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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.

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At least 1,459 records · Page 81
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NASA NTRS2013

Application Program Interface for the Orion Aerodynamics Database

The Application Programming Interface (API) for the Crew Exploration Vehicle (CEV) Aerodynamic Database has been developed to provide the developers of software an easily implemented, fully self-contained method of accessing the CEV Aerodynamic Database for use in their analysis and simulation tools. The API is programmed in C and provides a series of functions to interact with the database, such as initialization, selecting various options, and calculating the aerodynamic data. No special functions (file read/write, table lookup) are required on the host system other than those included with a standard ANSI C installation. It reads one or more files of aero data tables. Previous releases of aerodynamic databases for space vehicles have only included data tables and a document of the algorithm and equations to combine them for the total aerodynamic forces and moments. This process required each software tool to have a unique implementation of the database code. Errors or omissions in the documentation, or errors in the implementation, led to a lengthy and burdensome process of having to debug each instance of the code. Additionally, input file formats differ for each space vehicle simulation tool, requiring the aero database tables to be reformatted to meet the tool s input file structure requirements. Finally, the capabilities for built-in table lookup routines vary for each simulation tool. Implementation of a new database may require an update to and verification of the table lookup routines. This may be required if the number of dimensions of a data table exceeds the capability of the simulation tools built-in lookup routines. A single software solution was created to provide an aerodynamics software model that could be integrated into other simulation and analysis tools. The highly complex Orion aerodynamics model can then be quickly included in a wide variety of tools. The API code is written in ANSI C for ease of portability to a wide variety of systems. The input data files are in standard formatted ASCII, also for improved portability. The API contains its own implementation of multidimensional table reading and lookup routines. The same aerodynamics input file can be used without modification on all implementations. The turnaround time from aerodynamics model release to a working implementation is significantly reduced

Robinson, Philip E.↗
DOE OSTI2022

Estimating the impacts of natural gas power generation growth on solar electricity development: PJM's evolving resource mix and ramping capability

Abstract Expansion of distributed solar photovoltaic (PV) and natural gas‐fired generation capacity in the United States has put a renewed spotlight on methods and tools for power system planning and grid modernization. This article investigates the impact of increasing natural gas‐fired electricity generation assets on installed distributed solar PV systems in the Pennsylvania–New Jersey–Maryland (PJM) Interconnection in the United States over the period 2008–2018. We developed an empirical dynamic panel data model using the system‐generalized method of moments (system‐GMM) estimation approach. The model accounts for the impact of past and current technical, market and policy changes over time, forecasting errors, and business cycles by controlling for PJM jurisdictions‐level effects and year fixed effects. Using an instrumental variable to control for endogeneity, we concluded that natural gas does not crowd out renewables like solar PV in the PJM capacity market; however, we also found considerable heterogeneity. Such heterogeneity was displayed in the relationship between solar PV systems and electricity prices. More interestingly, we found no evidence suggesting any relationship between distributed solar PV development and nuclear, coal, hydro, or electricity consumption. In addition, considering policy effects of state renewable portfolio standards, net energy metering, differences in the PJM market structure, and other demand and cost‐related factors proved important in assessing their impacts on solar PV generation capacity, including energy storage as a non‐wire alternative policy technique. This article is categorized under: Photovoltaics > Economics and Policy Fossil Fuels > Climate and Environment Energy Systems Economics > Economics and Policy

29 ENERGY PLANNING, POLICY, AND ECONOMY↗
DOE OSTI2022

How to avoid multiple scattering in strongly scattering SANS and USANS samples

Small Angle Neutron Scattering (SANS) and Ultra Small Angle Neutron Scattering (USANS) are the only available experimental techniques to provide seamless non-destructive measurements of the geometry of the accessible and inaccessible pore structure of rocks from sub-nanopore size to the scale of macropores. They have therefore become the measurement of choice for tight reservoir rocks such as organic rich shales. A simplifying assumption in the analysis is, however, that during the path of neutrons through the sample each neutron is only scattered once. Shales are samples with a high scattering power and Multiple Scattering (MS) may occur which requires special modelling for deconvolution of the results. The approach to avoid MS is to simply reduce the sample thickness to <0.15–0.5 mm. Here, in this work, we present a systematic method on wavelength selection and preparation of samples to optimise extraction of microstructural data and minimise parasitic errors. Experimentally measured SAS transmission (TSAS) values are used as a practical criterion for estimation of the extent of MS. Generous beamtime allocations allowed robust testing revealing that sample thicknesses can be twice as thick as predicted using the standard protocol. Analysing thicker samples is particularly beneficial for statistically relevant characterisation of heterogeneous samples making the new protocol the method of choice for such samples.

