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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 433 records · Page 24
All sourcesNASA NTRSDOE OSTI
NASA NTRS1981

Numerical model of long-lived Jovian vortices

The extension of the measured zonal velocity profile into the adiabatic interior of Jupiter, while eddies and large oval structures are confined to a shallow stably-stratified upper layer, are assumed in a nonlinear numerical model of long-lived Jovian vortices. In agreement of the observed flows of Jupiter, each vortex is stationary with respect to the shear flow at a critical latitude that is close to the latitude of the vortex center. The solutions obtained are strongly nonlinear, in contrast to the solitary wave solutions that are the weakly nonlinear extensions of ultralong linear waves. The merging of two stable vortices upon collision, rather than the non-interaction predicted by solitary wave theory, is in keeping with Jovian vortex observations. It is suggested that long-lived vortices maintain themselves against dissipation by absorbing smaller vortices produced by convection.

Ingersoll, A. P.↗
NASA NTRS1985

Nonlinear adhesive behavior effects in a cracked orthotropic sheet stiffened by a semi-infinite orthotropic sheet

The stress-intensity factors are determined for a cracked orthotropic sheet adhesively bonded to an orthotropic stringer where the adhesive layer is modeled with a nonlinear stress-strain curve. By the use of Green's functions and the complex variable theory of orthotropic elasticity, a set of integral equations is obtained. The integral equations are replaced by an equivalent set of algebraic equations, which are solved to obtain the shear stress distribution in the adhesive layer, with which the crack-tip stress-intensity factors are found. When the adhesive was modeled with a nonlinear stress-strain curve, the peak shear stresses in the adhesive were considerably reduced in comparison to the solution for the linear elastic adhesive. This resulted in increases in the stress-intensity factors for the nonlinear adhesive solution compared to the linear adhesive solution. The nonlinear adhesive has no significant effect on the stress-intensity factor unless the near crack tip is beneath the stringer. It is assumed that the adhesive bond remains intact and it is predicted that onset of adhesive failure occurs at decreasing levels of applied stress as the crack propagates beneath the stringer.

Bigelow, C. A.↗
NASA NTRS1986

Nonlinear adhesive behavior effects in a cracked orthotropic sheet stiffened by a semi-infinite orthotropic sheet

The stress-intensity factors are determined for a cracked orthotropic sheet adhesively bonded to an orthotropic stringer where the adhesive layer is modeled with a nonlinear stress-strain curve. By the use of Green's functions and the complex variable theory of orthotropic elasticity, a set of integral equations is obtained. The integral equations are replaced by an equivalent set of algebraic equations, which are solved to obtain the shear stress distribution in the adhesive layer, with which the crack-tip stress-intensity factors are found. When the adhesive was modeled with a nonlinear stress-strain curve, the peak shear stresses in the adhesive were considerably reduced in comparison to the solution for the linear elastic adhesive. This resulted in increases in the stress-intensity factors for the nonlinear adhesive solution compared to the linear adhesive solution. The nonlinear adhesive has no significant effect on the stress-intensity factor unless the near crack tip is beneath the stringer. It is assumed that the adhesive bond remains intact and it is predicted that onset of adhesive failure occurs at decreasing levels of applied stress as the crack propagates beneath the stringer.

Bigelow, C. A.↗
NASA NTRS1977

Inverse solution of the pseudoscalar transfer equation through nonlinear matrix inversion

Nonlinear matrix inversion operators have been developed which, applied to observed radiances, infer maximal information regarding atmospheric scattering parameters and vertical distribution of radiant sources and sinks. The algorithm has the attractive feature of noise discrimination, attributing instrumental errors to extra-atmospheric sources.

