Results for “Set theory” — Page 33

DOE OSTI2024

Library of Advanced Materials for Engineering (LAMÉ) 5.18

Accurate and efficient constitutive modeling remains a cornerstone issue for solid mechanics analysis. Over the years, the LAMÉ advanced material model library has grown to address this challenge by implementing models capable of describing material systems spanning soft polymers to stiff ceramics including both isotropic and anisotropic responses. Inelastic behaviors including (visco)plasticity, damage, and fracture have all incorporated for use in various analyses. This multitude of options and flexibility, however, comes at the cost of many capabilities, features, and responses and the ensuing complexity in the resulting implementation. Therefore, to enhance confidence and enable the utilization of the LAMÉ library in application, this effort seeks to document and verify the various models in the LAMÉ library. Specifically, the broader strategy, organization, and interface of the library itself is first presented. The physical theory, numerical implementation, and user guide for a large set of models is then discussed. Importantly, a number of verification tests are performed with each model to not only have confidence in the model itself but also highlight some important response characteristics and features that may be of interest to end-users. Finally, in looking ahead to the future, approaches to add material models to this library and further expand the capabilities are presented.

36 MATERIALS SCIENCE↗

DOE OSTI2023

Library of Advanced Materials for Engineering (LAMÉ) 5.16

Accurate and efficient constitutive modeling remains a cornerstone issue for solid mechanics analysis. Over the years, the LAMÉ advanced material model library has grown to address this challenge by implementing models capable of describing material systems spanning soft polymers to stiff ceramics including both isotropic and anisotropic responses. Inelastic behaviors including (visco)plasticity, damage, and fracture have all incorporated for use in various analyses. This multitude of options and flexibility, however, comes at the cost of many capabilities, features, and responses and the ensuing complexity in the resulting implementation. Therefore, to enhance confidence and enable the utilization of the LAMÉ library in application, this effort seeks to document and verify the various models in the LAMÉ library. Specifically, the broader strategy, organization, and interface of the library itself is first presented. The physical theory, numerical implementation, and user guide for a large set of models is then discussed. Importantly, a number of verification tests are performed with each model to not only have confidence in the model itself but also highlight some important response characteristics and features that may be of interest to end-users. Finally, in looking ahead to the future, approaches to add material models to this library and further expand the capabilities are presented.

36 MATERIALS SCIENCE↗

DOE OSTI2024

Library of Advanced Materials for Engineering (LAMÉ) 5.22

Accurate and efficient constitutive modeling remains a cornerstone issue for solid mechanics analysis. Over the years, the LAMÉ advanced material model library has grown to address this challenge by implementing models capable of describing material systems spanning soft polymers to stiff ceramics including both isotropic and anisotropic responses. Inelastic behaviors including (visco)plasticity, damage, and fracture have all incorporated for use in various analyses. This multitude of options and flexibility, however, comes at the cost of many capabilities, features, and responses and the ensuing complexity in the resulting implementation. Therefore, to enhance confidence and enable the utilization of the LAMÉ library in application, this effort seeks to document and verify the various models in the LAMÉ library. Specifically, the broader strategy, organization, and interface of the library itself is first presented. The physical theory, numerical implementation, and user guide for a large set of models is then discussed. Importantly, a number of verification tests are performed with each model to not only have confidence in the model itself but also highlight some important response characteristics and features that may be of interest to end-users. Finally, in looking ahead to the future, approaches to add material models to this library and further expand the capabilities are presented.

36 MATERIALS SCIENCE↗

DOE OSTI2026

Library of Advanced Materials for Engineering (LAMÉ) 5.28

Accurate and efficient constitutive modeling remains a cornerstone issue for solid mechanics analysis. Over the years, the LAMÉ advanced material model library has grown to address this challenge by implementing models capable of describing material systems spanning soft polymers to stiff ceramics including both isotropic and anisotropic responses. Inelastic behaviors including (visco)plasticity, damage, and fracture have all incorporated for use in various analyses. This multitude of options and flexibility, however, comes at the cost of many capabilities, features, and responses and the ensuing complexity in the resulting implementation. Therefore, to enhance confidence and enable the utilization of the LAMÉ library in application, this effort seeks to document and verify the various models in the LAMÉ library. Specifically, the broader strategy, organization, and interface of the library itself is first presented. The physical theory, numerical implementation, and user guide for a large set of models is then discussed. Importantly, a number of verification tests are performed with each model to not only have confidence in the model itself but also highlight some important response characteristics and features that may be of interest to end-users. Finally, in looking ahead to the future, approaches to add material models to this library and further expand the capabilities are presented.

