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NASA NTRS1985

Interaction between a crack and a soft inclusion

With the application to weld defects in mind, the interaction problem between a planar-crack and a flat inclusion in an elastic solid is considered. The elastic inclusion is assumed to be sufficiently thin so that the thickness distribution of the stresses in the inclusion may be neglected. The problem is reduced to a system of four integral equations having Cauchy-type dominant kernels. The stress intensity factors are calculated and tabulated for various crack-inclusion geometries and the inclusion to matrix modulus ratios, and for general homogeneous loadiong conditions away from the crack-inclusion region.

Xue-Hui, L.↗

NASA NTRS1985

Exploratory flutter test in a cryogenic wind tunnel

A model consisting of a rigid wing with an integral, flexible beam support that was cantilever mounted from the wall in the NASA LaRC 0.3-m transonic cryogenic tunnel was used in a flutter analysis study. The wing had a rectangular planform of aspect ratio 1.5 and a 64A010 airfoil. Various considerations and procedures for conducting flutter tests in a cryogenic wind tunnel were evaluated. Flutter onset conditions were established from extrapolated subcritical response measurements. A flutter boundary was determined at cryogenic temperatures over a Mach number M range from 0.5 to 0.9. Flutter was obtained at two different Reynolds numbers R at M = 0.5 (R = 4.4 and 18.4 x 10 to the 6th power) and at M = 0.8 (R = 5.0 and 10.4 x 10 to the 6th power). Flutter analyses using subsonic lifting surface (kernel function) aerodynamics were made over the range of test conditions. To evaluate the Reynolds number effects at M = 0.5 and 0.8, the experimental results were adjusted using analytical trends to account for differences in the model test temperatures and mass ratios. The adjusted experimental results indicate that increasing Reynolds number from 5.0 to 20.0 x 10 to the 6th power decreased the dynamic pressure by 4.0 to 6.5 percent at M = 0.5 and 0.8.

Cole, S. R.↗

NASA NTRS1985

Recovering pointwise values of discontinuous data within spectral accuracy

The pointwise values of a function, f(x), can be accurately recovered either from its spectral or pseudospectral approximations, so that the accuracy solely depends on the local smoothness of f in the neighborhood of the point x. Most notably, given the equidistant function grid values, its intermediate point values are recovered within spectral accuracy, despite the possible presence of discontinuities scattered in the domain. (Recall that the usual spectral convergence rate decelerates otherwise to first order, throughout). To this end, a highly oscillatory smoothing kernel is employed in contrast to the more standard positive unit-mass mollifiers. In particular, post-processing of a stable Fourier method applied to hyperbolic equations with discontinuous data, recovers the exact solution modulo a spectrally small error. Numerical examples are presented.

Gottlieb, D.↗

NASA NTRS1985

Elasticity Solution of an Adhesively Bonded Cover Plate of Various Geometries

The plane strain of adhesively bonded structures consisting of two different isotropic adherends is considered. By expressing the x-y components of the displacements in terms of Fourier integrals and using the corresponding boundary and continuity conditions, the integral equations for the general problem are obtained and solved numerically by applying Gauss-Chebyshev integration scheme. The shear and the normal stresses in the adhesive are calculated for various geometries and material properties for a stiffened plate under uniaxial tension. Numerical results involving the stress intensity factors and the strain energy release rate are presented. The closed-form expressions for the Fredholm kernels are provided to obtain the solution for an arbitrary geometry and material properties. For the general geometry, the contribution of the normal stress is quite significant, while for symmetric geometries, the shear stress is dominant, the normal stress vanishes if the adherends are of the same material and the same thickness.

Aksel, G. N.↗

NASA NTRS1985

A new taxonomy for distributed computer systems based upon operating system structure

Characteristics of the resource structure found in the operating system are considered as a mechanism for classifying distributed computer systems. Since the operating system resources, themselves, are too diversified to provide a consistent classification, the structure upon which resources are built and shared are examined. The location and control character of this indivisibility provides the taxonomy for separating uniprocessors, computer networks, network computers (fully distributed processing systems or decentralized computers) and algorithm and/or data control multiprocessors. The taxonomy is important because it divides machines into a classification that is relevant or important to the client and not the hardware architect. It also defines the character of the kernel O/S structure needed for future computer systems. What constitutes an operating system for a fully distributed processor is discussed in detail.

