Earthquakes and Structures

  • 제17권3호
  • /
  • Pages.257-270
  • /
  • 2019
  • /
  • 2092-7614(pISSN)
  • /
  • 2092-7622(eISSN)
테크노프레스 (Techno-Press)
권호 표지
DOI QR코드

DOI QR Code

Bending behavior of laminated composite plates using the refined four-variable theory and the finite element method

  • 투고 : 2019.09.29
  • 심사 : 2019.06.10
  • 발행 : 2019.09.25
⟨ 이전 논문 다음 논문 ⟩

초록

The purpose of this work is to analyze the bending behavior of laminated composite plates using the refined fourvariable theory and the finite element method approach using an ANSYS 12 computational code. The analytical model is based on the multilayer plate theory of shear deformation of the nth-order proposed by Xiang et al 2011 using the theory principle developed by Shimpi and Patel 2006. Unlike other theories, the number of unknown functions in the present theory is only four, while five or more in the case of other theories of shear deformation. The formulation of the present theory is based on the principle of virtual works, it has a strong similarity with the classical theory of plates in many aspects, it does not require shear correction factor and gives a parabolic description of the shear stress across the thickness while filling the condition of zero shear stress on the free edges. The analysis is validated by comparing results with those in the literature.

키워드

참고문헌

  1. Abdelmalek, A., Bouazza, M., Zidour, M. and Benseddiq, N. (2019), "Hygrothermal effects on the free vibration behavior of composite plate using nth-order shear deformation theory: a micromechanical approach", Iran J. Sci. Technol. Tran. Mech. Eng., 43(1), 61-73. https://doi.org/10.1007/s40997-017-0140-y.
  2. Ambartsumyan, S.A. (1969), Theory of Anisotropic Plate, Technomic Publishing.
  3. Antar, K., Amara, K., Benyoucef, S., Bouazza, M. and Ellali, M. (2019), "Hygrothermal effects on the behavior of reinforcedconcrete beams strengthened by bonded composite laminate plates", Struct. Eng. Mech., 69(3), 327-334. https://doi.org/10.12989/sem.2019.69.3.327.
  4. Aydogdu, M. (2009), "A new shear deformation theory for laminated composite plates", Compos. Struct., 89, 94-101. https://doi.org/10.1016/j.compstruct.2008.07.008.
  5. Becheri, T., Amara, K., Bouazza, M. and Benseddiq, N. (2016), "Buckling of symmetrically laminated plates using nth-order shear deformation theory with curvature effects", Steel Compos. Struct., 21(6), 1347-1368. https://doi.org/10.12989/scs.2016.21.6.1347.
  6. Belkacem, A., Tahar, H.D., Abderrezak, R., Amine, B.M., Mohamed, Z. and Boussad, A. (2018), "Mechanical buckling analysis of hybrid laminated composite plates under different boundary conditions", Struct. Eng. Mech., 66(6), 761-769. https://doi.org/10.12989/sem.2018.66.6.761.
  7. Bhimaraddi, A. and Stevens, L.K. (1984), "A higher order theory for free vibration of orthotropic, homogeneous, and laminated rectangular plates", J. Appl. Mech., 51(1), 195-198. https://doi.org/10.1115/1.3167569.
  8. Biswal, M., Sahu, S.K., Asha, A.V. and Nanda, N. (2016), "Hygrothermal effects on buckling of composite shellexperimental and FEM results", Steel Compos. Struct., 22(6), 1445-1463. http://dx.doi.org/10.12989/scs.2016.22.6.1445.
  9. Bouazza, M., Lairedj, A., Benseddiq, N. and Khalki, S. (2016), "A refined hyperbolic shear deformation theory for thermal buckling analysis of cross-ply laminated plates", Mech. Res. Commun., 73, 117-126. https://doi.org/10.1016/j.mechrescom.2016.02.015.
  10. Bouazza, M. and Zenkour, A.M. (2018), "Free vibration characteristics of multilayered composite plates in a hygrothermal environment via the refined hyperbolic theory", Eur. Phys. J. Plus., 133, 217. https://doi.org/10.1140/epjp/i2018-12050-x
