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At least 469 records · Page 26
All sourcesNASA NTRSDOE OSTI
DOE OSTI2019

Recovery of Rare Earth Elements from Coal Mining Waste Materials

The objective of this proposed project was to locate coal overburden material that had rare earth elements (REEs) at concentrations of 300 ppm or higher. After securing the feedstock the next goal was to efficiently extract and purify the feedstocks to a purity of greater than 95%. A techno economic analysis was conducted to determine the economic viability of mining and processing REEs associated with Appalachian coal deposits. All aspects of mining, mineral processing, by-product potential, waste management, permitting and economics were examined. Attention was paid to the separation, degree of purification and marketing of Rare Earth elements. Along with REEs we evaluated the economics of the recovery of other metals of interest aong with the REEs. Our site location chosen was at the Jeddo Coal Site near Hazleton, Pennsylvania. The primary site was at the Upper Leigh High Mine. However, that changed to the North Eckley Mine site. We have analyzed a third site that will now be our second alternative to North Eckley. That site is the Highland mine site. This site is in a similar basin as the North Eckley site. During this project we evaluated various acids and extraction conditions. We have settled on using HCl as the acid of choice. One of the advantages of using HCl is it allows for easy removal of the highest contaminating metal, iron. When iron reacts with HCl in the presence of high chlorides it creates the anion complex FeCl 4 -1 . This FeCl 4 -1 complex will bind with an anion exchange resin. Greater than 99.8% of the iron is removed with this technique. Once the FeCl 4 -1 complex is bound to the anion exchange resin it can be released easily by just passing water over it. This water dilutes the FeCl 4 -1 to form FeCl 3 which is not anionic and therefore not attracted to the anion exchange resin. The FeCl 3 solution is a popular water flocculating agent used all over the world for water purification. We plan on this being one of our products produced. One of our goals was to create a multipurpose facility that was capable of handling multiple feedstocks. The proposed multipurpose facility will be able process all coal biproducts and coal products. These include 1.) clays that can easily be leached with ion exchange or acid 2.) Hard mineral deposits that can be leached with high pressure acid digestion 3.) Fly ash can be leached in the high-pressure acid digestion reactor. Fly ash is not a focus of this proposal but, the beneficial aspect of its utilization in this design cannot be overlooked. 4.) Acid Mine Drainage (AMD) Sludge is a high source of REE’s and can easily be dissolved to form a pregnant leach solution. Not shown on this simplified block flow diagram but crucial to its success is the recycle of acids. Our REE separation system is a continuous ion exchange process. The first stage is the separation of the non-REEs from the REEs. This is accomplished because the REEs are relatively larger than most of the non-REEs and typically have higher oxidation states (+3) than the non-REEs. In this step all the elements stick onto the column. However, as the columns are rinsed with various concentrations of acids different elements come off. For example, monovalent elements such as sodium and potassium elute off the column with a 1M HCl solution. Divalent elements such as calcium and magnesium do not elute until a 2M HCl solution is passed over the columns. The trivalent elements (REEs) are not eluted until a much higher concentrated acid is passed of the columns. Iron is also a trivalent, but it was removed in a prior anion exchange system. Aluminum is trivalent too, but it is much smaller than the REE atoms and elutes near the end of the 2 M HCl with the divalents. At the stage 2 and 3 our volume and masses have become too small to run on the continuous system. Therefore, we used a batch chromatography column or a flash chromatography column. The stage 2 process separates these REEs into 3 different fractions. A light, mid and heavy fraction. We calculated that we recovered greater than 90% of the REEs. This third column was packed with a different stationary phase. Five elements were chosen and purified to higher than 95% purity as shown by our internal testing. These elements were shipped to the DOE.

