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This paper illustrates the application of symbolic computation in connection with three aspects of mechanical systems: (1) The derivation of dynamical equations by Lagrangian methods; (2) The analysis and synthesis of kinematic mechanisms; and (3) A robot manipulator arm.
A three-dimensional element based on the total Lagrangian description of the motion of a layered anisotropic composite medium is developed, validated, and used to analyze layered composite shells. The element contains the following features: geometric nonlinearity, dynamic (transient) behavior, and arbitrary lamination scheme and lamina properties. Numerical results of nonlinear bending, natural vibration, and transient response are presented to illustrate the capabilities of the element.
The capability of simulating three dimensional two phase reactive flows with combustion in the liquid fuelled rocket engines is demonstrated. This was accomplished by modifying an existing three dimensional computer program (REFLAN3D) with Eulerian Lagrangian approach to simulate two phase spray flow, evaporation and combustion. The modified code is referred as REFLAN3D-SPRAY. The mathematical formulation of the fluid flow, heat transfer, combustion and two phase flow interaction of the numerical solution procedure, boundary conditions and their treatment are described.
The computer program designated 'VIPASA', which accurately treats buckling and vibration in prismatic plate assemblies with a response that varies sinusoidally in the longitudinal direction, has been found to be limited by the production of an in-plane shear loading of component plates that produces skewed mode shapes. These do not conform to desired support conditions. This problem is presently overcome through a coupling of the VIPASA stiffness matrices for different wavelength responses by means of the Lagrangian Multipliers method. The theory extends to supports at arbitrary locations, and even to the support provided by any elastic structure. The generality and capabilities of VIPASA have been retained in the computer program designated 'VICON', which permits constraints and a supporting structure consisting of any number of transverse beam columns.
In connection with studies of solar wind ionization state freezing, it is shown that, by using a Lagrangian approach of following individual fluid parcels, the techniques used previously for calculating ionization state variations in a steady state case can be extended straightforwardly to time-varying flows. The specific ionization state calculations presented are for a relatively simple picture of time-dependent coronal flow, based on a well-known model of a self-similar shock wave propagating through the corona. Time-dependent ionization effects for the sudden transition between two otherwise steady flows are likely to be limited to a narrow range of gas parcels which, having been shocked within the coronal freezing-in radius, pass a fixed interplanetary observer in an interval of a few tens of minutes. The amplitude of any rise in interplanetary ionization temperature associated with the coronal shock is likely to be considerably smaller than the jump in electron temperature that actually occurs in the corona.
The ISEE-3 spacecraft has been transferred in 1982 into an earth orbit which brings the satellite close to the tailward Lagrangian point L2 at about 220 R(E) and thus allows exploration of the distant geomagnetic tail. An initial analysis of energetic proton measurements greater than 30 keV from the Max-Planck-Institut/University of Maryland sensor system on ISEE-3 is reported. It has been found that suprathermal protons are a persistent feature of the distant tail. Differential intensitites at 30 keV are essentially constant between the lunar distance and 220 R(E) and about one order of magnitude smaller than in the near earth, or greater than about 20 R(E), plasma sheet. Assuming that these protons are convected with the local plasma flow, it is possible to derive plasma velocities. During time periods where a comparison is possible, these velocities compare favourably well with the velocities derived from the Los Alamos National Laboratory plasma analyzer on board the same spacecraft. The appearance of the plasma sheet, as evidenced by the suprathermal particles, is rather bursty. Anisotropies are large, and predominantly tailward.
A numerical method for computing nonplanar vortex wakes represented by finite-core vortices is presented. The approach solves for the velocity on an Eulerian grid, using standard finite-difference techniques; the vortex wake is tracked by Lagrangian methods. In this method, the distribution of continuous vorticity in the wake is replaced by a group of discrete vortices. An axially symmetric distribution of vorticity about the center of each discrete vortex is used to represent the finite-core model. Two distributions of vorticity, or core models, are investigated: a finite distribution of vorticity represented by a third-order polynomial, and a continuous distribution of vorticity throughout the wake. The method provides for a vortex-core model that is insensitive to the mesh spacing. Results for a simplified case are presented. Computed results for the roll-up of a vortex wake generated by wings with different spanwise load distributions are presented; contour plots of the flow-field velocities are included; and comparisons are made of the computed flow-field velocities with experimentally measured velocities.
A three-dimensional element based on the total Lagrangian description of large deformations of a layered anisotropic composite medium is developed, validated, and used to analyze layered composite shells. The element contains the following features: geometric nonlinearity, dynamic (transient) behavior, and arbitrary lamination scheme and lamina properties. Numerical results of nonlinear bending, natural vibration, and transient response are presented to illustrate the capabilities of the element.
Three instrumented super pressure balloons were flown throughout the southern hemisphere at 18 mbar, over a period of five months. The balloon trajectories, reconstructed from NIMBUS 6 satellite location data, have proved to be valuable indicators of midstratospheric structure and dynamics in the Lagrangian frame of reference. Several examples of high zonal and meridional winds are reported. Also shown in the analysis is a feature encountered between 30 S-40 S during a two-week period. The feature appears to be a breakdown of large-scale zonal flow and its replacement by weak cyclonic eddies. During the observational period the balloon motions document the spring reversal. Mean zonal wind speed analysis from balloon positions were obtained covering the area 15 S-65 S. The results presented here are in substantial agreement with those of Hartmann (1977).
