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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 577 records · Page 32
All sourcesNASA NTRSDOE OSTI
NASA NTRS1987

Roll-up of vorticity in adverse-pressure-gradient boundary layers

It is shown how the unsteady, nonlinear critical-layer equation determines the evolution of instability waves in a weak adverse-pressure-gradient boundary layer. Numerical solutions show that the nonlinearity halts the growth of these inviscidly unstable waves. The stabilizing effect of nonlinearity, in the present case, can be described as a consequence of either the increase (toward zero) of the phase jump across the critical layer or the roll-up of the critical-layer disturbance vorticity.

Goldstein, M. E.↗
NASA NTRS1973

Program for solution of ordinary differential equations

A program for the solution of linear and nonlinear first order ordinary differential equations is described and user instructions are included. The program contains a new integration algorithm for the solution of initial value problems which is particularly efficient for the solution of differential equations with a wide range of eigenvalues. The program in its present form handles up to ten state variables, but expansion to handle up to fifty state variables is being investigated.

Sloate, H.↗
NASA NTRS1983

Potential of minicomputer/array-processor system for nonlinear finite-element analysis

The potential of using a minicomputer/array-processor system for the efficient solution of large-scale, nonlinear, finite-element problems is studied. A Prime 750 is used as the host computer, and a software simulator residing on the Prime is employed to assess the performance of the Floating Point Systems AP-120B array processor. Major hardware characteristics of the system such as virtual memory and parallel and pipeline processing are reviewed, and the interplay between various hardware components is examined. Effective use of the minicomputer/array-processor system for nonlinear analysis requires the following: (1) proper selection of the computational procedure and the capability to vectorize the numerical algorithms; (2) reduction of input-output operations; and (3) overlapping host and array-processor operations. A detailed discussion is given of techniques to accomplish each of these tasks. Two benchmark problems with 1715 and 3230 degrees of freedom, respectively, are selected to measure the anticipated gain in speed obtained by using the proposed algorithms on the array processor.

Strohkorb, G. A.↗
NASA NTRS1974

Compressible seal flow analysis using the finite element method with Galerkin solution technique

High pressure gas sealing involves not only balancing the viscous force with the pressure gradient force but also accounting for fluid inertia--especially for choked flow. The conventional finite element method which uses a Rayleigh-Ritz solution technique is not convenient for nonlinear problems. For these problems, a finite element method with a Galerkin solution technique (FEMGST) was formulated. One example, a three-dimensional axisymmetric flow formulation has nonlinearities due to compressibility, area expansion, and convective inertia. Solutions agree with classical results in the limiting cases. The development of the choked flow velocity profile is shown.

Zuk, J.↗
NASA NTRS1972

Perturbed nonlinear differential equations

The existence of a solution defined for all t and possessing a type of boundedness property is established for the perturbed nonlinear system y = f(t,y) + F(t,y). The unperturbed system x = f(t,x) has a dichotomy in which some solutions exist and are well behaved as t increases to infinity, and some solution exists and are well behaved as t decreases to minus infinity. A similar study is made for a perturbed nonlinear differential equation defined on a half line, R+, and the existence of a family of solutions with special boundedness properties is established. The ideas are applied to integral manifolds.

Proctor, T. G.↗
NASA NTRS1992

A conjugate gradients/trust regions algorithms for training multilayer perceptrons for nonlinear mapping

This paper addresses the issue of applying a globally convergent optimization algorithm to the training of multilayer perceptrons, a class of Artificial Neural Networks. The multilayer perceptrons are trained towards the solution of two highly nonlinear problems: (1) signal detection in a multi-user communication network, and (2) solving the inverse kinematics for a robotic manipulator. The research is motivated by the fact that a multilayer perceptron is theoretically capable of approximating any nonlinear function to within a specified accuracy. The algorithm that has been employed in this study combines the merits of two well known optimization algorithms, the Conjugate Gradients and the Trust Regions Algorithms. The performance is compared to a widely used algorithm, the Backpropagation Algorithm, that is basically a gradient-based algorithm, and hence, slow in converging. The performances of the two algorithms are compared with the convergence rate. Furthermore, in the case of the signal detection problem, performances are also benchmarked by the decision boundaries drawn as well as the probability of error obtained in either case.

Madyastha, Raghavendra K.↗
NASA NTRS1972

Finite elements of nonlinear continua.

The finite element method is extended to a broad class of practical nonlinear problems, treating both theory and applications from a general and unifying point of view. The thermomechanical principles of continuous media and the properties of the finite element method are outlined, and are brought together to produce discrete physical models of nonlinear continua. The mathematical properties of the models are analyzed, and the numerical solution of the equations governing the discrete models is examined. The application of the models to nonlinear problems in finite elasticity, viscoelasticity, heat conduction, and thermoviscoelasticity is discussed. Other specific topics include the topological properties of finite element models, applications to linear and nonlinear boundary value problems, convergence, continuum thermodynamics, finite elasticity, solutions to nonlinear partial differential equations, and discrete models of the nonlinear thermomechanical behavior of dissipative media.

