Abstract
Design options are reviewed for the isotropic stretching of circular membrane apertures with three-point tensioning of regular (120 o ) symmetry. Four suspension paradigms are discussed. These are: (a) film triangles with parabolic catenary systems on the sides, (b) circular arc-triangular sheets with edge cables, (c) the latter with circular corner cutouts, and (d) film disks directly ten sioned around the circumference with radial catenary systems, so here named. The last two of these are newly proposed to reduce suspension forces for a given support system footprint — equivalently, to reduce the support footprint for given suspension loads. Mechanical and geometric relations are derived, but the radial catenary equation, formally established, is numerically solved. Of the design options, the radial catenary is found with a wide margin to be the most efficient, followed by the arc-circular perimeter with corner cutouts. The parabolic catenary is next; with simple arc-circular perimeter cables being the least efficient. The application of the observations made to more general contexts is touched upon, and additional means to further reduce support loads and -footprint are also highlighted.
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