Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “Matrix elements”

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.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 1,261 records · Page 70

Free-vibration characteristics and correlation of a space station split-blanket solar array

Two methods for studying the free-vibration characteristics of a large split-blanket solar array in a zero-g cantilevered configuration are presented. The zero-g configuration corrresponds to an on-orbit configuration of the Space Station solar array. The first method applies the equations of continuum mechanics to determine the natural frequencies of the array; the second uses the finite element method program, MSC/NASTRAN. The stiffness matrix from the NASTRAN solution was found to be erroneously grounded. The results from the two methods are compared. It is concluded that the grounding does not seriously compromise the solution to the elastic modes of the solar array. However, the correct rigid body modes need to be included to obtain the correct dynamic model.

Carney, Kelly S.↗

A unique set of micromechanics equations for high-temperature metal matrix composites

A unique set of micromechanic equations is presented for high-temperature metal matrix composites. The set includes expressions to predict mechanical properties, thermal properties and constituent microstresses for the unidirectional fiber reinforced ply. The equations are derived based on a mechanics of materials formulation assuming a square array unit cell model of a single fiber, surrounding matrix and an interphase to account for the chemical reaction which commonly occurs between fiber and matrix. A three-dimensional finite element analysis was used to perform a preliminary validation of the equations. Excellent agreement between properties predicted using the micromechanics equations and properties simulated by the finite element analyses are demonstrated. Implementation of the micromechanics equations as part of an integrated computational capability for nonlinear structural analysis of high temperature multilayered fiber composites is illustrated.

Hopkins, Dale A.↗

Free-vibration characteristics and correlation of a Space Station split-blanket solar array

Two methods for studying the free-vibration characteristics of a large split-blanket solar array in a zero-g cantilevered configuration are presented. The zero-g configuration corresponds to an on-orbit configuration of the Space Station solar array. The first method applies the equations of continuum mechanics to determine the natural frequencies of the array; the second uses the finite element method program, MSC/NASTRAN. The stiffness matrix from the NASTRAN solution was found to be erroneously grounded. The results from the two methods are compared. It is concluded that the grounding does not seriously compromise the solution to the elastic modes of the solar array. However, the correct rigid body modes need to be icluded to obtain the correct dynamic model.

Carney, Kelly S.↗

Vibration transmission through rolling element bearings. I - Bearing stiffness formulation. II - System studies

How vibratory motion can be transmitted from the rotating shaft to the casing and other connecting structures in rotating mechanical equipment is addressed here by developing a new mathematical model of precision rolling element bearings. A new grating stiffness matrix is proposed in order to demonstrate a coupling between the shaft bending motion and the flexural motion of the casing plate. It is shown that the translational bearing stiffness coefficients currently used in rotor dynamic models are a small subset of the proposed matrix. The theory is validated by examples, and the proposed bearing formulation is then extended to demonstrate its superiority over existing models in vibration transmission analyses. It is shown that the model can easily be incorporated into analytical or numerical models typically used for dynamic analyses.

Lim, T. C.↗

Solution of free-boundary problems using finite-element/Newton methods and locally refined grids - Application to analysis of solidification microstructure

A new method is presented for the solution of free-boundary problems using Lagrangian finite element approximations defined on locally refined grids. The formulation allows for direct transition from coarse to fine grids without introducing non-conforming basis functions. The calculation of elemental stiffness matrices and residual vectors are unaffected by changes in the refinement level, which are accounted for in the loading of elemental data to the global stiffness matrix and residual vector. This technique for local mesh refinement is combined with recently developed mapping methods and Newton's method to form an efficient algorithm for the solution of free-boundary problems, as demonstrated here by sample calculations of cellular interfacial microstructure during directional solidification of a binary alloy.

Tsiveriotis, K.↗

Dynamic analysis of Space Shuttle/RMS configuration using continuum approach

The initial assembly of Space Station Freedom involves the Space Shuttle, its Remote Manipulation System (RMS) and the evolving Space Station Freedom. The dynamics of this coupled system involves both the structural and the control system dynamics of each of these components. The modeling and analysis of such an assembly is made even more formidable by kinematic and joint nonlinearities. The current practice of modeling such flexible structures is to use finite element modeling in which the mass and interior dynamics is ignored between thousands of nodes, for each major component. The model characteristics of only tens of modes are kept out of thousands which are calculated. The components are then connected by approximating the boundary conditions and inserting the control system dynamics. In this paper continuum models are used instead of finite element models because of the improved accuracy, reduced number of model parameters, the avoidance of model order reduction, and the ability to represent the structural and control system dynamics in the same system of equations. Dynamic analysis of linear versions of the model is performed and compared with finite element model results. Additionally, the transfer matrix to continuum modeling is presented.

