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At least 433 records · Page 24
All sourcesNASA NTRSDOE OSTI
NASA NTRS2005

Finite Macro-Element Mesh Deformation in a Structured Multi-Block Navier-Stokes Code

A mesh deformation scheme is developed for a structured multi-block Navier-Stokes code consisting of two steps. The first step is a finite element solution of either user defined or automatically generated macro-elements. Macro-elements are hexagonal finite elements created from a subset of points from the full mesh. When assembled, the finite element system spans the complete flow domain. Macro-element moduli vary according to the distance to the nearest surface, resulting in extremely stiff elements near a moving surface and very pliable elements away from boundaries. Solution of the finite element system for the imposed boundary deflections generally produces smoothly varying nodal deflections. The manner in which distance to the nearest surface has been found to critically influence the quality of the element deformation. The second step is a transfinite interpolation which distributes the macro-element nodal deflections to the remaining fluid mesh points. The scheme is demonstrated for several two-dimensional applications.

Bartels, Robert E.↗
NASA NTRS2018

Tandem LA-ICP-MS & LIBS; A New Micro-Analytical Technique for the Measurement of Every Element in the Periodic Table

Laser Ablation ICP-MS (LA-ICP-MS) has been widely accepted as a microanalytical technique for in-situ trace (ppb) elemental analysis on the micron scale in a variety of geologic materials. LA-ICP-MS (single or multi-collector) provides both elemental and isotopic measurements critical for a wide range of geological research by generating a fine grained aerosol (nm scale) during the laser ablation event and delivering that aerosol to the ICP ion source of the mass spectrometer via an inert carrier gas. LA-ICP-MS, however, suffers from limitations in analyzing high ionization potential elements as well as elements subject to atmospheric and argon based interferences. LA-ICP-MS also has limitations in analyzing major elements due to detector saturation. An alternative laser ablation technique, Laser Induced Breakdown Spectroscopy (LIBS), employs an optical spectrometer integrated into the laser ablation system that analyzes the laser induced plasma at the sample surface across the entire optical spectrum for emission lines of every element in the periodic table. Elements that are difficult or impossible to measure with LA-ICP-MS are now possible to analyze with LIBS down to low ppm levels with CCD and/or ICCD detection. We introduce a new laser based technique, “Tandem LA-LIBS”, that combines LA for ICP-MS and LIBS into one integrated laser ablation system. This system has the effect of expanding the elemental coverage and the dynamic range of the laser ablation experiment as measurements from ppb to % level matrix elements can now be analyzed in a single ablation experiment. We present both femtosecond and nanosecond Tandem LA-LIBS quantitative and qualitative data on wide range of geological materials for those elements that are difficult or impossible by traditional LA-ICP-MS techniques such as F, H, O, N, C, S, halogens, etc. We also demonstrate that the simultaneous measurement of trace, minor and major elements are now possible in a single laser ablation experiment with Tandem LA-LIBS technology.

LA-ICP-MS↗
NASA NTRS2023

Temperature Effect on Silicate Melt-Sulfide-Metal Trace Element Partitioning in the Presence of Sulfur Under Reduced Conditions

The reduced nature of Mercury, enstatite chondrites, and the aubrite parent bodies (APB) have raised many questions regarding the geochemical behavior of typically lithophile, heat-producing, and rare-earth elements (REE) in magmas at low oxygen fugacity (fO2). Due to decreasing O availability at these low fO2, and an abundance of S(sup 2(-)), sulfur (S) acts as an important anion that changes the partitioning behavior of many elements and modifies the physical properties of silicate melts. Preliminary observations suggest that major and minor elements exhibit different geochemical affinities in highly reduced, S-rich systems compared to terrestrial rocks. The speciation and bonding environment of S, dictated by P/T/fO2 conditions, may strongly influence the degree to which S affects partitioning behavior. Here we investigate the partitioning behavior of major, minor, and trace elements between silicate melt, sulfide melt, and metal as well as the coordination chemistry of S in highly reduced silicate melts. Our work is focused on investigating solely the entropy-dependent temperature effect on partitioning of elements for which we currently have MESSENGER data (K, Na, Th, U, Si, Mg, Fe, Ti, Ca, Al, Cr, Mn, S, Cl) as well as a host of geochemically relevant trace elements such as REEs (P, Co, Ni, Mo, Ce, Nd, Sm, Eu, Gd, Dy, Yb). Previous studies in which temperature, pressure, and fO2 were co-varied found that as fO2 decreases, heat-producing elements U and Th become more chalcophile, while K becomes less chalcophile. Concurrently, nominally lithophile elements Mg and Ca become more chalcophile and were observed as minor elements in exsolved sulfides and bonded with S species in silicate melt. These studies, however, could not disentangle entropic effects from changes in the fO2. New temperature-dependent partitioning data from our work will be used to determine which elements are most likely to retain their lithophile character and hence be incorporated into silicates, and which elements are likely contained within the sulfide (chalcophile) and metal core (siderophile), setting the stage for the thermal and magmatic evolution of reduced planetary bodies.

