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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 415 records · Page 23
All sourcesNASA NTRSDOE OSTI
NASA NTRS1989

Results of including geometric nonlinearities in an aeroelastic model of an F/A-18

An integrated, nonlinear simulation model suitable for aeroelastic modeling of fixed-wing aircraft has been developed. While the author realizes that the subject of modeling rotating, elastic structures is not closed, it is believed that the equations of motion developed and applied herein are correct to second order and are suitable for use with typical aircraft structures. The equations are not suitable for large elastic deformation. In addition, the modeling framework generalizes both the methods and terminology of non-linear rigid-body airplane simulation and traditional linear aeroelastic modeling. Concerning the importance of angular/elastic inertial coupling in the dynamic analysis of fixed-wing aircraft, the following may be said. The rigorous inclusion of said coupling is not without peril and must be approached with care. In keeping with the same engineering judgment that guided the development of the traditional aeroelastic equations, the effect of non-linear inertial effects for most airplane applications is expected to be small. A parameter does not tell the whole story, however, and modes flagged by the parameter as significant also need to be checked to see if the coupling is not a one-way path, i.e., the inertially affected modes can influence other modes.

Buttrill, Carey S.↗
NASA NTRS1988

Scaling effects in the static large deflection response of graphite-epoxy composite beams

In the present investigation of scaling effects in the large-deflection response of graphite/epoxy composite beams, eight model beams ranging from 1/6 to full scale in size were subjected to an eccentric axial compressive load promoting large bending deformations and failures; the beams encompassed unidirectional, angle-ply, cross-ply, and quasi-isotropic types. The data obtained pertains to loads, end-displacements, strain measurememts, and qualitative failure measurements. Test results indicate that beam responses scale in the small-deflection region, but deviate as the response becomes nonlinear.

Jackson, Karen E.↗
NASA NTRS1989

Scattering of light by stochastically rough particles

The single particle phase function and the linear polarization for large stochastically deformed spheres have been calculated by Monte Carlo simulation using the geometrical optics approximation. The radius vector of a particle is assumed to obey a bivariate lognormal distribution with three free parameters: mean radius, its standard deviation and the coherence length of the autocorrelation function. All reflections/refractions which include sufficient energy have been included. Real and imaginary parts of the refractive index can be varied without any restrictions. Results and comparisons with some earlier less general theories are presented. Applications of this theory to the photometric properties of atmosphereless bodies and interplanetary dust are discussed.

Peltoniemi, Jouni I.↗
NASA NTRS1991

Effect of stiffness characteristics on the response of composite grid-stiffened structures

A study of the effect of stiffness discontinuities and structural parameters on the response of continuous-filament grid-stiffened flat panels is presented. The buckling load degradation due to manufacturing-introduced stiffener discontinuities associated with a filament cut-and-add approach at the stiffener intersections is investigated. The degradation of buckling resistance in isogrid flat panels subjected to uni-axial compression and combined axial compression and shear loading conditions and induced damage is quantified using FEM. The combined loading case is the most critical one. Nonsolid stiffener cross sections, such as a foam-filled blade or hat with a 0-deg dominant cap, result in grid-stiffened structures that are structurally very efficient for wing and fuselage applications. The results of a study of the ability of grid-stiffened structural concepts to enhance the effective Poisson's ratio of a panel are presented. Grid-stiffened concepts create a highly effective Poisson's ratio, which can produce large camber deformations for certain elastic tailoring applications.

Ambur, Damodar R.↗
NASA NTRS1991

Optical transitions in diamond at ultrahigh pressures

Optical studies on diamond at ultrahigh pressures are described which show that the unique properties of diamonds are affected by such stresses. Spectroscopic measurements show that the optical absorption edge shifts from UV to red with increasing pressures, and Raman scattering measurements how evidence for new structural transitions associated with large macroscopic deformation, beginning at a pressure of about 150 GPa. The changes are reversible and are associated with intense luminescence peaks at 2.0-2.2 eV under 458-514 nm radiation. These results may be related to the onset of bandgap closure in the approach to a new high-pressure phase. These spectral features must also be taken into account when diamond is used as optical windows for ultrahigh-pressure investigations.

Mao, H. K.↗
NASA NTRS1992

Elastic and plastic strain measurement in high temperature environment using laser speckle

Two laser speckle methods are described to measure strain in high temperature environment and thermal strain caused by high temperature. Both are non-contact, non-destructive and remote sensing techniques that can be automated. The methods have different but overlapping ranges of application with one being more suitable for large plastic deformation.

