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CivilComp Proceedings
ISSN 17593433 CCP: 83
PROCEEDINGS OF THE EIGHTH INTERNATIONAL CONFERENCE ON COMPUTATIONAL STRUCTURES TECHNOLOGY Edited by: B.H.V. Topping, G. Montero and R. Montenegro
Paper 192
Extension of the Finite Volume Method for Instability Analysis of Columns with Shear Effects N. Fallah and F. Hatami
Department of Civil Engineering, University of Guilan, Rasht, Iran N. Fallah, F. Hatami, "Extension of the Finite Volume Method for Instability Analysis of Columns with Shear Effects", in B.H.V. Topping, G. Montero, R. Montenegro, (Editors), "Proceedings of the Eighth International Conference on Computational Structures Technology", CivilComp Press, Stirlingshire, UK, Paper 192, 2006. doi:10.4203/ccp.83.192
Keywords: instability, buckling, column, shear effect, cell centred, finite volume.
Summary
In the past few years, the experiences gained with the finite volume method in the
computational structural mechanics [1,2,3] show promising perspectives of the
method. The method is simple in terms of concept and formulation; furthermore the
shear locking problem is not observed in the analysis of thin Timoshenko beams [1]
and also in the bending analysis of thin plates [2]. This paper presents a procedure
for calculating the buckling load of columns with shear effects, which introduces a
new scope of research for the instability analysis of structures by implementation of
the finite volume method.
To obtain the buckling load of a prismatic and nonprismatic column with arbitrary cross section, it is discretised into a number of twonode line elements along its length. In the cell centred finite volume method each element considered as a control volume or cell having a centre, which is located at the element centre. A cell has connections to the nearest neighbouring cells located on the right and left sides of the cell. The centres of the cells are considered as the computational points with two degrees of freedom, i.e. transverse displacement and section rotation. To estimate unknown variables and their derivatives at the faces of the cells, which appear in the equilibrium equations, the idea of an interim element is used [3]. The interim elements are twonode isoparametric elements in which linear variations are assumed for the unknowns [4]. The end nodes of the interim elements are located at the centres of the two cells lying on either side of the face. To apply boundary conditions to the solution procedure, two point cells are assumed at the ends of the column. Three types of boundary conditions are possible at the boundaries: displacement boundary condition, force boundary condition and a mixed boundary condition. Equations associated with the internal cells and the point cells provide the eigenvalue equation with the standard form, which can be solved to calculating the buckling load. The smallest of the eigenvalues represents the critical buckling load of the column. To verify the proposed formulation several test cases were studied by using a computer code developed based on the formulation presented. In these studies the results obtained were compared with the available analytical solutions. The test problems include columns as pinnedpinned, fixedfree, and fixedfixed with rectangular constant section, a tapered fixedfree column and a pinedpined step column. A monotonic convergence has been observed in all the problems studied. The accuracy of the results reveals the capability of the finite volume method in good predictions with the assumption of piece wise linear variation of displacement components. The results obtained are encouraging and reveal good performance of the finite volume method for the instability analysis of columns. The formulation presented here provides a basic procedure that could be extended to the instability analysis of plate and shell structures. References
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