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At least 343 records · Page 19

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NASA NTRS1985

Nonlinear quasi-fracture behavior of polymers

This paper deals with the nonlinear quasi-fracture behavior of polymers. Using the finite element method, the quasi-fracture model composed of an isolated craze opening with a nonlinear boundary envelope forces represented by oriented fibril domains is analyzed in simply-stressed rectangular plate. The stress distribution, the displacement profile, as well as the yield or plastic or flow zone adjacent to the craze tips are obtained. It is found that the variation of the stress distribution near the craze tip is not as sharp as that for an elastic crack. The initial load required for yielding or flowing is greater for the quasifracture as compared with that for a classical fracture. Under the same load the yield or flow zone is somewhat smaller as compared with that obtained on the basis of linear elastic-plastic fracture mechanics theory.

Sun, B. N.↗

NASA NTRS2005

Designing Adaptive Low-Dissipative High Order Schemes for Long-Time Integrations

A general framework for the design of adaptive low-dissipative high order schemes is presented. It encompasses a rather complete treatment of the numerical approach based on four integrated design criteria: (1) For stability considerations, condition the governing equations before the application of the appropriate numerical scheme whenever it is possible. (2) For consistency, compatible schemes that possess stability properties, including physical and numerical boundary condition treatments, similar to those of the discrete analogue of the continuum are preferred. (3) For the minimization of numerical dissipation contamination, efficient and adaptive numerical dissipation control to further improve nonlinear stability and accuracy should be used. (4) For practical considerations, the numerical approach should be efficient and applicable to general geometries, and an efficient and reliable dynamic grid adaptation should be used if necessary. These design criteria are, in general, very useful to a wide spectrum of flow simulations. However, the demand on the overall numerical approach for non-linear stability and accuracy is much more stringent for long-time integration of complex multiscale viscous shock/shear/turbulence/acoustics interactions and numerical combustion. Robust classical numerical methods for less complex flow physics are not suitable or practical for such applications. The present approach is designed expressly to address such flow problems, especially unsteady flows.

Yee, H. C.↗

NASA NTRS1987

A Taylor weak-statement algorithm for hyperbolic conservation laws

Finite element analysis, applied to computational fluid dynamics (CFD) problem classes, presents a formal procedure for establishing the ingredients of a discrete approximation numerical solution algorithm. A classical Galerkin weak-statement formulation, formed on a Taylor series extension of the conservation law system, is developed herein that embeds a set of parameters eligible for constraint according to specification of suitable norms. The derived family of Taylor weak statements is shown to contain, as special cases, over one dozen independently derived CFD algorithms published over the past several decades for the high speed flow problem class. A theoretical analysis is completed that facilitates direct qualitative comparisons. Numerical results for definitive linear and nonlinear test problems permit direct quantitative performance comparisons.

Baker, A. J.↗

NASA NTRS2012

Statistical Orbit Determination using the Particle Filter for Incorporating Non-Gaussian Uncertainties

The tracking of space objects requires frequent and accurate monitoring for collision avoidance. As even collision events with very low probability are important, accurate prediction of collisions require the representation of the full probability density function (PDF) of the random orbit state. Through representing the full PDF of the orbit state for orbit maintenance and collision avoidance, we can take advantage of the statistical information present in the heavy tailed distributions, more accurately representing the orbit states with low probability. The classical methods of orbit determination (i.e. Kalman Filter and its derivatives) provide state estimates based on only the second moments of the state and measurement errors that are captured by assuming a Gaussian distribution. Although the measurement errors can be accurately assumed to have a Gaussian distribution, errors with a non-Gaussian distribution could arise during propagation between observations. Moreover, unmodeled dynamics in the orbit model could introduce non-Gaussian errors into the process noise. A Particle Filter (PF) is proposed as a nonlinear filtering technique that is capable of propagating and estimating a more complete representation of the state distribution as an accurate approximation of a full PDF. The PF uses Monte Carlo runs to generate particles that approximate the full PDF representation. The PF is applied in the estimation and propagation of a highly eccentric orbit and the results are compared to the Extended Kalman Filter and Splitting Gaussian Mixture algorithms to demonstrate its proficiency.

Mashiku, Alinda↗

NASA NTRS1986

Application of the unsteady vortex-lattice method to the nonlinear two-degree-of-freedom aeroelastic equations

A means of numerically simulating flutter is established by implementing a predictor-corrector algorithm to solve the equations of motion. Aerodynamic loads are provided by the unsteady vortex lattice method (UVLM). This method is illustrated via the obtainment of stable and unstable responses to initial disturbances in the case of two-degree-of-freedom motion. It was found that for some angles of attack and dynamic pressure, the initial disturbance decays, for others it grows (flutter). When flutter occurs, the solution yields the amplitude and period of the resulting limit cycle. The preliminaray results attest to the feasibility of this method for studying flutter in cases that would be difficult to treat using a classical approach.

