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Keywords: element-free Galerkin method, continuous blending, d'Alembert principle, arches, geometric non-linearity, buckling.

Summary

This paper develops a numerical formulation for the in-plane elastic analysis of arches by using the element-free Galerkin (EFG) method [1]. In the strain expression, the effects of geometric non-linearities due to large deflections and rotations are taken into account [2]. 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 [3] and the d'Alembert principle developed by Gunter and Liu [4], 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 [5]. 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.

References

1: T. Belytschko, Y.Y. Lu, L.L. Gu, "Element-free Galerkin methods", International Journal for Numerical Methods in Engineering, 37(2), 229-256, 1994. doi:10.1002/nme.1620370205
2: Y.L. Pi, N.S. Trahair, "Non-linear elastic behavior of I-beams curved in plan", Journal of Structural Engineering ASCE, 123(9), 1201-1209, 1997. doi:10.1061/(ASCE)0733-9445(1997)123:9(1201)
3: S. Fernandez-Mendez, A. Huerta, "Imposing essential boundary conditions in mesh-free methods", Computer Methods in Applied Mechanics and Engineering, 193, 1257-1275, 2004. doi:10.1016/j.cma.2003.12.019
4: F.C. Gunther, K. Liu, "Implementation of boundary conditions for meshless methods", Computer Methods Applied Mechanics and Engineering, 163, 205-230, 1998. doi:10.1016/S0045-7825(98)00014-0
5: Y.L. Pi, N.S. Trahair, "Non-linear buckling and post-buckling of elastic arches", Engineering Structures, 20(7), 571-579, 1998. doi:10.1016/S0141-0296(97)00067-9

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Front Page Browse CCP CSETS CTR IJRT Other Authors Search Purchase Guide FAQ Contact us	Civil-Comp Proceedings ISSN 1759-3433 CCP: 91 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 Paper 95 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 doi:10.4203/ccp.91.95 purchase the full-text of this paper Full Bibliographic Reference for this paper 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. Summary This paper develops a numerical formulation for the in-plane elastic analysis of arches by using the element-free Galerkin (EFG) method [1]. In the strain expression, the effects of geometric non-linearities due to large deflections and rotations are taken into account [2]. 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 [3] and the d'Alembert principle developed by Gunter and Liu [4], 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 [5]. 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. References 1 T. Belytschko, Y.Y. Lu, L.L. Gu, "Element-free Galerkin methods", International Journal for Numerical Methods in Engineering, 37(2), 229-256, 1994. doi:10.1002/nme.1620370205 2 Y.L. Pi, N.S. Trahair, "Non-linear elastic behavior of I-beams curved in plan", Journal of Structural Engineering ASCE, 123(9), 1201-1209, 1997. doi:10.1061/(ASCE)0733-9445(1997)123:9(1201) 3 S. Fernandez-Mendez, A. Huerta, "Imposing essential boundary conditions in mesh-free methods", Computer Methods in Applied Mechanics and Engineering, 193, 1257-1275, 2004. doi:10.1016/j.cma.2003.12.019 4 F.C. Gunther, K. Liu, "Implementation of boundary conditions for meshless methods", Computer Methods Applied Mechanics and Engineering, 163, 205-230, 1998. doi:10.1016/S0045-7825(98)00014-0 5 Y.L. Pi, N.S. Trahair, "Non-linear buckling and post-buckling of elastic arches", Engineering Structures, 20(7), 571-579, 1998. doi:10.1016/S0141-0296(97)00067-9 purchase the full-text of this paper (price £20) go to the previous paper go to the next paper return to the table of contents return to the book description purchase this book (price £140 +P&P)
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