  11. Bouazza, M., Kenouza, Y., Benseddiq, N. and Zenkour Ashraf, M. (2017), "A two-variable simplified nth-higher-order theory for free vibration behavior of laminated plates", Compos Struct., 182, 533-541. https://doi.org/10.1016/j.compstruct.2017.09.041.
  12. Bouhadra, A., Tounsi, A., Bousahla, A.A., Benyoucef, S. and Mahmoud, S.R. (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.
  13. 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. https://doi.org/10.12989/was.2019.28.1.019.
  14. 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. http://dx.doi.org/10.12989/sem.2016.60.2.313.
  15. Chen, X. and Xu, C. (2016), "Effect oflocal wall thinning on ratcheting behavior of pressurized $90^{\circ}$ elbow pipe under reversed bending using finite element analysis", Steel Compos. Struct., 20(4), 703-753. https://doi.org/10.12989/scs.2018.28.3.389.
  16. Chikh, A., Tounsi, A., Hebali, H. and Mahmoud, S.R. (2017), "Thermal buckling analysis of cross-ply laminated plates using a simplified HSDT", Smart Struct. Syst., 19(3), 289-297. https://doi.org/10.12989/sss.2017.19.3.289.
  17. El-Abbasi, N. and Meguid, S.A. (2000), "A new shell element accounting for through thickness deformation", Comput. Meth. Appl. Mech. Eng., 189, 841-862. https://doi.org/10.1016/S0045-7825(99)00348-5.
  18. Ellali, M., Amara, K., Bouazza, M. and Bourada, F. (2018), "The buckling of piezoelectric plates on Pasternak elastic foundation using higher-order shear deformation plate theories", Smart Struct Syst., 21(1), 113-122. https://doi.org/10.12989/sss.2018.21.1.113.
  19. Fourn, H., Ait Atmane, H., Bourada, M., Bousahla, A.A., Tounsi, A. and Mahmoud, S.R. (2018), "A novel four variable refined plate theory for wave propagation in functionally graded material plates", Steel Compos. Struct., 27(1), 109-122. https://doi.org/10.12989/scs.2018.27.1.109.
  20. 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.
  21. Hanna, N.F. and Leissa, A.W. (1994), "A higher order shear deformationtheory for the vibration of thick plates", J. Sound Vib., 170(4), 545-555. https://doi.org/10.1006/jsvi.1994.1083.
  22. Hebali, H., Bakora, A., Tounsi, A. and Kaci, A. (2016), "A novel four variable refined plate theory for bending, buckling, and vibration of functionally graded plates", Steel Compos. Struct., 22(3), 473-495. https://doi.org/10.12989/scs.2016.22.3.473.
  23. Kar, V.R. and Panda, S.K. (2015a), "Large deformation bending analysis of functionally graded spherical shell using FEM", Struct. Eng. Mech., 53(4), 661-679. https://doi.org/10.12989/sem.2015.53.4.661.
  24. Karama, M., Afaq, K.S. and Mistou, S. (2003), "Mechanical behaviour of laminated composite beam by new multi-layered laminated composite structures model with transverse shear stress continuity", Int. J. Solid. Struct., 40(6), 1525-1546. https://doi.org/10.1016/S0020-7683(02)00647-9.
  25. Khetir, H., Bouiadjra, M.B., Houari, M.S.A., Tounsi, A. and Mahmoud, S.R. (2017), "A new nonlocal trigonometric shear deformation theory for thermal buckling analysis ofembedded nanosize FG plates", Struct. Eng. Mech., 64(4), 391-402. https://doi.org/10.12989/sem.2017.64.4.391.
  26. Kim, D.N. and Bathe, K.J. (2008), "A 4-node 3D-shell element to model shell surface tractions and incompressible behavior", Comput. Struct., 86, 2027-2041. https://doi.org/10.1016/j.compstruc.2008.04.019.
  27. Kim, S.E., Thai, H.T. and Lee, J. (2009), "Buckling analysis of plates using the two variable refined plate theory", Thin Wall. Struct., 47(4), 455-462. https://doi.org/10.1016/j.tws.2008.08.002.
