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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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NASA NTRS2010

Proceedings of the Second NASA Formal Methods Symposium

This publication contains the proceedings of the Second NASA Formal Methods Symposium sponsored by the National Aeronautics and Space Administration and held in Washington D.C. April 13-15, 2010. Topics covered include: Decision Engines for Software Analysis using Satisfiability Modulo Theories Solvers; Verification and Validation of Flight-Critical Systems; Formal Methods at Intel -- An Overview; Automatic Review of Abstract State Machines by Meta Property Verification; Hardware-independent Proofs of Numerical Programs; Slice-based Formal Specification Measures -- Mapping Coupling and Cohesion Measures to Formal Z; How Formal Methods Impels Discovery: A Short History of an Air Traffic Management Project; A Machine-Checked Proof of A State-Space Construction Algorithm; Automated Assume-Guarantee Reasoning for Omega-Regular Systems and Specifications; Modeling Regular Replacement for String Constraint Solving; Using Integer Clocks to Verify the Timing-Sync Sensor Network Protocol; Can Regulatory Bodies Expect Efficient Help from Formal Methods?; Synthesis of Greedy Algorithms Using Dominance Relations; A New Method for Incremental Testing of Finite State Machines; Verification of Faulty Message Passing Systems with Continuous State Space in PVS; Phase Two Feasibility Study for Software Safety Requirements Analysis Using Model Checking; A Prototype Embedding of Bluespec System Verilog in the PVS Theorem Prover; SimCheck: An Expressive Type System for Simulink; Coverage Metrics for Requirements-Based Testing: Evaluation of Effectiveness; Software Model Checking of ARINC-653 Flight Code with MCP; Evaluation of a Guideline by Formal Modelling of Cruise Control System in Event-B; Formal Verification of Large Software Systems; Symbolic Computation of Strongly Connected Components Using Saturation; Towards the Formal Verification of a Distributed Real-Time Automotive System; Slicing AADL Specifications for Model Checking; Model Checking with Edge-valued Decision Diagrams; and Data-flow based Model Analysis.

Munoz, Cesar↗
NASA NTRS1976

Nonlinear effects in thermal stress analysis of a solid propellant rocket motor

Direct characterization procedures were used to determine the relaxation modulus as a function of time, temperature, and state of strain. Using the quasi-elastic method of linearviscoelasticity, these properties were employed in a finite element computer code to analyze a thick-walled, nonlinear viscoelastic cylinder in the state of plane strain bonded to a thin (but stiff) elastic casing and subjected to slow thermal cooling. The viscoelastic solution is then expressed as a sequence of elastic finite element solutions. The strain-dependent character of the relaxation modulus is included by replacing the single relaxation curve used in the linear viscoelastic theory by a family of relaxation functions obtained at various strain levels. These functions may be regarded as a collection of stress histories or responses to specific loads (in this case, step strains) with which the cooldown solution is made to agree by iterations on the modulus and strain level.

Francis, E. C.↗
NASA NTRS1991

FDTD modeling of thin impedance sheets

Thin sheets of resistive or dielectric material are commonly encountered in radar cross section calculations. Analysis of such sheets is simplified by using sheet impedances. It is shown that sheet impedances can be modeled easily and accurately using Finite Difference Time Domain (FDTD) methods. These sheets are characterized by a discontinuity in the tangential magnetic field on either side of the sheet but no discontinuity in tangential electric field. This continuity, or single valued behavior of the electric field, allows the sheet current to be expressed in terms of an impedance multiplying this electric field.

Luebbers, Raymond↗
NASA NTRS1987

Power flow as a complement to statistical energy analysis and finite element analysis

Present methods of analysis of the structural response and the structure-borne transmission of vibrational energy use either finite element (FE) techniques or statistical energy analysis (SEA) methods. The FE methods are a very useful tool at low frequencies where the number of resonances involved in the analysis is rather small. On the other hand SEA methods can predict with acceptable accuracy the response and energy transmission between coupled structures at relatively high frequencies where the structural modal density is high and a statistical approach is the appropriate solution. In the mid-frequency range, a relatively large number of resonances exist which make finite element method too costly. On the other hand SEA methods can only predict an average level form. In this mid-frequency range a possible alternative is to use power flow techniques, where the input and flow of vibrational energy to excited and coupled structural components can be expressed in terms of input and transfer mobilities. This power flow technique can be extended from low to high frequencies and this can be integrated with established FE models at low frequencies and SEA models at high frequencies to form a verification of the method. This method of structural analysis using power flo and mobility methods, and its integration with SEA and FE analysis is applied to the case of two thin beams joined together at right angles.

