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At least 469 records · Page 26
All sourcesNASA NTRSDOE OSTI
NASA NTRS2014

Configuration and Assessment of the GISS ModelE2 Contributions to the CMIP5 Archive

We present a description of the ModelE2 version of the Goddard Institute for Space Studies (GISS) General Circulation Model (GCM) and the configurations used in the simulations performed for the Coupled Model Intercomparison Project Phase 5 (CMIP5). We use six variations related to the treatment of the atmospheric composition, the calculation of aerosol indirect effects, and ocean model component. Specifically, we test the difference between atmospheric models that have noninteractive composition, where radiatively important aerosols and ozone are prescribed from precomputed decadal averages, and interactive versions where atmospheric chemistry and aerosols are calculated given decadally varying emissions. The impact of the first aerosol indirect effect on clouds is either specified using a simple tuning, or parameterized using a cloud microphysics scheme. We also use two dynamic ocean components: the Russell and HYbrid Coordinate Ocean Model (HYCOM) which differ significantly in their basic formulations and grid. Results are presented for the climatological means over the satellite era (1980-2004) taken from transient simulations starting from the preindustrial (1850) driven by estimates of appropriate forcings over the 20th Century. Differences in base climate and variability related to the choice of ocean model are large, indicating an important structural uncertainty. The impact of interactive atmospheric composition on the climatology is relatively small except in regions such as the lower stratosphere, where ozone plays an important role, and the tropics, where aerosol changes affect the hydrological cycle and cloud cover. While key improvements over previous versions of the model are evident, these are not uniform across all metrics.

ocean model↗
NASA NTRSDate not supplied

Rational Design of Nanoplasmonic Array Geometries for Biosensing

Background: Molecular diagnostics provide early and accurate diagnosis, which is essential for the prevention and treatment of infectious as well as chronic diseases. These tests are designed to detect disease-specific bioanalytes such as nucleic acid (DNA or RNA) or protein (antigens, antibodies) biomarkers. In the context of infectious disease diagnosis, nucleic acid-based detection methods are known to provide more specific and sensitive results. Here, the presence of a unique sequence belonging to the pathogenic genomic material is targeted to identify species, organism, genera and/or antimicrobial resistant gene markers. The majority of the common nucleic acid based diagnostic techniques require amplification (polymerase chain reaction, isothermal amplification etc.) of the pathogenic genetic material prior to detection impacting diagnostic speed, complexity, and cost thereby limiting ease of use. Thus, the development of simplified nucleic acid-based diagnostics that can be even used in resource-poor settings may hugely benefit patients across the globe. Nanopath is a molecular diagnostics company utilizing a solid-state nanosensor to enable sequence-specific detection of target nucleic acids without the need of amplification. These nanostructures enable ultra-sensitive biomarker detection using geometric, feature-dependent properties highly dependent on the local dielectric environment, allowing them to be sensitive to low concentration binding events. This paper describes an application of this approach to provide highly relevant clinical information within a single doctor’s office visit. Intro: The Nanopath team is in collaboration with NASA (National Aeronautics and Space Administration) and NIST (National Institute of Standards and Technology) to push the bounds of the fundamental physics associated with their biosensing platform. The ability of metals to support electromagnetic surface waves gives rise to surface plasmons when optically illuminated. This property, and its strong sensitivity to changes in the local refractive index, allows for the use of metal nanoparticles as ultra-sensitive transducers. In prior work by members of this team, ensembles of randomly oriented nanoparticles (i.e., colloidal nanorods dispersed on chip) were employed for sequence-specific nucleic acid sensing (1-3). While these particle sensors have the advantage of rapid fabrication, they suffer from low sensitivity and quality factor due to the random particle dispersity. In contrast, in this study we employ ordered array nanoparticle ensembles which can be used to improve sensor sensitivity and figure-of-merit. Study Methods Overview: In this talk, we detail the results of sensing experiments and computational simulations to outline a rational design of the structure of these plasmonic nanoparticle arrays for biomolecular sensing. Through simulation and experiment, we iteratively tailor nanostructure dimension to provide high quality signal and large resonance shifts upon modeled nucleic acid binding. In particular, full-wave electromagnetic simulations were conducted using Lumerical photonic simulation software in which periodic boundary conditions were applied in the x- and y- dimensions for each of the nanoplasmonic sensor geometries. To simulate the resonance response to changes in the bulk solution in contact with the sensor surface, the refractive index of the surrounding media was changed appropriately. Nucleic acid hybridization events were modeled using either using spherical structures approximating the relevant radius of genomic material as estimated by polymer models, or as conformal layers with the known refractive indices for nucleic acids. On the basis of initial simulations, nanosensors were fabricated using traditional electron-beam lithography protocols at NIST. To evaluate consensus between simulations and experiments, bulk sensing experiments were carried out in which the resonance peaks were obtained by submerging the sensors in refractive index standards. Key nanosensor characteristics including resonance peak locations, resonance peak shifts as a function of refractive index, and figure of merit (FOM) of extinction curves were examined between the experimental and simulation results prior to proceeding with simulations on additional geometries and more complex solution conditions, and further device fabrication. This iterative process is repeated toward a rational design of nanoplasmonic array geometries for biosensing optimizing response for targeted disease detection. In summary, this study puts forth a methodology for rational design and characterization of regularly spaced nanoparticle arrays for optics-based biosensing. The results of this study will allow for more informed design of nanostructure geometries towards sequence-specific nucleic acid detection. These improved designs have the potential to improve clinical sensitivity and limit-of-detection across disease indication.

