Structural Engineering and Mechanics

  • 제85권6호
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  • Pages.765-780
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  • 2023
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  • 1225-4568(pISSN)
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  • 1598-6217(eISSN)
테크노프레스 (Techno-Press)
권호 표지
DOI QR코드

DOI QR Code

Buckling analysis of FG plates via 2D and quasi-3D refined shear deformation theories

  • Lemya Hanifi Hachemi Amar (Built Environment Research Laboratory, University of Science and Technology Houari Boumediene (USTHB)) ;
  • Fouad Bourada (Material and Hydrology Laboratory, University of Sidi Bel Abbes, Faculty of Technology, Civil Engineering Department) ;
  • Abdelmoumen Anis Bousahla (Laboratoire de Modelisation et Simulation Multi-echelle, Universite de Sidi BelAbbes) ;
  • Abdelouahed Tounsi (Material and Hydrology Laboratory, University of Sidi Bel Abbes, Faculty of Technology, Civil Engineering Department) ;
  • Kouider Halim Benrahou (Material and Hydrology Laboratory, University of Sidi Bel Abbes, Faculty of Technology, Civil Engineering Department) ;
  • Hind Albalawi (Department of Physics, College of Sciences, Princess Nourah bint Abdulrahman University (PNU)) ;
  • Abdeldjebbar Tounsi (Industrial Engineering and Sustainable Development Laboratory, University of Relizane, Faculty of Science & Technology, Mechanical Engineering Department)
  • 투고 : 2021.09.18
  • 심사 : 2023.01.16
  • 발행 : 2023.03.25
⟨ 이전 논문 다음 논문 ⟩

초록

In this work, a novel combined logarithmic, secant and tangential 2D and quasi-3D refined higher order shear deformation theory is proposed to examine the buckling analysis of simply supported uniform functionally graded plates under uniaxial and biaxial loading. The proposed formulations contain a reduced number of variables compared to others similar solutions. The combined function employed in this study ensures automatically the zero-transverse shear stresses at the free surfaces of the structure. Various models of the material distributions are considered (linear, quadratic, cubic inverse quadratic and power-law). The differentials stability equations are derived via virtual work principle with including the stretching effect. The Navier's approach is applied to solve the governing equations which satisfying the boundary conditions. Several comparative and parametric studies are performed to illustrates the validity and efficacity of the proposed model and the various factors influencing the critical buckling load of thick FG plate.

키워드

과제정보

Princess Nourah bint Abdulrahman University Researchers Supporting Project number (PNURSPHC2022/7), Princess Nourah bint Abdulrahman University, Riyadh, Saudi Arabia.

