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CivilComp Proceedings
ISSN 17593433 CCP: 96
PROCEEDINGS OF THE THIRTEENTH INTERNATIONAL CONFERENCE ON CIVIL, STRUCTURAL AND ENVIRONMENTAL ENGINEERING COMPUTING Edited by: B.H.V. Topping and Y. Tsompanakis
Paper 79
Large Displacement Stability Analysis of Columns using the Harmonic Coupled FiniteStrip Method D.D. Milašinovic^{1}, A. Borkovic^{2}, Z. Zivanov^{3}, P.S. Rakic^{3}, M. Hajdukovic^{3} and B. Furtula^{4}
^{1}Faculty of Civil Engineering, University of Novi Sad, Subotica, Serbia
D.D. MilaÂšinovic, A. Borkovic, Z. Zivanov, P.S. Rakic, M. Hajdukovic, B. Furtula, "Large Displacement Stability Analysis of Columns using the Harmonic Coupled FiniteStrip Method", in B.H.V. Topping, Y. Tsompanakis, (Editors), "Proceedings of the Thirteenth International Conference on Civil, Structural and Environmental Engineering Computing", CivilComp Press, Stirlingshire, UK, Paper 79, 2011. doi:10.4203/ccp.96.79
Keywords: harmonic coupled finitestrip method, stability analysis, columns.
Summary
The comparative efficiency of two harmonic coupled finitestrip 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 semianalytical finite element process [1]. The inplane behaviour is defined by the presupposition introduced in the studies of beams by Timošenko, which was later modified in the finitestrip method by Cheung [1]. The geometric nonlinear formulations [2] are based on the GreenLagrange expressions for inplane nonlinear strains and neglecting lowerorder terms in a manner consistent with the usual von Karman assumptions. The combination of bending and membrane actions leads to the harmonic coupled finitestrip method and the solution is obtained by using the NewtonRaphson method with an automatic simultaneously tracking the eigenvalues of the tangent stiffness matrix of the structure. Buckling occurs where the matrix becomes singular [3]. 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 postbuckling of different harmonic coupled formulations showing, in particular, some bifurcation points, large rotations and displacements and very important membranebending coupling. The harmonic coupled finitestrip 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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