new hyperbolic shear deformation theory for bending and free vibration analysis of isotropic, functionally graded, sandwich and laminated composite plates", Appl. Math. Model., 39(9), 2489-2508. https://doi.org/10.1016/j.apm.2014.10.045
  40. 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
  41. Nedri, K., El Meiche, N. and Tounsi, A. (2014), "Free vibration analysis of laminated composite plates resting on elastic foundations by using a refined hyperbolic shear deformation theory", Mech. Compos. Mater., 49(6), 641-650. https://doi.org/10.1007/s11029-013-9380-0
  42. Ould Larbi, L., Kaci, A., Houari, M.S.A. and Tounsi, A. (2013), "An efficient shear deformation beam theory based on neutral surface position for bending and free vibration of functionally graded beams", Mech. Based Des. Struct. Mach., 41(4), 421-433. https://doi.org/10.1080/15397734.2013.763713
  43. Reddy, J.N. (2002), Energy Principles and Variational Methods in Applied Mechanics, John Wiley & Sons Inc.
  44. Reddy, J.N. (2004), Mechanics of Laminated Composite Plates and Shells: Theory and Analysis, (2nd Ed.), CRC Press, Boca Raton, FL, USA.
  45. Saidi, H., Houari, M.S.A., Tounsi, A. and Adda Bedia, E.A. (2013), "Thermo-mechanical bending response with stretching effect of functionally graded sandwich plates using a novel shear deformation theory", Steel Compos. Struct., Int. J., 15(2), 221-245. https://doi.org/10.12989/scs.2013.15.2.221
  46. Sayyad, A.S. and Ghugal, Y.M. (2011), "Flexure of thick beams using new hyperbolic shear deformation theory", Int. J. Mech., 5, 113-122.
  47. Tounsi, A., Houari, M.S.A., Benyoucef, S. and Adda Bedia, E.A. (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
  48. Vo, T.P., Thai, H.T., Nguyen, T.K., Maheri, A. and Lee, J. (2014), "Finite element model for vibration and buckling of functionally graded sandwich beams based on a refined shear deformation theory", Eng. Struct., 64, 12-22. https://doi.org/10.1016/j.engstruct.2014.01.029
  49. Vo, T.P., Thai, H.T., Nguyen, T.K., Inam, F. and Lee, J. (2015), "A quasi-3D theory for vibration and buckling of functionally graded sandwich beams", Compos. Struct., 119, 1-12. https://doi.org/10.1016/j.compstruct.2014.08.006
  50. Xiang, S., Kang, G.-w., Yang, M.-s. 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
  51. Yaghoobi, H. and Yaghoobi, P. (2013), "Buckling analysis of sandwich plates with FGM face sheets resting on elastic foundation with various boundary conditions: An analytical approach", Meccanica, 48(8), 2019-2035. https://doi.org/10.1007/s11012-013-9720-0
  52. Zidi, M., Tounsi, A., Houari, M.S.A., Adda Bedia, E.A. and Anwar Beg, O. (2014), "Bending analysis of FGM plates under hygro-thermo-mechanical loading using a four variable refined plate theory", Aerosp. Sci. Technol., 34, 24-34. https://doi.org/10.1016/j.ast.2014.02.001

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  62. Influences of porosity on dynamic response of FG plates resting on Winkler/Pasternak/Kerr foundation using quasi 3D HSDT vol.24, pp.4, 2015, https://doi.org/10.12989/cac.2019.24.4.347
  63. Effect of nonlinear elastic foundations on dynamic behavior of FG plates using four-unknown plate theory vol.17, pp.5, 2015, https://doi.org/10.12989/eas.2019.17.5.447
  64. Dynamic instability and free vibration behavior of three-layered soft-cored sandwich beams on nonlinear elastic foundations vol.72, pp.4, 2015, https://doi.org/10.12989/sem.2019.72.4.525
  65. Effect of variable elastic foundations on static behavior of functionally graded plates using sinusoidal shear deformation vol.12, pp.24, 2019, https://doi.org/10.1007/s12517-019-4871-5
  66. Effect of Foam’s Heterogeneity on the Behaviour of Sandwich Panels vol.29, pp.4, 2019, https://doi.org/10.2478/ceer-2019-0047