Strganac, T. W.↗

NASA NTRS1989

A hybrid-perturbation-Galerkin technique which combines multiple expansions

A two-step hybrid perturbation-Galerkin method for the solution of a variety of differential equations type problems is found to give better results when multiple perturbation expansions are employed. The method assumes that there is parameter in the problem formulation and that a perturbation method can be sued to construct one or more expansions in this perturbation coefficient functions multiplied by computed amplitudes. In step one, regular and/or singular perturbation methods are used to determine the perturbation coefficient functions. The results of step one are in the form of one or more expansions each expressed as a sum of perturbation coefficient functions multiplied by a priori known gauge functions. In step two the classical Bubnov-Galerkin method uses the perturbation coefficient functions computed in step one to determine a set of amplitudes which replace and improve upon the gauge functions. The hybrid method has the potential of overcoming some of the drawbacks of the perturbation and Galerkin methods as applied separately, while combining some of their better features. The proposed method is applied, with two perturbation expansions in each case, to a variety of model ordinary differential equations problems including: a family of linear two-boundary-value problems, a nonlinear two-point boundary-value problem, a quantum mechanical eigenvalue problem and a nonlinear free oscillation problem. The results obtained from the hybrid methods are compared with approximate solutions obtained by other methods, and the applicability of the hybrid method to broader problem areas is discussed.

Geer, James F.↗

NASA NTRS1988

A geometrically nonlinear theory of shear deformable laminated composite plates and its use in the postbuckling analysis

This paper is devoted to the formulation of a higher-order, geometrically nonlinear theory of anisotropic symmetrically-laminated composite plates and to the analysis, in this context, of their postbuckling behavior. Special attention is given to the postbuckling analysis of plates made of transversely isotropic layers for which case, the influence played by the degree of transversal-isotropy of the layers as well as by the goemetrical parameters of the panel is investigated. Finally, the results obtained within the present higher-order theory are compared with their first order transverse shear deformation as well as with their classical (Kirchhoff) counterparts and a number of conclusions concerning their range of applicability and the influence of various parameters are presented.

Librescu, L.↗

NASA NTRS1990

A hybrid perturbation-Galerkin technique that combines multiple expansions

A two-step hybrid perturbation-Galerkin method for the solution of a variety of differential equations type problems is found to give better results when multiple perturbation expansions are employed. The method assumes that there is parameter in the problem formulation and that a perturbation method can be used to construct one or more expansions in this perturbation coefficient functions multiplied by computed amplitudes. In step one, regular and/or singular perturbation methods are used to determine the perturbation coefficient functions. The results of step one are in the form of one or more expansions each expressed as a sum of perturbation coefficient functions multiplied by a priori known gauge functions. In step two the classical Bubnov-Galerkin method uses the perturbation coefficient functions computed in step one to determine a set of amplitudes which replace and improve upon the gauge functions. The hybrid method has the potential of overcoming some of the drawbacks of the perturbation and Galerkin methods as applied separately, while combining some of their better features. The proposed method is applied, with two perturbation expansions in each case, to a variety of model ordinary differential equations problems including: a family of linear two-boundary-value problems, a nonlinear two-point boundary-value problem, a quantum mechanical eigenvalue problem and a nonlinear free oscillation problem. The results obtained from the hybrid methods are compared with approximate solutions obtained by other methods, and the applicability of the hybrid method to broader problem areas is discussed.

Geer, James F.↗

NASA NTRS1980

Mode I fracture behavior of nonlinear materials

A finite element analysis is presented for the Mode I fracture behavior of cracked plates (stationary crack) made of different nonlinear materials (elastoplastic or elastic locking). The assumed stress-strain behavior of the nonlinear materials was piecewise linear. For each given 'stationary' crack size, the corresponding critical remote tensile stress was calculated based on the maximum crack-tip stress failure criterion. It was found that in the log-log plots of the critical remote stress versus critical crack length, the fracture data of the piecewise linear materials obey a 'stepwise-linear-inverse-square-root' fracture law. It is also shown how the fracture data of the piecewise linear materials can be fitted by proper piecewise graphical shifting of the classical 'inverse-square-root' fracture curve for the linearly elastic materials.

