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NASA NTRS1986

A simple nonlinear joint model

Hertzian contact theory is applied to a butt joint with specially mismatched bearing surfaces to devise a simple mathematical model of nonlinear axial force-displacement behavior in jointed members. Normalized tangent stiffness-force plots, for several values of a joint imperfection parameter, are presented for the sample case of solid structural members of circular section. The results illustrate the potential problem of high joint compliance at low axial-force levels, as well as the generally desirable stiffening and linearizing effects of preload. A nonlinear oscillator problem based on the static model is also formulated and solved to illustrate the effect of amplitude on natural frequency. As expected, natural frequency is low when amplitude is small. The results call attention to the important roles that tight tolerances and preload are expected to play in the design and fabrication of deployable and erectable truss-type space structures.

Fichter, W. B.↗

NASA NTRS1991

Advances in modeling the pressure correlation terms in the second moment equations

In developing turbulence models, various model constraints were proposed in an attempt to make the model equations more general (or universal). The most recent of these are the realizability principle, the linearity principle, the rapid distortion theory, and the material indifference principle. Several issues are discussed concerning these principles and special attention is payed to the realizability principle. Realizability (defined as the requirement of non-negative energy and Schwarz' inequality between any fluctuating quantities) is the basic physical and mathematical principle that any modeled equation should obey. Hence, it is the most universal, important and also the minimal requirement for a model equation to prevent it from producing unphysical results. The principle of realizability is described in detail, the realizability conditions are derived for various turbulence models, and the model forms are proposed for the pressure correlation terms in the second moment equations. Detailed comparisons of various turbulence models with experiments and direct numerical simulations are presented. As a special case of turbulence, the two dimensional two-component turbulence modeling is also discussed.

Shih, Tsan-Hsing↗

NASA NTRS1992

Advances in modeling the pressure correlation terms in the second moment equations

Shih, Tsan-Hsing↗

NASA NTRS1989

Parallel eigenanalysis of finite element models in a completely connected architecture

A parallel algorithm is presented for the solution of the generalized eigenproblem in linear elastic finite element analysis, (K)(phi) = (M)(phi)(omega), where (K) and (M) are of order N, and (omega) is order of q. The concurrent solution of the eigenproblem is based on the multifrontal/modified subspace method and is achieved in a completely connected parallel architecture in which each processor is allowed to communicate with all other processors. The algorithm was successfully implemented on a tightly coupled multiple-instruction multiple-data parallel processing machine, Cray X-MP. A finite element model is divided into m domains each of which is assumed to process n elements. Each domain is then assigned to a processor or to a logical processor (task) if the number of domains exceeds the number of physical processors. The macrotasking library routines are used in mapping each domain to a user task. Computational speed-up and efficiency are used to determine the effectiveness of the algorithm. The effect of the number of domains, the number of degrees-of-freedom located along the global fronts and the dimension of the subspace on the performance of the algorithm are investigated. A parallel finite element dynamic analysis program, p-feda, is documented and the performance of its subroutines in parallel environment is analyzed.

Akl, F. A.↗

NASA NTRS1985

Variability simulations with a steady, linearized primitive equations model

Solutions of the steady, primitive equations on a sphere, linearized about a zonally symmetric basic state are computed for the purpose of simulating monthly mean variability in the troposphere. The basic states are observed, winter monthly mean, zonal means of zontal and meridional velocities, temperatures and surface pressures computed from the 15 year NMC time series. A least squares fit to a series of Legendre polynomials is used to compute the basic states between 20 H and the equator, and the hemispheres are assumed symmetric. The model is spectral in the zonal direction, and centered differences are employed in the meridional and vertical directions. Since the model is steady and linear, the solution is obtained by inversion of a block, pente-diagonal matrix. The model simulates the climatology of the GFDL nine level, spectral general circulation model quite closely, particularly in middle latitudes above the boundary layer. This experiment is an extension of that simulation to examine variability of the steady, linear solution.

Kinter, J. L., III↗

NASA NTRS1968

Survey of fracture toughness test methods

Comprehensive survey presents current methods of fracture toughness testing that are based on linear elastic fracture mechanics. General principles of the basic two dimensional crack stress field model are discussed in relation to real three dimensional specimens. Methods of test instrumentation and procedure are described.

Brown, W. F., Jr.↗

NASA NTRS1979

Identification evaluation methods

Methods for airplane parameter estimation, the equation error method, output error method, and two advanced methods are presented and their basic properties described. The advanced methods include the maximum likelihood and extended Kalman filter method. For a better understanding of the estimation techniques a first-order scalar differential equation is used as a model of the system under test. Application of the methods to a general multivariable linear system is briefly outlined. A note on the parameter estimation in the frequency domain is also presented. Numerical examples along with the comparison of results from various methods are given.