Ramakrishnan, Jayant↗

A phyllosilicate-sulfide vein in Kaidun

A fragment of a carbonaceous chondrite (#53.12, maximal dimension about 2 mm) containing a phyllosilicate-sulfide vein was found during an inspection of small pieces of the Kaidun meteorite. Phyllosilicate veins are apparently rare in carbonaceous chondrites and have so far only been reported from the Y82162 CI chondrite. In hand sample the vein was visible on two perpendicular faces. The polished section prepared from one side displays a complex structure. A single vein, 150 microns in width, bifurcates, and each branch narrows toward a large rounded object (RO). The section contains abundant ROs, most of them less than or equal to 100 microns in diameter. The vein has sharp contacts to the surrounding matrix, whereas the RO contacts are diffuse. The phyllosilicate in the main vein has a massive texture along the contact, which becomes platy toward the vein center where the crystals protrude into an open space. The texture of the largest RO resembles that of a barred olivine (BO) chondrule. Some of the smaller ROs also texturally resemble chondrules. The BO chondrule contains rounded sulfide-silicate objects and small metal grains covered by oxides. Phyllosilicates of the main vein consist mainly of serpentine. The phyllosilicate near the contact with the matrix has low contents of minor elements and a high Mg/Fe ratio. The composition changes in a regular manner toward the center: Al, Na, Ca, Ni, and S increase, indicating increasing amounts of sulfates admixed. The phyllosilicate vein could only have formed after a substantial rock was formed. Mechanical stress probably opened a crack that was subsequently filled by phyllosilicate, pyrrhotite, and finally by a (Fe,Mg)-sulfate. The source of the matter mobilized to form the vein could have been within the rock itself or outside. No compositional or mineralogical zoning is apparent at the vein-rock contacts. The nature of the transporting agent (liquid H2O or vapor) must also remain an enigma. M. Zolensky has recently observed similar phyllosilicate-filled veins in dark, wet clasts in the Al Rais CR chondrite.

Ivanov, A. V.↗

A Note on Multigrid Theory for Non-nested Grids and/or Quadrature

We provide a unified theory for multilevel and multigrid methods when the usual assumptions are not present. For example, we do not assume that the solution spaces or the grids are nested. Further, we do not assume that there is an algebraic relationship between the linear algebra problems on different levels. What we provide is a computationally useful theory for adaptively changing levels. Theory is provided for multilevel correction schemes, nested iteration schemes, and one way (i.e., coarse to fine grid with no correction iterations) schemes. We include examples showing the applicability of this theory: finite element examples using quadrature in the matrix assembly and finite volume examples with non-nested grids. Our theory applies directly to other discretizations as well.

Douglas, C. C.↗

The Effect of Alloying on Topologically Close Packed Phase Instability in Advanced Nickel-Based Superalloy Rene N6

An investigation was conducted to describe topologically close packed (TCP) phase instability as a function of composition in the advanced Ni-base superalloy Rene N6. TCP phases are detrimental to overall high-temperature performance of Ni-base superalloys because of their brittle nature and because they deplete the Ni-rich matrix of potent solid solution strengthening elements. Thirty-four variations of polycrystalline Rene N6 determined from a design-of-experiments approach were cast and homogenized at 1315"C for 80 hours followed by exposure at 10930C for 400 hours to promote TCP formation. The alloys had the following composition ranges in atomic percent: Co 10.61 to 16.73%, Mo 0.32 to 1.34%, W 1.85 to 2.52%, Re 1.80 to 2.1 1 %, Ta 2.36 to 3.02%, Al 11.90 to 14.75%, and Cr 3.57 to 6.23%. Physical and chemical characteristics of all n-ticrostructures obtained were described using various analytical techniques. From these observations, a mathematical description of TCP occurrence (omega and P phase) was generated for polycrystalline Rene N6.

