Structural Engineering and Mechanics

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Out-of-plane elastic buckling of truss beams

  • Fedoroff, Alexis (Department of Civil and Structural Engineering, Aalto University) ;
  • Kouhia, Reijo (Department of Engineering Design, Tampere University of Technology)
  • Received : 2011.07.06
  • Accepted : 2013.02.19
  • Published : 2013.03.10
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Abstract

In this article we will present a method to directly evaluate the critical point of a non-linear system by using the solution of a polynomial eigenvalue approximation as a starting point for an iterative non-linear system solver. This method will be used to evaluate out-of-plane buckling properties of truss structures for which the lateral displacement of the upper chord has been prevented. The aim is to assess for a number of example structures whether or not the linearized eigenvalue solution gives a relevant starting point for an iterative non-linear system solver in order to find the minimum positive critical load.

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References

  1. Attard, M. (1990), "General non-dimensional equation for lateral buckling", Thin-Walled Structures, 9(1-4), Special Volume on Thin-Walled Structures: Developments in Theory and Practice, 417-435. https://doi.org/10.1016/0263-8231(90)90056-5
  2. Battini, J.M., Pacoste, C. and Eriksson, A. (2003), "Improved minimal augmentation procedure for direct computation of critical points", Computer Methods in Applied Mechanics and Engineering, 192(16-18), 2169-2185. https://doi.org/10.1016/S0045-7825(03)00254-8
  3. Chan, S.L. and Cho, S.H. (2008), "Second-order analysis and design of angle trusses Part I: elastic analysis and design", Engineering Structures, 30(3), 616-625. https://doi.org/10.1016/j.engstruct.2007.05.010
  4. Golubitsky, M. and Schaeffer, D. (1985), "Singularities and Groups in Bifurcation Theory", Applied Mathematical Sciences, 17, Springer Verlag.
  5. Hancock, G., Davids, A., Key, P., Lau, S. and Rasmussen, K. (1990), "Recent developments in the buckling and nonlinear analysis of thin-walled structural members", Thin-Walled Structures, 9(1-4), Special Volume on Thin-Walled Structures: Developments in Theory and Practice, 309-338. https://doi.org/10.1016/0263-8231(90)90050-9
  6. Iwicki, P. (2010), "Sensitivity analysis of critical forces of trusses with side bracing", Journal of Constructional Steel Research, 66(7), 923-930. https://doi.org/10.1016/j.jcsr.2010.02.004
  7. Govaerts, W. (2000), "Numerical methods for bifurcations of dynamical equilibria", Society for Industrial and Applied Mathematics, Philadelphia.
  8. Keener, J. and Keller, H. (1973), "Perturbed bifurcation theory", Archive for Rational Mechanics and Analysis, 50, 159-175. https://doi.org/10.1007/BF00703966
  9. Koiter, W.T. (1945), "Over de stabiliteit van het elastisch evenwicht", PhD Thesis, Technische Hogeschool, Delft, English tranlations: NASA TT F10, 833 (1967) and AFFDL, TR-7025 (1970).
  10. Lopez, S. (2002), "Detection of bifurcation points along a curve traced by continuation method", International Journal for Numerical Methods in Engineering, 53, 983-1004. https://doi.org/10.1002/nme.326
  11. Masur, E.F. and Cukurs, A. (1956), Lateral Buckling of Plane Frameworks, Engineering Research Institute, The University of Michigan Ann Arbor, Project 2480.
  12. Moore, G. and Spence, A. (1980), "The calculation of turning points of non-linear equations", SIAM Journal of Num. Analysis, 17, 567-576. https://doi.org/10.1137/0717048
  13. Mäkinen, J., Kouhia, R., Fedoroff, A. and Marjamäki, H. (2012), "Direct computation of critical equilibrium states for spatial beams and frames", International Journal for Numerical Methods in Engineering, 89(2), 135-153. https://doi.org/10.1002/nme.3233
  14. Rheinboldt, W.C. (1986), Numerical Analysis of Parametrized Nonlinear Equations, Wiley.
  15. Riks, E. (1974), "The incremental solution of some basic problems in elastic stability", Technical Report NLR TR 74005 U, National Aerospace Laboratory, The Netherlands.
  16. Schardt, R. (1966), "Eine erweiterung der technische biegetheorie zur berechnung prismatischer faltwerke", Stahlbau, 35, 161-171.
  17. Seydel, R. (1979), "Numerical calculation of branch points in nonlinear equations", Numer. Math., 33, 339- 352. https://doi.org/10.1007/BF01398649
  18. Sridharan, S. and Rafael, B. (1985), "Interactive buckling analysis with finite strips", International Journal for Numerical Methods in Engineering, 21, John Wiley and Sons, Ltd.
  19. Trahair, N. and Vacharajittiphan, P. (1975), "Analysis of Lateral Buckling in Plane Frames", Journal of the Structural Division, 101(7), 1497-1516.
  20. Trahair, N. and Chan, S.L. (2003), "Out-of-plane advanced analysis of steel structures", Engineering Structures, 25, 1627-1637. https://doi.org/10.1016/S0141-0296(03)00134-2
  21. Trahair, N. (2009), "Buckling analysis design of steel frames", Journal of Constructional Steel Research, 65, 1459-1463. https://doi.org/10.1016/j.jcsr.2009.03.012
  22. Vlasov, V.Z. (1961), Thin-walled Elastic Beams, National Science Foundation and Department of Commerce.
  23. Vrcelj, Z. and Bradford, M.A. (2006), "Elastic distortional buckling of continuously restraine I-section beam-columns", Journal of Constructional Steel Research, 62, 223-230. https://doi.org/10.1016/j.jcsr.2005.07.014
  24. Wriggers, P. and Simo, J.C. (1990), "A general procedure for the direct computation of turning and bifurcation problems", Computer Methods in Applied Mechanics and Engineering, 30, 155-176.