Steel and Composite Structures

Techno-Press (테크노프레스)
권호 표지
DOI QR코드

DOI QR Code

Large deflection analysis of a fiber reinforced composite beam

  • Akbas, Seref D. (Department of Civil Engineering, Bursa Technical University, Yildirim Campus)
  • Received : 2018.03.02
  • Accepted : 2018.03.28
  • Published : 2018.06.10
⟨ Previous Next ⟩

Abstract

The objective of this work is to analyze large deflections of a fiber reinforced composite cantilever beam under point loads. In the solution of the problem, finite element method is used in conjunction with two dimensional (2-D) continuum model. It is known that large deflection problems are geometrically nonlinear problems. The considered non-linear problem is solved considering the total Lagrangian approach with Newton-Raphson iteration method. In the numerical results, the effects of the volume fraction and orientation angles of the fibre on the large deflections of the composite beam are examined and discussed. Also, the difference between the geometrically linear and nonlinear analysis of fiber reinforced composite beam is investigated in detail.

Keywords

References

  1. Abdelaziz H.H., Meziane, M.A.A., 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., Int. J., 25(6), 693-704.
  2. Abualnour, M., Houari, M.S.A., Tounsi, A. and Mahmoud, S.R. (2018), "A novel quasi-3D trigonometric plate theory for free vibration analysis of advanced composite plates", Compos. Struct., 184, 688-697. https://doi.org/10.1016/j.compstruct.2017.10.047
  3. Akbas, S.D. (2013a), "Geometrically nonlinear static analysis of edge cracked Timoshenko beams composed of functionally graded material", Math. Problems Eng., 2013, 14 p. DOI: 10.1155/2013/871815
  4. Akbas, S.D. (2013b), "Free vibration characteristics of edge cracked functionally graded beams by using finite element method", Int. J. Eng. Trends Technol., 4(10), 4590-4597.
  5. Akbas, S.D. (2014), "Large post-buckling behavior of Timoshenko beams under axial compression loads", Struct. Eng. Mech., Int. J., 51(6), 955-971. https://doi.org/10.12989/sem.2014.51.6.955
  6. Akbas, S.D. (2015a), "On post-buckling behavior of edge cracked functionally graded beams under axial loads", Int. J. Struct. Stabil. Dyn., 15(4), 1450065. DOI: 10.1142/S0219455414500655
  7. Akbas, S.D. (2015b), "ost-buckling analysis of axially functionally graded three-dimensional beams", Int. J. Appl. Mech., 7(3), 1550047. DOI: 10.1142/S1758825115500477
  8. Akbas, S.D. (2015c), "Large deflection analysis of edge cracked simple supported beams", Struct. Eng. Mech., Int. J., 54(3), 433-451. https://doi.org/10.12989/sem.2015.54.3.433
  9. Akbas, S.D. (2015d), "Wave propagation of a functionally graded beam in thermal environments", Steel Compos. Struct., Int. J., 19(6), 1421-1447. https://doi.org/10.12989/scs.2015.19.6.1421
  10. Akbas, S.D. (2015e), "Free vibration and bending of functionally graded beams resting on elastic foundation", Res. Eng. Struct. Mater., 1(1).
  11. Akbas, S.D. (2016a), "Post-buckling analysis of edge cracked columns under axial compression loads", Int. J. Appl. Mech., 8(8), 1650086. https://doi.org/10.1142/S1758825116500861
  12. Akbas, S.D. (2016b), "Analytical solutions for static bending of edge cracked micro beams", Struct. Eng. Mech., Int. J., 59(3), 579-599. https://doi.org/10.12989/sem.2016.59.3.579
  13. Akbas, S.D. (2016c), "Forced vibration analysis of viscoelastic nanobeams embedded in an elastic medium", Smart Struct. Syst., Int. J., 18(6), 1125-1143. https://doi.org/10.12989/sss.2016.18.6.1125
  14. Akbas, S.D. (2017a), "Free vibration of edge cracked functionally graded microscale beams based on the modified couple stress theory", Int. J. Struct. Stabil. Dyn., 17(3), 1750033. https://doi.org/10.1142/S021945541750033X
  15. Akbas, S.D. (2017b), "Static, Vibration, and Buckling Analysis of Nanobeams", In: Nanomechanics, (A. Vakhrushev Ed.), InTech, pp.123-137.