(U)SANS↗
DOE OSTI2022

Revisiting Multi-Material Composite Structures with Homogenized Composite Properties

Composite structures inherently develop residual stresses during their curing process. Driven predominately by mismatched thermal strains between differing materials or ply orientations, but also affected by curing process phenomena like polymer shrinkage, these residual stresses can lead to failure within composite structures. There are several methods varying in complexity that can be used to model the development of residual stresses, all of which are capable of capturing sufficient detail to understand the residual stress state at the ply level. However, explicitly modeling all plies of a layup in a composite structure can be prohibitively expensive based on the number of plies, structure size, and required element size. The computational cost can be reduced through the homogenization of the composite layup without losing much fidelity of the overall response of the structure. The homogenization process reduces the many plies of a laminate to a single lamina that reduces complexity and increases the mesh size where a single element can span multiple plies. This report focuses on verification and validation efforts for a homogenization process using a suite of finite element simulations rather than an analytic solution derived from classical laminate theory. Initial verification using representative element volumes indicated there was minimal error in the homogenization process; however, this compounded to a small, but acceptable error in strip and split ring experimental composite structures. The error does under predict the residual stress state in the strip and split ring and should be accounted for when simulating composite structures with homogenized properties.

36 MATERIALS SCIENCE↗
DOE OSTI2026

Variation in surface properties as error sources in dynamic temperature measurements

Most temperature measurement methods rely upon the assumption of a single uniform source as part of the analysis in inferring an observed temperature T from the surface of a material. This is true for the radiometric and spectroscopic methods we rely upon in shock physics. However, there are obvious cases where this is a poor assumption that can cause large errors in analysis, such as the measurement of emission from a surface composed of more than one material, such as a rusted surface of Fe and Fe 2 O 3 , or a multi-material surface that could be produced through alloying methods (e.g., mokume gane) or 3D printing. Here we perform an initial examination of the effects of varied surface properties upon the analysis using idealized test data to constrain when we may have better confidence in the resulting calculations. We also examine the structures of the fits to test whether, in principle, comparing the fit with ideal gray bodies would reveal such a structure and enable the researcher to identify when a two-temperature fitting model should be used instead of a single- T model or a wavelength-dependent emissivity model.

36 MATERIALS SCIENCE↗
NASA NTRS1989

Temperature dependence of attitude sensor coalignments on the Solar Maximum Mission (SMM)

Results are presented on the temperature correlation of the relative coalignment between the fine pointing sun sensor (FPSS) and fixed head star trackers (FHSTs) on the Solar Maximum Mission (SMM). This correlation can be caused by spacecraft electronic and mechanical effects. Routine daily measurements reveal a time dependent sensor coalignment variation. The magnitude of the alignment variation is on the order of 120 arc seconds (arc sec), which greatly exceeds the prelaunch thermal structural analysis estimate of 15 acr sec. Differences between FPSS-only and FHST-only yaw solutions as a function of mission day are correlated with the relevant spacecraft temperature. If unaccounted for, the sensor misalignments due to thermal effects are a significant source of error in attitude determination accuracy. Prominent sources of temperature variation are identified and correlated with the temperature profile observed on the SMM. It was determined that even relatively small changes in spacecraft temperature can affect the coalignments between the attitude hardware on the SMM and the science instrument support plate and that frequent recalibration of sensor alignments is necessary to compensate for this effect. An alterntive to frequent recalibration is to model the variation of alignments as a function of temperature and use this to maintain accurate ground or onboard alignment estimates. These flight data analysis results may be important consierations for prelaunch analysis of future missions.

