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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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NASA NTRS1972

Stresses near a flat inclusion in bonded dissimilar materials.

The plane elastostatic problem for bonded materials containing a flat inclusion is considered. It is assumed that the inclusion is located parallel to or on the interface and may be rigid or elastic with negligible bending rigidity. The integral equations for various cases are derived and their solutions are described. The stress state around the singular points are investigated and a pair of stress intensity factors similar to that for crack problems are defined. A series of numerical examples for two bonded half planes and for a half plane is worked out. The stress intensity factors are presented as functions of the ratio of the distance from the interface to the length of the inclusion.

Erdogan, F.↗
NASA NTRS1972

Turbulent boundary layer on a rotating helical blade.

Investigation of the boundary-layer characteristics on a helical blade of large chord length, enclosed in an annulus and rotating in a fluid otherwise at rest. The three-dimensional form of momentum integral equations is derived, and is used to predict the boundary-layer growth and limiting streamline angles on the blade surface. The measurements are in general agreement with the predictions. The wall shear stress correlation, which includes both Reynolds number and rotation parameters, valid for a rotating blade operating at zero pressure gradient, is derived. Radial and tangential velocity profiles, the tangential component of turbulence intensity, and blade static pressures are measured at several locations on the blade surface. The nature of flow near the blade tip is discussed. An expression for the radial velocity profile, valid in the outer region of the boundary layer, is derived theoretically.

Lakshminarayana, B.↗
NASA NTRS1972

Nonlinear actuator disk theory.

Results obtained from a recent investigation of the flowfield induced by a heavily loaded actuator disk. First, the governing nonlinear integral equations are formulated from two different points of view, and the iterative solution is briefly outlined. Calculated flow patterns are presented for representative advance ratios and blade circulation distributions. For the static condition, the experimentally observed lingering of the tip vortices in the propeller plane, and the insensitivity of the streamline pattern to thrust coefficient are both accounted for, and a 'dividing streamline' - apparently not previously discussed in the literature, is predicted for the nonstatic case. Finally, the relationship between the actuator disk flow and the zero harmonic of the flowfield induced by a finite-bladed propeller is considered.

Greenberg, M. D.↗
NASA NTRS1972

Random gravitational encounters and the evolution of spherical systems. III - Halo.

The accumulation of stars in the halo of a spherical stellar system, together with the escape of stars from the system, result from stellar encounters within a dense central core. The resultant halo structure is studied both analytically and numerically for an isolated system. On the assumption that conditions in the central core remain constant with time, a simple steady-state solution is obtained for the outermost halo, or 'fringe', defined as the region from which stars may escape after a few additional orbits through the central core of the system. In this steady-state solution the density in phase space, obtained from a simple integral equation for the fringe region, is found to vary nearly linearly with the total energy of a star per unit mass for energies which are less than the energy of escape.

Spitzer, L., Jr.↗
NASA NTRS1972

A sandwich plate with a part-through and a debonding crack.

The stress analysis of a metal base plate stiffened by a fiber-reinforced composite layer is considered. It is assumed that the two materials are bonded through an adhesive of constant thickness which is treated as a two-dimensional shear spring in the analysis. The metal plate is assumed to contain a through crack of finite length. The composite plate has no flaws. However, due to the high stress concentration around the crack and on the interface, a debonding crack is assumed to exist, encircling the crack in the base plate. The problem is reduced to a pair of integral equations of the second kind with Fredholm-type kernels. By solving these equations the stress intensity factor in the base plate, the boundary of the debonding crack, and the interface shear stresses acting on the adhesive are calculated.

Erdogan, F.↗
NASA NTRS1972

Statistical versus nonstatistical temperature inversion methods

Vertical temperature profiles are derived from radiation measurements by inverting the integral equation of radiative transfer. Because of the nonuniqueness of the solution, the particular temperature profile obtained depends on the numerical inversion technique used and the type of auxiliary information incorporated in the solution. The choice of an inversion algorithm depends on many factors; including the speed and size of computer, the availability of representative statistics, and the accuracy of initial data. Results are presented for a numerical study comparing two contrasting inversion methods: the statistical-matrix inversion method and the nonstatistical-iterative method. These were found to be the most applicable to the problem of determining atmospheric temperature profiles. Tradeoffs between the two methods are discussed.

Smith, W. L.↗
NASA NTRS1972

The inverse scattering problem at fixed angular momentum for nonlocal separable interactions

The problem of inverse scattering at fixed angular momentum is considered. The problem is particularized to the case of nonlocal separable interactions. A brief survey of the inverse problem for nonlocal separable interactions is presented. This problem can be solved exactly by integration. It amounts to solving singular integral equations of the Hilbert-Mushkhelishvili type, which have been studied extensively in the past and appear in many areas of physics, including theory of elasticity and dispersions relations in high energy physics.

Chadan, K.↗
NASA NTRS1972

Application of a stochastic inverse to the geophysical inverse problem

The inverse problem for gross earth data can be reduced to an undertermined linear system of integral equations of the first kind. A theory is discussed for computing particular solutions to this linear system based on the stochastic inverse theory presented by Franklin. The stochastic inverse is derived and related to the generalized inverse of Penrose and Moore. A Backus-Gilbert type tradeoff curve is constructed for the problem of estimating the solution to the linear system in the presence of noise. It is shown that the stochastic inverse represents an optimal point on this tradeoff curve. A useful form of the solution autocorrelation operator as a member of a one-parameter family of smoothing operators is derived.

