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At least 109 records · Page 6
All sourcesNASA NTRSDOE OSTI
NASA NTRS1985

A critical assessment of viscous models of trench topography and corner flow

Stresses for Newtonian viscous flow in a simple geometry (e.g., corner flow, bending flow) are obtained in order to study the effect of imposed velocity boundary conditions. Stress for a delta function velocity boundary condition decays as 1/R(2); for a step function velocity, stress goes as 1/R; for a discontinuity in curvature, the stress singularity is logarithmic. For corner flow, which has a discontinuity of velocity at a certain point, the corresponding stress has a 1/R singularity. However, for a more realistic circular-slab model, the stress singularity becomes logarithmic. Thus the stress distribution is very sensitive to the boundary conditions, and in evaluating the applicability of viscous models of trench topography it is essential to use realistic geometries. Topography and seismicity data from northern Hoshu, Japan, were used to construct a finite element model, with flow assumed tangent to the top of the grid, for both Newtonian and non-Newtonian flow (power law 3 rheology). Normal stresses at the top of the grid are compared to the observed trench topography and gravity anomalies. There is poor agreement. Purely viscous models of subducting slables with specified velocity boundary conditions do not predict normal stress patterns compatible with observed topography and gravity. Elasticity and plasticity appear to be important for the subduction process.

Zhang, J.↗
NASA NTRS1987

Probabilistic SSME blades structural response under random pulse loading

The purpose is to develop models of random impacts on a Space Shuttle Main Engine (SSME) turbopump blade and to predict the probabilistic structural response of the blade to these impacts. The random loading is caused by the impact of debris. The probabilistic structural response is characterized by distribution functions for stress and displacements as functions of the loading parameters which determine the random pulse model. These parameters include pulse arrival, amplitude, and location. The analysis can be extended to predict level crossing rates. This requires knowledge of the joint distribution of the response and its derivative. The model of random impacts chosen allows the pulse arrivals, pulse amplitudes, and pulse locations to be random. Specifically, the pulse arrivals are assumed to be governed by a Poisson process, which is characterized by a mean arrival rate. The pulse intensity is modelled as a normally distributed random variable with a zero mean chosen independently at each arrival. The standard deviation of the distribution is a measure of pulse intensity. Several different models were used for the pulse locations. For example, three points near the blade tip were chosen at which pulses were allowed to arrive with equal probability. Again, the locations were chosen independently at each arrival. The structural response was analyzed both by direct Monte Carlo simulation and by a semi-analytical method.

Shiao, Michael↗
NASA NTRS2016

Metabolomic and Genomic Markers of Atherosclerosis as Related to Oxidative Stress, Inflammation, and Vascular Function in Twin Astronauts

Background: Future human space travel will consist primarily of long-duration missions onboard the International Space Station (ISS) or exploration-class missions to Mars, its moons, or nearby asteroids. Astronauts participating in long-duration missions may be at an increased risk of oxidative stress and inflammatory damage due to radiation, psychological stress, altered physical activity, nutritional insufficiency, and hyperoxia during extravehicular activity. By studying one identical twin during his 1-year ISS mission and one ground-based twin, this work extends a current NASA-funded investigation to determine whether these spaceflight factors contribute to an accelerated progression of atherosclerosis. This study of twins affords a unique opportunity to examine the spaceflight-related atherosclerosis risk independent of the confounding factors associated with different genotypes. Purpose: The purpose of this investigation is to determine whether biomarkers of oxidative and inflammatory stress are elevated during and after long-duration spaceflight and determine if a relation exists between levels of these biomarkers and structural and functional indices of atherosclerotic risk measured in the carotid and brachial arteries. These physiological and biochemical data will be extended by using an exploratory approach to investigate the relationship between intermediate phenotypes and risk factors for atherosclerosis and the metabolomic signature from plasma and urine samples. Since metabolites are often the indirect products of gene expression, we will simultaneously assess gene expression and DNA methylation in leukocytes. Hypothesis: We predict that the space-flown twin will experience elevated biomarkers of oxidative stress and inflammatory damage, altered arterial structure and function, accelerated telomere shortening, dysregulation of genes associated with oxidative stress and inflammation, and a metabolic profile shift that is associated with elevated atherosclerosis risk factors. Conversely, these will not be observed in the ground-based twin. Methods: We will measure blood and urine biomarkers of oxidative stress and inflammation as well as arterial structure and function (carotid intima-medial thickness and brachial artery flow-mediated dilation) in one twin astronaut before, during, and after long-duration spaceflight and in his twin serving as a ground-based control. Furthermore, we will measure metabolomics (targeted and untargeted approaches) and genomic markers (DNA methylation, mRNA gene expression, telomere length) to elucidate the molecular mechanisms involved. A panel of biomarkers of oxidative and inflammatory stress will be measured in venous blood samples and 24-hour (in-flight) and 48-hour (pre- and post-flight) urine pools twice before flight, early (flight days 15 and 60) and late (2 weeks before landing) during the mission, and early in the post-flight recovery phase (approximately 3-5 days after landing). Arterial structure, assessed from measures of intima-media thickness, will be measured at the same times. Arterial function will be assessed using brachial flow-mediated dilation, a well-validated measure used to assess endothelium-dependent vasodilation and a sensitive predictor of atherosclerotic risk, only before and after spaceflight. Discussion: Pre- and in-flight data collection is in progress for the space-flown twin, and similar data have been obtained from the ground-based twin. Blood and urine samples will be batch processed when received from ISS after the conclusion of the 1-year mission. Results from these individual subjects will be compared to the larger complement of subjects participating in the companion study currently ongoing in ISS astronauts.