  67. Wave dispersion properties in imperfect sigmoid plates using various HSDTs vol.33, pp.5, 2015, https://doi.org/10.12989/scs.2019.33.5.699
  68. Dynamic Behavior of a Bidirectional Functionally Graded Sandwich Beam under Nonuniform Motion of a Moving Load vol.2020, pp.None, 2015, https://doi.org/10.1155/2020/8854076
  69. Vibration analysis of FG porous rectangular plates reinforced by graphene platelets vol.34, pp.2, 2020, https://doi.org/10.12989/scs.2020.34.2.215
  70. Influence of porosity distribution on vibration analysis of GPLs-reinforcement sectorial plate vol.35, pp.1, 2015, https://doi.org/10.12989/scs.2020.35.1.111
  71. Bending analysis of softcore and hardcore functionally graded sandwich beams vol.18, pp.4, 2020, https://doi.org/10.12989/eas.2020.18.4.481
  72. Vibrational characteristic of FG porous conical shells using Donnell's shell theory vol.35, pp.2, 2015, https://doi.org/10.12989/scs.2020.35.2.249
  73. Influence of internal pores and graphene platelets on vibration of non-uniform functionally graded columns vol.35, pp.2, 2015, https://doi.org/10.12989/scs.2020.35.2.295
  74. Nonlinear deflection responses of layered composite structure using uncertain fuzzified elastic properties vol.35, pp.6, 2015, https://doi.org/10.12989/scs.2020.35.6.753
  75. Vibration behavior of functionally graded sandwich beam with porous core and nanocomposite layers vol.36, pp.1, 2020, https://doi.org/10.12989/scs.2020.36.1.001
  76. Vibration behavior of trapezoidal sandwich plate with functionally graded-porous core and graphene platelet-reinforced layers vol.36, pp.1, 2015, https://doi.org/10.12989/scs.2020.36.1.047
  77. Size-dependent free vibration and buckling analysis of sigmoid and power law functionally graded sandwich nanobeams with microstructural defects vol.234, pp.18, 2015, https://doi.org/10.1177/0954406220916481
  78. Vibration analysis of sandwich sector plate with porous core and functionally graded wavy carbon nanotube-reinforced layers vol.37, pp.6, 2015, https://doi.org/10.12989/scs.2020.37.6.711
  79. Study and analysis of the free vibration for FGM microbeam containing various distribution shape of porosity vol.77, pp.2, 2015, https://doi.org/10.12989/sem.2021.77.2.217
  80. Vibration analysis of damaged core laminated curved panels with functionally graded sheets and finite length vol.38, pp.5, 2015, https://doi.org/10.12989/scs.2021.38.5.477
  81. 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, 2015, https://doi.org/10.12989/scs.2021.39.1.095
  82. Vibration and nonlinear dynamic analysis of variable thickness sandwich laminated composite panel in thermal environment vol.23, pp.5, 2015, https://doi.org/10.1177/1099636219899402
  83. Mechanical analysis of bi-functionally graded sandwich nanobeams vol.11, pp.1, 2015, https://doi.org/10.12989/anr.2021.11.1.055
  84. On static buckling of multilayered carbon nanotubes reinforced composite nanobeams supported on non-linear elastic foundations vol.40, pp.3, 2021, https://doi.org/10.12989/scs.2021.40.3.389
  85. A n-order refined theory for free vibration of sandwich beams with functionally graded porous layers vol.79, pp.3, 2015, https://doi.org/10.12989/sem.2021.79.3.279
  86. Static bending analysis of functionally graded sandwich beams using a novel mixed beam element based on first-order shear deformation theory vol.4, pp.None, 2021, https://doi.org/10.1016/j.finmec.2021.100039
  87. Natural frequency analysis of sigmoid functionally graded sandwich beams in the framework of high order shear deformation theory vol.276, pp.None, 2015, https://doi.org/10.1016/j.compstruct.2021.114564
  88. Finite element bending analysis of symmetric and non-symmetric functionally graded sandwich beams using a novel parabolic shear deformation theory vol.235, pp.11, 2021, https://doi.org/10.1177/14644207211005096