Foudriat, E. C.↗

NASA NTRS1984

Analysis of the magnetic field configuration of a filament-associated flare from X-ray, UV, and optical observations

X-ray and ultraviolet observations from SMM of a filament-associated event on November 22, 1980 are examined in conjunction with ground-based optical observations, in order to determine the magnetic field configuration involved in the flaring process. Evidence that the flare was produced by gradual energy release in a large sheared magnetic loop which interacted with another smaller loop is found. Nonthermal processes, as indicated by hard X-ray emission and impulsive UV kernels, were produced in the interaction of the two loops. Although this flare shared some of the characteristics of Long Duration (class II) Events, no indication of a helmet-type configuration, as generally envisaged for class II events, was found. On the contrary, the magnetic configuration of the November 22, 1980 event was more similar to that of a compact (class I) flare, although on a much larger spatial scale and longer time scale.

Cheng, C.-C.↗

NASA NTRS1985

A pressurized cylindrical shell with a fixed end which contains an axial part-through or through crack

In this paper a cylindrical shell having a very stiff end plate or a flange is considered. It is assumed that near the end the cylinder contains an axial flow which may be modeled as a part-through surface crack or through crack. The primary objective is to study the effect of the end constraining on the stress intensity factor which is the main fracture mechanics parameter. The applied loads acting on the cylinder are assumed to be axisymmetric. Thus the crack problem under consideration is symmetric with respect to the plane of the crack and consequently only the mode I stress intensity factors are nonzero. With this limitation, the general perturbation problem for a cylinder with a built-in end containing an axial crack is considered. Reissner's shell theory is used to formulate the problem. The part-through crack problem is treated by using a line-spring model. In the case of a crack tip terminating at the fixed end it is shown that the integral equation of the shell problem has the same generalized Cauchy kernel as the corresponding plane stress elasticity problem. Even though the problem is formulated for a general surface crack profile and arbitrary crack surface tractions, the numerical results are obtained only for a semielliptic part-through axial crack located at the inside or outside surface of the cylinder and for internal pressure acting on the cylinder. The stress intensity factors are calculated and presented for a relatively wide range of dimensionless length parameters of the problem.

Yahsi, O. S.↗

NASA NTRS1985

Stability, accuracy, and efficiency of some underintegrated methods in finite element computations

In an attempt to increase computational efficiency in the numerical solution of highly nonlinear problems in solid and fluid mechanics, underintegrated finite element methods have been employed by many analysts. Underintegration refers to the use of a rule of an order lower than that required to integrate polynomial integrands exactly. The main drawback of this technique is related to the production of rank-deficient stiffness matrices, or equivalently an expanded kernel of the governing linear momentum operators. Such a development can introduce numerical instabilities. In order to overcome this difficulty, artificial stiffness or viscosity methods, or other stabilization methods have been proposed. One approach involves the elimination of spurious modes in a postprocessing operation. The present study is concerned with this a posteriori elimination method, taking into account the results which can be expected from it, and some of its possible extensions.