Klein, V.↗

NASA NTRS2004

GVE-Based Dynamics and Control for Formation Flying Spacecraft

Formation flying is an enabling technology for many future space missions. This paper presents extensions to the equations of relative motion expressed in Keplerian orbital elements, including new initialization techniques for general formation configurations. A new linear time-varying form of the equations of relative motion is developed from Gauss Variational Equations and used in a model predictive controller. The linearizing assumptions for these equations are shown to be consistent with typical formation flying scenarios. Several linear, convex initialization techniques are presented, as well as a general, decentralized method for coordinating a tetrahedral formation using differential orbital elements. Control methods are validated using a commercial numerical propagator.

Breger, Louis↗

NASA NTRS1988

Properties of finite difference models of non-linear conservative oscillators

Finite-difference (FD) approaches to the numerical solution of the differential equations describing the motion of a nonlinear conservative oscillator are investigated analytically. A generalized formulation of the Duffing and modified Duffing equations is derived and analyzed using several FD techniques, and it is concluded that, although it is always possible to contstruct FD models of conservative oscillators which are themselves conservative, caution is required to avoid numerical solutions which do not accurately reflect the properties of the original equation.

Mickens, R. E.↗

NASA NTRS1973

On optimal modeling of systems.

A procedure for modeling a linear system by an optimal finite-dimensional approximation is developed on the basis of Sard's (1967) generalized spline. Error bounds are given, and the application of the procedure is illustrated by two presented examples. The procedure may be employed, not only in the modeling of conventional lumped-parameter and distributed-parameter continuous dynamical systems, but also in mathematical operations such as those involved in pattern recognition and picture enhancement problems.

De Figueiredo, R. J. P.↗

NASA NTRS1988

Global impact of the Antarctic ozone hole: Simulations with a 3-D chemical transport model

A study of the Antarctic ozone hole was made with a 3-D chemical transport model using linearized photochemistry for ozone based on observed distribution. The tracer model uses the winds and convection from the GISS general circulation model (8 deg x 10 deg x 23 layers). A 3-year control run of the ozone distribution is compared with the observed climatology. In two experiments, a hypothetical Antarctic ozone hole is induced on October 1 and on November 1; the tracer model is integrated for 1 year with the standard linearized chemistry. The initial depletion, 90 percent of the O sub 3 poleward of 70 S between 25 and 180 mbar, amounts to about 5 percent of the total O sub 3 in the Southerm Hemisphere. As the vortex breaks down and the hole is dispersed, significant depletions to column ozone, of order 10 D.U., occur as far north as 36 S during Austral summer. One year later, about 25 percent of the original depletion remains, mostly below 100 mbar and poleward of 30 S. Details of the calculations are shown, along with a budget analysis showing the fraction of the hole filled in by photochemistry versus that transported into the troposhere.

Prather, Michael J.↗

NASA NTRS1992

Transfer of contrast sensitivity in linear visual networks

Contrast sensitivity is a useful measure of the ability of an observer to distinguish contrast signals from noise. Although usually applied to human observers, contrast sensitivity can also be defined operationally for individual visual neurons. In a model linear neuron consisting of a filter and noise source, this operational measure is a function of filter gain, noise power spectrum, signal duration, and a performance criterion. This definition allows one to relate the sensitivities of linear neurons at different levels in the visual pathway. Mathematical formulas describing these relationships are derived, and the general model is applied to the specific problem of relating the sensitivities of parvocellular LGN neurons and cortical simple cells in the primate.

Watson, Andrew B.↗

NASA NTRS1991

Applicability/evaluation of flux based representations for linear/higher order elements for heat transfer in structures - Generalized gamma(T)-family

The applicability and evaluation of a generalized gamma(T) family of flux-based representations are examined for two different thermal analysis formulations for structures and materials which exhibit no phase change effects. The so-called H-theta and theta forms are demonstrated for numerous test models and linear and higher-order elements. The results show that the theta form with flux-based representations is generally superior to traditional approaches.

Namburu, R. R.↗

NASA NTRS1994

Towards enhancing and delaying disturbances in free shear flows

The family of shear flows comprising the jet, wake, and the mixing layer are subjected to perturbations in an inviscid incompressible fluid. By modeling the basic mean flows as parallel with piecewise linear variations for the velocities, complete and general solutions to the linearized equations of motion can be obtained in closed form as functions of all space variables and time when posed as an initial value problem. The results show that there is a continuous as well as the discrete spectrum that is more familiar in stability theory and therefore there can be both algebraic and exponential growth of disturbances in time. These bases make it feasible to consider control of such flows. To this end, the possibility of enhancing the disturbances in the mixing layer and delaying the onset in the jet and wake is investigated. It is found that growth of perturbations can be delayed to a considerable degree for the jet and the wake but, by comparison, cannot be enhanced in the mixing layer. By using moving coordinates, a method for demonstrating the predominant early and long time behavior of disturbances in these flows is given for continuous velocity profiles. It is shown that the early time transients are always algebraic whereas the asymptotic limit is that of an exponential normal mode. Numerical treatment of the new governing equations confirm the conclusions reached by use of the piecewise linear basic models. Although not pursued here, feedback mechanisms designed for control of the flow could be devised using the results of this work.