Lee, Stuart M. C.↗
NASA NTRS1992

Cyclic axial-torsional deformation behavior of a cobalt-base superalloy

Multiaxial loading, especially at elevated temperature, can cause the inelastic response of a material to differ significantly from that predicted by simple flow rules, i.e., von Mises or Tresca. To quantify some of these differences, the cyclic high-temperature, deformation behavior of a wrought cobalt-based superalloy, Haynes 188, is investigated under combined axial and torsional loads. Haynes 188 is currently used in many aerospace gas turbine and rocket engine applications, e.g., the combustor liner for the T800 turboshaft engine for the RAH-66 Comanche helicopter and the liquid oxygen posts in the main injector of the space shuttle main engine. The deformation behavior of this material is assessed through the examination of hysteresis loops generated from a biaxial fatigue test program. A high-temperature axial, torsional, and combined axial-torsional fatigue data base has been generated on Haynes 188 at 760 C. Cyclic loading tests have been conducted on uniform gauge section tubular specimens in a servohydraulic axial-torsional test rig. Test control and data acquisition were accomplished with a minicomputer. In this paper, the cyclic hardening characteristics and typical hysteresis loops in the axial stress versus axial strain, shear stress versus engineering shear strain, axial strain versus engineering shear strain, and axial stress versus shear stress spaces are presented for cyclic, in-phase and out-of-phase, axial torsional tests. For in-phase tests three different values of the proportionality constant, lambda (ratio of engineering shear strain amplitude to axial strain amplitude), are examined, viz., 0.86, 1.73, and 3.46. In the out-of-phase tests, three different values of the phase angle, phi (between the axial and engineering shear strain waveforms), are studied, viz., 30, 60, and 90 deg with lambda = 1.73. The cyclic hardening behaviors of all the tests conducted on Haynes 188 at 760 C are evaluated using the von Mises equivalent stress-strain and the maximum shear stress-maximum engineering shear strain (Tresca) curves. Comparisons are also made between the hardening behaviors of cyclic axial, torsional, and combined in-phase and out-of-phase axial-torsional fatigue tests. These comparisons are accomplished through simple Ramberg-Osgood type stress-strain functions for cyclic, axial stress-strain and shear stress-engineering shear strain curves.