Pitone, D. S.↗
NASA NTRS2007

Theorizing Land Cover and Land Use Change: The Peasant Economy of Colonization in the Amazon Basin

This paper addresses deforestation processes in the Amazon basin. It deploys a methodology combining remote sensing and survey-based fieldwork to examine, with regression analysis, the impact household structure and economic circumstances on deforestation decisions made by colonist farmers in the forest frontiers of Brazil. Unlike most previous regression-based studies, the methodology implemented analyzes behavior at the level of the individual property. The regressions correct for endogenous relationships between key variables, and spatial autocorrelation, as necessary. Variables used in the analysis are specified, in part, by a theoretical development integrating the Chayanovian concept of the peasant household with spatial considerations stemming from von Thuenen. The results from the empirical model indicate that demographic characteristics of households, as well as market factors, affect deforestation in the Amazon. Thus, statistical results from studies that do not include household-scale information may be subject to error. From a policy perspective, the results suggest that environmental policies in the Amazon based on market incentives to small farmers may not be as effective as hoped, given the importance of household factors in catalyzing the demand for land. The paper concludes by noting that household decisions regarding land use and deforestation are not independent of broader social circumstances, and that a full understanding of Amazonian deforestation will require insight into why poor families find it necessary to settle the frontier in the first place.

Caldas, Marcellus↗
NASA NTRS2023

JWST NIRCam Defocused Imaging Photometric Stability Performance and How It Can Sense Mirror Tilts

We use JWST NIRCam short-wavelength photometry to capture a transit lightcurve of the exoplanet HAT-P-14 b to assess performance as part of instrument commissioning. The short-wavelength precision is 152 ppm per 27 s integration as measured over the full time series compared to a theoretical limit of 107 ppm, after corrections to spatially correlated 1/f noise. Persistence effects from charge trapping are well fit by an exponential function with short characteristic timescales, settling on the order of 5–15 minutes. The short-wavelength defocused photometry is also uniquely well suited to measure the real-time wave-front error of JWST. Analysis of the images and reconstructed wave-front maps indicates that two different hexagonal primary mirror segments exhibited “tilt events,” where they changed orientation rapidly in less than ∼1.4 s. In some cases, the magnitude and timing of the flux jumps caused by tilt events can be accurately predicted with a telescope model. These tilt events can be sensed by simultaneous longer-wavelength NIRCam grism spectral images alone in the form of changes to the point-spread function, diagnosed from the full width at half maximum. They can also be sensed with the fine guidance sensor instrument from difference images. Tilt events possibly from sudden releases of stress in the backplane structure behind the mirrors were expected during the commissioning period because they were found in ground-based testing. Tilt events have shown signs of decreasing in frequency but have not disappeared completely. The detectors exhibit some minor (less than 1%) deviations from linear behavior in the first few groups of each integration, potentially impacting absolute fluxes and transit depths on bright targets, where only a handful of groups are possible. Overall, the noise is within 50% of the theoretical photon noise and read noise. This bodes well for high-precision measurements of transiting exoplanets and other time variable targets.

Everett Schlawin↗
DOE OSTI2026

Validating a Dynamic PWR Safety and Security Model?

Nuclear power plants (NPPs) are assessed for safety and security using separate models that cannot capture how an attacker's decisions and a plant's response unfold together in real time, leaving regulators and operators without a complete picture of true plant vulnerability. Traditional probabilistic risk assessment (PRA) methods treat adversarial events as fixed initiators with predetermined outcomes, and are structurally incapable of representing the time-dependent interplay between physical security events, safety system response, and operator mitigative actions. At Idaho National Laboratory (INL), I contributed to the development and validation of Modeling and Analysis for Safety and Security using the Dynamic EMRALD Framework (MASS-DEF). Where static PRA relies on event-tree logic that cannot evolve mid-scenario, MASS-DEF couples a time-dependent dynamic PRA tool EMRALD (Event Modeling Risk Assessment using Linked Diagrams) with attack simulation software, allowing attacker behavior, plant system states, and operator actions to interact across time. My work focused on validating a general Pressurized Water Reactor (PWR) model. I traced model logic against PWR plant to identified errors in logic and confirm accuracy. I then built and tested attack scenarios against a general PWR model to verify that the model produced expected outcomes across all logical pathways. I also contributed a section to a related technical paper applying the same EMRALD platform to radiation dose modeling. Results show that MASS-DEF can quantitatively demonstrate that many plants exceed their regulatory security thresholds. This demonstrated margin provides a technically defensible basis for reducing the number of guards without compromising regulatory compliance. Physical security costs represent roughly 10% of annual operating budgets, making such reductions directly meaningful to INL's mission of sustaining existing commercial NPPs. This internship strengthened my understanding of nuclear systems, probabilistic modeling, and technical writing, and has solidified my pursuit of a career at a national laboratory.