  16. Akbas, S.D. (2017c), "Stability of A Non-Homogenous Porous Plate by Using Generalized Differantial Quadrature Method", Int. J. Eng. Appl. Sci., 9(2), 147-155.
  17. Akbas, S.D. (2017d), "Forced vibration analysis of functionally graded nanobeams", Int. J. Appl. Mech., 9(7), 1750100. https://doi.org/10.1142/S1758825117501009
  18. Akbas, S.D. (2017e), "Post-buckling responses of functionally graded beams with porosities", Steel Compos. Struct., Int. J., 24(5), 579-589.
  19. Akbas, S.D. (2017f), "Vibration and static analysis of functionally graded porous plates", J. Appl. Computat. Mech., 3(3), 199-207.
  20. Akbas, S.D. (2017g), "Nonlinear static analysis of functionally graded porous beams under thermal effect", Coupled Syst. Mech., Int. J., 6(4), 399-415.
  21. Akbas, S.D. (2018a), "Post-buckling responses of a laminated composite beam", Steel Compos. Struct., Int. J., 26(6), 733-743.
  22. Akbas, S.D. (2018b), "Post-buckling responses of a laminated composite beam", Steel Compos. Struct., Int. J., 26(6), 733-743. DOI: https://doi.org/10.12989/scs.2018.26.6.733
  23. Akbas, S.D. (2018c), "Forced vibration analysis of functionally graded porous deep beams", Compos. Struct., 185, 293-302.
  24. Akbas, S.D. and Kocaturk, T. (2012), "Post-buckling analysis of Timoshenko beams with temperature-dependent physical properties under uniform thermal loading", Struct. Eng. Mech., Int. J., 44(1), 109-125. https://doi.org/10.12989/sem.2012.44.1.109
  25. Akgoz, B. and Civalek, O. (2011), "Nonlinear vibration analysis of laminated plates resting on nonlinear two-parameters elastic foundations", Steel Compos. Struct., Int. J., 11(5), 403-421. https://doi.org/10.12989/scs.2011.11.5.403
  26. Alam, M.A. and Al Riyami, K. (2018), "Shear strengthening of reinforced concrete beam using natural fibre reinforced polymer laminates", Constr. Build. Mater., 162, 683-696. https://doi.org/10.1016/j.conbuildmat.2017.12.011
  27. Amada, S. and Nagase, Y. (1996), "Analysis of large deflection of bamboo as functionally graded material", Transact. Japan Soc. Mech. Engr., Part A, 62(599), 1672-1676. https://doi.org/10.1299/kikaia.62.1672
  28. Argyridi, A. and Sapountzakis, E. (2016), "Generalized Warping In Flexural-Torsional Buckling Analysis of Composite Beams", J. Appl. Computat. Mech., 2(3), 152-173.
  29. Attia, A., Bousahla, A.A., Tounsi, A., Mahmoud, S.R. and Alwabli, A.S. (2018), "A refined four variable plate theory for thermoelastic analysis of FGM plates resting on variable elastic foundations", Struct. Eng. Mech., Int. J., 65(4), 453-464.
  30. Belabed, Z., Houari, M.S.A., Tounsi, A., Mahmoud, S.R., 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
  31. Belabed, Z., Bousahla, A.A., Houari, M.S.A., Tounsi, A. and Mahmoud, S.R. (2018), "A new 3- unknown hyperbolic shear deformation theory for vibration of functionally graded sandwich plate", Earthq. Struct., Int. J., 14(2), 103-115.
