Geometry attained by pressurized membranes

Abstract

An intensive investigation has been carried out to study the surface profiles obtained as a result of the large deformations of pressurized membranes. The study shows that the inflated membrane shapes may have the requisite surface accuracy for use in future large space apertures. Both analytical and experimental work have been carried out. On the analytical side, the classical work of Hencky on flat circular membranes was extended to eliminate the limitations it imposed; namely a lateral non-follower pressure with no pre-stress. The result is a computer program for the solution of the pressurized circular membrane problem. The reliability of the computer program is demonstrated via verification against FAIM, a nonlinear finite element solver developed primarily for the analysis of inflated membrane shapes. The experimental work includes observations made by Veal on the (W-shaped) deviations between the membrane deflected shape and the predicted profile. More recent measurements have been made of the deformations of pressurized flat circular and parabolic membranes using photogrammetric techniques. The surface error quantification analyses include the effect of material properties, geometric properties, loading uncertainties, and boundary conditions. These effects are very easily handled by the special FEM code FAIM which had recently been enhanced to predict the on-orbit dynamics, RF, and solar concentration characteristics of inflatable parabolic antennas/reflectors such as the IAE that flew off the space shuttle Endeavour in May 1996. The results of measurements have been compared with analyses and their ramifications on precision-shape, large-aperture parabolic space reflectors are discussed. Results show that very large space apertures with surface slope error accuracies on the order to space reflectors are discussed. Results show that very large space apertures with surface slope error accuracies on the order of 1 milliradian or less are feasible. Surface shape accuracies of less than 1 mm RMS have been attained on ground measurements.