01 COAL, LIGNITE, AND PEAT↗
DOE OSTI2023

Preserving Superconvergence of Spectral Elements for Curved Domains via $h$ and $p$-Geometric Refinement

Spectral element methods (SEM), extensions of finite element methods (FEM), have emerged as significant techniques for solving partial differential equations in physics and engineering. SEM can potentially deliver superior accuracy due to the potential superconvergence in nodal solutions for well-shaped tensor-product elements. However, the accuracy of SEM often degrades in complex geometries due to geometric inaccuracies near curved boundaries and the loss of superconvergence with simplicial or non-tensor-product elements. To overcome the first issue, we propose using h- and p-geometric refinement, which refines the mesh near high-curvature regions and increases the degree of geometric basis functions, respectively. We show that when using mixed-element meshes with tensor-product elements in the interior of the domain, curvature-based geometric refinement near boundaries can improve the accuracy of the interior elements by reducing pollution errors and preserving the superconvergence in nodal solutions. To address the second issue, we introduce a post-processing technique using the adaptive extended stencil finite element method (AES-FEM) to recover the accuracy near the curved boundaries. The combination of curvature-based geometric refinement and accurate post-processing offers an effective and easier-to-implement alternative to methods reliant on exact geometries. We demonstrate our techniques by solving the convection-diffusion equation in 2D and show up to two orders of magnitude of improvement in the solution accuracy, even when the elements are poorly shaped near boundaries.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

Trace elements and heavy metals in black vultures ( Coragyps atratus ) and turkey vultures ( Cathartes aura ) in the southeastern United States

Many vulture species worldwide are declining at alarming rates due to a variety of anthropogenic causes, including exposure to pollutants and pharmaceuticals through consumption of contaminated carrion. However, little is known about the extent to which vultures are exposed to various contaminants as well as toxicity thresholds for trace elements and heavy metals. Our objective was to quantify levels of trace elements and heavy metals within black vulture (Coragyps atratus) and turkey vulture (Cathartes aura) tissues to determine the extent to which populations in the southeastern United States are exposed to carrion that contains high levels of contaminants. We collected black vulture liver samples and examined differences in trace element and heavy metal concentrations between sexes and age classes (adult and juvenile). Further, we collected 81 blood and 42 feather samples from additional black and turkey vultures and compared differences between species and age classes. We found similar element concentrations between juvenile and adult black vultures with the exception of Cu, where levels 40 were higher in juveniles compared to adults. However, we did observe substantial differences in element concentrations between species for both blood and feather samples, with black vultures generally having higher concentrations of most elements. Our data revealed higher element levels in both species compared to toxicity thresholds found in other bird of prey species, such as blood and liver toxicity threshold suggestions for Pb poisoning in Falconiformes. Further, while average contaminant levels were generally low, extreme outliers were observed for some elements, including Pb, suggesting some individuals were exposed to high levels of potentially toxic elements. In conclusion, more research is needed to better understand contaminant exposure in black and turkey vultures across a broader geographic region, as well as elucidate toxicity thresholds and non-lethal impacts of contaminant exposure in these species.

63 RADIATION, THERMAL, AND OTHER ENVIRON. POLLUTAN↗
DOE OSTI2018

A comprehensive first-principles study of solute elements in dilute Ni alloys: Diffusion coefficients and their implications to tailor creep rate

Diffusion regulates a vast number of materials properties and phenomena such as creep, the focus of the present work. However, a deep understanding of the effect of how each alloying element in a Ni-base superalloy affects properties such as diffusion and creep is far from complete. Here, in this study, we report temperature-dependent dilute solute diffusion coefficients and their implications to tailor the creep rate for 26 transition metal solute elements, X's, in fcc Ni using first-principles calculations. Calculations are performed using the five-frequency model for dilute solute diffusion and the nudged elastic band method within the local density approximation. Thermodynamic properties at finite temperatures for all configurations are calculated using the quasi-harmonic Debye model. In general, the fastest diffusing solute elements in Ni are found at the left side of the periodic table and the slowest diffusing solute elements are found in group VIIB. In particular, the present work indicates that the diffusivity of the dilute solute elements is correlated to the compressibility of each solute element on the respective Ni 31 X supercell, and not as strongly to the ionic radius of the solute elements, as previously suggested. Finally, results from the diffusivity study are combined with the previous results of elastic constants and stacking fault energies, and hence, a relative creep rate ratio for these 26 solute elements is modeled. It is shown that in most cases, slower diffusing solute elements provide the most creep resistance. This is true even at higher temperatures, due mainly to the solute's strong bonding with Ni atoms in the host lattice.

