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At least 847 records · Page 47

Robust penalty method for structural synthesis

The Sequential Unconstrained Minimization Technique (SUMT) offers an easy way of solving nonlinearly constrained problems. However, this algorithm frequently suffers from the need to minimize an ill-conditioned penalty function. An ill-conditioned minimization problem can be solved very effectively by posing the problem as one of integrating a system of stiff differential equations utilizing concepts from singular perturbation theory. This paper evaluates the robustness and the reliability of such a singular perturbation based SUMT algorithm on two different problems of structural optimization of widely separated scales. The report concludes that whereas conventional SUMT can be bogged down by frequent ill-conditioning, especially in large scale problems, the singular perturbation SUMT has no such difficulty in converging to very accurate solutions.

Kamat, M. P.↗

Preliminary Orbit Determination System (PODS) for Tracking and Data Relay Satellite System (TDRSS)-tracked target Spacecraft using the homotopy continuation method

The Preliminary Orbit Determination System (PODS) provides early orbit determination capability in the Trajectory Computation and Orbital Products System (TCOPS) for a Tracking and Data Relay Satellite System (TDRSS)-tracked spacecraft. PODS computes a set of orbit states from an a priori estimate and six tracking measurements, consisting of any combination of TDRSS range and Doppler tracking measurements. PODS uses the homotopy continuation method to solve a set of nonlinear equations, and it is particularly effective for the case when the a priori estimate is not well known. Since range and Doppler measurements produce multiple states in PODS, a screening technique selects the desired state. PODS is executed in the TCOPS environment and can directly access all operational data sets. At the completion of the preliminary orbit determination, the PODS-generated state, along with additional tracking measurements, can be directly input to the differential correction (DC) process to generate an improved state. To validate the computational and operational capabilities of PODS, tests were performed using simulated TDRSS tracking measurements for the Cosmic Background Explorer (COBE) satellite and using real TDRSS measurements for the Earth Radiation Budget Satellite (ERBS) and the Solar Mesosphere Explorer (SME) spacecraft. The effects of various measurement combinations, varying arc lengths, and levels of degradation of the a priori state vector on the PODS solutions were considered.

Kirschner, S. M.↗

Nonlinear stability and control study of highly maneuverable high performance aircraft, phase 2

This research should lead to the development of new nonlinear methodologies for the adaptive control and stability analysis of high angle-of-attack aircraft such as the F18 (HARV). The emphasis has been on nonlinear adaptive control, but associated model development, system identification, stability analysis and simulation is performed in some detail as well. Various models under investigation for different purposes are summarized in tabular form. Models and simulation for the longitudinal dynamics have been developed for all types except the nonlinear ordinary differential equation model. Briefly, studies completed indicate that nonlinear adaptive control can outperform linear adaptive control for rapid maneuvers with large changes in alpha. The transient responses are compared where the desired alpha varies from 5 degrees to 60 degrees to 30 degrees and back to 5 degrees in all about 16 sec. Here, the horizontal stabilator is the only control used with an assumed first-order linear actuator with a 1/30 sec time constant.

Mohler, R. R.↗

Finite element nonlinear panel flutter with arbitrary temperatures in supersonic flow

A finite element frequency domain method for predicting nonlinear flutter response of panels with temperature effects is presented. By using the principle of virtual work, the element nonlinear stiffness formulation for a panel under a combined thermal and aerodynamic loads is derived on the bases of von Karman's large deflection plate theory, the first-order piston theory aerodynamics and the quasi-steady thermal stress theory. The system equations of motion can be mathematically separated into two sets of equations and then solved in sequence. The first set of equations yields the panel thermal-aerodynamic equilibrium and the second set of equations of motion leads to the flutter limit-cycle oscillations. Stability and flutter boundaries can also be obtained from the two sets of system equations. Finite element large amplitude limit-cycle flutter results at different uniform temperatures are obtained for a simply supported square panel and are compared with existing Galerkin/time integration and other finite element solutions. Effects of nonuniform temperature distributions, panel length-to-width ratios, and boundary conditions on flutter responses of rectangular and triangular panels are presented.

