Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “Methods”

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.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 1,063 records · Page 59
All sourcesNASA NTRSDOE OSTI
NASA NTRS1972

Approximation method for the kinetic Boltzmann equation

The further development of a method for approximating the Boltzmann equation is considered and a case of pseudo-Maxwellian molecules is treated in detail. A method of approximating the collision frequency is discussed along with a method for approximating the moments of the Boltzmann collision integral. Since the return collisions integral and the collision frequency are expressed through the distribution function moments, use of the proposed methods make it possible to reduce the Boltzmann equation to a series of approximating equations.

Shakhov, Y. M.↗
NASA NTRS1972

Generation and application of the equations of condition for high order Runge-Kutta methods

This thesis develops the equations of condition necessary for determining the coefficients for Runge-Kutta methods used in the solution of ordinary differential equations. The equations of condition are developed for Runge-Kutta methods of order four through order nine. Once developed, these equations are used in a comparison of the local truncation errors for several sets of Runge-Kutta coefficients for methods of order three up through methods of order eight.

Haley, D. C.↗
NASA NTRS1973

Plane elasto-plastic analysis of v-notched plate under bending by boundary integral equation method

A method of solution is presented, which, when applied to the elasto-plastic analysis of plates having a v-notch on one edge and subjected to pure bending, will produce stress and strain fields in much greater detail than presently available. Application of the boundary integral equation method results in two coupled Fredholm-type integral equations, subject to prescribed boundary conditions. These equations are replaced by a system of simultaneous algebraic equations and solved by a successive approximation method employing Prandtl-Reuss incremental plasticity relations. The method is first applied to number of elasto-static problems and the results compared with available solutions. Good agreement is obtained in all cases. The elasto-plastic analysis provides detailed stress and strain distributions for several cases of plates with various notch angles and notch depths. A strain hardening material is assumed and both plane strain and plane stress conditions are considered.

Rzasnicki, W.↗
NASA NTRS1973

The development of accurate and efficient methods of numerical quadrature

Some new methods for performing numerical quadrature of an integrable function over a finite interval are described. Each method provides a sequence of approximations of increasing order to the value of the integral. Each approximation makes use of all previously computed values of the integrand. The points at which new values of the integrand are computed are selected in such a way that the order of the approximation is maximized. The methods are compared with the quadrature methods of Clenshaw and Curtis, Gauss, Patterson, and Romberg using several examples.

Feagin, T.↗
NASA NTRS1973

Net radiation method for enclosure systems involving partially transparent walls

The net radiation method is developed for analyzing radiation heat transfer in enclosure systems involving partially transparent walls. One such system is an enclosure with windows in it. The conventional net radiation method was developed for enclosures having opaque walls. If a partially transparent wall is present, it will permit radiation to enter and leave the enclosure. The net radiation equations are developed here for gray and semigray enclosures with one or more windows. Another system of interest, such as in a flat plate solar collector, consists of a series of parallel transparent layers. The transmission characteristics of such window systems are obtained by the net radiation method, and the technique appears to be more convenient than the ray tracing method which has been used in the past. Relations are developed for windows consisting of any number of parallel layers having differing absorption coefficients and differing surface reflectivities, and for systems composed of parallel transmitting layers and opaque plates.

Siegel, R.↗
NASA NTRS1973

A study of numerical methods of solution of the equations of motion of a controlled satellite under the influence of gravity gradient torque

Numerical methods of integration of the equations of motion of a controlled satellite under the influence of gravity-gradient torque are considered. The results of computer experimentation using a number of Runge-Kutta, multi-step, and extrapolation methods for the numerical integration of this differential system are presented, and particularly efficient methods are noted. A large bibliography of numerical methods for initial value problems for ordinary differential equations is presented, and a compilation of Runge-Kutta and multistep formulas is given. Less common numerical integration techniques from the literature are noted for further consideration.

Thompson, J. F.↗
NASA NTRS1973

Corner pressures and fillet shock locations for symmetrical corners by an approximate method.

