SEARCH · Search NASA

Results for “Integral equations”

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.

SourceResearch connectionFrom yearThrough year

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

At least 739 records · Page 41

All sources NASA NTRS DOE OSTI

NASA NTRS1975

Prediction of unsteady aerodynamic loadings caused by leading edge and trailing edge control surface motions in subsonic compressible flow: Analysis and results

A theoretical analysis and computer program was developed for the prediction of unsteady lifting surface loadings caused by motions of leading edge and trailing edge control surfaces having sealed gaps. The final form of the downwash integral equation was formulated by isolating the singularities from the nonsingular terms and using a preferred solution process to remove and evaluate the downwash discontinuities in a systematic manner. Comparisons of theoretical and experimental pressure data are made for several control surface configurations. The comparisons indicate that reasonably accurate theoretical pressure distributions and generalized forces may be obtained for a wide variety of control surface configurations. Spanwise symmetry or antisymmetry of motion, and up to six control surfaces on each half span can be accommodated.

Rowe, W. S.↗

NASA NTRS1974

Removal of seeing and instrumental blur effects from astronomical scanner observations

The Phillips-Twomey method for solving simultaneous integral equations is applied to the problem of removing blur effects arising from atmospheric and instrumental sources from astronomical observations made with photoelectric area-scanning instruments. Details of the method and the effects of observational errors on the quality of the results are discussed in the context of applications to actual observations of stars and the planet Saturn.

Clements, A. E.↗

NASA NTRS1975

A corrugated horn antenna using V-shape corrugations

Corrugated horns use corrugations on the E-plane walls that are operating in the cutoff condition. In this paper, attention is focused on replacing the rectangular shaped corrugation with a V-shaped corrugation. The properties of the V corrugations are obtained using an integral equation solution; the results of the computational studies indicate that for operation of the V corrugations in the forbidden zone the depth of the corrugations lie between 0.3125 to 0.625 times the wavelength in contrast to the rectangular corrugations where the corresponding depth is 0.25 to 0.5 times the wavelength. The radiation patterns and impedance of two identical rectangular horns with corrugated E-plane walls using either V or rectangular corrugations are directly compared.

Mentzer, C. A.↗

NASA NTRS1975

Advanced panel-type influence coefficient methods applied to subsonic flows

An advanced technique for solving the linear integral equations of three-dimensional subsonic potential flows (steady, inviscid, irrotational and incompressible) about arbitrary configurations is presented. It involves assembling select, logically consistent networks whose construction comprises four tasks, which are described in detail: surface geometry definition; singularity strength definition; control point and boundary condition specification; and calculation of induced potential or velocity. The technique is applied to seven wing examples approached by four network types: source/analysis, doublet/analysis, source/design, and doublet/design. The results demonstrate the forgiveness of the model to irregular paneling and the practicality of combined analysis/design boundary conditions. The appearance of doublet strength mismatch is a valuable indicator of locally inadequate paneling.

Johnson, F. T.↗

NASA NTRS1975

The use of local basis functions in unsteady aerodynamics

This paper reports a successful demonstration of using local basis functions to solve Kussner's integral equation for unsteady airloads. Pressure basis functions are defined over relatively small subsets of the aerodynamic surface and are zero elsewhere. This formulation combines the accuracy and smoothness of distribution methods with the simplicity and versatility of panel methods. Application is made to subsonic compressible flow about oscillating planar surfaces with controls. Numerical results are presented. Convergence with respect to panel size, extensions to more general classes of solutions, and areas needing additional investigation are discussed.

Fromme, J.↗

NASA NTRS1975

The inclusion problem with a crack crossing the boundary

A solution is given to the problems of a crack in an elastic inclusion with one or both ends approaching and terminating at the interface, of two collinear cracks (one in the inclusion and one in the matrix), and of a crack crossing the interface. The problems are formulated in terms of a system of singular integral equations. In the second case, the dominant parts of the kernels become generalized Cauchy kernels giving rise to stress singularities of powers other than one over the square root. For this case stress intensity factors are defined and some detailed results are presented for various crack-inclusion geometries and material combinations.

Erdogan, F.↗

NASA NTRS1974

Critical point parameters of helium

Calculations of the critical point parameters of the helium isotopes using integral equation closures for the pair distribution function are reported for two pair potentials.

Bruch, L. W.↗

NASA NTRS1975

A half plane and a strip with an arbitrarily located crack

The paper introduces a technique to deal 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 NTRS1975

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

An infinite stringer which is assumed to be partially bonded to a plate through a layer of adhesive is considered. The stringer is assumed to have 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 will be obtained from the solution of a system of Fredholm integral equations which represent the continuity of displacements along the line of bond.

Arin, K.↗

NASA NTRS1975

Transverse cracks in a strip with reinforced surfaces

The symmetrical problem of two transverse cracks in an elastic strip with reinforced surfaces is formulated in terms of a singular integral equation. The special cases of one central crack or two edge cracks are discussed. Numerical methods for solving the problems with internal cracks are outlined and stress intensity factors are presented for various geometries and degrees of surface reinforcement.