Ritzert, Frank↗

Evidence of Microfossils in Carbonaceous Chondrites

Investigations have been carried out on freshly broken, internal surfaces of the Murchison, Efremovka and Orgueil carbonaceous chondrites using Scanning Electron Microscopes (SEM) in Russia and the Environmental Scanning Electron Microscope (ESEM) in the United States. These independent studies on different samples of the meteorites have resulted in the detection of numerous spherical and ellipsoidal bodies (some with spikes) similar to the forms of uncertain biogenicity that were designated "organized elements" by prior researchers. We have also encountered numerous complex biomorphic microstructures in these carbonaceous chondrites. Many of these complex bodies exhibit diverse characteristics reminiscent of microfossils of cyanobacteria such as we have investigated in ancient phosphorites and high carbon rocks (e.g. oil shales). Energy Dispersive Spectroscopy (EDS) analysis and 2D elemental maps shows enhanced carbon content in the bodies superimposed upon the elemental distributions characteristic of the chondritic matrix. The size, distribution, composition, and indications of cell walls, reproductive and life cycle developmental stages of these bodies are strongly suggestive of biology' These bodies appear to be mineralized and embedded within the meteorite matrix, and can not be attributed to recent surface contamination effects. Consequently, we have interpreted these in-situ microstructures to represent the lithified remains of prokaryotes and filamentous cyanobacteria. We also detected in Orgueil microstructures morphologically similar to fibrous kerite crystals. We present images of many biomorphic microstructures and possible microfossils found in the Murchison, Efremovka, and Orgueil chondrites and compare these forms with known microfossils from the Cambrian phosphate-rich rocks (phosphorites) of Khubsugul, Northern Mongolia.

Hoover, Richard B.↗

Evidence for Microfossils in Ancient Rocks and Meteorites

The McKay et all. detection of chemical biomarkers and possible microfossils in an ancient meteorite from Mars (ALH84001) stimulated research in several areas of importance to the newly emerging field of Astrobiology. Their report resulted in a search for additional evidence of microfossils in ancient terrestrial rocks and meteorites. These studies of ancient rocks and meteorites were conducted independently (and later collaboratively) in the United States and Russia using the SEM, Environmental Scanning Electron Microscope (ESEM), and Field Emission Scanning Electron Microscope (FESEM). We have encountered in-situ in freshly broken carbonaceous chondrites a large number of complex microstructures that appear to be lithified microbial forms. The meteoritic microstructures have characteristics similar to the lithified remains of filamentous cyanobacteria and bacterial microfossils we have found in ancient phosphorites, ancient graphites and oil shales. Energy Dispersive Spectroscopy (EDS) and Link microprobe analysis shows the possible microfossils have a distribution of chemical elements characteristic of the meteorite rock matrix, although many exhibit a superimposed carbon enhancement. We have concluded that the mineralized bodies encountered embedded in the rock matrix of freshly fractured meteoritic surfaces can not be dismissed as recent surface contaminants. Many of the forms found in-situ in the Murchison, Efremovka, and Orgueil carbonaceous meteorites are strikingly similar to microfossils of coccoid bacteria, cyanobacteria and fungi such as we have found in the Cambrian phosphorites of Khubsugul, Mongolia and high carbon Phanerozoic and Precambrian rocks of the Siberian and Russian Platforms.

Hoover, Richard B.↗

Migration Processes and Volatiles Inventory to the Inner Planets

Comets and asteroids colliding with the terrestrial planets can deliver volatiles and organic or prebiotic compounds to the planets, thereby depositing on the planets the fundamental building-blocks for life. The inner planets contain heavier and cosmically less abundant elements in an iron-silicate matrix than the giant planets. This can be caused by the following three mechanisms: uneven fractionation and condensation in the accretionary disk; unequal degree of degassing of the composed matter; and heterogeneous accretion. Asteroid-size bodies consisting of the last low-temperature condensates (similar to most primitive chondritic meteorites, and enriched in hydrated silicates and trapped gases) are believed to have fallen onto the inner planets during the process of the giant planets formation. The relative contribution of either endogenous (i.e. outgassing) or exogenous (i.e. asteroid/comet collisions) sources is difficult to assess, although it is constrained by the pattern of noble gas abundances in the planetary atmospheres.

Marov, M. Y.↗

Active Piezoelectric Vibration Control of Subscale Composite Fan Blades

As part of the Fundamental Aeronautics program, researchers at NASA Glenn Research Center (GRC) are investigating new technologies supporting the development of lighter, quieter, and more efficient fans for turbomachinery applications. High performance fan blades designed to achieve such goals will be subjected to higher levels of aerodynamic excitations which could lead to more serious and complex vibration problems. Piezoelectric materials have been proposed as a means of decreasing engine blade vibration either through a passive damping scheme, or as part of an active vibration control system. For polymer matrix fiber composite blades, the piezoelectric elements could be embedded within the blade material, protecting the brittle piezoceramic material from the airflow and from debris. To investigate this idea, spin testing was performed on two General Electric Aviation (GE) subscale composite fan blades in the NASA GRC Dynamic Spin Rig Facility. The first bending mode (1B) was targeted for vibration control. Because these subscale blades are very thin, the piezoelectric material was surface-mounted on the blades. Three thin piezoelectric patches were applied to each blade two actuator patches and one small sensor patch. These flexible macro-fiber-composite patches were placed in a location of high resonant strain for the 1B mode. The blades were tested up to 5000 rpm, with patches used as sensors, as excitation for the blade, and as part of open- and closed-loop vibration control. Results show that with a single actuator patch, active vibration control causes the damping ratio to increase from a baseline of 0.3% critical damping to about 1.0% damping at 0 RPM. As the rotor speed approaches 5000 RPM, the actively controlled blade damping ratio decreases to about 0.5% damping. This occurs primarily because of centrifugal blade stiffening, and can be observed by the decrease in the generalized electromechanical coupling with rotor speed.