Description of an approximate method for predicting the pressure in the immediate corner region and the shock structure on stream-aligned, sharp-leading-edge, symmetrical corner configurations. The method is basically the two-shock method developed by Charwat and Redekopp (1966), with the additional assumption that the corner fillet shock can be located from the calculated pressure in the corner. Corner pressures are correlated over a wide range of Mach numbers in air and helium for different corner wedge angles. The shock structure calculated by this method is compared with supersonic and hypersonic data.

Watson, R. D.↗
NASA NTRS1973

A comparison of two transient methods of measuring thermal conductivity of particulate samples.

A comparison is made of the line source (LS) method and the differential line source (DLS) method of measuring thermal conductivity of particulate materials in vacuum. The DLS method requires more instrumentation in the measuring circuitry (an additional amplifier and a differentiating circuit), but since it does not require a stable temperature to initiate a test, it does not need a sample temperature control system. DLS tests can be taken as the temperature in the samples is rising from liquid nitrogen temperature to room temperature. This eliminates the practice of extrapolating thermal conductivity over this large temperature range. Also, the advantages of reduced test time, data reduction time, and small sample temperature rise enable the experimenter to take about 7-12 DLS tests in the time of 2 LS tests. Test data from the two methods agree very well.

Scott, R. W.↗
NASA NTRS1973

A new method for calculating correction factors for near-field gain measurements.

A new method is demonstrated with which near-field antenna gain correction factors can be calculated directly from measured far-field pattern data by using a spherical wave expansion of the pattern. This eliminates the need for any assumptions regarding antenna aperture field distributions. For illustration, the method is applied to the case of a horn antenna. A comparison of the calculation results with direct measurement data shows an agreement within 0.03 dB. The method, when compared to the method used by Chu and Semplak (1965), is found to show similar agreement.

Ludwig, A. C.↗
NASA NTRS1973

Method for estimating fracture strength of specially orthotropic composite laminates.

A method is presented for estimating the stress intensity factor characteristic of crack extension in a specially orthotropic advanced fiber composite laminate, based on the elastic properties and ultimate principal strengths of a lamina, the laminate construction, and the experimentally determined value of the characteristic stress intensity factor of an arbitrary angle-plied, midplane symmetric laminate. A comparison of the results obtained from this method with limited experimental data for graphite/epoxy laminates indicates that the method is quite accurate for this particular material system. The predictive method is also used, in conjunction with experimental data, to estimate the size of a damage zone surrounding the crack tip.

Konish, H. J., Jr.↗
NASA NTRS1973

Boundary-integral methods in elasticity and plasticity

Recently developed methods that use boundary-integral equations applied to elastic and elastoplastic boundary value problems are reviewed. Direct, indirect, and semidirect methods using potential functions, stress functions, and displacement functions are described. Examples of the use of these methods for torsion problems, plane problems, and three-dimensional problems are given. It is concluded that the boundary-integral methods represent a powerful tool for the solution of elastic and elastoplastic problems.

Mendelson, A.↗
NASA NTRS1973

Analysis of axisymmetrical vibration of a partially liquid-filled elastic sphere by the method of Green's function

The longitudinal dynamic behavior of launch vehicles is largely determined by their huge liquid propellant masses which are spring supported by the elastic tank walls. Throughout much of the powered flight time, these masses constitute a high percentage of the entire vehicle mass and, therefore, may dominate the fundamental modes of the vehicle. In this report, a spherical container is considered. The analysis is based on a Galerkin approach, in the course of which a second-order differential equation must be solved. The solution has been obtained by the method of Green's function. This method is favorable because it displays the manner in which the analysis can be extended to partially liquid-filled general shells of revolution. The computer programs currently available for partially liquid-filled propellant tanks are based on the finite element methods and result in analytical models having as many as several hundred degrees of freedom. The method applied in this report results in a model having less than 10 degrees of freedom as can be shown by numerical evaluation. Therefore, it will be possible to analyze propellant tanks using much less computer time with comparable accuracy.

Glaser, R. F.↗
NASA NTRS1973

The constraint method: A new finite element technique

An approch to the finite element method which utilizes families of conforming finite elements based on complete polynomials is presented. Finite element approximations based on this method converge with respect to progressively reduced element sizes as well as with respect to progressively increasing orders of approximation. Numerical results of static and dynamic applications of plates are presented to demonstrate the efficiency of the method. Comparisons are made with plate elements in NASTRAN and the high-precision plate element developed by Cowper and his co-workers. Some considerations are given to implementation of the constraint method into general purpose computer programs such as NASTRAN.

