Shape and Stress Analysis of Symmetric CRTS Reflectors

The Collapsible Rib Tensioned Surface CRTS re ector is a new concept for multipur pose deployable membrane re ectors that is being developed by the European Space Agency It is based on the inherent geometrical stability of a doubly curved membrane with high in plane sti ness maintained in a state of tension by a series of exible ribs The shape of a CRTS re ector is not uniquely determined It results from a compromise between the best possible approximation to a paraboloidal surface and a nearly uniform bi axial state of prestress of the membrane surface to avoid the formation of wrinkles This report investigates the shape and stress distribution of CRTS re ectors both analytically and experimentally The analytical part of the study establishes a method ology for the preliminary design of symmetric re ectors of given aperture focal length and target rms error The concepts of a reference surface and of an equilibrium surface are introduced and algorithms are developed to compute these surfaces and their asso ciated rms error Then the cutting pattern for making the membrane is computed and the rms error of the actual surface is predicted Estimates are made of the rms error of CRTS re ectors with apertures of and m with and ribs The experimental part of the study compares the measurements of prestress and shape in a one sixth sector of a m diameter re ector with ribs with predictions obtained from the computational study