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Method of initial parameters used in differential equations for bending and internal stress forces occurring in rectangular orthotropic plates lying on elastic foundation
Elastoplastic flow equations character in three independent variables, noting solution methods for initial and boundary value problems
Normalized multidimensional Newton-Raphson method eliminating initial guess, using two- transformation technique
Study presents methods and initial procedures which may be obtained for development of more efficient uniform network analysis input language and theoretical tools to prove equivalence of data representations.
Although the derivation is concerned with solutions for plane regions with prescribed boundary values, the approach presented could by easily generalized to higher dimensions. The initial-value method is derived by a combination of invariant imbedding techniques and the Fredholm integral equation method of representation of the potential as a function of a dilayer distribution on the boundary of the region in question.
The need for a canister that can release its contents without disturbing the contents dynamically is discussed. The solution of this problem by the use of a frangible glass canister is considered. The basic theory applicable to frangible glass and the method of initiating a command flaw are discussed. A brief description of the test program and the results of a flight test are presented.
Error drift in the ERTS orbit maintenance problem is determined from the actual ground trace errors that the spacecraft experienced over the first 3 1/2 repeat cycles. Actual data are fitted to a parametric model of ground trace error by a least squares method, and initial offsets to these key parameters as well as their rates of change are extrapolated forward analytically to obtain the future ground trace drift in orbital estimates.
Numerical methods of integration of the equations of motion of a controlled satellite under the influence of gravity-gradient torque are considered. The results of computer experimentation using a number of Runge-Kutta, multi-step, and extrapolation methods for the numerical integration of this differential system are presented, and particularly efficient methods are noted. A large bibliography of numerical methods for initial value problems for ordinary differential equations is presented, and a compilation of Runge-Kutta and multistep formulas is given. Less common numerical integration techniques from the literature are noted for further consideration.
A 333 mN electrothermal thruster designed to use MIL-grade hydrazine was demonstrated to be suitable for operation with low freezing point monopropellants containing hydrazine azide, monomethylhydrazine, unsymmetrical-dimethylhydrazine and ammonia. The steady-state specific impulse was greater than 200 sec for all propellants. The pulsed-mode specific impulse for an azide blend exceeded 175 sec for pulse widths greater than 50 msec; propellants containing carbonaceous species delivered 175 sec pulsed-mode specific impulses for pulse widths greater than 100 msec. Longer thrust chamber residence times were required for the carbonaceous propellants; the original thruster design was modified by increasing the characteristic chamber length and screen packing density. Specific recommendations were made for the work required to design and develop flight worthy thrusters, including methods to increase propellant dispersal at injection, thruster geometry changes to reduce holding power levels and methods to initiate the rapid decomposition of the carbonaceous propellants.
A multiple-scattering method is described which is applicable to the transient plasma problem concerning the interaction between transient electromagnetic waves and plasmas. The method starts with the time-dependent wave fields scattered by a linear electric dipole when illuminated by a transient plane wave. It avoids the use of Fourier transform methods and provides additional physical insight into the origin of the frequency-dispersive properties of material media. The results are applicable only to cold plasmas since spatial dispersion is neglected, implying that effects due to thermal velocities of electrons - such as incoherent scatter - are not covered by the theory. The advantages of the method for initiation of the student into transient electromagnetics in dispersive media are identified as conceptual simplicity and computational simplicity. The entire analysis is in the time domain.
An apparatus and procedure are described for evaluating the toxicity of the gases evolved from the smoldering combustion of seating and bedding materials. The method combines initiation of smoldering combustion in fabric/cushion combinations by a lighted cigarette and exposure of laboratory animals to the gases evolved. The ratio of the surface available for smoldering to the compartment volume in this apparatus is approximately five times the ratio expected in a California living room, and 100 times the ratio expected in a wide-body aircraft passenger cabin. Based on fabric/cushion combinations tested, the toxicity of gases from smoldering combustion does not appear to be a significant hazard in aircraft passenger cabins, but seems to be a basis for careful selection of materials for residential environments.
A nonlinear analysis which is necessary to adequately model elastic helicopter rotor blades experiencing moderately large deformations was examined. The analysis must be based on an appropriate description of the blade's deformation geometry including elastic bending and twist. Built-in pretwist angles complicate the deformation process ant its definition. Relationships between the twist variables associated with different rotation sequences and corresponding forms of the transformation matrix are lasted. Relationships between the twist variables associated with first, the pretwist combined with the deformation twist are included. Many of the corresponding forms of the transformation matrix for the two cases are listed. It is shown that twist variables connected with the combined twist treatment are related to those where the pretwist is applied initially. A method to determine the relationships and some results are outlined. A procedure to evaluate the transformation matrix that eliminates the Eulerlike sequence altogether is demonstrated. The resulting form of the transformation matrix is unaffected by rotation sequence or pretwist treatment.
