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At least 757 records · Page 42
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NASA NTRS1986

The crack-inclusion interaction problem

The general plane elastostatic problem of interaction between a crack and an inclusion is considered. The Green's functions for a pair of dislocations and a pair of concentrated body forces are used to generate the crack and the inclusion. Integral equations are obtained for a line crack and an elastic line inclusion having an arbitrary relative orientation and size. The nature of stress singularity around the end points of rigid and elastic inclusions is described and three special cases of this intersection problem are studied. The problem is solved for an arbitrary uniform stress state away from the crack-inclusion region. The nonintersecting crack-inclusion problem is considered for various relative size, orientation, and stiffness parameters, and the stress intensity factors at the ends of the inclusion and the crack are calculated. For the crack-inclusion intersection case, special stress intensity factors are defined and are calculated for various values of the parameters defining the relative size and orientation of the crack and the inclusion and the stiffness of the inclusion.

Liu, X.-H.↗
NASA NTRS1986

Sensitivity analysis of discrete structural systems

Methods for calculating sensitivity derivatives for discrete structural systems are surveyed, primarily covering literature published during the past two decades. Methods are described for calculating derivatives of static displacements and stresses, eigenvalues and eigenvectors, transient structural response, and derivatives of optimum structural designs with respect to problem parameters. The survey is focused on publications developed in nonstructural fields such as electronics, controls, and physical chemistry which are directly applicable to structural problems. Most notable among the nonstructural-based methods are the adjoint variable technique from control theory, and the Green's function and FAST methods from physical chemistry.

Adelman, H. M.↗
NASA NTRS1986

Use of speckle for determining the response characteristics of Doppler imaging radars

An optical model is developed for imaging optical radars such as the SAR on Seasat and the Shuttle Imaging Radar (SIR-B) by analyzing the Doppler shift of individual speckles in the image. The signal received at the spacecraft is treated in terms of a Fresnel-Kirchhoff integration over all backscattered radiation within a Huygen aperture at the earth. Account is taken of the movement of the spacecraft along the orbital path between emission and reception. The individual points are described by integration of the point source amplitude with a Green's function scattering kernel. Doppler data at each point furnishes the coordinates for visual representations. A Rayleigh-Poisson model of the surface scattering characteristics is used with Monte Carlo methods to generate simulations of Doppler radar speckle that compare well with Seasat SAR data SIR-B data.

Tilley, D. G.↗
NASA NTRS1984

Structural sensitivity analysis: Methods, applications, and needs

Some innovative techniques applicable to sensitivity analysis of discretized structural systems are reviewed. These techniques include a finite-difference step-size selection algorithm, a method for derivatives of iterative solutions, a Green's function technique for derivatives of transient response, a simultaneous calculation of temperatures and their derivatives, derivatives with respect to shape, and derivatives of optimum designs with respect to problem parameters. Computerized implementations of sensitivity analysis and applications of sensitivity derivatives are also discussed. Finally, some of the critical needs in the structural sensitivity area are indicated along with Langley plans for dealing with some of these needs.

Adelman, H. M.↗
NASA NTRS1987

Origin and evolution of osmoregulatory mechanisms in blue-green algae (cyanobacteria) as a function of metabolic and structural complexity: Reflections of Precambrian paleobiology

Major accomplishments underlying the basic understanding of cyanobacterial resistance to salt tolerance and osmotic stress were made. The methodology proposed included: the tracing of the pathways of formation of osmoregulatory solutes by traditional methods involving C-14 labelled substrates; gas chromatography; amino acid analysis; X-ray analysis using scanning transmission electron microscopy; and most importantly, C-13 labelled substrates, followed by Nuclear Magnetic Resonance (NMR) spectroscopy. It was found that the cyanobacteria employ a diversity of organic, osmoregulatory solutes. Osmoregulatory solutes were found to serve four functions: adjustment of water activity, noninhibition of enzymes; lowering of K sub m of enzymes to allow functioning at normal levels when the intracellular salt accumulates, and extending the pH optimum of enzymes as intracellular pH rises due to proton-potassium ion pump action during osmoregulation. Differences in osmoregulatory solutes may, but are not always, be attributed to differences in nutritional capabilities. The mechanism of osmoregulation and concomitant salt tolerance in halophilic cyanobacteria was elucidated. The activities of betaine and S-Adenosylhomocysteine hydrolase are discussed.