36 MATERIALS SCIENCE↗

DOE OSTI2026

Library of Advanced Materials for Engineering (LAMÉ) 5.30

Accurate and efficient constitutive modeling remains a cornerstone issue for solid mechanics analysis. Over the years, the LAMÉ advanced material model library has grown to address this challenge by implementing models capable of describing material systems spanning soft polymers to stiff ceramics including both isotropic and anisotropic responses. Inelastic behaviors including (visco)plasticity, damage, and fracture have all incorporated for use in various analyses. This multitude of options and flexibility, however, comes at the cost of many capabilities, features, and responses and the ensuing complexity in the resulting implementation. Therefore, to enhance confidence and enable the utilization of the LAMÉ library in application, this effort seeks to document and verify the various models in the LAMÉ library. Specifically, the broader strategy, organization, and interface of the library itself is first presented. The physical theory, numerical implementation, and user guide for a large set of models is then discussed. Importantly, a number of verification tests are performed with each model to not only have confidence in the model itself but also highlight some important response characteristics and features that may be of interest to end-users. Finally, in looking ahead to the future, approaches to add material models to this library and further expand the capabilities are presented.

36 MATERIALS SCIENCE↗

DOE OSTI2025

Efficient Hamiltonian encoding algorithms for extracting quantum control mechanism as interfering pathway amplitudes in the Dyson series

Hamiltonian encoding is a methodology for revealing the mechanism behind the dynamics governing controlled quantum systems. In this paper, following Mitra and Rabitz \cite{abhra_1}, we define mechanism via pathways of eigenstates that describe the evolution of the system, where each pathway is associated with a complex-valued amplitude corresponding to a term in the Dyson series. The evolution of the system is determined by the constructive and destructive interference of these pathway amplitudes. Pathways with similar attributes can be grouped together into pathway classes. The amplitudes of pathway classes are computed by modulating the Hamiltonian matrix elements and decoding the subsequent evolution of the system rather than by direct computation of the individual terms in the Dyson series. The original implementation of Hamiltonian encoding was computationally intensive and became prohibitively expensive in large quantum systems. This paper presents two new encoding algorithms that calculate the amplitudes of pathway classes by using techniques from graph theory and algebraic topology to exploit patterns in the set of allowed transitions, greatly reducing the number of matrix elements that need to be modulated. These new algorithms provide an exponential decrease in both computation time and memory utilization with respect to the Hilbert space dimension of the system. To demonstrate the use of these techniques, they are applied to two illustrative state-to-state transition problems.

Abrams, Erez [Princeton University, Massachusetts ↗

NASA NTRS1972

Does Io's ionosphere influence Jupiter's radio bursts.

Goldreich and Lynden-Bell's theory of Jupiter's Io-correlated decametric radiation sets a lower limit to Io's conductivity, high enough to carry the current associated with the radiated power. Dermott's analysis of conductivities of rocks and ice shows no such conductivity at Io's temperature. However, we show that if Io has even a small atmosphere, say of methane as suggested by Binder and Cruikshank, or of argon or nitrogen, it will have an ionosphere with adequate conductivity to meet the above criterion. A requirement for higher conductivity was found by Goldreich and Lynden-Bell on the basis of motion of magnetic lines past Io. This requirement appears to us unnecessary in view of experiments which prove that motion of the lines is not the source of the electromotance.

Webster, D. L.↗

NASA NTRS1971

Optimization of life support systems and their systems reliability

The identification, analysis, and optimization of life support systems and subsystems have been investigated. For each system or subsystem that has been considered, the procedure involves the establishment of a set of system equations (or mathematical model) based on theory and experimental evidences; the analysis and simulation of the model; the optimization of the operation, control, and reliability; analysis of sensitivity of the system based on the model; and, if possible, experimental verification of the theoretical and computational results. Research activities include: (1) modeling of air flow in a confined space; (2) review of several different gas-liquid contactors utilizing centrifugal force: (3) review of carbon dioxide reduction contactors in space vehicles and other enclosed structures: (4) application of modern optimal control theory to environmental control of confined spaces; (5) optimal control of class of nonlinear diffusional distributed parameter systems: (6) optimization of system reliability of life support systems and sub-systems: (7) modeling, simulation and optimal control of the human thermal system: and (8) analysis and optimization of the water-vapor eletrolysis cell.