Duffy, Kirsten P.↗

Copper-Multiwall Carbon Nanotubes and Copper-Diamond Composites for Advanced Rocket Engines

This paper reports on the research effort to improve the thermal conductivity of the copper-based alloy NARloy-Z (Cu-3 wt.%Ag-0.5 wt.% Zr), the state-of-the-art alloy used to make combustion chamber liners in regeneratively-cooled liquid rocket engines, using nanotechnology. The approach was to embed high thermal conductivity multiwall carbon nanotubes (MWCNTs) and diamond (D) particles in the NARloy-Z matrix using powder metallurgy techniques. The thermal conductivity of MWCNTs and D have been reported to be 5 to 10 times that of NARloy-Z. Hence, 10 to 20 vol. % MWCNT finely dispersed in NARloy-Z matrix could nearly double the thermal conductivity, provided there is a good thermal bond between MWCNTs and copper matrix. Quantum mechanics-based modeling showed that zirconium (Zr) in NARloy-Z should form ZrC at the MWCNT-Cu interface and provide a good thermal bond. In this study, NARloy-Z powder was blended with MWCNTs in a ball mill, and the resulting mixture was consolidated under high pressure and temperature using Field Assisted Sintering Technology (FAST). Microstructural analysis showed that the MWCNTs, which were provided as tangles of MWCNTs by the manufacturer, did not detangle well during blending and formed clumps at the prior particle boundaries. The composites made form these powders showed lower thermal conductivity than the base NARloy-Z. To eliminate the observed physical agglomeration, tangled multiwall MWCNTs were separated by acid treatment and electroless plated with a thin layer of chromium to keep them separated during further processing. Separately, the thermal conductivities of MWCNTs used in this work were measured, and the results showed very low values, a major factor in the low thermal conductivity of the composite. On the other hand, D particles embedded in NARloy-Z matrix showed much improved thermal conductivity. Elemental analysis showed migration of Zr to the NARloy-Z-D interface to form ZrC, which appeared to provide a low contact thermal resistance. These results are consistent with the quantum mechanics-based model predictions. NARloy-Z-D composites have relatively high thermal conductivities and are promising for further development.

Bhat, Biliyar N.↗

Copper Multiwall Carbon Nanotubes and Copper-Diamond Composites for Advanced Rocket Engines

This paper reports on the research effort to improve the thermal conductivity of the copper-based alloy NARloy-Z (Cu-3 wt.%Ag-0.5 wt.% Zr), the state-of-the-art alloy used to make combustion chamber liners in regeneratively-cooled liquid rocket engines, using nanotechnology. The approach was to embed high thermal conductivity multiwall carbon nanotubes (MWCNTs) and diamond (D) particles in the NARloy-Z matrix using powder metallurgy techniques. The thermal conductivity of MWCNTs and D have been reported to be 5 to 10 times that of NARloy-Z. Hence, 10 to 20 vol. % MWCNT finely dispersed in NARloy-Z matrix could nearly double the thermal conductivity, provided there is a good thermal bond between MWCNTs and copper matrix. Quantum mechanics-based modeling showed that zirconium (Zr) in NARloy-Z should form ZrC at the MWCNT-Cu interface and provide a good thermal bond. In this study, NARloy-Z powder was blended with MWCNTs in a ball mill, and the resulting mixture was consolidated under high pressure and temperature using Field Assisted Sintering Technology (FAST). Microstructural analysis showed that the MWCNTs, which were provided as tangles of MWCNTs by the manufacturer, did not detangle well during blending and formed clumps at the prior particle boundaries. The composites made form these powders showed lower thermal conductivity than the base NARloy-Z. To eliminate the observed physical agglomeration, tangled multiwall MWCNTs were separated by acid treatment and electroless plated with a thin layer of chromium to keep them separated during further processing. Separately, the thermal conductivities of MWCNTs used in this work were measured, and the results showed very low values, a major factor in the low thermal conductivity of the composite. On the other hand, D particles embedded in NARloy-Z matrix showed much improved thermal conductivity. Elemental analysis showed migration of Zr to the NARloy-Z-D interface to form ZrC, which appeared to provide a low contact thermal resistance. These results are consistent with the quantum mechanics-based model predictions. NARloy-Z-D composites have relatively high thermal conductivities and are promising for further development.

