DOI QR코드

DOI QR Code

Investigation of the Instability of FGM box beams

  • Ziane, Noureddine (Laboratoire des Structures et Materiaux Avances dans le Genie Civil et Travaux Publics, Universite de Djillali Liabes) ;
  • Meftah, Sid Ahmed (Laboratoire des Structures et Materiaux Avances dans le Genie Civil et Travaux Publics, Universite de Djillali Liabes) ;
  • Ruta, Giuseppe (Department of Structural & Geotechnical Engineering, Faculty of Civil & Industrial Engineering, Sapienza University) ;
  • Tounsi, Abdelouahed (Laboratoire des Materiaux et Hydrologie, Universite de Sidi Bel Abbes) ;
  • Adda Bedia, El Abbas (Laboratoire des Materiaux et Hydrologie, Universite de Sidi Bel Abbes)
  • 투고 : 2015.01.30
  • 심사 : 2015.03.24
  • 발행 : 2015.05.10

초록

A general geometrically non-linear model for lateral-torsional buckling of thick and thin-walled FGM box beams is presented. In this model primary and secondary torsional warping and shear effects are taken into account. The coupled equilibrium equations obtained from Galerkin's method are derived and the corresponding tangent matrix is used to compute the critical moments. General expression is derived for the lateral-torsional buckling load of unshearable FGM beams. The results are validated by comparison with a 3D finite element simulation using the code ABAQUS. The influences of the geometrical characteristics and the shear effects on the buckling loads are demonstrated through several case studies.

키워드

참고문헌

  1. Abaqus standard user's manual version 6.4. (2003), Hibbit, Karlsson and Sorensen Inc., Pawtucket, RI, USA.
  2. 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
  3. 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., 53(6), 1143-1165. https://doi.org/10.12989/sem.2015.53.6.1143
  4. 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
  5. 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
  6. 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., 14, 85-104. https://doi.org/10.12989/scs.2013.14.1.085
  7. 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., 18(2), 409-423. https://doi.org/10.12989/scs.2015.18.2.409
  8. 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. Meth., 11(6), 1350082. https://doi.org/10.1142/S0219876213500825
  9. Cortinez, V.H. and Piovan, M.T. (2002), "Vibration and buckling of composite thin walled beams with shear deformability", J Sound Vib., 258(4), 701-23. https://doi.org/10.1006/jsvi.2002.5146
  10. Dung, D.V. and Hoa, L.K. (2013), "Research on nonlinear torsional buckling and post-buckling of eccentrically stiffened functionally graded thin circular cylindrical shells", Compos. Part B, 51, 300-309. https://doi.org/10.1016/j.compositesb.2013.03.030
  11. Erkmen, R.E. (2014), "Shear deformable hybrid finite-element formulation for buckling analysis of thinwalled members", Finite Elem. Anal. Des., 82, 32-45. https://doi.org/10.1016/j.finel.2013.12.005
  12. Erkmen, R.E. and Attard, M.M. (2011), "Lateral-torsional buckling analysis of thin-walled beams including shear and pre-buckling deformation effects", Int. J. Mech. Sci., 53, 918-925. https://doi.org/10.1016/j.ijmecsci.2011.08.006
  13. Fraternali, F. and Feo, L. (2000), "On a moderate rotation theory of thin-walled composite beams", Compos. Part B, 31, 141-58. https://doi.org/10.1016/S1359-8368(99)00079-7
  14. 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, 795-810. https://doi.org/10.1007/s11012-013-9827-3
  15. Fu, C.C and Hsu, Y.T. (1995), "The development of an improved curvilinear thin-walled Vlasov element", Comput. Struct., 54, 147-159. https://doi.org/10.1016/0045-7949(94)P4141-Y
  16. Gjelskin, A. (1981), The Theory of Thin-Walled Bars, John Wiley an Sons Inc, New York, USA.
  17. Goncalves, R. (2012), "A geometrically exact approach to lateral-torsional buckling of thin-walled beams with deformable cross-section", Comput. Struct., 106-107, 9-19. https://doi.org/10.1016/j.compstruc.2012.03.017
  18. Hebali, H., Tounsi, A., Houari, M.S.A., Bessaim, A. and Adda Bedia, E.A. (2014), "New quasi-3D hyperbolic shear deformation theory for the static and free vibration analysis of functionally graded plates", J. Eng. Mech., ASCE, 140, 374-383. https://doi.org/10.1061/(ASCE)EM.1943-7889.0000665
  19. 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. Meth., 11(5), 135007.
  20. Kim, N.I., Shin, D.K. and Kim, M.Y. (2008), "Flexural-torsional buckling loads for spatially coupled stability analysis of thin-walled composite columns", Adv. Eng. Softw., 39, 949-961. https://doi.org/10.1016/j.advengsoft.2008.03.001
  21. Kim, Y.Y. and Kim J.H. (1999), "Thin-walled closed box element for static and dynamic analysis", Int. J. Numer. Meth. Eng., 45, 473-490. https://doi.org/10.1002/(SICI)1097-0207(19990610)45:4<473::AID-NME603>3.0.CO;2-B
  22. Lanc, D., Vo, T.P., Turkalj, G. and Lee, J. (2015), "Buckling analysis of thin-walled functionally graded sandwich box beams", Thin Wall. Struct., 86, 148-156. https://doi.org/10.1016/j.tws.2014.10.006
  23. Lofrano, E., Paolone, A. and Ruta, G. (2013), "A numerical approach for the stability analysis of open thinwalled beams", Mech. Res. Commun., 48, 76- 86. https://doi.org/10.1016/j.mechrescom.2012.12.008
  24. Machado, S.P. and Cortinez, V.H. (2005), "Lateral buckling of thin-walled composite bisymmetric beams with prebuckling and shear deformation", Eng. Struct., 27, 1185-1196. https://doi.org/10.1016/j.engstruct.2005.02.018
  25. Machado, S.P. and Cortinez, V.H. (2005), "Non-linear model for thin-walled composite beams with shear deformation", Thin Wall. Struct., 43, 1615-1645. https://doi.org/10.1016/j.tws.2005.06.008
  26. Mohri, F., Azrar, L. and Potier-Ferry, M. (2002), "Lateral post-buckling analysis of thin-walled open section beams", Thin Wall. Struct., 40, 1013-1036. https://doi.org/10.1016/S0263-8231(02)00043-5
  27. Paulsen, F. and Welo, T. (2001), "Cross-sectional deformations of rectangular hollow sections in bending. Part II-Analytical models", Int. J. Mech. Sci., 43, 131-152. https://doi.org/10.1016/S0020-7403(99)00107-1
  28. Pignataro, M., Rizzi, N., Ruta, R. and Varano. V. (2010), "The effects of warping constraints on the buckling of thin-walled structures", J. Mech. Mater. Struct., 4(10), 1711-1727. https://doi.org/10.2140/jomms.2009.4.1711
  29. Ruta, G.C., Varano, V., Pignataro, M. and Rizzi, L.R. (2008), "A beam model for the flexural-torsional buckling of thin-walled members with some applications", Thin Wall. Struct., 46(7), 816-822. https://doi.org/10.1016/j.tws.2008.01.020
  30. Sapkas, A. and kollar, L.P. (2002), "Lateral-torsional buckling of composite beams", Int. J. Solid. Struct., 39, 2939-2963. https://doi.org/10.1016/S0020-7683(02)00236-6
  31. Shen, H. (2009), "Torsional buckling and postbuckling of FGM cylindrical shells in thermal environments", Int. J. Nonlin. Mech., 44, 644-657. https://doi.org/10.1016/j.ijnonlinmec.2009.02.009
  32. Sokolnikoff, I.S. (1946), Mathematical Theory of Elasticity, McGraw-Hill, New York, USA.
  33. 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
  34. 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. Tech., 24, 209-220. https://doi.org/10.1016/j.ast.2011.11.009
  35. Vlasov, V.Z. (1962), Thin Walled Elastic Beams, Moscow, French Translation, Pieces Longues en Voiles Minces, Eyrolles, Paris, France.
  36. Wakashima, K., Hirano, T. and Niino, M. (1990), "Functionally gradient materials (FGM) architecture: a new type of ceramic/metal assemblage designed for hot structural components >>, Space Applications of Advanced Structural Materials, Noordwijk, March.
  37. Ziane, N., Meftah, S.A., Belhadj, H.A., Tounsi, A. and Bedia, E.A. (2013), "Free vibration analysis of thin and thick-walled FGM box beams", Int. J. Mech. Sci., 66, 273-282. https://doi.org/10.1016/j.ijmecsci.2012.12.001
  38. 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. Tech., 34, 24-34. https://doi.org/10.1016/j.ast.2014.02.001