36 MATERIALS SCIENCE↗
DOE OSTI2016

Densely ionizing radiation affects DNA methylation of selective LINE-1 elements

Long Interspersed Nucleotide Element 1 (LINE-1) retrotransposons are heavily methylated and are the most abundant transposable elements in mammalian genomes. Here, we investigated the differential DNA methylation within the LINE-1 under normal conditions and in response to environmentally relevant doses of sparsely and densely ionizing radiation. We demonstrate that DNA methylation of LINE-1 elements in the lungs of C57BL6 mice is dependent on their evolutionary age, where the elder age of the element is associated with the lower extent of DNA methylation. Exposure to 5-aza-2′-deoxycytidine and methionine-deficient diet affected DNA methylation of selective LINE-1 elements in an age- and promoter type-dependent manner. Exposure to densely IR, but not sparsely IR, resulted in DNA hypermethylation of older LINE-1 elements, while the DNA methylation of evolutionary younger elements remained mostly unchanged. We also demonstrate that exposure to densely IR increased mRNA and protein levels of LINE-1 via the loss of the histone H3K9 dimethylation and an increase in the H3K4 trimethylation at the LINE-1 5′-untranslated region, independently of DNA methylation. Our findings suggest that DNA methylation is important for regulation of LINE-1 expression under normal conditions, but histone modifications may dictate the transcriptional activity of LINE-1 in response to exposure to densely IR. - Highlights: • DNA methylation of LINE-1 elements is dependent on their evolutionary age. • Densely ionizing radiation affects DNA methylation of selective LINE-1 elements. • Radiation-induced reactivation of LINE-1 is DNA methylation-independent. • Histone modifications dictate the transcriptional activity of LINE-1.

60 APPLIED LIFE SCIENCES↗
DOE OSTI2024

Evaluation of flow-induced plate deflection for University of Missouri research reactor low-enriched uranium fuel element

The University of Missouri Research Reactor (MURR), located on the campus of the University of Missouri in Columbia, Missouri, is one of the six United States (U.S.) High Performance Research Reactors (USHPRR), including one critical facility, that are actively collaborating with the U.S. Department of Energy (DOE) National Nuclear Security Administration (NNSA) Office of Material Management and Minimization (M3) Reactor Conversion Program to convert from highly enriched uranium (HEU, ≥20 wt% U-235) fuel to low-enriched uranium (LEU, <20 wt% U-235) fuel. A new type of very high-density LEU fuel based on a monolithic alloy of uranium and 10 wt% molybdenum (U-10Mo) is expected to allow conversion of some USHPRR, including MURR. In the design of its fuel elements, MURR is using thin parallel curved fuel plates separated by coolant channels. In this work, fluid-structure interaction (FSI) analysis of the MURR LEU fuel element is performed at the element level (as compared to the plate level analysis), which models all components of the LEU fuel element, including fuel plates and the supporting structures. Therefore, the effect of supporting structures on the flow distribution within the element and the fuel plate deflection are evaluated. In addition to the element nominal flow rate and dimensions, the tolerances in the geometry of the coolant channel and plate thickness, the effect of a comb on plate deflection, and the uncertainty of the flow rate per element are evaluated. For the LEU fuel plates, which are thinner than the current HEU plates, the predicted plate deflection is found to be small compared to the fabrication and assembly tolerances. Thus, the FSI-induced deflections are not expected to noticeably reduce the coolant flow rate or predicted safety margins in the limiting channels for the MURR LEU fuel element. In addition to the simulation work, a hydraulic performance test of the MURR LEU fuel element is currently being planned to support conversion to the use of LEU fuel.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗
DOE OSTI2023

