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NASA NTRS1997

Global-Local Finite Element Analysis for Thermo-Mechanical Stresses in Bonded Joints

An analysis of adhesively bonded joints using conventional finite elements does not capture the singular behavior of the stress field in regions where two or three dissimilar materials form a junction with or without free edges. However, these regions are characteristic of the bonded joints and are prone to failure initiation. This study presents a method to capture the singular stress field arising from the geometric and material discontinuities in bonded composites. It is achieved by coupling the local (conventional) elements with global (special) elements whose interpolation functions are constructed from the asymptotic solution.

Shkarayev, S.↗

NASA NTRS2005

Application of Video Image Correlation Techniques to the Space Shuttle External Tank Foam Materials

Results that illustrate the use of a video-image-correlation-based displacement and strain measurement system to assess the effects of material nonuniformities on the behavior of the sprayed-on foam insulation (SOFI) used for the thermal protection system on the Space Shuttle External Tank are presented. Standard structural verification specimens for the SOFI material with and without cracks and subjected to mechanical or thermal loading conditions were tested. Measured full-field displacements and strains are presented for selected loading conditions to illustrate the behavior of the foam and the viability of the measurement technology. The results indicate that significant strain localization can occur in the foam because of material nonuniformities. In particular, elongated cells in the foam can interact with other geometric or material discontinuities in the foam and develop large-magnitude localized strain concentrations that likely initiate failures. Furthermore, some of the results suggest that continuum mechanics and linear elastic fracture mechanics might not adequately represent the physical behavior of the foam, and failure predictions based on homogeneous linear material models are likely to be inadequate.

Hilburger, Mark W.↗

NASA NTRS2006

Application of Video Image Correlation Techniques to the Space Shuttle External Tank Foam Materials

Hilburger, Mark W.↗

NASA NTRS1973

Analysis of high-aspect-ratio jet-flap wings of arbitrary geometry

An analytical technique to compute the performance of an arbitrary jet-flapped wing is developed. The solution technique is based on the method of Maskell and Spence in which the well-known lifting-line approach is coupled with an auxiliary equation providing the extra function needed in jet-flap theory. The present method is generalized to handle straight, uncambered wings of arbitrary planform, twist, and blowing (including unsymmetrical cases). An analytical procedure is developed for continuous variations in the above geometric data with special functions to exactly treat discontinuities in any of the geometric and blowing data. A rational theory for the effect of finite wing thickness is introduced as well as simplified concepts of effective aspect ratio for rapid estimation of performance.

Lissaman, P. B. S.↗

NASA NTRS1967

Metallurgical and geometrical factors affecting elevated temperature tensile properties of discontinuous tungsten fiber reinforced composites.

Length-to-diameter ratio and fiber orientation correlation to tensile properties at elevated temperatures for fiber reinforced composites

Petrasek, D. W.↗

NASA NTRS2023

Velocity Discontinuity Propagation Model Validation Using an Approximate Point Source in Motion

The classic geometric acoustic solution for propagation through a mean flow velocity discontinuity is evaluated experimentally using an approximate point source in motion. The geometric approximation of the pressure field in both the frequency and time domains is first revisited for arbitrary subsonic flow and source motion along the flow axis. The derivation, computed via the method of stationary phase, shows the expected Doppler behavior of the radiated acoustic field due to the source motion acting in conjunction with the convective amplification effect for a stationary source in flow. The model is validated with a minimally intrusive, approximate point source of heat in the Quiet Flow Facility at the NASA Langley Research Center. Within the limitations of the experiment in this open-jet wind tunnel, data generally show agreement with the model across a range of flow speeds and microphone positions for a broad range of frequencies. Where disagreement between measurement and theory is noted, possible causes are discussed.

wind tunnel testing↗

NASA NTRS1992

Search for partial systemic Lyman edges in nearby quasars

IUE archival spectra of nearby quasars with redshifts in the range 0.4-2.3 were searched for changes in the continuum at the systemic Lyman edge positions. Thirty-nine percent of the sample do not show any discontinuities. Twenty-nine percent of the sample show complete Lyman edges at redshifts less than the quasar redshift. These objects have associated narrow absorption lines; hence the intervening gas responsible for the absorption is extrinsic to the quasar and its environment. Twenty-two percent of the sample show Lyman edges at the quasar redshift with associated narrow absorption lines. In these objects the gas is associated with the AGN or its host galaxy. Ten percent of the sample have Lyman edges with no known associated absorption lines. If Lyman edge discontinuities are due to optically thick, geometrically thin accretion disks, which are randomly oriented to the line of sight, these results indicate that the Lyman edge discontinuity, either in emission or absorption, has to be not more than 15 percent in most quasars.