sensor↗
NASA NTRS2023

Thermomechanical Property Prediction of Amorphous and Crystal PEKK via Molecular Dynamics

Traditionally, advanced aerospace composites have been manufactured using thermoset resins. However, recently, thermoplastics have been investigated for use in the manufacturing of composite materials due to their unique manufacturing characteristics. Thermoplastic resins can be reshaped and formed, along with the added benefit of being recyclable, which thermoset resin cannot. Thermoplastic materials undergo a crystallization process during manufacturing which affects the percent crystallinity of the material. The crystallization needs to be understood better to maximize the potential of thermoplastic resins. PEKK is a thermoplastic material with good chemical, thermal, and mechanical loading resistance. PEKK is also a material NASA is interested in for developing new bonded joint technology. The crystalline microstructure of PEKK is at the micrometer length scale, and it is of interest to model the effects of the crystallinity structure on PEKK’s bulk properties. Molecular dynamics (MD) is a simulation tool that allows for property-structure relationships between atomistic structure and nanometer-length portions of a material. This makes MD a useful tool for developing the structure-property relationship of PEKK. However, the micrometer length scale of PEKK’s crystal structure is too large for MD. Thus, a hybrid approach to modeling PEKK’s microstructure is proposed in this work where MD models are built of both the amorphous and crystalline phases of PEKK. The engineering material properties can be obtained using MD at the nanometer length scale. A micromechanics approach can then generate the micrometer length scale of the crystallinity and the effective properties can be homogenized. The objective of this paper is to show the MD model workflow and the MD-predicted properties of PEKK. The properties can then be homogenized with different crystalline percentages to build design graphs that can be used to tailor PEKK for specific composite applications.

poly ether ketone ketone↗
NASA NTRS1997

Cold-Flow Study of Low Frequency Pressure Instability in Hybrid Rocket Motors

Past experience with hybrid rockets has shown that certain motor operating conditions are conducive to the formation of low frequency pressure oscillations, or flow instabilities, within the motor. Both past and present work in the hybrid propulsion community acknowledges deficiencies in the understanding of such behavior, though it seems probable that the answer lies in an interaction between the flow dynamics and the combustion heat release. Knowledge of the fundamental flow dynamics is essential to the basic understanding of the overall stability problem. A first step in this direction was a study conducted at NASA Marshall Space Flight Center (MSFC), centered around a laboratory-scale two dimensional water flow model of a hybrid rocket motor. Principal objectives included: (1) visualization of flow and measurement of flow velocity distributions: (2) assessment of the importance of shear layer instabilities in driving motor pressure oscillations; (3) determination of the interactions between flow induced shear layers with the mainstream flow, the secondary (wall) throughflow, and solid boundaries; (4) investigation of the interactions between wall flow oscillations and the mainstream flow pressure distribution.

