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NASA NTRS1950

Critical stress of ring-stiffened cylinders in torsion

A chart in terms of nondimensional parameters is presented for the theoretical critical stress in torsion of simply supported cylinders stiffened by identical equally spaced rings of zero torsional stiffness. The results are obtained by solving the equation of equilibrium by means of the Galerkin method. Comparison of the theoretical results with experimental results indicates that ring-stiffened cylinders buckle, on the average, at a buckling stress about 15 percent below the theoretical buckling stress. (author)

Stein, Manuel↗

NASA NTRS1953

Deflection and Stress Analysis of Thin Solid Wings of Arbitrary Plan Form with Particular Reference to Delta Wings

The structural analysis of arbitrary solid cantilever wings by small-deflection thin-plate theory is reduced to the solution of linear ordinary differential equations by the assumption that the chordwise deflections at any spanwise station may be expressed in the form of a power series in which the coefficients are functions of the spanwise coordinate. If the series is limited to the first two and three terms (that is, if linear and parabolic chordwise deflections, respectively, are assumed), the differential equations for the coefficients are solved exactly for uniformly loaded solid delta wings of constant thickness ratio. For cases for which exact solutions to the differential equations cannot be obtained, a numerical procedure is derived. Experimental deflection and stress data for constant-thickness delta-plate specimens of 45 degree and 60 degree sweep are presented and are found to compare favorably with the present theory.

Stein, Manuel↗

NASA NTRS1982

Postbuckling of orthotropic composite plates loaded in compression

The nonlinear large deflection equations of von Karman are written for 'specially' orthotropic plates. The equations are then manipulated to determine the parameters required to establish postbuckling behavior. It is found that only two new parameters are needed beyond those required for buckling. By assuming trigonometric functions in one direction, the plate equations are converted into ordinary nonlinear differential equations which are solved numerically using a two point boundary problem solver that makes use of Newton's method. The postbuckling behavior is obtained for simply supported and clamped, long, rectangular, orthotropic plates covering the complete range of dimensions and material properties.

Stein, M.↗

NASA NTRS1984

Analytical results for postbuckling behavior of plates in compression and shear

The postbuckling behavior of long rectangular isotropic and orthotropic plates is determined. By assuming trigonometric functions in one direction, the nonlinear partial differential equations of von Karman large deflection plate theory are converted into nonlinear ordinary differential equations. The ordinary differential equations are solved numerically using an available boundary value problem solver which makes use of Newton's method. Results for longitudinal compression show different postbuckling behavior between isotropic and orthotropic plates. Results for shear show that change in inplane edge constraints can cause large change in postbuckling stiffness.

Stein, M.↗

NASA NTRS1985

Analytical results for post-buckling behaviour of plates in compression and in shear

Stein, M.↗

NASA NTRS1951

Torsion and transverse bending of cantilever plates

The problem of combined bending and torsion of cantilever plates of variable thickness, such as might be considered for solid thin high-speed airplane or missile wings, is considered in this paper. The deflections of the plate are assumed to vary linearly across the chord; minimization of the potential energy by means of the calculus of variations then leads to two ordinary linear differential equations for the bending deflections and the twist of the plate. Because the cantilever is analyzed as a plate rather than as a beam, the effect of constraint against axial warping in torsion is inherently included. The application of this method to specific problems involving static deflection, vibration, and buckling of cantilever plates is presented. In the static-deflection problems, taper and sweep are considered.

WINGS, SOLID↗

NASA NTRS1983

Postbuckling of long orthotropic plates in combined shear and compression

The nonlinear large-deflection partial differential equations of von karman for orthotropic plates loaded in combined shear and compression are converted into a set of first-order nonlinear ordinary differential equations by assuming trigonometric functions in one direction. These equations are solved numerically using a two point boundary problem solver which makes use of Newton's method. Results are obtained which determine the postbuckling behavior of rectangular plates with loading up to about three times the buckling load. Both isotropic and orthotropic composite plates are considered. Results show that orthotropic plates may behave quite differently than isotropic plates and that in-plane boundary conditions are important for plates loaded in shear.