King, J. I. F.↗
NASA NTRS1988

The analysis of non-linear dynamic behavior (including snap-through) of postbuckled plates by simple analytical solution

Static postbuckling and nonlinear dynamic analysis of plates are usually accomplished by multimode analyses, although the methods are complicated and do not give straightforward understanding of the nonlinear behavior. Assuming single-mode transverse displacement, a simple formula is derived for the transverse load displacement relationship of a plate under in-plane compression. The formula is used to derive a simple analytical expression for the static postbuckling displacement and nonlinear dynamic responses of postbuckled plates under sinusoidal or random excitation. Regions with softening and hardening spring behavior are identified. Also, the highly nonlinear motion of snap-through and its effects on the overall dynamic response can be easily interpreted using the single-mode formula. Theoretical results are compared with experimental results obtained using a buckled aluminum panel, using discrete frequency and broadband point excitation. Some important effects of the snap-through motion on the dynamic response of the postbuckled plates are found.

Ng, C. F.↗
NASA NTRS1989

A stable numerical solution method in-plane loading of nonlinear viscoelastic laminated orthotropic materials

In response to the tremendous growth in the development of advanced materials, such as fiber-reinforced plastic (FRP) composite materials, a new numerical method is developed to analyze and predict the time-dependent properties of these materials. Basic concepts in viscoelasticity, laminated composites, and previous viscoelastic numerical methods are presented. A stable numerical method, called the nonlinear differential equation method (NDEM), is developed to calculate the in-plane stresses and strains over any time period for a general laminate constructed from nonlinear viscoelastic orthotropic plies. The method is implemented in an in-plane stress analysis computer program, called VCAP, to demonstrate its usefulness and to verify its accuracy. A number of actual experimental test results performed on Kevlar/epoxy composite laminates are compared to predictions calculated from the numerical method.

Gramoll, K. C.↗
NASA NTRS1988

Dynamic structural correlation via nonlinear programming techniques

A solution to the correlation between structural dynamic test results and finite element analyses of the same components is presented in this paper. Basically, the method can be categorized as a Levenberg-Marquardt type Gauss-Newton method which requires only the differences between FE modal analyses and test results and their first derivatives with respect to preassigned design variables. With proper variable normalization and equation scaling, the method has been made numerically better-conditioned and the inclusion of the Levenberg-Marquardt technique overcomes any remaining difficulty encountered in inverting singular or near-singular matrices. An important feature is that each iteration requires only one function evaluation along with the associated design sensitivity analysis and so the procedure is computationally efficient.

Ting, T.↗
NASA NTRS1999

Dynamical Chaos in the Wisdom-Holman Integrator: Origins and Solutions

We examine the nonlinear stability of the Wisdom-Holman (WH) symplectic mapping applied to the integration of perturbed, highly eccentric (e-0.9) two-body orbits. We find that the method is unstable and introduces artificial chaos into the computed trajectories for this class of problems, unless the step size chosen 1s small enough that PeriaPse is always resolved, in which case the method is generically stable. This 'radial orbit instability' persists even for weakly perturbed systems. Using the Stark problem as a fiducial test case, we investigate the dynamical origin of this instability and argue that the numerical chaos results from the overlap of step-size resonances; interestingly, for the Stark-problem many of these resonances appear to be absolutely stable. We similarly examine the robustness of several alternative integration methods: a time-regularized version of the WH mapping suggested by Mikkola; the potential-splitting (PS) method of Duncan, Levison, Lee; and two original methods incorporating approximations based on Stark motion instead of Keplerian motion. The two fixed point problem and a related, more general problem are used to conduct a comparative test of the various methods for several types of motion. Among the algorithms tested, the time-transformed WH mapping is clearly the most efficient and stable method of integrating eccentric, nearly Keplerian orbits in the absence of close encounters. For test particles subject to both high eccentricities and very close encounters, we find an enhanced version of the PS method-incorporating time regularization, force-center switching, and an improved kernel function-to be both economical and highly versatile. We conclude that Stark-based methods are of marginal utility in N-body type integrations. Additional implications for the symplectic integration of N-body systems are discussed.

