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PROCEEDINGS OF THE EIGHTH INTERNATIONAL CONFERENCE ON COMPUTATIONAL STRUCTURES TECHNOLOGY
Edited by: B.H.V. Topping, G. Montero and R. Montenegro
The Use of the Medial-Axis Construction in the Design of Cable-Membrane Structures
Department of Information Sciences, Pollack Mihály Faculty of Engineering, University of Pécs, Hungary
P. Iványi, "The Use of the Medial-Axis Construction in the Design of Cable-Membrane Structures", in B.H.V. Topping, G. Montero, R. Montenegro, (Editors), "Proceedings of the Eighth International Conference on Computational Structures Technology", Civil-Comp Press, Stirlingshire, UK, Paper 89, 2006. doi:10.4203/ccp.83.89
Keywords: medial-axis, mesh generation, cable-membrane structures, conceptual design tool.
Cable-membrane structures are generally very attractive architectural landmarks. All aspects of their design have been investigated throughout the years [1,2,3,4,5]
The design of cable-membrane structures is different from "standard" steel and concrete structures as the shape of the structure is dictated by the internal forces and external loading. This behaviour is due to the fact, that cables and membranes have no out-of-line and out-of-surface stiffnesses therefore they undergo large displacements under loading which is perpendicular to the line of the cable or to the surface of the membrane. This behaviour results in geometric non-linear behaviour. Furthermore this structural behaviour has a great influence on the shape of the structure which should be considered during the design.
The main aim of this paper is to present a new idea for the conceptual design of cable-membrane structures. During the conceptual design the client specifies all requirements for the structure. The designer, an architect or a civil-engineer, tries to satisfy these requirements and prepares some drawings of the shape of the structure. It is possible to use the shapes of structures that have been already built, or the designer may try to find new shapes. In this step an automatic conceptual design tool can be very useful. This paper shows how the medial-axis construction method with some modifications can be used as a conceptual design tool for cable-membrane structures with antyclastic shapes.
The medial axis can be defined as follows: if a two dimensional domain is given, then the medial axis of this domain is the locus of the centers of the maximal, empty circles inside the domain . In this paper the medial-axis of the two dimensional domain is contructed from the Delaunay triangulation of the domain. The method follows the approach of Damrong and Erickson  but with a modified set of rules. For the Delaunay triangulation only the boundary is supplied and no internal points are generated. If the triangulation is fine enough (not coarse), then the dual of the Delaunay triangulation (the Voronoi diagram) can approximate the medial axis. The algorithm to determine the medial-axis of a two dimensional domain contains the following steps:
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