SEARCH · Search NASA

Results for “conditional”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

SourceResearch connectionFrom yearThrough year

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

At least 451 records · Page 25

All sources NASA NTRS DOE OSTI

DOE OSTI2013

Conditional Dependence in Microbial Forensic Assays - A Primer

This report provides an introduction to the topic of conditional dependence in the context of microbial forensic assays. Conditional dependence between two items of evidence E1 and E2 occurs when they are both used to support a hypothesis, but E1 affects the probability of E2 and vice versa. Ignoring this dependence can lead to very large errors in estimating the diagnosticity of the combined evidence. To introduce readers to this concept, a number of definitions of conditional dependence that have been used by authors in the past have been collected together and compared. Formal mathematical relationships that constrain conditional dependence are summarized. There are several specific scenarios in which unrecognized conditional dependence can arise in microbial forensic contexts. This report provides some notional examples that illustrate dramatic effects of conditional dependence on the weight of microbial forensic evidence, and discusses the relevance of these observations for the validation of microbial forensic assays. A two-parameter model that describes the transition between various limiting forms of conditional dependence relations is provided in an appendix.

59 BASIC BIOLOGICAL SCIENCES↗

DOE OSTI2018

Evaluation of flow and heat transfer inside lean pre-mixed combustor systems under reacting flow conditions

The objective of the present work was to develop methodologies to measure heat transfer within a reacting gas turbine combustor. To accomplish this, an optically accessible research combustor system was designed and constructed at Virginia Tech, capable of operating at 650 K inlet temperature, maximum air mass flow rates of 1.3 kg/s, and flame temperatures over 1800 K. Flow and heat transfer measurements at non-reacting and reacting conditions were carried out for Reynolds numbers (Re) with respect to the combustor diameter ranging from ~11 500 to ~140 000 (depending on the condition). Particle Image Velocimetry (PIV) was used to measure the non-reacting flow field within the burner, leading to the identification of coherent structures in the flow that accounted for over 30% of the flow fluctuation kinetic energy along the swirling jet shear layers. The capability of infrared (IR) thermography to image surface temperatures through a fused silica (quartz) glass was demonstrated at non-reacting conditions. IR thermography was then used to measure the non-reacting steady state heat transfer along the combustor liner. A peak in heat transfer was identified at ~1 nozzle diameter downstream of the combustor dome plate. The peak Nusselt number along the liner was over 18 times higher than that predicted from fully developed turbulent pipe flow correlations, which have traditionally been used to estimate flame side combustor heat transfer. For the reacting measurements, a novel time-dependent heat transfer methodology was developed that allowed for the investigation of transient heat loads, including those occurring during engine ignition and shutdown. The methodology was validated at non-reacting conditions, by comparing results from an experiment with changing flow temperature, to the results obtained at steady state. The difference between the time-dependent and the steady state measurements were between 3% and 17.3% for different mass flow conditions. The time-dependent methodology was applied to reacting conditions for combustor Reynolds numbers of ~12 000 and ~24 000. At an equivalence ratio of ~0.5 and a combustor Reynolds number of ~12 000, the peak heat load location in reaction was shifted downstream by 0.2 nozzle diameters compared to the non-reacting cases. At higher equivalence ratios, and more visibly at a Reynolds number of ~24 000, the heat transfer distribution along the combustor liner exhibited two peaks, upstream and downstream of the impingement location (X/DN = 0.8-1.0 and X/DN ≈ 2.5). Reacting PIV was performed at Re = 12 000 showing the presence of a strong corner recirculation, which could potentially convect reactants upstream of the impingement point, leading to the double peak structure observed. The methodologies developed have provided insight into heat transfer within gas turbine combustors. The methods can be used to explore additional conditions and expand the dataset beyond what is presented, to fully characterize reacting combustor heat transfer.

