Computational & Technology Resources
an online resource for computational,
engineering & technology publications
Civil-Comp Proceedings
ISSN 1759-3433
CCP: 91
PROCEEDINGS OF THE TWELFTH INTERNATIONAL CONFERENCE ON CIVIL, STRUCTURAL AND ENVIRONMENTAL ENGINEERING COMPUTING
Edited by: B.H.V. Topping, L.F. Costa Neves and R.C. Barros
Paper 24

Local and Global Buckling and Post-Buckling Analysis of Thin-Walled Members using Enhanced Beam Finite Elements

R.M. Gonçalves1, D. Camotim2 and M. Ritto-Corrêa2

1High Technological School of Barreiro, Polytechnic Institute of Setúbal, Lavradio, Portugal
2ICIST/IST Civil Engineering Department, Lisbon Technical University, Portugal

Full Bibliographic Reference for this paper
, "Local and Global Buckling and Post-Buckling Analysis of Thin-Walled Members using Enhanced Beam Finite Elements", in B.H.V. Topping, L.F. Costa Neves, R.C. Barros, (Editors), "Proceedings of the Twelfth International Conference on Civil, Structural and Environmental Engineering Computing", Civil-Comp Press, Stirlingshire, UK, Paper 24, 2009. doi:10.4203/ccp.91.24
Keywords: thin-walled members, local-global buckling, local-global post-buckling, large displacements, finite rotations, beam finite elements.

Summary
One-dimensional (beam) finite elements are capable of handling cross-section in-plane and out-of-plane (warping) deformation provided the member kinematic description is enriched with an appropriate set of cross-section deformation modes. Such "enhanced" beam finite elements offer noteworthy advantages with respect to shell finite elements or finite strips, namely (i) a significant reduction in the number of degrees-of-freedom required to achieve a similar accuracy and (ii) a clearer perception of the structural behaviour under consideration, due to the modal nature of the solution obtained.

To the authors best knowledge, the first geometrically exact beam formulation specifically developed for thin-walled members, allowing for arbitrary cross-section in-plane and out-of-plane deformation, was recently developed by the authors [1,2]. This paper is devoted to illustrating the application and capabilities of the ensuing beam finite element to analyse the local or global buckling or post-buckling behaviour of thin-walled members. Several illustrative examples are presented and discussed, including comparisons with the solutions provided by finite strip and shell finite element models. Among the various conclusions drawn from the work reported, the following ones deserve to be especially mentioned:

  1. The beam kinematic description involves genuine wall relative rotations and arbitrary deformation modes to model the cross-section in- and out-of-plane deformation (although Kirchhoff's assumption is deemed valid). The wall relative rotations provide a simple and meaningful geometric description of the cross-section in-plane distortion and make it possible to employ a local co-rotational description of the wall "local-plate" displacements.
  2. The illustrative examples show that the beam finite element provides results that are in very good agreement with the ones yielded by sophisticated shell finite element models, despite the huge disparity between the number of degrees-of-freedom involved in the two models.
  3. Although all the illustrative examples concern elastic beams, the proposed formulation can readily handle other small strain constitutive laws and, in particular, small strain plasticity may be implemented in a standard fashion.

References
1
R. Gonçalves, M. Ritto-Corrêa, D. Camotim, "A large displacement and finite rotation thin-walled beam finite element formulation", III European Conference on Computational Mechanics, C.A. Mota Soares et al., (editors), 693, 2006. doi:10.1007/1-4020-5370-3_693
2
R. Gonçalves, "Analysis of Thin-Walled Beams with Deformable Cross-Section: New Formulations and Applications", Ph.D. Thesis in Civil Engineering, IST, Technical University of Lisbon, Portugal, 2004. (in Portuguese)

purchase the full-text of this paper (price £20)

go to the previous paper
go to the next paper
return to the table of contents
return to the book description
purchase this book (price £140 +P&P)