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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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All sourcesNASA NTRSDOE OSTI
NASA NTRS1961

Cross-Sectional Deformations of Monocoque Beams and Their Effects on the Natural Vibration Frequencies

The variational principle, differential equations, and boundary conditions governing the cross-sectional distortions due to inertia loading of a two-dimensional model of a thin monocoque wing are shown. A theoretical analysis of this simplified model is made in order to determine the nature of the coupling between the cross-sectional modes and the spanwise deformation modes. General solutions are obtained in finite-difference form for arbitrary cross sections and an exact solution is presented for a parabolic-arc cross section of constant cover thickness. The application of these results in evaluating the coupled frequencies of the actual structure is discussed. Frequencies evaluated for a parabolic-arc monocoque beam show good agreement with experimental values.

Thomson, Robert G.↗
NASA NTRS1998

The Role of Multiphysics Simulation in Multidisciplinary Analysis

This article describes the applications of the Spectrum(Tm) Solver in Multidisciplinary Analysis (MDA). Spectrum, a multiphysics simulation software based on the finite element method, addresses compressible and incompressible fluid flow, structural, and thermal modeling as well as the interaction between these disciplines. Multiphysics simulation is based on a single computational framework for the modeling of multiple interacting physical phenomena. Interaction constraints are enforced in a fully-coupled manner using the augmented-Lagrangian method. Within the multiphysics framework, the finite element treatment of fluids is based on Galerkin-Least-Squares (GLS) method with discontinuity capturing operators. The arbitrary-Lagrangian-Eulerian method is utilized to account for deformable fluid domains. The finite element treatment of solids and structures is based on the Hu-Washizu variational principle. The multiphysics architecture lends itself naturally to high-performance parallel computing. Aeroelastic, propulsion, thermal management and manufacturing applications are presented.

Rifai, Steven M.↗
NASA NTRS2002

On the Formulation of Weakly Singular Displacement/Traction Integral Equations; and Their Solution by the MLPG Method

In this paper, a very simple method is used to derive the weakly singular traction boundary integral equation based on the integral relationships for displacement gradients. The concept of the MLPG method is employed to solve the integral equations, especially those arising in solid mechanics. A moving Least Squares (MLS) interpolation is selected to approximate the trial functions in this paper. Five boundary integral Solution methods are introduced: direct solution method; displacement boundary-value problem; traction boundary-value problem; mixed boundary-value problem; and boundary variational principle. Based on the local weak form of the BIE, four different nodal-based local test functions are selected, leading to four different MLPG methods for each BIE solution method. These methods combine the advantages of the MLPG method and the boundary element method.

Atluri, Satya N.↗
NASA NTRS2003

Approximating the Helium Wavefunction in Positronium-Helium Scattering

In the Kohn variational treatment of the positronium- hydrogen scattering problem the scattering wave function is approximated by an expansion in some appropriate basis set, but the target and projectile wave functions are known exactly. In the positronium-helium case, however, a difficulty immediately arises in that the wave function of the helium target atom is not known exactly, and there are several ways to deal with the associated eigenvalue in formulating the variational scattering equations to be solved. In this work we will use the Kohn variational principle in the static exchange approximation to d e t e e the zero-energy scattering length for the Ps-He system, using a suite of approximate target functions. The results we obtain will be compared with each other and with corresponding values found by other approximation techniques.

DiRienzi, Joseph↗
NASA NTRS2006

Model Predictive Optimal Control of a Time-Delay Distributed-Parameter Systems

This paper presents an optimal control method for a class of distributed-parameter systems governed by first order, quasilinear hyperbolic partial differential equations that arise in many physical systems. Such systems are characterized by time delays since information is transported from one state to another by wave propagation. A general closed-loop hyperbolic transport model is controlled by a boundary control embedded in a periodic boundary condition. The boundary control is subject to a nonlinear differential equation constraint that models actuator dynamics of the system. The hyperbolic equation is thus coupled with the ordinary differential equation via the boundary condition. Optimality of this coupled system is investigated using variational principles to seek an adjoint formulation of the optimal control problem. The results are then applied to implement a model predictive control design for a wind tunnel to eliminate a transport delay effect that causes a poor Mach number regulation.