42 ENGINEERING↗

DOE OSTI2018

A Deterministic and Probabilistic Framework for Forecasting of Time-Series Damage States and Associated End-of-lIfe of a Pressurizer Water Reactor Surge Line under Design-Basis and Grid-Load-Following Loading Conditions

Argonne National Laboratory in support of the Department of Energy’s Light Water Reactor Sustainability (LWRS) program. The present semi-annual report covers the period between May 2018 and September 2018. In this report, we present the work performed to further improve the capability for structural integrity prediction. Part of this work focused on validating a computational fluid dynamics model for modeling thermal stratification. We also present finite element (FE) model based thermal-mechanical stress analysis of a pressurized water reactor (PWR) surge line under grid-load-following loading condition. In addition, we present work related to end-of-life prediction of a PWR surge line based on ASME code and NUREG-6909 deterministic approaches under design-basis and grid-load-following conditions. Our research in this report period also majorly involved with the development of a strategy for probabilistic fatigue life estimation. First, we applied a Weibull probabilistic modeling approach based on end-of-life fatigue data (traditional S~N data under in-air and PWR water conditions) to estimate the probabilistic life for a given strain amplitude. Second, we developed a data analytics based Markov-Chain-Monte-Carlo (MCMC) model for probabilistic modeling of time-series fatigue damage states and the associated probabilistic end-of-life of a component. Unlike the Weibull type approach, the MCMC type may not require a large number of fatigue tests for estimating the end-of-life for given loading and environmental conditions. We demonstrated the use of this framework through symmetric fatigue tests (stress- or strain-ontrolled tests either under in-air or PWR-water conditions) obtained from our earlier experiments. The MCMC model can use base time-series data either obtained from a model or fatigue experiment. Since experimental data are typically more accurate than model-calculated data, we used experiment-based time-series data to demonstrate the MCMC framework. However, when performing a complex experiment is not possible (due to time and costs involved), a model-based approach can be used to generate the time-series data. Similar model-based data are presented in our earlier report (e.g. for cyclic hardening damage states of a PWR surge line under constant amplitude and design-basis loading [1]). However, for the MCMC work in this report, we used experiment-based time-series damage states obtained from fatigue experiments under design-basis and grid-load-following loading conditions. The experimental loading inputs were based on thermal-mechanical FE model results of a typical PWR surge line. Then, we used the experimental time-series damage state data for forecasting the probabilistic time-series damage states and end-of-life of the PWR surge line. Based on this MCMC modeling strategy, and with the assumed loading, environment and thermal-mechanical boundary conditions, we have estimated that a 316SS-pure base metal PWR surge line would survive at least 159 years with zero failure probability.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

DOE OSTI2017

Influence of Photospheric Magnetic Conditions on the Catastrophic Behaviors of Flux Ropes in Solar Active Regions

Since only the magnetic conditions at the photosphere can be routinely observed in current observations, it is of great significance to determine the influences of photospheric magnetic conditions on solar eruptive activities. Previous studies about catastrophe indicated that the magnetic system consisting of a flux rope in a partially open bipolar field is subject to catastrophe, but not if the bipolar field is completely closed under the same specified photospheric conditions. In order to investigate the influence of the photospheric magnetic conditions on the catastrophic behavior of this system, we expand upon the 2.5-dimensional ideal magnetohydrodynamic model in Cartesian coordinates to simulate the evolution of the equilibrium states of the system under different photospheric flux distributions. Our simulation results reveal that a catastrophe occurs only when the photospheric flux is not concentrated too much toward the polarity inversion line and the source regions of the bipolar field are not too weak; otherwise no catastrophe occurs. As a result, under certain photospheric conditions, a catastrophe could take place in a completely closed configuration, whereas it ceases to exist in a partially open configuration. This indicates that whether the background field is completely closed or partially open is not the only necessary condition for the existence of catastrophe, and that the photospheric conditions also play a crucial role in the catastrophic behavior of the flux rope system.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2024

Including Neutrino-driven Convection in the Force Explosion Condition to Predict Explodability of Multidimensional Core-collapse Supernovae (FEC+)

Abstract Most massive stars end their lives with core collapse. However, it is not clear which explode as a core-collapse supernova (CCSN), leaving behind a neutron star, and which collapse to a black hole, aborting the explosion. One path to predict explodability without expensive multidimensional simulations is to develop analytic explosion conditions. These analytic conditions also provide a deeper understanding of the explosion mechanism and they provide some insight into why some simulations explode and some do not. The analytic force explosion condition (FEC) reproduces the explosion conditions of spherically symmetric CCSN simulations. In this follow-up manuscript, we include the dominant multidimensional effect that aids explosion—neutrino-driven convection—in the FEC. This generalized critical condition (FEC+) is suitable for multidimensional simulations and has potential to accurately predict explosion conditions of two- and three-dimensional CCSN simulations. We show that adding neutrino-driven convection reduces the critical condition by ∼30%, which is consistent with previous multidimensional simulations.