참고문헌

  1. 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 .
  2. Akavci, S.S. and Tanrikulu, A.H. (2015), "Static and free vibration analysis of functionally graded plates based on a new quasi-3D and 2D shear deformation theories", Compos. Part B: Eng., 83, 203-215. https://doi.org/10.1016/j.compositesb.2015.08.043.
  3. Akbas, S.D. (2022), "Moving-load dynamic analysis of AFG beams under thermal effect", Steel Compos. Struct., 42(5), 649-655. https://doi.org/10.12989/scs.2022.42.5.649.
  4. Alimoradzadeh, M. and Akbas, S.D. (2022), "Nonlinear dynamic behavior of functionally graded beams resting on nonlinear viscoelastic foundation under moving mass in thermal environment", Struct. Eng. Mech., 81(6), 705-714. https://doi.org/10.12989/sem.2022.81.6.705.
  5. Ambartsumian, S.A. (1958), "On the theory of bending plates", Izv Otd Tech NaukAN SSSR, 5, 69-77.
  6. Ansari, R., Torabi, J. and Hassani, R. (2018), "In-plane and shear buckling analysis of FG-CNTRC annular sector plates based on the third-order shear deformation theory using a numerical approach", Comput. Math. Appl., 75(2), 486-502. https://doi.org/10.1016/j.camwa.2017.09.022.
  7. Azandariani, M.G., Gholami, M. and Nikzad, A. (2022), "Eringen's nonlocal theory for non-linear bending analysis of BGF Timoshenko nanobeams", Adv. Nano Res., 12(1), 37-47. https://doi.org/10.12989/anr.2022.12.1.037.
  8. Bateni, M., Kiani, Y. and Eslami, M.R. (2013), "A comprehensive study on stability of FGM plates", Int. J. Mech. Sci., 75, 134-144. https://doi.org/10.1016/j.ijmecsci.2013.05.014.
  9. Bendada, A., Boutchicha, D., Khatir, S., Magagnini, E., Capozucca, R. and Wahab, M.A. (2020), "Mechanical characterization of an epoxy panel reinforced by date palm petiole particle", Steel Compos. Struct., 35(5), 627-634. https://doi.org/10.12989/scs.2020.35.5.627.
  10. Carrera, E., Brischetto, S., Cinefra, M. and Soave, M. (2011), "Effects of thickness stretching in functionally graded plates and shells", Compos. Part B: Eng., 42(2), 123-133. https://doi.org/10.1016/j.compositesb.2010.10.005.
  11. Chinnapandi, L.B.M., Pitchaimani, J. and Eltaher, M.A. (2022), "Vibro-acoustics of functionally graded porous beams subjected to thermo-mechanical loads", Steel Compos. Struct., 44(6), 829-843. https://doi.org/10.12989/scs.2022.44.6.829.
  12. Cho, J.R. (2022), "Nonlinear bending analysis of functionally graded CNT-reinforced composite plates", Steel Compos. Struct., 42(1), 23-32. https://doi.org/10.12989/scs.2022.42.1.023.
  13. Cuong-Le, T., Nguyen, K.D., Nguyen-Trong, N., Khatir, S., Nguyen-Xuan, H. and Abdel-Wahab, M. (2020a), "A threedimensional solution for free vibration and buckling of annular plate, conical, cylinder and cylindrical shell of FG porouscellular materials using IGA", Compos. Struct., 259, 113216. https://doi.org/10.1016/j.compstruct.2020.113216.
  14. Cuong-Le, T., Nguyen, K.D., Hoang-Le, M., Sang-To, T., PhanVu, P., Abdel Wahab, M. (2022a), "Nonlocal strain gradient IGA numerical solution for static bending, free vibration and buckling of sigmoid FG sandwich nanoplate", Physica B: Condens. Matt., 631, 413726. https://doi.org/10.1016/j.physb.2022.413726.
  15. Cuong-Le, T., Nguyen, K.D., Lee, J. Rabczuk, T. and NguyenXuan, H. (2022b), "A 3D nano scale IGA for free vibration and buckling analyses of multi-directional FGM nanoshells", Nanotechnol., 33(6), 065703. https://doi.org/10.1088/1361-6528/ac32f9.
  16. Cuong-Le, T., Nguyen, T.N., Vu, T.H., Khatir, S. and Abdel Wahab, M. (2020b), "A geometrically nonlinear size-dependent hypothesis for porous functionally graded micro-plate", Eng. Comput., 38(2022), 449-460. https://doi.org/10.1007/s00366-020-01154-0.