Xue, David Y.↗

Attitude stability of a spinning spacecraft during appendage deployment/retraction

The work presented is motivated by the need for a national satellite rescue policy, not the ad hoc policy now in place. In studying different approaches for a national policy, the issue of capture and stabilization of a tumbling spacecraft must be addressed. For a rescue mission involving a tumbling spacecraft, it may be advantageous to have a rescue vehicle which is compact and 'rigid' during the rendezvous/capture phase. After capture, passive stabilization techniques could be utilized as an efficient means of detumbling the resulting system (i.e., both the rescue vehicle and captures spacecraft). Since the rescue vehicle is initially compact and 'rigid,' significant passive stabilization through energy dissipation can only be achieved through the deployment of flexible appendages. Once stabilization is accomplished, retraction of the appendages before maneuvering the system to its final destination may also prove advantageous. It is therefore of paramount interest that we study the effect of appendage deployment/retraction on the attitude stability of a spacecraft. Particular interest should be paid to appendage retraction, since if this process is destabilizing, passive stabilization as proposed may not be useful. Over the past three decades, it has been an 'on-again-off-again affair' with the problem of spacecraft appendage deployment. In most instances, these studies have been numerical simulations of specific spacecraft configurations for which there were specific concerns. The primary focus of these studies was the behavior of the appendage during deployment; the effects of appendage retraction was considered only in one of these studies. What is missing in the literature is a thorough study of the effects of appendage deployment/retraction on the attitude stability of a spacecraft. This paper presents a rigorous analysis of the stability of a spinning spacecraft during the deployment or the retraction of an appendage. The analysis is simplified such that meaningful insights into the problem can be inferred; it is not overly simplified such that critical dynamical behavior is neglected. The system is analyzed assuming that the spacecraft hub is rigid. The appendage deployment mechanism is modeled as a point mass on a massless rod whose length undergoes prescribed changes. Simplified flexibility effects of the appendage are included. The system is examined for stability by linearizing the equations in terms of small deviations from steady, noninterfering coning motion. Routh's procedure for analyzing small deviations from steady motion in dynamical systems is utilized in the analysis. The system of equations are nondimensionalized to facilitate parametric studies. The results are presented in terms of a reduced number of nondimensional parameters so that some general conclusions may be drawn. Verification of the linear analysis is presented through numerical simulations of the complete nonlinear, nonautonomous, coupled equations.

Fitz-Coy, Norman↗

Optimization methods, flux conserving methods for steady state Navier-Stokes equation

Navier-Stokes equation as discretized by new flux conserving method proposed by Chang and Scott results in the system: vector F(vector x) = 0, where F is a vector valued function. The Optimization method we use is based on Quasi-Newton methods: given a nonlinear function vector F(vector x) = 0, we solve, Delta(vector x) = -BF(vector x), where Delta(vector x) is the correction term and B is the inverse Jacobian of F(x). Then, iteratively, vector(x(sub (i+1))) = vector(x (sub i)) + alpha.Delta(vector x(sub i)), where alpha is a line search correction term determined by a line search routine. We use the BFCG's update the Jacobian matrix B(sub k) at each iteration. It is well known that B(sub k) approaches B(*) at the solution X(*). This algorithm has several advantages over the Newton-Raphson method. For example, we do not need to calculate the Jacobian matrix at each iteration which is computationally very expensive.

Adeyeye, John↗

A deterministic particle method for one-dimensional reaction-diffusion equations

We derive a deterministic particle method for the solution of nonlinear reaction-diffusion equations in one spatial dimension. This deterministic method is an analog of a Monte Carlo method for the solution of these problems that has been previously investigated by the author. The deterministic method leads to the consideration of a system of ordinary differential equations for the positions of suitably defined particles. We then consider the time explicit and implicit methods for this system of ordinary differential equations and we study a Picard and Newton iteration for the solution of the implicit system. Next we solve numerically this system and study the discretization error both analytically and numerically. Numerical computation shows that this deterministic method is automatically adaptive to large gradients in the solution.