Cuschieri, J. M.↗
DOE OSTI2024

Giant Graviton Expansion from Bubbling Geometry: Discreteness from Quantized Geometry

The superconformal index of half-BPS states in N = 4 supersymmetric Yang-Mills with gauge group U⁡(N) admits an expansion in terms of giant gravitons, J N (q) = J ∞ ⁡(q)⁢Σ$^{∞}_{m=0}$ q m⁢N ⁢ J^ m ⁡(q), where m is the number of giant gravitons and J ∞ ⁡(q) is the graviton index. The expansion can be viewed as the implementation of trace relations for finite N. We derive this expansion directly in supergravity from the class of half-BPS solutions due to Lin, Lunin, and Maldacena in type IIB supergravity. The moduli space of these configurations can be quantized using covariant quantization methods. We show how this quantization leads to the precise expression for the expansion in terms of giant gravitons. Our proposal provides a derivation of the giant graviton expansion directly in terms of quantized supergravity degrees of freedom, and it recovers discrete data via quantum geometries that are classically nonsmooth.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
NASA NTRS2020

Model-Reference Adaptive Control of Distributed Lagrangian Infinite-Dimensional Systems Using Hamilton’s Principle

This paper presents a Hamilton's principle for distributed control of infinite-dimensional systems modeled by a distributed form of the Euler-Lagrange method. The distributed systems are governed by a system of linear partial differential equations in space and time. A generalized potential energy expression is developed that can capture most physical systems including those systems that have no spatial distribution. The Hamilton's principle is applied to derive distributed feedback control methods without resorting to the standard weak-form discretization approach to convert an infinite-dimensional systems to a finite-dimensional systems. It can be shown by the principle of least action that the distributed control synthesized by the Hamilton's principle is a minimum-norm control. A model-reference adaptive control framework is developed for distributed Lagrangian systems in the presence of uncertainty. The theory is demonstrated by an application of adaptive flutter suppression control of a flexible aircraft wing.

Nguyen, Nhan T.↗
DOE OSTI2024

A practical approach to calculating magnetic Johnson noise for precision measurements

Magnetic Johnson noise is an important consideration for many applications involving precision magnetometry, and its significance will only increase in the future with improvements in measurement sensitivity. The fluctuation–dissipation theorem can be utilized to derive analytic expressions for magnetic Johnson noise in certain situations, but when used in conjunction with finite element analysis tools, the combined approach is particularly powerful as it provides a practical means to calculate the magnetic Johnson noise arising from conductors of arbitrary geometry and permeability. In this paper, we demonstrate this method to be one of the most comprehensive approaches presently available to calculate thermal magnetic noise. In particular, its applicability is shown to not be limited to cases where the noise is evaluated at a point in space but also can be expanded to include cases where the magnetic field detector has a more general shape, such as a finite-size loop, a gradiometer, or a detector that consists of a polarized atomic species trapped in a volume. Furthermore, some physics insights gained through studies made using this method are discussed.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
NASA NTRS1975

Finite-element solution for a combined radiative-conductive analysis with mixed diffuse-specular surface characteristics

The finite-element method has been applied to solve a combined radiative-conductive heat transfer problem for a large space telescope similar to those used in orbiting satellites. The derivation of the underlying matrices and associated solution algorithm for a 2-D triangular element is presented in detail. The resulting expressions for this triangular element typify such an analysis, which yields constitutive matrices when the heat equation is cast in the matrix form. The relevant matrices include those pertaining to thermal conductance, internal heat generation, radiative exchanges, and all possible external thermal loadings. Emphasis is placed on the treatment of non-linear radiative interchange between surfaces in an enclosure having mixed diffuse-specular surface characteristics. Essential differences in governing equations describing these distinctive surface characteristics are identified. Concluding remarks are drawn from an example simulating a Cassegrainian space telescope.