Jenkins, Rhonald M.↗
NASA NTRSDate not supplied

Recommended DSMC Collision Model Parameters for Planetary Entry

Hybrid simulation frameworks combining Computational Fluid Dynamics (CFD) and Direct Simulation Monte Carlo (DSMC) are frequently employed to efficiently perform high-fidelity simulations of environments consisting of both continuum and rarified flow. DSMC is a stochastic, particle-based method which solves the fundamental Boltzmann equation and is therefore necessary for high-Knudsen flow where continuum-based assumptions governing CFD break down. However, the DSMC methodology is generally computationally inefficient to model the continuum regime. In a CFD/DSMC hybrid approach, obtaining an accurate, high-fidelity solution hinges on the consistent treatment of transport properties and the thermo-chemical models employed within the two solvers. In principle, in regions where CFD and DSMC are both employed, the same gas mixture under the same conditions should have the same properties, regardless of simulation type. Observed differences should be due to non-equilibrium processes, rather than differences in physical models. The goal of this work is to provide a comprehensive DSMC transport database encompassing the vast majority of known gas species encountered during Earth or other planetary atmospheric entry. This goal is largely possible due to recently performed ab initio quantum chemistry calculations. Combined with other high-fidelity data, the planned database will consist of collision integral data for over 200 neutral and ionized species and over 20000 binary collisions. From these collision integrals, Nelder-Mead optimization is used to compute collision-specific Variable Soft Sphere (VSS) collision model parameters, fitted from 300 K to 20000 K. Initial comparisons of transport properties of relevant equilibrium gas mixtures show great agreement between CFD and DSMC-derived results. The completed database can be readily applied to model binary collisions of any gas mixture containing the included species over the specified temperature range, making it a valuable tool for future planetary probe modeling efforts. An example is shown below in Fig. 1. Equilibrium mixture transport properties for a 35-species mixture composed originally of 10% air and 90% pyrolysis species of a carbon-phenolic ablator material [4] are computed using both fitted VSS Parameters and the original CFD collision integral values. Deviations in computed properties between the two approaches are less than 5% for the entire temperature range.

M. R. Gosma↗
NASA NTRSDate not supplied

Exoplanet Yield Sensitivity for the Hybrid Lyot Coronagraph from end-to-end modeling for LUVOIR-A

NASA's future direct imaging flagship mission will require telescope mirror segmentation to survey a statistically significant population of nearby stellar systems by increasing aperture size beyond that achieved by traditional space-borne monolithic apertures thus far. Segmentation is a path for the size expansion, but it entails a challenge due to the introduction of temporal pupil discontinuities in terms of both phase and amplitude. Modeling of the integrated performance of the coronagraph with the expected dynamical profile of the telescope is an important step toward realistic estimates of the mission's science yields. We present results of a study using the hybrid Lyot coronagraph with a 15-m on-axis, segmented optical telescope assembly (OTA), akin to that of the Large UV / Optical /Infrared (LUVOIR) mission. We have developed a high-fidelity, end-to-end model as part of the Segmented Coronagraph Design and Analysis (SCDA) study that includes diffractive optical propagations at the 1e-10 contrast level across the optical train including the OTA and intermediate re-imaging optics inside the coronagraph instrument. We perform a sensitivity analysis to assess the contrast sensitivity to wavefront perturbations for a set of key telescope terms including segment-level low-order and mid-spatial frequency aberrations and evaluate expected exoplanet yields obtained in the presence of these sets of aberrations. Industry-provided segment-level wavefront aberration datasets involving the following mechanisms are input to the end-to-end model: (1) thermal gradients and accelerations, and (2) telescope dynamics including line-of-sight and segment jitter. Dynamically averaged PSFs in the presence of aberrations are fed into AYO (Altruistic Yield Optimization), a mission design reference simulator, that then assesses the scientific yield sensitivities.