Bhat, Biliyar N.↗

Analysis and Characterization of Damage Utilizing an Orthotropic Generalized Composite Material Model Suitable for Use in Impact Problems

The need for accurate material models to simulate the deformation, damage and failure of polymer matrix composites under impact conditions is becoming critical as these materials are gaining increased usage in the aerospace and automotive communities. In order to address a series of issues identified by the aerospace community as being desirable to include in a next generation composite impact model, an orthotropic, macroscopic constitutive model incorporating both plasticity and damage suitable for implementation within the commercial LS-DYNA computer code is being developed. The plasticity model is based on extending the Tsai-Wu composite failure model into a strain hardening-based orthotropic plasticity model with a non-associative flow rule. The evolution of the yield surface is determined based on tabulated stress-strain curves in the various normal and shear directions and is tracked using the effective plastic strain. To compute the evolution of damage, a strain equivalent semi-coupled formulation is used in which a load in one direction results in a stiffness reduction in multiple material coordinate directions. A detailed analysis is carried out to ensure that the strain equivalence assumption is appropriate for the derived plasticity and damage formulations that are employed in the current model. Procedures to develop the appropriate input curves for the damage model are presented and the process required to develop an appropriate characterization test matrix is discussed.

Impact↗

Effects of Adiabatic Heating on the High Strain Rate Deformation of Polymer Matrix Composites

Polymer matrix composites (PMCs) are increasingly being used in aerospace structures that are expected to experience complex dynamic loading conditions throughout their lifetime. As such, a detailed understanding of the high strain rate behavior of the constituents, particularly the strain rate, temperature, and pressure dependent polymer matrix, is paramount. In this paper, preliminary efforts in modeling experimentally observed temperature rises due to plastic deformation in PMCs subjected to dynamic loading are presented. To this end, an existing isothermal viscoplastic polymer constitutive formulation is extended to model adiabatic conditions by incorporating temperature dependent elastic properties and modifying the components of the inelastic strain rate tensor to explicitly depend on temperature. It is demonstrated that the modified polymer constitutive model is capable of capturing strain rate and temperature dependent yield as well as thermal softening associated with the conversion of plastic work to heat at high rates of strain. The modified constitutive model is then embedded within a strength of materials based micromechanics framework to investigate the manifestation of matrix thermal softening, due to the conversion of plastic work to heat, on the high strain rate response of a T700Epon 862 (T700E862) unidirectional composite. Adiabatic model predictions for high strain rate composite longitudinal tensile, transverse tensile, and in-plane shear loading are presented. Results show a substantial deviation from isothermal conditions; significant thermal softening is observed for matrix dominated deformation modes (transverse tension and in-plane shear), highlighting the importance of accounting for the conversion of plastic work to heat in the polymer matrix in the high strain rate analysis of PMC structures.

polymer matrix composites↗

Multiphysics Modeling of Electrode Dissolution under Hydrodynamic Conditions in Low Conductivity Water

Efficient plug-flow electrochemical reactors are characterized by their ability to effectively convert species with significant ionic strength and/or with the assistance of a well-behaved electrolyte. Because of the classic electroconductivity requirement, electrochemical reactors are not particularly attractive options for applications with low-conductivity conditions, especially for low-pressure feeds. However, these reactors can still find application in dedicated processes such as ultra-clean water conditioning and biological-coupled separation systems. Consequently, a multi-physics model was developed using COMSOL Multiphysics to characterize different reactor-design conditions based on the Tertiary Current Distribution which accounts for the effects of expected variations in electrolyte composition and ionic strength on the electrochemical process, as well as solution resistance and electrode kinetics. The modelling framework presented here employs single-phase laminar fluid flow, the Nernst-Planck equation, the water-based electroneutrality condition, and concentration-dependent overpotentials. This investigation particularly explores the electrolysis process of “anodic dissolution,” in which elemental species dissociate from the solid matrix of the electrode and enter the liquid phase of the electrolyte as soluble ions. The reactor configuration of interest has a rectangular parallel-electrode design and is operated galvanostatically. A series of parametric studies are carried out to inspect the response of the system when hydrodynamic, kinetic, and geometric conditions are changed. The parametric sweep resulted in variable effluent concentrations and system voltage, which reveal underlaying optimization patterns for electrode dissolution in low conductivity water.

Multiphysics↗