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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 25

Updated Lagrangian Formulation for Nonlinear Stability Analysis of Flexibly Connected Thin-Walled Frames

G. Turkalj, J. Brnic and D. Lanc

Department of Engineering Mechanics, Faculty of Engineering, University of Rijeka, Croatia

Full Bibliographic Reference for this paper
G. Turkalj, J. Brnic, D. Lanc, "Updated Lagrangian Formulation for Nonlinear Stability Analysis of Flexibly Connected Thin-Walled Frames", 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 25, 2009. doi:10.4203/ccp.91.25
Keywords: thin-walled framed structures, nonlinear stability, beam element, updated Lagrangian formulation, flexible connections.

Summary
Stability limit state evaluation of frame-type structures is frequently carried out under the assumption of ideal frame connections, i.e. two extreme idealisations for connections are used: fully (perfectly) rigid and frictionless (ideal) pinned [1]. Such models simplify the stability analysis significantly, but often cannot represent the real structural behaviour because real connections exhibit a flexible or semi-rigid behaviour which falls in between the two idealised cases. The behaviour of flexible connections is the result of a complex interaction among various components of the connection construction itself [2]. Therefore, conventional numerical analysis procedures must be broadened by incorporating real connection characteristics in order to replace the idealized connection approach, which improves the accuracy of the structural analysis [3,4].

This paper presents a two-node (14 degrees of freedom) beam element for the numerical simulation of nonlinear stability behaviour of flexibly connected space frames composed of the straight and prismatic thin-walled beam members. The equations of equilibrium are derived using the updated Lagrangian incremental description and the nonlinear displacement field of thin-walled cross-sections. Force recovery is performed according to the external stiffness approach [5]. Internal moments are calculated by the Euler-Bernoulli-Navier theory for bending and the Timoshenko-Vlasov theory for torsion. As a result of the applied displacement field which includes second-order displacement terms resulting from large rotations, the joint moment equilibrium conditions of adjacent non-collinear elements are ensured. Material non-linearity is introduced for an elastic-perfectly plastic material through the plastic hinge formation at the ends of the finite elements and for this a corresponding plastic reduction matrix is applied [6]. Flexible connections are allowed to occur at finite element nodes by modifying stiffness matrices of a conventional beam element. A special transformation matrix is derived for that purpose. On the basis of this, a computer program called THINWALL v.2 is developed and validated using test problems.

References
1
W. McGuire, R.H. Gallagher, R. Ziemian, "Matrix structural analysis", John Wiley & Sons, New York, 2000.
2
M. Ivanyi, C.C. Baniotopoulos, "Semi-rigid connections in structural steelwork", Springer-Verlag, Wien, 2000.
3
G.E. Blandford, "Stability analysis of flexibly connected thin-walled space frames", Computers & Structures, 53(4), 839-847, 1994. doi:10.1016/0045-7949(94)90372-7
4
S.L. Chan, P.P.T. Chui, "Non-linear static and cyclic analysis of steel frames with semi-rigid connections", Elsevier, Amsterdam, 2000.
5
G. Turkalj, J. Brnic, J. Prpic-Orsic, "Large rotation analysis of elastic thin-walled beam-type structures using ESA approach", Computers & Structures, 81(18-19), 1851-1864, 2003. doi:10.1016/S0045-7949(03)00206-2
6
G. Turkalj, J. Brnic, "Nonlinear stability analysis of thin-walled frames using UL-ESA formulation", International Journal of Structural Stability and Dynamics, 4(1), 45-67, 2004. doi:10.1142/S0219455404001094

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