98 - NUCLEAR DISARMAMENT, SAFEGUARDS, AND PHYSICAL↗
DOE OSTI2018

A digital twin for rapid qualification of 3D printed metallic components

The customized production of complex components by 3D printing has been hailed as a potentially transformative tool in manufacturing with important applications in health care, automotive and aerospace industries. However, after about a quarter of a century of research and development, only a handful of commercial alloys can be printed and the market value of all 3D printed products now amounts to a negligible portion of the manufacturing economy. This difficulty is attributable to a remarkable diversity in structure and properties of the printed components and susceptibility to defects. In addition, the current practice of qualifying components by prolonged trial and error with expensive printing equipment and feed stock material confine the printed products to a niche market where the high product cost and the delay in the qualification are not critical factors. In this report we explain how a digital twin or a digital replica of the printing machine will reduce the number of trial and error tests to obtain desired product attributes and reduce the time required for part qualification to make the printed components cost effective. It is shown that a comprehensive digital twin of 3D printing machine consisting of mechanistic, control and statistical models of 3D printing, machine learning and big data can reduce the volume of trial and error testing, reduce defects and shorten time between the design and production.

36 MATERIALS SCIENCE↗
DOE OSTI2021

Fourier-like Thermal Relaxation of Nanoscale Explosive Hot Spots

Hot spots are local regions of high temperature that are widely considered to govern explosive initiation. Hot spot dynamics rests on a delicate balance between heat generation due to chemical reactions and heat loss through thermal conduction, making accurate determinations of the conductivity under extreme conditions a key component of predictive explosive models. We develop here an approach to directly determine the thermal transport properties of explosive hot spots with realistic initial structures through a combination of molecular dynamics (MD) and diffusive heat equation (HEq) modeling. Effective thermal conductivity values are determined by fitting HEq models to MD predictions of long timescale hot spot relaxation. The approach is applied to model hot spots in the molecular crystalline explosive 1,3,5-triamino-2,4,6-trinitrobenzene (TATB) for a range of shock strengths and two limiting cases for impact orientation. Isotropic and anisotropic HEq models yield similar results, despite TATB exhibiting some of the largest and most anisotropic thermal conductivity values for explosive near normal conditions. The conductivity is found to be a strong function of density, which parametrically captures dependence on temperature, pressure, and material state. The associated root-mean-square errors of the fitted HEq models are approximately 5% of MD predicted final equilibrium temperatures. Here, the conductivity values determined here for TATB hot spots are considerably larger than those used in a prior hot spot criticality study, which may significantly impact predictions for critical hot spot sizes. The approach provides a convenient foundation for determining the effective thermal conductivity for hot spot problems in other explosives and directly yields information on reasonable approximations that might be taken in higher-level models for those materials.

36 MATERIALS SCIENCE↗
DOE OSTI2023

Motion Planning Algorithms for Safety and Quantum Computing Efficiency

Motion planning remains a fundamental problem in robotics. Sampling-based algorithms use randomization to allow efficient solutions to this complex problem. As mobile robots and autonomous vehicles become more prevalent in everyday life, motion planning must be applied to increasingly challenging scenarios. Safety has become a paramount concern in motion planning for ensuring robotic applications enrich human lives. To date, many motion planning techniques to increase safety in the face of uncertain and dynamic environments have been developed. This dissertation first addresses distributional safety of Rapidly-Exploring Random Trees (RRT) through our algorithm W-Safe RRT. To acknowledge distributional uncertainty and poor modeling, W-Safe RRT uses the Wasserstein metric to provide a probabilistic bound on the distributional distance between a robot and obstacles. Human-interpretable environmental agent classification allows online safety margin adaptation. We propose and analyze an integrating region method for online classification that increases actor labeling accuracy based on behavioral feature values when compared to state of the art methods. The method performs class assignments based on local maximum likelihood in a created behavioral feature-space, allowing a notion of classification uncertainty. Model-based methods with safety guarantees can quickly become computationally in tractable, especially with multiple agents, higher dimensions, and plentiful unknowns. Sampling based algorithms have been parallelized for computation with multi-core computers and GPUs. We consider the use of quantum algorithms and computers for sampling-based motion planning for the first time. Quantum computing performs operations on superpositions of states and can solve certain problems much more efficiently than classical computers, but introduces previously unseen challenges. With Quantum-RRT, we recast the motion planning problem into a database-search structure and use Quantum Amplitude Amplification to find reachable states in the database with a quadratic performance increase over classical methods. We address two error sources with this method: quantum measurement and quantum oracle errors. We then extend this method to Parallel Quantum-RRT, which uses a manager-worker architecture with multiple parallel quantum workers to increase database search efficiency. We compare algorithm architectures and characterize probabilities of multiple workers finding solutions. Lastly, we test in simulation the quantum algorithms against classical versions in a wide variety of scenarios, concluding that a similar parallelization improvement is to be found in the quantum case as was found in the parallelization of classical RRT.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