Jacquotte, O.-P.↗

NASA NTRS1986

Divergence study of a high-aspect ratio, forward-swept wing

An experimental wind-tunnel study to determine the divergence characteristics of a high-aspect ratio, forward-swept wing has been conducted in the NASA Langley Research Center (LaRC) Transonic Dynamics Tunnel (TDT). The rectangular wing used for this study had a panel aspect ratio of 9.16 (lambda = 0 deg.) and the sweep angle could be set at lambda = 0 deg., -15 deg., -30 deg., -45 deg., or -60 deg. A rectangular wing tip shape was tested at each of these sweep angles. In addition, a tip shape parallel to the freestream flow was tested for a wing sweep angle of lambda = -45 deg. The root of the wing was cantilever mounted to the wall of the wind tunnel. Divergence conditions were measured at M = 0.4 for each sweep angle and tip configuration tested. Subcritical response techniques were used to extrapolate to the divergence conditions during the wind-tunnel test. The primary objective of this test was to obtain data which could be used to verify for this configuration the divergence prediction capability of an aeroelastic analysis code. Subsonic lifting surface theory (kernel function) aerodynamics are utilized by this particular code. The analytical predictions of divergence were found to be significantly conservative at all forward sweep angles. At lambda = -45 deg., the analysis was 14 percent conservative. The effect of the two tip shapes on the divergence dynamic pressure was predicted accurately by the analysis. The divergence condition for the tip shape parallel to the flow occurred at a dynamic pressure 14 percent higher than the divergence condition with a rectangular tip shape.

Cole, S. R.↗

NASA NTRS1986

Algorithms versus architectures for computational chemistry

The algorithms employed are computationally intensive and, as a result, increased performance (both algorithmic and architectural) is required to improve accuracy and to treat larger molecular systems. Several benchmark quantum chemistry codes are examined on a variety of architectures. While these codes are only a small portion of a typical quantum chemistry library, they illustrate many of the computationally intensive kernels and data manipulation requirements of some applications. Furthermore, understanding the performance of the existing algorithm on present and proposed supercomputers serves as a guide for future programs and algorithm development. The algorithms investigated are: (1) a sparse symmetric matrix vector product; (2) a four index integral transformation; and (3) the calculation of diatomic two electron Slater integrals. The vectorization strategies are examined for these algorithms for both the Cyber 205 and Cray XMP. In addition, multiprocessor implementations of the algorithms are looked at on the Cray XMP and on the MIT static data flow machine proposed by DENNIS.

Partridge, H.↗

NASA NTRS1986

Approximating linearizations for nonlinear systems

The following problem is examined: given a nonlinear control system dot-x(t) = f(x(t)) + the sum to m terms(i=1) u sub i (t)g sub i (x(t)) on R(n) and a point x(0) in R(n), approximate the system near x(0) by a linear system. One approach is to use the usual Taylor series linearization. However, the controllability properties of both the nonlinear and linear systems depend on certain Lie brackets of the vector field under consideration. This suggests that a linear approximation based on Lie bracket matching should be constructed at x(0). In general, the linearizations based on the Taylor method and the Lie bracket approach are different. However, under certain mild assumptions, it is shown that there is a coordinate system for R(n) near x(0) in which these two types of linearizations agree. The importance of this agreement is indicated by examining the time responses of the nonlinear system and its linear approximation and comparing the lower order kernels in Volterra expansions of each.

Hunt, L. R.↗

NASA NTRS1986

On the solution of integral equations with a generalized cauchy kernal

A certain class of singular integral equations that may arise from the mixed boundary value problems in nonhonogeneous materials is considered. The distinguishing feature of these equations is that in addition to the Cauchy singularity, the kernels contain terms that are singular only at the end points. In the form of the singular integral equations adopted, the density function is a potential or a displacement and consequently the kernal has strong singularities of the form (t-x)(-2), x(n-2) (t+x)(n), (n is = or 2, 0 x, t b). The complex function theory is used to determine the fundamental function of the problem for the general case and a simple numerical technique is described to solve the integral equation. Two examples from the theory of elasticity are then considered to show the application of the technique.

Kaya, A. C.↗

NASA NTRS1986

Compliance matrices for cracked bodies

An algorithm is presented which can be used to develop compliance matrices for cracked bodies. The method relies on the numerical solution of singular integral equations with Cauchy-type kernels and provides an efficient and accurate procedure for relating applied loadings to crack opening displacements. The algorithm should be of interest to those performing repetitive calculations in the analysis of experimental results obtained from fracture specimens.

