Structural Engineering and Mechanics

  • 제51권6호
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  • Pages.955-971
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  • 2014
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  • 1225-4568(pISSN)
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  • 1598-6217(eISSN)
테크노프레스 (Techno-Press)
권호 표지
DOI QR코드

DOI QR Code

Large post-buckling behavior of Timoshenko beams under axial compression loads

  • Akbas, Seref D. (Department of Civil Engineering, Bursa Technical University, Yildrim Campus)
  • 투고 : 2014.01.09
  • 심사 : 2014.05.18
  • 발행 : 2014.09.25
⟨ 이전 논문 다음 논문 ⟩

초록

Large post-buckling behavior of Timoshenko beams subjected to non-follower axial compression loads are studied in this paper by using the total Lagrangian Timoshenko beam element approximation. Two types of support conditions for the beams are considered. In the case of beams subjected to compression loads, load rise causes compressible forces end therefore buckling and post-buckling phenomena occurs. It is known that post-buckling problems are geometrically nonlinear problems. The considered highly non-linear problem is solved considering full geometric non-linearity by using incremental displacement-based finite element method in conjunction with Newton-Raphson iteration method. There is no restriction on the magnitudes of deflections and rotations in contradistinction to von-Karman strain displacement relations of the beam. The beams considered in numerical examples are made of lower-Carbon Steel. In the study, the relationships between deflections, rotational angles, critical buckling loads, post-buckling configuration, Cauchy stress of the beams and load rising are illustrated in detail in post-buckling case.