Ko, W. L.↗

NASA NTRS1976

Rigid rotators

The two-particle, steady-state Schroedinger equation is transformed to center of mass and internuclear distance vector coordinates, leading to the free particle wave equation for the kinetic energy motion of the molecule and a decoupled wave equation for a single particle of reduced mass moving in a spherical potential field. The latter describes the vibrational and rotational energy modes of the diatomic molecule. For fixed internuclear distance, this becomes the equation of rigid rotator motion. The classical partition function for the rotator is derived and compared with the quantum expression. Molecular symmetry effects are developed from the generalized Pauli principle that the steady-state wave function of any system of fundamental particles must be antisymmetric. Nuclear spin and spin quantum functions are introduced and ortho- and para-states of rotators, along with their degeneracies, are defined. Effects of nuclear spin on entropy are deduced. Next, rigid polyatomic rotators are considered and the partition function for this case is derived. The patterns of rotational energy levels for nonlinear molecules are discussed for the spherical symmetric top, for the prolate symmetric top, for the oblate symmetric top, and for the asymmetric top. Finally, the equilibrium energy and specific heat of rigid rotators are derived.

Source record↗

NASA NTRS1974

Low thrust space vehicle trajectory optimization using regularized variables

Optimizing the trajectory of a low thrust space vehicle usually means solving a nonlinear two point boundary value problem. In general, accuracy requirements necessitate extensive computation times. In celestial mechanics, regularizing transformations of the equations of motion are used to eliminate computational and analytical problems that occur during close approaches to gravitational force centers. It was shown in previous investigations that regularization in the formulation of the trajectory optimization problem may reduce the computation time. In this study, a set of regularized equations describing the optimal trajectory of a continuously thrusting space vehicle is derived. The computational characteristics of the set are investigated and compared to the classical Newtonian unregularized set of equations. The comparison is made for low thrust, minimum time, escape trajectories and numerical calculations of Keplerian orbits. The comparison indicates that in the cases investigated for bad initial guesses of the known boundary values a remarkable reduction in the computation time was achieved. Furthermore, the investigated set of regularized equations shows high numerical stability even for long duration flights and is less sensitive to errors in the guesses of the unknown boundary values.

Schwenzfeger, K. J.↗

NASA NTRSDate not supplied

Analysis and Application of Novel and Heritage Acceleration Limiting Algorithms for SLS on Ascent

National Aeronautics and Space Administration (NASA) is currently building the Space Launch System (SLS) Block-1 launch vehicle, to be used as the crewed heavy-lift vehicle for the Artemis series of missions. The SLS Block-1 guidance subsystem utilizes a nonlinear algorithm derived from Shuttle heritage for limiting the vehicle’s induced maximum axial acceleration during ascent flight, known as g-limiting. Even though g-limiting has demonstrated stability and robustness through several design analysis cycles and the extensive Shuttle flight history, there are no available documents that demonstrate that this algorithm has been proven stable through conventional controls stability analysis. This paper highlights the non-linear nature of g-limit, presents an alternative methodology to employ a linear version of this algorithm, performs assessment of selected linear gains using classical stability analysis and, conducts a comparison of both approaches through Six Degrees-of-Freedom (6-DOF) Monte Carlo (MC) simulations.

Jason Everett↗

NASA NTRS1990

Finite element two-dimensional panel flutter at high supersonic speeds and elevated temperature

A consistent finite element formulation for flutter of two-dimensional panels including effects of temperature variation along panel length is presented. The von Karman nonlinear strain-displacement relation is used to account for the large-deflections, and the quasi-steady first-order piston theory is employed for aerodynamic loading in the finite-element formulation. The panel flutter under combined thermal/aerodynamic loading can be separated into solving two problems in sequence. They are: (1) postbuckling deflection, stresses and buckling stability boundary, and (2) critical dynamic pressure and linear flutter boundary. The solution procedures in solving these problems are presented in detail. Finite element results of two-dimensional panels with uniform temperature change are compared with classic analytical solutions. Influence of nonuniform temperature distributions on critical buckling temperature, flutter deflection and stresses, and flutter boundary is also given.

Xue, David Y.↗

NASA NTRS1999

Fast Quantum Algorithm for Predicting Descriptive Statistics of Stochastic Processes

Stochastic processes are used as a modeling tool in several sub-fields of physics, biology, and finance. Analytic understanding of the long term behavior of such processes is only tractable for very simple types of stochastic processes such as Markovian processes. However, in real world applications more complex stochastic processes often arise. In physics, the complicating factor might be nonlinearities; in biology it might be memory effects; and in finance is might be the non-random intentional behavior of participants in a market. In the absence of analytic insight, one is forced to understand these more complex stochastic processes via numerical simulation techniques. In this paper we present a quantum algorithm for performing such simulations. In particular, we show how a quantum algorithm can predict arbitrary descriptive statistics (moments) of N-step stochastic processes in just O(square root of N) time. That is, the quantum complexity is the square root of the classical complexity for performing such simulations. This is a significant speedup in comparison to the current state of the art.

