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At least 973 records · Page 54

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A Nonlinear Viscoelastic-Viscoplastic Constitutive Model for Epoxy Polymers

The objective of this paper is to develop a nonlinear viscoelastic–viscoplastic constitutive model for epoxy polymers. The classic nonlinear viscoelasticity model is reformulated to yield a closed-form incremental constitutive relation, which relates the stress increments to the viscoelastic strain increments. A viscoplasticity model, which consists of the Drucker–Prager yield function, nonlinear isotropic and kinematic hardening laws, and the Perzyna viscosity function, is subsequently developed. The nonlinear viscoelasticity and the vis-coplasticity models are then implemented in a radial return algorithm. A closed-form algorithmic tangent operator is derived to facilitate model implementation. The nonlinear viscoelasticity model is validated by reproducing the test data for polymethyl methacrylate(PMMA). The present constitutive model’s capabilities are demonstrated through modeling viscoelastic–viscoplastic PMMA loaded at different strain rates. The mechanics of structure genome-based micromechanics approach, embedded with the present constitutive model, is used to homogenize a unidirectional fiber-reinforced composite with a PMMA matrix, subjected to uniaxial and shear loading at different strain rates. The viscoelastic characterization of PMT-F7 epoxy is evaluated by comparing the predicted creep–recovery responses by the present constitutive model with the experimental ones.

Liang Zhang↗

DOE OSTI2011

Chiral symmetry restoration at finite density in large N{sub c} QCD

At large N{sub c}, cold nuclear matter is expected to form a crystal and thus spontaneously break translational symmetry. The description of chiral symmetry breaking and translational symmetry breaking can become intertwined. Here, the focus is on aspects of chiral symmetry breaking and its possible restoration that are by construction independent of the nature of translational symmetry breaking - namely spatial averages of chiral order parameters. A system will be considered to be chirally restored provided all spatially averaged chiral order parameters are zero. A critical question is whether chiral restoration in this sense is possible for phases in which chiral order parameters are locally nonzero but whose spatial averages all vanish. We show that this is not possible unless all chirally invariant observables are spatially uniform. This result is first derived for Skyrme-type models, which are based on a nonlinear sigma model and by construction break chiral symmetry on a point-by-point basis. A no-go theorem for chiral restoration (in the average sense) for all models of this type is obtained by showing that in these models there exist chirally symmetric order parameters that cannot be spatially uniform. Next, we will show that the no-go theorem applies to large N{sub c} QCD in any phase that has a nonzero but spatially varying chiral condensate. The theorem is demonstrated by showing that in a putative chirally restored phase, the field configuration can be reduced to that of a nonlinear sigma model. It is also shown that this no-go theorem is fully consistent with the vanishing of the spatial average of the chiral condensate (1/2)Tr(U) (as happens in 'half-skyrmion' configurations). This is because the chiral condensate is only one of an infinite set of chiral order parameters, some of which must be nonzero. It is also shown that while an approximation of a unit cell of a Skyrme crystal as a hypersphere does lead to a phase that is chirally restored (in the average sense), this is an artifact of the approximation.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

NASA NTRS1978

Nonlinear analysis and performance evaluation of the Annular Suspension and Pointing System (ASPS)

The Annular Suspension and Pointing System (ASPS) can provide high accurate fine pointing for a variety of solar-, stellar-, and Earth-viewing scientific instruments during space shuttle orbital missions. In this report, a detailed nonlinear mathematical model is developed for the ASPS/Space Shuttle system. The equations are augmented with nonlinear models of components such as magnetic actuators and gimbal torquers. Control systems and payload attitude state estimators are designed in order to obtain satisfactory pointing performance, and statistical pointing performance is predicted in the presence of measurement noise and disturbances.

