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At least 973 records · Page 54

Programming the gradient projection algorithm

The gradient projection method of numerical optimization which is applied to problems having linear constraints but nonlinear objective functions is described and analyzed. The algorithm is found to be efficient and thorough for small systems, but requires the addition of auxiliary methods and programming for large scale systems with severe nonlinearities. In order to verify the theoretical results a digital computer is used to simulate the algorithm.

Hargrove, A.↗

Rapid torque-limited line-of-sight pointing of SCOLE (Spacecraft Control Laboratory Experiment) configuration

The design concept of a control for rapid torque-limited slewing of a rigid-mast version of the NASA SCOLE configuration is presented and demonstrated by means of numerical simulation. The time-optimal control problem for the system is decomposed into separate single-axis problems, expanding analytically the implicit nonlinear transcendental expression for the SCOLE line-of-sight error, and the final Euler attitude angles and slew angles are determined. The simulation results are presented in tables and graphs, and it is found that bang-bang or bang-pause-bang slew maneuvers with control moment applied to the Shuttle and control force applied to the reflector, and with a 5-deg/s slew-rate limit, produce the best pointing accuracy and the shortest slew times, although the specified line-of-sight error of 0.02 deg cannot be achieved using such open-loop single-axis maneuvers.

Lin, J. G.↗

The role of computerized symbolic manipulation in rotorcraft dynamics analysis

The potential role of symbolic manipulation programs in development and solution of the governing equations for rotorcraft dynamics problems is discussed and illustrated. Nonlinear equations of motion for a helicopter rotor blade represented by a rotating beam are developed making use of the computerized symbolic manipulation program MACSYMA. The use of computerized symbolic manipulation allows the analyst to concentrate on more meaningful tasks, such as establishment of physical assumptions, without being sidetracked by the tedious and trivial details of the algebraic manipulations. Furthermore, the resulting equations can be produced, if necessary, in a format suitable for numerical solution. A perturbation-type solution for the resulting dynamical equations is shown to be possible with a combination of symbolic manipulation and standard numerical techniques. This should ultimately lead to a greater physical understanding of the behavior of the solution than is possible with purely numerical techniques. The perturbation analysis of the flapping motion of a rigid rotor blade in forward flight is presented, for illustrative purposes, via computerized symbolic manipulation with a method that bypasses Floquet theory.

Crespo Da Silva, Marcelo R. M.↗

A new approximation method for stress constraints in structural synthesis

A new approximation method for dealing with stress constraints in structural synthesis is presented. The finite element nodal forces are approximated and these are used to create an explicit, but often nonlinear, approximation to the original problem. The principal motivation is to create the best approximation possible, in order to reduce the number of detailed finite element analyses needed to reach the optimum. Examples are offered and compared with published results, to demonstrate the efficiency and reliability of the proposed method.

Vanderplaats, Garret N.↗

Theoretical modelling of the fine structures in sunspots

Until a decade ago most solar physicists thought of a sunspot as the upper end of a giant flux tube floating vertically. The existence of umbral dots and penumbral grains has been known for several decades. On the basis of available observations, they seem to be regions of photospheric intensity with upflowing gas motion and magnetic fields much weaker than in the surrounding sunspot surface. It has also been suggested that the differences in the appearances of umbral dots and granular cells are caused by the highly nonlinear nature of the convection problem in the presense of strong magnetic fields. The main ideas are presented here without any equations. It can be shown that a pocket of field free gas surrounded by a vertical magnetic field in the presence of gravity takes up the shape of a tapering column ending at a vertex at the top. Some convection is expected to take place in the trapped field free gas, whereas the magnetic field around it makes those regions stable against convection. Eventually the apex of the tapering column reaches the photospheric surface where the bulging of the magnetic field makes the field no longer able to close on the field free gas and trap it underneath.

Choudhuri, Arnab Rai↗

A decomposition-based design optimization method with applications

A two-level design optimization metholology is described. A progress report of its application to Printed Wiring Board (PWB) assembly examples is given. The design of PWB assemblies is a complex task which is generally conducted as a sequential process. Individual PWBs are usually designed first, followed by the composition of the PWBs into an assembly. As a result, optimizing design considerations such as assembly reliability cannot be accomplished. This study showed that a two-level decomposition method can be employed to optimize for reliability at both the PWB- and the assembly-level in a coupled manner. The two-level decomposition method also resolved the mixed-integer nonlinear programming nature of the problem rather easily.

Azarm, Shapour↗

The 3-D inelastic analyses for computational structural mechanics

The 3-D inelastic analysis method is a focused program with the objective to develop computationally effective analysis methods and attendant computer codes for three-dimensional, nonlinear time and temperature dependent problems present in the hot section of turbojet engine structures. Development of these methods was a major part of the Hot Section Technology (HOST) program over the past five years at Lewis Research Center.