Ballarini, R.↗

NASA NTRS1985

Coronal X-ray activity preceding solar flares

The characteristics of coronal emplacements preceding solar flares were investigated based on a comprehensive survey of Skylab soft X-ray images. A search interval of 30 min before flare was used in the X-ray observations. X-ray images with preflare enhancements were compared with high resolution H-alpha images and photospheric magnetograms and preflare enhancements were found in a statistically significant number of the observed preflare intervals. The enhancement events consisted of loops, kernels, and sinuous features with one to three separate preflare structures appearing in each interval. Typical gas pressures in the preflare X-ray features were estimated on the order of a few dyne per sq cm and densities were 4-10 x 10 to the -9th per cu cm for assumed average temperatures. H-alpha brightenings in the form of knots and patches were found in conjunction with the X-ray preflare features in nearly all of the intervals. It is concluded that H-alpha emission is characteristic of preflare emission processes. The observational data are interpreted within the framework of existing loop preheating models, and the results are discussed in detail.

Webb, D. F.↗

NASA NTRS1986

Divergence study of a high-aspect ratio, forward-swept wing

A study has been conducted in the NASA-Langley Transonic Dynamics wind tunnel to determine the divergence characteristics of a high aspect ratio forward swept wing of rectangular planform, for sweep angles of zero, -15, -30, -45, and -60 deg. In addition to a rectangular wingtip, a tip whose geometry lay parallel with the freestream flow was tested at a sweep angle of -45 deg. The primary objective was to obtain data that could be used to verify the divergence prediction capabilities of an aeroelastic analysis code employing kernel function aerodynamics. The analytical predictions of convergence were found to be conservative for all forward sweep angles, and the effect of the two tip shapes on divergence dynamic pressure were accurately predicted.

Cole, S. R.↗

NASA NTRS1985

He II emission from solar flares

The first monochromatic images of a solar flare in the 4686-angstrom line of He II are presented. The observations were obtained in the intense (X10) flare 1984 May 20. The emission comes from footprint kernels with peak intensity 3.3 times the photosphere, or 0.9 times after subtraction of photospheric background and continuum. This value is about twice that recorded by spectroscopic observers and far exceeds most published data for the intensity of the resonance line at 304 angstroms and the Balmer alpha line of He II at 1640 angstroms. The intensities of the He II lines were calculated for a range of temperature and electron density, using a six-level atom with enhanced XUV incoming flux.

Zirin, H.↗

NASA NTRS1985

The great flare of 1982 June 6

The great soft X-ray (SXR) flare (X12) of the past solar maximum was observed by Hinotori and by Big Bear Solar Observatory (BBSO) on June 6, 1982. Hinotori data consist of hard X-ray (HXR) and SXR images in the rise and decay of the flare, high-resolution soft X-ray spectra throughout the flare, and HXR and gamma-ray data. The BBSO data include films of H-alpha, H-alpha blue wing, D3 and longitudinal magnetic field, as well as video tapes of continuum. Images in HXR, SXR, H-alpha, D3 and the continuum are compared and SXR spectra analyzed. The flare resulted from extended motion of a large spot shearing the magnetic field. D3 and white-light images exhibit a progression from fast flashes to two ribbons, while both HXR and SXR are centered on the optical kernels. The continuum emission shows the same temporal behavior as the HXR at 160 keV. In its early phases, the Fe XXV line was double-peaked, and a decreasing blueshifted (up to 400 km/sec) component was observed, from which the evaporation rate of chromospheric material was estimated. It is suggested that this upflow is adequate to supply the coronal cloud. Flare energetics are discussed in detail, and it is concluded that a significant amount of energy was deposited in the corona, and that nonthermal electrons are the major energy input.

Tanaka, K.↗

NASA NTRS1985

A new approach to approximating the linear quadratic optimal control law for hereditary systems with control delays

A factorization approach is presented for deriving approximations to the optimal feedback gain for the linear regulator-quadratic cost problem associated with time-varying functional differential equations with control delays. The approach is based on a discretization of the state penalty which leads to a simple structure for the feedback control law. General properties of the Volterra factors of Hilbert-Schmidt operators are then used to obtain convergence results for the feedback kernels.

Milman, M. H.↗