피인용 문헌

  1. A nonlocal zeroth-order shear deformation theory for free vibration of functionally graded nanoscale plates resting on elastic foundation vol.20, pp.2, 2016, https://doi.org/10.12989/scs.2016.20.2.227
  2. Thermal effects on the instabilities of porous FGM box beams vol.134, 2017, https://doi.org/10.1016/j.engstruct.2016.12.039
  3. On bending, buckling and vibration responses of functionally graded carbon nanotube-reinforced composite beams vol.19, pp.5, 2015, https://doi.org/10.12989/scs.2015.19.5.1259
  4. Theory of thin-walled functionally graded sandwich beams with single and double-cell sections vol.157, 2016, https://doi.org/10.1016/j.compstruct.2016.07.024
  5. Nonlinear analysis of thin-walled Al/Al 2 O 3 FG sandwich I-beams with mono-symmetric cross-section vol.69, 2018, https://doi.org/10.1016/j.euromechsol.2017.11.010
  6. Geometrically nonlinear coupled analysis of thin-walled $$\hbox {Al/Al}_{2}\hbox {O}_{3}$$Al/Al2O3 FG sandwich box beams with single and double cells pp.1619-6937, 2018, https://doi.org/10.1007/s00707-018-2238-8
  7. Bending and stability analysis of size-dependent compositionally graded Timoshenko nanobeams with porosities vol.6, pp.1, 2017, https://doi.org/10.12989/amr.2017.6.1.045
  8. Optimization of flexure stiffness of FGM beams via artificial neural networks by mixed FEM vol.75, pp.5, 2020, https://doi.org/10.12989/sem.2020.75.5.633