  17. 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.
  18. Du, M., Liu, J., Ye, W., Yang, F. and Lin, G. (2022), "A new semianalytical approach for bending, buckling and free vibration analyses of power law functionally graded beams", Struct. Eng. Mech., 81(2), 179-194. https://doi.org/10.12989/sem.2022.81.2.179.
  19. Farzam, A. and Hassani, B. (2018), "Thermal and mechanical buckling analysis of FG carbon nanotube reinforced composite plates using modified couple stress theory and isogeometric approach", Compos. Struct., 206, 774-790. https://doi.org/10.1016/j.compstruct.2018.08.030.
  20. Ferreira, A.J.M., Castro, L.M.S. and Bertoluzza, S. (2009), "A high order collocation method for the static and vibration analysis of composite plates using a first-order theory", Compos. Struct., 89(3), 424-432. https://doi.org/10.1016/j.compstruct.2008.09.006.
  21. 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.
  22. Hagos, R.W., Choi, G., Sung, H. and Chang, S. (2022), "Substructuring-based dynamic reduction method for vibration analysis of periodic composite structures", Compos. Mater. Eng., 4(1), 43-62. https://doi.org/10.12989/cme.2022.4.1.043.
  23. Huang, X., Shan, H., Chu, W. and Chen, Y. (2022), "Computational and mathematical simulation for the sizedependent dynamic behavior of the high-order FG nanotubes, including the porosity under the thermal effects", Adv. Nano Res., 12(1), 101-115. https://doi.org/10.12989/anr.2022.12.1.101.
  24. Khatir, S., Tiachacht, S., Cuong-Le, T., Quoc Bui, T. and Abdel Wahab, M. (2019), "Damage assessment in composite laminates using ANN-PSO-IGA and Cornwell indicator", Compos. Struct., 230, 111509. https://doi.org/10.1016/j.compstruct.2019.111509.
  25. Kiani, Y. (2019), "NURBS-based thermal buckling analysis of graphene platelet reinforced composite laminated skew plates", J. Therm. Stress., 43(1), 1-19. https://doi.org/10.1080/01495739.2019.1673687.
  26. Kiani, Y. and Eslami, M.R. (2013), "Instability of heated circular FGM plates on a partial Winkler-type foundation", Acta Mechanica, 224(5), 1045-1060. https://doi.org/10.1007/s00707-012-0800-3.
  27. Kiani, Y. and Eslami, M.R. (2014), "Nonlinear thermo-inertial stability of thin circular FGM plates", J. Franklin Inst., 351(2), 1057-1073. https://doi.org/10.1016/j.jfranklin.2013.09.013.
  28. Kiani, Y. and Eslami, M.R. (2015), "thermal postbuckling of imperfect circular functionally graded material plates: Examination of Voigt, Mori-Tanaka, and self-consistent schemes", J. Press. Ves. Technol., 137(2), 021201. https://doi.org/10.1115/1.4026993.
  29. Kiani, Y. and Mirzaei, M. (2018), "Rectangular and skew shear buckling of FG-CNT reinforced composite skew plates using Ritz method", Aerosp. Sci. Technol., 77, 388-398. https://doi.org/10.1016/j.ast.2018.03.022.
  30. Kumar, H.S.N. and Kattimani, S. (2022), "Nonlinear analysis of two-directional functionally graded doubly curved panels with porosities", Struct. Eng. Mech., 82(4), 477-490. https://doi.org/10.12989/sem.2022.82.4.477.
  31. Levinson, M. (1980), "An accurate simple theory of static and dynamics of elastic plates", Mech. Res. Commun., 7, 343-350. https://doi.org/10.1016/0093-6413(80)90049-X.
  32. Liu, Y. (2011), "A refined shear deformation plate theory", Int. J. Comput. Meth. Eng. Sci. Mech., 12(3), 141-149. https://doi.org/10.1080/15502287.2011.564267.
  33. Liu, Y., Wang, X., Liu, L., Wu, B. and Yang, Q. (2022), "On the forced vibration of high-order functionally graded nanotubes under the rotation via intelligent modelling", Adv. Nano Res., 13(1), 47-61. https://doi.org/10.12989/anr.2022.13.1.047.
