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Results for “approximation theory”

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 73 records · Page 4
All sourcesNASA NTRSDOE OSTI
NASA NTRS1973

Mechanics of wheel-soil interaction

An approximate theory for wheel-soil interaction is presented which forms the basis for a practical solution to the problem. It is shown that two fundamental observations render the problem determinate: (1) The line of action of the resultant of radial stresses acting at the wheel soil interface approximately bisects the wheel-soil contact angle for all values of slip. (2) A shear stress surface can be hypothesized. The influence of soil inertia forces is also evaluated. A concept of equivalent cohesion is introduced which allows a convenient experimental comparison for both cohesive and frictional soils. This theory compares favorably with previous analyses and experimental data, and shows that soil inertia forces influencing the motion of a rolling wheel can be significant.

Houland, H. J.↗
NASA NTRS1979

General Potential Theory of Arbitrary Wing Sections

The problem of determining the two dimensional potential flow around wing sections of any shape is examined. The problem is condensed into the compact form of an integral equation capable of yielding numerical solutions by a direct process. An attempt is made to analyze and coordinate the results of earlier studies relating to properties of wing sections. The existing approximate theory of thin wing sections and the Joukowski theory with its numerous generalizations are reduced to special cases of the general theory of arbitrary sections, permitting a clearer perspective of the entire field. The method which permits the determination of the velocity at any point of an arbitrary section and the associated lift and moments is described. The method is also discussed in terms for developing new shapes of preassigned aerodynamical properties.

Theodorsen, T.↗
NASA NTRS1980

Scattering by nonspherical particles of size comparable to wavelength - A new semi-empirical theory and its application to tropospheric aerosols

A semiempirical theory is developed which is based on simple physical principles and comparisons with laboratory measurements. The ultimate utility of this approach rests on its ability to successfully reproduce the observed single-scattering phase function for a wide variety of particle shapes, sizes and refractive indices. This approximate theory is developed for evaluating the interaction of randomly oriented, nonspherical particles with the total intensity component of electromagnetic radiation. Mie theory is used when the particle size parameter x (ratio of particle circumference to wavelength) is less than some upper bound x sub zero (about 5). For x greater than x sub zero, the interaction is divided into three components: diffraction, external reflection and transmission. The application of the theory is illustrated by considering the influence of the shape of tropospheric aerosols on their contribution to the earth's global albedo.

Pollack, J. B.↗
NASA NTRS1990

Spectral methods for time dependent problems

Spectral approximations are reviewed for time dependent problems. Some basic ingredients from the spectral Fourier and Chebyshev approximations theory are discussed. A brief survey was made of hyperbolic and parabolic time dependent problems which are dealt with by both the energy method and the related Fourier analysis. The ideas presented above are combined in the study of accuracy stability and convergence of the spectral Fourier approximation to time dependent problems.

Tadmor, Eitan↗
NASA NTRS1986

Computational methods for optimal linear-quadratic compensators for infinite dimensional discrete-time systems

An abstract approximation theory and computational methods are developed for the determination of optimal linear-quadratic feedback control, observers and compensators for infinite dimensional discrete-time systems. Particular attention is paid to systems whose open-loop dynamics are described by semigroups of operators on Hilbert spaces. The approach taken is based on the finite dimensional approximation of the infinite dimensional operator Riccati equations which characterize the optimal feedback control and observer gains. Theoretical convergence results are presented and discussed. Numerical results for an example involving a heat equation with boundary control are presented and used to demonstrate the feasibility of the method.

Gibson, J. S.↗
NASA NTRS1978

Preliminary study of the effect of the turbulent flow field around complex surfaces on their acoustic characteristics

Fundamental theories for noise generated by flow over surfaces exist for only a few simple configurations. The role of turbulence in noise generation by complex surfaces should be essentially the same as for simple configurations. Examination of simple-surface theories indicates that the spatial distributions of the mean velocity and turbulence properties are sufficient to define the noise emission. Measurements of these flow properties were made for a number of simple and complex surfaces. The configurations were selected because of their acoustic characteristics are quite different. The spatial distribution of the turbulent flow properties around the complex surfaces and approximate theory are used to locate and describe the noise sources, and to qualitatively explain the varied acoustic characteristics.

Olsen, W. A.↗
NASA NTRS1992

Vibration of thick composite laminates - Analytic theory and finite element approximations

Two versions of a (1,2) higher-order laminate plate theory are extended to elastodynamics, and their performance on free vibration problems for homogeneous and laminated plates is examined. Both versions are based on continuously varying through-the-thickness linear and parabolic distributions for the inplane and transverse displacements, respectively. They also use continuous parabolic distributions for the transverse shear strains. The theory is capable of providing an improved accuracy as compared to other approximate theories and accurately predicting the lowest thickness-stretch frequencies which cannot be obtained with shear-deformable theories. The theory is considered to be particularly well-suited for generating simple and efficient variationally-based displacement finite elements leading to C sup 0 elements with only five degrees of freedom per node.

Tessler, A.↗
NASA NTRS1985

Finite amplitude gravity waves: Harmonics, advective steepening, breaking and saturation

A simple theory is presented which determines details of the breaking and saturation of a gravity wave as it propagates upward in the atmosphere. Breaking and saturation are here due to nonlinear advection analogous to the breaching of a surface wave and to the breaking of a planetary wave. Much simplification is obtained by the assumption that in a wave packet consisting of a primary wave and its harmonics, the primary wave remains dominant. This assumption, referred to a quasi-monochromatic approximation, is suggested by observations. Determined by this approximate theory are: a detailed picture of the waveform as it steepens and breaks; harmonics of the wave; the turbulence generation; and an underlying relationship between superadiabatic lapse rate and saturation by wave-wave interactions.

Weinstock, J.↗
NASA NTRS1960

Applications of a General Finite-Difference Method for Calculating Bending Deformations of Solid Plates

This paper reports the findings of an investigation of a finite - difference method directly applicable to calculating static or simple harmonic flexures of solid plates and potentially useful in other problems of structural analysis. The method, which was proposed in doctoral thesis by John C. Houbolt, is based on linear theory and incorporates the principle of minimum potential energy. Full realization of its advantages requires use of high-speed computing equipment. After a review of Houbolt's method, results of some applications are presented and discussed. The applications consisted of calculations of the natural modes and frequencies of several uniform-thickness cantilever plates and, as a special case of interest, calculations of the modes and frequencies of the uniform free-free beam. Computed frequencies and nodal patterns for the first five or six modes of each plate are compared with existing experiments, and those for one plate are compared with another approximate theory. Beam computations are compared with exact theory. On the basis of the comparisons it is concluded that the method is accurate and general in predicting plate flexures, and additional applications are suggested. An appendix is devoted t o computing procedures which evolved in the progress of the applications and which facilitate use of the method in conjunction with high-speed computing equipment.

Walton, William C., Jr.↗
NASA NTRS1981

Recursive algorithms for two-dimensional smoothing using bicubic hermite polynomial

It is noted that in the past, smoothing splines originated from approximation theory have been successfully applied to data filtering and image smoothing problems. Even though the nonrecursive technique of smoothing splines gives an optimal solution, the amount of computation increases rapidly with the size of the two-dimensional data. A derivation is presented here of quarter-plane filtering algorithms that provide smoothed estimates of function values and their derivatives by fitting two-dimensional smoothing splines in a recursive manner. The derivation procedure sheds light on specific problems encountered in two-dimensional filtering problems. What is more, the amount of computation for this recursive processor increases only linearly with the size of the two-dimensional data. Because of certain approximations introduced in its derivation, this recursive processor becomes suboptimal.

Kim, C. S.↗