Gogilashvili, Mariam (ORCID:0000000269448052)↗

DOE OSTI2023

Engine Operating Conditions, Fuel Property Effects, and Associated Fuel–Wall Interaction Dependencies of Stochastic Preignition

This work for the Coordinating Research Council (CRC) explores dependencies on the opportunity for fuel to impinge on internal engine surfaces (i.e., fuel–wall impingement) as a function of fuel properties and engine operating conditions and correlates these data with measurements of stochastic preignition (SPI) propensity. SPI rates are directly coupled with laser–induced florescence measurements of dye-doped fuel dilution measurements of the engine lubricant, which provides a surrogate for fuel–wall impingement. Literature suggests that SPI may have several dependencies, one being fuel–wall impingement. However, it remains unknown if fuel-wall impingement is a fundamental predictor and source of SPI or is simply a causational factor of SPI. In this study, these relationships on SPI and fuel-wall impingement are explored using 4 fuels at 8 operating conditions per fuel, for 32 total test points. The fuels were directly injected at two different injection timings: an earlier injection timing that initially targets the piston crown and a later injection timing that targets the cylinder liner. At each injection timing, the engine was operated at both 90°C and 70°C coolant and lubricant temperatures, and 185 and 200 kPa absolute intake manifold pressure. This work serves as an exploratory effort to down select conditions and provide initial fuel properties of interest for a secondary study to explore fuel property specific effects on fuel-wall interaction and SPI propensity. Significant findings from this initial operating condition and fuel property exploratory work are: 1. reduced engine operating coolant and lubricant temperatures, along with 2. retarded injection timings were required to increase SPI propensity. Moreover, at these conditions some fuel specific effects were also observed; specifically, increased ethanol content increased measured dye–wall (i.e., fuel–wall) interaction. However, despite increased dye–wall interaction, the increased volatility of the ethanol containing fuels also reduced the estimated fuel retention in the top-ring zone and associated measured SPI propensity. Thus, the findings of this unique approach to explore relationships between fuel-wall impingement and SPI highlight that SPI propensity is more directly proportional to retained fuel, and not simply fuel–wall impingement. Furthermore, fuel retention was found to be directly influenced by complex fuel property and engine operating condition relationships. Either retarded injection timings and/or increased fuel volatility increased fuel wall-impingement, while less volatile fuels and/or reduced coolant temperatures increased fuel retention. Therefore, for a given operating condition, the data highlights that greater volatile fuels exhibit increased fuel wall impingement without increased fuel retention or SPI propensity, while less volatile fuels could exhibit reduced fuel-wall impingement but increased fuel retention and SPI propensity rates.

33 ADVANCED PROPULSION SYSTEMS↗

DOE OSTI2013

Multiple Chronic Medical Conditions and Health-Related Quality of Life in Older Adults, 2004–2006

Understanding longitudinal relationships among multiple chronic conditions, limitations in activities of daily living, and health-related quality of life is important for identifying potential opportunities for health promotion and disease prevention among older adults. This study assessed longitudinal associations between multiple chronic conditions and limitations in activities of daily living on health-related quality of life among older adults (≥65 years) from 2004 through 2006, using data from the Medicare Health Outcomes Survey (N = 27,334). Using a longitudinal path model, we found the numbers of chronic conditions at baseline and 2-year follow-up were independently associated with more limitations in activities of daily living at 2-year follow-up. In addition, more limitations in activities of daily living at 2-year follow-up were associated with worse health-related quality of life during the follow-up time period. The association between multiple chronic conditions and indices of health-related quality of life was mediated by changes in limitations in activities of daily living. Both baseline and new multiple chronic conditions led to worse health in terms of activities of daily living and health related quality of life and should be considered important outcomes to intervene on for improved long-term health. In addition, public health practitioners should consider addressing classes of multiple chronic conditions by using interventions designed to reduce the emergence of multiple chronic conditions, such as physical activity, reductions in smoking rates, and improved and coordinated access to health care services.

59 BASIC BIOLOGICAL SCIENCES↗

NASA NTRS1975

Effect of starvation on film thickness and traction under elastohydrodynamic rolling and sliding conditions

Traction measurements under starved elastohydrodynamic conditions were obtained for a point-contact geometry. Simultaneous measurements of the film thickness and the location of the inlet lubricant boundary were made. Optical interferometry was used to measure film thickness. The thickness of a starved film for combined rolling and sliding conditions varies with the location of the inlet boundary in the same way as previously found for pure rolling conditions. When the fluid velocity distribution is calculated in the inlet region by a Reynolds lubrication analysis, backflow is seen to occur over a portion of the inlet region. Backflow is essential for the establishment of a flooded condition. The location of certain fluid velocity conditions within the inlet region, as suggested in the literature, does not adequately describe the onset of starvation. For the same slide-roll ratio a starved film was observed to possess greater traction than a flooded film. Traction measurements under starved conditions were also compared with those under flooded conditions for equivalent shear rates in the Hertzian region. When the shear rates within the Hertzian region were low and the film was severely starved, the measured tractions were lower than expected. This may be due to large shear stresses developed by the large pressure gradients that are generated in the inlet region when it is severely starved.

