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PROCEEDINGS OF THE SEVENTH INTERNATIONAL CONFERENCE ON COMPUTATIONAL STRUCTURES TECHNOLOGY
Edited by: B.H.V. Topping and C.A. Mota Soares
Partial Interaction Analysis of Composite Beams by Means of the Finite Difference Method, the Finite Element Method, the Direct Stiffness Method and the Analytical Solution: A Comparative Study
G. Ranzi+, M.A. Bradford*, F. Gara# and G. Leoni#
+Department of Civil Engineering, The University of Sydney, Australia
G. Ranzi, M.A. Bradford, F. Gar, G. Leon, "Partial Interaction Analysis of Composite Beams by Means of the Finite Difference Method, the Finite Element Method, the Direct Stiffness Method and the Analytical Solution: A Comparative Study", in B.H.V. Topping, C.A. Mota Soares, (Editors), "Proceedings of the Seventh International Conference on Computational Structures Technology", Civil-Comp Press, Stirlingshire, UK, Paper 189, 2004. doi:10.4203/ccp.79.189
Keywords: closed form solutions, composite beams, direct stiffness method, finite difference method, finite element method, partial shear interaction.
This paper presents a comparison among available structural analysis formulations for composite beams with partial shear interaction. In the comparison all materials are assumed to behave in a linear-elastic fashion. The formulations considered are the finite difference method [1,2], the finite element method , the direct stiffness method  and the exact analytical model . The former two require a spatial discretisation to be specified along the beam length, while the latter two do not require any discretisation. Using the solution of the exact analytical model as a reference the accuracy of the three formulations has been tested for the cases of a simply supported beam and of a propped cantilever subjected to a uniformly distributed load. The comparison is carried out at various level of shear connection stiffness.
With regard to the finite element formulations that were considered, it was found that the behaviour of the 8 degree of freedom (DOF) finite element was numerically unstable, while the 10 DOF element seemed to provide reliable results when compared with the exact analytical result, or the results of the direct stiffness approach. The finite difference method was also observed to behave well. The results obtained using the finite element and finite difference methods converge with an error of less than about 1% when the number of elements (or stations) exceeds 20 for a low value of the length to depth ratio of the element. The direct stiffness method was shown to be robust, and to converge very rapidly for the three loading conditions considered.
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