Chiang, Fu-Pen↗
NASA NTRS1994

Sub-ply level scaling approach investigated for graphite-epoxy composite beam columns

Scale model graphite-epoxy composite specimens were fabricated using the 'sub-ply level' approach and tested as beam-columns under an eccentric axial load to determine the effect of specimen size on flexural response and failure. In the current research project, although the fiber diameters are not scaled, the thickness of the pre-preg material itself has been scaled by adjusting the number of fibers through the thickness of a single ply. Three different grades of graphite-epoxy composite material (AS4/3502) were obtained from Hercules, Inc., in which the number of fibers through the thickness of a single ply was reduced (Grade 190 with 12 to 16 fibers, Grade 95 with 6 to 8 fibers, and Grade 48 with 3 to 4 fibers). Thus, using the sub-ply level approach, a baseline eight ply quasi-isotropic laminate could be fabricated using either the Grade 48 or Grade 95 material and the corresponding full-scale laminate would be constructed from Grade 95 or standard Grade 190 material, respectively. Note that in the sub-ply level approach, the number of ply interfaces is constant for the baseline and full-scale laminates. This is not true for the ply level and sublaminate level scaled specimens. The three grades of graphite-epoxy composite material were used to fabricate scale model beam-column specimens with in-plane dimensions of 0.5*n x 5.75*n, where n=1,2,4 corresponsing to 1/4, 1/2, and full-scale factors. Angle ply, cross ply, and quasi-isotropic laminate stacking sequences were chosen for the investigation and the test matrices for each laminate type are given. Specimens in each laminate family with the same in-plane dimensions but different thicknesses were tested to isolate the influence of the thickness dimension on the flexural response and failure. Also, specific lay-ups were chosen with blocked plies and dispersed plies for each laminate type. Specimens were subjected to an eccentric axial load until failure. The load offset was introduced through a set of hinges which were attached to the platens of a standard load test machine. Three sets of geometrically scaled hinges were used to ensure that scaled loading conditions were applied. This loading condition was chosen because it promotes large flexural deformations and specimens fail at the center of the beam, away from the grip supports. Five channels of data including applied vertical load, end shortening displacement, strain from gages applied back-to-back at the midspan of the beam, and rotation of the hinge from a bubble inclinometer were recorded for each specimen. The beam-column test configuration was used previously to study size effects in ply level scaled composite specimens of the same material system, sizes, and stacking sequences. Thus, a direct comparison between the two scaling approaches is possible. Ply level scaled beam-columns with angle ply, cross ply, and quasi-isotropic lay-ups exhibited no size dependencies in the flexural response, but significant size effects in strength. The reduction in strength with increasing specimen size was not predicted successfully by analysis techniques. It is anticipated that results from this investigation will lead to a better understanding of the strength scale effect in composite structures.

Jackson, Karen E.↗
NASA NTRS1994

Hydrodynamically induced fluid transfer and non-convective double-diffusion in microgravity sliding solvent diffusion cells

Microgravity can provide a diffusion-dominated environment for double-diffusion and diffusion-reaction experiments otherwise disrupted by buoyant convection or sedimentation. In sliding solvent diffusion cells, a diffusion interface between two liquid columns is achieved by aligning two offset sliding wells. Fluid in contact with the sliding lid of the cavities is subjected to an applied shear stress. The momentum change by the start/stop action of the well creates an additional hydrodynamical force. In microgravity, these viscous and inertial forces are sufficiently large to deform the diffusion interface and induce hydrodynamic transfer between the wells. A series of KC-135 parabolic flight experiments were conducted to characterize these effects and establish baseline data for microgravity diffusion experiments. Flow visualizations show the diffusion interface to be deformed in a sinusoidal fashion following well alignment. After the wells were separated again in a second sliding movement, the total induced liquid transfer was determined and normalized by the well aspect ratio. The normalized transfer decreased linearly with Reynolds number from 3.3 to 4.0% (w/v) for Re = 0.4 (Stokes flow) to a minimum of 1.0% for Re = 23 to 30. Reynolds numbers that provide minimum induced transfers are characterized by an interface that is highly deformed and unsuitable for diffusion measurements. Flat diffusion interfaces acceptable for diffusion measurements are obtained with Reynolds numbers on the order of 7 to 10. Microgravity experiments aboard a sounding rocket flight verified counterdiffusion of different solutes to be diffusion dominated. Ground control experiments showed enhanced mixing by double-diffusive convection. Careful selection of experimental parameters improves initial conditions and minimizes induced transfer rates.