From ash to oxides: Recovery of rare-earth elements as a step towards valorization of coal fly ash waste

Coal fly ash (CFA) is both a valuable waste material and a potential source of environmental contamination. The inclusion of metals such as rare-earth elements offer a possible incentive towards waste valorization if the metals can be extracted and recovered in an economical manner. Rare-earth elements (REEs) have many technological applications and are critically important in the manufacture of electric vehicles, communication devices, and industrial magnets. However, the global supply of rare-earth elements has faced shortages and price shocks. Current methods for separating and isolating individual rare-earth elements use large amounts of energy and organic solvents, raising concerns over environmental impacts. These factors have led to the investigation of nontraditional sources and separation techniques for these elements. Here, we describe a column-based system that uses a newly developed ligand-associated organosilica sorbent to concentrate and separate rare-earth elements from fly ash leachate. The fly ash used in this study originally contained 0.024 wt% rare-earth elements and the final oxide powder after enrichment contained > 10 wt% rare-earth elements, which is a enrichment of > 400 times. This process requires no additional organic solvents after the sorbent media has been synthesized, offering an alternative to the current standard using solvent extraction for rare-earth element recovery.

42 ENGINEERING↗
DOE OSTI2017

Finite-element modelling of multilayer X-ray optics

Multilayer optical elements for hard X-rays are an attractive alternative to crystals whenever high photon flux and moderate energy resolution are required. Prediction of the temperature, strain and stress distribution in the multilayer optics is essential in designing the cooling scheme and optimizing geometrical parameters for multilayer optics. The finite-element analysis (FEA) model of the multilayer optics is a well established tool for doing so. Multilayers used in X-ray optics typically consist of hundreds of periods of two types of materials. The thickness of one period is a few nanometers. Most multilayers are coated on silicon substrates of typical size 60 mm × 60 mm × 100–300 mm. The high aspect ratio between the size of the optics and the thickness of the multilayer (10 7 ) can lead to a huge number of elements for the finite-element model. For instance, meshing by the size of the layers will require more than 10 16 elements, which is an impossible task for present-day computers. Conversely, meshing by the size of the substrate will produce a too high element shape ratio (element geometry width/height > 10 6 ), which causes low solution accuracy; and the number of elements is still very large (10 6 ). In this work, by use of ANSYS layer-functioned elements, a thermal-structural FEA model has been implemented for multilayer X-ray optics. The possible number of layers that can be computed by presently available computers is increased considerably.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2017

A Mobile Element in mutS Drives Hypermutation in a Marine Vibrio

ABSTRACT Bacteria face a trade-off between genetic fidelity, which reduces deleterious mistakes in the genome, and genetic innovation, which allows organisms to adapt. Evidence suggests that many bacteria balance this trade-off by modulating their mutation rates, but few mechanisms have been described for such modulation. Following experimental evolution and whole-genome resequencing of the marine bacterium Vibrio splendidus 12B01, we discovered one such mechanism, which allows this bacterium to switch to an elevated mutation rate. This switch is driven by the excision of a mobile element residing in mutS , which encodes a DNA mismatch repair protein. When integrated within the bacterial genome, the mobile element provides independent promoter and translation start sequences for mutS —different from the bacterium’s original mutS promoter region—which allow the bacterium to make a functional mutS gene product. Excision of this mobile element rejoins the mutS gene with host promoter and translation start sequences but leaves a 2-bp deletion in the mutS sequence, resulting in a frameshift and a hypermutator phenotype. We further identified hundreds of clinical and environmental bacteria across Betaproteobacteria and Gammaproteobacteria that possess putative mobile elements within the same amino acid motif in mutS . In a subset of these bacteria, we detected excision of the element but not a frameshift mutation; the mobile elements leave an intact mutS coding sequence after excision. Our findings reveal a novel mechanism by which one bacterium alters its mutation rate and hint at a possible evolutionary role for mobile elements within mutS in other bacteria. IMPORTANCE DNA mutations are a double-edged sword. Most mutations are harmful; they can scramble precise genetic sequences honed over thousands of generations. However, in rare cases, mutations also produce beneficial new traits that allow populations to adapt to changing environments. Recent evidence suggests that some bacteria balance this trade-off by altering their mutation rates to suit their environment. To date, however, we know of few mechanisms that allow bacteria to change their mutation rates. We describe one such mechanism, driven by the action of a mobile element, in the marine bacterium Vibrio splendidus 12B01. We also found similar mobile genetic sequences in the mutS genes of many different bacteria, including clinical and agricultural pathogens. These mobile elements might play an as yet unknown role in the evolution of these important bacteria.

