Approximating paraboloids with axisymmetric pressurized membranes

Greschik, Gyula; Palisoc, Art; Cassapakis, C.; Veal, Gordon; Mikulas, Martin M.

doi:10.2514/6.1998-2102

Cited by 20 publications

(21 citation statements)

References 2 publications

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“…More recently, AM, a high precision analysis code for axisymmetric membranes capable of modeling wrinkling was developed. [5,6] Its accuracy and precision are such that it is applicable upwards to optical frequencies. The initial validations of both FAIMand AM were carried out by comparing its results against the Hencky [7] solution, namely the deflection of a flat circular membrane due to a lateral load.…”

Section: Analytical and Numxxical Solutionsmentioning

confidence: 99%

Geometry Attained by Pressurized Membranes

Palisoc¹,

Veal²,

Cassapakis³

et al. 2006

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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 finure large space apertures. Both analytical and experimental work have been carried out. On the analytical side, the classical work of Hen&y 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.[5]The reliability ofthe computer program is demonstrated via verification against FAZJ4, a nonlinear fmite element solver developed primarily for the analysis of inflated membrane shapes. The experimental work includes observations made by Veal[ 111 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 (effect of seams), loading uncertainties, and boundary conditions. These effects are very easily handled by the special FEM code FAZA4which had recently been enhanced to predict the on-orbit dynamics, RF, and solar concennation characteristics of inflatable parabolic antennas/reflectors such as the IAE (Inflatable Antenna Experiment) 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 of 1 milliradian or less are feasible. Surface shape accuracies of less than 1 mm RMS have been attained on ground measurements.

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Section: Analytical and Numxxical Solutionsmentioning

confidence: 99%

Geometry Attained by Pressurized Membranes

Palisoc¹,

Veal²,

Cassapakis³

et al. 2006

Self Cite

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“…Substituting the solutions of Eq. (22) and 0 = β into Eqs. (10a), (10b) and (11), we obtain the deflection and the surface error for an inflatable optimum-3 membrane.…”

Section: ) Optimum-2 and Optimum-3 Membranesmentioning

confidence: 99%

“…al. 22) investigated the effect of uniform radial edge support displacements on the achieved surface accuracy of an axisymmetric membrane using a numerical method. Kato and Natori 23) studied the effects of curved edges, the size, the position in a reflector and the rotation angle about the normal axis, etc.…”

Section: Introductionmentioning

confidence: 99%

Surface Accuracy Analysis of an Inflatable Rectangular Membrane of a Space Reflector

Kato

2006

Trans. JSASS Space Tech. Japan

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The surface accuracy of an inflatable rectangular membrane subjected to pressure and isotropic tension in a reflector is investigated. The inflatable membrane is assumed to be placed at an arbitrary location in a reflector with an arbitrary rotation angle α between the side of the membrane and the principal direction on the ideal parabolic surface. The edges of the membrane are assumed to coincide with an elliptic or a hyperbolic paraboloidal surface. The deflection of the membrane is obtained analytically based on the linear equation (Poisson's Equation) for a pressurized membrane. Different kinds of surface error optimizations with respect to the pressure/tension ratio q and parameters that determine the edge deflection of the membrane are carried out. The effects of q, α , the aspect ratio λ and the location of the membrane upon each surface error of the optimum membranes are examined. The surface error of an inflatable rectangular membrane whose edges coincide with the approximate parabolic surface (APS) of a reflector is found to be zero on the assumption that the appropriate pressure/tension ratio is applied. With the exception of an inflatable flat-edge-optimum membrane, each surface error of inflatable optimum membranes takes a value of zero or increases monotonically as the distance from the vertex increases, and the surface error also takes a value of zero or constant, or decreases as λ increases or decreases away from one. Moreover the surface error is found to be well below that of the unpressurized optimum membranes when the membranes are located near the vertex of the reflector.

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“…For gossamer structures, analytical characterizations of on-orbit shape distortions (Ref. [12][13][14][15][16][17] are important because the space environment is difficult to simulate on the ground. Ground testing limitations include the difficulties of simulating support-free operation and control under extremely low structural loadings brought on by zero-gravity conditions of space, as well as the inherent difficulty that full scale gossamer antennas may not be able to withstand high loads in the ground environment.…”

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confidence: 99%

Structural Test and Analysis of a Hybrid Inflatable Antenna

Gaspar

Mann²,

Sreekantamurthy³

et al. 2007

48th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics, and Materials Conference

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NASA is developing ultra-lightweight structures technology for communication antennas for space missions. One of the research goals is to evaluate the structural characteristics of inflatable and rigidizable antennas through test and analysis. Being able to test and analyze the structural characteristics of a full scale antenna is important to enable the simulation of various mission scenarios to determine system performance in space. Recent work completed to evaluate a Hybrid Inflatable Antenna concept will be discussed. Tests were completed on a 2-m prototype to optimize its static shape and identify its modal dynamics that are important for analytical model validation. These test results were used to evaluate a preliminary finite element model of the antenna, and this model development and correlation activity is also described in the paper.

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Approximating paraboloids with axisymmetric pressurized membranes

Cited by 20 publications

References 2 publications

Geometry Attained by Pressurized Membranes

Geometry Attained by Pressurized Membranes

Surface Accuracy Analysis of an Inflatable Rectangular Membrane of a Space Reflector

Structural Test and Analysis of a Hybrid Inflatable Antenna

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