Fluid dynamic computer codes for the simulation of flows in gas turbine engine combustion systems are being developed. NASA is currently sponsoring a two-phase program for the evaluation of the performance of current codes, taking into account also an improvement of accuracy, if needed. The present investigation forms a part of this program. The numerical technique used includes a Lagrangian spray model for liquid fuels. The spray model, in conjunction with the turbulence model, determines the distribution of fuel in the burning zone of the combustor. The numerical technique was applied to a hollow-cone pressure atomizer spraying water into a coflowing confined airstream.
It is pointed out that the redeployment of ISEE 3 from its continuous monitoring of the solar wind in a large orbit about the upstream Lagrangian point to an extended magnetotail orbit has afforded an opportunity for deep-tail passage of October 1982, and in the radial range from 200 to 220 R(E) during the near-apogee part of the second tail passage in January-February 1983. Attention is given to instrumentation and data sets, spacecraft positions, and observational data.
A spectral element method that combines the generality of the finite element method with the accuracy of spectral techniques is proposed for the numerical solution of the incompressible Navier-Stokes equations. In the spectral element discretization, the computational domain is broken into a series of elements, and the velocity in each element is represented as a high-order Lagrangian interpolant through Chebyshev collocation points. The hyperbolic piece of the governing equations is then treated with an explicit collocation scheme, while the pressure and viscous contributions are treated implicitly with a projection operator derived from a variational principle. The implementation of the technique is demonstrated on a one-dimensional inflow-outflow advection-diffusion equation, and the method is then applied to laminar two-dimensional (separated) flow in a channel expansion. Comparisons are made with experiment and previous numerical work.
Report presents two general methods for reducing mathematical complexities of state equations of robot-arm dynamics. Robot arms contain both rotary and linear joints. Both methods start with homogenous coordinates and Lagrangian formulation of mechanics briefly summarized in report. First method uses matrix-analysis techniques; second, vector-analysis techniques. Vector-analysis method includes new differential-vector representation of centripetal and Coriolis forces.
A general approach is required for describing matter of behavior when the failure is likely to involve growth and coalescence of a large number of fractures. Failures of this kind appear frequently in rapid dynamic processes, particularly in the formation of spall fragments. An approach to formulating constitutive relations that accounts for the opening, shear and growth of an ensemble of cracks is discussed. The approach accounts for plastic flow accompanying fragmentation. The resulting constitutive relations were incorporated into a Lagrangian computer program. A theoretical approach to coalescence is described. The simplest formulation uses a linear Liouville equation, with crack growth limited by the mean free path of cracks, assumed constant. This approach allows for an anisotropic distribution of cracks. An alternative approach in which the decrease of the mean free path with increasing crack size is accounted for, but the crack distribution is assumed isotropic is described. A reduction of the governing Liouville equation to an ordinary differential equation of third order is possible, and the result can be used to determine how mean free path decreases with increasing crack size.
LANDSAT visible imagery and a one-dimensional Lagrangian boundary layer model were used to hypothesize the nature and the development of the marine boundary layer during a winter episode of strong seaward cold air advection. Over-water heating and moistening of the cold, dry continental air is estimable from linear relations involving horizontal gradients of the near-surface air temperature and humidity. A line of enhanced convection paralleling the Atlantic U.S. coast from south of New York Bay to the vicinity of Virginia Beach, VA was attributed to stronger convergence at low levels. This feature was characterized as a mesoscale front. With the assistance of a three-dimensional mesoscale boundary layer model, initialized with data obtained from the MASEX, the marine boundary layer can be mapped over the entire Atlantic coastal domain and the evolution of the boundary layer can be studied as a function of different characteristics of important surface level forcings. The effects on boundary layer growth due to the magnitude and pattern of sea surface temperature, to the shape of the coastline, and to atmospheric conditions, such as the orientation of the prevailing wind are examined.
An analysis of a case study of the favorable impact of satellite data assimilation on model cyclone prediction is discussed. Also discussed is the isolation of systematic biases in the vertical structure of satellite derived temperatures which in all probability negatively impact the prediction of ocean cyclones during periods of rapid baroclinic amplification. Access to CYBER 205 and transfer of software for Eulerian and quasi-Lagrangian diagnostic studies of atmospheric circulation are discussed.
A number of papers have been presented on the evaluation of energy release rate for thermoelasticity and corresponding J integral. Two main approaches were developed to treat energy release rate in elasticity. The first is based on direct calculation of the potential energy rate with respect to crack length. The second makes use of Lagrangian formalism. The translational and expansional energy release rates in thermoelasticity are studied by employing the formalism of irreversible thermodynamics and the Crack Layer Approach.
A two-dimensional/axisymmetric program for the simulation of three-phase reactive flows is presented. The three phases are: a multiple-species gaseous phase, a single-species liquid phase, and a particulate droplet phase. The liquid and gaseous phases are described with continuous Eulerian equations, while the droplets are described in a discrete Lagrangian fashion. The three phases are fully coupled together. An atomization model, a multireaction chemical kinetics model, and a subgrid scale turbulence model completes the description of a general liquid/gas bipropellant combustion process. The code development criteria and qualitative features are highlighted.