Keywords: thin-walled members, local-global buckling, local-global post-buckling, large displacements, finite rotations, beam finite elements.

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.

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)

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