Yopp, John H.↗
NASA NTRS1986

Radiation pattern analysis of the tapered slot antenna, appendix 1

A theoretical model for the tapered slot antenna is presented. The model is valid for any smooth taper of the slot. The problem is solved by modeling the slot electric field and using the half plane Green's function to compute the far fields. The aperture field is obtained by affecting a stepped approximation to the continuous taper and utilizing the uniform wide slot line data. The uniform wide slot line is solved by the spectral Galerkin's technique and closed form experssions are developed for the slot wave length and the slot characteristic impedance. Numerous comparisons with measurement are made to demonstrate the versatility of the model in treating an arbitrary slot taper.

Janaswamy, Ramakrishna↗
NASA NTRS1986

Nonlinear adhesive behavior effects in a cracked orthotropic sheet stiffened by a semi-infinite orthotropic sheet

The stress-intensity factors are determined for a cracked orthotropic sheet adhesively bonded to an orthotropic stringer where the adhesive layer is modeled with a nonlinear stress-strain curve. By the use of Green's functions and the complex variable theory of orthotropic elasticity, a set of integral equations is obtained. The integral equations are replaced by an equivalent set of algebraic equations, which are solved to obtain the shear stress distribution in the adhesive layer, with which the crack-tip stress-intensity factors are found. When the adhesive was modeled with a nonlinear stress-strain curve, the peak shear stresses in the adhesive were considerably reduced in comparison to the solution for the linear elastic adhesive. This resulted in increases in the stress-intensity factors for the nonlinear adhesive solution compared to the linear adhesive solution. The nonlinear adhesive has no significant effect on the stress-intensity factor unless the near crack tip is beneath the stringer. It is assumed that the adhesive bond remains intact and it is predicted that onset of adhesive failure occurs at decreasing levels of applied stress as the crack propagates beneath the stringer.

Bigelow, C. A.↗
NASA NTRS1986

A mechanism for tectonic deformation on Venus

In the absence of identifiable physiographic features directly associated with plate tectonics, alternate mechanisms are sought for the intense tectonic deformation observed in radar images of Venus. One possible mechanism is direct coupling into an elastic lithosphere of the stresses associated with convective flow in the interior. Spectral Green's function solutions have been obtained for stresses in an elastic lithosphere overlying a Newtonian interior with an exponential depth dependence of viscosity, and a specified surface-density distribution driving the flow. At long wavelengths and for a rigid elastic/fluid boundary condition, horizontal normal stresses in the elastic lid are controlled by the vertical shear stress gradient and are directly proportional to the depth of the density disturbance in the underlying fluid. The depth and strength of density anomalies in the Venusian interior inferred by analyses of long wavelength gravity data suggest that stresses in excess of 100 MPa would be generated in a 10 km thick elastic lid unless a low viscosity channel occurring beneath the lid or a positive viscosity gradient uncouples the flow stresses. The great apparent depth of compensation of topographic features argues against this, however, thus supporting the importance of the coupling mechanism. If there is no elastic lid, stresses will also be very high near the surface, providing also that the viscosity gradient is negative.

Phillips, Roger J.↗
NASA NTRS1987

An Euler code calculation of blade-vortex interaction noise

An Euler code has been developed for calculation of noise radiation due to the interaction of a distributed vortex with a Joukowski airfoil. THe time-dependent incompressible flow field is first determined and then integrated to yield the resulting sound production through use of the elegant low-frequency Green's function approach. This code has several interesting numerical features involved in the vortex motion and in continuous satisfaction of the Kutta condition. In addition, it removes the limitations on Reynolds number and is much more efficient than an earlier Navier-Stokes code. Results indicate that the noise production is due to the deceleration and subsequent acceleration of the vortex as it approaches and passes the airfoil. Predicted acoustic levels and frequencies agree with measured data although a precise comparison would require the strength, size, and position of the incoming vortex to be known.