  32. Beldjelili, Y., Tounsi, A. and Mahmoud, S.R. (2016), "Hygrothermo-mechanical bending of S-FGM plates resting on variable elastic foundations using a four-variable trigonometric plate theory", Smart Struct. Syst., Int. J., 18(4), 755-786. https://doi.org/10.12989/sss.2016.18.4.755
  33. Bellifa, H., Benrahou, K.H., Hadji, L., Houari, M.S.A. and Tounsi, A. (2016), "Bending and free vibration analysis of functionally graded plates using a simple shear deformation theory and the concept the neutral surface position", J. Brazil. Soc. Mech. Sci. Eng., 38(1), 265-275. https://doi.org/10.1007/s40430-015-0354-0
  34. Bellifa, H., Bakora, A., Tounsi, A., Bousahla, A.A. and Mahmoud, S.R. (2017), "An efficient and simple four variable refined plate theory for buckling analysis of functionally graded plates", Steel Compos. Struct., Int. J., 25(3), 257-270.
  35. Benchohra, M., Driz, H., Bakora, A., Tounsi, A., Adda Bedia, E.A. and Mahmoud, S.R. (2018), "A new quasi-3D sinusoidal shear deformation theory for functionally graded plates", Struct. Eng. Mech., Int. J., 65(1), 19-31.
  36. Bennoun, M., Houari, M.S.A. and Tounsi, A. (2016), "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
  37. Benselama, K., El Meiche, N., Bedia, E.A.A. and Tounsi, A. (2015), "Buckling analysis in hybrid cross-ply composite laminates on elastic foundation using the two variable refined plate theory", Struct. Eng. Mech., Int. J., 55(1), 47-64. https://doi.org/10.12989/sem.2015.55.1.047
  38. Bouafia, K., Kaci, A., Houari, M.S.A., Benzair, A. and Tounsi, A. (2017), "A nonlocal quasi-3D theory for bending and free flexural vibration behaviors of functionally graded nanobeams", Smart Struct. Syst., Int. J., 19(2), 115-126. https://doi.org/10.12989/sss.2017.19.2.115
  39. 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
  40. Boukhari, A., Atmane, H.A., Tounsi, A., Adda, B. and Mahmoud, S.R. (2016), "An efficient shear deformation theory for wave propagation of functionally graded material plates", Struct. Eng. Mech., Int. J., 57(5), 837-859. https://doi.org/10.12989/sem.2016.57.5.837
  41. Bounouara, F., Benrahou, K.H., Belkorissat, I. and Tounsi, A. (2016), "A nonlocal zeroth-order shear deformation theory for free vibration of functionally graded nanoscale plates resting on elastic foundation", Steel Compos. Struct., Int. J., 20(2), 227-249. https://doi.org/10.12989/scs.2016.20.2.227
  42. 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
  43. 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. Computat. Methods, 11(6), 1350082. https://doi.org/10.1142/S0219876213500825
  44. Cardoso, J.B., Benedito, N.M. and Valido, A.J. (2009), "Finite element analysis of thin-walled composite laminated beams with geometrically nonlinear behavior including warping deformation", Thin-Wall. Struct., 47(11), 1363-1372. https://doi.org/10.1016/j.tws.2009.03.002
  45. 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., Int. J., 19(3), 289-297. https://doi.org/10.12989/sss.2017.19.3.289
  46. Civalek, O. (2013), "Nonlinear dynamic response of laminated plates resting on nonlinear elastic foundations by the discrete singular convolution-differential quadrature coupled approaches", Compos. Part B: Eng., 50, 171-179. https://doi.org/10.1016/j.compositesb.2013.01.027
  47. Cunedioglu, Y. and Beylergil, B. (2014), "Free vibration analysis of laminated composite beam under room and high temperatures", Struct. Eng. Mech., Int. J., 51(1), 111-130. https://doi.org/10.12989/sem.2014.51.1.111
  48. Di Sciuva, M. and Icardi, U. (1995), "Large deflection of adaptive multilayered Timoshenko beams", Compos. Struct., 31(1), 49-60. https://doi.org/10.1016/0263-8223(95)00001-1
  49. Donthireddy, P. and Chandrashekhara, K. (1997), "Nonlinear thermomechanical analysis of laminated composite beams", Adv. Compos. Mater., 6(2), 153-166. https://doi.org/10.1163/156855197X00049
  50. Draiche, K., Tounsi, A. and Mahmoud, S.R. (2016), "A refined theory with stretching effect for the flexure analysis of laminated composite plates", Geomech. Eng., Int. J., 11(5), 671-690. https://doi.org/10.12989/gae.2016.11.5.671
  51. Ebrahimi, F. and Hosseini, S.H.S. (2017), "Surface effects on nonlinear dynamics of NEMS consisting of double-layered viscoelastic nanoplates", Eur. Phys. J. Plus, 132(4), p. 172. https://doi.org/10.1140/epjp/i2017-11400-6
  52. El-Haina, F., Bakora, A., Bousahla, A.A., Tounsi, A. and Mahmoud, S.R. (2017), "A simple analytical approach for thermal buckling of thick functionally graded sandwich plates", Struct. Eng. Mech., Int. J., 63(5), 585-595.