Mascagni, Michael↗

Textbook Multigrid Efficiency for Computational Fluid Dynamics Simulations

Considerable progress over the past thirty years has been made in the development of large-scale computational fluid dynamics (CFD) solvers for the Euler and Navier-Stokes equations. Computations are used routinely to design the cruise shapes of transport aircraft through complex-geometry simulations involving the solution of 25-100 million equations; in this arena the number of wind-tunnel tests for a new design has been substantially reduced. However, simulations of the entire flight envelope of the vehicle, including maximum lift, buffet onset, flutter, and control effectiveness have not been as successful in eliminating the reliance on wind-tunnel testing. These simulations involve unsteady flows with more separation and stronger shock waves than at cruise. The main reasons limiting further inroads of CFD into the design process are: (1) the reliability of turbulence models; and (2) the time and expense of the numerical simulation. Because of the prohibitive resolution requirements of direct simulations at high Reynolds numbers, transition and turbulence modeling is expected to remain an issue for the near term. The focus of this paper addresses the latter problem by attempting to attain optimal efficiencies in solving the governing equations. Typically current CFD codes based on the use of multigrid acceleration techniques and multistage Runge-Kutta time-stepping schemes are able to converge lift and drag values for cruise configurations within approximately 1000 residual evaluations. An optimally convergent method is defined as having textbook multigrid efficiency (TME), meaning the solutions to the governing system of equations are attained in a computational work which is a small (less than 10) multiple of the operation count in the discretized system of equations (residual equations). In this paper, a distributed relaxation approach to achieving TME for Reynolds-averaged Navier-Stokes (RNAS) equations are discussed along with the foundations that form the basis of this approach. Because the governing equations are a set of coupled nonlinear conservation equations with discontinuities (shocks, slip lines, etc.) and singularities (flow- or grid-induced), the difficulties are many. This paper summarizes recent progress towards the attainment of TME in basic CFD simulations.

Brandt, Achi↗

Generalized simulation technique for turbojet engine system analysis

A nonlinear analog simulation of a turbojet engine was developed. The purpose of the study was to establish simulation techniques applicable to propulsion system dynamics and controls research. A schematic model was derived from a physical description of a J85-13 turbojet engine. Basic conservation equations were applied to each component along with their individual performance characteristics to derive a mathematical representation. The simulation was mechanized on an analog computer. The simulation was verified in both steady-state and dynamic modes by comparing analytical results with experimental data obtained from tests performed at the Lewis Research Center with a J85-13 engine. In addition, comparison was also made with performance data obtained from the engine manufacturer. The comparisons established the validity of the simulation technique.

Seldner, K.↗

Analytical stability and simulation response study for a coupled two-body system

An analytical stability study and a digital simulation response study of two connected rigid bodies are documented. Relative rotation of the bodies at the connection is allowed, thereby providing a model suitable for studying system stability and response during a soft-dock regime. Provisions are made of a docking port axes alignment torque and a despin torque capability for encountering spinning payloads. Although the stability analysis is based on linearized equations, the digital simulation is based on nonlinear models.

Tao, K. M.↗

Computational methods in nonlinear structural and solid mechanics; Proceedings of the Symposium, Washington, D.C., October 6-8, 1980. Symposium sponsored by the George Washington University and NASA

Topics discussed include computational strategies for nonlinear problems in structural mechanics, time integration techniques and the numerical solution of nonlinear algebraic equations, material characterization and nonlinear fracture mechanics, nonlinear interaction problems, and seismic response and the nonlinear analysis of concrete structures. Also considered are nonlinear problems for nuclear reactors, crash dynamics and impact problems, nonlinear problems of fibrous composites and advanced nonlinear applications, and computerized symbolic manipulation and nonlinear analysis software systems.

Noor, A. K.↗

A Lagrange-D'Alembert formulation of the equations of motion of a helicopter carrying an externally suspended load

The exact nonlinear equations of motion are derived for a helicopter with an extenal load suspended by fore and aft, rigid-link cables. Lagrange's form of D'Alembert's principle is used. Ten degrees of freedom are necessary to represent the motion of this system in an inertial reference frame: six for the helicopter relative to inertial space and four for the load relative to the helicopter.

Weber, J. M.↗

Total energy-rate feedback for automatic glide-slope tracking during wind-shear penetration

Low-altitude wind shear is recognized as an infrequent but significant hazard to all aircraft during the take-off and landing phases of flight. A total energy-rate sensor was developed for measuring the specific total energy rate of an airplane with respect to the air mass. Control-system designs, both with and without energy-rate feedback, for the approach to landing of a transport airplane through a severe-wind-shear and gust environment are presented in order to evaluate this application of the sensor. A system model incorporates wind-shear-dynamics equations with the airplane equations of motion to permit analysis of the control systems under various wind-shear conditions. The control systems are designed using optimal-output feedback and are analyzed using frequency-domain control-theory techniques. Control-system performance is evaluated using a complete nonlinear simulation of the airplane combined with a severe-wind-shear and gust data package. This evaluation is concerned with control system stability and regulation capability only.