  28. Lo, K.H., Christensen, R.M. and Wu, E.M. (1977), "A high-order theory of plate deformation. Part 2, Laminated plates", J. Appl. Mech., 44(4), 669-676. https://doi.org/10.1115/1.3424155.
  29. Mantari, J.L, Oktem, A.S. and Guedes Soares, C. (2012), "A new higher order shear deformation theory for sandwich and composite laminated plates", Compos. Part B: Eng., 43, 1489-1499. https://doi.org/10.1016/j.compositesb.2011.07.017.
  30. Menasria, A., Bouhadra, A., Tounsi, A., Bousahla, A.A. and Mahmoud, S.R. (2017), "A new andsimple 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.
  31. Meziane, M.A.A., 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.
  32. Mindlin, R.D. (1951), "Inuence of rotary inertia and shear on exural motions of isotropic, elastic plates", J. Appl. Mech., 18, 31-38. https://doi.org/10.1115/1.4010217
  33. Nakasone, Y., Yoshimoto, S. and Stolarski, T.A. (2006), Engineering Analysis with Ansys Software, Elsevier, Butterworth-Heinemann Linacre House, Jordan Hill, Oxford OX2 8DP30 Corporate Drive, Burlington.
  34. Narendar, S. (2011), "Buckling analysis of micro-/nano-scale plates based on two variable refined plate theory incorporating nonlocal scale effects", Compos. Struct., 93(12), 3093-3103. https://doi.org/10.1016/j.compstruct.2011.06.028.
  35. Noor, A.K. (1975), "Stability of multilayered composite plate", Fibre. Sci. Technol., 8, 81-89. https://doi.org/10.1016/0015-0568(75)90005-6.
  36. Pagano, N.J. (1970), "Exact solution for rectangular bidirectional composites and sandwich plates", J. Compos.Mater., 4(1), 20-34. https://doi.org/10.1177/002199837000400102.
  37. Patel, S.N. (2014), "Nonlinear bending analysis of laminated composite stiffened plates", Steel Compos. Struct., 17(6), 867-890. http://dx.doi.org/10.12989/scs.2014.17.6.867.
  38. Piscopo, V. (2010), "Refined buckling analysis of rectangular plates under uniaxial and biaxial compression", World Acad. Sci., Eng. Technol., 46, 554-561.
  39. Reddy, J.N. (1984), "A simple higher-order theory for laminated composite plates", J. Appl. Mech., 51, 745-752. https://doi.org/10.1115/1.3167719.
  40. Reddy, J.N. (1984), Energy and Variational Methods in Applied Mechanics, John Wiley and Sons, New York.
  41. Reddy, J.N. (2004), Mechanics of Laminated Composite Plates and Shells, Theory and Analysis, 2nd Edition, CRC Press, New York.
  42. Reddy, J.N. and Phan, N.D. (1985), "Stability and vibration of isotropic, orthotropic and laminated plates according to a higher-order shear deformation theory", J. Sound Vib., 98(2), 157-170. https://doi.org/10.1016/0022-460X(85)90383-9.
  43. Reissner, E. (1945), "The effect of transverse shear deformation on the bending of elastic plates", J. Appl. Mech., 12, 69-77.
  44. Reza Barati, M. and Shahverdi, H. (2016), "A four-variable plate theory for thermal vibration of embedded FG nanoplates under non-uniform temperature distributions with different boundary conditions", Struct. Eng. Mech., 60(4), 707-727. https://doi.org/10.12989/sem.2016.60.4.707.
  45. Rezaiee-Pajand, M. and Arabi, E. (2016), "A curved triangular element for nonlinear analysis of laminated shells", Compos. Struct., 153(1), 538-548. https://doi.org/10.1016/j.compstruct.2016.06.052.
  46. Rezaiee-Pajand, M., Arabi, E. and Masoodi, A.R. (2018), "A triangular shell element for geometrically nonlinear analysis", Acta Mechanica, 229(1), 323-342. https://doi.org/10.1007/s00707-017-1971-8.
  47. Rezaiee-Pajand, M., Masoodi, A.R. and Arabi, E. (2018), "Geometrically nonlinear analysis of FG doubly-curved and hyperbolical shells via laminated by new element", Steel Compos. Struct., 28(3), 389-401. http://dx.doi.org/10.12989/scs.2016.22.6.1445.