Lee, H.-P.↗
NASA NTRS2000

Simulation of Aluminum Micro-mirrors for Space Applications at Cryogenic Temperatures

Closed form and finite element models are developed to predict the device response of aluminum electrostatic torsion micro-mirrors fabricated on silicon substrate for space applications at operating temperatures of 30K. Initially, closed form expressions for electrostatic pressure arid mechanical restoring torque are used to predict the pull-in and release voltages at room temperature. Subsequently, a detailed mechanical finite element model is developed to predict stresses and vertical beam deflection induced by the electrostatic and thermal loads. An incremental and iterative solution method is used in conjunction with the nonlinear finite element model and closed form electrostatic equations to solve. the coupled electro-thermo-mechanical problem. The simulation results are compared with experimental measurements at room temperature of fabricated micro-mirror devices.

Kuhn, J. L.↗
NASA NTRS1989

Crack-face displacements for embedded elliptic and semi-elliptical surface cracks

Analytical expressions for the crack-face displacements of an embedded elliptic crack in infinite solid subjected to arbitrary tractions are obtained. The tractions on the crack faces are assumed to be expressed in a polynomial form. These displacements expressions complete the exact solution of Vijayakumar and Atluri, and Nishioki and Atluri. For the special case of an embedded crack in an infinite solid subjected to uniform pressure loading, the present displacements agree with those by Green and Sneddon. The displacement equations derived were used with the finite-element alternating method (FEAM) for the analysis of a semi-elliptic surface crack in a finite solid subjected to remote tensile loading. The maximum opening displacements obtained with FEAM are compared to those with the finite-element method with singularity elements. The maximum crack opening displacements by the two methods showed good agreement.

Raju, I. S.↗
NASA NTRS1990

Crack-face displacements for an embedded elliptic crack in an infinite solid subjected to arbitrary tractions

Analytical expression for the crack-face displacements of an embedded elliptic crack in infinite solid subjected to arbitrary traction are obtained. The tractions on the crack faces are assumed to be expressed in a polynomial form. These displacements expressions complete the exact solution of Vijayakumar and Atluri, and Nishioki and Atluri. For the special case of an embedded crack in an infinite solid subjected to uniform pressure loading, the present displacements agree with those by Green and Sneddon. The displacement equations derived were used with the finite-element alternating method (FEAM) for the analysis of a semi-elliptic surface crack in a finite solid subjected to remote tensile loading. The maximum opening displacements obtained with FEAM are compared to those with the finite-element method with singularity elements. The maximum crack opening displacements by the two methods showed good agreement.

Raju, I. S.↗
NASA NTRS1992

An approximate solution for interlaminar stresses in laminated composites: Applied mechanics program

An approximate solution for interlaminar stresses in finite width, laminated composites subjected to uniform extensional, and bending loads is presented. The solution is based upon the principle of minimum complementary energy and an assumed, statically admissible stress state, derived by considering local material mismatch effects and global equilibrium requirements. The stresses in each layer are approximated by polynomial functions of the thickness coordinate, multiplied by combinations of exponential functions of the in-plane coordinate, expressed in terms of fourteen unknown decay parameters. Imposing the stationary condition of the laminate complementary energy with respect to the unknown variables yields a system of fourteen non-linear algebraic equations for the parameters. Newton's method is implemented to solve this system. Once the parameters are known, the stresses can be easily determined at any point in the laminate. Results are presented for through-thickness and interlaminar stress distributions for angle-ply, cross-ply (symmetric and unsymmetric laminates), and quasi-isotropic laminates subjected to uniform extension and bending. It is shown that the solution compares well with existing finite element solutions and represents an improved approximate solution for interlaminar stresses, primarily at interfaces where global equilibrium is satisfied by the in-plane stresses, but large local mismatch in properties requires the presence of interlaminar stresses.

Rose, Cheryl A.↗
NASA NTRS1973

An approach to the analysis of performance of quasi-optimum digital phase-locked loops.

An approach to the analysis of performance of quasi-optimum digital phase-locked loops (DPLL's) is presented. An expression for the characteristic function of the prior error in the state estimate is derived, and from this expression an infinite dimensional equation for the prior error variance is obtained. The prior error-variance equation is a function of the communication system model and the DPLL gain and is independent of the method used to derive the DPLL gain. Two approximations are discussed for reducing the prior error-variance equation to finite dimension. The effectiveness of one approximation in analyzing DPLL performance is studied.