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2016

Safety envelope for load tolerance of structural element design based on multi-stage testing

Structural elements, such as stiffened panels and lap joints, are basic components of aircraft structures. For aircraft structural design, designers select predesigned elements satisfying the design load requirement based on their load-carrying capabilities. Therefore, estimation of safety envelope of structural elements for load tolerances would be a good investment for design purpose. In this article, a method of estimating safety envelope is presented using probabilistic classification, which can estimate a specific level of failure probability under both aleatory and epistemic uncertainties. An important contribution of this article is that the calculation uncertainty is reflected in building a safety envelope using Gaussian process, and the effect of element test data on reducing the calculation uncertainty is incorporated by updating the Gaussian process model with the element test data. It is shown that even one element test can significantly reduce the calculation uncertainty due to lacking knowledge of actual physics, so that conservativeness in a safety envelope is significantly reduced. The proposed approach was demonstrated with a cantilever beam example, which represents a structural element. The example shows that calculation uncertainty provides about 93% conservativeness against the uncertainty due to a few element tests. As a result, it is shown that even a single element test can increase the load tolerance modeled with the safety envelope by 20%.

42 ENGINEERING↗
DOE OSTI2019

The Origin of Chemical Elements: Connecting Laboratory Nuclear Astrophysics with Astronomical Observations through Nucleosynthesis Modeling

Nuclear astrophysics is a field at the frontier of nuclear science which continues to enjoy significant progress and exciting prospects for the future. It addresses the fundamental question of where and how the chemical elements are made. Except for hydrogen and helium, all other chemical elements are made either in stars or in cosmic explosions such as supernovae or neutron star mergers. To understand the formation of elements we need to understand the relevant nuclear physics processes that govern the interaction between nuclei. We need to understand the conditions in the star or the explosion under which these nuclear processes take place. And we need to understand how individual events of element formation contribute to the overall chemical enrichment of our Galaxy over time. Experimental facilities allow for terrestrial experiments on the nuclear physics governing the element synthesis. Earth-based and space-based telescopes probe the Galaxy around us and provide information about the conditions in stars and supernovae, and about the chemical element enrichment of these different environments. Numerical simulations of stars, supernovae, and other astrophysical phenomena allow us to probe the conditions of extreme densities and temperatures required for element synthesis. Nucleosynthesis research is ideally posed to integrate advances from all three of these areas and advance our understanding of how and where elements are made. Nucleosynthesis research provides theory support for experiments and observations. And it makes predictions that can be tested in nuclear physics experiments and astronomical observations. The goals of this award were in three main areas: 1. Develop and implement an effective core-collapse supernova model that is computationally efficient and that captures the relevant physics for the scientific questions of interest 2. Advance our understanding of the synthesis of the lightest heavy elements 3. Increase the realism of supernova nucleosynthesis and determine its dependence on the properties of the exploding star As the projects progressed, an additional focus was added to this list: 1. Study the explosion properties and the signals from the most massive stars.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2024