Hardin, J. C.↗
NASA NTRS1987

Displacements of the earth's surface due to atmospheric loading - Effects of gravity and baseline measurements

Atmospheric mass loads and deforms the earth's crust. By performing a convolution sum between daily, global barometric pressure data and mass loading Green's functions, the time dependent effects of atmospheric loading, including those associated with short-term synoptic storms, on surface point positioning measurements and surface gravity observations are estimated. The response for both an oceanless earth and an earth with an inverted barometer ocean is calculated. Load responses for near-coastal stations are significantly affected by the inclusion of an inverted barometer ocean. Peak-to-peak vertical displacements are frequently 15-20 mm with accompanying gravity perturbations of 3-6 micro Gal. Baseline changes can be as large as 20 mm or more. The perturbations are largest at higher latitudes and during winter months. These amplitudes are consistent with the results of Rabbel and Zschau (1985), who modeled synoptic pressure disturbances as Gaussian functions of radius around a central point. Deformation can be adequately computed using real pressure data from points within about 1000 km of the station. Knowledge of local pressure, alone, is not sufficient. Rabbel and Zschau's hypothesized corrections for these displacements, which use local pressure and the regionally averaged pressure, prove accurate at points well inland but are, in general, inadequate within a few hundred kilometers of the coast.

Van Dam, T. M.↗
NASA NTRS1987

Effective propagation constants in dense random media under effective medium approximation

The effective medium approximation is applied to study the effective propagation constants in a dense random medium. The dyadic Green's function is introduced to establish the effective medium approximation formalism for electromagnetic waves. The multiple scattering equations and the Lippmann-Schwinger equations for the transition operator are obtained in the configuration average form. The dispersion equations of multiple scattering is derived by using a standard method in quantum mechanics. To obtain an expression for the effective propagation constants the matrix elements of the configuration average dyadic transiton operator are calculated in momentum representation. Numerical illustations are carried out to demonstrate the difference in the effective propagation constants between the use of this approximation and the well-known quasi-crystalline approximation. A comparison is made with measured loss tangent in dry snow.

Zhu, P. Y.↗
NASA NTRS1987

Dynamic topography and gravity anomalies for fluid layers whose viscosity varies exponentially with depth

Adopting the formalism of Parsons and Daly (1983), analytical integral equations (Green's function integrals) are derived which relate gravity anomalies and dynamic boundary topography with temperature as a function of wavenumber for a fluid layer whose viscosity varies exponentially with depth. In the earth, such a viscosity profile may be found in the asthenosphere, where the large thermal gradient leads to exponential decrease of viscosity with depth, the effects of a pressure increase being small in comparison. It is shown that, when viscosity varies rapidly, topography kernels for both the surface and bottom boundaries (and hence the gravity kernel) are strongly affected at all wavelengths.

Revenaugh, Justin↗
NASA NTRS1987

Ring vortex/cylinder sound production revisited

The acoustic radiation produced by the passage of a vortex ring near a circular cylinder is calculated utilizing the Coriolis acceleration of the vortex as the source term and the low frequency Green's function approach. Necessary integrals are evaluated exactly via complex integration techniques. The results exhibit good agreement (on a Pascal basis) with experimental data. Of particular interest is the rotation of the directivity pattern during this transient encounter and the extreme sensitivity of the results to the distance at which the vortex passes by the cylinder.

Hardin, Jay C.↗
NASA NTRS1987

Analysis of the tapered slot antenna

A method for calculating the radiation pattern of end-fire tapered slot antennas with or without dielectric substrate is presented. The method involves a two-step procedure: (1) determine the field distribution of a traveling wave along the tapered slot, and (2) compute the radiation from this slot field by using the half-plane Green's function to account for termination effects. Acceptable estimates of the slot field usually can be obtained from a stepped approximation to the tapered geometry. The method has been verified by comparisons to measured patterns for various dielectric substrates and antenna dimensions. However, the effect of lateral truncation has not yet been successfully modeled. Experimental patterns showing this effect are presented.

