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NASA NTRS1987

On computing eigensolution sensitivity data using free vibration solutions

A simplified method of computing eigensolution sensitivity derivatives in structural dynamics is developed. It is shown that if the elements of stiffness and mass matrices associated with a design variable are homogeneous functions of that design variable, then eigenvalue derivatives can be computed from element strain and kinetic energies. Furthermore, if cross-mode energies are known, eigensolution derivatives of modified systems can be computed approximately using assume mode reanalysis formulation. A ten bar truss example is used to illustrate the present formulations.

Wang, B. P.↗

NASA NTRS1987

Sensitivity analysis for large-scale problems

The development of efficient techniques for calculating sensitivity derivatives is studied. The objective is to present a computational procedure for calculating sensitivity derivatives as part of performing structural reanalysis for large-scale problems. The scope is limited to framed type structures. Both linear static analysis and free-vibration eigenvalue problems are considered.

Noor, Ahmed K.↗

NASA NTRS1986

Cometary atmospheres: Modeling the spatial distribution of observed neutral radicals

Progress during the second year of a program of research on the modeling of the spatial distributions of cometary radicals is discussed herein in several major areas. New scale length laws for cometary C2 and CN were determined which explain that the previously-held apparent drop of the C2/CN ratio for large heliocentric distances does not exist and that there is no systematic variation. Monte Carlo particle trajectory model (MCPTM) analysis of sunward and anti-sunward brightness profiles of cometary C2 was completed. This analysis implies a lifetime of 31,000 seconds for the C2 parent and an ejection speed for C2 of approximately 0.5 km/sec upon dissociation from the parent. A systematic reanalysis of published C3 and OH data was begun. Preliminary results find a heliocentric distance dependence for C3 scale lengths with a much larger variation than for C2 and CN. Scale lengths for OH are generally somewhat larger than currently accepted values. The MCPTM was updated to include the coma temperature. Finally, the collaborative effort with the University of Arizona programs has yielded some preliminary CCD images of Comet P/Halley.

Combi, Michael R.↗

NASA NTRS1987

The role of plasma wave turbulence in the formation of shock waves in collisionless plasmas

A data set containing measurements for approximately 100 shock crossings was compiled, and plasma wave profiles were plotted in conjunction with magnetic field data. Three emissions analyzed include upstream electron plasma oscillations, ion acoustic noise, and low frequency electromagnetic noise. The data demonstrate that the observed waves are consistent with generation by the kinetic cross-field streaming instability. Reanalysis of shock overshoots prompted by the presence of plasma feet upstream of nominally subcritical shocks leads to the conclusion that no firm evidence exists for a sharp subcritical supercritical transition. Electron plasma oscillations persist up to the ramps of subcritical shocks and begin decaying at the front edge of the feet of supercritical shocks. Their intensity is anticorrelated with the amplitude of the foot ion acoustic noise. Wave measurements support the predicted predominance of lower hybrid-like modes over ion acoustic noise in the production of resistive (plasma) heating. Evidence for variable shock normal angles is seen upstream from nominally quasiparallel shocks. The first cases of very strong electron heating observed at the terrestrial bow shock were discovered.

Mellott, M. M.↗

NASA NTRS1987

Approximations to eigenvalues of modified general matrices

The reanalysis of non-self-adjoint dynamic models is computationally very expensive in design optimization applications. This paper describes several approximations that can be applied to eigenvalues of non-hermitian matrices to reduce that computational cost. Approximations based on eigenvalue derivatives, generalized Rayleigh quotient and the trace theorem are presented and their accuracy and computational cost are estimated. The accuracy and cost estimates are verified by applying the approximations to random matrices and matrices arising in flutter analysis of compressor blades. Recommendations are made for selection of the best approximation when the derivatives are available and when they are not. In particular, it is concluded that the quadratic approximation for eigenvalues should never be used as higher order approximations are always more accurate as well as more efficient.

Murthy, Durbha V.↗

NASA NTRS1987

Reexamination of the SAS 2 Cygnus X-3 data

Recent observations of Cygnus X-3 have shown marked variability of the radiation on short time scales. In particular, the bursts lasting on the order of 10 minutes, seen in both the infrared and very high energy (greater than 10 to the 11th eV) gamma-ray regions, and the time-variations on many scales at high energies, have stimulated a reanalysis of the March 6 to 13, 1973 SAS 2 high-energy gamma-ray data. Although a clear periodicity in the E greater 35 MeV gamma radiation is observed at the 4.79 hr period seen in X-rays, there is no evidence for major variations of the radiation from one day to the next, and no statistically significant evidence for bursts on the 10-minute time scale seen in the infrared or very high energy ranges. If the excess observed had been predominantly in the form of ten minute bursts even at a rate as high as two/day, a clearly significant set of bursts would have been seen.