The aeroacoustic problem associated with the radiation of fan noise from the inlet of a turbofan aircraft engine, the dimensions of which are generally many times larger than the acoustical wavelengths of the major energy-carrying frequencies, is considered. In the present approach, a conventional finite element solution in the inner region is compatibly matched to a 'wave envelope' finite element solution in a large but finite outer region. The inclusion of a wavelike variation with the correct asymptotic decay in the shape functions for the outer region preserves the correct behavior of the solution at large distances. The method is initially presented for a simple one-dimensional model based on the solution of Webster's horn equation. Results are presented for the specific case of a uniform cylindrical section joined to a conical expansion, and also for a simple axisymmetric test case of the calculation of acoustical pressure generated by a vibrating circular piston located at the center of an infinite rigid baffle.
Among the topics discussed are mesoscale processes and variability, regional and cyclonic scale motions and their prediction modeling, fronts, mesoscale instabilities, buoyancy (gravity) waves and topographic forcing, buoyant convection, boundary layers, and observational technology. The specific issues investigated include methods for initializing mesoscale forecast models, an energy theory for the propagation of gravity currents, a theory for rain bands within extratropical cyclones, the morning glory as a nonlinear wave phenomenon, cumulus clouds, the prediction of severe convection, planetary boundary layer parameterization, and three-dimensional wind field analysis from Doppler radar data.
An investigation was carried out to quantitatively evaluate left ventricular volume flow rate, momentum, force and impulse derived from application of conservation principles for mass and momentum of blood within the ventricle during the ejection phase. An automated digital image processing system was developed and applied to left ventricular angiograms which are computer processed and analyzed frame by frame to determine the dynamical relations by numerical methods. The initial experience with force and impulse has indicated that neither quantity seemed to be a sensitive indicator of coronary artery disease as evaluated by qualitative angiography for the particular patient group studied. Utilization of the dynamical relations in evaluating human left ventricular performance requires improved means of measurement and interpretation of clinical studies.
Fatigue cracks are a major problem in designing structures subjected to cyclic loading. Cracks frequently occur in structures such as aircraft and spacecraft. The inspection intervals of many aircraft structures are based on crack-propagation lives. Therefore, improved prediction of propagation lives under flight-load conditions (variable-amplitude loading) are needed to provide more realistic design criteria for these structures. The main thrust was to develop a three-dimensional, nonlinear, elastic-plastic, finite element program capable of extending a crack and changing boundary conditions for the model under consideration. The finite-element model is composed of 8-noded (linear-strain) isoparametric elements. In the analysis, the material is assumed to be elastic-perfectly plastic. The cycle stress-strain curve for the material is shown Zienkiewicz's initial-stress method, von Mises's yield criterion, and Drucker's normality condition under small-strain assumptions are used to account for plasticity. The three-dimensional analysis is capable of extending the crack and changing boundary conditions under cyclic loading.
Research in cognitive science suggests that much of cognition involves the rapid manipulation of complex data structures. However, it is very unclear how this could be realized in neural networks or connectionist systems. A core question is: how could the interconnectivity of items in an abstract-level data structure be neurally encoded? The answer appeals mainly to positional relationships between activity patterns within neural arrays, rather than directly to neural connections in the traditional way. The new method was initially devised to account for abstract symbolic data structures, but it also supports cognitively useful spatial analogue, image-like representations. As the neural model is based on massive, uniform, parallel computations over 2D arrays, the massively parallel processor is a convenient tool for simulation work, although there are complications in using the machine to the fullest advantage. An MPP Pascal simulation program for a small pilot version of the model is running.
A three-dimensional, time-dependent, MHD disturbance propagating through a steady inhomogeneous MHD flow is analyzed by a numerical model based on the Lax-Wendroff finite difference method. The initial steady MHD flow is assumed to be supersonic and super-Alfvenic. The background steady MHD flow is obtained by dropping the time-dependent terms in the unsteady MHD equations. A transient MHD disturbance corresponding to a MHD shock is generated at the lower radial boundary surface. The resulting development and propagation of 3-D MHD disturbances interacting with the background steady MHD flow are numerically simulated in this first application to the field of interplanetary physics. Detailed descriptions of the mathematical formulation and numerical methodology are presented. Example computations are performed to demonstrate the validity of the formulation and the capabilities of the model.