high-contrast imaging↗
NASA NTRS2008

Hybrid LES/RANS Simulation of Transverse Sonic Injection into a Mach 2 Flow

A computational study of transverse sonic injection of air and helium into a Mach 1.98 cross-flow is presented. A hybrid large-eddy simulation / Reynolds-averaged Navier-Stokes (LES/RANS) turbulence model is used, with the two-equation Menter baseline (Menter-BSL) closure for the RANS part of the flow and a Smagorinsky-type model for the LES part of the flow. A time-dependent blending function, dependent on modeled turbulence variables, is used to shift the closure from RANS to LES. Turbulent structures are initiated and sustained through the use of a recycling / rescaling technique. Two higher-order discretizations, the Piecewise Parabolic Method (PPM) of Colella and Woodward, and the SONIC-A ENO scheme of Suresh and Huyhn are used in the study. The results using the hybrid model show reasonably good agreement with time-averaged Mie scattering data and with experimental surface pressure distributions, even though the penetration of the jet into the cross-flow is slightly over-predicted. The LES/RANS results are used to examine the validity of commonly-used assumptions of constant Schmidt and Prandtl numbers in the intense mixing zone downstream of the injection location.

Boles, John A.↗
NASA NTRS2014

Engineering Risk Assessment of Space Thruster Challenge Problem

The Engineering Risk Assessment (ERA) team at NASA Ames Research Center utilizes dynamic models with linked physics-of-failure analyses to produce quantitative risk assessments of space exploration missions. This paper applies the ERA approach to the baseline and extended versions of the PSAM Space Thruster Challenge Problem, which investigates mission risk for a deep space ion propulsion system with time-varying thruster requirements and operations schedules. The dynamic mission is modeled using a combination of discrete and continuous-time reliability elements within the commercially available GoldSim software. Loss-of-mission (LOM) probability results are generated via Monte Carlo sampling performed by the integrated model. Model convergence studies are presented to illustrate the sensitivity of integrated LOM results to the number of Monte Carlo trials. A deterministic risk model was also built for the three baseline and extended missions using the Ames Reliability Tool (ART), and results are compared to the simulation results to evaluate the relative importance of mission dynamics. The ART model did a reasonable job of matching the simulation models for the baseline case, while a hybrid approach using offline dynamic models was required for the extended missions. This study highlighted that state-of-the-art techniques can adequately adapt to a range of dynamic problems.

Assessment↗
NASA NTRS2013

Experimental and Analytical Characterization of the Macromechanical Response for Triaxial Braided Composite Materials