Wedeven, L. D.↗

NASA NTRS1978

Condition sensor system and method

The condition sensor system comprises a condition detector which produces a pulse when a parameter of the monitored condition exceeds a desired threshold. A resettable condition counter counts each pulse. A resettable timer is preset to produce a particular time frame. The counter produces a condition signal when the accumulated number of pulses within the time frame is equal to or greater than a preset count. Control means responsive to the incoming pulses and to the condition signal produce control signals that control utilization devices. After a suitable delay, the last detected pulse simultaneously resets the pulse counter and the timer, and prepares them for sensing another condition occurrence within the time frame. The invention has particular utility in the process of detecting rocking motions of blind people. A controlled, audible, bio-feedback signal is provided which constitutes a warning to the blind person that he is rocking.

Polhemus, J. T.↗

NASA NTRS1989

Aircraft and ground vehicle friction measurements obtained under winter runway conditions

Tests with specially instrumented NASA B-737 and B-727 aircraft together with several different ground friction measuring devices have been conducted for a variety of runway surface types and wetness conditions. This effort is part of the Joint FAA/NASA Aircraft/Ground Vehicle Runway Friction Program aimed at obtaining a better understanding of aircraft ground handling performance under adverse weather conditions, and defining relationships between aircraft and ground vehicle tire friction measurements. Aircraft braking performance on dry, wet, snow-, and ice-covered runway conditions is discussed together with ground vehicle friction data obtained under similar runway conditions. For the wet, compacted snow- and ice-covered runway conditions, the relationship between ground vehicles and aircraft friction data is identified. The influence of major test parameters on friction measurements such as speed, test tire characteristics, and surface contaminant-type are discussed. The test results indicate that use of properly maintained and calibrated ground vehicles for monitoring runway friction conditions should be encouraged particularly under adverse weather conditions.

Yager, Thomas J.↗

NASA NTRS1993

Radiative interactions in molecular gases under local and nonlocal thermodynamic equilibrium conditions

Basic formulations, analyses, and numerical procedures are presented to investigate radiative heat interactions in diatomic and polyatomic gases under local and nonlocal thermodynamic equilibrium conditions. Essential governing equations are presented for both gray and nongray gases. Information is provided on absorption models, relaxation times, and transfer equations. Radiative flux equations are developed which are applicable under local and nonlocal thermodynamic equilibrium conditions. The problem is solved for fully developed laminar incompressible flows between two parallel plates under the boundary condition of a uniform surface heat flux. For specific applications, three diatomic and three polyatomic gases are considered. The results are obtained numerically by employing the method of variation of parameters. The results are compared under local and nonlocal thermodynamic equilibrium conditions at different temperature and pressure conditions. Both gray and nongray studies are conducted extensively for all molecular gases considered. The particular gases selected for this investigation are CO, NO, OH, CO2, H2O, and CH4. The temperature and pressure range considered are 300-2000 K and 0.1-10 atmosphere, respectively. In general, results demonstrate that the gray gas approximation overestimates the effect of radiative interaction for all conditions. The conditions of NLTE, however, result in underestimation of radiative interactions. The method developed for this study can be extended to solve complex problems of radiative heat transfer involving nonequilibrium phenomena.

Tiwari, S. N.↗

NASA NTRS1993

Surface boundary conditions for the numerical solution of the Euler equations

We consider the implementation of boundary conditions at solid walls in inviscid Euler solutions by upwind, finite-volume methods. We review some current methods for the implementation of surface boundary conditions and examine their behavior for the problem of an oblique shock reflecting off a planar surface. We show the importance of characteristic boundary conditions for this problem and introduce a method of applying the classical flux-difference splitting of Roe as a characteristic boundary condition. Consideration of the equivalent problem of the intersection of two (equal and opposite) oblique shocks was very illuminating on the role of surface boundary conditions for an inviscid flow and led to the introduction of two new boundary-condition procedures, denoted as the symmetry technique and the curvature-corrected symmetry technique. Examples of the effects of the various surface boundary conditions considered are presented for the supersonic blunt body problem and the subcritical compressible flow over a circular cylinder. Dramatic advantages of the curvature-corrected symmetry technique over the other methods are shown, with regard to numerical entropy generation, total pressure loss, drag and grid convergence.