  53. Emam, S.A. and Nayfeh, A.H. (2009), "Postbuckling and free vibrations of composite beams", Compos. Struct., 88(4), 636-642. https://doi.org/10.1016/j.compstruct.2008.06.006
  54. Felippa, C.A. (2018), "Notes on Nonlinear Finite Element Methods". URL: http://www.colorado.edu/engineering/cas/courses.d/NFEM.d/NFEM.Ch11.d/NFEM.Ch11.pdf
  55. Fraternali, F. and Bilotti, G. (1997), "Nonlinear elastic stress analysis in curved composite beams", Comput. Struct., 62(5), 837-859. https://doi.org/10.1016/S0045-7949(96)00301-X
  56. Ganapathi, M., Patel, B.P., Saravanan, J. and Touratier, M. (1998), "Application of spline element for large-amplitude free vibrations of laminated orthotropic straight/curved beams", Compos. Part B: Eng., 29(1), 1-8. https://doi.org/10.1016/S1359-8368(97)00025-5
  57. Ge, W.J., Ashour, A.F., Ji, X., Cai, C. and Cao, D.F. (2018), "Flexural behavior of ECC-concrete composite beams reinforced with steel bars", Constr. Build. Mater., 159, 175-188. https://doi.org/10.1016/j.conbuildmat.2017.10.101
  58. Ghazavi, A. and Gordaninejad, F. (1989), "Nonlinear bending of thick beams laminated from bimodular composite materials", Compos. Sci. Technol., 36(4), 289-298. https://doi.org/10.1016/0266-3538(89)90043-2
  59. 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
  60. Hebali, H., Tounsi, A., Houari, M. S. A., Bessaim, A. and Bedia, E.A.A. (2014), "New quasi-3D hyperbolic shear deformation theory for the static and free vibration analysis of functionally graded plates", J. Eng. Mech., 140(2), 374-383. https://doi.org/10.1061/(ASCE)EM.1943-7889.0000665
  61. Houari, M.S.A., Tounsi, A., Bessaim, A. and Mahmoud, S.R. (2016), "A new simple three-unknown sinusoidal shear deformation theory for functionally graded plates", Steel Compos. Struct., Int. J., 22(2), 257-276. https://doi.org/10.12989/scs.2016.22.2.257
  62. Kaci, A., Houari, M.S.A., Bousahla, A.A., Tounsi, A. and Mahmoud, S.R. (2018), "Post-buckling analysis of sheardeformable composite beams using a novel simple twounknown beam theory", Struct. Eng. Mech., Int. J., 65(5), 621-631.