Stein, M.↗

NASA NTRS1995

A new technique for ground simulation of hypervelocity debris

A series of hypervelocity damage experiments were preformed on spacecraft materials. These experiments employed a technique which accelerates micro flyer plates simulating space debris traveling at 3 to 8 km/sec. The apparatus used to propel the micro flyer plates was compact and fit well into a space environmental chamber equipped with instrumentation capable of analyzing the vapor ejected from the sample. Mechanical damage to the sample was also characterized using optical and scanning electron microscpopy. Data for this work was obtained from hypervelocity impacts on a polysulfone resin and a graphite polysulfone composite. Polysulfone was selected because it was flown on the Long Duration Exposure Facility (LDEF) which spent several years in low earth orbit (LEO). Chemistry of the vapor produced by the impact was analyzed with a time of flight mass spectrometer, (TOFMS). This represents the first time that ejected vapors from hypervelocity collisions were trapped and analyzed with a mass spectrometer. With this approach we are able to study changes in the vapor chemistry as a function of time after impact, obtain a velocity measurement of the vapor, and estimate a temperature of the surface at time of impact using dynamic gas equations. Samples of the vapor plume may be captured and examined by transmission electron microscopy. Studies were also conducted to determine mechanical damage to a graphite polysulfone composite and a polysulfone resin. Impact craters were examined under optical and scanning electron microscopes. The collision craters in the matrix were typical of those shown in conventional shock experiments. However, the hypervelocity collisions with the graphite polysulfone composite were remarkably different than those with the resin.

Roybal, R.↗

NASA NTRS1986

An approximate buckling analysis for rectangular orthotropic plates with centrally located cutouts

An approximate analysis for predicting buckling of rectangular orthotropic composite plates with centrally located cutouts is presented. In this analysis, prebuckling and buckling problems are converted from a two-dimensional to a one-dimensional system of linear differential equations with variable coefficients. The conversion is accomplished by expressing the displacements as series with each element containing a trigonometric function of one coordinate and a coefficient that is an arbitrary function of the other coordinate. Ordinary differential equations are then obtained from a variational principle. Analytical results obtained from the approximate analysis are compared with finite element analyses for isotropic plates and for specially orthotropic plates with central circular cutouts of various sizes. Experimental results for the specially orthotropic plates are also presented. In nearly all cases, the approximate analysis predicts the buckling mode shapes correctly and predicts the buckling loads to within a few percent of the finite element and experimental results.

Nemeth, M. P.↗

NASA NTRS1986

Shock-tube pyrolysis of acetylene - Sensitivity analysis of the reaction mechanism for soot formation

The impact of thermodynamic parameters on the sensitivity of model predictions of soot formation by shock-tube pyrolysis of acetylene were assessed analytically. The pyrolysis process was treated as having three components: initiation, the initial pyrolysis stages; cyclization, formation of larger molecules and radicals and small aromatic molecules; and polymerization, further growth of aromatic rings. Rate equations are reviewed for each component. Thermodynamic effects were assessed by varying the C2H-H and C2H3-H bond energies and the Ct-(Ct) group additivity value. Any change in the C2H-H bond energy had a significant impact on the temperature and the maximum amount of the soot yield. The findings underscore the necessity of using accurate thermodynamic data for modeling high-temperature chemical kinetics.

Frenklach, M.↗

NASA NTRS1984

Statistical tests of additional plate boundaries from plate motion inversions

The application of the F-ratio test, a standard statistical technique, to the results of relative plate motion inversions has been investigated. The method tests whether the improvement in fit of the model to the data resulting from the addition of another plate to the model is greater than that expected purely by chance. This approach appears to be useful in determining whether additional plate boundaries are justified. Previous results have been confirmed favoring separate North American and South American plates with a boundary located beween 30 N and the equator. Using Chase's global relative motion data, it is shown that in addition to separate West African and Somalian plates, separate West Indian and Australian plates, with a best-fitting boundary between 70 E and 90 E, can be resolved. These results are generally consistent with the observation that the Indian plate's internal deformation extends somewhat westward of the Ninetyeast Ridge. The relative motion pole is similar to Minster and Jordan's and predicts the NW-SE compression observed in earthquake mechanisms near the Ninetyeast Ridge.