Krenk, S.↗

NASA NTRS1975

Elliptical cutouts in cylindrical shells

The stress concentrations due to an elliptical cutout in a shallow cylindrical shell are determined by means of a system of singular integral equations, solved numerically. Three loading conditions are considered: tension, and internal pressure. Results confirm those obtained by previous authors by other methods and extend the range of parameters over which results are available.

Tsai, C.-J.↗

NASA NTRS1975

Steady subsonic flow around finite-thickness wings

The general method for analyzing steady subsonic potential aerodynamic flow around a lifting body having arbitrary shape is presented. By using the Green function method, an integral representation for the potential is obtained. Under small perturbation assumption, the potential at any point, P, in the field depends only upon the values of the potential and its normal derivative on the surface of the body. Hence if the point P approaches the surface of the body, the representation reduces to an integral equation relating the potential and its normal derivative (which is known from the boundary conditions) on the surface. The question of uniqueness is examined and it is shown that, for thin wings, the operator becomes singular as the thickness approaches zero. This fact may yield numerical problems for very thin wings. However, numerical results obtained for a rectangular wing in subsonic flow show that these problems do not appear even for thickness ratio tau = .001. Comparison with existing results shows that the proposed method is at least as fast and accurate as the lifting surface theories.

Kuo, C. C.↗

NASA NTRS1975

A cracked sheet stiffened by several partially debonded intact or broken stringers

The effect of several stringers on the stress intensity factors at the tips of a crack is considered. The stringers which were continuously attached to the plate and placed perpendicular to the crack may be partially debonded due to high stress concentrations. Since the stringers may even break under excessive loading conditions, both intact and broken stringers are considered to investigate the effect of rupture. The continuity of displacements along the bond lines leads to an integral equation which is solved to give the shear stress distribution in the adhesive and the stress intensity factors at the crack tips.

Arin, K.↗

NASA NTRS1975

Fully unsteady subsonic and supersonic potential aerodynamics for complex aircraft configurations with applications to flutter

A general formulation is presented for the analysis of steady and unsteady, subsonic and supersonic aerodynamics for complex aircraft configurations. The theoretical formulation, the numerical procedure, the description of the program SOUSSA (steady, oscillatory and unsteady, subsonic and supersonic aerodynamics) and numerical results are included. In particular, generalized forces for fully unsteady (complex frequency) aerodynamics for a wing-body configuration, AGARD wing-tail interference in both subsonic and supersonic flows as well as flutter analysis results are included. The theoretical formulation is based upon an integral equation, which includes completely arbitrary motion. Steady and oscillatory aerodynamic flows are considered. Here small-amplitude, fully transient response in the time domain is considered. This yields the aerodynamic transfer function (Laplace transform of the fully unsteady operator) for frequency domain analysis. This is particularly convenient for the linear systems analysis of the whole aircraft.

Tseng, K.↗

NASA NTRS1975

A finite element analysis of the exact nonlinear formulation of a lifting surface in steady incompressible flow, with the evaluation of the correct wake geometry

The problem of steady incompressible flow for lifting surfaces is considered. An integral equation is solved relating the values 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 and the wake are divided into small quadrilateral surface elements. The values of the potential discontinuity and the normal derivative of the potential are assumed to be constant within each lifting surface element and equal to their values at the centroids of the lifting surface elements. This yields a set of linear algebraic equations. An iteration procedure is used to obtain the wake geometry: the velocities at the corner points of the wake elements are calculated and the wake streamlines are aligned to be parallel to the velocity vector. The procedure is repeated until convergence is attained.

Suciu, E. O.↗

NASA NTRS1976

Investigations of electromagnetic scattering by columnar ice crystals

An integral equation approach was developed to determine the scattering and absorption of electromagnetic radiation by thin walled cylinders of arbitrary cross-section and refractive index. Based on this method, extensive numerical data was presented at infrared wavelengths for hollow hexagonal cross section cylinders which simulate columnar sheath ice crystals.

Weil, H.↗

NASA NTRS1976

Steady incompressible variable thickness shear layer aerodynamics

A shear flow aerodynamic theory for steady incompressible flows is presented for both the lifting and non lifting problems. The slow variation of the boundary layer thickness is considered. The slowly varying behavior is treated by using multitime scales. The analysis begins with the elementary wavy wall problem and, through Fourier superpositions over the wave number space, the shear flow equivalents to the aerodynamic transfer functions of classical potential flow are obtained. The aerodynamic transfer functions provide integral equations which relate the wall pressure and the upwash. Computational results are presented for the pressure distribution, the lift coefficient, and the center of pressure travel along a two dimensional flat plate in a shear flow. The aerodynamic load is decreased by the shear layer, compared to the potential flow. The variable thickness shear layer decreases it less than the uniform thickness shear layer based upon equal maximum shear layer thicknesses.

Chi, M. R.↗

NASA NTRS1976

The stress distribution in tempered glass due to a crack

A model describing the failure in tempered glass is proposed and a method of solution is presented. An infinite elastic strip is assumed to represent the glass and the loads vanish everywhere on the boundary as well as at infinity. The problem is solved using the integral equations technique where the input is the residual stresses in the glass.

Arin, K.↗