B A Anzures↗
DOE OSTI2019

Extended virtual element method for the Laplace problem with singularities and discontinuities

In this paper, we propose the extended virtual element method (X-VEM) to treat singularities and crack discontinuities that arise in the Laplace problem. The virtual element method (VEM) is a stabilized Galerkin formulation on arbitrary polytopal meshes, wherein the basis functions are implicit (virtual)—they are not known explicitly nor do they need to be computed within the problem domain. In this work, suitable projection operators are used to decompose the bilinear form on each element into two parts: a consistent term that reproduces the first-order polynomial space and a correction term that ensures stability. A similar approach is pursued in the X-VEM with a few notable extensions. To capture singularities and discontinuities in the discrete space, we augment the standard virtual element space with an additional contribution that consists of the product of virtual nodal basis (partition-of-unity) functions with enrichment functions. For discontinuities, basis functions are discontinuous across the crack and for singularities a weakly singular enrichment function that satisfies the Laplace equation is chosen. For the Laplace problem with a singularity, we devise an extended projector that maps functions that lie in the extended virtual element space onto linear polynomials and the enrichment function, whereas for the discontinuous problem, the consistent element stiffness matrix has a block-structure that is readily computed. An adaptive homogeneous numerical integration method is used to accurately and efficiently (no element-partitioning is required) compute integrals with integrands that are weakly singular. Once the element projection matrix is computed, the same steps as in the standard VEM are followed to compute the element stabilization matrix. Numerical experiments are performed on quadrilateral and polygonal (convex and nonconvex elements) meshes for the problem of an $\textit{L}$-shaped domain with a corner singularity and the problem of a cracked membrane under mode III loading, and results are presented that affirm the sound accuracy and demonstrate the optimal rates of convergence in the $\textit{L}^2$ norm and energy of the proposed method.

42 ENGINEERING↗
DOE OSTI2013

Higher-order adaptive finite-element methods for Kohn–Sham density functional theory

We present an efficient computational approach to perform real-space electronic structure calculations using an adaptive higher-order finite-element discretization of Kohn–Sham density-functional theory (DFT). To this end, we develop an a priori mesh-adaption technique to construct a close to optimal finite-element discretization of the problem. We further propose an efficient solution strategy for solving the discrete eigenvalue problem by using spectral finite-elements in conjunction with Gauss–Lobatto quadrature, and a Chebyshev acceleration technique for computing the occupied eigenspace. The proposed approach has been observed to provide a staggering 100–200-fold computational advantage over the solution of a generalized eigenvalue problem. Using the proposed solution procedure, we investigate the computational efficiency afforded by higher-order finite-element discretizations of the Kohn–Sham DFT problem. Our studies suggest that staggering computational savings—of the order of 1000-fold—relative to linear finite-elements can be realized, for both all-electron and local pseudopotential calculations, by using higher-order finite-element discretizations. On all the benchmark systems studied, we observe diminishing returns in computational savings beyond the sixth-order for accuracies commensurate with chemical accuracy, suggesting that the hexic spectral-element may be an optimal choice for the finite-element discretization of the Kohn–Sham DFT problem. A comparative study of the computational efficiency of the proposed higher-order finite-element discretizations suggests that the performance of finite-element basis is competing with the plane-wave discretization for non-periodic local pseudopotential calculations, and compares to the Gaussian basis for all-electron calculations to within an order of magnitude. Further, we demonstrate the capability of the proposed approach to compute the electronic structure of a metallic system containing 1688 atoms using modest computational resources, and good scalability of the present implementation up to 192 processors.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2019

