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Civil-Comp Proceedings
ISSN 1759-3433
CCP: 88
PROCEEDINGS OF THE NINTH INTERNATIONAL CONFERENCE ON COMPUTATIONAL STRUCTURES TECHNOLOGY
Edited by: B.H.V. Topping and M. Papadrakakis
Paper 147

A Boundary Element - Differential Equation Method Coupling for Plate-Beam Interaction

J.B. Paiva1 and A.V. Mendonça2

1Structures Department, São Carlos Engineering School, University of São Paulo, Brazil
2Department of Technology of Civil Construction, Federal University of Paraiba, João Pessoa PB, Brazil

Full Bibliographic Reference for this paper
, "A Boundary Element - Differential Equation Method Coupling for Plate-Beam Interaction", in B.H.V. Topping, M. Papadrakakis, (Editors), "Proceedings of the Ninth International Conference on Computational Structures Technology", Civil-Comp Press, Stirlingshire, UK, Paper 147, 2008. doi:10.4203/ccp.88.147
Keywords: boundary element method, plate-beam interaction, building slabs.

Summary
The boundary element method (BEM) was first applied to building slab analysis by Bezine [1], who considered the problem of plates with internal boundary conditions that could be used to simulate rigid columns connected to the plate. Since then, several authors have used the BEM in building slab analysis [2,3]. The major problem in coupling the plate with the beam is that the finite elements used to represent beams and columns need three variables (w, partial w /partial x1 and partial w /partial x2) at each node in the plate domain, whereas for nodes located on the boundary of the plate, the BEM employs only two, w and partial w /partial n.

In this article, a new boundary element formulation for the analysis of the plate-beam interaction is presented, in which the plate is modeled by a BEM formulation with three variables at each boundary node [4] and the beam is replaced by its actions on the plate, a distributed load and end forces. Each beam element has three nodes, each with two nodal values, w and partial w /partial x1, and the transverse displacement of the beam is approximated by a fifth degree polynomial that represents the differential equation analytical solution for the beam under transverse loading with linear variation. After the beam differential equation has been solved, the plate-beam interactions can be written in terms of the beam nodal variables, w and partial w /partial x1. With this transformation, a final system of equations can be written, involving only the nodal displacements of the beams and plate boundary nodes and the tractions at the boundary of the plate. By imposing the boundary conditions and solving the system of equations, the displacements and tractions on the beams and plate can readily be calculated.

References
1
Bezine G. "A boundary integral equation method for plate flexure with conditions inside the domain", Int. J. for Numerical Methods in Engineering, 17:1647-1657, 1981. doi:10.1002/nme.1620171106
2
Paiva J.B., Venturini W.S., "Boundary element algorithm for building floor slab analysis", Boundary Element Technology Conference, Adelaide (Austr.), Nov., 1985.
3
Hartley G.A., Abdel-Akher A., Chen P., "Boundary element analysis of thin plates internally bounded by rigid patches", Int. J. for Numerical Methods in Engineering, 35: 1771-1785, 1992. doi:10.1002/nme.1620350904
4
Oliveira Neto L., Paiva J.B. "Cubic approximation for the transverse displacement in BEM for elastic plates analysis", Engineering Analysis with Boundary Elements, v.28, p.869-880, 2004. doi:10.1016/j.enganabound.2003.12.003

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