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Geodesic shells Girling, Peter Richmond

Abstract

The analysis and design is presented for a shell composed of flat triangular plates approximating a smooth spherical shell. The geometry is based on the subdivision of the icosahedron and dodecahedron into many plane triangles. All corners of these triangles lie on a circumscribing sphere so that as the triangles become more numerous, the shell more nearly approximates a true sphere. The geometry is tabulated for a few of the possible subdivisions but may have to be carried further if a particularly large shell composed of relating small triangles is required. While some of the geometry is similar to geodesic domes already constructed, the structural analysis is entirely different. Previous geodesic domes are space trusses where the applied loads are supported predominantly by axial force in the truss bars. The structures considered here are frameless and the loads are therefore supported by shell action. The exact analysis to such a shell was not obtained since the solution is not composed of tabulated functions. However, an approximate analysis is presented which, in part, is a modification of smooth shell theory. Since the shell is composed of flat plates, the bending and buckling of individual triangles are additional design problems considered that are not present in more conventional shell design. In order to verify parts of the theoretical analysis, experimental studies were conducted with a plexiglas model. The experimental results verify the application of smooth shell theory to geodesic shells and determine the distribution of membrane stress. Finally the various design aspects are brought together and illustrated by the inclusion of the design notes for a typical shell.

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