Rare earth elements of fly ash from Wyoming's Powder River Basin coal

The advancement and increasing interests in green energy production and environmental protection technologies have spurred the demand for rare earth elements. On the other hand, the U.S. has to rely 100% on import of these materials as the industry was crashed because of the environmental issues associated with mining and processing, and more importantly lack competitiveness. As rare earth elements have many applications in defense and national security sectors, some of the elements were listed as strategic materials or critical materials because of the uncertainties in supply and prices. Therefore, it has become imperative in searching for alternative resources for supplying rare earth elements including unconventional resources. With the strong incentive, coal fly ash is identified as one of the candidates among them. In this study, we present rare earth element data for the 42 ash samples (all derived from Powder River Basin coal) that we collected from seven states (UT, WY, IO, WI, ND, CO, and MI) representing 158 million tons of fly ash. Overall, the results indicate scattered distributions of rare earth elements with concentration ranging from 156 to 590 ppm although all the ash samples originated from the same coal basin (Powder River Basin). The rare earth element resource in these ashes is estimated between 74000 and 106000 t. The ash samples were also characterized by elemental analysis, XRD, SEM-EDS and BET surface area. The characterizations of the ashes were discussed as they might have implications in the subsequent rare earth element extraction processes. In summary, fly ash may represent a potential resource for rare earth element production.

01 COAL, LIGNITE, AND PEAT↗
DOE OSTI2021

Patterns of Element Incorporation in Calcium Carbonate Biominerals Recapitulate Phylogeny for a Diverse Range of Marine Calcifiers

Elemental ratios in biogenic marine calcium carbonates are widely used in geobiology, environmental science, and paleoenvironmental reconstructions. It is generally accepted that the elemental abundance of biogenic marine carbonates reflects a combination of the abundance of that ion in seawater, the physical properties of seawater, the mineralogy of the biomineral, and the pathways and mechanisms of biomineralization. Here we report measurements of a suite of nine elemental ratios (Li/Ca, B/Ca, Na/Ca, Mg/Ca, Zn/Ca, Sr/Ca, Cd/Ca, Ba/Ca, and U/Ca) in 18 species of benthic marine invertebrates spanning a range of biogenic carbonate polymorph mineralogies (low-Mg calcite, high-Mg calcite, aragonite, mixed mineralogy) and of phyla (including Mollusca, Echinodermata, Arthropoda, Annelida, Cnidaria, Chlorophyta, and Rhodophyta) cultured at a single temperature (25°C) and a range of p CO 2 treatments (ca. 409, 606, 903, and 2856 ppm). This dataset was used to explore various controls over elemental partitioning in biogenic marine carbonates, including species-level and biomineralization-pathway-level controls, the influence of internal pH regulation compared to external pH changes, and biocalcification responses to changes in seawater carbonate chemistry. The dataset also enables exploration of broad scale phylogenetic patterns of elemental partitioning across calcifying species, exhibiting high phylogenetic signals estimated from both uni- and multivariate analyses of the elemental ratio data (univariate: λ = 0–0.889; multivariate: λ = 0.895–0.99). Comparing partial R 2 values returned from non-phylogenetic and phylogenetic regression analyses echo the importance of and show that phylogeny explains the elemental ratio data 1.4–59 times better than mineralogy in five out of nine of the elements analyzed. Therefore, the strong associations between biomineral elemental chemistry and species relatedness suggests mechanistic controls over element incorporation rooted in the evolution of biomineralization mechanisms.

58 GEOSCIENCES↗
DOE OSTI2020

Catalytic influence of light element incorporation in the lattice of palladium

The alloying of metals with foreign elements is a common approach for manipulating catalytic properties of active sites. For palladium-based catalysts, incorporation of light elements receives far less attention than Pd-metal alloys even though incorporated light element are catalytically significant. Due to their small size, light elements (H, B, C, and O) can occupy octahedral sites in Pd to form an interstitial phase, while palladium adjusts its lattice to accommodate the incorporation of larger light elements (S and P) to form distinct phases. The incorporated light element modifies the electronic structure of palladium, influencing the binding energy of substrates and reactive intermediates. Pd hydride and oxide often form in situ during hydrogenation or oxidation reactions, respectively, representing the (more, less) active phase of the catalyst. Further, the reactive interstitial hydrogen dissolved in Pd tends to hydrogenate reactants completely and unselectively. Pd oxide can be the active phase for oxidation reactions, and the incorporated oxygen or oxygen vacancies may participate in the reaction directly. Incorporated light elements change geometric aspects of Pd ensembles, serving the role of site blocking, ensemble isolation, or serve as an additional active site, endowing Pd with bifunctional character. We review the synthetic approaches for incorporating light elements into the palladium lattice. We summarize the catalytic influence of light element incorporation into the palladium lattice with respect to electronic and geometric modification, in situ incorporated hydrogen and oxygen, and discuss the influence of light element incorporation into Pd on specific reactions (i.e., selective hydrogenation, oxidation, electrocatalysis, and C—C cross coupling).