Nguyen, Nhan↗
NASA NTRS2004

Development of New Modeling and Analysis Tools for Solar Sails

Existing finite-element-based structural analysis codes are ineffective in treating deployable gossamer space systems, including solar sails that are formed by long space-deployable booms and extremely large thin-film membrane apertures. Recognizing this, the NASA Space transportation Technology Program has initiated and sponsored a focused research effort to develop new and computationally efficient structural modeling and analysis tools for solar sails. The technical approach of this ongoing effort will be described. Two solution methods, the Distributed Transfer Function Method and the Parameter-Variation-Principle method, based on which the technical approach was formatted are also discussed.

boom↗
NASA NTRS2010

Nondimensional Parameters and Equations for Nonlinear and Bifurcation Analyses of Thin Anisotropic Quasi-Shallow Shells

A comprehensive development of nondimensional parameters and equations for nonlinear and bifurcations analyses of quasi-shallow shells, based on the Donnell-Mushtari-Vlasov theory for thin anisotropic shells, is presented. A complete set of field equations for geometrically imperfect shells is presented in terms general of lines-of-curvature coordinates. A systematic nondimensionalization of these equations is developed, several new nondimensional parameters are defined, and a comprehensive stress-function formulation is presented that includes variational principles for equilibrium and compatibility. Bifurcation analysis is applied to the nondimensional nonlinear field equations and a comprehensive set of bifurcation equations are presented. An extensive collection of tables and figures are presented that show the effects of lamina material properties and stacking sequence on the nondimensional parameters.

Nemeth, Michael P.↗
NASA NTRS2010

Using MERRA Gridded Innovations for Quantifying Uncertainties in Analysis Fields and Diagnosing Observing System Inhomogeneities

MERRA is a NASA reanalysis for the satellite era using a major new version of the Goddard Earth Observing System Data Assimilation System Version 5 (GEOS-5). The project focuses on historical analyses of the hydrological cycle on a broad range of weather and climate time scales and places the NASA EOS suite of observations in a climate context. The characterization of uncertainty in reanalysis fields is a commonly requested feature by users of such data. While intercomparison with reference data sets is common practice for ascertaining the realism of the datasets, such studies typically are restricted to long term climatological statistics and seldom provide state dependent measures of the uncertainties involved. In principle, variational data assimilation algorithms have the ability of producing error estimates for the analysis variables (typically surface pressure, winds, temperature, moisture and ozone) consistent with the assumed background and observation error statistics. However, these "perceived error estimates" are expensive to obtain and are limited by the somewhat simplistic errors assumed in the algorithm. The observation minus forecast residuals (innovations) by-product of any assimilation system constitutes a powerful tool for estimating the systematic and random errors in the analysis fields. Unfortunately, such data is usually not readily available with reanalysis products, often requiring the tedious decoding of large datasets and not so-user friendly file formats. With MERRA we have introduced a gridded version of the observations/innovations used in the assimilation process, using the same grid and data formats as the regular datasets. Such dataset empowers the user with the ability of conveniently performing observing system related analysis and error estimates. The scope of this dataset will be briefly described. We will present a systematic analysis of MERRA innovation time series for the conventional observing system, including maximum-likelihood estimates of background and observation errors, as well as global bias estimates. Starting with the joint PDF of innovations and analysis increments at observation locations we propose a technique for diagnosing bias among the observing systems, and document how these contextual biases have evolved during the satellite era covered by MERRA.

da Silva, Arlindo↗
NASA NTRS2011

Dynamic Shape Reconstruction of Three-Dimensional Frame Structures Using the Inverse Finite Element Method