Pollmann, Konrad W.↗
NASA NTRS1995

Large-scale landslide simulations: Global deformation, velocities and basal friction

The cause of the apparent small friction exhibited by long runout landslides has long been speculated upon. In an attempt to provide some insight into the matter, this paper describes results obtained from a discrete particle computer simulation of landslides composed of up to 1,000,000 two-dimensional discs. While simplified, the results show many of the characteristics of field data (the volumetric effect on runout, preserved strata, etc.) and with allowances made for the two-dimensional nature of the simulation, the runouts compare well with those of actual landslides. The results challenge the current view that landslides travel as a nearly solid block riding atop a low friction basal layer. Instead, they show that the mass is completely shearing and indicate that the apparent friction coefficient is an increasing function of shear rate. The volumetric effect can then be understood. With all other conditions being equal, different size slides appear to travel with nearly the same average velocity; however, as the larger landslides are thicker, they experience smaller shear rates and correspondingly smaller frictional resistance.

Campbell, Charles S.↗
NASA NTRS1996

Global and Local Stress Analyses of McDonnell Douglas Stitched/RFI Composite Wing Stub Box

This report contains results of structural analyses performed in support of the NASA structural testing of an all-composite stitched/RFI (resin film infusion) wing stub box. McDonnell Douglas Aerospace Company designed and fabricated the wing stub box. The analyses used a global/local approach. The global model contains the entire test article. It includes the all-composite stub box, a metallic load-transition box and a metallic wing-tip extension box. The two metallic boxes are connected to the inboard and outboard ends of the composite wing stub box, respectively. The load-transition box was attached to a steel and concrete vertical reaction structure and a load was applied at the tip of the extension box to bend the wing stub box upward. The local model contains an upper cover region surrounding three stringer runouts. In that region, a large nonlinear deformation was identified by the global analyses. A more detailed mesh was used for the local model to obtain more accurate analysis results near stringer runouts. Numerous analysis results such as deformed shapes, displacements at selected locations, and strains at critical locations are included in this report.

Wang, John T.↗
NASA NTRS2000

Effects of Heat Treatment on the Ballistic Impact Properties of Inconel 718 for Jet Engine Fan Containment Applications

The effects of heat treating Inconel 718 on the ballistic impact response and failure mechanisms were studied. Two different annealing conditions and an aged condition were considered. Large differences in the static properties were found between the annealed and the aged material, with the annealed condition having lower strength and hardness and greater elongation than the aged. Correspondingly large differences were found in the velocity required to penetrate material in the two conditions in impact tests involving 12.5 mm diameter, 25.4 mm long cylindrical Ti-6-4 projectiles impacting flat plates at velocities in the range of 150 to 300 m/sec. The annealed material was able to absorb over 25 percent more energy than the aged. This is contrary to results observed for ballistic impact response for higher velocity impacts typically encountered in military applications where it has been shown that there exists a correlation between target hardness and ballistic impact strength. Metallographic examination of impacted plates showed strong indication of failure due to adiabatic shear. In both materials localized bands of large shear deformation were apparent, and microhardness measurements indicated an increase in hardness in these bands compared to the surrounding material. These bands were more localized in the aged material than in the annealed material. In addition the annealed material underwent significantly greater overall deformation before failure. The results indicate that high elongation and better strain hardening capabilities reduce the tendency for shear to localize and result in an unstable adiabatic shear failure. This supports empirical containment design methods that relate containment thickness to the static toughness.

Pereira, J. Michael↗
NASA NTRS1999

Effects of Heat Treatment on the Ballistic Impact Properties of Inconel 718 for Jet Engine Fan Containment Applications