Stein, S.↗

NASA NTRS1992

Evolution of a magnetic flux tube in two-dimensional penetrative convection

Highly supercritical compressible convection is simulated in a two-dimensional domain in which the upper half is unstable to convection while the lower half is stably stratified. This configuration is an idealization of the layers near the base of the solar convection zone. Once the turbulent flow is well developed, a toroidal magnetic field B sub tor is introduced to the stable layer. The field's evolution is governed by an advection-diffusion-type equation, and the Lorentz force does not significantly affect the flow. After many turnover times the field is stratified such that the absolute value of B sub tor/rho is approximately constant in the convective layer, where rho is density, while in the stable layer this ratio decreases linearly with depth. Consequently most of the magnetic flux is stored in the overshoot layer. The inclusion of rotation leads to travelling waves which transport magnetic flux latitudinally in a manner reminiscent of the migrations seen during the solar cycle.

Jennings, R. L.↗

NASA NTRS1984

Error analysis and correction of discrete solutions from finite element codes

Many structures are an assembly of individual shell components. Therefore, results for stresses and deflections from finite element solutions for each shell component should agree with the equations of shell theory. This paper examines the problem of applying shell theory to the error analysis and the correction of finite element results. The general approach to error analysis and correction is discussed first. Relaxation methods are suggested as one approach to correcting finite element results for all or parts of shell structures. Next, the problem of error analysis of plate structures is examined in more detail. The method of successive approximations is adapted to take discrete finite element solutions and to generate continuous approximate solutions for postbuckled plates. Preliminary numerical results are included.

Thurston, G. A.↗

NASA NTRS2011

Assessing the Age of an Asteroid's Surface with Data from the International Rosetta Mission

Rosetta is an international mission led by the European Space Agency (ESA) with key support and instrumentation from the National Aeronautics and Space Administration (NASA). Rosetta is currently on a ten-year mission to catch comet 67P/Churyumov-Gerasimenko (C-G); throughout its voyage, the spacecraft has performed flybys of two main belt asteroids (MBA): Steins and Lutetia. Data on the physical, chemical, and geological properties of these asteroids are currently being processed and analyzed. Accurate interpretation of such data is fundamental in the success of Rosetta's mission and overall objectives. Post-flyby data analyses strive to correlate the size, shape, volume, and rotational rate of Lutetia, in addition to interpreting its multi-color imagining, albedo, and spectral mapping. Although advancements in science have contributed to the examination of celestial bodies, methods to analyze asteroids remain largely empirical, not semi-empirical, nor ab initio. This study aims to interpret and document the scientific methods currently utilized in the characterization of asteroid (21) Lutetia in order to render these processes and methods accessible to the public. Examples include a standardized technique for assessing the age of an asteroid surface, complete with clickable reference maps, methodology of grouping surface characteristics together, and a standardized power law equation for the age. Other examples include determining the density of an object. Context for what both density and age mean is a bi-product of this study. Results of the study will aid in the development of pedagogical material on asteroids for public use, and in creation of an academic database for selected targets that might be used as a reference.

asteriods↗

NASA NTRS2013

Approach to Integrate Global-Sun Models of Magnetic Flux Emergence and Transport for Space Weather Studies

The Sun lies at the center of space weather and is the source of its variability. The primary input to coronal and solar wind models is the activity of the magnetic field in the solar photosphere. Recent advancements in solar observations and numerical simulations provide a basis for developing physics-based models for the dynamics of the magnetic field from the deep convection zone of the Sun to the corona with the goal of providing robust near real-time boundary conditions at the base of space weather forecast models. The goal is to develop new strategic capabilities that enable characterization and prediction of the magnetic field structure and flow dynamics of the Sun by assimilating data from helioseismology and magnetic field observations into physics-based realistic magnetohydrodynamics (MHD) simulations. The integration of first-principle modeling of solar magnetism and flow dynamics with real-time observational data via advanced data assimilation methods is a new, transformative step in space weather research and prediction. This approach will substantially enhance an existing model of magnetic flux distribution and transport developed by the Air Force Research Lab. The development plan is to use the Space Weather Modeling Framework (SWMF) to develop Coupled Models for Emerging flux Simulations (CMES) that couples three existing models: (1) an MHD formulation with the anelastic approximation to simulate the deep convection zone (FSAM code), (2) an MHD formulation with full compressible Navier-Stokes equations and a detailed description of radiative transfer and thermodynamics to simulate near-surface convection and the photosphere (Stagger code), and (3) an MHD formulation with full, compressible Navier-Stokes equations and an approximate description of radiative transfer and heating to simulate the corona (Module in BATS-R-US). CMES will enable simulations of the emergence of magnetic structures from the deep convection zone to the corona. Finally, a plan will be summarized on the development of a Flux Emergence Prediction Tool (FEPT) in which helioseismology-derived data and vector magnetic maps are assimilated into CMES that couples the dynamics of magnetic flux from the deep interior to the corona.