Koratkar, A. P.↗

NASA NTRS2015

Three-Dimensional Piecewise-Continuous Class-Shape Transformation of Wings

Class-Shape Transformation (CST) is a popular method for creating analytical representations of the surface coordinates of various components of aerospace vehicles. A wide variety of two- and three-dimensional shapes can be represented analytically using only a modest number of parameters, and the surface representation is smooth and continuous to as fine a degree as desired. This paper expands upon the original two-dimensional representation of airfoils to develop a generalized three-dimensional CST parametrization scheme that is suitable for a wider range of aircraft wings than previous formulations, including wings with significant non-planar shapes such as blended winglets and box wings. The method uses individual functions for the spanwise variation of airfoil shape, chord, thickness, twist, and reference axis coordinates to build up the complete wing shape. An alternative formulation parameterizes the slopes of the reference axis coordinates in order to relate the spanwise variation to the tangents of the sweep and dihedral angles. Also discussed are methods for fitting existing wing surface coordinates, including the use of piecewise equations to handle discontinuities, and mathematical formulations of geometric continuity constraints. A subsonic transport wing model is used as an example problem to illustrate the application of the methodology and to quantify the effects of piecewise representation and curvature constraints.

Olson, Erik D.↗

NASA NTRS1987

Strain energy release rates of composite interlaminar end-notch and mixed-mode fracture: A sublaminate/ply level analysis and a computer code

A computer code is presented for the sublaminate/ply level analysis of composite structures. This code is useful for obtaining stresses in regions affected by delaminations, transverse cracks, and discontinuities related to inherent fabrication anomalies, geometric configurations, and loading conditions. Particular attention is focussed on those layers or groups of layers (sublaminates) which are immediately affected by the inherent flaws. These layers are analyzed as homogeneous bodies in equilibrium and in isolation from the rest of the laminate. The theoretical model used to analyze the individual layers allows the relevant stresses and displacements near discontinuities to be represented in the form of pure exponential-decay-type functions which are selected to eliminate the exponential-precision-related difficulties in sublaminate/ply level analysis. Thus, sublaminate analysis can be conducted without any restriction on the maximum number of layers, delaminations, transverse cracks, or other types of discontinuities. In conjunction with the strain energy release rate (SERR) concept and composite micromechanics, this computational procedure is used to model select cases of end-notch and mixed-mode fracture specimens. The computed stresses are in good agreement with those from a three-dimensional finite element analysis. Also, SERRs compare well with limited available experimental data.

Valisetty, R. R.↗

NASA NTRS2005

Multi-Dimensional Spectral Difference Method for Unstructured Grids

A new, high-order, conservative, and efficient method for conservation laws on unstructured grids is developed. It combines the best features of structured and unstructured grid methods to attain computational efficiency and geometric flexibility; it utilizes the concept of discontinuous and high-order local representations to achieve conservation and high accuracy; and it is based on the finite-difference formulation for simplicity. Universal reconstructions are obtained by distributing unknowns in a geometrically similar manner for all unstructured cells. Placements of the unknown and flux points with various order of accuracy are given for the line, triangular and tetrahedral elements. The data structure of the new method permits an optimum use of cache memory, resulting in further computational efficiency on modern computers. A new pointer system is developed that reduces memory requirements and simplifies programming for any order of accuracy. Numerical solutions are presented and compared with the exact solutions for wave propagation problems in both two and three dimensions to demonstrate the capability of the method. Excellent agreement has been found. The method is simpler and more efficient than previous discontinuous Galerkin and spectral volume methods for unstructured grids.

