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PROCEEDINGS OF THE THIRTEENTH INTERNATIONAL CONFERENCE ON CIVIL, STRUCTURAL AND ENVIRONMENTAL ENGINEERING COMPUTING
Edited by: B.H.V. Topping and Y. Tsompanakis
Large Displacement Stability Analysis of Columns using the Harmonic Coupled Finite-Strip Method
D.D. Milašinovic1, A. Borkovic2, Z. Zivanov3, P.S. Rakic3, M. Hajdukovic3 and B. Furtula4
1Faculty of Civil Engineering, University of Novi Sad, Subotica, Serbia
D.D. Mila¬šinovic, A. Borkovic, Z. Zivanov, P.S. Rakic, M. Hajdukovic, B. Furtula, "Large Displacement Stability Analysis of Columns using the Harmonic Coupled Finite-Strip Method", in B.H.V. Topping, Y. Tsompanakis, (Editors), "Proceedings of the Thirteenth International Conference on Civil, Structural and Environmental Engineering Computing", Civil-Comp Press, Stirlingshire, UK, Paper 79, 2011. doi:10.4203/ccp.96.79
Keywords: harmonic coupled finite-strip method, stability analysis, columns.
The comparative efficiency of two harmonic coupled finite-strip formulations is being assessed for the analysis of the nonlinear behaviour of columns, which are compressed axially. The buckling problem discussed is solved using the harmonic coupled Fourier series treatment. The well known uncoupled formulation, first developed in the context of thin plate bending analysis, represents a semi-analytical finite element process . The in-plane behaviour is defined by the presupposition introduced in the studies of beams by Timošenko, which was later modified in the finite-strip method by Cheung . The geometric nonlinear formulations  are based on the Green-Lagrange expressions for in-plane nonlinear strains and neglecting lower-order terms in a manner consistent with the usual von Karman assumptions. The combination of bending and membrane actions leads to the harmonic coupled finite-strip method and the solution is obtained by using the Newton-Raphson method with an automatic simultaneously tracking the eigenvalues of the tangent stiffness matrix of the structure. Buckling occurs where the matrix becomes singular . Computations of the stiffness matrix for different strips are independent and can be carried out in parallel on a cluster with a suitable numbers of nodes. Such an approach allows substantial speedup as the computation of each stiffness matrix requires a large number of arithmetic operations. An illustrative example include pre- and post-buckling of different harmonic coupled formulations showing, in particular, some bifurcation points, large rotations and displacements and very important membrane-bending coupling. The harmonic coupled finite-strip method (HCFSM) presented herein is enclosed within a theoretical and numerical solution for an elastic stability problem of columns. The paper presents the influence of several geometrical parameters on equilibrium paths and on the values of critical load.
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