Joshi, S. M.↗

NASA NTRS1974

Study report on guidelines and test procedures for investigating stability of nonlinear cardiovascular control system models

A general study of the stability of nonlinear as compared to linear control systems is presented. The analysis is general and, therefore, applies to other types of nonlinear biological control systems as well as the cardiovascular control system models. Both inherent and numerical stability are discussed for corresponding analytical and graphic methods and numerical methods.

Fitzjerrell, D. G.↗

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.↗

DOE OSTI2010

Introduction of Nonlinear Properties Into Hierachical Models of Nb3Sn Strands

The development of computational models representing Rutherford cable formation and deformation is necessary to investigate the strain state in the superconducting filaments in Nb{sub 3}Sn magnets. The wide variety of length scales within accelerator magnets suggests usage of a hierarchical structure within the model. As part of an ongoing investigation at LBNL, a three-dimensional simplified nonlinear multiscale model is developed as a way to extend previous linear elastic versions. The inclusion of plasticity models into the problem formulation allows an improved representation of strand behavior compared to the linear elastic model. This formulation is applied to a single Nb{sub 3}Sn strand to find its effective properties as well as the strain state in the conductor under loading.

43 PARTICLE ACCELERATORS↗

DOE OSTI2016

A topological proof of chaos for two nonlinear heterogeneous triopoly game models

We rigorously prove the existence of chaotic dynamics for two nonlinear Cournot triopoly game models with heterogeneous players, for which in the existing literature the presence of complex phenomena and strange attractors has been shown via numerical simulations. In the first model that we analyze, costs are linear but the demand function is isoelastic, while, in the second model, the demand function is linear and production costs are quadratic. As concerns the decisional mechanisms adopted by the firms, in both models one firm adopts a myopic adjustment mechanism, considering the marginal profit of the last period; the second firm maximizes its own expected profit under the assumption that the competitors' production levels will not vary with respect to the previous period; the third firm acts adaptively, changing its output proportionally to the difference between its own output in the previous period and the naive expectation value. The topological method we employ in our analysis is the so-called “Stretching Along the Paths” technique, based on the Poincaré-Miranda Theorem and the properties of the cutting surfaces, which allows to prove the existence of a semi-conjugacy between the system under consideration and the Bernoulli shift, so that the former inherits from the latter several crucial chaotic features, among which a positive topological entropy.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

NASA NTRS2016

Advanced Control Considerations for Turbofan Engine Design

This paper covers the application of a model-based engine control (MBEC) methodology featuring a self tuning on-board model for an aircraft turbofan engine simulation. The nonlinear engine model is capable of modeling realistic engine performance, allowing for a verification of the advanced control methodology over a wide range of operating points and life cycle conditions. The on-board model is a piece-wise linear model derived from the nonlinear engine model and updated using an optimal tuner Kalman Filter estimation routine, which enables the on-board model to self-tune to account for engine performance variations. MBEC is used here to show how advanced control architectures can improve efficiency during the design phase of a turbofan engine by reducing conservative operability margins. The operability margins that can be reduced, such as stall margin, can expand the engine design space and offer potential for efficiency improvements. Application of MBEC architecture to a nonlinear engine simulation is shown to reduce the thrust specific fuel consumption by approximately 1% over the baseline design, while maintaining safe operation of the engine across the flight envelope.

control↗

NASA NTRS1987

Numerical solution of turbulent flow past a backward facing step using a nonlinear K-epsilon model

The problem of turbulent flow past a backward facing step is important in many technological applications and has been used as a standard test case to evaluate the performance of turbulence models in the prediction of separated flows. It is well known that the commonly used kappa-epsilon (and K-l) models of turbulence yield inaccurate predictions for the reattachment points in this problem. By an analysis of the mean vorticity transport equation, it will be argued that the intrinsically inaccurate prediction of normal Reynolds stress differences by the Kappa-epsilon and K-l models is a major contributor to this problem. Computations using a new nonlinear kappa-epsilon model (which alleviates this deficiency) are made with the TEACH program. Comparisons are made between the improved results predicted by this nonlinear kappa-epsilon model and those obtained from the linear kappa-epsilon model as well as from second-order closure models.

