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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 721 records · Page 40
All sourcesNASA NTRSDOE OSTI
NASA NTRS1974

Fracture and contact problems for an elastic wedge

The plane elastostatic contact problem for an infinite elastic wedge of arbitrary angle is discussed. The medium is loaded through a frictionless rigid wedge of a given symmetric profile. Using the Mellin transform formulation the mixed boundary value problem is reduced to a singular integral equation with the contact stress as the unknown function. With the application of the results to the fracture of the medium in mind, the main emphasis in the study has been on the investigation of the singular nature of the stress state around the apex of the wedge and on the determination of the contact pressure.

Erdogan, F.↗
NASA NTRS1973

Impedance of strip-traveling waves on an elastic half space - Asymptotic solution

The dynamic normal-load distribution across a strip that is required to maintain a plane progressive wave along its length is studied for the case where the strip is of infinite length and lies on the surface of a homogeneous isotropic elastic half space. This configuration is proposed as a preliminary idealized model for analyzing the dynamic interaction between soils and flexible foundations. The surface load distribution across the strip and the motion of the strip are related by a pair of dual integral equations. An asymptotic solution is obtained for the limiting case of small wavelength. The nature of this solution depends importantly on the propagation velocity of the strip-traveling wave in comparison with the Rayleigh wave speed, the shear wave speed and the dilatational wave speed. When the strip-traveling wave propagates faster than the Rayleigh wave speed, a pattern of trailing Rayleigh waves is shed from the strip. The limiting amplitude of the trailing waves is provided by the asymptotic solution.

Crandall, S. H.↗
NASA NTRS1973

Modelling a particular class of stochastic systems

In this paper a method is given for obtaining a mathematical model of a class of black boxes having multiple inputs and multiple outputs in terms of Ito stochastic integral equations. This method is applicable to the class of black boxes having ergodic correlation functions when there is zero applied input. The point of view adopted in this paper is phenomenological in that it is desired that calculations made using the mathematical model should be 'close' to what is actually observed at the output of the black box.

Eyman, E. D.↗
NASA NTRS1974

A finite element method for potential aerodynamics around complex configurations

A general formulation for steady and oscillatory, subsonic and supersonic, potential linearized aerodynamic flow around complex configurations is presented. A linear integral equation relating the unknown potential on the surface of the body to the known downwash is used. The formulation is applied to the analysis of the flow field around wings and wing-body combinations. The surface is divided into small quadrilateral elements which are approximated with a hyperboloidal surface. The potential is assumed to be constant within each element. This yields a set of linear algebraic equations. The coefficients are evaluated analytically. Numerical results for steady and oscillatory, subsonic and supersonic flows indicate that the method, intrinsically general and flexible, is also fast, accurate and in excellent agreement with existing results.

Chen, L.-T.↗
NASA NTRS1974

Stability of partially lined combustors with distributed combustion

An integral method for theoretical evaluation of the stability of confined flows with mass sources is presented. This method is applied to evaluate the effect of partial length acoustic liners on liquid propellant combustors with distributed combustion sources. The combustor is modeled as a right circular cylinder terminated by a multiorifice (constant Mach number) nozzle. The spatial spread of combustion in the chamber is represented by an arbitrary number of pressure sensitive planar mass sources. On the cylindrical periphery of the chamber is an acoustic absorber of arbitrary length, position, and damping capability. Integral equations are developed from the partial differential equations describing the nonsteady flow and are solved iteratively. Results are given in terms of linear neutral stability plots using a pressure sensitive combustion response. Calculations indicate that increasing the axial spread of combustion increases the stability of the combustor and the effectiveness of the absorber. The most effective linear placement appears at the location of greatest combustion concentration.

Baer, M. R.↗
NASA NTRS1974

Properties of cutoff corrugated surfaces for corrugated horn design

Corrugated horns involve a junction between the corrugated surface and a conducting ground plane. Proper horn design requires an understanding of the electromagnetic properties of the corrugated surface and this junction. An integral equation solution has been used to study the influence of corrugation density and tooth thickness on the power loss, surface current, and the scattering from a ground plane/corrugated surface junction.

Mentzer, C. A.↗
NASA NTRS1974

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 in the paper include the stress intensity factors, the strain energy release rates, and the probable clevage angles giving the direction of crack propagation.

Erdogan, F.↗
NASA NTRS1974

A plate with a crack, stiffened by a partially debonded stringer

The effect of a partially debonded infinite stringer on the stress intensity factor at the crack tip is investigated. It is assumed that the stringer is bonded to an isotropic plate through an adhesive, along a line perpendicular to the crack. Due to the high stress concentration around the crack tip and on the adhesive, partial debonding is assumed to develop between the stringer and the plate. The integral equation, obtained from the continuity of displacements along the line where the stringer and the plate are bonded, is solved numerically to give the shear stress distribution between the plate and the stringer and the stress intensity factors at both crack tips.