  63. Kisa, M. (2004), "Free vibration analysis of a cantilever composite beam with multiple cracks", Compos. Sci. Technol., 64(9), 1391-1402. https://doi.org/10.1016/j.compscitech.2003.11.002
  64. Kim, T. and Dugundji, J. (1993), "Nonlinear large amplitude vibration of composite helicopter blade atlarge static deflection", AIAA Journal, 31(5), 938-946. https://doi.org/10.2514/3.11708
  65. Kocaturk, T. and Akbas, S.D. (2010), "Geometrically non-linear static analysis of a simply supported beam made of hyperelastic material", Struct. Eng. Mech., Int. J., 35(6), 677-697. https://doi.org/10.12989/sem.2010.35.6.677
  66. Kocaturk, T. and Akbas, S.D. (2011), "Post-buckling analysis of Timoshenko beams with various boundary conditions under non-uniform thermal loading", Struct. Eng. Mech., Int. J., 40(3), 347-371. https://doi.org/10.12989/sem.2011.40.3.347
  67. Kocaturk, T. and Akbas, S.D. (2012), "Post-buckling analysis of Timoshenko beams made of functionally graded material under thermal loading", Struct. Eng. Mech., Int. J., 41(6), 775-789. https://doi.org/10.12989/sem.2012.41.6.775
  68. Kocaturk, T. and Akbas, S.D. (2013), "Thermal post-buckling analysis of functionally graded beams with temperaturedependent physical properties", Steel Compos. Struct., Int. J., 15(5), 481-505. https://doi.org/10.12989/scs.2013.15.5.481
  69. Kolli, M. and Chandrashekhara, K. (1997), "Non-linear static and dynamic analysis of stiffened laminated plates", Int. J. Non-Linear Mech., 32(1), 89-101. https://doi.org/10.1016/S0020-7462(96)00016-9
  70. Krawczuk, M., Ostachowicz, W. and Zak, A. (1997), "Modal analysis of cracked, unidirectional composite beam", Compos. Part B: Eng., 28(5-6), 641-650. https://doi.org/10.1016/S1359-8368(97)82238-X
  71. Kurtaran, H. (2015), "Geometrically nonlinear transient analysis of thick deep composite curved beams with generalized differential quadrature method", Compos. Struct., 128, 241-250. https://doi.org/10.1016/j.compstruct.2015.03.060
  72. Latifi, M., Kharazi, M. and Ovesy, H.R. (2016), "Nonlinear dynamic response of symmetric laminated composite beams under combined in-plane and lateral loadings using full layerwise theory", Thin-Wall. Struct., 104, 62-70. https://doi.org/10.1016/j.tws.2016.03.006
  73. Li, Z.M. and Qiao, P. (2015), "Buckling and postbuckling behavior of shear deformable anisotropic laminated beams with initial geometric imperfections subjected to axial compression", Eng. Struct., 85, 277-292. https://doi.org/10.1016/j.engstruct.2014.12.028
  74. Li, Z.M. and Yang, D.Q. (2016), "Thermal postbuckling analysis of anisotropic laminated beams with tubular cross-section based on higher-order theory", Ocean Eng., 115, 93-106. https://doi.org/10.1016/j.oceaneng.2016.02.017
  75. Liu, Y. and Shu, D.W. (2015), "Effects of edge crack on the vibration characteristics of delaminated beams", Struct. Eng. Mech., Int. J., 53(4), 767-780. https://doi.org/10.12989/sem.2015.53.4.767
  76. Loja, M.A.R., Barbosa, J.I. and Soares, C.M.M. (2001), "Static and dynamic behaviour of laminated composite beams", Int. J. Struct. Stabil. Dyn., 1(4), 545-560. https://doi.org/10.1142/S0219455401000354
  77. Machado, S.P. (2007), "Geometrically non-linear approximations on stability and free vibration of composite beams", Eng. Struct., 29(12), 3567-3578. https://doi.org/10.1016/j.engstruct.2007.08.009
  78. Mahi, 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
  79. Mareishi, S., Rafiee, M., He, X.Q. and Liew, K.M. (2014), "Nonlinear free vibration, postbuckling and nonlinear static deflection of piezoelectric fiber-reinforced laminated composite beams", Compos. Part B: Eng., 59, 123-132. https://doi.org/10.1016/j.compositesb.2013.11.017
  80. Malekzadeh, P. and Vosoughi, A.R. (2009), "DQM large amplitude vibration of composite beams on nonlinear elastic foundations with restrained edges", Commun. Nonlinear Sci. Numer. Simul., 14(3), 906-915. https://doi.org/10.1016/j.cnsns.2007.10.014
  81. Manthena, V.R., Lamba, N.K. and Kedar, G.D. (2016), "Springbackward phenomenon of a transversely isotropic functionally graded composite cylindrical shell", J. Appl. Computat. Mech., 2(3), 134-143.