Speziale, C. G.↗

NASA NTRS1988

Numerical solution of turbulent flow past a backward facing step using a nonlinear K-epsilon model

The problem of turbulent flow past a backward facing step is important in many technological applications and has been used as a standard test case to evaluate the performance of turbulence models in the prediction of separated flows. It is well known that the commonly used kappa-epsilon (and K-l) models of turbulence yield inaccurate predictions for the reattachment points in this problem. By an analysis of the mean vorticity transport equation, it will be argued that the intrinsically inaccurate prediction of normal Reynolds stress differences by the kappa-epsilon and K-l models is a major contributor to this problem. Computations using a new nonlinear Kappa-epsilon model (which alleviates this deficiency) are made with the TEACH program. Comparisons are made between the improved results predicted by this nonlinear kappa-epsilon model and those obtained from the linear kappa-epsilon model as well as from second-order closure models.

Speziale, C. G.↗

DOE OSTI2015

Decreasing the temporal complexity for nonlinear, implicit reduced-order models by forecasting

Implicit numerical integration of nonlinear ODEs requires solving a system of nonlinear algebraic equations at each time step. Each of these systems is often solved by a Newton-like method, which incurs a sequence of linear-system solves. Most model-reduction techniques for nonlinear ODEs exploit knowledge of system's spatial behavior to reduce the computational complexity of each linear-system solve. However, the number of linear-system solves for the reduced-order simulation often remains roughly the same as that for the full-order simulation. We propose exploiting knowledge of the model's temporal behavior to (1) forecast the unknown variable of the reduced-order system of nonlinear equations at future time steps, and (2) use this forecast as an initial guess for the Newton-like solver during the reduced-order-model simulation. To compute the forecast, we propose using the Gappy POD technique. As a result, the goal is to generate an accurate initial guess so that the Newton solver requires many fewer iterations to converge, thereby decreasing the number of linear-system solves in the reduced-order-model simulation.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2015

Statistical properties of three-dimensional two-fluid plasma model

The nonlinear dynamics of incompressible non-dissipative two-fluid plasma model is investigated through classical Gibbs ensemble methods. Liouville's theorem of phase space for each wave number is proved, and the absolute equilibrium spectra for Galerkin truncated two-fluid model are calculated. In two-fluid theory, the equilibrium is built on the conservation of three quadratic invariants: the total energy and the self-helicities for ions and electrons fluid, respectively. The implications of statistic equilibrium spectra with arbitrary ratios of conserved invariants are discussed.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2024

Learning physics-based reduced-order models from data using nonlinear manifolds

Here we present a novel method for learning reduced-order models of dynamical systems using nonlinear manifolds. First, we learn the manifold by identifying nonlinear structure in the data through a general representation learning problem. The proposed approach is driven by embeddings of low-order polynomial form. A projection onto the nonlinear manifold reveals the algebraic structure of the reduced-space system that governs the problem of interest. The matrix operators of the reduced-order model are then inferred from the data using operator inference. Numerical experiments on a number of nonlinear problems demonstrate the generalizability of the methodology and the increase in accuracy that can be obtained over reduced-order modeling methods that employ a linear subspace approximation.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2018

