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Multi-dimensional generalizations of a one-dimensional finite element shock capturing scheme are proposed. A scalar model problem is used to emphasize that 'preferred directions' are important in multi-dimensional applications. Schemes are developed for the two-dimensional Euler equations. One, based upon characteristics, employs the Mach lines and streamlines as preferred directions.
A new general-purpose optimization program for engineering design is described. ADS (Automated Design Synthesis) is a FORTRAN program for nonlinear constrained (or unconstrained) function minimization. The optimization process is segmented into three levels: Strategy, Optimizer, and One-dimensional search. At each level, several options are available so that a total of nearly 100 possible combinations can be created. An example of available combinations is the Augmented Lagrange Multiplier method, using the BFGS variable metric unconstrained minimization together with polynomial interpolation for the one-dimensional search.
An expert system called EXADS has been developed to aid users of the Automated Design Synthesis (ADS) general purpose optimization program. ADS has approximately 100 combinations of strategy, optimizer, and one-dimensional search options from which to choose. It is difficult for a nonexpert to make this choice. This expert system aids the user in choosing the best combination of options based on the users knowledge of the problem and the expert knowledge stored in the knowledge base. The knowledge base is divided into three categories; constrained problems, unconstrained problems, and constrained problems being treated as unconstrained problems. The inference engine and rules are written in LISP, contains about 200 rules, and executes on DEC-VAX (with Franz-LISP) and IBM PC (with IQ-LISP) computers.
The General Rotorcraft Aeromechanical Stability Program (GRASP), which is a hybrid between finite element programs and spacecraft-oriented multibody programs, is described in terms of its design and capabilities. Numerical results from GRASP are presented and compared with the results from an existing, special-purpose coupled rotor/body aeromechanical stability program and with experimental data of Dowell and Traybar (1975 and 1977) for large deflections of an end-loaded cantilevered beam. The agreement is excellent in both cases.
A general, gauge-invariant analysis of the large-scale anisotropies in the cosmic background radiation produced by arbitrary scalar, vector, or tensor perturbations in open, closed, or flat Robertson-Walker spacetimes (with no cosmological constant) is presented. The multipole moment predictions for the scale invariant spectrum and Omega = 1 universe predicted by inflationary cosmologies are contrasted with those for other spectra and for open and closed universes. Using the measured value of the dipole moment, limits are set on the expected value of the quadrupole moment as a function of Omega for various spectra.
A diagnostic package developed to analyze runs made by the National Center for Atmospheric Research thermosphere general circulation model is used to calculate neutral parcel trajectories in the high-latitude E and F regions. Parcel trajectories are presented for a number of different cases to illustrate the main characteristics of F region parcel transport in the winter high-latitude region. Several examples of E region parcel trajectories are similarly analyzed, concentrating on both the southern (summer) and northern (winter) regions. F region parcel trajectories are calculated backward in time from passage over a given geographical location to illustrate the 'genesis' of those parcels whose velocities can be monitored from a ground-based Fabry-Perot observatory.
A general analytical theory of the five main satellites of Uranus, including the secular and short period terms hereafter denoted by GUST, is presented. A comparison is made with an internal numerical integration with nominal masses of Veillet (1983). The precision of the theory goes from about 10 km for Miranda to 100 km for Oberon. The short period terms in the motions of Titania and Oberon are larger than 500 km. They should make possible the determination of the masses of the outer satellites through the optical data of Voyager encounter.
A procedure is provided for generalizing the method of harmonic balance to obtain higher-order approximations to the periodic solutions of differential equations for two systems, one a conservative system and the other nonconservative. The procedure is currently being applied to investigate the possible solution behaviors of singular, nonlinear oscillators, where the usual perturbation methods do not work.
The rainout-determined lifetimes of highly soluble particulate and gaseous atmospheric compounds are investigated using general circulation model simulations in which removal is explicitly calculated in terms of the local, model-produced precipitation rates. The calculations indicate that because of the episodic and asymmetric nature of rainout, species' lifetimes depend not only on the amount of precipitation but also on the characteristics of the precipitation regime (such as duration and frequency of the precipitation events) and on the direction of the tracer main flow (determined by the species' average mixing ratio gradient). For this reason, averaged rainout lifetimes of tracers flowing downstream from the stratosphere are found to differ substantially from those of tracers of surface origin flowing upward or tracers of a more ubiquitous tropospheric source. These results imply that the use of a first-order parameterization to simulate rainout in a photochemical model that does not explicitly calculate precipitation can be inadequate in representing this process. A computationally efficient parameterization that includes the effects of intermittence and asymmetry of rainout is proposed, and it is shown how this parameterization can be used to estimate rainout-determined tropospheric residence times from observational data sets. A review of published estimates of submicron aerosol tropospheric residence times based on observations shows that these are consistent with the model results.
The stiffness-matrix formulation for the rectangular finite element described by Melosh (1963) and Weaver and Johnston (1984) is generalized to orthotropic materials with material axes not necessarily coincident with the x and y axes; i.e., the condition d(13) = d(23) = 0 is removed. Also included are explicit expressions for the element load vector associated with nonuniform temperature increase in the element. Applications to the analysis of thermal stresses in thin Si-crystal ribbons subjected to temperature changes with highly nonuniform lengthwise and transverse gradients (Utku et al., 1986) and to the simulation of the thermoviscoelastic behavior of growing Si ribbons (Utku and Ray, 1986) are indicated.