  82. Menasria, A., Bouhadra, A., Tounsi, A., Bousahla, A.A. and Mahmoud, S.R. (2017), "A new and simple HSDT for thermal stability analysis of FG sandwich plates", Steel Compos. Struct., Int. J., 25(2), 157-175.
  83. 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
  84. Mororo, L.A.T., Melo, A.M.C.D. and Parente Jr., E. (2015), "Geometrically nonlinear analysis of thin-walled laminated composite beams", Latin Am. J. Solids Struct., 12(11), 2094-2117. https://doi.org/10.1590/1679-78251782
  85. Oliveira, B.F. and Creus, G.J. (2003), "Nonlinear viscoelastic analysis of thin-walled beams in composite material", Thin-Wall. Struct., 41(10), 957-971. https://doi.org/10.1016/S0263-8231(03)00042-9
  86. Omidvar, B. and Ghorbanpoor, A. (1996), "Nonlinear FE solution for thin-walled open-section composite beams", J. Struct. Eng., 122(11), 1369-1378. https://doi.org/10.1061/(ASCE)0733-9445(1996)122:11(1369)
  87. Pagani, A. and Carrera, E. (2017), "Large-deflection and postbuckling analyses of laminated composite beams by Carrera Unified Formulation", Compos. Struct., 170, 40-52. https://doi.org/10.1016/j.compstruct.2017.03.008
  88. Pai, P.F. and Nayfeh, A.H. (1992), "A nonlinear composite beam theory", Nonlinear Dyn., 3(4), 273-303. https://doi.org/10.1007/BF00045486
  89. Patel, S.N. (2014), "Nonlinear bending analysis of laminated composite stiffened plates", Steel Compos. Struct., Int. J., 17(6), 867-890. https://doi.org/10.12989/scs.2014.17.6.867
  90. Patel, B.P., Ganapathi, M. and Touratier, M. (1999), "Nonlinear free flexural vibrations/post-buckling analysis of laminated orthotropic beams/columns on a two parameter elastic foundation", Compos. Struct., 46(2), 189-196. https://doi.org/10.1016/S0263-8223(99)00054-9
  91. Oucif, C., Ouzaa, K. and Mauludin, L.M. (2017), "Cyclic and monotonic behavior of strengthened and unstrengthened square reinforced concrete columns", J. Appl. Computat. Mech. DOI: 10.22055/JACM.2017.23514.1159-
  92. Salehi, M. and Falahatgar, S.R. (2010), "Geometrically non-linear analysis of unsymmetrical fiber-reinforced laminated annular sector composite plates", Scientia Iranica. Transaction B, Mech. Eng., 17(3), 205.
  93. Shen, H.S. (2001), "Thermal postbuckling behavior of imperfect shear deformable laminated plates with temperature-dependent properties", Comput. Methods Appl. Mech. Eng., 190(40-41), 5377-5390. https://doi.org/10.1016/S0045-7825(01)00172-4
  94. Shen, H.S., Chen, X. and Huang, X.L. (2016), "Nonlinear bending and thermal postbuckling of functionally graded fiber reinforced composite laminated beams with piezoelectric fiber reinforced composite actuators", Compos. Part B: Eng., 90, 326-335. https://doi.org/10.1016/j.compositesb.2015.12.030
  95. Shen, H.S., Lin, F. and Xiang, Y. (2017), "Nonlinear bending and thermal postbuckling of functionally graded graphenereinforced composite laminated beams resting on elastic foundations", Eng. Struct., 140, 89-97. https://doi.org/10.1016/j.engstruct.2017.02.069
  96. Singh, G., Rao, G.V. and Iyengar, N.G.R. (1992), "Nonlinear bending of thin and thick unsymmetrically laminated composite beams using refined finite element model", Comput. Struct., 42(4), 471-479. https://doi.org/10.1016/0045-7949(92)90114-F
  97. Stoykov, S. and Margenov, S. (2014), "Nonlinear vibrations of 3D laminated composite beams", Math. Problems Eng.
  98. Topal, U. (2017), "Buckling load optimization of laminated composite stepped columns", Struct. Eng. Mech., Int. J., 62(1), 107-111.