Rauch, Kevin P.↗
NASA NTRS2006

Verification of Numerical Solutions for the Deployment of the Highly Nonlinear MARSIS Antenna Boom Lenticular Joints

The MARSIS antenna booms are constructed using lenticular hinges between straight boom segments in a novel design which allows the booms to be extremely lightweight while retaining a high stiffness and well defined structural properties once they are deployed. Lenticular hinges are elegant in form but are complicated to model as they deploy dynamically and require highly specialized nonlinear techniques founded on carefully measured mechanical properties. Results from component level testing were incorporated into a highly specialized ADAMS model which employed an automated damping algorithm to account for the discontinuous boom lengths formed during the deployment. Additional models with more limited capabilities were also developed in both DADS and ABAQUS to verify the ADAMS model computations and to help better define the numerical behavior of the models at the component and system levels. A careful comparison is made between the ADAMS and DADS models in a series of progressive steps in order to verify their numerical results. Different trade studies considered in the model development are outlined to demonstrate a suitable level of model fidelity. Some model sensitivities to various parameters are explored using subscale and full system models. Finally, some full system DADS models are exercised to illustrate the limitations of traditional modeling techniques for variable geometry systems which were overcome in the ADAMS model.

Mars↗
NASA NTRS2009

Coupled Particle Transport and Pattern Formation in a Nonlinear Leaky-Box Model

Effects of particle-particle coupling on particle characteristics in nonlinear leaky-box type descriptions of the acceleration and transport of energetic particles in space plasmas are examined in the framework of a simple two-particle model based on the Fokker-Planck equation in momentum space. In this model, the two particles are assumed coupled via a common nonlinear source term. In analogy with a prototypical mathematical system of diffusion-driven instability, this work demonstrates that steady-state patterns with strong dependence on the magnetic turbulence but a rather weak one on the coupled particles attributes can emerge in solutions of a nonlinearly coupled leaky-box model. The insight gained from this simple model may be of wider use and significance to nonlinearly coupled leaky-box type descriptions in general.

Barghouty, A. F.↗
NASA NTRS1984

A simplified method for elastic-plastic-creep structural analysis

A simplified inelastic analysis computer program (ANSYPM) was developed for predicting the stress-strain history at the critical location of a thermomechanically cycled structure from an elastic solution. The program uses an iterative and incremental procedure to estimate the plastic strains from the material stress-strain properties and a plasticity hardening model. Creep effects are calculated on the basis of stress relaxation at constant strain, creep at constant stress or a combination of stress relaxation and creep accumulation. The simplified method was exercised on a number of problems involving uniaxial and multiaxial loading, isothermal and nonisothermal conditions, dwell times at various points in the cycles, different materials and kinematic hardening. Good agreement was found between these analytical results and nonlinear finite element solutions for these problems. The simplified analysis program used less than 1 percent of the CPU time required for a nonlinear finite element analysis.

Kaufman, A.↗
NASA NTRS1985

A simplified method for elastic-plastic-creep structural analysis

A simplified inelastic analysis computer program (ANSYPM) was developed for predicting the stress-strain history at the critical location of a thermomechanically cycled structure from an elastic solution. The program uses an iterative and incremental procedure to estimate the plastic strains from the material stress-strain properties and a plasticity hardening model. Creep effects are calculated on the basis of stress relaxation at constant strain, creep at constant stress or a combination of stress relaxation and creep accumulation. The simplified method was exercised on a number of problems involving uniaxial and multiaxial loading, isothermal and nonisothermal conditions, dwell times at various points in the cycles, different materials and kinematic hardening. Good agreement was found between these analytical results and nonlinear finite element solutions for these problems. The simplified analysis program used less than 1 percent of the CPU time required for a nonlinear finite element analysis.

Kaufman, A.↗
NASA NTRS1985

On local total strain redistribution using a simplified cyclic inelastic analysis based on an elastic solution

Strain redistribution corrections were developed for a simplified inelastic analysis procedure to economically calculate material cyclic response at the critical location of a structure for life prediction purposes. The method was based on the assumption that the plastic region in the structure is local and the total strain history required for input can be defined from elastic finite element analyses. Cyclic stress-strain behavior was represented by a bilinear kinematic hardening model. The simplified procedure has been found to predict stress-strain response with reasonable accuracy for thermally cycled problems but needs improvement for mechanically load cycled problems. This study derived and incorporated Neuber type corrections in the simplified procedure to account for local total strain redistribution under cyclic mechanical loading. The corrected simplified method was exercised on a mechanically load cycled benchmark notched plate problem. Excellent agreement was found between the predicted material response and nonlinear finite element solutions for the problem. The simplified analysis computer program used 0.3 percent of the CPU time required for a nonlinear finite element analysis.