Dadone, A.↗

NASA NTRS1982

Susceptibility of the squirrel monkey to different motion conditions

The exact stimulus eliciting vomiting in animal studies of motion sickness is difficult to specify because the vestibular stimulation produced by many motion conditions is confounded by voluntary movements with animals. This is an important problem because experiments with animal models of motion sickness can provide useful information about antimotion sickness drugs or the role of neural mechanisms, only when animals are exposed to the same motion stimuli in each experimental session. A series of tests were conducted to determine the susceptibility of 15 adult squirrel monkeys to motion sickness in freely moving and restrained test conditions. Canal stimulation was varied by exposing the monkey in freely moving conditions to varying degrees of angular velocity (60, 90, 120, 150 deg/sec), and in restrained conditions to one angular velocity (150 deg/sec) and to cross-coupling effects of whole-body roll movements during rotation. Otolith stimulation was investigated by using sinusoidal vertical linear acceleration during free movement conditions, and off-vertical rotation and earth-horizontal (BBQ) rotation while restrained. The percentage of freely moving animal vomiting during vertical axis rotation was 27, 93, 86, and 92 for the angular velocities of 60, 90, 120, and 150 deg/sec respectively. None of the monkeys vomited during vertical axis rotation or cross-coupled rotation when restrained. Otolith stimulation appears to be a less provocative stimulus for the squirrel monkey as the percentage of animals vomiting were 13, 0, and 7 for the conditions of free movement during oscillation, restraint during off-vertical, and BBQ rotation respectively. Motion sickness to the point of vomiting occurred regularly only in conditions where self-motion was possible. Such effects could occur because voluntary movement during motion augments vestibular effects by producing self-inflicted cross-coupling, but the failure to elicit vomiting with experimenter-coupling cross-coupling argues against this interpretation. Alternatively, these results might imply that feedback from movement control mechanisms may play an important role in sensory conflict as suggested by Oman's sensory-motor conflict theory.

R A Fox↗

NASA NTRS1994

A non-local computational boundary condition for duct acoustics

A non-local boundary condition is formulated for acoustic waves in ducts without flow. The ducts are two dimensional with constant area, but with variable impedance wall lining. Extension of the formulation to three dimensional and variable area ducts is straightforward in principle, but requires significantly more computation. The boundary condition simulates a nonreflecting wave field in an infinite duct. It is implemented by a constant matrix operator which is applied at the boundary of the computational domain. An efficient computational solution scheme is developed which allows calculations for high frequencies and long duct lengths. This computational solution utilizes the boundary condition to limit the computational space while preserving the radiation boundary condition. The boundary condition is tested for several sources. It is demonstrated that the boundary condition can be applied close to the sound sources, rendering the computational domain small. Computational solutions with the new non-local boundary condition are shown to be consistent with the known solutions for nonreflecting wavefields in an infinite uniform duct.

Zorumski, William E.↗

NASA NTRS1995

Solution of the three-dimensional Helmholtz equation with nonlocal boundary conditions

The Helmholtz equation is solved within a three-dimensional rectangular duct with a nonlocal radiation boundary condition at the duct exit plane. This condition accurately models the acoustic admittance at an arbitrarily-located computational boundary plane. A linear system of equations is constructed with second-order central differences for the Helmholtz operator and second-order backward differences for both local admittance conditions and the gradient term in the nonlocal radiation boundary condition. The resulting matrix equation is large, sparse, and non-Hermitian. The size and structure of the matrix makes direct solution techniques impractical; as a result, a nonstationary iterative technique is used for its solution. The theory behind the nonstationary technique is reviewed, and numerical results are presented for radiation from both a point source and a planar acoustic source. The solutions with the nonlocal boundary conditions are invariant to the location of the computational boundary, and the same nonlocal conditions are valid for all solutions. The nonlocal conditions thus provide a means of minimizing the size of three-dimensional computational domains.