Janaswamy, Ramakrishna↗
NASA NTRS1988

Mode-medium instability in an unstable resonator

The mode-medium instability of an active medium in an unstable resonator is investigated. The asymptotic solution due to Horwitz (1973), valid for large Fresnel numbers in an empty cavity, is modified by introducing gain/phase sheets in front of the resonator mirrors. The effect of medium coupling to the mode in the cavity is obtained by introducing a general time-independent Green's function in the Fox-Li (1961) formulation. The time evolution is then obtained by repeated integration of the beam propagation in the cavity. The diffractive terms are shown to grow rapidly at the expense of the geometric term. This instability responsible for the deterioration of the beam quality is studied numerically for a CO2 lasing system as an example.

Sung, C. C.↗
NASA NTRS1988

A nonlinear analysis of an equilibrium craze. I - Problem formulation and solution. II - Simulations of craze and crack growth

A numerical method is developed for the determinations of the equilibrium shape of a craze in an infinite elastic plane whose fibrils exhibit very general nonlinear force-displacement behavior. The problem formulation is based on the superposition of the relevant elasticity Green's function; the solution of the resulting nonlinear problem is obtained by using Picard's successive approximation scheme. The model is used to investigate the effect of nonlinear fibril behavior on the mechanics of craze and crack growth, and the results are compared with the Dugdale model.

Ungsuwarungsri, T.↗
NASA NTRS1989

On the structure of pressure fluctuations in simulated turbulent channel flow

Pressure fluctuations in a turbulent channel flow are investigated by analyzing a database obtained from a direct numerical simulation. Detailed statistics associated with the pressure fluctuations are presented. Characteristics associated with the rapid (linear) and slow (nonlinear) pressure are discussed. It is found that the slow pressure fluctuations are larger than the rapid pressure fluctuations throughout the channel except very near the wall, where they are about the same magnitude. This is contrary to the common belief that the nonlinear source terms are negligible compared to the linear source terms. Probability density distributions, power spectra, and two-point correlations are examined to reveal the characteristics of the pressure fluctuations. The global dependence of the pressure fluctuations and pressure-strain correlations are also examined by evaluating the integral associated with Green's function representations of them. In the wall region where the pressure-strain terms are large, most contributions to the pressure-strain terms are from the wall region (i.e., local), whereas away from the wall where the pressure-strain terms are small, contributions are global. Structures of instantaneous pressure and pressure gradients at the wall and the corresponding vorticity field are examined.

Kim, John↗
NASA NTRS1989

Nonlinear mesomechanics of composites with periodic microstructure

This work is concerned with modeling the mechanical deformation or constitutive behavior of composites comprised of a periodic microstructure under small displacement conditions at elevated temperature. A mesomechanics approach is adopted which relates the microimechanical behavior of the heterogeneous composite with its in-service macroscopic behavior. Two different methods, one based on a Fourier series approach and the other on a Green's function approach, are used in modeling the micromechanical behavior of the composite material. Although the constitutive formulations are based on a micromechanical approach, it should be stressed that the resulting equations are volume averaged to produce overall effective constitutive relations which relate the bulk, volume averaged, stress increment to the bulk, volume averaged, strain increment. As such, they are macromodels which can be used directly in nonlinear finite element programs such as MARC, ANSYS and ABAQUS or in boundary element programs such as BEST3D. In developing the volume averaged or efective macromodels from the micromechanical models, both approaches will require the evaluation of volume integrals containing the spatially varying strain distributions throughout the composite material. By assuming that the strain distributions are spatially constant within each constituent phase-or within a given subvolume within each constituent phase-of the composite material, the volume integrals can be obtained in closed form. This simplified micromodel can then be volume averaged to obtain an effective macromodel suitable for use in the MARC, ANSYS and ABAQUS nonlinear finite element programs via user constitutive subroutines such as HYPELA and CMUSER. This effective macromodel can be used in a nonlinear finite element structural analysis to obtain the strain-temperature history at those points in the structure where thermomechanical cracking and damage are expected to occur, the so called damage critical points of the structure.

Walker, Kevin P.↗