Williams Colin P.↗

NASA NTRS1993

Wall interference and boundary simulation in a transonic wind tunnel with a discretely slotted test section

A computational simulation of a transonic wind tunnel test section with longitudinally slotted walls is developed and described herein. The nonlinear slot model includes dynamic pressure effects and a plenum pressure constraint, and each slot is treated individually. The solution is performed using a finite-difference method that solves an extended transonic small disturbance equation. The walls serve as the outer boundary conditions in the relaxation technique, and an interaction procedure is used at the slotted walls. Measured boundary pressures are not required to establish the wall conditions but are currently used to assess the accuracy of the simulation. This method can also calculate a free-air solution as well as solutions that employ the classical homogeneous wall conditions. The simulation is used to examine two commercial transport aircraft models at a supercritical Mach number for zero-lift and cruise conditions. Good agreement between measured and calculated wall pressures is obtained for the model geometries and flow conditions examined herein. Some localized disagreement is noted, which is attributed to improper simulation of viscous effects in the slots.

Al-Saadi, Jassim A.↗

NASA NTRS1989

Active vibration mitigation of distributed parameter, smart-type structures using Pseudo-Feedback Optimal Control (PFOC)

A new, near-optimal feedback control technique is introduced that is shown to provide excellent vibration attenuation for those distributed parameter systems that are often encountered in the areas of aeroservoelasticity and large space systems. The technique relies on a novel solution methodology for the classical optimal control problem. Specifically, the quadratic regulator control problem for a flexible vibrating structure is first cast in a weak functional form that admits an approximate solution. The necessary conditions (first-order) are then solved via a time finite-element method. The procedure produces a low dimensional, algebraic parameterization of the optimal control problem that provides a rigorous basis for a discrete controller with a first-order like hold output. Simulation has shown that the algorithm can successfully control a wide variety of plant forms including multi-input/multi-output systems and systems exhibiting significant nonlinearities. In order to firmly establish the efficacy of the algorithm, a laboratory control experiment was implemented to provide planar (bending) vibration attenuation of a highly flexible beam (with a first clamped-free mode of approximately 0.5 Hz).

Patten, W. N.↗

NASA NTRS1993

The effect of crossflow on Taylor vortices: A model problem

A number of practically relevant problems involving the impulsive motion or the rapid rotation of bodies immersed in fluid are susceptible to vortex-like instability modes. Depending upon the configuration of any particular problem the stability properties of any high-wavenumber vortices can take on one of two distinct forms. One of these is akin to the structure of Gortler vortices in boundary layer flows while the other is similar to the situation for classical Taylor vortices. Both the Gortler and Taylor problems have been extensively studied when crossflow effects are excluded from the underlying base flows. Recently, studies were made concerning the influence of crossflow on Gortler modes and a linearized stability analysis is used to examine crossflow properties for the Taylor mode. This work allows us to identify the most unstable vortex as the crossflow component increases and it is shown how, like the Gortler case, only a very small crossflow component is required in order to completely stabilize the flow. Our investigation forms the basis for an extension to the nonlinear problem and is of potential applicability to a range of pertinent flows.

Otto, S. R.↗

NASA NTRS1994

Coupling of microprocesses and macroprocesses due to velocity shear: An application to the low-altitude ionosphere

Recent observations indicate that low-altitude (below 1500 km) ion energization and thermal ion upwelling are colocated in the convective flow reversal region. In this region the convective velocity V(sub perpendicular) is generally small but spatial gradients in V(sub perpendicular) can be large. As a result, Joule heating is small. The observed high level of ion heating (few electron volts or more) cannot be explained by classical Joule heating alone but requires additional heating sources such as plasma waves. At these lower altitudes, sources of free energy are not obvious and hence the nature of ion energization remains ill understood. The high degree of correlation of ion heating with shear in the convective velocity (Tsunoda et al., 1989) is suggestive of an important role of velocity shear in this phenomenon. We provide more recent evidence for this correlation and show that even a small amount of velocity shear in the transverse flow is sufficient to excite a large-scale Kelvin-Helmholtz mode, which can nonlinearly steepen and give rise to highly stressed regions of strongly sheared flows. Futhermore, these stressed regions of strongly sheared flows may seed plasma waves in the range of ion cyclotron to lower hybrid frequencies, which are potential sources for ion heating. This novle two-step mechanism for ion energization is applied to typical observations of low-altitude thermal ion upwelling events.

Ganguli, G.↗