Oden, J. T.↗
NASA NTRS1988

Exact solutions and low-frequency instability of the adiabatic auroral arc model

The adiabatic auroral arc model couples a kinetic theory parallel current driven by mirror forces to horizontal ionospheric currents; the resulting equations are nonlinear. Some exact stationary solutions to these equations, some of them based on the Liouville equation, are developed, with both latitudinal and longitudinal spatial variations. These Liouville equation exact solutions are related to stability boundaries of low-frequency instabilities such as Kelvin-Helmholtz, as shown by a study of a simplified model.

Cornwall, John M.↗
NASA NTRS1980

Three dimensional inelastic finite element analysis of laminated composites

Formulations of the inelastic response of laminated composites to thermal and mechanical loading are used as the basis for development of the computer NALCOM (Nonlinear Analysis of Laminated Composites) computer program which uses a fully three dimensional isoparametric finite element with 24 nodes and 72 degrees of freedom. An incremental solution is performed with nonlinearities introduced as pseudoloads computed for initial strains. Equilibrium iteration may be performed at every step. Elastic and elastic-plastic response of boron/epoxy and graphite/epoxy graphite/epoxy and problems of curing 0/90 sub s Gr/Ep laminates with and without circular holes are analyzed. Mechanical loading of + or - 45sub s Gr/Ep laminates is modeled and symmetry conditions which exist in angle-ply laminates are discussed. Results are compared to experiments and other analytical models when possible. All models are seen to agree reasonably well with experimetnal results for off-axis tensile coupons. The laminate analyses show the three dimensional effects which are present near holes and free corners.

Griffin, O. H., Jr.↗
NASA NTRS1991

Critical problems of computational aeroacoustics

The aeroacoustics of rigid boundaries is discussed. Lighthill gave a formulation of this problem in which he showed that the sources of the acoustic field were quadrupole in nature. We have preferred a different formulation of the problem, in which the quadrupoles are sources for a nonlinear wave equation, as opposed to the linear one used by Lighthill. This is given here in a figure which also gives further details of a solution procedure for the Euler equations appropriate for the aeroelastic problem and motivated by the analysis of Crow. In accordance with our formulation, we contend that an algorithm for accurate solutions of an inhomogeneous nonlinear wave equation is of prime importance.

Rogers, Joel C. W.↗
NASA NTRS1994

Development of the NASA/FLAGRO computer program for analysis of airframe structures

The NASA/FLAGRO (NASGRO) computer program was developed for fracture control analysis of space hardware and is currently the standard computer code in NASA, the U.S. Air Force, and the European Agency (ESA) for this purpose. The significant attributes of the NASGRO program are the numerous crack case solutions, the large materials file, the improved growth rate equation based on crack closure theory, and the user-friendly promptive input features. In support of the National Aging Aircraft Research Program (NAARP); NASGRO is being further developed to provide advanced state-of-the-art capability for damage tolerance and crack growth analysis of aircraft structural problems, including mechanical systems and engines. The project currently involves a cooperative development effort by NASA, FAA, and ESA. The primary tasks underway are the incorporation of advanced methodology for crack growth rate retardation resulting from spectrum loading and improved analysis for determining crack instability. Also, the current weight function solutions in NASGRO or nonlinear stress gradient problems are being extended to more crack cases, and the 2-d boundary integral routine for stress analysis and stress-intensity factor solutions is being extended to 3-d problems. Lastly, effort is underway to enhance the program to operate on personal computers and work stations in a Windows environment. Because of the increasing and already wide usage of NASGRO, the code offers an excellent mechanism for technology transfer for new fatigue and fracture mechanics capabilities developed within NAARP.

Forman, R. G.↗
NASA NTRS2021

Convex Optimization Guidance for Precision Landing on Titan

Precision landing is an anticipated technology for future interplanetary missions. Autonomous spacecraft Entry, Descent and Landing (EDL) on the surface of a planetary body with a degree of precision in the order of meters is highly challenging. In this paper, a successive convexification guidance algorithm is utilized to simulate autonomous precision landing sequences on Saturn’s moon Titan. Due to its unique geophysical features, studying the science of matter within Titan’s atmosphere and beneath its surface is one of NASA’s most important planetary science objectives. As part of the Space Exploration Technology Directorate, a parafoil is proposed for landing on Titan due to its cost effectiveness, ease of deployment, low mass compared to the prospective payload and capabilities of precise autonomous delivery. This paper focuses on path optimization and guidance law development for high-fidelity dynamics parafoil tuning in the dense and adverse wind atmosphere of Titan, defined as a nonlinear and nonconvex optimal control problem. The powerful successive convexification method is used to solve the problem accordingly. The algorithm is designed such that the converged solution adheres to the nonlinear dynamics and kinematics in accordance with the original formulation, while respecting the state and control constraints. The six-degree-of-freedom (6DoF) simulations results show that this robust method is suitable for autonomous interplanetary applications.