Fichtel, C. E.↗

NASA NTRS1987

Octree based automatic meshing from CSG models

Finite element meshes derived automatically from solid models through recursive spatial subdivision schemes (octrees) can be made to inherit the hierarchical structure and the spatial addressability intrinsic to the underlying grid. These two properties, together with the geometric regularity that can also be built into the mesh, make octree based meshes ideally suited for efficient analysis and self-adaptive remeshing and reanalysis. The element decomposition of the octal cells that intersect the boundary of the domain is emphasized. The problem, central to octree based meshing, is solved by combining template mapping and element extraction into a procedure that utilizes both constructive solid geometry and boundary respresentation techniques. Boundary cells that are not intersected by the edge of the domain boundary are easily mapped to predefined element topology. Cells containing edges (and vertices) are first transformed into a planar polyhedron and then triangulated via element extractors. The modeling environments required for the derivation of planar polyhedra and for element extraction are analyzed.

Perucchio, Renato↗

NASA NTRS1987

Geometrical and topological issues in octree based automatic meshing

Finite element meshes derived automatically from solid models through recursive spatial subdivision schemes (octrees) can be made to inherit the hierarchical structure and the spatial addressability intrinsic to the underlying grid. These two properties, together with the geometric regularity that can also be built into the mesh, make octree based meshes ideally suited for efficient analysis and self-adaptive remeshing and reanalysis. The element decomposition of the octal cells that intersect the boundary of the domain is discussed. The problem, central to octree based meshing, is solved by combining template mapping and element extraction into a procedure that utilizes both constructive solid geometry and boundary representation techniques. Boundary cells that are not intersected by the edge of the domain boundary are easily mapped to predefined element topology. Cells containing edges (and vertices) are first transformed into a planar polyhedron and then triangulated via element extractor. The modeling environments required for the derivation of planar polyhedra and for element extraction are analyzed.

Saxena, Mukul↗

NASA NTRS1988

Shape sensitivity analysis of flutter response of a laminated wing

A method is presented for calculating the shape sensitivity of a wing aeroelastic response with respect to changes in geometric shape. Yates' modified strip method is used in conjunction with Giles' equivalent plate analysis to predict the flutter speed, frequency, and reduced frequency of the wing. Three methods are used to calculate the sensitivity of the eigenvalue. The first method is purely a finite difference calculation of the eigenvalue derivative directly from the solution of the flutter problem corresponding to the two different values of the shape parameters. The second method uses an analytic expression for the eigenvalue sensitivities of a general complex matrix, where the derivatives of the aerodynamic, mass, and stiffness matrices are computed using a finite difference approximation. The third method also uses an analytic expression for the eigenvalue sensitivities, but the aerodynamic matrix is computed analytically. All three methods are found to be in good agreement with each other. The sensitivities of the eigenvalues were used to predict the flutter speed, frequency, and reduced frequency. These approximations were found to be in good agreement with those obtained using a complete reanalysis.

Bergen, Fred D.↗

NASA NTRS1989

High accuracy thermal conductivity measurements near the lambda transition of helium with very high temperature resolution

Over the past few years extensive thermal conductivity measurements near the lambda point of helium were made. The original goal of measuring the thermal conductivity with a resolution of t = T/T sub lambda -1 of 3 x 10(-8) was reached, but with somewhat less accuracy than was hoped. Subtle effects in the apparatus near the transition were observed which reduced the ability to interpret the results. Nevertheless, for resolution of t is greater than or equal to 10(-7) reliable data was obtained, extending previous measurements by more than an order of magnitude. Deviations from theoretical predictions were observed for t is less than or equal to 3 x 10(-6) leading to the question of the validity of the present renormalization group analysis of transport properties, at least for the case of helium. This anomaly led to closer examination of the boundary effects in the measurements. During the experiments a totally unexpected effect in the very dilute He-3 - He-4 mixtures was observed which led to the explanation of the anomalous results. The concentration dependence of the thermal conductivity near T sub lambda in the superfluid phase was found to deviate strongly from the predictions. The results gave an independent verification of this behavior and caused reanalysis of the Khalatnikov theory of hydrodynamics of the mixtures. An alternative solution was found which is in better agreement with the experiment.

Fairbank, William M.↗

NASA NTRS1989

Iterative methods for design sensitivity analysis

A numerical method is presented for design sensitivity analysis, using an iterative-method reanalysis of the structure generated by a small perturbation in the design variable; a forward-difference scheme is then employed to obtain the approximate sensitivity. Algorithms are developed for displacement and stress sensitivity, as well as for eignevalues and eigenvector sensitivity, and the iterative schemes are modified so that the coefficient matrices are constant and therefore decomposed only once.