Fan, L. T.↗

NASA NTRS1977

Axel dust on Saturn and Titan

The observed sharp drop in the geometric albedo of Titan shortward of 6000 A (also observed for Jupiter and Saturn) has been tentatively attributed to the presence of small absorbing particles referred to as Axel dust. The properties of Axel dust particles are studied, with the effect of scattering included through Mie theory, in an attempt to obtain a physically plausible set of parameters that properly characterizes the dust. Quantitative characteristics of the dust are described, scattering and absorption properties of various particle size distributions are calculated, and fits are made to observations of Titan and Saturn. It is found that: (1) a flat distribution of particle radii up to 0.1 micron and an imaginary part of the refractive index that varies as the -2.5 power of wavelength produce a good fit for Titan provided the extinction optical depth of the satellite's atmosphere is about 10 at 5000 A; (2) a clear layer of about 7 km-am hydrogen is required above the dust for a good fit to Saturn with the same dust properties; and (3) the inclusion of dust significantly increases the computed abundance of methane over the value given by reflecting-layer models.

Podolak, M.↗

NASA NTRS1977

An experimental study of the fracture behavior of laminated graphite/epoxy composites

The results of an experimental investigation on the fracture behavior of unidirectional and multidirectional laminated graphite/epoxy composites is reported. Critical tensile fracture stresses for constant head rate uniaxial specimens containing single-edge notches, double-edge notches, and centrally located circular holes are presented. Results are reported for loads and notches at various angles to the fiber direction. Evidence of notch sensitivity and stable crack growth is presented. Self-similar crack growth is shown to occur for only a limited set of circumstances. Critical stresses are compared to the theories of Waddoups et al and Whitney et al. These comparisons are presented using isotropic and orthotropic stress concentration factors together with a finite width correction factor. The results tend to show that use of only isotropic correction factors allow good correlation between theory and experiment.

Brinson, H. F.↗

NASA NTRS1980

Stability of large horizontal-axis axisymmetric wind turbines

The stability of large horizontal-axis, axisymmetric, power producing wind turbines is examined within the framework of an analytical model which includes dynamic coupling of the rotor, tower, and power generating system. The aerodynamic loading is derived from blade element theory. Stability is determined by the eigenvalues of a set of linearized constant-coefficient differential equations. All results presented are based on a 3-bladed, 300-ft diameter, 2.0-MW wind turbine. It is shown that unstable or weakly stable behavior can be caused by aerodynamic forces due to motion of the rotor blades and tower in the plane of rotation or by mechanical coupling between the rotor system and the tower.

Hirschbein, M. S.↗

NASA NTRS1983

Spinning fluids in the Einstein-Cartan theory

An Eulerian variational principle for a spinning fluid in the Einstein-Cartan metric-torsion theory is presented. The variational principle yields the complete set of field equations for the system. The symmetric energy-momentum tensor is a sum of a perfect-fluid term and a spin term.

Ray, J. R.↗

NASA NTRS1984

Creep-rupture reliability analysis

A probabilistic approach to the correlation and extrapolation of creep-rupture data is presented. Time temperature parameters (TTP) are used to correlate the data, and an analytical expression for the master curve is developed. The expression provides a simple model for the statistical distribution of strength and fits neatly into a probabilistic design format. The analysis focuses on the Larson-Miller and on the Manson-Haferd parameters, but it can be applied to any of the TTP's. A method is developed for evaluating material dependent constants for TTP's. It is shown that optimized constants can provide a significant improvement in the correlation of the data, thereby reducing modelling error. Attempts were made to quantify the performance of the proposed method in predicting long term behavior. Uncertainty in predicting long term behavior from short term tests was derived for several sets of data. Examples are presented which illustrate the theory and demonstrate the application of state of the art reliability methods to the design of components under creep.