Preserving Superconvergence of Spectral Elements for Curved Domains

Spectral element methods (SEM), extensions of finite element methods (FEM), have emerged as significant techniques for solving partial differential equations in physics and engineering. SEM can potentially deliver superior accuracy due to the potential superconvergence in nodal solutions for well-shaped tensor-product elements. However, the accuracy of SEM often degrades in complex geometries due to geometric inaccuracies near curved boundaries and the loss of superconvergence with simplicial or non-tensor-product elements. To overcome the first issue, we propose using geometric refinement, which both refines the mesh near high-curvature regions and increases the degree of geometric basis functions. We show that when using mixed-element meshes with tensor-product elements in the interior of the domain, curvature-based geometric refinement near boundaries can improve the accuracy of the interior elements by reducing pollution errors and preserving the superconvergence in nodal solutions. To address the second issue, we introduce ApSEM, a post-processing technique using the adaptive extended stencil finite element method (AES-FEM) to recover the accuracy near the curved boundaries. The combination of curvature-based geometric refinement and accurate post-processing offers an effective and easier-to-implement alternative to methods reliant on exact geometries. We demonstrate our techniques by solving the convection-diffusion equation in 2D and 3D and show up to two orders of magnitude of improvement in the solution accuracy, even when the elements are poorly shaped near boundaries. We also show the efficiency of ApSEM as it can recover superconvergence in nodal solutions without drastically increasing the computational cost.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

Rare earth element enrichment in coal and coal-adjacent strata of the Uinta Region, Utah and Colorado

This study aims to quantify rare earth element enrichment within coal and coal-adjacent strata in the Uinta Region of central Utah and western Colorado. Rare earth elements are a subset of critical minerals as defined by the U.S. Geological Survey. These elements are used for a wide variety of applications, including renewable energy technology in the transition toward carbon-neutral energy. While rare earth element enrichment has been associated with Appalachian coals, there has been a more limited evaluation of western U.S. coals. Here, samples from six active mines, four idle/historical mines, four mine waste piles, and seven stratigraphically complete cores within the Uinta Region were geochemically evaluated using portable X-ray fluorescence ( n = 3,113) and inductively coupled plasma-mass spectrometry ( n = 145) elemental analytical methods. Results suggest that 24%–45% of stratigraphically coal-adjacent carbonaceous shale and siltstone units show rare earth element enrichment (>200 ppm), as do 100% of sampled igneous material. A small subset (5%–8%) of coal samples display rare earth element enrichment, specifically in cases containing volcanic ash. This study proposes two multi-step depositional and diagenetic models to explain the enrichment process, requiring the emplacement and mobilization of rare earth element source material due to hydrothermal and other external influences. Historical geochemical evaluations of Uinta Region coal and coal-adjacent data are sparse, emphasizing the statistical significance of this research. These results support the utilization of active mines and coal processing waste piles for the future of domestic rare earth element extraction, offering economic and environmental solutions to pressing global demands.

Coe, Haley H.↗
NASA NTRS1976

The development of the Poincare-similar elements with eccentric anomaly as the independent variable

A new set of element differential equations for the perturbed two-body motion is derived. The elements are canonical and are similar to the classical canonical Poincare elements, which have time as the independent variable. The phase space is extended by introducing the total energy and time as canonically conjugated variables. The new independent variable is, to within an additive constant, the eccentric anomaly. These elements are compared to the Kustaanheimo-Stiefel (KS) element differential equations, which also have the eccentric anomaly as the independent variable. For several numerical examples, the accuracy and stability of the new set are equal to those of the KS solution. This comparable accuracy result can probably be attributed to the fact that both sets have the same time element and very similar energy elements. The new set has only 8 elements, compared to 10 elements for the KS set. Both sets are free from singularities due to vanishing eccentricity and inclination.