Increasingly, carbon composite structures are being used in aerospace applications. Their highstrength, high-stiffness, and low-weight properties make them good candidates for replacing many aerospace structures currently made of aluminum or steel. Recently, many of the aircraft engine manufacturers have developed new commercial jet engines that will use composite fan cases. Instead of using traditional composite layup techniques, these new fan cases will use a triaxially braided pattern, which improves case performance. The impact characteristics of composite materials for jet engine fan case applications have been an important research topic because Federal regulations require that an engine case be able to contain a blade and blade fragments during an engine blade-out event. Once the impact characteristics of these triaxial braided materials become known, computer models can be developed to simulate a jet engine blade-out event, thus reducing cost and time in the development of these composite jet engine cases. The two main problems that have arisen in this area of research are that the properties for these materials have not been fully determined and computationally efficient computer models, which incorporate much of the microscale deformation and failure mechanisms, are not available. The research reported herein addresses some of the deficiencies present in previous research regarding these triaxial braided composite materials. The current research develops new techniques to accurately quantify the material properties of the triaxial braided composite materials. New test methods are developed for the polymer resin composite constituent and representative composite coupons. These methods expand previous research by using novel specimen designs along with using a noncontact measuring system that is also capable of identifying and quantifying many of the microscale failure mechanisms present in the materials. Finally, using the data gathered, a new hybrid micromacromechanical computer model is created to simulate the behavior of these composite material systems under static and ballistic impact loading using the test data acquired. The model also quantifies the way in which the fiber/matrix interface affects material response under static and impact loading. The results show that the test methods are capable of accurately quantifying the polymer resin under a variety of strain rates and temperature for three loading conditions. The resin strength and stiffness data show a clear rate and temperature dependence. The data also show the hydrostatic stress effects and hysteresis, all of which can be used by researchers developing composite constitutive models for the resins. The results for the composite data reveal noticeable differences in strength, failure strain, and stiffness in the different material systems presented. The investigations into the microscale failure mechanisms provide information about the nature of the different material system behaviors. Finally, the developed computer model predicts composite static strength and stiffness to within 10 percent of the gathered test data and also agrees with composite impact data, where available.

Littell, Justin D.↗
NASA NTRS2008

Aeroacoustic Simulations of Tandem Cylinders with Subcritical Spacing

Tandem cylinders are being studied because they model a variety of component level interactions of landing gear. The present effort is directed at the case of two identical cylinders with their centroids separated in the streamwise direction by 1.435 diameters. Experiments in the Basic Aerodynamic Research Tunnel and Quiet Flow Facility at NASA Langley Research Center have provided an extensive experimental database of the nearfield flow and radiated noise. The measurements were conducted at a Mach number of 0.1285 and Reynolds number of 1.66x10(exp 5) based on the cylinder diameter. A trip was used on the upstream cylinder to insure a fully turbulent flow separation and, hence, to simulate a major aspect of high Reynolds number flow. The parallel computational effort uses the three-dimensional Navier-Stokes solver CFL3D with a hybrid, zonal turbulence model that turns off the turbulence production term everywhere except in a narrow ring surrounding solid surfaces. The experiments exhibited an asymmetry in the surface pressure that was persistent despite attempts to eliminate it through small changes in the configuration. To model the asymmetry, the simulations were run with the cylinder configuration at a nonzero but small angle of attack. The computed results and experiments are in general agreement that vortex shedding for the spacing studied herein is weak relative to that observed at supercritical spacings. Although the shedding was subdued in the simulations, it was still more prominent than in the experiments. Overall, the simulation comparisons with measured near-field data and the radiated acoustics are reasonable, especially if one is concerned with capturing the trends relative to larger cylinder spacings. However, the flow details of the 1.435 diameter spacing have not been captured in full even though very fine grid computations have been performed. Some of the discrepancy may be associated with the simulation s inexact representation of the experimental configuration, but numerical and flow modeling errors are also likely contributors to the observed differences.