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2018

Body burden of toxic metals and rare earth elements in non-smokers, cigarette smokers and electronic cigarette users

Highlights: • The role of smoking as a source for 42 inorganic element intakes was explored. • The exposure levels of non-smoker, cigarette smokers and e-cigarette users was compared. • Cigarette smokers showed the highest levels of Cu, Mo, Zn, Sb, and Sr. • E-cigarettes users presented the highest concentrations of Se, Ag, and V. • Be, Eu and La were detected more frequently among e-cigarette users. Smoking is considered an important source for inorganic elements, most of them toxic for human health. During the last years, there has been a significant increase in the use of e-cigarettes, although the role of them as source of inorganic elements has not been well established. A cross-sectional study including a total of 150 subjects from Brasov (Romania), divided into three groups (non-smokers, cigarette smokers and electronic cigarettes smokers) were recruited to disclose the role of smoking on the human exposure to inorganic elements. Concentration of 42 elements, including trace elements, elements in the ATSDR's priority pollutant list and rare earth elements (REE) were measured by ICP-MS in the blood serum of participants. Cigarette smokers showed the highest levels of copper, molybdenum, zinc, antimony, and strontium. Electronic cigarette (e-cigarette) users presented the highest concentrations of selenium, silver, and vanadium. Beryllium, europium and lanthanides were detected more frequently among e-cigarette users (20.6%, 23.5%, and 14.7%) than in cigarette smokers (1.7%, 19.0%, and 12.1%, respectively); and the number of detected REE was also higher among e-cigarette users (11.8% of them showed more than 10 different elements). Serum levels of cerium and erbium increased as the duration of the use of e-cigarettes was longer. We have found that smoking is mainly a source of heavy metals while the use of e-cigarettes is a potential source of REE. However, these elements were detected at low concentrations.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2014

A Single Whole-Body Low Dose X-Irradiation Does Not Affect L1, B1 and IAP Repeat Element DNA Methylation Longitudinally

The low dose radioadaptive response has been shown to be protective against high doses of radiation as well as aging-induced genomic instability. We hypothesised that a single whole-body exposure of low dose radiation would induce a radioadaptive response thereby reducing or abrogating aging-related changes in repeat element DNA methylation in mice. Following sham or 10 mGy X-irradiation, serial peripheral blood sampling was performed and differences in Long Interspersed Nucleic Element 1 (L1), B1 and Intracisternal-A-Particle (IAP) repeat element methylation between samples were assessed using high resolution melt analysis of PCR amplicons. By 420 days post-irradiation, neither radiation- or aging-related changes in the methylation of peripheral blood, spleen or liver L1, B1 and IAP elements were observed. Analysis of the spleen and liver tissues of cohorts of untreated aging mice showed that the 17–19 month age group exhibited higher repeat element methylation than younger or older mice, with no overall decline in methylation detected with age. This is the first temporal analysis of the effect of low dose radiation on repeat element methylation in mouse peripheral blood and the first to examine the long term effect of this dose on repeat element methylation in a radiosensitive tissue (spleen) and a tissue fundamental to the aging process (liver). Our data indicate that the methylation of murine DNA repeat elements can fluctuate with age, but unlike human studies, do not demonstrate an overall aging-related decline. Furthermore, our results indicate that a low dose of ionising radiation does not induce detectable changes to murine repeat element DNA methylation in the tissues and at the time-points examined in this study. This radiation dose is relevant to human diagnostic radiation exposures and suggests that a dose of 10 mGy X-rays, unlike high dose radiation, does not cause significant short or long term changes to repeat element or global DNA methylation.