Bonacuse, Peter J.↗
NASA NTRS1995

Cyclic Axial-Torsional Deformation Behavior of a Cobalt-Base Superalloy

The cyclic, high-temperature deformation behavior of a wrought cobalt-base super-alloy, Haynes 188, is investigated under combined axial and torsional loads. This is accomplished through the examination of hysteresis loops generated from a biaxial fatigue test program. A high-temperature axial, torsional, and combined axial-torsional fatigue database has been generated on Haynes 188 at 760 C. Cyclic loading tests have been conducted on uniform gage section tubular specimens in a servohydraulic axial-torsional test rig. Test control and data acquisition were accomplished with a minicomputer. The fatigue behavior of Haynes 188 at 760 C under axial, torsional, and combined axial-torsional loads and the monotonic and cyclic deformation behaviors under axial and torsional loads have been previously reported. In this paper, the cyclic hardening characteristics and typical hysteresis loops in the axial stress versus axial strain, shear stress ,versus engineering shear strain, axial strain versus engineering shear strain. and axial stress versus shear stress spaces are presented for cyclic in-phase and out-of-phase axial-torsional tests. For in-phase tests, three different values of the proportionality constant lambda (the ratio of engineering shear strain amplitude to axial strain amplitude, are examined, viz. 0.86, 1.73, and 3.46. In the out-of-phase tests, three different values of the phase angle, phi (between the axial and engineering shear strain waveforms), are studied, viz., 30, 60, and 90 degrees with lambda equals 1.73. The cyclic hardening behaviors of all the tests conducted on Haynes 188 at 760 C are evaluated using the von Mises equivalent stress-strain and the maximum shear stress-maximum engineering shear strain (Tresca) curves. Comparisons are also made between the hardening behaviors of cyclic axial, torsional, and combined in-phase (lambda = 1.73 and phi = 0) and out-of-phase (lambda = 1.73 and phi = 90') axial-torsional fatigue tests. These comparisons are accomplished through simple Ramberg-Osgood type stress-strain functions for cyclic, axial stress-strain and shear stress-engineering shear strain curves.

Bonacuse, Peter J.↗
NASA NTRS2011

Production of functional proteins: balance of shear stress and gravity

A method for the production of functional proteins including hormones by renal cells in a three dimensional culturing process responsive to shear stress uses a rotating wall vessel. Natural mixture of renal cells expresses the enzyme 1-.alpha.-hydroxylase which can be used to generate the active form of vitamin D: 1,25-diOH vitamin D.sub.3. The fibroblast cultures and co-culture of renal cortical cells express the gene for erythropoietin and secrete erythropoietin into the culture supernatant. Other shear stress response genes are also modulated by shear stress, such as toxin receptors megalin and cubulin (gp280). Also provided is a method of treating an in-need individual with the functional proteins produced in a three dimensional co-culture process responsive to shear stress using a rotating wall vessel.

Goodwin, Thomas John↗
NASA NTRS2017

Metabolomic and Genomic Markers of Atherosclerosis as Related to Oxidative Stress, Inflammation, and Vascular Function in Twin Astronauts

BACKGROUND: Future human space travel will consist primarily of long-duration missions onboard the International Space Station (ISS) or exploration-class missions to Mars, its moons, or nearby asteroids. Astronauts participating in long-duration missions may be at an increased risk of oxidative stress and inflammatory damage due to radiation, psychological stress, altered physical activity, nutritional insufficiency, and hyperoxia during extravehicular activity. By studying one identical twin during his 1-year ISS mission and his ground-based twin, this work extends a current NASA-funded investigation to determine whether these spaceflight factors contribute to an accelerated progression of atherosclerosis. This study of twins affords a unique opportunity to examine spaceflight-related atherosclerosis risk that is independent of the confounding factors associated with different genotypes. PURPOSE: The purpose of this investigation was to determine whether biomarkers of oxidative and inflammatory stress are elevated during and after long-duration spaceflight and determine if a relation exists between levels of these biomarkers and structural and functional indices of atherosclerotic risk measured in the carotid and brachial arteries. These physiological and biochemical data will be extended by using an exploratory approach to investigate the relationship between intermediate phenotypes and risk factors for atherosclerosis and the metabolomic signature from plasma and urine samples. Since metabolites are often the indirect products of gene expression, we simultaneously assessed gene expression and DNA methylation in leukocytes. HYPOTHESIS: We predict that, compared to the ground-based twin, the space-flown twin will experience elevated biomarkers of oxidative stress and inflammatory damage, altered arterial structure and function, accelerated telomere shortening, dysregulation of genes associated with oxidative stress and inflammation, and a metabolic profile shift that is associated with elevated atherosclerosis risk factors. METHODS: In the space-flown twin, a panel of biomarkers of oxidative and inflammatory stress were measured in venous blood samples and in 24-h (in-flight) and 48-h (pre- and post-flight) urine pools collected twice before flight, six times during the mission (~FD15, 75, 180, 240, 300, 335), and early in the post-flight recovery phase (3-5 days after landing). We also measured metabolomic (targeted and untargeted approaches) and genomic markers (DNA methylation, mRNA gene expression, telomere length) in these samples. Arterial structure, assessed from measures of intima-media thickness, also were measured using standard clinical ultrasound at the same time points. Arterial function was assessed using brachial flow-mediated dilation, a well-validated measure used to assess endothelium-dependent vasodilation and a sensitive predictor of atherosclerotic risk, only before and after spaceflight. All of the same measures were obtained in the ground-based twin, but less frequently. DISCUSSION: All data collection has been completed for both the space-flown twin and the ground-based twin. Vascular structure and function measures have been analyzed, blood and urine samples have been batch-processed. Results from these individuals will be compared to each other, to data from other Twin Study investigations, and to the larger complement of subjects participating in the companion study currently ongoing in ISS astronauts.