키워드

참고문헌

  1. Akbas, S.D. and Kocaturk, T. (2012), "Post-buckling analysis of Timoshenko beams with temperaturedependent physical properties under uniform thermal loading", Struct. Eng. Mech., 44(1), 109-125. https://doi.org/10.12989/sem.2012.44.1.109
  2. Anandrao, K.S., Gupta, R.K., Ramchandran, P. and Rao, G.V. (2012), "Non-linear free vibrations and postbuckling analysis of shear flexible functionally graded beams", Struct. Eng. Mech., 44(3), 339-361. https://doi.org/10.12989/sem.2012.44.3.339
  3. Aristizabal-Ochoa, J.D. (2007), "Large deflection and postbuckling behavior of Timoshenko beam-columns with semi-rigid connections including shear and axial effects", Eng. Struct., 29(6), 991-1003 https://doi.org/10.1016/j.engstruct.2006.07.012
  4. Brojan, M. and Kosel, F. (2011), "Approximative formula for post-buckling analysis of non-linearly elastic columns with superellipsoidal cross-sections", J. Reinf. Plast. Compos., 30(5), 409-415. https://doi.org/10.1177/0731684410397897
  5. Cederbaum, G. (2000), "Post-buckling behavior of poroelastic columns", Int. J. Mech. Sci., 42(4), 771-783. https://doi.org/10.1016/S0020-7403(99)00022-3
  6. Challamel, N. (2011), "On the post-buckling of elastic beams on gradient foundation", Compt. Rend. Mecanique, 339(6), 396-405. https://doi.org/10.1016/j.crme.2011.04.003
  7. Challamel, N. (2012), "On geometrically exact post-buckling of composite columns with interlayer slip-The partially composite elastica", Int. J. Nonlin. Mech., 47(3), 7-17. https://doi.org/10.1016/j.ijnonlinmec.2012.01.001
  8. Dado, M., Al-Sadder, S. and Abuzeid, O. (2004), "Post-buckling behavior of two elastica columns linked with a rotational spring", Int. J. Nonlin. Mech., 39(10), 1579-1587. https://doi.org/10.1016/j.ijnonlinmec.2004.01.003
  9. Dolecek, V., Isic, S. and Voloder, A. (2009), "An analysis of beam elongation influence to postbuckling displacements under displacement dependent axial force", Mechanika, 4, 25-30.
  10. Dourakopoulos, J.A. and Sapountzakis, E.J. (2010), "Postbuckling analysis of beams of arbitrary cross section using BEM", Eng. Struct., 32(11), 3713-3724. https://doi.org/10.1016/j.engstruct.2010.08.016
  11. Emam, S.A. (2011), "Analysis of shear-deformable composite beams in postbuckling", Compos. Struct., 94(1), 24-30. https://doi.org/10.1016/j.compstruct.2011.07.024
  12. Fallah, A. and Aghdam, M.M. (2011), "Nonlinear free vibration and post-buckling analysis of functionally graded beams on nonlinear elastic foundation", Eur. J. Mech. A-Solid., 30(4), 571-583. https://doi.org/10.1016/j.euromechsol.2011.01.005
  13. Felippa, C.A. (2014), Notes on Nonlinear Finite Element Methods, http://www.colorado.edu/engineering/cas/courses.d/NFEM.d/NFEM.Ch10.d/NFEM.Ch10.pdf, Retrieved January.
  14. Gunda, J.B. and Rao, G.V. (2013), "Post-buckling analysis of composite beams: a simple intuitive formulation", Sadhana-Academy Proceedings In Engineering, 38(3), 447-459.
  15. Gupta, R.K., Gunda, J.B., Janardhan, G.R. and Rao, G.V. (2010), "Post-buckling analysis of composite beams: Simple and accurate closed-form expressions", Compos. Struct., 92(8), 1947-1956. https://doi.org/10.1016/j.compstruct.2009.12.010
  16. Humer, A. (2013), "Exact solutions for the buckling and postbuckling of shear-deformable beams", ACTA Mechanika, 224(7), 1493-1525. https://doi.org/10.1007/s00707-013-0818-1
  17. Ji, J.C. and Hansen, C.H. (2000), "Non-linear response of a post-buckled beam subjected to a harmonic axial excitation", J. Sound Vib., 237(2), 303-318. https://doi.org/10.1006/jsvi.2000.3028
  18. 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., 40(3), 347-371. https://doi.org/10.12989/sem.2011.40.3.347
  19. Kocaturk, T. and Akbas, S.D. (2012), "Post-buckling analysis of Timoshenko beams made of functionally graded material under thermal loading", Struct. Eng. Mech., 41(6), 775-789. https://doi.org/10.12989/sem.2012.41.6.775
  20. Kounadis, A.N. and Ioannidis, G.I. (1994), "Lateral postbuckling analysis of beam-columns", J. Eng. Mech., ASCE, 120(4), 695-706. https://doi.org/10.1061/(ASCE)0733-9399(1994)120:4(695)
  21. Kounadis, A.N. (2006), "Recent advances on postbuckling analyses of thin-walled structures: Beams, frames and cylindrical shells", J. Construct. Steel Res., 62(11), 1101-1115. https://doi.org/10.1016/j.jcsr.2006.06.014
  22. Le Grognec, P. and Le van, A. (2011), "On the plastic bifurcation and post-bifurcation of axially compressed beams", Int. J. Nonlin. Mech., 46(5), 693-702. https://doi.org/10.1016/j.ijnonlinmec.2011.02.001
  23. Li, S.R. and Zhou, Y. (2005), "Post-buckling of a hinged-fixed beam under uniformly distributed follower forces", Mech. Res. Commun., 32(4), 359-367. https://doi.org/10.1016/j.mechrescom.2004.10.019
  24. Mazzilli, C.E.N. (2009), "Buckling and post-buckling of extensible rods revisited: A multiple-scale solution", Int. J. Nonlin. Mech., 44, 200-208. https://doi.org/10.1016/j.ijnonlinmec.2008.11.005
  25. Moradi, S. and Taheri, F. (1999), "Postbuckling analysis of delaminated composite beams by differential quadrature method", Compos. Struct., 46(1), 33-39. https://doi.org/10.1016/S0263-8223(99)00040-9
  26. Nakashima, M., Nakamura, T. And Wakabayashi, M. (1983), "Post-Buckling Instability of Steel Beam-Columns", J. Struct. Eng., ASCE, 109(6), 1414-1430. https://doi.org/10.1061/(ASCE)0733-9445(1983)109:6(1414)
  27. Nayfeh, A.H. and Emam, S.A. (2008), "Exact solution and stability of postbuckling configurations of beams", Nonlin. Dyn., 54(4), 395-408. https://doi.org/10.1007/s11071-008-9338-2
  28. Rahimi, G.H., Gazor, M.S., Hemmatnezhad, M. and Toorani, H. (2013), "On the postbuckling and free vibrations of FG Timoshenko beams", Compos. Struct., 95, 247-253. https://doi.org/10.1016/j.compstruct.2012.07.034
  29. Saetiew, W. and Chucheepsakul, S. (2012a), "Post-buckling of linearly tapered column made of nonlinear elastic materials obeying the generalized Ludwick constitutive law", Int. J. Mech. Sci., 65(1), 83-96. https://doi.org/10.1016/j.ijmecsci.2012.09.006
  30. Saetiew, W. and Chucheepsakul, S. (2012b), "Post-buckling of simply supported column made of nonlinear elastic materials obeying the generalized Ludwick constitutive law", Zamm-Zeitschrift Fur Angewandte Mathematik Und Mechanik, 92(6), 479-489. https://doi.org/10.1002/zamm.201100081
  31. Sepahi, O., Forouzan, M.R. and Malekzadeh, P. (2010), "Post-buckling analysis of variable cross-section cantilever beams under combined load via differential quadrature method", Ksce J. Civil Eng., 14(2), 207-214. https://doi.org/10.1007/s12205-010-0207-4
  32. Wu, B. (1995), "Influence of shear deformation on the buckling of elastically supported beams", Arch. Appl. Mech., 65(3), 133-141. https://doi.org/10.1007/s004190050008
  33. Yuan, Z. and Wang, X. (2011), "Buckling and post-buckling analysis of extensible beam-columns by using the differential quadrature method", Comput. Math. Appl., 62(12), 4499-4513. https://doi.org/10.1016/j.camwa.2011.10.029
  34. Zhang, Y. and Murphy, K.D. (2013), "Jumping instabilities in the post-buckling Of a beam on a partial nonlinear foundation", Acta Mechanica Solida Sinica, 26(5), 500-513. https://doi.org/10.1016/S0894-9166(13)60045-2
  35. Zhu, Y.Y., Hu, Y.J. and Cheng, C.J. (2011), "Analysis of nonlinear stability and post-buckling for Euler-type beam-column structure", Appl. Math. Mech.-English Edition, 32(6), 719-728. https://doi.org/10.1007/s10483-011-1451-x
  36. Zyczkowski, M. (2004), "Post-buckling analysis of non-prismatic columns under general behaviour of loading", Int. J. Nonlin. Mech., 40(4), 445-463.
  37. Zienkiewichz, O.C. and Taylor, R.L. (2000), The Finite Element Method, Fifth Edition, Volume 2: Solid, Mechanics, Butterworth-Heinemann, Oxford.

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