Polk, D. R.↗
NASA NTRS1983

A refined finite element for vibration analysis of twisted blades based on beam theory

A finite element method of discretizing beam segments of pretwisted rotating blades is presented. Employing the matrix displacement method, stiffness and mass properties are developed from basic mechanics of a pretwisted beam theory. By introducing the proper displacement functions, the effect of rotor blade rotational motion on the stiffness matrix is obtained systematically from the kinetic energy expression. Comparing with other beam elements the derivation of this element is more fundamental. This allows one to apply the same approach to more complicated problems including nonlinear effects or complex dynamic motions. Illustrative examples are given comparing numerical results with available data and other numerical solutions from rotating and nonrotating force fields. These examples show that accurate prediction of vibration frequencies for pretwisted blades can be obtained by employing a quite modest number of degrees of freedom.

Sisto, F.↗
NASA NTRS1989

Reflection of solar radiation by a cylindrical cloud

Potential applications of an analytic method for computing the solar radiation reflected by a cylindrical cloud are discussed, including studies of radiative transfer within finite clouds and evaluations of these effects on other clouds and on remote sensing problems involving finite clouds. The pattern of reflected sunlight from a cylindrical cloud as seen at a large distance has been considered and described by the bidirectional function method for finite cloud analysis, as previously studied theoretically for plane-parallel atmospheres by McKee and Cox (1974); Schmetz and Raschke (1981); and Stuhlmann et al. (1985). However, the lack of three-dimensional radiative transfer solutions for anisotropic scattering media have hampered theoretical investigations of bidirectional functions for finite clouds. The present approach permits expression of the directional variation of the radiation field as a spherical harmonic series to any desired degree and order.

Smith, G. L.↗
NASA NTRS1993

Discrete ordinates solutions of nongray radiative transfer with diffusely reflecting walls

Nongray gas radiation in a plane parallel slab bounded by gray, diffusely reflecting walls is studied using the discrete ordinates method. The spectral equation of transfer is averaged over a narrow wavenumber interval preserving the spectral correlation effect. The governing equations are derived by considering the history of multiple reflections between two reflecting wails. A closure approximation is applied so that only a finite number of reflections have to be explicitly included. The closure solutions express the physics of the problem to a very high degree and show relatively little error. Numerical solutions are obtained by applying a statistical narrow-band model for gas properties and a discrete ordinates code. The net radiative wail heat fluxes and the radiative source distributions are obtained for different temperature profiles. A zeroth-degree formulation, where no wall reflection is handled explicitly, is sufficient to predict the radiative transfer accurately for most cases considered, when compared with increasingly accurate solutions based on explicitly tracing a larger number of wail reflections without any closure approximation applied.

Menart, J. A.↗
NASA NTRS2002

Fidelity of the Integrated Force Method Solution

The theory of strain compatibility of the solid mechanics discipline was incomplete since St. Venant's 'strain formulation' in 1876. We have addressed the compatibility condition both in the continuum and the discrete system. This has lead to the formulation of the Integrated Force Method. A dual Integrated Force Method with displacement as the primal variable has also been formulated. A modest finite element code (IFM/Analyzers) based on the IFM theory has been developed. For a set of standard test problems the IFM results were compared with the stiffness method solutions and the MSC/Nastran code. For the problems IFM outperformed the existing methods. Superior IFM performance is attributed to simultaneous compliance of equilibrium equation and compatibility condition. MSC/Nastran organization expressed reluctance to accept the high fidelity IFM solutions. This report discusses the solutions to the examples. No inaccuracy was detected in the IFM solutions. A stiffness method code with a small programming effort can be improved to reap the many IFM benefits when implemented with the IFMD elements. Dr. Halford conducted a peer-review on the Integrated Force Method. Reviewers' response is included.

Hopkins, Dale↗
NASA NTRS2003

Calculation of the Full Scattering Amplitude without Partial Wave Decomposition II: Inclusion of Exchange

As is well known, the full scattering amplitude can be expressed as an integral involving the complete scattering wave function. We have shown that the integral can be simplified and used in a practical way. Initial application to electron-hydrogen scattering without exchange was highly successful. The Schrodinger equation (SE), which can be reduced to a 2d partial differential equation (pde), was solved using the finite element method. We have now included exchange by solving the resultant SE, in the static exchange approximation, which is reducible to a pair of coupled pde's. The resultant scattering amplitudes, both singlet and triplet, calculated as a function of energy are in excellent agreement with converged partial wave results.

Shertzer, Janine↗