The Delunay Triangulation in the Design of Architectural Gridshells

Abstract

The design of original gridshell forms has become an increasingly complex process, which aims to search for unique spatial systems which are also effective engineering solutionsboth architecturally as well as structurally. The search for synergistic solutions which combine the aesthetics of the form with structural logic is supported by modern bionic tendencies. They allow the reproduction of the organic shapes not only by means of proportions, but also by mimicking the biological developmental processes and by understanding the logic of the structural forms occurring in nature. The analogies between architectural design and morphogenesis of biological forms have increased the interest in bionic structures as a whole. The improvement of digital tools based on algorithmic codes has enabled architects to implement their bold designs based on the logic of Nature's technologies.One of the most interesting bionic methods of discretization of structural surfaces is Delaunay triangulation, a dual graph of the Voronoi Diagram, which describes the divisions of the plane and space found in nature. Examples can be found in the patterns of a dragonfly wing, giraffe's mottled skin or a turtle's shell. The Delaunay divisions are more and more often used in the design of architectural forms based on gridshells. Solutions for such systems are obtained through generative modeling, and the algorithm responsible for the surface discretization is incorporated into 3D modeling programs. A big advantage of using digital generators in the search for optimal architectural and structural solutions is the ability to model multiple-variants and to the easily modify them (the models result from iterations of the entered numerical data).The paper will present the trends in the development of spatial bionic gridshells based on Delaunay triangulation, as well as the results from own research on selected gridshells. The undertaken analyses compare material efficiency on two analyzed cases.

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Architectural Design Optimisation in Reticulated Free-Form Canopies

“…This numerical method aims to find a geometry in which all forces are in equilibrium, allowing the structure's minimum area (length) to be located. Dynamic relaxation significantly minimizes materials in the systems visible in earlier studies of curvilinear designs [54]. The generative design tool used in the research was chosen based on the availability and accessible of using this tool by architects to generate the catenary model based on selected boundary conditions.…”

“…Study 1 aimed to identify the most beneficial divisions in the random Delaunay triangulation pattern of a gridshell. Geometries were generated based on the previous authors' research experiment [54,55].…”