Mansour, Nagi N.↗

NASA NTRS1998

Structure and Dynamics of the Solar Chromosphere

The problem of chromospheric dynamics and heating consists of two problems: one, concerning the magnetic network on the boundary of supergranulation cells (CB), where the oscillation period is seven minutes, and the other, concerning the cell interior (CI), where the oscillation period is three minutes. The observational data on the oscillations and the emission of radiation can be used to determine the structure and dynamics of the atmosphere provided answers are known to three critical questions, concerning: the nature of the waves powering the bright points, the origin of the observed oscillation periods and the mechanism of chromospheric heating. The recent modeling of the dynamics of the CI, which combines a sophisticated treatment of gas dynamics and radiative transfer in a one-dimensional model with empirical velocity input from the observations, answered the first of these questions: the waves powering K(sub 2upsilon), bright points are propagating acoustic waves. This firm conclusion declares invalid the model of Leibacher & Stein, which explains the observed period with standing acoustic waves in a chromospheric cavity. On the third question, the heating of the chromosphere in the CI, their model predicts that the temperature in the chromosphere is declining in the outward direction up to a height of at least I Mm most of the time, so even the time-average temperature is dropping monotonically in the outward direction, implying that lines formed in the chromosphere up to a height of at least 1 Mm appear in absorption most of the time and everywhere in the CI. The problem of the CI can be resolved with a two-component model, which combines a model for K(sub 2upsilon), bright points with a model for the background. The bright point model has the same aims as the CS94 model, except that the empirical driving from the LRK93 observations is replaced by impulsive excitation, as suggested by the properties of the Klein-Gordon equation.

Kalkofen, Wolfgang↗

NASA NTRS1978

Application of a trigonometric finite difference procedure to numerical analysis of compressive and shear buckling of orthotropic panels

A numerical analysis developed for the buckling of rectangular orthotropic layered panels under combined shear and compression is described. This analysis uses a central finite difference procedure based on trigonometric functions instead of using the conventional finite differences which are based on polynomial functions. Inasmuch as the buckle mode shape is usually trigonometric in nature, the analysis using trigonometric finite differences can be made to exhibit a much faster convergence rate than that using conventional differences. Also, the trigonometric finite difference procedure leads to difference equations having the same form as conventional finite differences; thereby allowing available conventional finite difference formulations to be converted readily to trigonometric form. For two-dimensional problems, the procedure introduces two numerical parameters into the analysis. Engineering approaches for the selection of these parameters are presented and the analysis procedure is demonstrated by application to several isotropic and orthotropic panel buckling problems. Among these problems is the shear buckling of stiffened isotropic and filamentary composite panels in which the stiffener is broken. Results indicate that a break may degrade the effect of the stiffener to the extent that the panel will not carry much more load than if the stiffener were absent.

Stein, M.↗

NASA NTRS1993

On the physics of waves in the solar atmosphere: Wave heating and wind acceleration

This paper presents work performed on the generation and physics of acoustic waves in the solar atmosphere. The investigators have incorporated spatial and temporal turbulent energy spectra in a newly corrected version of the Lighthill-Stein theory of acoustic wave generation in order to calculate the acoustic wave energy fluxes generated in the solar convective zone. The investigators have also revised and improved the treatment of the generation of magnetic flux tube waves, which can carry energy along the tubes far away from the region of their origin, and have calculated the tube energy fluxes for the sun. They also examine the transfer of the wave energy originated in the solar convective zone to the outer atmospheric layers through computation of wave propagation and dissipation in highly nonhomogeneous solar atmosphere. These waves may efficiently heat the solar atmosphere and the heating will be especially significant in the chromospheric network. It is also shown that the role played by Alfven waves in solar wind acceleration and coronal hole heating is dominant. The second part of the project concerned investigation of wave propagation in highly inhomogeneous stellar atmospheres using an approach based on an analytic tool developed by Musielak, Fontenla, and Moore. In addition, a new technique based on Dirac equations has been developed to investigate coupling between different MHD waves propagating in stratified stellar atmospheres.

Musielak, Z. E.↗