Lee, Stuart M. C.↗
NASA NTRS1971

Stress, fighting and neuroendocrine function.

Plasma concentrations of pituitary adrenocorticotrophic hormone (ACTH) and adrenocortical steroids in rats after testing in the shock-induced fighting paradigm were examined. The investigations provide data consistent with the view that psychological aspects of the stressful situation are important in determining the effects of shock on physiological function. The data indicate that the pituitary-adrenal response can be attenuated by the expression of an organized pattern of behavior.

Conner, R. L.↗
NASA NTRS1980

Long-time creep behavior of the niobium alloy C-103

The creep behavior of C-103 was studied as a function of stress, temperature, and grain size for test times to 19000 hr. Over the temperature range 827 to 1204 C and the stress range 6.89 to 138 MPa, only tertiary (accelerating) creep was observed. The creep strain epsilon can be related to time t by an exponential relation epsilon = epsilon(0) + K e raised to power (st) - 1), where epsilon (0) is initial creep strain, K is the tertiary creep strain parameter, and s is the tertiary creep rate parameter. The observed stress exponent 2.87 is similar to the three power law generally observed for secondary (linear) creep of Class I solid solutions. The apparent activation energy 374 kj/g mol is close to that observed for self diffusion of pure niobium. The initial tertiary creep rate was slightly faster for fine grained than for coarse-grained material. The strain parameter K can be expressed as a combination of power functions of stress and grain size and an exponential function of temperature. Strain time curves generated by using calculated values for K and s showed reasonable agreement with observed curves to strains of at least 4 percent. The time to 1 percent strain was related to stress, temperature, and grain size in a similar manner as the initial tertiary creep rate.

Titran, R. H.↗
NASA NTRS1985

The evolution of impact basins - Cooling, subsidence, and thermal stress

The present study is concerned with an assessment of the contribution of thermal contraction and thermal stress to the topography and tectonics of large lunar impact basins. Exploratory models are developed, giving attention to the temperature structure following basin formation, the subsequent cooling of the basin region, and the resulting thermal displacements and stresses as functions of time. The subsidence and stress at the surface are compared with topography and tectonic features in the comparatively well-preserved Orientale basin. The results of the comparison are used as a basis to derive approximate constraints on the quantity and distribution of heat implanted during the basin-formation process.

Bratt, S. R.↗
NASA NTRS2004

Production of functional proteins: balance of shear stress and gravity

The present invention provides a method for production of functional proteins including hormones by renal cells in a three dimensional co-culture process responsive to shear stress using a rotating wall vessel. Natural mixture of renal cells expresses the enzyme 1-a-hydroxylase which can be used to generate the active form of vitamin D: 1,25-diOH vitamin D3. The fibroblast cultures and co-culture of renal cortical cells express the gene for erythropoietin and secrete erythropoietin into the culture supernatant. Other shear stress response genes are also modulated by shear stress, such as toxin receptors megalin and cubulin (gp280). Also provided is a method of treating in-need individual with the functional proteins produced in a three dimensional co-culture process responsive to shear stress using a rotating wall vessel.

Goodwin, Thomas John↗
NASA NTRS2007

Production of functional proteins: balance of shear stress and gravity

The present invention provides a method for production of functional proteins including hormones by renal cells in a three dimensional co-culture process responsive to shear stress using a rotating wall vessel. Natural mixture of renal cells expresses the enzyme 1-a-hydroxylase which can be used to generate the active form of vitamin D: 1,25-diOH vitamin D3. The fibroblast cultures and co-culture of renal cortical cells express the gene for erythropoietin and secrete erythropoietin into the culture supernatant. Other shear stress response genes are also modulated by shear stress, such as toxin receptors megalin and cubulin (gp280). Also provided is a method of treating in-need individual with the functional proteins produced in a three dimensional co-culture process responsive to shear stress using a rotating wall vessel.