Hwang, S. Y.↗
NASA NTRS1985

On local total strain redistribution using a simplified cyclic inelastic analysis based on an elastic solution

Strain redistribution corrections were developed for a simplified inelastic analysis procedure to economically calculate material cyclic response at the critical location of a structure for life prediction purposes. The method was based on the assumption that the plastic region in the structure is local and the total strain history required for input can be defined from elastic finite element analyses. Cyclic stress-strain behavior was represented by a bilinear kinematic hardening model. The simplified procedure has been found to predict stress-strain response with reasonable accuracy for thermally cycled problems but needs improvement for mechanically load cycled problems. This study derived and incorporated Neuber type corrections in the simplified procedure to account for local total strain redistribution under cyclic mechanical loading. The corrected simplified method was exercised on a mechanically load cycled benchmark notched plate problem. Excellent agreement was found between the predicted material response and nonlinear finite element solutions for the problem. The simplified analysis computer program used 0.3 percent of the CPU time required for a nonlinear finite element analysis.

Hwang, S. Y.↗
NASA NTRS1991

Nonlinear evolution of modes in a compressible boundary layer

The nonlinear stability of an oblique mode propagating in a 2D compressible boundary layer is considered under the long wave-length approximation. The growth rate of the wave is assumed to be small so that the ideas of nonlinear critical layers can be applied. It is shown that the spatial/temporal evolution of the mode is governed by a pair of coupled unsteady nonlinear equations for the disturbance vorticity and density. Expressions for the linear growth rate shows clearly the effects of wall heating and cooling, and in particular how heating destabilizes the boundary layer for these long wavelength inviscid modes at 0(1) Mach numbers. The numerical solution of the nonlinear problem is discussed and some results are presented.

Gajjar, J. S. B.↗
NASA NTRS1997

Using High-Order Methods on Lower-Order Geometries

The desire to obtain acoustic information from the numerical solution of a nonlinear system of equations is a demanding proposition for a computational algorithm. High-order accuracy is required for the propagation of high-frequency, low-amplitude waves. The accuracy of an algorithm can be compromised by low-order errors that naturally occur in the solution of a particular problem. Such errors arise from two sources: the presence of discontinuities in the flow field or because the geometry on which the problem is defined is not everywhere smooth to the order of the scheme. The performance of high-order accurate essentially non-oscillatory (ENO) schemes on piecewise smooth solutions is well documented. Herein, the performance of these methods on smooth solutions defined on piecewise smooth geometries is investigated. The propagation of sound in a quasi-one-dimensional nozzle is considered as a test case. Some of the issues involved in the extension to two spatial dimensions are discussed.

Casper, Jay↗
DOE OSTI2024

Generalization error guaranteed auto-encoder-based nonlinear model reduction for operator learning

Many physical processes in science and engineering are naturally represented by operators between infinite-dimensional function spaces. The problem of operator learning, in this context, seeks to extract these physical processes from empirical data, which is challenging due to the infinite or high dimensionality of data. An integral component in addressing this challenge is model reduction, which reduces both the data dimensionality and problem size. In this paper, we utilize low-dimensional nonlinear structures in model reduction by investigating Auto-Encoder-based Neural Network (AENet). AENet first learns the latent variables of the input data and then learns the transformation from these latent variables to corresponding output data. Our numerical experiments validate the ability of AENet to accurately learn the solution operator of nonlinear partial differential equations. Furthermore, we establish a mathematical and statistical estimation theory that analyzes the generalization error of AENet. Finally, our theoretical framework shows that the sample complexity of training AENet is intricately tied to the intrinsic dimension of the modeled process, while also demonstrating the robustness of AENet to noise.

Auto-encoder↗