The effects of heat treating Inconel 718 on the ballistic impact response and failure mechanisms were studied. Two different annealing conditions and an aged condition were considered. Large differences in the static properties were found between the annealed and the aged material, with the annealed condition having lower strength and hardness and greater elongation than the aged. High strain rate tests show similar results. Correspondingly large differences were found in the velocity required to penetrate material in the two conditions in impact tests involving 12.5 mm diameter, 25.4 mm long cylindrical Ti-6-4 projectiles impacting flat plates at velocities in the range of 150 to 300 m/sec. The annealed material was able to absorb over 25 percent more energy than the aged. This is contrary to results observed for ballistic impact response for higher velocity impacts typically encountered in military applications where it has been shown that there exists a correlation between target hardness and ballistic impact strength. Metallographic examination of impacted plates showed strong indication of failure due to adiabatic shear. In both materials localized bands of large shear deformation were apparent, and microhardness measurements indicated an increase in hardness in these bands compared to the surrounding material. These bands were more localized in the aged material than in the annealed material. In addition the annealed material underwent significantly greater overall deformation before failure. The results indicate that lower elongation and reduced strain hardening behavior lead to a transition from shear to adiabatic shear failure, while high elongation and better strain hardening capabilities reduce the tendency for shear to localize and result in an unstable adiabatic shear failure. This supports empirical containment design methods that relate containment thickness to the static toughness.

Pereira, J. Michael↗
NASA NTRS2001

Effects of Heat Treatment on the Ballistic Impact Properties of Inconel 718 for Jet Engine Fan Containment Applications

The effects of heat treating Inconel 718 on the ballistic impact response and failure mechanisms were studied. Two different annealing conditions and an aged condition were considered. Large differences in the static properties were found between the annealed and the aged material, with the annealed condition having lower strength and hardness and greater elongation than the aged. High strain rate tests show similar results. Correspondingly large differences were found in the velocity required to penetrate material in the two conditions in impact tests involving 12.5 mm diameter, 25.4 mm long cylindrical Ti-6-4 projectiles impacting flat plates at velocities in the range of 150 to 300 m/sec. The annealed material was able to absorb over 25 percent more energy than the aged. This is contrary to results observed for ballistic impact response for higher velocity impacts typically encountered in military applications where it has been shown that there exists a correlation between target hardness and ballistic impact strength. Metallographic examination of impacted plates showed strong indication of failure due to adiabatic shear. In both materials localized bands of large shear deformation were apparent, and microhardness measurements indicated an increase in hardness in these bands compared to the surrounding material. These bands were more localized in the aged material than in the annealed material. In addition the annealed material underwent significantly greater overall deformation before failure. The results indicate that lower elongation and reduced strain hardening behavior lead to a transition from shear to adiabatic shear failure, while high elongation and better strain hardening capabilities reduce the tendency for shear to localize and result in an unstable adiabatic shear failure. This supports empirical containment design methods that relate containment thickness to the static toughness.

Pereira, J. Michael↗
NASA NTRS2000

An Interconnected Network of Core-Forming Melts Produced by Shear Deformation

The formation mechanism of terrestrial planetary is still poorly understood, and has been the subject of numerous experimental studies. Several mechanisms have been proposed by which metal-mainly iron with some nickel-could have been extracted from a silicate mantle to form the core. Most recent models involve gravitational sinking of molten metal or metal sulphide through a partially or fully molten mantle that is often referred to as a'magma ocean. Alternative models invoke percolation of molten metal along an interconnected network (that is, porous flow) through a solid silicate matrix. But experimental studies performed at high pressures have shown that, under hydrostatic conditions, these melts do not form an interconnected network, leading to the widespread assumption that formation of metallic cores requires a magma ocean. In contrast, here we present experiments which demonstrate that shear deformation to large strains can interconnect a significant fraction of initially isolated pockets of metal and metal sulphide melts in a solid matrix of polycrystalline olivine. Therefore, in a dynamic (nonhydrostatic) environment, percolation remains a viable mechanism for the segregation and migration of core-forming melts in a solid silicate mantle.

Bruhn, D.↗
NASA NTRS2002

Molten-Metal Droplet Deposition on a Moving Substrate in Microgravity: Aiding the Development of Novel Technologies for Microelectronic Assembly