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2020

Multi-Element Water Content System Instrument Handbook

The SEA Model WCM-2000 multi-element water content system was designed to provide aircraft and wind tunnel users with a single, rugged sensor to simultaneously measure liquid water content (LWC), total water content (TWC), and ice water content (IWC). The instrument consists of four heated stainless steel elements, each with a different shape or size. Each element is directly heated by low-voltage DC current flowing through the element. These elements are maintained at a constant temperature, typically 140°C, by a digital closed-loop control system. Three of the heated elements are exposed directly to the airstream and incoming cloud water. A fourth element, the reference/comp element, is arranged to be exposed to the airflow but not to incoming cloud water. This element is used to establish the “dry power term” that is subtracted from the other three elements’ power readings to establish the measured water content.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2021

Involute Working Group – FSI Analysis of Fuel Plates Using Finite Volume and Finite Element Methods

The three involute plate research reactors RHF, HFIR, and FRM II have expressed an interest in using computational software to carry their steady-state safety analysis. Since these tools represent a significant departure from the methods used currently (one-dimensional), the acceptability of the new approach by regulators requires thorough verification and validation of these tools. Therefore, Argonne National Laboratory and the three involute-plate reactors formed an informal group called the Involute Working Group aiming at qualifying computational tools to perform steady-state safety analysis. The present report focuses on a comparison of finite volume and finite element methods to model solids in fluid-structure interaction problems with the goal to estimate the coolant flow-induced fuel plate deflections obtained with the two methods. The finite volume method will be obsoleted in STARCCM+ by the end of 2021, nevertheless, this evaluation is important because the method was used by ANL researchers to model the response of the fuel plates, despite its drawbacks, which are discussed in the report. It was essential to check how those estimates compare to the results obtained with the finite element method that is considered superior for structural analysis. Various geometries, i.e., flat, cylindrical and circle-involute fuel plates, as well as coolant flow speed, were considered. The comparison shows that, independently of the plate geometry, the finite volume method significantly underestimates the deflection as compared to finite element method for coarser meshes. When the discretization is developed as a result of a mesh sensitivity study using finite element method, the result obtained using finite volume method can be a few times smaller than the corresponding finite element method solution. A code-to-code comparison , between STAR-CCM+ and LS-DYNA was included in the analysis. Within the LS-DYNA models, two types of finite element formulations were used: solid and shell finite elements. Mesh sensitivity study showed that both approaches converge to a similar value that was obtained with STAR-CCM+ finite element solver. The evaluation of the computational solvers was extended by adding two benchmark cases from the STAR-CCM+ Verification Suite and presented in the Appendix A. The selected cases are: (1) bending of a cantilever beam under external load, and (2) cylindrical shell deformation analysis, known in the literature as ‘Scordelis-Lo roof’. The problems were solved with finite volume, and finite element methods, and the results confirmed the previously discussed findings. The analysis shows that the finite element solver is superior to the finite volume solver in terms of representation of model geometry and estimating the structural behavior of fuel plates. Depending on the ratio of the load to the flexibility of the plate, the finite volume solver can greatly under- or overestimate the structural response if a very carefully selected mesh is not used.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2023

Superheavy Elements in Kilonovae

Abstract As LIGO-Virgo-KAGRA enters its fourth observing run, a new opportunity to search for electromagnetic counterparts of compact object mergers will also begin. The light curves and spectra from the first “kilonova” associated with a binary neutron star merger (NSM) suggests that these sites are hosts of the rapid neutron capture (“ r ”) process. However, it is unknown just how robust elemental production can be in mergers. Identifying signposts of the production of particular nuclei is critical for fully understanding merger-driven heavy-element synthesis. In this study, we investigate the properties of very neutron-rich nuclei for which superheavy elements ( Z ≥ 104) can be produced in NSMs and whether they can similarly imprint a unique signature on kilonova light-curve evolution. A superheavy-element signature in kilonovae represents a route to establishing a lower limit on heavy-element production in NSMs as well as possibly being the first evidence of superheavy-element synthesis in nature. Favorable NSM conditions yield a mass fraction of superheavy elements X Z ≥104 ≈ 3 × 10 −2 at 7.5 hr post-merger. With this mass fraction of superheavy elements, we find that the component of kilonova light curves possibly containing superheavy elements may appear similar to those arising from lanthanide-poor ejecta. Therefore, photometric characterizations of superheavy-element rich kilonova may possibly misidentify them as lanthanide-poor events.