Hodge, Steve L.↗

NASA NTRS1994

Radiation boundary condition and anisotropy correction for finite difference solutions of the Helmholtz equation

In this paper finite-difference solutions of the Helmholtz equation in an open domain are considered. By using a second-order central difference scheme and the Bayliss-Turkel radiation boundary condition, reasonably accurate solutions can be obtained when the number of grid points per acoustic wavelength used is large. However, when a smaller number of grid points per wavelength is used excessive reflections occur which tend to overwhelm the computed solutions. Excessive reflections are due to the incompability between the governing finite difference equation and the Bayliss-Turkel radiation boundary condition. The Bayliss-Turkel radiation boundary condition was developed from the asymptotic solution of the partial differential equation. To obtain compatibility, the radiation boundary condition should be constructed from the asymptotic solution of the finite difference equation instead. Examples are provided using the improved radiation boundary condition based on the asymptotic solution of the governing finite difference equation. The computed results are free of reflections even when only five grid points per wavelength are used. The improved radiation boundary condition has also been tested for problems with complex acoustic sources and sources embedded in a uniform mean flow. The present method of developing a radiation boundary condition is also applicable to higher order finite difference schemes. In all these cases no reflected waves could be detected. The use of finite difference approximation inevita bly introduces anisotropy into the governing field equation. The effect of anisotropy is to distort the directional distribution of the amplitude and phase of the computed solution. It can be quite large when the number of grid points per wavelength used in the computation is small. A way to correct this effect is proposed. The correction factor developed from the asymptotic solutions is source independent and, hence, can be determined once and for all. The effectiveness of the correction factor in providing improvements to the computed solution is demonstrated in this paper.

Tam, Christopher K. W.↗

NASA NTRS1997

Application of PML Absorbing Boundary Conditions to the Benchmark Problems of Computational Aeroacoustics

Accurate numerical non-reflecting boundary conditions are important in all the proposed benchmark problems of the Second Workshop. Recently, a new absorbing boundary condition has been developed using Perfectly Matched Layer (PML) equations for the Euler equations. In this approach, a region with a width of a few grid points is introduced adjacent to the non-reflecting boundaries. In the added region, Perfectly Matched Layer equations are constructed and applied so that the out-going waves are absorbed inside the layer with little reflection to the interior domain. It will be demonstrated in the present paper that the proposed absorbing boundary condition is quite general and versatile, applicable to radiation boundaries as well as inflow and outflow boundaries. It is also easy to implement. The emphasis of the paper will be on the application of the PML absorbing boundary condition to problems in Categories 1, 2, and 3. In Category 1, solutions of problems 1 and 2 are presented. Both problems are solved using a multi-domain polar grid system. Perfectly Matched Layer equations for a circular boundary are constructed and their effectiveness assessed. In Category 2, solutions of problem 2 are presented. Here, in addition to the radiation boundary conditions at the far field in the axisymmetric coordinate system, the inflow boundary condition at the duct inlet is also dealt with using the proposed Perfectly Match Layer equations. At the inlet, a PML domain is introduced in which the incident duct mode is simulated while the waves reflected from the open end of the duct are absorbed at the same time. In Category 3, solutions of all three problems are presented. Again, the PML absorbing boundary condition is used at the inflow boundary so that the incoming vorticity wave is simulated while the outgoing acoustic waves are absorbed with very little numerical reflection. All the problems are solved using central difference schemes for spatial discretizations and the optimized Low-Dissipation and Low-Dispersion Runge-Kutta scheme for the time integration. Issues of numerical accuracy and efficiency are also addressed.

Hu, Fang Q.↗

NASA NTRS1999

Compatibility Conditions of Structural Mechanics

The theory of elasticity has camouflaged a deficiency in the compatibility formulation since 1860. In structures the ad hoc compatibility conditions through virtual "cuts" and closing "gaps" are not parallel to the strain formulation in elasticity. This deficiency in the compatibility conditions has prevented the development of a direct stress determination method in structures and in elasticity. We have addressed this deficiency and attempted to unify the theory of compatibility. This work has led to the development of the integrated force method for structures and the completed Beltrami-Michell formulation for elasticity. The improved accuracy observed in the solution of numerical examples by the integrated force method can be attributed to the compliance of the compatibility conditions. Using the compatibility conditions allows mapping of variables and facile movement among different structural analysis formulations. This paper reviews and illustrates the requirement of compatibility in structures and in elasticity. It also describes the generation of the conditions and quantifies the benefits of their use. The traditional analysis methods and available solutions (which have been obtained bypassing the missed conditions) should be verified for compliance of the compatibility conditions.

Patnaik, Surya N.↗