  48. Rezaiee-Pajand, M., Masoodi, A.R. and Arabi, E. (2018), "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.
  49. Rezaiee-Pajand, M., Shahabian, F. and Tavakoli, F.H. (2012), "A new higher-order triangular plate Bending element for the analysis of laminated composite and sandwich plates", Struct. Eng. Mech., 43(2), 253-271. https://doi.org/10.12989/sem.2012.43.2.253.
  50. Senthilnathan, N.R., Chow, S.T., Lee, K.H. and Lim, S.P. (1987), "Buckling of shear-deformable plates", AIAA J., 25(9), 1268-1271. https://doi.org/10.2514/3.48742.
  51. Shaheen, Y.B., Mahmoud, A.M. and Refat, H.M. (2016), "Structural performance of ribbed ferrocement plates reinforced with composite materials", Struct. Eng. Mech., 60(4), 567-594. http://dx.doi.org/10.12989/sem.2016.60.4.567.
  52. Shimpi, R.P. (2002), "Refined plate theory and its variants", AIAA J., 40(1), 137-46. https://doi.org/10.2514/2.1622.
  53. Shimpi, R.P. and Patel, H.G. (2006), "A two variable refined plate theory for orthotropic plate analysis", Int. J. Solid. Struct., 43(23), 6783-6799. https://doi.org/10.1016/j.ijsolstr.2006.02.007.
  54. Soldatos, K.P. (1992), "A transverse shear deformation theory for homogeneous monoclinic plates", Acta Mech., 94(3), 195-200. https://doi.org/10.1007/BF01176650.
  55. Soldatos, K.P. and Timarci, T. (1993), "A unified formulation of laminated composite, shear deformable, five-degrees-of-freedom cylindrical shell theories", Compos. Struct., 25(1-4), 165-171. https://doi.org/10.1016/0263-8223(93)90162-J.
  56. Thai, H.T. (2012), "A nonlocal beam theory for bending, buckling, and vibration of nanobeams", Int. J. Eng. Sci., 52, 56-64. https://doi.org/10.1016/j.ijengsci.2011.11.011.
  57. 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.
  58. Thai, H.T. and Kim, S.E. (2010), "Free vibration of laminated composite plates using two variable refined plate theory", Int. J. Mech. Sci., 52, 626-633. https://doi.org/10.1016/j.ijmecsci.2010.01.002.
  59. Touratier, M. (1991), "An efficient standard plate theory", Eng. Sci., 29(8), 901-916. https://doi.org/10.1016/0020-7225(91)90165-Y.
  60. Whitney, J.M. and Sun, C.T. (1973), "A higher order theory for extensional motion of laminated composites", J. Sound Vib., 30(1), 85-97. https://doi.org/10.1016/S0022-460X(73)80052-5.
  61. Xiang, S. and Kang, G.W. (2013b), "A nth-order shear deformation theory for the bending analysis on the functionally graded plates", Eur. J. Mech. A/Solid., 37, 336-343. https://doi.org/10.1016/j.euromechsol.2012.08.005.
  62. Xiang, S., Jiang, S.X., Bi, Z.Y., Jin, Y.X. and Yang, M.S. (2011b), "A nth-order meshless generalization of Reddy's third-order shear deformation theory for the free vibration on laminated composite plates", Compos. Struct., 93(2), 299-307. https://doi.org/10.1016/j.compstruct.2010.09.015.
  63. Xiang, S., Jin, Y.X., Bi, Z.Y., Jiang, S.X. and Yang, M.S. (2011a), "A n-order shear deformation theory for free vibration of functionally graded and composite sandwich plates", Compos. Struct., 93(11), 2826-2832. https://doi.org/10.1016/j.compstruct.2011.05.022.
  64. Xiang, S., Kang, G.W. and Xing, B. (2012), "A nth-order shear deformation theory for the free vibration analysis on the isotropic plates", Meccanica, 47(8), 1913-1921. https://doi.org/10.1007/s11012-012-9563-0.
  65. Xiang, S., Kang, G.W., Yang, M.S. and Zhao, Y. (2013a), "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.
  66. Younsi, A., Tounsi, A., Zaoui, F.Z., Bousahla, A.A. and Mahmoud, S.R. (2018), "Novel quasi-3D and 2D shear deformation theories for bending and free vibration analysis of FGM plates", Geomech. Eng., 14(6), 519-532. https://doi.org/10.12989/gae.2018.14.6.519.