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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 1,387 records · Page 77
All sourcesNASA NTRSDOE OSTI
NASA NTRS1984

Approximation techniques for parameter estimation and feedback control for distributed models of large flexible structures

Approximation ideas are discussed that can be used in parameter estimation and feedback control for Euler-Bernoulli models of elastic systems. Focusing on parameter estimation problems, ways by which one can obtain convergence results for cubic spline based schemes for hybrid models involving an elastic cantilevered beam with tip mass and base acceleration are outlined. Sample numerical findings are also presented.

Banks, H. T.↗
NASA NTRS1984

Stability and Convergence of Underintegrated Finite Element Approximations

The effects of underintegration on the numerical stability and convergence characteristics of certain classes of finite element approximations were analyzed. Particular attention is given to hourglassing instabilities that arise from underintegrating the stiffness matrix entries and checkerboard instabilities that arise from underintegrating constrain terms such as those arising from incompressibility conditions. A fundamental result reported here is the proof that the fully integrated stiffness is restored in some cases through a post-processing operation.

Oden, J. T.↗
NASA NTRS1983

The unconditional instability of inflow-dependent boundary conditions in difference approximations to hyperbolic systems

The stability of finite difference approximations to initial boundary hyperbolic systems is studied. As is well known, a proper specification of boundary conditions for such systems is essential for their solutions to be well defined. A discrete analogue of the above is proved - if the numerical boundary conditions are consistent with an inflow part of the problem, they render the overall computation unstable. An example of the inviscid gasdynamics equations is considered. Previously announced in STAR as N81-33874

Tadmor, E.↗
NASA NTRS1983

Numerical approximations to nonlinear conservation laws with locally varying time and space grids

Numerical approximations to the initial value problem for nonlinear systems of conservation laws are considered. The considered system is said to be hyperbolic when all eigenvalues of every real linear combination of the Jacobian matrices are real. Solutions may develop discontinuities in finite time, even when the initial data are smooth. In the investigation, explicit finite difference methods which use locally varying time grids are considered. The global CFL restriction is replaced by a local restriction. The numerical flux function is studied from a finite volume viewpoint, and a differencing technique is developed at interface points between regions of distinct time increments.

Osher, S.↗
NASA NTRS1984

Comparison of an analytical approximation for particle motion in a current sheet with precise numerical calculations

Approximate analytic solutions exist for particle motion in a one-dimensional current sheet with a constant normal magnetic field component. These solutions are tested against precise numerical calculations, and a range of validity of the analytic solutions is inferred. For example, in the geomagnetic tail neutral sheet, for a dawn-dusk electric field of 0.1-1 mV/m, lobe field of 10-40 nT, and sheet thickness of 1000 km, the analytic solutions serve as a good predictor of particle motion when the normal magnetic field component is less than 3 or 4 nT. By using the analytic solutions, initial distribution functions are mapped into final (accelerated) distributions, and the analytic mappings are compared with numerical mappings.

Speiser, T. W.↗
NASA NTRS1984

Optimum design sensitivity based on approximation concepts and dual methods

An optimum design sensitivity analysis capability is reported which exploits the approximation concepts-dual method formulation of the minimum weight structural sizing problem. An efficient iterative solution technique is used to facilitate determination of sensitivity derivatives for both primal and dual variables. Estimates on the useful range of parameter perturbations, over which the optimum design sensitivity projections can be expected to yield satisfactory revised optimum designs, are also obtained. Numerical results for several example problems will be presented to illustrate the effectiveness of the capability reported.

Schmit, L. A.↗
NASA NTRS1984

Dual approximations in optimal control

A dual approximation for the solution to an optimal control problem is analyzed. The differential equation is handled with a Lagrange multiplier while other constraints are treated explicitly. An algorithm for solving the dual problem is presented.

Hager, W. W.↗
NASA NTRS1982

Approximating a finite element model of a hybrid deployable truss by a discrete mass model

The NASTRAN finite element model of the MSFC/hybrid deployable truss is approximated by a model consisting of four bodies serially connected by a spring hinge suspension. The truss is decomposed into four serially connected modules determining the total mass and rotational inertias for a rigid body with its mass center on the axis of the truss for each module. A five-body cantilever truss model is developed along with an undamped form of this model. Spring coefficient values are generated to match eigenvalues of the latter model with those of the NASTRAN model. Damping coefficients are then determined that provide n percent of critical damping for the model.

Chichester, F. D.↗
NASA NTRS1984

Relaxation and approximate factorization methods for the unsteady full potential equation

The unsteady form of the full potential equation is solved in conservation form, using implicit methods based on approximate factorization and relaxation schemes. A local time linearization for density is introduced to enable solution to the equation in terms of phi, the velocity potential. A novel flux-biasing technique is applied to generate proper forms of the artificial viscosity, to treat hyperbolic regions with shocks and sonic lines present. The wake is properly modeled by accounting not only for jumps in phi, but also for jumps in higher derivatives of phi obtained from requirements of density continuity. The far field is modeled using the Riemann invariants to simulate nonreflecting boundary conditions. Results are presented for flows over airfoils, cylinders, and spheres. Comparisons are made with available Euler and full potential results.