Lockard, David P.↗
NASA NTRS2007

Tandem Cylinder Noise Predictions

In an effort to better understand landing-gear noise sources, we have been examining a simplified configuration that still maintains some of the salient features of landing-gear flow fields. In particular, tandem cylinders have been studied because they model a variety of component level interactions. The present effort is directed at the case of two identical cylinders spatially separated in the streamwise direction by 3.7 diameters. Experimental measurements from the Basic Aerodynamic Research Tunnel (BART) and Quiet Flow Facility (QFF) at NASA Langley Research Center (LaRC) have provided steady surface pressures, detailed off-surface measurements of the flow field using Particle Image Velocimetry (PIV), hot-wire measurements in the wake of the rear cylinder, unsteady surface pressure data, and the radiated noise. The experiments were conducted at a Reynolds number of 166 105 based on the cylinder diameter. A trip was used on the upstream cylinder to insure a fully turbulent shedding process and simulate the effects of a high Reynolds number flow. The parallel computational effort uses the three-dimensional Navier-Stokes solver CFL3D with a hybrid, zonal turbulence model that turns off the turbulence production term everywhere except in a narrow ring surrounding solid surfaces. The current calculations further explore the influence of the grid resolution and spanwise extent on the flow and associated radiated noise. Extensive comparisons with the experimental data are used to assess the ability of the computations to simulate the details of the flow. The results show that the pressure fluctuations on the upstream cylinder, caused by vortex shedding, are smaller than those generated on the downstream cylinder by wake interaction. Consequently, the downstream cylinder dominates the noise radiation, producing an overall directivity pattern that is similar to that of an isolated cylinder. Only calculations based on the full length of the model span were able to capture the complete decay in the spanwise correlation, thereby producing reasonable noise radiation levels.

Lockard, David P.↗
NASA NTRS2004

Numerical Study of Flow Past a Circular Cylinder Using RANS, Hybrid RANS/LES and PANS Formulations

Two multiscale type turbulence models are implemented in the PAB3D solver. The models are based on modifying the Reynolds Averaged Navier-Stokes (RANS) equations. The first scheme is a hybrid RANS/LES model utilizing the two-equation (k(sub epsilon)) model with a RANS/LES transition function dependent on grid spacing and the computed turbulence length scale. The second scheme is a modified version of the partially averaged Navier-Stokes (PANS) model, where the unresolved kinetic energy parameter (f(sub k)) is allowed to vary as a function of grid spacing and the turbulence length scale. Solutions from these models are compared to RANS results and experimental data for a stationary and rotating cylinder. The parameter f(sub k) varies between zero and one and has the characteristic to be equal to one in the viscous sub layer, and when the RANS turbulent viscosity becomes smaller than the LES viscosity. The formulation, usage methodology, and validation example are presented to demonstrate the enhancement of PAB3D's time-accurate and turbulence modeling capabilities. The models are compared to RANS results and experimental data for turbulent separated flows (TS) and laminar separated flows (LS) around stationary and rotating cylinders. For a stationary cylinder, the TS case is accurately simulated using the general two-equation k(sub epsilon) turbulence model (eddy-viscosity model). PAB3D accurately predicts the drag coefficient (CD), lift coefficient (CL) and the Strouhal number (St). The LS case was a challenge for the RANS computation with an eddy-viscosity turbulence model. The RANS/LES and PANS performed well and showed marked improvements over the RANS solution. The modified PANS model was the most accurate. For the rotating cylinder, the spin ratio varied from zero to one, and the PANS results were in good agreement with published experimental data. RANS/LES and PANS capture both temporal and spatial fluctuations and produce large-scale structures that do not occur in the RANS simulation. The current results show promise for the capability of PANS in simulating unsteady and complex flow phenomena.

Elmiligui, Alaa A.↗
NASA NTRS2016

NASA Environmentally Responsible Aviation Hybrid Wing Body Flow-Through Nacelle Wind Tunnel CFD

Wind tunnel tests of a 5.75 scale model of the Boeing Hybrid Wing Body (HWB) configuration were conducted in the NASA Langley Research Center (LaRC) 14x22 and NASA Ames Research Center (ARC) 40x80 low speed wind tunnels as part of the NASA Environmentally Responsible Aviation (ERA) Project. Computational fluid dynamics (CFD) simulations of the flow-through nacelle (FTN) configuration of this model were performed before and after the testing. This paper presents a summary of the experimental and CFD results for the model in the cruise and landing configurations.