Mooij, Edwin↗
NASA NTRS1947

The Elasto-Plastic Stability of Plates

This article explains results developed from the following research: 'The Stability of Plates and Shells beyond the Elastic Limit.' A significant improvement is found in the derivation of the relations between the stress factors and the strains resulting from the instability of plates and shells. In a strict analysis, the problem reduces to the solution of two simultaneous nonlinear partial differential equations of the fourth order in the deflection and stress function, and in the approximate analysis to a single linear equation of the Bryan type. Solutions are given for the special cases of a rectangular plate buckling into a cylindrical form, and of an arbitrarily shaped plate under uniform compression. These solutions indicate that the accuracy obtained by the approximate method is satisfactory.

Ilyushin, A. A.↗
NASA NTRS1992

Boundary formulations for shape sensitivity of temperature dependent conductivity problems

Used in concert with the Kirchhoff transformation, implicit differentiation of the discretized boundary integral equations governing the conduction of heat in solids with temperature dependent thermal conductivity is shown to generate an accurate and economical approach for computation of shape sensitivities. For problems with specified temperature and heat flux boundary conditions, a linear problem results for both the analysis and sensitivity analysis. In problems with either convection or radiation boundary conditions, a nonlinear problem is generated. Several iterative strategies are presented for the solution of the resulting sets of nonlinear equations and the computational performances examined in detail. Multizone analysis and zone condensation strategies are demonstrated to provide substantive computational economies in this process for models with either localized nonlinear boundary conditions or regions of geometric insensitivity to design variables. A series of nonlinear example problems is presented that have closed form solutions. Exact analytical expressions for the shape sensitivities associated with these problems are developed and these are compared with the sensitivities computed using the boundary element formulation.

Kane, James H.↗
NASA NTRS1991

Solution of the Navier-Stokes equations for a driven cavity

The flow field in a lid driven cavity is determined by integration of the incompressible Navier-Stokes equations. The numerical integration is accomplished via an operator splitting method known as the theta-scheme. This splitting separates the problem into the solution of a quasi-stokes problem and a nonlinear convection problem. Some details of solution methods used for the two subproblems and results obtained for the driven cavity are described. The schemes developed for the quasi-Stokes problem are more advanced at this stage than those for the nonlinear problem. However, the approaches used for both parts are outlined. As a model problem, a two dimensional square cavity with sides of unit length and a lid moving with unit velocity from left to right is considered. The Navier-Stokes equations are discretized in space on a uniform staggered or MAC mesh. The time discretization is accomplished via the theta-scheme.

Semeraro, B. D.↗
DOE OSTI2024

Effect of causality constraints on Bayesian analyses of heavy-ion collisions

There have long been questions about the limits to the validity of relativistic fluid dynamics and whether it is being used outside its regime of validity in modern simulations of relativistic heavy-ion collisions. An important new tool for answering this question is a causality analysis in the nonlinear regime—if the solutions of the evolution equations do not respect relativistic causality, then they are not a faithful representation of the underlying relativistic theory (in this case, quantum chromodynamics). Using this nonlinear criterion, it has recently been shown that hydrodynamics is indeed being used outside its regime of validity in simulations, at least sometimes. Here we explore the phenomenological implications, particularly the quantitative effects of demanding limits on acausality in modern Bayesian parameter estimation. We find that, while typically only a small fraction of the system's energy is initially in an acausal regime, placing strict limits on the allowed energy fraction significantly changes the preferred properties of the initial condition, which in turn alters the extracted medium properties such as bulk viscosity, where large values are no longer favored. Furthermore, these findings highlight the importance of developing better theoretical descriptions of the early-time, out-of-equilibrium dynamics of relativistic heavy-ion collisions.

Bayesian methods↗
NASA NTRS1957

On the Use of the Harmonic Linearizaiton Method in the Automatic Control Theory

The method of harmonic linearization (harmonic balance), first proposed by N. M. Krylov and N. N. Bogolyubov for the approximate investigation of nonlinear vibrations, has been developed and received wide practical application to problems in the theory of automatic control. Recently, some doubt has been expressed on the legitimacy of application of the method to these problems, and assertions were made on the absence in them of a small parameter of any kind. Nevertheless, the method gives practical, acceptable results and is a simple and powerful means in engineering computations. Hence, the importance of questions arises as to its justification. The underlying principle of the method is the replacement of the given nonlinear equation by a linear equation. In establishing the method, a small parameter is considered whose presence makes it possible to speak, with some degree of approximation, of the solution of this new equation to the solution of the given nonlinear equation. In an article by the author, certain considerations were given on the presence of the small parameter, but this question has not as yet received a final answer. In the present report, a somewhat different approach to the problem is applied that permits: (a) establishing, in the clearest manner, the form of the presence of the small parameter in nonlinear problems of control theory, solvable by the method of harmonic linearization; (b) connecting it with previous intuitive physical concepts (with the "filter property") and extending the class of problems possessing this property; and (c) discussing various generalizations of the method.

Popov, E. P.↗