  99. 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
  100. Xie, M. and Adams, D.F. (1996), "A nonlinear finite element analysis for composite materials", Finite Elem. Anal. Des., 22(3), 211-223. https://doi.org/10.1016/0168-874X(95)00055-X
  101. Valido, A.J. and Cardoso, J.B. (2003), "Geometrically nonlinear composite beam structures: Design sensitivity analysis", Eng. Optimiz., 35(5), 531-551. https://doi.org/10.1080/03052150310001604784
  102. Vinson, J.R. and Sierakowski, R.L. (2002), "The behavior of Structures Composed of Composite Materials", Kluwer Academic Publishers, ISBN 978-140-2009-04-4, Netherlands.
  103. Vo, T.P. and Lee, J. (2009), "Geometrically nonlinear analysis of thin-walled composite box beams", Comput. Struct., 87(3-4), 236-245. https://doi.org/10.1016/j.compstruc.2008.10.002
  104. Yahia, S.A., Atmane, H.A., 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
  105. Yazid, M., Heireche, H., Tounsi, A., Bousahla, A.A. and Houari, M.S.A. (2018), "A novel nonlocal refined plate theory for stability response of orthotropic single-layer graphene sheet resting on elastic medium", Smart Struct. Syst., Int. J., 21(1), 15-25.
  106. Youcef, D.O., Kaci, A., Benzair, A. Bousahla, A.A. and Tounsi, A. (2018), "Dynamic analysis of nanoscale beams including surface stress effects", Smart Struct. Syst., Int. J., 21(1), 65-74.
  107. Youzera, H., Meftah, S.A., Challamel, N. and Tounsi, A. (2012), "Nonlinear damping and forced vibration analysis of laminated composite beams", Compos. Part B: Eng., 43(3), 1147-1154. https://doi.org/10.1016/j.compositesb.2012.01.008
  108. Zidi, M., Tounsi, A., Houari, M.S.A. and Beg, O.A. (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
  109. Zine, A., Tounsi, A., Draiche, K., Sekkal, M. and Mahmoud, S.R. (2018), "A novel higher-order shear deformation theory for bending and free vibration analysis of isotropic and multilayered plates and shells", Steel Compos. Struct., Int. J., 26(2), 125-137.

Cited by

  1. Hygrothermal Post-Buckling Analysis of Laminated Composite Beams vol.11, pp.1, 2018, https://doi.org/10.1142/s1758825119500091
  2. Dynamic analysis of a laminated composite beam under harmonic load vol.9, pp.6, 2020, https://doi.org/10.12989/csm.2020.9.6.563
  3. Monitoring and control of multiple fraction laws with ring based composite structure vol.10, pp.2, 2021, https://doi.org/10.12989/anr.2021.10.2.129
  4. Forced Vibration Analysis of Composite Beams Reinforced by Carbon Nanotubes vol.11, pp.3, 2018, https://doi.org/10.3390/nano11030571
  5. Effect of suction on flow of dusty fluid along exponentially stretching cylinder vol.10, pp.3, 2018, https://doi.org/10.12989/anr.2021.10.3.263
  6. Dynamic Analysis of a Fiber-Reinforced Composite Beam under a Moving Load by the Ritz Method vol.9, pp.9, 2021, https://doi.org/10.3390/math9091048
  7. Analysis of Equivalent Flexural Stiffness of Steel-Concrete Composite Beams in Frame Structures vol.11, pp.21, 2021, https://doi.org/10.3390/app112110305