Shape and stress analysis of edge-tensioned membranes

Abstract:

This dissertation presents the results of a study on the shape distortion and the stress distribution after deployment in a Collapsible Rib Tensioned Surface (CRTS) antenna reflector, a novel concept proposed by Rits (Rits 1996) of the European Space Technology Centre. The CRTS reflector consists of three main elements: a parabolic membrane, a series of foldable ribs, and an expandable hub.

The hub is in its contracted state during folding and deployment, then the ribs are released by the stored strain energy expanding the membrane. Once the ribs are fully deployed, the hub is expanded, pushing the ribs in radial direction until the pre-stress of the membrane reaches a desired level. The surface accuracy is controlled by the cutting pattern of the membrane.

A computer program written in Matlab is modified to analyse the pre-stressing and shaping of the membrane reflector. This program is used to estimate the best achievable accuracy of axi-symmetric reflector of different dimensions, and with different numbers of ribs. It also produces the cutting pattern for the 2-D membrane elements to form the required 3-D doubly curved shape.

An experiment is carried to validate the results from the program on a model consisting of a single sector of a 1 metre diameter reflector with 6 ribs. The two supporting ribs are made according to the given profile. They are able to slide in and out radially from the hub, to prestress the membrane.

Strain gauges are glued to the membrane in order to monitor the strain and the position of the ribs, length of the edge cable, etc. are adjusted until, the strains achieve the values predicted by the computational analysis. At this point, the shape of the surface is measured, from several targets on the surface, using an industrial measurement system consisting of three electronic theodolites. These results are compared with the analytical predictions. This study provides very valuable information for the further development of the CRTS reflector.

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