Enabling Robust Exoplanet Atmospheric Retrievals with Gaussian Processes

Atmospheric retrievals are essential tools for interpreting exoplanet transmission and eclipse spectra, enabling quantitative constraints on the chemical composition, aerosol properties, and thermal structure of planetary atmospheres. The James Webb Space Telescope (JWST) offers unprecedented spectral precision, resolution, and wavelength coverage, unlocking transformative insights into the formation, evolution, climate, and potential habitability of planetary systems. However, this opportunity is accompanied by challenges: modeling assumptions and unaccounted-for noise or signal sources can bias retrieval outcomes and their interpretation. To address these limitations, we introduce a Gaussian process (GP)-aided atmospheric retrieval framework that flexibly accounts for unmodeled features and correlated noise in exoplanet spectra. We validate this method on synthetic JWST observations, and show that GP-aided retrievals reduce bias in inferred abundances and better capture model–data mismatches than traditional approaches. We also introduce the concept of mean squared error to quantify the trade-off between bias and variance, arguing that this metric more accurately reflects retrieval performance than bias alone. We then reanalyze the NIRISS/SOSS JWST transmission spectrum of WASP-96 b, finding that GP-aided retrievals yield broader constraints on CO 2 and H 2 O, possibly alleviating tension between previous retrieval results and equilibrium predictions. Our GP framework provides precise and accurate constraints while highlighting regions where models fail to explain the data. As JWST matures and future facilities come online, a deeper understanding of the limitations of both data and models will be essential, and GP-enabled retrievals like the one presented here offer a principled path forward.

Rotman, Yoav [Arizona State Univ., Tempe, AZ (Unit↗
NASA NTRS1973

Currents in Florida lightning return strokes.

The transmission line return stroke model is used to derive individual current versus time wave forms from measured electric fields. A total of 98 strokes in 21 flashes at distances less than or equal to 10 km and 63 strokes in 18 flashes at distances between 10 and 32 km are analyzed for current wave shape and magnitude. For the closer strokes, return stroke velocity is also determined from the electric field wave forms. Eighteen detailed current and field wave forms and a statistical distribution of peak currents are presented. Return stroke channel currents are found to exhibit a sharp initial peak which currents measured in tall structures at the base of the lightning channel apparently do not exhibit. A complete discussion of errors is given.

Uman, M. A.↗
NASA NTRS1998

Passive Microwave Spectral Imaging of Amospheric Structure

The primary objective of this research was to improve the scientific foundation necessary to full realization of the meteorological potential of the NOAA Advanced Microwave Sounding Unit (AMSU) recently first launched on the NOAA-15 satellite in May, 1998. These advances were made in four main areas: (1) improvements, based on aircraft observations, in the atmospheric transmittance expressions used for interpreting AMSU and similar data; (2) development of neural network retrieval methods for cloud top altitude estimates of approximately 1-km accuracy under cirrus shields--the altitude is that of the larger ice particles aloft, which is related to precipitation rate; (3) analysis of early AMSU flight data with respect to its precipitation sensitivity and fine-scale thermal structure; and (4) improvements to the 54-GHz and 118-GHz MTS aircraft imaging spectrometer now operating on the NASA ER-2 aircraft. More specifically, the oxygen transmittance expressions near 118 GHz were in better agreement with aircraft data when the temperature dependence exponent of the 118.75-GHz linewidth was increased from the MPM92 value (Liebe et al., 1992) of 0.8 to 0.97+/-0.03. In contrast, the observations 52.5-55.8 GHz were consistent with the MPM92 model. Neural networks trained on comparisons of 118-GHz spectral data and coincident stereoscopic video images of convective cells observed from 20-km altitude yielded agreement in their peak altitudes within as little as 1.36 km rms, much of which is stereoscopic error. Imagery using these methods produced useful characterizations for Cyclone Oliver in 1993 and other storms (Schwartz et al., 1996; Spina et al., 1998). Similar neural network techniques yielded simulated rms errors in relative humidity retrievals of 6-14 percent over ocean and 6-15 percent over land at pressure levels from 1013 to 131 mbar (Cabrera-Mercader and Staelin, 1995).