Liu, Yen↗

NASA NTRS1996

Systematic Underestimation of Earthquake Magnitudes from Large Intracontinental Reverse Faults: Historical Ruptures Break Across Segment Boundaries

Because most large-magnitude earthquakes along reverse faults have such irregular and complicated rupture patterns, reverse-fault segments defined on the basis of geometry alone may not be very useful for estimating sizes of future seismic sources. Most modern large ruptures of historical earthquakes generated by intracontinental reverse faults have involved geometrically complex rupture patterns. Ruptures across surficial discontinuities and complexities such as stepovers and cross-faults are common. Specifically, segment boundaries defined on the basis of discontinuities in surficial fault traces, pronounced changes in the geomorphology along strike, or the intersection of active faults commonly have not proven to be major impediments to rupture. Assuming that the seismic rupture will initiate and terminate at adjacent major geometric irregularities will commonly lead to underestimation of magnitudes of future large earthquakes.

Rubin, C. M.↗

NASA NTRS1993

(abstract) The SIR-C/X-SAR Mission

The Shuttle Imaging Radar-C and X-Band Synthetic Aperture Radar (SIR-C/X-SAR) is a cooperative experiment between the National Aeronautics and Space Administration (NASA), the German Space Agency (DARA), and the Italian Space Agency (ASI). The experiment is the next evolutionary step in NASA's Spaceborne Imaging Radar (SIR) program that began with the Seasat SAR in 1978, and continued with SAR -A in 1981 and SAR-B in 1984. The program will eventually lead to the Earth Observing System (EOS) SAR later in this decade. SIR-C will provide increased capability over Seasat, SIR-A, and SIR-B by acquiring polarimetric images simultaneously at two microwave frequencies: L-band (wavelength 24 cm) and C-band (wavelength 6 cm). X-SAR will operate at X-band (wavelength 3 cm) with VV polarization, resulting in a three-frequency capability. Because radar backscatter is most strongly influenced by objects comparable in size to the radar wavelength, this multifrequency capability will provide information about the Earth's surface over a wide range of scales not discernable with single-frequency experiments. The polarimetric data will yield quantitative information about the surface geometric structure, vegetation dielectric properties, and surface discontinuities. The first SIR-C/X-SAR flight is planned for early in 1994, with two subsequent flights in different seasons to enable data aquisition under different environmental conditions. SIR-C/X-SAR will collect data for a period of 6 to 9 days during each flight. The instrument will be flown in a 57(deg) inclination orbit with a nomimal orbit altitude of 215 km. This altitude will result in a slightly drifting orbit. The latest status of the SIR-C/X-SAR mission and instrument design, science activities, and expected results will be presented.

SIR-C/XSAR radar backscatter surface geometric str↗

NASA NTRS1992

A curvilinear, anisotropic, p-version, brick finite element based on geometric entities

A 'brick' solid finite element is presently developed on the basis of the p-version analysis, and used to demonstrate the FEM concept of 'geometric entities'. This method eliminates interelement discontinuities between low- and high-order elements, allowing very fine control over the shape-function order in various parts of the model. Attention is given to the illustrative cases of a one-element model of an elliptic pipe, and a square cross-section cantilevered beam.

Hinnant, Howard E.↗

NASA NTRS2005

Numerical Evaluation of P-Multigrid Method for the Solution of Discontinuous Galerkin Discretizations of Diffusive Equations

This paper describes numerical experiments with P-multigrid to corroborate analysis, validate the present implementation, and to examine issues that arise in the implementations of the various combinations of relaxation schemes, discretizations and P-multigrid methods. The two approaches to implement P-multigrid presented here are equivalent for most high-order discretization methods such as spectral element, SUPG, and discontinuous Galerkin applied to advection; however it is discovered that the approach that mimics the common geometric multigrid implementation is less robust, and frequently unstable when applied to discontinuous Galerkin discretizations of di usion. Gauss-Seidel relaxation converges 40% faster than block Jacobi, as predicted by analysis; however, the implementation of Gauss-Seidel is considerably more expensive that one would expect because gradients in most neighboring elements must be updated. A compromise quasi Gauss-Seidel relaxation method that evaluates the gradient in each element twice per iteration converges at rates similar to those predicted for true Gauss-Seidel.