Goodwin, Thomas John↗
NASA NTRS2007

Composite Overwrap Pressure Vessels: Mechanics and Stress Rupture Lifing Philosophy

The NASA Engineering and Safety Center (NESC) has been conducting an independent technical assessment to address safety concerns related to the known stress rupture failure mode of filament wound pressure vessels in use on Shuttle and the International Space Station. The Shuttle's Kevlar-49 fiber overwrapped tanks are of particular concern due to their long usage and the poorly understood stress rupture process in Kevlar-49 filaments. Existing long term data show that the rupture process is a function of stress, temperature and time. However due to the presence of load sharing liners and the complex manufacturing procedures, the state of actual fiber stress in flight hardware and test articles is not clearly known. Indeed non-conservative life predictions have been made where stress rupture data and lifing procedures have ignored the contribution of the liner in favor of applied pressure as the controlling load parameter. With the aid of analytical and finite element results, this paper examines the fundamental mechanical response of composite overwrapped pressure vessels including the influence of elastic-plastic liners and degraded/creeping overwrap properties. Graphical methods are presented describing the non-linear relationship of applied pressure to Kevlar-49 fiber stress/strain during manufacturing, operations and burst loadings. These are applied to experimental measurements made on a variety of vessel systems to demonstrate the correct calibration of fiber stress as a function of pressure. Applying this analysis to the actual qualification burst data for Shuttle flight hardware revealed that the nominal fiber stress at burst was in some cases 23% lower than what had previously been used to predict stress rupture life. These results motivate a detailed discussion of the appropriate stress rupture lifing philosophy for COPVs including the correct transference of stress rupture life data between dissimilar vessels and test articles.

Thesken, John C.↗
NASA NTRS2009

Composite Overwrap Pressure Vessels: Mechanics and Stress Rupture Lifting Philosophy

The NASA Engineering and Safety Center (NESC) has been conducting an independent technical assessment to address safety concerns related to the known stress rupture failure mode of filament wound pressure vessels in use on Shuttle and the International Space Station. The Shuttle s Kevlar-49 (DuPont) fiber overwrapped tanks are of particular concern due to their long usage and the poorly understood stress rupture process in Kevlar-49 filaments. Existing long term data show that the rupture process is a function of stress, temperature and time. However due to the presence of load sharing liners and the complex manufacturing procedures, the state of actual fiber stress in flight hardware and test articles is not clearly known. Indeed nonconservative life predictions have been made where stress rupture data and lifing procedures have ignored the contribution of the liner in favor of applied pressure as the controlling load parameter. With the aid of analytical and finite element results, this paper examines the fundamental mechanical response of composite overwrapped pressure vessels including the influence of elastic plastic liners and degraded/creeping overwrap properties. Graphical methods are presented describing the non-linear relationship of applied pressure to Kevlar-49 fiber stress/strain during manufacturing, operations and burst loadings. These are applied to experimental measurements made on a variety of vessel systems to demonstrate the correct calibration of fiber stress as a function of pressure. Applying this analysis to the actual qualification burst data for Shuttle flight hardware revealed that the nominal fiber stress at burst was in some cases 23 percent lower than what had previously been used to predict stress rupture life. These results motivate a detailed discussion of the appropriate stress rupture lifing philosophy for COPVs including the correct transference of stress rupture life data between dissimilar vessels and test articles.

