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Civil-Comp Proceedings
ISSN 1759-3433
CCP: 83
PROCEEDINGS OF THE EIGHTH INTERNATIONAL CONFERENCE ON COMPUTATIONAL STRUCTURES TECHNOLOGY
Edited by: B.H.V. Topping, G. Montero and R. Montenegro
Paper 191

Generalised Beam Theory Formulation to Analyse the Post-Buckling Behaviour of FRP Composite Thin-Walled Members

N.F. Silva, N. Silvestre and D. Camotim

Department of Civil Engineering and Architecture, ICIST/IST, Technical University of Lisbon, Portugal

Full Bibliographic Reference for this paper
N.F. Silva, N. Silvestre, D. Camotim, "Generalised Beam Theory Formulation to Analyse the Post-Buckling Behaviour of FRP Composite Thin-Walled Members", in B.H.V. Topping, G. Montero, R. Montenegro, (Editors), "Proceedings of the Eighth International Conference on Computational Structures Technology", Civil-Comp Press, Stirlingshire, UK, Paper 191, 2006. doi:10.4203/ccp.83.191
Keywords: generalized beam theory, geometrically non-linear formulation, elastic post-buckling analysis, FRP composite thin-walled members, geometric imperfections.

Summary
This paper presents a geometrically non-linear generalised beam theory (GBT) formulation intended to analyse the elastic post-buckling behaviour of arbitrary thin-walled composite prismatic members. This formulation is an extension to recent GBT developments in areas of (i) post-buckling analysis of isotropic members [1] and (ii) linear (first order) and buckling analyses of orthotropic FRP composite members [2,3]. However, the cross-section analysis, a key task in the performance of a GBT analysis, was carried out by means of a novel approach, (i) based on the solution of a series of auxiliary eigenvalue problems involving constitutive tensors and (ii) able to handle any type of cross-section shape. Its application was illustrated through the determination of the deformation modes of a cross-section combining a closed cell with a branched open wall assembly. The output of this analysis consists of a complete set of deformation modes that includes global, distortional, local-plate, warping shear and transverse extension modes, (Figure 1 shows the most relevant ones for the case of a lipped channel section).

A GBT-based non-linear beam finite element is developed and its implementation leads to the definition of a system of non-linear equilibrium equations which (i) is valid in the large deformation range, (ii) accounts for the presence of initial geometrical imperfections and (iii) takes advantage of the unique GBT mode decomposition features. The geometrically non-linear equilibrium equations, which take into account all material (mechanical) coupling effects, are derived from an energy approach and numerically implemented by means of a standard incremental-iterative procedure. In order to validate and illustrate the application of the proposed geometrically non-linear formulation, numerical results concerning the distortional post-buckling behaviour of simply supported initially imperfect FRP composite lipped channel columns (uniformly compressed members) with cross-ply orthotropy are presented and discussed (see Figures 1 and 2). For validation purposes, the post-buckling results are also compared with values yielded by ABAQUS shell finite element analyses.

Figure 1: Orthotropic lipped channel member cross-section (a) geometry and material properties, (b) GBT discretisation and (c) most relevant deformation mode features.
Figure 2: Outward and inward column (a) distortional post-buckling equilibrium paths vs. , (b) modal participation diagrams and (c) evolution of the mid-span normal stress distribution along the outer layer mid-line (=20cm; =0.1cm; ).

References
1
N. Silvestre and D. Camotim, "Non-linear generalised beam theory for cold-formed steel members", International Journal of Structural Stability and Dynamics, 3(4), 461-490, 2003. doi:10.1142/S0219455403001002
2
N. Silvestre and D. Camotim, "First and second-order generalised beam theory for arbitrary orthotropic materials", Thin-Walled Structures, 40(9), 755-789 + 791-820, 2002. doi:10.1016/S0263-8231(02)00025-3
3
N.F. Silva, N. Silvestre and D. Camotim, "GBT formulation to analyse the buckling behaviour of FRP composite branched thin-walled members", "Proceedings of III European Conference on Computational Mechanics: Solids, Structures and Coupled Problems in Engineering" (Lisbon, 5-9/6), 2006. (in press) doi:10.1007/1-4020-5370-3_705

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