Hopkins, D. A.↗

Hyperbolic conservation laws and numerical methods

The mathematical structure of hyperbolic systems and the scalar equation case of conservation laws are discussed. Linear, nonlinear systems and the Riemann problem for the Euler equations are also studied. The numerical methods for conservation laws are presented in a nonstandard manner which leads to large time steps generalizations and computations on irregular grids. The solution of conservation laws with stiff source terms is examined.

Leveque, Randall J.↗

Maximum orbit plane change with heat-transfer-rate considerations

Two aerodynamic maneuvers are considered for maximizing the plane change of a circular orbit: gliding flight with a maximum thrust segment to regain lost energy (aeroglide) and constant altitude cruise with the thrust being used to cancel the drag and maintain a high energy level (aerocruise). In both cases, the stagnation heating rate is limited. For aeroglide, the controls are the angle of attack, the bank angle, the time at which the burn begins, and the length of the burn. For aerocruise, the maneuver is divided into three segments: descent, cruise, and ascent. During descent the thrust is zero, and the controls are the angle of attack and the bank angle. During cruise, the only control is the assumed-constant angle of attack. During ascent, a maximum thrust segment is used to restore lost energy, and the controls are the angle of attack and bank angle. The optimization problems are solved with a nonlinear programming code known as GRG2. Numerical results for the Maneuverable Re-entry Research Vehicle with a heating-rate limit of 100 Btu/ft(2)-s show that aerocruise gives a maximum plane change of 2 deg, which is only 1 deg larger than that of aeroglide. On the other hand, even though aerocruise requires two thrust levels, the cruise characteristics of constant altitude, velocity, thrust, and angle of attack are easy to control.

Lee, J. Y.↗

Radiobrightness of diurnally heated, freezing soil

Freezing and thawing soils exhibit unique radiometric characteristics. To examine these characteristics, diurnal insolation is modeled as one-dimensional heating of a moist soil half-space during a typical fall at a northern Great Plains site. The one-dimensional heat flow equation is nonlinear because both the enthalpy (the change in internal energy with temperature at constant pressure) and the thermal conductivity of freezing soils are nonlinear functions of temperature. The problem is particularly difficult because phase boundaries propagate in time, and because soils, particularly clay-rich soils, freeze over a range of temperatures rather than at 0 C. Diurnal radiobrightness curves at 10.7, 18.0, and 37.0-GHz were computed for each month. The 37.0-GHz radiobrightness best tracks soil surface temperature; the 10.7-37.0-GHz spectral gradient of thawed soils is strongly positive; the spectral gradient of frozen soils is slightly negative; and the midnight-to-noon spectral gradient is shifted by approximately +0.1 K/GHz by diurnal changes in the surface temperature and the thermal gradient. These observations support the use of the scanning multichannel microwave radiometer 37.0-GHz radiobrightness and its 10.7-37.0-GHz spectral gradient as discriminants in a frozen soil classifier for high-latitude prairie.

England, Anthony W.↗

Time-optimal aircraft pursuit-evasion with a weapon envelope constraint

The optimal pursuit-evasion problem between two aircraft, including nonlinear point-mass vehicle models and a realistic weapon envelope, is analyzed. Using a linear combination of flight time and the square of the vehicle acceleration as the performance index, a closed-form solution is obtained in nonlinear feedback form. Due to its modest computational requirements, this guidance law can be used for onboard real-time implementation.

Menon, P. K. A.↗

Investigation of the Finite Element Software Packages at KSC

The useful and powerful features of NASTRAN and three real world problems for the testing of the capabilities of different NASTRAN versions are discussed. The test problems involve direct transient analysis, nonlinear analysis, and static analysis. The experiences in using graphics software packages are also discussed. It was found that MSC/XL can be more useful if it can be improved to generate picture files of the analysis results and to extend its capabilities to support finite element codes other than MSC/NASTRAN. It was found that the current version of SDRC/I-DEAS (version VI) may have bugs in the module 'Data Loader'.

Lu, Chu-Ho↗

Shape selection criterion for cellular array during constrained growth of binary alloys - Need for low gravity experiment

Development of steady-state periodic cellular array is one of the critical problems in the study of nonlinear pattern formation during directional solidification of binary alloys. The criterion which establishes the values of cell tip radius and spacing under given growth condition is not known. Theoretical models, such as marginal stability and microscopic solvability, have been developed for purely diffusive regime. However, the experimental conditions where cellular structures are stable are precisely the ones where the convection effects are predominant. Thus, the critical data for meaningful evaluation of cellular array growth models can only be obtained by partial directional solidification and quenching experiments carried out in the low gravity environment of space.