Atkins, H. L.↗

NASA NTRS1992

Analysis for delamination initiation in postbuckled dropped-ply laminates

The compression strength of dropped-ply, graphite-epoxy laminated plates for the delamination mode of failure is studied by analysis and corroborated with experiments. The nonlinear response of the test specimens is modeled by a geometrically nonlinear finite element analysis. The methodology for predicting delamination is based on a quadratic interlaminar stress criterion evaluated at a characteristic distance from the ply drop-off. The compression strength of specimens exhibiting a linear response is greater than the compression strength of specimens with the same layup exhibiting a geometrically nonlinear response. The analyses for both linear and nonlinear response show that severe interlaminar stress gradients occur in the interfaces at the drop-off because of the thickness/stiffness discontinuity. However, these interlaminar stress distributions are altered in the geometrically nonlinear response such that, with increasing load, their growth at the center of the laminate is retarded while their growth near the unloaded supported edge is increased.

Davila, Carlos G.↗

NASA NTRS2000

Experiment Evaluation of Bifurcation in Sands

The basic principles of bifurcation analysis have been established by several investigators, however several issues remain unresolved, specifically how do stress level, grain size distribution, and boundary conditions affect general bifurcation phenomena in pressure sensitive and dilatant materials. General geometrical and kinematics conditions for moving surfaces of discontinuity was derived and applied to problems of instability of solids. In 1962, the theoretical framework of bifurcation by studying the acceleration waves in elasto-plastic (J2) solids were presented. Bifurcation analysis for more specific forms of constitutive behavior was examined by studying localization in pressure-sensitive, dilatant materials, however, analyses were restricted to plane deformation states only. Bifurcation analyses were presented and applied to predict shear band formations in sand under plane strain condition. The properties of discontinuous bifurcation solutions for elastic-plastic solids under axisymmetric and plane strain loading conditions were studied. The study focused on theory, but also references and comparisons to experiments were made. The current paper includes a presentation of a summary of bifurcation analyses for biaxial and triaxial (axisymmetric) loading conditions. The Coulomb model is implemented using incremental piecewise scheme to predict the constitutive relations and shear band inclination angles. Then, a comprehensive evaluation of bifurcation phenomena is presented based on data from triaxial experiments performed under microgravity conditions aboard the Space Shuttle under very low effective confining pressure (0.05 to 1.30 kPa), in which very high peak friction angles (47 to 75 degrees) and dilatancy angles (30 to 31 degrees) were measured. The evaluation will be extended to include biaxial experiments performed on the same material under low (10 kPa) and moderate (100 kPa) confining pressures. A comparison between the behavior under biaxial and triaxial loading conditions will be presented, and related issues concerning influence of confining pressure will be discussed.

Alshibi, Khalid A.↗

NASA NTRS1985

Geometric-optical Modeling of a Conifer Forest Canopy

The objective of this research is to explore how the geometry of trees in forest stands influences the reflectance of the forest as imaged from space. Most plant canopy modeling has viewed the canopy as an assemblage of plane-parallel layers on top of a soil surface. For these models, leaf angle distribution, leaf area index, and the angular transmittance and reflectance of leaves are the primary optical and geometric parameters. Such models are now sufficiently well developed to explain most of the variance in angular reflectance measurements observed from homogeneous plant canopies. However, forest canopies as imaged by airborne and spaceborne scanners exhibit considerable variance at quite a different scale. Brightness values vary strongly from one pixel to the next primarily as a function of the number of trees they contain. At this scale, the forest canopy is nonuniform and discontinuous. This research focuses on a discrete-element, geometric-optical view of the forest canopy.

Strahler, A. H.↗

NASA NTRS1991

Improved finite-element methods for rotorcraft structures

An overview of the research directed at improving finite-element methods for rotorcraft airframes is presented. The development of a modification to the finite element method which eliminates interelement discontinuities is covered. The following subject areas are discussed: geometric entities, interelement continuity, dependent rotational degrees of freedom, and adaptive numerical integration. This new methodology is being implemented as an anisotropic, curvilinear, p-version, beam, shell, and brick finite element program.

Hinnant, Howard E.↗