A robust and efficient computational method for reconstructing the three-dimensional displacement field of truss, beam, and frame structures, using measured surface-strain data, is presented. Known as shape sensing , this inverse problem has important implications for real-time actuation and control of smart structures, and for monitoring of structural integrity. The present formulation, based on the inverse Finite Element Method (iFEM), uses a least-squares variational principle involving strain measures of Timoshenko theory for stretching, torsion, bending, and transverse shear. Two inverse-frame finite elements are derived using interdependent interpolations whose interior degrees-of-freedom are condensed out at the element level. In addition, relationships between the order of kinematic-element interpolations and the number of required strain gauges are established. As an example problem, a thin-walled, circular cross-section cantilevered beam subjected to harmonic excitations in the presence of structural damping is modeled using iFEM; where, to simulate strain-gauge values and to provide reference displacements, a high-fidelity MSC/NASTRAN shell finite element model is used. Examples of low and high-frequency dynamic motion are analyzed and the solution accuracy examined with respect to various levels of discretization and the number of strain gauges.

Gherlone, Marco↗
NASA NTRS2021

AIRS Point Spread Function Reconstruction using AIRS and MODIS Data

The purpose of this work is to use data from the Atmospheric Infrared Sounder (AIRS) and the Moderate Resolution Imaging Spectroradiometer (MODIS) to refine our knowledge of post-launch AIRS point spread functions (PSFs), including suspected changes over the mission. We develop methodology, by deriving mathematical optimization formulation based on variational principles and Sobolev gradient descent, for reconstruction of AIRS spatial response functions. We use the data over the ocean, collected for the duration of a day, to reconstruct a single PSF. We examine the repeatability of our reconstructions by computing PSFs based on data collected during two consecutive days, and also investigating the change in the reconstructions by comparing the reconstructed PSF based on data collected in the beginning and the middle of the mission. We also quantify uncertainties in our reconstruction results.

Vese, Luminita↗
NASA NTRS1991

Extrema Principles Of Dissipation In Fluids

Report discusses application of principle of least action and other variational or extrema principles to dissipation of energy and production of entropy in fluids. Principle of least action applied successfully to dynamics of particles and to quantum mechanics, but not universally accepted that variational principles applicable to thermodynamics and hydrodynamics. Report argues for applicability of some extrema principles to some simple flows.

Horne, W. Clifton↗
NASA NTRSDate not supplied

A Physics-Based Work-Energy Formulation for Real-Time Trajectory Guidance of A Lunar Lander

Throughout the years, many researchers have calculated and optimized trajectory solutions for lunar landing systems by employing sophisticated mathematical methods, that include: Hamilton’s Principle of Variation, Pontryagin’s maximum principle, and well known convex-optimization techniques among others. Many of these approaches typically require expensive computational resources to achieve convergence in the solution. In an effort to reduce complexity and the computational load required to obtain real-time guidance commands, a simple physics-based work-energy approach has been formulated. This approach is based on the dissipation of the mechanical energy of the vehicle to its final desired energy state required to achieve a safe landing. The rocket engine(s) employed during landing (among other maneuvers) dissipates mechanical energy by both doing work against the velocity vector of the vehicle (thus defining the trajectory path), and by jettisoning mass. Therefore, by solving the energy dissipation problem at every step of the maneuver, a much simpler formulation that naturally and quickly attains convergence is obtained. This formulation is not limited to approach, landing, and divert maneuvers, but in principle it can be employed during de-orbiting, braking burn, ascent, as well as orbit insertion.