Criminale, W. O.↗

NASA NTRS1985

Numerical analysis of flow non-uniformity in the hot gas manifold of the Space Shuttle main engine

Three-dimensional viscous flow in a conceptual hot gas manifold (HGM) for the Space Shuttle Main Engine High Pressure Fuel Turbopump (SSME HPFTP) was numerically analyzed. A finite difference scheme was used to solve the Navier-Stokes equations. The exact geometry of the SSME HGM was modeled using boundary fitted curvilinear coordinates and the General Interpolants Method (GIM) code. Slight compressibility of the subsonic flow was modeled using a linearized equation of state with artificial compressibility. A time relaxation method was used to obtain a steady state solution. The feasibility and potential usefulness of computational methods in assisting the design of SSME components which involves the flow of fluids within complex geometrical shapes is demonstrated.

Thoenes, J.↗

NASA NTRS1993

Nonlinear probabilistic finite element models of laminated composite shells

A probabilistic finite element analysis procedure for laminated composite shells has been developed. A total Lagrangian finite element formulation, employing a degenerated 3-D laminated composite shell with the full Green-Lagrange strains and first-order shear deformable kinematics, forms the modeling foundation. The first-order second-moment technique for probabilistic finite element analysis of random fields is employed and results are presented in the form of mean and variance of the structural response. The effects of material nonlinearity are included through the use of a rate-independent anisotropic plasticity formulation with the macroscopic point of view. Both ply-level and micromechanics-level random variables can be selected, the latter by means of the Aboudi micromechanics model. A number of sample problems are solved to verify the accuracy of the procedures developed and to quantify the variability of certain material type/structure combinations. Experimental data is compared in many cases, and the Monte Carlo simulation method is used to check the probabilistic results. In general, the procedure is quite effective in modeling the mean and variance response of the linear and nonlinear behavior of laminated composite shells.

Engelstad, S. P.↗

NASA NTRS2012

Experimenting with the GMAO 4D Data Assimilation

The Global Modeling and Assimilation Office (GMAO) has been working to promote its prototype four-dimensional variational (4DVAR) system to a version that can be exercised at operationally desirable configurations. Beyond a general circulation model (GeM) and an analysis system, traditional 4DV AR requires availability of tangent linear (TL) and adjoint (AD) models of the corresponding GeM. The GMAO prototype 4DVAR uses the finite-volume-based GEOS GeM and the Grid-point Statistical Interpolation (GSI) system for the first two, and TL and AD models derived ITom an early version of the finite-volume hydrodynamics that is scientifically equivalent to the present GEOS nonlinear GeM but computationally rather outdated. Specifically, the TL and AD models hydrodynamics uses a simple (I-dimensional) latitudinal MPI domain decomposition, which has consequent low scalability and prevents the prototype 4DV AR ITom being used in realistic applications. In the near future, GMAO will be upgrading its operational GEOS GCM (and assimilation system) to use a cubed-sphere-based hydrodynamics. This versions of the dynamics scales to thousands of processes and has led to a decision to re-derive the TL and AD models for this more modern dynamics, thus taking advantage of a two-dimensional MPI decomposition and improved scalability properties. With the aid of the Transformation of Algorithms in FORTRAN (l'AF) automatic adjoint generation tool and some hand-coding, a version of the cubed-sphere-based TL and AD models, with a simplified vertical diffusion scheme, is now available, enabling multiple configurations of standard implementations of 4DV AR in GEOS. Concurrent to this development, collaboration with the National Centers for Environmental Prediction (NCEP) and the Earth System Research Laboratory (ESRL) has allowed GMAO to implement a hybrid-ensemble capability within the GEOS data assimilation system. Both 3Dand 4D-ensemble capabilities are presently available thus allowing GMAO to now evaluate the performance and benefit of various ensemble and variational assimilation strategies. This presentation will cover the most recent developments taking place at GMAO and show results from various comparisons from traditional techniques to more recent ensemble-based ones.

Todling, R.↗

NASA NTRS1999

Mars Crustal Remanent Magnetism: An Extinct Dynamo Leaves a Record of Field Reversals in the Heavily Cratered Highlands

The Mars Global Surveyor spacecraft, in a highly elliptical polar orbit about Mars, obtained vector magnetic field measurements just above the surface of Mars (altitudes > 100 kilometers). Crustal magnetization, largely confined to the most ancient, heavily cratered Mars highlands, is frequently organized in east-west trending linear features, the largest of which extends over 2000 km. A representative set of survey passes are modeled using uniformly magnetized thin plates and a generalized inverse methodology. Crustal remanent magnetization exceeds that deduced for the largest terrestrial magnetic anomalies by more than an order of magnitude. Groups of quasi-parallel linear features of alternating magnetic polarity are found. They are reminiscent of similar magnetic features associated with sea floor spreading and crustal genesis on Earth but with a much larger spatial scale.

Connerney, John E.↗