Driven by advancements in microelectronics manufacturing, this research investigates the oblique (non-axisymmetric) impact of liquid-metal droplets on flat substrates. The problem of interest is relevant to the development of the novel technology of on-demand dispension (printing) of microscopic solder deposits for the surface mounting of microelectronic devices. The technology, known as solder jetting, features on-demand deposition of miniature solder droplets (30 to 120 microns in diameter) in very fine, very accurate patterns using techniques analogous to those developed for the ink-jet printing industry. Despite its promise, severe limitations exist currently with regards to the throughput rates of the technology; some of these limitations are largely due to the lack of the capability for reliable prediction of solder bump positioning and shapes, especially under ballistic deposition conditions where the droplet impact phenomena are inherently three-dimensional. The study consists of a theoretical and an experimental component. The theoretical work uses a finite element formulation to simulate numerically the non-axisymmetric (3-D) fluid mechanics and heat transfer phenomena of a liquid solder droplet impacting at an angle alpha on a flat substrate. The work focuses on the pre-solidification regime. The modeling of the most challenging fluid mechanics part of the process has been completed successfully. It is based upon the full laminar Navier-Stokes equations employing a Lagrangian frame of reference. Due to the large droplet deformation, the surface (skin) as well as the volumetric mesh have to be regenerated during the calculations in order to maintain the high accuracy of the numerical scheme. The pressure and velocity fields are then interpolated on the newly created mesh. The numerical predictions are being tested against experiments, for cases where wetting phenomena are not important. For the impact parameters used in the example shown (We = 2.38, Fr = 16300, Re = 157), the droplet rolls along the substrate, but its shape remains practically axisymmetric for all impact angles within the range from 0 to 60 deg. Interestingly, the substrate/droplet contact area during the recoiling phase of the impact is not a monotonically decreasing function of time. The experimental component of the research tests the numerical predictions and provides necessary input data (contact angles) for the theoretical model. The experiments are performed in microgravity (2.2s drop tower of the NASA GRC) in order to allow for the use of mm-size solder droplets, which make feasible the performance of accurate measurements, while maintaining similitude of the relevant fluid dynamic groups (Re, Fr, We, Ste). Preliminary oblique impact experiments have been performed using water droplets in normal gravity.