Tsai, C.↗
NASA NTRS1974

Application of boundary integral method to elastoplastic analysis of v-notched beams

The boundary integral equation method was applied in the solution of the plane elastoplastic problems. The use of this method was illustrated by obtaining stress and strain distributions for a number of specimens with a single edge notch and subjected to pure bending. The boundary integral equation method reduced the non-homogeneous biharmonic equation to two coupled Fredholm-type integral equations. These integral equations were replaced by a system of simultaneous algebraic equations and solved numerically in conjunction with the method of successive elastic solutions.

Rzasnicki, W.↗
NASA NTRS1974

The computation of steady nozzle flow by a time-dependent method

The steady flow in two-dimensional and axisymmetric nozzles was computed using a time-dependent method. In this method the interior mesh points were computed using the MacCormack finite-difference scheme, while a characteristic scheme was used to calculate the boundary mesh points. No explicit artificial viscosity term was included. The fluid was assumed to be a perfect gas. This method was used to compute the flow in a 45 deg - 15 deg conical, converging-diverging nozzle, a 15 deg conical, converging nozzle, and a 10 deg conical, plug nozzle. Good agreement between the numerical solution and experimental data was found. In contrast to previous time-dependent methods, the computational times were less than one minute on a CDC 6600 computer.

Cline, M. C.↗
NASA NTRS1974

Application of boundary integral method to elastoplastic analysis of V-notched beams

The boundary integral equation method was applied in the solution of the plane elastoplastic problem. The use of this method was illustrated by obtaining stress and strain distributions for a number of specimens with a single-edge notch and subjected to pure bending. The boundary integral equation method reduced the inhomogeneous biharmonic equation to two coupled Fredholm-type integral equations. These integral equations were replaced by a system of simultaneous algebraic equations and solved numerically in conjunction with a method of successive elastic solutions.

Rzasnicki, W.↗
NASA NTRS1974

Analysis of complex elastic structures by a Rayleigh-Ritz component modes method using Lagrange multipliers

The free vibrations of elastic structures of arbitrary complexity were analyzed in terms of their component modes. The method was based upon the use of the normal unconstrained modes of the components in a Rayleigh-Ritz analysis. The continuity conditions were enforced by means of Lagrange Multipliers. Examples of the structures considered are: (1) beams with nonuniform properties; (2) airplane structures with high or low aspect ratio lifting surface components; (3) the oblique wing airplane; and (4) plate structures. The method was also applied to the analysis of modal damping of linear elastic structures. Convergence of the method versus the number of modes per component and/or the number of components is discussed and compared to more conventional approaches, ad-hoc methods, and experimental results.

Klein, L. R.↗
NASA NTRS1974

The Vortex Lattice Method for the Rotor-Vortex Interaction Problem

The rotor blade-vortex interaction problem and the resulting impulsive airloads which generate undesirable noise levels are discussed. A numerical lifting surface method to predict unsteady aerodynamic forces induced on a finite aspect ratio rectangular wing by a straight, free vortex placed at an arbitrary angle in a subsonic incompressible free stream is developed first. Using a rigid wake assumption, the wake vortices are assumed to move downsteam with the free steam velocity. Unsteady load distributions are obtained which compare favorably with the results of planar lifting surface theory. The vortex lattice method has been extended to a single bladed rotor operating at high advance ratios and encountering a free vortex from a fixed wing upstream of the rotor. The predicted unsteady load distributions on the model rotor blade are generally in agreement with the experimental results. This method has also been extended to full scale rotor flight cases in which vortex induced loads near the tip of a rotor blade were indicated. In both the model and the full scale rotor blade airload calculations a flat planar wake was assumed which is a good approximation at large advance ratios because the downwash is small in comparison to the free stream at large advance ratios. The large fluctuations in the measured airloads near the tip of the rotor blade on the advance side is predicted closely by the vortex lattice method.

Padakannaya, R.↗