Peralta-Duran, A.↗

NASA NTRS1985

Fatigue life analysis of a turboprop reduction gearbox

A fatigue life analysis of the Allison T56/501 turboprop reduction gearbox was developed. The life and reliability of the gearbox was based on the lives and reliabilities of the main power train bearings and gears. The bearing and gear lives were determined using the Lundberg-Palmgren theory and a mission profile. The five planet bearing set had the shortest calculated life among the various gearbox components, which agreed with field experience where the planet bearing had the greatest incidences of failure. The analytical predictions of relative lives among the various bearings were in reasonable agreement with field experience. The predicted gearbox life was in excellent agreement with field data when the material life adjustment factors alone were used. The gearbox had a lower predicted life in comparison with field data when no life adjustment factors were used or when lubrication life adjustment factors were used either alone or in combination with the material factors.

Lewicki, D. G.↗

NASA NTRS1985

Creep-rupture reliability analysis

A probabilistic approach to the correlation and extrapolation of creep-rupture data is presented. Time temperature parameters (TTP) are used to correlate the data, and an analytical expression for the master curve is developed. The expression provides a simple model for the statistical distribution of strength and fits neatly into a probabilistic design format. The analysis focuses on the Larson-Miller and on the Manson-Haferd parameters, but it can be applied to any of the TTP's. A method is developed for evaluating material dependent constants for TTP's. It is shown that optimized constants can provide a significant improvement in the correlation of the data, thereby reducing modelling error. Attempts were made to quantify the performance of the proposed method in predicting long term behavior. Uncertainty in predicting long term behavior from short term tests was derived for several sets of data. Examples are presented which illustrate the theory and demonstrate the application of state of the art reliability methods to the design of components under creep.

Peralta-Duran, A.↗

NASA NTRS1985

Vibrations of twisted cantilever plates - A comparison of theoretical results

As a result of significant differences in the published results for various methods of analysis involving the use of finite element techniques, there are now some questions regarding the adequacy of these methods to predict accurately the vibratory characteristics of highly twisted cantilever plates. In an attempt to help in a resolution of the arising problems, a joint government/industry/university research effort was initiated. The primary objective of the present paper is to summarize the theoretical methods used in the study and show samples of the obtained results. The study provided 19 sets of theoretical results which are derived from beam theory, shell theory, and finite element methods.

Kielb, R. E.↗

NASA NTRS1986

Fatigue life analysis of a turboprop reduction gearbox

A fatigue life analysis of the Allison T56/501 turboprop reduction gearbox was developed. The life and reliability of the gearbox was based on the lives and reliabilities of the main power train bearings and gears. The bearing and gear lives were determined using the Lundberg-Palmgren theory and a mission profile. The five planet bearing set had the shortest calculated life among the various gearbox components, which agreed with field experience where the planet bearing had the greatest incidences of failure. The analytical predictions of relative lives among the various bearings were in reasonable agreement with field experience. The predicted gearbox life was in excellent agreement with field data when the material life adjustment factors alone were used. The gearbox had a lower predicted life in comparison with field data when no life adjustment factors were used or when lubrication life adjustment factors were used either alone or in combination with the material factors.

Lewicki, D. G.↗

NASA NTRS1989

A new adaptive control approach for aerospace vehicles with parameter uncertainties

A new stochastic adaptive control structure is developed for the problem of combined parameter estimation and control of aerospace vehicles with changing parameters. Parameter uncertainties are modeled as first-order Gauss-Markov processes, and are introduced to the system dynamics through a small parameter. It is assumed that an accurate inertial measurement unit gives perfect measurements of the state variables. Since the stochastic system is assumed to be Gauss-Markov, the density function of the parameters given these measurements is conditionally Gaussian. Based on this conditionally Gaussian density, the problem of minimizing a quadratic cost over an infinite time horizon can be set up within the framework of stochastic optimal control theory. The optimal feedback control law is derived from a straightforward expansion of the Hamilton-Jacobi-Bellman equation, based on the LQG solution. The resulting nonlinear controller is applied to the pitch axis control of a space platform with uncertain moments of inertia and is shown to produce marked improvement over a fixed controller.

Hahn, Yungsun↗