  34. 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.
  35. Man, Y. (2022), "On the dynamic stability of a composite beam via modified high-order theory", Comput. Concrete, 30(2), 151-164. https://doi.org/10.12989/cac.2022.30.2.151.
  36. Mansouri, L., Djebbar, A., Khatir, S. and Abdel Wahab, M. (2018), "Effect of hygrothermal aging in distilled and saline water on the mechanical behaviour of mixed short fibre/woven composites", Compos. Struct., 207, 816-825. https://doi.org/10.1016/j.compstruct.2018.09.067.
  37. Mantari, J.L. and Guedes Soares, C. (2012), "Generalized hybrid quasi-3D shear deformation theory for the static analysis of advanced composite plates", Compos. Struct., 94(8), 2561-2575. https://doi.org/10.1016/j.compstruct.2012.02.019.
  38. 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.
  39. Mohammadi, M., Saidi, A.R. and Jomehzadeh, E. (2010), "Levy solution for buckling analysis of functionally graded rectangular plates", Appl. Compos. Mater., 17(2), 81-93. https://doi.org/10.1007/s10443-009-9100-z.
  40. Mula, S.N., Leite, A.M.S. and Loja, M.A.R. (2022), "Analytical and numerical study of failure in composite plates", Compos. Mater. Eng., 4(1), 23-41. https://doi.org/10.12989/cme.2022.4.1.023.
  41. Nguyen, T.K., Sab, K. and Bonnet, G. (2007), "Shear correction factors for functionally graded plates", Mech. Adv. Mater. Struct., 14(8), 567-575. https://doi.org/10.1080/15376490701672575.
  42. Pitakthapanaphong, S. and Busso, E.P. (2002), "Self-consistent elasto-plastic stress solutions for functionally graded material systems subjected to thermal transients", J. Mech. Phys. Solid., 50, 695-716. https://doi.org/10.1016/S0022-5096(01)00105-3.
  43. Polat, A. and Kaya, Y. (2022), "Analysis of discontinuous contact problem in two functionally graded layers resting on a rigid plane by using finite element method", Comput. Concrete, 29(4), 247-253. https://doi.org/10.12989/cac.2022.29.4.247.
  44. 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.
  45. Reddy, J.N. (2004.), Mechanics of Laminated Composite Plates and Shells: Theory and Analysis, 2nd Edition, CRC Press, Boca Raton.
  46. Reddy, B.S., Kumar, J.S., Reddy, C.E. and Reddy, K.V.K. (2013), "Buckling analysis of functionally graded material plates using higher order shear deformation theory", J. Compos., 2013, Article ID 808764. https://doi.org/10.1155/2013/808764.
  47. Rezaiee-Pajand, M., Sobhani, E. and Masoodi, A.R. (2022), "Vibrational behavior of exponentially graded joined conicalconical shells", Steel Compos. Struct., 43(5), 603-623. https://doi.org/10.12989/scs.2022.43.5.603.
  48. Saha, R. and Maiti, P.R. (2012), "Buckling of simply supported FGM plates under uniaxial load", Int. J. Civil Struct. Eng., 2(4), 1035-1050.
  49. Ruocco, E. and Reddy, J.N. (2019), "A closed-form solution for buckling analysis of orthotropic Reddy plates and prismatic plate structures", Compos. Part B: Eng., 169, 258-273. https://doi.org/10.1016/j.compositesb.2019.03.015.
  50. 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.
  51. 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.
  52. Shi, G. (2007), "A new simple third-order shear deformation theory of plates", Int. J. Solid. Struct., 44(13), 4399-4417. https://doi.org/10.1016/j.ijsolstr.2006.11.031.
  53. Singh, S.J. and Harsha, S.P. (2019), "Buckling analysis of FGM plates under uniform, linear and non-linear in-plane loading", J. Mech. Sci. Technol., 33(4), 1761-1767. https://doi.org/10.1007/s12206-019-0328-8.