Shankar, V.↗
NASA NTRS1985

Spline methods for approximating quantile functions and generating random samples

Two cubic spline formulations are presented for representing the quantile function (inverse cumulative distribution function) of a random sample of data. Both B-spline and rational spline approximations are compared with analytic representations of the quantile function. It is also shown how these representations can be used to generate random samples for use in simulation studies. Comparisons are made on samples generated from known distributions and a sample of experimental data. The spline representations are more accurate for multimodal and skewed samples and to require much less time to generate samples than the analytic representation.

Schiess, J. R.↗
NASA NTRS1985

The eigenvalues of the pseudospectral Fourier approximation to the operator sin (2x) d/dx

It is shown that the eigenvalues Z sub i of the pseudospectral Fourier approximation to the operator sin(2x) curly d/curly dx satisfy (R sub e) (Z sub i) = + or - 1 or (R sub e)(Z sub I) = 0. Whereas this does not prove stability for the Fourier method, applied to the hyperbolic equation U sub t = sin (2x)(U sub x) - pi x pi; it indicates that the growth in time of the numerical solution is essentially the same as that of the solution to the differential equation.

Tal-Ezer, H.↗
NASA NTRS1985

Approximate neutral point of a subsonic canard aircraft

An approximate formula is derived for the position of the neutral point in canard aircraft. This formula accounts for the aerodynamic interference between the wing (rear wing) and the canard (forward wing). Topics covered include determination of the canard downwash derivative, determination of the canard and wing liftslopes including the aerodynamic interference, and calculation of the neutral point position.

Phillips, J. D.↗
NASA NTRS1985

Approximation Techniques for Parameter Estimation and Feedback Control for Distributed Models of Large Flexible Structures

Approximation ideas that can be used in parameter estimation and feedback control for Euler-Bernoulli models of elastic systems are discussed. Focusing on parameter estimation problems, the authors outline how one can obtain convergence results for cubic spline-based schemes for hybrid models involving an elastic cantilevered beam with tip mass and base acceleration. Sample numerical findings are also presented.

Banks, H. T.↗
NASA NTRS1984

Approximate analysis for resonance of an incompressible shear layer plus edges

A method for approximately analyzing the feedback between downstream and upstream edges in incompressible shear flow is described. The shear flow is modeled by a vortex sheet. Equations for resonance eigenvalues are derived. After the reduction of growth rate by finite shear layer thickness is allowed for, agreement is found between calculated resonances and those that have been observed experimentally.

Durbin, P. A.↗
NASA NTRS1985

Recent improvements in efficiency, accuracy, and convergence for implicit approximate factorization algorithms

In 1977 and 1978, general purpose centrally space differenced implicit finite difference codes in two and three dimensions have been introduced. These codes, now called ARC2D and ARC3D, can run either in inviscid or viscous mode for steady or unsteady flow. Since the introduction of the ARC2D and ARC3D codes, overall computational efficiency could be improved by making use of a number of algorithmic changes. These changes are related to the use of a spatially varying time step, the use of a sequence of mesh refinements to establish approximate solutions, implementation of various ways to reduce inversion work, improved numerical dissipation terms, and more implicit treatment of terms. The present investigation has the objective to describe the considered improvements and to quantify advantages and disadvantages. It is found that using established and simple procedures, a computer code can be maintained which is competitive with specialized codes.

Pulliam, T. H.↗
NASA NTRS1985

Entropy condition satisfying approximations for the full potential equation of transonic flow

A class of conservative difference approximations for the steady full potential equation was presented. They are, in general, easier to program than the usual density biasing algorithms, and in fact, differ only slightly from them. Rigorous proof indicated that these new schemes satisfied a new discrete entropy inequality, which ruled out expansion shocks, and that they have sharp, steady, discrete shocks. A key tool in the analysis is the construction of a new entropy inequality for the full potential equation itself. Results of some numerical experiments using the new schemes are presented.

Osher, S.↗
NASA NTRS1985

Identifying approximate linear models for simple nonlinear systems

This paper addresses the identification (realization) of approximate linear models from response data for certain nonlinear dynamic systems. Response characteristics for several typical nonlinear joints are analyzed mathematically and represented by series expansions. The parameters of the series expansion are then compared with the modal parameters of a linear model identified by the Eigensystem Realization Algorithm. The agreement of the identified model and the analytically derived representation is excellent for the cases studied. Also laboratory data from a model which exhibited stiffening behavior was analyzed using the Eigensystem Realization algorithm and Fast Fourier Transform. The laboratory experiment demonstrated the ability of the technique to recover the model characteristics using real data.

Horta, L. G.↗