Wind Tunnel Testing↗
NASA NTRS2016

NASA Environmentally Responsible Aviation Hybrid Wing Body Flow-Through Nacelle Wind Tunnel CFD

Wind tunnel tests of a 5.75% scale model of the Boeing Hybrid Wing Body (HWB) configuration were conducted in the NASA Langley Research Center (LaRC) 14'x22' and NASA Ames Research Center (ARC) 40'x80' low speed wind tunnels as part of the NASA Environmentally Responsible Aviation (ERA) Project. Computational fluid dynamics (CFD) simulations of the flow-through nacelle (FTN) configuration of this model were performed before and after the testing. This paper presents a summary of the experimental and CFD results for the model in the cruise and landing configurations.

Environmentally Responsible Aviation↗
NASA NTRS2023

Numerical Investigation of C L,max Prediction on the NASA High-Lift Common Research Model

An assessment of a Hybrid RANS/LES (HRLES) approach for C L,max prediction is presented for the NASA High-Lift Common Research Model (CRM-HL). Both free air and wind tunnel configurations of the CRM-HL are investigated and the results are compared to the QinetiQ wind tunnel experiments and two other numerical approaches: Reynolds Averaged Navier-Stokes (RANS) and Wall-Modeled Large Eddy Simulations (WMLES). For the free-air configuration, HRLES is shown to address some of the known shortcomings with RANS and prevent inboard and outboard flow separation particularly in the region of C L,max and post-stall. To achieve these improvements over RANS, LES-appropriate grids and numerical discretizations are required. It was also found that when applying HRLES to a RANS best practice grid and numerics that the HRLES method significantly underperformed RANS. For the in-tunnel configuration, HRLES showed good agreement with the loads, surface pressure and oil-flow photographs obtained in the experiment. HRLES was able to improve upon the RANS simulations, which showed a sharp loss of lift at the two highest angles-of-attack due to large scale inboard and outboard separation on the wing, by correctly predicting the corner flow separation and showing remarkably close agreement in the flow topologies with the experiment.

TTT↗
NASA NTRS1976

On a 3-D singularity element for computation of combined mode stress intensities

A special three-dimensional singularity element is developed for the computation of combined modes 1, 2, and 3 stress intensity factors, which vary along an arbitrarily curved crack front in three dimensional linear elastic fracture problems. The finite element method is based on a displacement-hybrid finite element model, based on a modified variational principle of potential energy, with arbitrary element interior displacements, interelement boundary displacements, and element boundary tractions as variables. The special crack-front element used in this analysis contains the square root singularity in strains and stresses, where the stress-intensity factors K(1), K(2), and K(3) are quadratically variable along the crack front and are solved directly along with the unknown nodal displacements.

Atluri, S. N.↗
NASA NTRS1977

A NASTRAN DMAP alter for the coupling of modal and physical coordinate substructures

A method is described to derive a generalized coordinate model consisting of flexible cantilever modes and rigid body modes from a physical coordinate model using a direct matrix abstraction procedure alter to rigid format 3. This model can readily be coupled to other substructures using modal synthesis techniques. It allows the use of a reduced size model for structural analyses while maintaining the capability of recovering the accelerations, forces, stresses, etc., from the original, large, complex model. This output recovery is accomplished with the use of a loads transformation matrix which relates the output parameters to the modal coordinate accelerations. In addition, a method is described to synthesize structural models consisting of hybrid coordinates for use in dynamic response analyses where one structure is described using physical coordinates and the other using generalized modal coordinates.

Wilson, T. L.↗
NASA NTRS1979

The Sr and Nd isotopic record of Apollo 12 basalts - Implications for lunar geochemical evolution

Alkali, alkaline earth, and rare earth element data are reported for several Apollo 12 basalts which are representative of the four Apollo 12 magma types. Results confirm the heterogeneity of the lunar mantle and show that the Sm/Nd ratio of at least the Apollo 12 ilmenite basalts was decreased by 13-24% during magma genesis. In addition, whole mare basalt Sm-Nd data are not collinear on an isochron diagram; thus it is no longer possible to explain these data via mixing of 'primitive material' and 'early differentiates' as in the hybridization and assimilation models.

Nyquist, L. E.↗