Belegundu, A. D.↗

NASA NTRS1989

Design sensitivity analysis of boundary element substructures

The ability to reduce or condense a three-dimensional model exactly, and then iterate on this reduced size model representing the parts of the design that are allowed to change in an optimization loop is discussed. The discussion presents the results obtained from an ongoing research effort to exploit the concept of substructuring within the structural shape optimization context using a Boundary Element Analysis (BEA) formulation. The first part contains a formulation for the exact condensation of portions of the overall boundary element model designated as substructures. The use of reduced boundary element models in shape optimization requires that structural sensitivity analysis can be performed. A reduced sensitivity analysis formulation is then presented that allows for the calculation of structural response sensitivities of both the substructured (reduced) and unsubstructured parts of the model. It is shown that this approach produces significant computational economy in the design sensitivity analysis and reanalysis process by facilitating the block triangular factorization and forward reduction and backward substitution of smaller matrices. The implementatior of this formulation is discussed and timings and accuracies of representative test cases presented.

Kane, James H.↗

NASA NTRS1989

The tropospheric response pattern to solar activity forcing

It is tempting to speculate on the possibility that solar flares sometimes are the initial cause of and atmospheric disturbance, which cumulative effect may give rise to a correlation at the 11 year timescale. Reasons to reconsider the possible relevance of solar flare response studies are stated. The discovery of the apparently decisive role of the Quasi-Biennial Oscillations (QBO) in establishing the atmospheric response pattern to solar forcing may throw new light on some of the earlier published relations. Reanalysis of old data in some cases may be advisable. Data on solar flares and their effects on the earth's atmosphere might be a promising candidate for reexamination.

Schuurmans, C. J. E.↗

NASA NTRS1989

A new partitioning strategy for efficient re-analysis of large structural systems

A computational procedure is presented for the reanalysis of large unsymmetric structural systems. The procedure is based on a novel partitioning strategy in which the responses of both the original and modified structures are approximated by symmetric and antisymmetric response vectors, each obtained by using only a fraction of the degrees of freedom of the discrete model of the structure. The procedure is applied to linear static analysis of framed structures. Design modifications consisted of removing members, resulting in topologically unsymmetric structures. The efficient application of the procedure on sequential computers as well as on multiprocessor computers is discussed, and its effectiveness is demonstrated by means of two numerical examples.

Noor, Ahmed K.↗

NASA NTRS1990

Neurobiological computational models in structural analysis and design

The present paper examines the role of neural computing strategies in structural analysis and design. A principal focus of the work resides in the use of neural networks to represent the force-displacement relationship in static structural analysis. Such models provide computationally efficient capabilities for reanalysis, and appear to be well suited for application in numerical optimum design. The paper presents an overview of the neural computing approach, with special emphasis on supervised learning techniques adopted in the present work. Special features of such learning strategies which have a direct bearing on numerical accuracy and efficiency, are examined in the context of representative structural optimization problems.

Hajela, P.↗

NASA NTRS1989

1960 Chile - New estimate of polar motion excitation

A recent reanalysis of the International Latitude Serivce (ILS) polar motion data-day has been processed using Kalman filtering techniques to generate the polar motion excitation function over the time-span from 1960 to 1965. The resulting excitation function has been examined for the effects of 1960 Chile in an attempt to determine experimentally how large earthquake affect polar motion. The resulting upper bound of about 75 x 10 to the 22nd N-m for a 10-deg dip (about 36 x 10 to the 22nd N-m for 20-deg dip) is consistent with results obtained from previous seismic studies, including a recent normal mode excitation result. Following future great earthquakes, monitoring of polar motion by space-based techniques such as VLBI should continue at high temporal resolution for several weeks in order to directly measure the rheological parameters of the upper mantle.

Slade, M. A.↗

NASA NTRS1990

Corrections regarding the Lellouch et al. (1989) analysis of Mars atmospheric C-12O and C-13O spectra

Lellouch et al. (1989) obtained atmospheric CO mixing ratios from Martian C-12O and C-13O microwave spectra that were 3-5 times greater than the Kaplan et al. (1969) IR measurememts; they also inferred a factor-of-2 increase in atmospheric CO abundance between September, 1986 and January, 1987. A reanalysis has been conducted of the Lellouch material, and more detailed treatment of the radiative transfer analysis indicates that its observations are consistent with the Kaplan CO volume mixing ratio determination. It is also ascertained that the Lellouch atmospheric temperature profiles are in error, with no evidence being found for the extreme temperature inversions inferred for the lowest 5 km of the Martian atmosphere.

Clancy, R. Todd↗

NASA NTRS1990

International Ultraviolet Explorer observations of Venus SO2 and SO

Results of recent International Ultraviolet Explorer observations of Venus made on January 20, 1987 and April 2 and 3, 1988 are presented along with a reanalysis of the 1979 observations (Conway et al., 1979). The observations indicate that the amount of sulfur dioxide at the cloud tops of Venus declined by a factor of 8 + or - 4 from 380 + or - 70 ppb in 1979 to 50 + or - 20 ppb in 1987 and 1988. These values are consistent with the Pioneer Venus results. Absorption features of sulfur monoxide are identified for the first time, and the SO mixing ratio above the cloud level is estimated to be 20 + or - 10 ppb for 1979. This is consistent with photochemical models by Winick and Stewart (1980) and Yung and DeMore (1982) and with the upper limit from Wilson et al. (1981).

Na, Chan Y.↗