Belcastro, C. M.↗

A computational procedure for large rotational motions in multibody dynamics

A computational procedure suitable for the solution of equations of motion for multibody systems is presented. The present procedure adopts a differential partitioning of the translational motions and the rotational motions. The translational equations of motion are then treated by either a conventional explicit or implicit direct integration method. A principal feature of this procedure is a nonlinearly implicit algorithm for updating rotations via the Euler four-parameter representation. This procedure is applied to the rolling of a sphere through a specific trajectory, which shows that it yields robust solutions.

Park, K. C.↗

Galactic cosmic-ray mediation of a spherical solar wind flow. 1: The steady state cold gas hydrodynamical approximation

Realistic models of the outer heliosphere should consider that the interstellar cosmic-ray pressure becomes comparable to pressures in the solar wind at distances more than 100 AU from the Sun. The cosmic-ray pressure dynamically affects solar wind flow through deceleration. This effect, which occurs over a scale length of the order of the effective diffusion length at large radial distances, has important implications for cosmic-ray modulation and acceleration. As a first step toward solution of this nonlinear problem, a steady state numerical model was developed for a relatively cold spherical solar wind flow which encounters the confining isotropic pressure of the surrounding Galactic medium. This pressure is assumed to be dominated by energetic particles (Galactic cosmic rays). The system of equations, which are solved self-consistently, includes the relevant hydrodynamical equations for the solar wind flow and the spherical cosmic-ray transport equation. To avoid the closure parameter problem of the two-fluid model, the latter equation is solved for the energy-dependent cosmic-ray distribution function.

Le Roux, J. A.↗

Analysis Method for Inelastic, Adhesively Bonded Joints with Anisotropic Adherends

A one-dimensional analysis method for evaluating adhesively bonded joints composed of anisotropic adherends and adhesives with nonlinear material behavior is presented in the proposed paper. The strain and resulting stress field in a general, bonded joint overlap are determined by using a variable-step, finite-difference solution algorithm to iteratively solve a system of first-order differential equations. Applied loading is given by a system of combined extensional, bending, and shear forces that are applied to the edge of the joint overlap. Adherends are assumed to behave as linear, cylindrically bent plates using classical laminated plate theory that includes the effects of first-order transverse shear deformation. Using the deformation theory of plasticity and a modified von-Mises yield criterion, inelastic material behavior is modeled in the adhesive layer. Results for the proposed method are verified against previous results from the literature and shown to be in excellent agreement. An additional case that highlights the effects of transverse shear deformation between similar adherends is also presented.

Smeltzer, Stanley S., III↗

Detecting Moving Targets by Use of Soliton Resonances

A proposed method of detecting moving targets in scenes that include cluttered or noisy backgrounds is based on a soliton-resonance mathematical model. The model is derived from asymptotic solutions of the cubic Schroedinger equation for a one-dimensional system excited by a position-and-time-dependent externally applied potential. The cubic Schroedinger equation has general significance for time-dependent dispersive waves. It has been used to approximate several phenomena in classical as well as quantum physics, including modulated beams in nonlinear optics, and superfluids (in particular, Bose-Einstein condensates). In the proposed method, one would take advantage of resonant interactions between (1) a soliton excited by the position-and-time-dependent potential associated with a moving target and (2) eigen-solitons, which represent dispersive waves and are solutions of the cubic Schroedinger equation for a time-independent potential.

Zak, Michael↗

Nonlinear computation of wing-body-vertical tail-wake flows at low supersonic speeds

A numerical method based on the conservation form of the full potential equation has been applied to the problem of three-dimensional supersonic flows with embedded subsonic regions. The governing equation is cast in a nonorthogonal coordinate system, and the theory of characteristics is used to accurately monitor the type-dependent flow field. A conservative switching scheme is employed to transition from the supersonic marching procedure to a subsonic relaxation algorithm and vice versa. The newly developed computer program can handle arbitrary geometries with fuselage, wing, vertical tail and wake components at combined angle of attack and sideslip. Results are presented for a low supersonic Mach numbers flow over the Shuttle orbiter (including the OMS pods and vertical tail), and for flows over a realistic fighter type configuration. Comparisons with experimental data are shown to be in good agreement for various cases.

Szema, K.-Y.↗