Jordan, T. H.↗
NASA NTRS1973

The inclusion problem with a crack crossing the boundary

The problem of an elastic plane containing an elastic inclusion is considered. It is assumed that both the plane and the inclusion contain a radial crack and the two cracks are collinear. The problem is formulated in terms of a system of singular integral equations. In the interesting limiting cases in which the crack tips approach the interface from either one or both sides, the dominant parts of the kernels become generalized Cauchy kernels giving rise to stress singularities of other than minus 1/2 power. For these unusual cases of a crack terminating at or crossing the interface stress intensity factors are defined and some detailed results are given for various crack-inclusion geometries and material combinations.

Erdogan, F.↗
NASA NTRS1973

The X-ray Emissivity of the Universe: 2-200 Kev

Observational results on the diffuse X-ray background between 2 and 200 keV are reported. Data are presented as a function of the volume emissivity function B (E) (ergs/sec cu Mpc keV emitted at energy E). The prescription for this is first to establish the spectral intensity I (E) (ergs/sec sq cm ster keV) measured at the earth, second to subtract the contribution due to known, discrete sources, and third to unfold the integral equation which relates the measured intensity to the emissivity.

Schwartz, D.↗
NASA NTRS1973

Bonded half planes containing an arbitrarily oriented crack

The plane elastostatic problem for two bonded half planes containing an arbitrarily oriented crack in the neighborhood of the interface is considered. Using Mellin transforms, the problem is formulated as a system of singular integral equations. The equations are solved for various crack orientations, material combinations, and external loads. The numerical results given include the stress intensity factors, tHe strain energy release rates, and tHe probable cleavage angles giving the direction of crack propagation.

Erdogan, F.↗
NASA NTRS1973

Interaction between parallel cracks in layered composites

The plane strain problem of a multi-layered composite with parallel cracks is considered. The main objective is to study the interaction between parallel and collinear cracks. The problem is formulated in terms of a set of simultaneous singular integral equations which are solved numerically. The effect of material properties on the interaction between cracks is also demonstrated.

Ratwani, M.↗
NASA NTRS1973

A half plane and a strip with an arbitrarily located crack

A technique is presented for dealing with the problem of an elastic domain containing an arbitrarily oriented internal crack. The problem is formulated as a system of integral equations for a fictitious layer of body forces imbedded in the plane along a closed smooth curve encircling the original domain. The problems of a half plane with a crack in the neighborhood of its free boundary and of an infinite strip containing a symmetrically located internal crack with an arbitrary orientation are considered as examples. In each case the stress intensity factors are computed and are given as functions of the crack angle.

Erdogan, F.↗
NASA NTRS1972

Dipole receiver characteristics in the presence of sea water

The receive properties for a dipole in the presence of sea water were obtained by solving integral equations for currents along the unloaded dipole and its image. For dipoles of 0.1 wavelength or higher above the sea surface, the performance resembled that of a dipole over a perfectly conducting plane; for dipoles within 0.1 wavelength above the sea surface, the relative gain dropped in about the same proportion as the relative reduction in the strength of the resultant electric field. An insulated wavelength/2 dipole with a conjugate load matched in free space had a relative power gain of 17 db below isotropic at the sea surface.

Kao, P. S.↗
NASA NTRS1973

A parametric study of cut-off corrugated surface properties

Corrugated horns involve a junction between the corrugated surface and a conducting groundplane. Proper horn design requires an understanding of the electromagnetic properties of the corrugated surface and this junction. Therefore, an integral equation solution has been used to study the influence of corrugation density and shape on the power loss. Surface current, and the scattering from a groundplane-corrugated surface junction. Both square and vee shape corrugations have been considered over the range of corrugation depths where the surface acts as a cut-off corrugated surface.

Mentzer, C. A.↗
NASA NTRS1973

Transonic flow past lifting wings.

Work conducted by Norstrud (1971) has been extended to lifting flows with the inclusion of embedded continuous supercritical regions. The approach taken follows some fundamental steps proposed for two-dimensional flows by Oswatitsch (1950). The governing integral equation is replaced by a system of nonlinear algebraic equations. The method of parametric differentiation is applied to the solution of this system of equations. The analytical analysis is discussed together with a numerical analysis in the case of a wing configuration with arbitrary thickness distribution.

Norstrud, H.↗
NASA NTRS1973

The transonic aerofoil problem with embedded shocks.

The integral equation approach to the mixed flow problem of infinite wings at high subsonic speeds is adopted for non-circulatory and circulatory (lifting) flows. The solutions are determined from a system of non-linear algebraic equations and, to ensure always unique solutions, the method of differentiation with respect to a parameter has been applied. The resulting Cauchy problem is then solved with the linearised flow solution as the initial value vector. For the case of embedded shocks in the flow field, the method of steepest descent has been added to the calculation scheme. Results for subcritical and supercritical flows past aerofoils are given and compared with solutions obtained by finite-difference techniques.

Norstrud, H.↗
NASA NTRS1973

A penny shaped crack in a filament-reinforced matrix. 2: The crack problem

The elastostatic interaction problem between a penny-shaped crack and a slender inclusion or filament in an elastic matrix was formulated. For a single filament as well as multiple identical filaments located symmetrically around the crack the problem is shown to reduce to a singular integral equation. The solution of the problem is obtained for various geometries and filament-to-matrix stiffness ratios, and the results relating to the angular variation of the stress intensity factor and the maximum filament stress are presented.

Pacella, A. H.↗