  54. Sofiyev, A.H., Deniz, A., Akcay, I.H., Yusufogclu, E. (2006), "The vibration and stability of a three-layered conical shell containing an FGM layer subjected to axial compressive load", Acta Mechanica, 183, 129-144. https://doi.org/10.1007/s00707-006-0328-5.
  55. Soldatos, K.P. (1992), "A transverse shear deformation theory for homogeneous monoclinic plates", Acta Mechanica, 94(3-4), 195-220. https://doi.org/10.1007/BF01176650.
  56. 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(3), 1008-1022. https://doi.org/10.1016/j.apm.2011.07.062.
  57. Thinh, T.I., Tu, T.M., Quoc, T.H. and Long, N.V. (2016), "Vibration and buckling analysis of functionally graded plates using new Eight-Unknown higher order shear deformation theory", Lat. Am. J. Solid. Struct., 13(3), 456-477. https://doi.org/10.1590/1679-78252522 .
  58. Touratier, M. (1991), "An efficient standard plate theory", Int. J. Eng. Sci., 29(8), 901-916. https://doi.org/10.1016/0020-7225(91)90165-Y.
  59. Tran, T.M. and Cuong-Le, T. (2022), "A Nonlocal IGA numerical solution for free vibration and buckling analysis of Porous Sigmoid Functionally Graded (P-SFGM) nanoplate", Int. J. Struct. Stab. Dyn., 22(16), 2250193. https://doi.org/10.1142/S0219455422501930.
  60. 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.
  61. Wang, C.M., Reddy, J.N. and Lee, K.H. (2000), Shear Deformable Beams and Plates: Relationships with Classical Solutions, Elsevier.
  62. Yaylaci, M., Abanoz, M., Yaylaci, E.U., Olmez, H., Sekban, D.M. and Birinci, A. (2022), "The contact problem of the functionally graded layer resting on rigid foundation pressed via rigid punch", Steel Compos. Struct., 43(5), 661-672. https://doi.org/10.12989/scs.2022.43.5.661.
  63. Yin, H.M., Sun, L.Z. and Paulino, G.H. (2004), "Micromechanicsbased elastic model for functionally graded materials with particle interactions", Acta Materialia, 52(12), 3535-3543. https://doi.org/10.1016/j.actamat.2004.04.007.
  64. Yu, T., Zhang, J., Hu, H. and Bui, T.Q. (2019), "A novel sizedependent quasi-3D isogeometric beam model for twodirectional FG microbeams analysis", Compos. Struct., 211, 76-88. https://doi.org/10.1016/j.compstruct.2018.12.014.
  65. Zenkour, A.M. and Aljadani, M.H. (2018), "Mechanical buckling of functionally graded plates using a refined higher-order shear and normal deformation plate theory", Adv. Aircraft Spacecraft Sci., 5(6), 615-632. https://doi.org/10.12989/aas.2018.5.6.615.
  66. Zenzen, R., Khatir, S., Belaidi, I., Cuong-Le, T. and Abdel Wahab, M. (2020), "A modified transmissibility indicator and Artificial Neural Network for damage identification and quantification in laminated composite structures", Composite Structures, 248, 112497. https://doi.org/10.1016/j.compstruct.2020.112497.
  67. Zhang, Z., Yang, Q. and Jin, C. (2022), "Axisymmetric vibration analysis of a sandwich porous plate in thermal environment rested on Kerr foundation", Steel Compos. Struct., 43(5), 581-601. https://doi.org/10.12989/scs.2022.43.5.581.
  68. Zhao, J.L., Chen, X., She, G.L., Jing, Y., Bai, R.Q., Yi, J., Pu, H.Y. and Lu, J. (2022), "Vibration characteristics of functionally graded carbon nanotube-reinforced composite double-beams in thermal environments", Steel Compos. Struct., 43(6), 797-808. https://doi.org/10.12989/scs.2022.43.6.797.
  69. Zhao, X., Lee, Y.Y. and Liew, K.M. (2009), "Mechanical and thermal buckling analysis of functionally graded plates", Compos. Struct., 90(2), 161-171. https://doi.org/10.1016/j.compstruct.2009.03.005.
  70. Zhou, L., Moradi, Z., Al-Tamimi, H.M. and Elhosiny Ali, H. (2022), "On propagation of elastic waves in an embedded sigmoid functionally graded curved beam", Steel Compos. Struct., 44(1), 17-31. https://doi.org/10.12989/scs.2022.44.1.017.