Tewari, Surendra N.↗

CAN-DO, CFD-based Aerodynamic Nozzle Design and Optimization program for supersonic/hypersonic wind tunnels

A design program is developed which incorporates a modern approach to the design of supersonic/hypersonic wind-tunnel nozzles. The approach is obtained by the coupling of computational fluid dynamics (CFD) with design optimization. The program can be used to design a 2D or axisymmetric, supersonic or hypersonic, wind-tunnel nozzles that can be modeled with a calorically perfect gas. The nozzle design is obtained by solving a nonlinear least-squares optimization problem (LSOP). The LSOP is solved using an iterative procedure which requires intermediate flowfield solutions. The nozzle flowfield is simulated by solving the Navier-Stokes equations for the subsonic and transonic flow regions and the parabolized Navier-Stokes equations for the supersonic flow regions. The advantages of this method are that the design is based on the solution of the viscous equations eliminating the need to make separate corrections to a design contour, and the flexibility of applying the procedure to different types of nozzle design problems.

Korte, John J.↗

A parallelizable load balancing algorithm

We present a parallelizable load balancing algorithm for grid-based problems that employs a give and take concept among neighboring subdomains. The algorithm is found to converge very quickly to almost perfect load balance while minimizing the surface-to-volume ratio of the domains. The algorithm can be used for problems whose volume cost grows nonlinearly with the number of elements, because it measures continuously the computational cost to be incurred for each subdomain. This is an advantage over most algorithms currently in use (e.g., recursive subdivision), which assume a linear relationship between the computational cost and the number of elements.

Loehner, Rainald↗

Optimal glass-ceramic structures: Components of giant mirror telescopes

Detailed investigations are carried out on optimal glass-ceramic mirror structures of terrestrial space technology (optical telescopes). In order to find an optimum design, a nonlinear multi-criteria optimization problem is formulated. 'Minimum deformation' at 'minimum weight' are selected as contradictory objectives, and a set of further constraints (quilting effect, optical faults etc.) is defined and included. A special result of the investigations is described.

Eschenauer, Hans A.↗

Raman-shifting an ArF excimer laser to generate new lines for obtaining optical diagnostic based information in flow fields

The application of tunable excimer lasers in combustion and flow diagnostics is almost routine nowadays. The properties of this laser system that enable density and temperature measurements in supersonic and hypersonic flow fields to be conducted are its high power, high repetition rate, and high spectral brightness. The limitation imposed by this system on these measurements is the paucity of lines in the wavelength region, the vacuum-ultraviolet, where species of interest, such as OH, N2, O2, H2, H2O, CO, NO, etc., are susceptible to electronic excitation to high-lying states. To circumvent this problem one normally resorts to nonlinear optical techniques such as frequency conversion via stimulated Raman scattering (SRS), more commonly known as Raman shifting or Raman mixing, to extend these nonintrusive and nonperturbing techniques to the shorter wavelengths in the VUV region and, for that matter, to longer wavelengths in the infrared region, if the need arises. The theoretical basis of SRS and its application are well documented in the literature. In essence, the Raman shift is a consequence of the inelastic scattering of the incident radiation by the sample. Most of the scattered radiation from the molecules of the sample is unchanged in frequency. However, a small fraction of the incident radiation is changed in frequency. This shift is a result of the fact that some of the incident photons on colliding with the molecules of the sample give up some of their energy and emerge with a lower energy resulting in the lower-frequency Stokes radiation. Other incident photons may increase their energy by colliding with the vibrationally excited molecules of the medium and emerge as higher-frequency antistokes radiation. The generation of the latter is the main objective of this project. The process, however, depends on several factors, including the beam quality of the pump laser, the cross-section of the gaseous medium, the gas pressure, and the ambient temperature of the gas near the focal region. Furthermore, since the Raman shifting process is polarization sensitive, it is necessary to have all of the laser energy in a single polarization. These factors were taken into consideration in the execution of the project. The implementation of the Raman shift was accomplished by focusing the 193 nm output of an ArF excimer laser (Lamda-Physik LPX 150) into a 1-meter long high pressure recirculating Raman cell filled with H2 gas. The laser system was modified in order to improve the mode quality of the pump beam to enhance the Raman shifting. To accomplish this feat, a prism beam expander and grating on the oscillator discharge provided wavelength tuning over the excimer gain profile. Furthermore, a triple-pass configuration, as opposed to unstable resonator optics, was employed in the operation of the amplifier cavity so that when the oscillator output radiation, focused by a 51-cm focal length fused silica lens through a 50 micron pinhole (serving as a spatial filter) and recollimated with a 25-cm focal length lens, was fed into the amplifier, it was injection locked, thereby providing tunable radiation with relatively low divergence. The forward scattered radiation emanating from the impingement of the modified pump beam on the Raman cell was detected using an energy meter after the latter had been separated from it using a dispersing prism.

Koker, Edmond B.↗

Spurious Numerical Solutions Of Differential Equations

Paper presents detailed study of spurious steady-state numerical solutions of differential equations that contain nonlinear source terms. Main objectives of this study are (1) to investigate how well numerical steady-state solutions of model nonlinear reaction/convection boundary-value problem mimic true steady-state solutions and (2) to relate findings of this investigation to implications for interpretation of numerical results from computational-fluid-dynamics algorithms and computer codes used to simulate reacting flows.

Lafon, A.↗