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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
In-Plane Analysis of Arches by using the Element-Free Galerkin Method
R.E. Erkmen and M.A. Bradford
Centre for Infrastructure Engineering and Safety, School of Civil and Environmental Engineering, The University of New South Wales, Sydney, Australia
R.E. Erkmen, M.A. Bradford, "In-Plane Analysis of Arches by using the Element-Free Galerkin Method", 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 95, 2009. doi:10.4203/ccp.91.95
Keywords: element-free Galerkin method, continuous blending, d'Alembert principle, arches, geometric non-linearity, buckling.
This paper develops a numerical formulation for the in-plane elastic analysis of arches by using the element-free Galerkin (EFG) method . In the strain expression, the effects of geometric non-linearities due to large deflections and rotations are taken into account . The incremental form of the non-linear equilibrium equations are obtained by using the principle of virtual work. The EFG shape functions are constructed to have third order completeness. A cubic spline function is used as the weight function in moving least-squares (MLS) approximation. Two alternative approaches, the continuous blending method developed by Huerta and Fernandez-Mendez  and the d'Alembert principle developed by Gunter and Liu , are adopted to impose the boundary conditions. Using these two approaches, pinned as well as fixed end conditions are imposed for the arch. The efficacy of both EFG formulations is illustrated by comparing the results with those based on an accurate C1 finite element formulation developed by Pi and Trahair . Unlike the C1 finite element formulation, the EFG formulation developed in the paper contains nodal parameters associated only with the displacement field and it does not require rotations and, or higher order derivatives as primary unknowns. As a result, the EFG formulation reduces the degrees of freedom per node. Both snap-through and anti-symmetric bifurcational type arch behaviour are shown to be captured by the EFG formulations. Because of this, the formulations developed in the paper are suitable for the analysis of shallow as well as deep arches.
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