Bond, V. R.↗
NASA NTRS1988

Evidence for a single impact at the Cretaceous-Tertiary boundary from trace elements

Not only meteoritic elements (Ir, Ni, Au, Pt metals), but also some patently non-meteoritic elements (As, Sb) are enriched at the K-T boundary. Eight enriched elements at 7 K-T sites were compared and it was found that: All have fairly constant proportions to Ir and Kilauea (invoked as an example of a volcanic source of Ir by opponents of the impact theory) has too little of 7 of these 8 elements to account for the boundary enrichments. The distribution of trace elements at the K-T boundary was reexamined using data from 11 sites for which comprehensive are available. The meteoritic component can be assessed by first normalizing the data to Ir, the most obviously extraterrestrial element, and then to Cl chondrites. The double normalization reduces the concentration range from 11 decades to 5 and also facilitates the identification of meteoritic elements. At sites where trace elements were analyzed in sub-divided samples of boundary clay, namely, Caravaca (SP), Stevns Klint (DK), Flaxbourne River (NZ) and Woodside Creek (NZ), Sb, As and Zn are well correlated with Ir across the boundary implying a common deposition mechanism. Elemental carbon is also enriched by up to 10,000 x in boundary clay from 5 K-T sides and is correlated with Ir across the boundary at Woodside Creek. While biomass would appear to be the primary fuel source for this carbon a contribution from a fossil fuel source may be necessary in order to account for the observed C abundance.

Gilmour, Iain↗
NASA NTRS1990

Direct formulation of a 4-node hybrid shell element with rotational degrees of freedom

A simple 4-node assumed-stress hybrid quadrilateral shell element with rotational or 'drilling' degrees of freedom is formulated. The element formulation is based directly on a 4-node element rather than being derived from an 'internal' 8-node isoparametric element. The formulation is based on the principle of minimum complementary energy. The membrane part of the element has 12 degrees of freedom. The bending part of the element also has 12 degrees of freedom. The bending part of the element uses the Reissner-Mindlin plate theory which takes into account the transverse shear effects. Quadratic variations for both in-plane and out-of-plane displacement fields and linear variations for both in-plane and out-of-plane rotation fields are assumed along the edges of the element. The element passes the patch test, is nearly insensitive to mesh distortion, has no spurious modes, and is invariant with respect to node numbering.

Aminpour, Mohammad A.↗
NASA NTRS1990

Behaviour of plate elements based on the first-order shear deformation theory

A new analytical technique to assess the performance of shear deformable elements is presented, which makes it possible to determine a priori whether a given element will lock when used to model thin structures. The role that shear constraints play in determining the behavior of thin elements was established by comparing the results of key numerical tests with the predictions of element behavior made by studying the form of the shear constraints. Conclusions regarding locking behavior and the effects of reduced integration in thin shear deformable elements are presented, including the findings (1) that singularity of the shear stiffness matrix is not sufficient to avoid locking; (2) that the effect of mesh refinement on an element that contains spurious constraints is two-fold; and (3) that reduced integration does not remove spurious constraints but rather relaxes them. The results of the study are in agreement with previous studies of Mindlin plate elements in regarding Lagrangian elements as superior to serendipity elements when either full or reduced integration is employed.

Averill, R. C.↗
NASA NTRS1987

A new methodology for free wake analysis using curved vortex elements

A method using curved vortex elements was developed for helicopter rotor free wake calculations. The Basic Curve Vortex Element (BCVE) is derived from the approximate Biot-Savart integration for a parabolic arc filament. When used in conjunction with a scheme to fit the elements along a vortex filament contour, this method has a significant advantage in overall accuracy and efficiency when compared to the traditional straight-line element approach. A theoretical and numerical analysis shows that free wake flows involving close interactions between filaments should utilize curved vortex elements in order to guarantee a consistent level of accuracy. The curved element method was implemented into a forward flight free wake analysis, featuring an adaptive far wake model that utilizes free wake information to extend the vortex filaments beyond the free wake regions. The curved vortex element free wake, coupled with this far wake model, exhibited rapid convergence, even in regions where the free wake and far wake turns are interlaced. Sample calculations are presented for tip vortex motion at various advance ratios for single and multiple blade rotors. Cross-flow plots reveal that the overall downstream wake flow resembles a trailing vortex pair. A preliminary assessment shows that the rotor downwash field is insensitive to element size, even for relatively large curved elements.

Bliss, Donald B.↗