Arin, K.↗
NASA NTRS1974

Interaction between parallel cracks in layered composites

The plane strain problem of a millilayered 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 NTRS1974

Electromagnetic diffraction efficiencies for plane reflection diffraction gratings

The theory and computer programs, based on electromagnetic theory, for the analysis and design of echelle gratings were developed. The gratings are designed for instruments that operate in the ultraviolet portion of the spectrum. The theory was developed so that the resulting computer programs will be able to analyze deep (up to 30 wavelengths) gratings by including as many as 100 real or homogeneous diffraction orders. The program calculates the complex amplitude coefficient for each of the diffracted orders. A check on the numerical method used to solve the integral equations is provided by a conservation of energy calculation.

Marathay, A. S.↗
NASA NTRS1974

Lectures on the scattering of light

The exact (Mie) theory for the scattering of a plane wave by a dielectric sphere is presented. Since this infinite series solution is computationally impractical for large spheres, another formulation is given in terms of an integral equation valid for a bounded, but otherwise general array of scatterers. This equation is applied to the scattering by a single sphere, and several methods are suggested for approximating the scattering cross section in closed form. A tensor scattering matrix is introduced, in terms of which some general scattering theorems are derived. The application of the formalism to multiple scattering is briefly considered.

Saxon, D. S.↗
NASA NTRS1974

A note on the effect of bending stiffness of stringers attached to a plate with a crack

An infinite stringer partially bonded to a plate through a layer of adhesive is considered. The stringer had bending as well as longitudinal stiffness. The effect of the stringer's bending rigidity on the stress intensity factor at the tip of the crack is illustrated. Shear stress distribution between the plate and the stringer and the stress intensity factors are obtained from the solution of a system of Fredholm integral equations. The continuity of displacements along the line of bond is represented by the equations.

Arin, K.↗
NASA NTRS1974

Penny-shaped crack in a fiber-reinforced matrix

Using a slender inclusion model developed earlier, the elastostatic interaction problem between a penny-shaped crack and elastic fibers in an elastic matrix is formulated. For a single set and for multiple sets of fibers oriented perpendicularly to the plane of the crack and distributed symmetrically on concentric circles, the problem was reduced to a system of singular integral equations. Techniques for the regularization and for the numerical solution of the system are outlined. For various fiber geometries numerical examples are given, and distribution of the stress intensity factor along the crack border was obtained. Sample results showing the distribution of the fiber stress and a measure of the fiber-matrix interface shear are also included.

Narayanan, T. V.↗
NASA NTRS1974

Contact and crack problems for an elastic wedge

The contact and the crack problems for an elastic wedge of arbitrary angle are considered. The problem is reduced to a singular integral equation which, in the general case, may have a generalized Cauchy kernel. The singularities under the stamp as well as at the wedge apex were studied, and the relevant stress intensity factors are defined. The problem was solved for various wedge geometries and loading conditions. The results may be applicable to certain foundation problems and to crack problems in symmetrically loaded wedges in which cracks initiate from the apex.

Erdogan, F.↗
NASA NTRS1974

A finite-element method for lifting surfaces in steady incompressible subsonic flow

The problem of potential steady subsonic flow for lifting surfaces is considered. This problem requires the solution of an integral equation relating the value of the potential discontinuity on the lifting surface and its wake to the values of the normal derivative of the potential which are known from the boundary conditions. The lifting surface is divided into small (quadrilateral hyperboloidal) surface elements, which are described in terms of the Cartesian components of the four corner points. The values of the potential discontinuity and the normal derivative of the potential are assumed to be constant within each element and equal to their values at the centroids of the elements. This yields a set of linear algebraic equations. Numerical results are in good agreement with existing ones.

Morino, L.↗
NASA NTRS1975

Prediction of unsteady aerodynamic loadings caused by leading edge and trailing edge control surface motions in subsonic compressible flow: Computer program description

A digital computer program has been developed to calculate unsteady loadings caused by motions of lifting surfaces with leading edge or trailing edge controls based on the subsonic kernel function approach. The pressure singularities at hinge line and side edges have been extracted analytically as a preliminary step to solving the integral equation by collocation. The program calculates generalized aerodynamic forces for user supplied deflection modes. Optional intermediate output includes pressure at an array of points, and sectional generalized forces. From one to six controls on the half span can be accommodated.

Redman, M. C.↗
NASA NTRS1975

Downward continuation of gravity information from satellite to satellite tracking or satellite gradiometry in local areas

Integral formulas in the parameter domain are used instead of a representation by spherical harmonics. The neglected regions will cause a truncation error. The application of the discrete form of the integral equations connecting the satellite observations with surface gravity anomalies is discussed in comparison with the least squares prediction method. One critical point of downward continuation is the proper choice of the boundary surface. Practical feasibilities are in conflict with theoretical considerations. The properties of different approaches for this question are analyzed.

Rummel, R.↗