Guidance↗
NASA NTRSDate not supplied

A Physics-Based Work-Energy Formulation for Real-Time Trajectory Guidance of a Lunar Lander

Throughout the years, many researchers have calculated and optimized trajectory solutions for lunar landing systems by employing sophisticated mathematical methods, that include: Hamilton’s Principle of Variation, Pontryagin’s maximum principle, and well known convex-optimization techniques among others. Many of these approaches typically require expensive computational resources to achieve convergence in the solution. In an effort to reduce complexity and the computational load required to obtain real-time guidance commands, a simple physics-based work-energy approach has been formulated. This approach is based on the dissipation of the mechanical energy of the vehicle to its final desired energy state required to achieve a safe landing. The rocket engine(s) employed during landing (among other maneuvers) dissipates mechanical energy by both doing work against the velocity vector of the vehicle (thus defining the trajectory path), and by jettisoning mass. Therefore, by solving the energy dissipation problem at every step of the maneuver, a much simpler formulation that naturally and quickly attains convergence is obtained. This formulation is not limited to approach, landing, and divert maneuvers, but in principle it can be employed during de-orbiting, braking burn, ascent, as well as orbit insertion.

Guidance↗
NASA NTRS2000

Limits on Line Bisector Variability for Stars with Extrasolar Planets

We present an analysis of high-resolution synoptic spectra of ten F- and G-type stars, seven of which exhibit periodic radial velocity variations due to the presence of one or more substellar companions. We searched for subtle periodic variations in photospheric line asymmetry, as characterized by line bisectors. In principle, periodic variations in line asymmetry observed at lower spectral resolution could mimic the radial velocity signature of a companion, but we find no significant evidence of such behavior in our data. Observations were obtained from 1998 March to 1999 February using the National Solar Observatory (NSO) 1.52-m McMath-Pierce Solar Telescope Facility on Kitt Peak in conjunction with the solar-stellar spectrograph, achieving a resolving power of 1.2x10(exp5). To characterize line asymmetry, we first measured line bisectors for the unblended Fe I photospheric line at 625.26 nm. To improve sensitivity to small fluctuations, we then combined points in each bisector to form a velocity displacement with respect to the line core. We searched for periodic variations in this displacement, finding no substantial difference between stars with substellar companions and those without reported companions. We find no correlation between bisector velocity displacement and the known orbital phase of substellar companions around our target stars. Simulations of a periodic signal with noise levels that mimic our measurement errors suggest that we can exclude bisector variations with amplitudes greater than about 20 m/s. These results support the conclusion that extrasolar planets best explain the observed periodic variations in radial velocity.

Povich, M. S.↗
DOE OSTI2022

A Realistic Theory of Quantum Measurement

Abstract We propose that the ontic understanding of quantum mechanics can be extended to a fully realistic theory that describes the evolution of the wavefunction at all times, including during a measurement. In such an approach the wave equation should reduce to the standard wave equation when there is no measurement, and describe state reduction when the system is measured. The general wave equation must be nonlinear and nonlocal, and we require it to be time-symmetric; consequently, this approach is not a new interpretation but a new theory. The wave equation is an integrodifferential equation (IDE). The time symmetry requirement leads to a retrocausal approach, in which the wave equation is solved subject to initial and final conditions to determine history at intermediate times. We propose that different outcomes from (apparently) identically prepared experiments may result from uncontrolled parameters; both the nonlocality and the retrocausality of the theory imply that Bell’s Theorem cannot rule out such “hidden variables.” Beginning with Hamilton’s principle, we demonstrate the construction of such a theory by replacing the action with a functional designed to give rise to a nonlinear, nonlocal IDE as the wave equation. This IDE reduces to the standard wave equation (a differential equation) in the absence of a measurement, but exhibits state reduction to a single eigenvalue when the system interacts with another system with the properties of a measurement apparatus. We demonstrate several desirable features of this theory; for other properties we indicate their plausibility and possible avenues to a proof.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
NASA NTRS1993

Geomagnetic field models incorporating physical constraints on the secular variation

This proposal has been concerned with methods for constructing geomagnetic field models that incorporate physical constraints on the secular variation. The principle goal that has been accomplished is the development of flexible algorithms designed to test whether the frozen flux approximation is adequate to describe the available geomagnetic data and their secular variation throughout this century. These have been applied to geomagnetic data from both the early and middle part of this century and convincingly demonstrate that there is no need to invoke violations of the frozen flux hypothesis in order to satisfy the available geomagnetic data.

Constable, Catherine↗