Thesken, John C.↗
NASA NTRS2016

Mid and Thermal Infrared Remote Sensing at the Jet Propulsion Laboratory

The mid and thermal infrared (MTIR) for the Earth surface is defined between 3 and 14µm. In the outer solar system, objects are colder and their Planck response shifts towards longer wavelengths. Hence for these objects (e.g. icy moons, polar caps, comets, Europa), the thermal IR definition usually stretches out to 50µm and beyond. Spectroscopy has been a key part of this scientific exploration because of its ability to remotely determine elemental and mineralogical composition. Many key gas species such as methane, ammonia, sulfur, etc. also have vibrational bands which show up in the thermal infrared spectrum above the background response. Over the past few decades, the Jet Propulsion Laboratory has been building up a portfolio of technology to capture the MTIR for various scientific applications. Three recent sensors are briefly reviewed: The airborne Hyperspectral thermal emission spectrometer (HyTES), the ECOsystem Spaceborne Thermal Radiometer Experiment on Space Station (ECOSTRESS) and Mars Climate Sounder (MCS)/DIVINER. Each of these sensors utilize a different technology to provide a remote sensing product based on MTIR science. For example, HyTES is a push-brooming hyperspectral imager which utilizes a large format quantum well infrared photodetector (QWIP). The goal is to transition this to a new complementary barrier infrared photodetector (CBIRD) with a similar long wave cut-off and increased sensitivity. ECOSTRESS is a push-whisk Mercury Cadmium Telluride (MCT) based high speed, multi-band, imager which will eventually observe and characterize plant/vegetation functionality and stress index from the International Space Station (ISS) across the contiguous United States (CONUS). MCS/DIVINER utilizes thermopile technology to capture the thermal emission from the polar caps and shadow regions of the moon. Each sensor utilizes specific JPL technology to capture unique science. similar long wave cut-off and increased sensitivity. ECOSTRESS is a push-whisk Mercury Cadmium Telluride (MCT) based high speed, multi-band, imager which will eventually observe and characterize plant/vegetation functionality and stress index from the International Space Station (ISS) across the contiguous United States (CONUS). MCS/DIVINER utilizes thermopile technology to capture the thermal emission from the polar caps and shadow regions of the moon. Each sensor utilizes specific JPL technology to capture unique science.

Johnson, William R.↗
NASA NTRS1996

Cytokines and macrophage function in humans - role of stress

We have begun this study to commence the determination of the role of mild chronic stress in the effects of space flight on macrophage/monocyte function, a component of the immune response. Medical students undergoing regular periods of stress and relaxation have been shown to be an excellent model for determining the effects of stress on immune responses. We have begun using this model using the macrophage/monocyte as model leukocyte. The monocyte/macrophage plays a central role in immunoregulation. The studies to be included in this three year project are the effects of stress on: (1) interactions of monocytes with microbes, (2) monocyte production of cytokines, (3) monocyte phagocytosis and activity, and (4) monocyte expression of cell surface antigens important in immune responses. Stress hormone levels will also be carried out to determine if there is a correlation between stress effects on immune responses and hormonal levels. Psychological testing to insure subjects are actually stressed or relaxed at the time of testing will also be carried out. The results obtained from the proposed studies should be comparable with space flight studies with whole animals and isolated cell cultures. When complete this study should allow the commencement of the establishment of the role of stress as one compartment of the induction of immune alterations by space flight.

Sonnenfeld, Gerald↗
NASA NTRS1976

Cardiovascular function during sustained +G/z/ stress

The development of aerospace systems capable of very high levels of positive vertical accelerators stress has created a need for a better understanding of the cardiovascular responses to acceleration. Using a canine model, the heart and cardiovascular system were instrumented to continuously measure coronary blood flow, cardiac output, left ventricular and aortic root pressure, and oxygen saturation in the aorta, coronary sinus, and right ventricle. The animals were exposed to acceleration profiles up to +6 G, 120 s at peak G; a seatback angle of 45 deg was simulated in some experiments. Radiopaque contrast medium was injected to visualize the left ventricular chamber, coronary vasculature, aorta, and branches of the aorta. The results suggest mechanisms responsible for arrhythmias which may occur, and subendocardial hemorrhage which has been reported in other animals.

Erickson, H. H.↗
NASA NTRS1988

A hybrid-stress finite element for linear anisotropic elasticity

Standard assumed displacement finite elements with anisotropic material properties perform poorly in complex stress fields such as combined bending and shear and combined bending and torsion. A set of three dimensional hybrid-stress brick elements were developed with fully anisotropic material properties. Both eight-node and twenty-node bricks were developed based on the symmetry group theory of Punch and Atluri. An eight-node brick was also developed using complete polynomials and stress basis functions and reducing the order of the resulting stress parameter matrix by applying equilibrium constraints and stress compatibility constraints. Here the stress compatibility constraints must be formulated assuming anisotropic material properties. The performance of these elements was examined in numerical examples covering a broad range of stress distributions. The stress predictions show significant improvement over the assumed displacement elements but the calculation time is increased.

Fly, Gerald W.↗