Staelin, David H.↗
NASA NTRS2001

Modeling, Modal Properties, and Mesh Stiffness Variation Instabilities of Planetary Gears

Planetary gear noise and vibration are primary concerns in their applications in helicopters, automobiles, aircraft engines, heavy machinery and marine vehicles. Dynamic analysis is essential to the noise and vibration reduction. This work analytically investigates some critical issues and advances the understanding of planetary gear dynamics. A lumped-parameter model is built for the dynamic analysis of general planetary gears. The unique properties of the natural frequency spectra and vibration modes are rigorously characterized. These special structures apply for general planetary gears with cyclic symmetry and, in practically important case, systems with diametrically opposed planets. The special vibration properties are useful for subsequent research. Taking advantage of the derived modal properties, the natural frequency and vibration mode sensitivities to design parameters are investigated. The key parameters include mesh stiffnesses, support/bearing stiffnesses, component masses, moments of inertia, and operating speed. The eigen-sensitivities are expressed in simple, closed-form formulae associated with modal strain and kinetic energies. As disorders (e.g., mesh stiffness variation. manufacturing and assembling errors) disturb the cyclic symmetry of planetary gears, their effects on the free vibration properties are quantitatively examined. Well-defined veering rules are derived to identify dramatic changes of natural frequencies and vibration modes under parameter variations. The knowledge of free vibration properties, eigen-sensitivities, and veering rules provide important information to effectively tune the natural frequencies and optimize structural design to minimize noise and vibration. Parametric instabilities excited by mesh stiffness variations are analytically studied for multi-mesh gear systems. The discrepancies of previous studies on parametric instability of two-stage gear chains are clarified using perturbation and numerical methods. The operating conditions causing parametric instabilities are expressed in closed-form suitable for design guidance. Using the well-defined modal properties of planetary gears, the effects of mesh parameters on parametric instability are analytically identified. Simple formulae are obtained to suppress particular instabilities by adjusting contact ratios and mesh phasing.

Parker, Robert G.↗
DOE OSTI2022

Density functional theory of water with the machine-learned DM21 functional

The delicate interplay between functional-driven and density-driven errors in density functional theory (DFT) has hindered traditional density functional approximations (DFAs) from providing an accurate description of water for over 30 years. Recently, the deep-learned DeepMind 21 (DM21) functional has been shown to overcome the limitations of traditional DFAs as it is free of delocalization error. To determine if DM21 can enable a molecular-level description of the physical properties of aqueous systems within Kohn–Sham DFT, we assess the accuracy of the DM21 functional for neutral, protonated, and deprotonated water clusters. Furthermore, we find that the ability of DM21 to accurately predict the energetics of aqueous clusters varies significantly with cluster size. Additionally, we introduce the many-body MB-DM21 potential derived from DM21 data within the many-body expansion of the energy and use it in simulations of liquid water as a function of temperature at ambient pressure. We find that size-dependent functional-driven errors identified in the analysis of the energetics of small clusters calculated with the DM21 functional result in the MB-DM21 potential systematically overestimating the hydrogen-bond strength and, consequently, predicting a more ice-like local structure of water at room temperature.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
NASA NTRS1998

Recent Advances in the Method of Forces: Integrated Force Method of Structural Analysis

Stress that can be induced in an elastic continuum can be determined directly through the simultaneous application of the equilibrium equations and the compatibility conditions. In the literature, this direct stress formulation is referred to as the integrated force method. This method, which uses forces as the primary unknowns, complements the popular equilibrium-based stiffness method, which considers displacements as the unknowns. The integrated force method produces accurate stress, displacement, and frequency results even for modest finite element models. This version of the force method should be developed as an alternative to the stiffness method because the latter method, which has been researched for the past several decades, may have entered its developmental plateau. Stress plays a primary role in the development of aerospace and other products, and its analysis is difficult. Therefore, it is advisable to use both methods to calculate stress and eliminate errors through comparison. This paper examines the role of the integrated force method in analysis, animation and design.

Patnaik, Surya N.↗