Megaridis, C. M.↗
NASA NTRS2004

Workshop on Oxygen in the Terrestrial Planets

This volume contains abstracts that have been accepted for presentation at the Workshop on Oxygen in the Terrestrial Planets, July 20-23,2004, Santa Fe, New Mexico. The contents include: 1) Experimental Constraints on Oxygen and Other Light Element Partitioning During Planetary Core Formation; 2) In Situ Determination of Fe(3+)/SigmaFe of Spinels by Electron Microprobe: An Evaluation of the Flank Method; 3) The Effect of Oxygen Fugacity on Large-Strain Deformation and Recrystallization of Olivine; 4) Plagioclase-Liquid Trace Element Oxygen Barometry and Oxygen Behaviour in Closed and Open System Magmatic Processes; 5) Core Formation in the Earth: Constraints from Ni and Co; 6) Oxygen Isotopic Compositions of the Terrestrial Planets; 7) The Effect of Oxygen Fugacity on Electrical Conduction of Olivine and Implications for Earth s Mantle; 8) Redox Chemical Diffusion in Silicate Melts: The Impact of the Semiconductor Condition; 9) Ultra-High Temperature Effects in Earth s Magma Ocean: Pt and W Partitioning; 10) Terrestrial Oxygen and Hydrogen Isotope Variations: Primordial Values, Systematics, Subsolidus Effects, Planetary Comparisons, and the Role of Water; 11) Redox State of the Moon s Interior; 12) How did the Terrestrial Planets Acquire Their Water?; 13) Molecular Oxygen Mixing Ratio and Its Seasonal Variability in the Martian Atmosphere; 14) Exchange Between the Atmosphere and the Regolith of Mars: Discussion of Oxygen and Sulfur Isotope Evidence; 15) Oxygen and Hydrogen Isotope Systematics of Atmospheric Water Vapor and Meteoric Waters: Evidence from North Texas; 16) Implications of Isotopic and Redox Heterogeneities in Silicate Reservoirs on Mars; 17) Oxygen Isotopic Variation of the Terrestrial Planets; 18) Redox Exchanges in Hydrous Magma; 19) Hydrothermal Systems on Terrestrial Planets: Lessons from Earth; 20) Oxygen in Martian Meteorites: A Review of Results from Mineral Equilibria Oxybarometers; 21) Non-Linear Fractionation of Oxygen Isotopes Implanted in Lunar Metal Grains: Solar, Lunar or Terrestrial Origin? 22) Isotopic Zoning in the Inner Solar System; 23) Redox Conditions on Small Bodies; 24) Determining the Oxygen Fugacity of Lunar Pyroclastic Glasses Using Vanadium Valence - An Update; 25) Mantle Redox Evolution and the Rise of Atmospheric O2; 26) Variation of Kd for Fe-Mg Exchange Between Olivine and Melt for Compositions Ranging from Alkaline Basalt to Rhyolite; 27) Determining the Partial Pressure of Oxygen (PO,) in Solutions on Mars; 28) The Influence of Oxygen Environment on Kinetic Properties of Silicate Rocks and Minerals; 29) Redox Evolution of Magmatic Systems; 30) The Constancy of Upper Mantlefo, Through Time Inferred from V/Sc Ratios in Basalts: Implications for the Rise in Atmospheric 0 2; 31) Nitrogen Solubility in Basaltic Melt. Effects of Oxygen Fugacity, Melt Composition and Gas Speciation; 32) Oxygen Isotope Anomalies in the Atmospheres of Earth and Mars; 33) The Effect of Oxygen Fugacity on Interdiffusion of Iron and Magnesium in Magnesiowiistite 34) The Calibration of the Pyroxene Eu-Oxybarometer for the Martian Meteorites; 35) The Europium Oxybarometer: Power and Pitfalls; 36) Oxygen Fugacity of the Martian Mantle from PigeoniteMelt Partitioning of Samarium, Europium and Gadolinium; 37) Oxidation-Reduction Processes on the Moon: Experimental Verification of Graphite Oxidation in the Apollo 17 Orange Glasses; 38) Oxygen and Core Formation in the Earth; 39) Geologic Record of the Atmospheric Sulfur Chemistry Before the Oxygenation of the Early Earth s Atmosphere; 40) Comparative Planetary Mineralogy: V/(CrCAl) Systematics in Chromite as an Indicator of Relative Oxygen Fugacity; 41) How Well do Sulfur Isotopes Constrain Oxygen Abundance in the Ancient Atmospheres? 42) Experimental Constraints on the Oxygen Isotope (O-18/ O-16) Fractionation in the Ice vapor and Adsorbant vapor Systems of CO2 at Conditions Relevant to the Surface of Mars; 43) Micro-XANES Measurements on Experimental Spinels andhe Oxidation State of Vanadium in Spinel-Melt Pairs; 44) Testing the Magma Ocean Hypothesis Using Metal-Silicate Partitioning of Te, Se and S; 45) Solubility of Oxygen in Liquid Iron at High Pressure and Consequences for the Early Differentiation of Earth and Mars Metallic Liquid Segregation in Planetesimals; 46) Oxygen Fugacity of Lunar Basalts and the Lunar Mantle. Range of fo2 and the Effectiveness of Oxybarometers; 47) Thermodynamic Study of Dissociation Processes of Molecular Oxygen in Vapor over Oxide Compounds; 48) Oxygen Profile of a Thermo-Haliophilic Community in the Badwater Salt Flat; 49) Oxygen Barometry Using Synchrotron MicroXANES of Vanadium; 50) Mass-Independent Isotopic Fractionation of Sulfur from Sulfides in the Huronian Supergroup, Canada; 51) Mass Independent Isotopes and Applications to Planetary Atmospheres; 52) Electrical Conductivity, Oxygen Fugacity, and Mantle Materials; 53) Crustal Evolution and Maturation on Earth: Oxygen Isotope Evidence; 54) The Oxygen Isotope Composition of the Moon: Implications for Planet Formation; 55) Oxygen Isotope Composition of Eucrites and Implications for the Formation of Crust on the HED Parent Body; and 56) The Role of Water in Determining the Oxygen Isotopic Composition of Planets.

Source record↗
NASA NTRS2003

Fully Nonlinear Modeling and Analysis of Precision Membranes

High precision membranes are used in many current space applications. This paper presents a fully nonlinear membrane theory with forward and inverse analyses of high precision membrane structures. The fully nonlinear membrane theory is derived from Jaumann strains and stresses, exact coordinate transformations, the concept of local relative displacements, and orthogonal virtual rotations. In this theory, energy and Newtonian formulations are fully correlated, and every structural term can be interpreted in terms of vectors. Fully nonlinear ordinary differential equations (ODES) governing the large static deformations of known axisymmetric membranes under known axisymmetric loading (i.e., forward problems) are presented as first-order ODES, and a method for obtaining numerically exact solutions using the multiple shooting procedure is shown. A method for obtaining the undeformed geometry of any axisymmetric membrane with a known inflated geometry and a known internal pressure (i.e., inverse problems) is also derived. Numerical results from forward analysis are verified using results in the literature, and results from inverse analysis are verified using known exact solutions and solutions from the forward analysis. Results show that the membrane theory and the proposed numerical methods for solving nonlinear forward and inverse membrane problems are accurate.

Pai, P. Frank↗