79 ASTRONOMY AND ASTROPHYSICS↗
NASA NTRS1975

On a numerical sufficiency test for monotonic convergence of finite element models

Finite element analyses characterized by monotonic convergence include the discipline for meaningful measurements of convergence rate and consequently economical extrapolation. Few proposers of element models guarantee monotonic convergence for their elements. Thus, a need exists for an automatic test to classify available element models. This paper describes such a test - a test can be performed using a digital computer to guarantee that a particular element model imbues monotonicity. It describes the test and its basis. It examines seven element models for a rectangular membrane to illustrate the value of the tests. Besides confirming results already known, the application yields new data. It 'proves' monotonicity for two improved models, defines the range of element proportions for which another element can be guaranteed to exhibit monotonicity, and suggests that another element is deficient. In the special case of absolutely convergent membrane displacement models, proof of monotonicity is a necessary and sufficient condition to insure that upper bound estimates of strain energy are developed. Accordingly, the test furnishes a proof of bound solutions independently of requirements on displacement continuity the element basis may or may not satisfy.

Melosh, R. J.↗
NASA NTRS1979

The response of a disturbed pipe flow to an upstanding roughness element

The paper describes measurements of mean velocity, turbulence intensity and Reynolds shear stress made downstream of a ring-type roughness element of rectangular cross section situated downstream of an identical element. The distance between the elements was varied, and velocity and turbulence profiles in the wake of the downstream element are compared with wake profiles behind a single element. The results show that the leading element can increase the power law exponent of the velocity profile as the spacing between elements is reduced. Turbulence generated in the wake of the first element raises turbulence intensity in the outer region of the wake of the second. The internal boundary layer originating with the second element grows at a rate which depends on the spacing. It is postulated that the internal boundary layers of subsequent roughness elements are determinants in the formation of a periodic wall layer.

Chang, J.↗
NASA NTRS1986

Improved isoparametric solid and membrane elements

Improvements that were made to the COSMIC NASTRAN elements CIHEX1 and QDMEM1 are described. These elements are isoparametric representations of solid and membrane elastic behavior. Recent papers by the authors have shown the official COSMIC versions of these elements to be inferior to those available in the MacNeal-Schwendler Corporation (MSC) version of NASTRAN in that they are overly stiff for some loadings. Modifications were made to these elements which reduce the order of integration for shear terms and, for the eight-mode solid element, add additional strain functions. The resulting element formulations give behavior similar to that of the MSC elements. The changes made in the element formulations are discussed and results of test problems are compared with results from the official COSMIC elements and with the MSC elements.

Case, W. R.↗
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. This direct formulation requires fewer computations than a similar element that is derived from an internal 8-node isoparametric element in which the midside degrees of freedom are eliminated in favor of rotational degree of freedom at the corner nodes. The formulation is based on the principle of minimum complementary energy. The membrane part of the element has 12 degrees of freedom including rotational degrees of freedom. The bending part of the element also has 12 degrees of freedom. The bending part of the 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 Cartesian-coordinate system is chosen such as to make the stress field invariant with respect to node numbering. The membrane part of the stress field is based on a 9-parameter equilibrating stress field, while the bending part is based on a 13-parameter equilibrating stress field. The element passes the patch test, is nearly insensitive to mesh distortion, does not lock, possesses the desirable invariance properties, has no spurious modes, and produces accurate and reliable results.

Aminpour, Mohammad A.↗
NASA NTRS1992

An assumed-stress hybrid 4-node shell element with drilling degrees of freedom

An assumed-stress hybrid/mixed 4-node quadrilateral shell element is introduced that alleviates most of the deficiencies associated with such elements. The formulation of the element is based on the assumed-stress hybrid/mixed method using the Hellinger-Reissner variational principle. The membrane part of the element has 12 degrees of freedom including rotational or 'drilling' degrees of freedom at the nodes. 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 contributions. The element formulation is derived from an 8-node isoparametric element by expressing the midside displacement degrees of freedom in terms of displacement and rotational degrees of freedom at corner nodes. The element passes the patch test, is nearly insensitive to mesh distortion, does not 'lock', possesses the desirable invariance properties, has no hidden spurious modes, and for the majority of test cases used in this paper produces more accurate results than the other elements employed herein for comparison.

Aminpour, M. A.↗