Keywords: thin-walled beams, composite, laminate, buckling, nonlinearity, finite elements.

Composite materials are very suitable for structural applications where high strength to weight and stiffness to weight ratios are required. Fibre reinforced laminates in the form of thin-walled beams have been increasingly used during the past few decades in engineering practice, particularly in aerospace engineering, shipbuilding and in the automobile industry. Such weight-optimised structural components are commonly very susceptible to buckling failure because of their slenderness hence stability problems should be considered in their design [1].

A finite element model for stability analysis of three-dimensional framed structures with thin-walled laminated composite cross sections is presented in this paper. The beam cross-section geometry is discretised using quadratic monitoring areas and the structural discretisation is performed throughout the one-dimensional finite element. The model takes into account the effects of large displacements on the response of space frames subjected to conservative and static external loads.

Classical lamination theory for thin fibre-reinforced laminates is employed in this paper. The model is applicable to any arbitrary laminate stacking sequence, shape of the cross section and boundary conditions. The shear strain of the middle surface is assumed to be zero and the cross-section is not distorted in its own plane.

The stability analysis is performed in a load-deflection manner [2]. The non-linear response of a load-carrying structure should be solved using numerical methods, e.g. the finite element method, and some of incremental descriptions such as the total and updated Lagrangian ones, respectively, or the co-rotational description. Each description utilises a different structural configuration for the system quantities. This results in the form of a set of non-linear equilibrium equations of the structure. This set can be further linearised and should be solved using some incremental-iterative scheme.

The co-rotational description, used in this paper, is linear on the element level and all geometrically non-linear effects are introduced through the transformation from the local to the global coordinate system. The local co-rotational system follows the element chord during the deformation and allows the use of simplified strain-displacement relations on the local element level [3,4]. Verification examples utilising a numerical algorithm developed on the basis of the above mentioned procedure are presented to demonstrate the accuracy of this model [5,6].

1

N.A. Alfutov, "Stability of Elastic Structures", Springer-Verlag, Berlin, 2000.

2

Y.B. Yang, S.R. Kuo, "Theory & Analysis of Nonlinear Framed Structures", Prentice Hall, New York, 1994.

3

B.A. Izzuddin, "Conceptual issues in geometrically nonlinear analysis of 3D framed structures", Computer Methods in Applied Mechanics and Engineering, 191, 1029-1053, 2001. doi:10.1016/S0045-7825(01)00317-6

4

D. Lanc, G. Turkalj, J. Brnic, "Finite-element model for creep buckling analysis of beam-type structures", Communications in Numerical Methods in Engineering, 24, 989-1008, 2007. doi:10.1002/cnm.1004

5

J. Lee, S.E. Kim, "Lateral buckling analysis of thin-walled laminated channel-section beams", Composite Structures, 56, 391-399, 2002. doi:10.1016/S0263-8223(02)00022-3

6

V.H. Cortinez, M.T. Piovan, "Stability of composite thin-walled beams with shear deformability", Computers & Structures, 8, 978-990, 2006. doi:10.1016/j.compstruc.2006.02.017

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