The NASA Goddard Laboratory for Atmospheres (GLA) analysis/forecast system was run in two different parallel modes in order to evaluate the influence that data from satellites and other FGGE observation platforms can have on analyses of large scale circulation; in the first mode, data from all observation systems were used, while in the second only conventional upper air and surface reports were used. The GLA model was also integrated for the same period without insertion of any data; an independent objective analysis based only on rawinsonde and pilot balloon data is also performed. A small decrease in the vigor of the general circulation is noted to follow from the inclusion of satellite observations.
A hybrid stress general shell element is developed based on the Hellinger-Reissner principle modified for relaxed element compatibility conditions. The element is based on a consistent first order thin shell theory with Love Kirchhoff hypotheses. It is of quadrilateral shape with only four corner nodes and five degrees of freedom per node. The geometry of the element is approximated through a bi-cubic polynomial surface patch. Numerical examples consist of torsion-loaded slit cylinder and pinched cylinder with open ends and rigid diaphragmed ends. Also, the representation of the rigid body motion is studied by series of parametric eigenvalue analysis of the stiffness matrix.
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.
An investigation is conducted of the effect of a single engine, untapered low wing general aviation aircraft propeller's swirl on the craft's stall pattern. The asymmetrical character of the propeller's swirl can trigger an early stall of one of the wings, aggravating the spin-entry condition. It is shown that the combination of this propeller-induced effect with adverse sideslip can result in large and abrupt changes in the rolling moment, in such conditions as uncoordinated low speed turning maneuvers where the pilot yaws the aircraft with wings level, rather than rolling it.
The Oregon State University/Lawrence Livermore National Laboratory general circulation model has been employed as a vehicle for suggesting and exploring various means of converting narrow-band measurements of reflected solar radiation from the earth-atmosphere system to broad-band quantities. For purely illustrative purposes within the model's solar radiation routine, a narrow-band filter function consisting of a square-wave window extending from 0.5 to 0.9 microns is adopted. A limitation of the model, for this sort of endeavor, is that it does not include the wavelength dependence of surface albedos. Nevertheless, the model simulations tend to mimic the calibration of a narrow-band instrument, utilizing reflected solar radiation from the earth-atmosphere system as simultaneously measured by a collocated broad-band instrument; for the model, however, this is done in terms of fluxes, in contrast to instrument-measured radiances. The model results suggest that it might be preferable to perform narrow- to broad-band conversions in terms of planetary albedo (or an equivalent quantity), rather than in terms of reflected fluxes or radiances. Further improvement is achieved if, for instruments that can differentiate between clear and overcast conditions, separate clear and overcast calibrations are performed.
The spectral energetics of the Northern Hemisphere circulation during blocking episodes of the FGGE year is investigated with gridded analyses of observational data and parallel simulation experiments. The purpose of this study is to describe the energetics distinctions of the observed and simulated blockings in the context of the general circulation and to assess the capability of the model to simulate blockings. In the observed circulation a pronounced winter blocking is developed and maintained by the nonlinear wave-wave interaction L(1) from the kinetic energy source for n = 3-10, where L(n) is the transfer of eddy kinetic energy from all other wavenumbers to wavenumber n. In the case of the double blocking in the winter, both L(1) and L(2) support the blocking. The kinetic energy source of n = 10 for upscale input at n = 1 and 2 is supported by the baroclinic conversion at n = 3-10. The simulated winter circulation shows strong baroclinic conversion at all wavenumbers, including ultralong waves. However, the simulation fails to produce pronounced blocking for the absence of L(1), and the converted energy cascades down to shorter waves. The wave-mean transfer of kinetic energy from the large-scale disturbances to the zonal mean component further prevents the accumulation of the kinetic energy at the ultralong waves. In contrast to the winter situation, the summer blocking seems to be directly supported by both L(4) and baroclinic conversion at other planetary-scale waves. Consequently, the summer circulation is better simulated than the winter circulation.
A linear primitive-equation stationary-wave model is developed to describe Northern Hemisphere winter stationary eddies on a sphere, and simulation results are compared with the predictions of a flat-lower-boundary GCM in extensive graphs and maps. The linear model is shown to reproduce the general behavior of the GCM well, with 10-30-percent underestimation of amplitudes in the Northern Hemisphere extratropical upper troposphere. The response to global heating plus transient eddy flux convergences is then decomposed into responses to total tropical forcing (heating plus transients) and total extratropical forcing (upper and lower tropospheric transients and latent, sensible, and radiative heating). The quality of the simulation is found to deteriorate rapidly if transient forcing is omitted, although somewhat better results are obtained by substituting thermal damping for transient forcing. The importance of low-level-transient parameterization for theories of time-mean low-level flow is emphasized.
The elastic interactions of a two-dimensional configuration consisting of a crack with an array of microcracks located near the tip are studied. The general form of the solution is based on the potential representations and approximations of tractions on the microcracks by polynomials. In the second part, the technique is applied to two simple two-dimensional configurations involving one and two microcracks. The problems of stress shielding and stress amplification (the reduction or increase of the effective stress intensity factor due to the presence of microcracks) are discussed, and the refinements introduced by higher order polynomial approximations are illustrated.