Stability of Solutions of Initial Boundary-Balue Problems of Aerohydroelasticity

In designing structures and devices interacting with the flow of gas or liquid, it is necessary to solve the problems associated with the investigation of the stability required for their functioning and operational reliability. The definition of stability of an elastic body taken in the article corresponds to Lyapunov’s concept of stability of a dynamical system. On the base of the proposed nonlinear mathematical model the dynamic stability of the elastic aileron of the wing taking into account the incident subsonic flow of gas or liquid (in an ideal model of an incompressible environment) is investigated. Also a nonlinear mathematical model of the device relating to the vibration technique, which is intended for intensification of technological processes, for example, the process of mixing, is considered. The action of these devices is based on the oscillations of elastic elements during the gas or liquid flow. The dynamic stability of the elastic element located on one wall of the flow channel with the subsonic flow of gas or liquid (in an ideal model of a compressible environment) is investigated. Both models are described by a coupled nonlinear system of differential equations for the unknown functions — the potential of the gas velocity and deformation of the elastic element. On the basis of the construction of functionals, we obtain the sufficient conditions of the stability, the imposed restrictions on the free-stream velocity of the gas, the flexural stiffness of the elastic element, and other parameters of the mechanical system. The examples of construction of the stability regions for particular parameters of the mechanical system are presented.

42 ENGINEERING↗

NASA NTRS2000

A Comparison of Experimental and Theoretical Results for Magnetic Bearings

A comprehensive program was undertaken to experimentally characterize the static and dynamic characteristics of a heteropolar magnetic bearing and to develop nonlinear theoretical models capable of accurately predicting magnetic bearing performance. This paper presents the results for the static characteristics of the magnetic bearing and a comparison with the predictions from the analytical model. The results indicate that the nonlinear theoretical model can accurately predict the static characteristics of the magnetic bearing.

Hibbs, Robert I., Jr.↗

DOE OSTI2013

Nonlinearity measure and internal model control based linearization in anti-windup design

This paper considers the problem of internal model control based linearization in anti-windup design. The nonlinearity measure concept is used for quantifying the control system degree of nonlinearity. The linearizing effect of a modified internal model control structure is presented by comparing the nonlinearity measures of the open-loop and closed-loop systems. It is shown that the linearization properties are improved by increasing the control system local feedback gain. However, it is emphasized that at the same time the stability of the system deteriorates. The conflicting goals of stability and linearization are resolved by solving the design problem in different frequency ranges.

97 MATHEMATICS AND COMPUTING↗

NASA NTRS1987

Mesoscale lake-effect snowstorms in the vicinity of Lake Michigan - Linear theory and numerical simulations

Mesoscale lake-effect snowstorms in the vicinity of Lake Michigan are studied by a linear steady-state analytic model and a nonlinear time-dependent numerical model with parameterized subgrid-scale physics. The solutions of the linear model show that the orientation of the mean wind field to the surface heating pattern is crucial to the shapes of the disturbances. The results indicate that the relative warmth of the lake surface can induce three updraft centers under a westerly wind, two updraft centers/bands under a northwesterly wind, and a convergence band under a northerly wind. Such convergences are caused by the interaction between the mean wind and the local circulations forced by the curved thermal contrasts. The numerical results from the nonlinear model not only produce convergence patterns very similar to those found in the linear theory and in other numerical studies, but also capture the transient property in some of the lake-induced disturbances. All of these results are qualitatively confirmed by satellite images.

Hsu, Hsiao-Ming↗

NASA NTRS1984

A dynamical basis for the parameterization of organized deep convection in large-scale numerical models

A hierarchy of steady, nonlinear, semianalytic models of different types of convection were produced. These provide a theoretical framework for determining cloud outflow fluxes of both dynamic and thermodynamic quantities, which can be used to formulate dynamical transports in parameterization schemes. This was achieved by exploiting certain Lagrangian conservation properties of steady flow, from which an equation for the vertical displacement of particles can be obtained and the outflow entropy, energy and momentum fluxes and the infow/outflow mass fluxes can be determined from solution to the equation. These fluxes are determined in terms of grid scale parameters such as convective available potential energy (CAPE), cloud layer shear, and horizontal pressure gradients. Five main types of system models are identified, respectively representing archtypes of convection in zero shear, large shear, midlatitude squall lines, tropical squall lines and cellular convection. The downdraught is an important aspect in the first four of these and the cloud scale transport of momentum is very distinctive.

Moncrieff, M. W.↗