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At least 577 records · Page 32

A Linear Programming Approach to Routing Control in Networks of Constrained Nonlinear Positive Systems with Concave Flow Rates

We consider control design for positive compartmental systems in which each compartment's outflow rate is described by a concave function of the amount of material in the compartment.We address the problem of determining the routing of material between compartments to satisfy time-varying state constraints while ensuring that material reaches its intended destination over a finite time horizon. We give sufficient conditions for the existence of a time-varying state-dependent routing strategy which ensures that the closed-loop system satisfies basic network properties of positivity, conservation and interconnection while ensuring that capacity constraints are satisfied, when possible, or adjusted if a solution cannot be found. These conditions are formulated as a linear programming problem. Instances of this linear programming problem can be solved iteratively to generate a solution to the finite horizon routing problem. Results are given for the application of this control design method to an example problem. Key words: linear programming; control of networks; positive systems; controller constraints and structure.

Positive Systems↗

Parallel processors and nonlinear structural dynamics algorithms and software

A nonlinear structural dynamics finite element program was developed to run on a shared memory multiprocessor with pipeline processors. The program, WHAMS, was used as a framework for this work. The program employs explicit time integration and has the capability to handle both the nonlinear material behavior and large displacement response of 3-D structures. The elasto-plastic material model uses an isotropic strain hardening law which is input as a piecewise linear function. Geometric nonlinearities are handled by a corotational formulation in which a coordinate system is embedded at the integration point of each element. Currently, the program has an element library consisting of a beam element based on Euler-Bernoulli theory and trianglar and quadrilateral plate element based on Mindlin theory.

Belytschko, Ted↗

LOGISTIC FUNCTION PROFILE FIT: A least-squares program for fitting interface profiles to an extended logistic function

The extended logistic function provides a physically reasonable description of interfaces such as depth profiles or line scans of surface topological or compositional features. It describes these interfaces with the minimum number of parameters, namely, position, width, and asymmetry. Logistic Function Profile Fit (LFPF) is a robust, least-squares fitting program in which the nonlinear extended logistic function is linearized by a Taylor series expansion (equivalent to a Newton-Raphson approach) with no apparent introduction of bias in the analysis. The program provides reliable confidence limits for the parameters when systematic errors are minimal and provides a display of the residuals from the fit for the detection of systematic errors. The program will aid researchers in applying ASTM E1636-10, 'Standard practice for analytically describing sputter-depth-profile and linescan-profile data by an extended logistic function,' and may also prove useful in applying ISO 18516: 2006, 'Surface chemical analysis-Auger electron spectroscopy and x-ray photoelectron spectroscopy-determination of lateral resolution.' Examples are given of LFPF fits to a secondary ion mass spectrometry depth profile, an Auger surface line scan, and synthetic data generated to exhibit known systematic errors for examining the significance of such errors to the extrapolation of partial profiles.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗

Crash simulation of composite and aluminum helicopter fuselages using a finite-element program

This paper describes a mathematical investigation of the crash-impact responses of an all-composite helicopter cockpit section incorporating an energy absorbing concept and one of conventional aluminum construction, using the Grumman DYCAST finite-element nonlinear structural dynamics computer program. The overall objective of this initial investigation was to explore the application of DYCAST to the design of future helicopter structures. The specific purposes are to assess the value of the finite-element code as a crashworthiness design analysis tool, and to compare the responses of the two fuselage sections. The results indicate that the finite-element simulation is a powerful analysis tool, providing sufficient detail to evaluate individual structural components, and that the crashworthiness of an all-composite cockpit section could be enhanced with energy-absorbing concepts

Winter, R.↗

Supersonic second order analysis and optimization program user's manual

Approximate nonlinear inviscid theoretical techniques for predicting aerodynamic characteristics and surface pressures for relatively slender vehicles at supersonic and moderate hypersonic speeds were developed. Emphasis was placed on approaches that would be responsive to conceptual configuration design level of effort. Second order small disturbance theory was utilized to meet this objective. Numerical codes were developed for analysis and design of relatively general three dimensional geometries. Results from the computations indicate good agreement with experimental results for a variety of wing, body, and wing-body shapes. Case computational time of one minute on a CDC 176 are typical for practical aircraft arrangement.

Clever, W. C.↗

Coupled bending-torsion steady-state response of pretwisted, nonuniform rotating beams using a transfer-matrix method

Using the Newtonian method, the equations of motion are developed for the coupled bending-torsion steady-state response of beams rotating at constant angular velocity in a fixed plane. The resulting equations are valid to first order strain-displacement relationships for a long beam with all other nonlinear terms retained. In addition, the equations are valid for beams with the mass centroidal axis offset (eccentric) from the elastic axis, nonuniform mass and section properties, and variable twist. The solution of these coupled, nonlinear, nonhomogeneous, differential equations is obtained by modifying a Hunter linear second-order transfer-matrix solution procedure to solve the nonlinear differential equations and programming the solution for a desk-top personal computer. The modified transfer-matrix method was verified by comparing the solution for a rotating beam with a geometric, nonlinear, finite-element computer code solution; and for a simple rotating beam problem, the modified method demonstrated a significant advantage over the finite-element solution in accuracy, ease of solution, and actual computer processing time required to effect a solution.

Gray, Carl E., Jr.↗

Aircraft equilibrium spin characteristics

Program provides analytic solutions to nonlinear equations of motion describing spin conditions. Stability characteristics also are determined. Program can be used to study effects of aerodynamic and inertial parameters on spin and could be modified to compute equilibrium conditions for steady maneuvers. Program is written in FORTRAN IV for batch execution on CYBER 173.

Adams, W. M., Jr.↗

Parameter estimation and error analysis in environmental modeling and computation

A method for the estimation of parameters and error analysis in the development of nonlinear modeling for environmental impact assessment studies is presented. The modular computer program can interactively fit different nonlinear models to the same set of data, dynamically changing the error structure associated with observed values. Parameter estimation techniques and sequential estimation algorithms employed in parameter identification and model selection are first discussed. Then, least-square parameter estimation procedures are formulated, utilizing differential or integrated equations, and are used to define a model for association of error with experimentally observed data.

Kalmaz, E. E.↗

A computer program to automatically generate state equations and macro-models

A computer program, PROSE, that produces nonlinear state equations from a simple topological description of an electrical or mechanical network is described. Unnecessary states are also automatically eliminated, so that a simplified terminal circuit model is obtained. The program also prints out the eigenvalues of a linearized system and the sensitivities of the eigenvalue of largest magnitude.

Garrett, S. J.↗

Elevated temperature crack growth

The problem of crack growth in hot path components such as combustor liners is complicated by several practical and theoretical considerations. The loading environment of such components involves high temperature levels and gradients that lead to considerations such as thermal stresses, crack closure, hold time, inelastic strains (both time dependent and independent), and Thermal Mechanical Fatigue (TMF). In general, a good understanding of the influence of these factors on crack growth was not obtained. At the same time, several nonlinear fracture mechanics parameters were suggested for such applications; however, most of the proposed methods were not tested for broad applications such as required for hot section components. It was the purpose of this program to evaluate proposed nonlinear methods by performing a thorough experimental and analytical study. The results illustrated that much progress was made in developing nonlinear methods.

Kim, K. S.↗

Nonlinear sonic boom analysis including the asymmetric effects

A numerical program is developed which takes into account the nonlinear effects of high Mach number, the entropy change across the shock, the entropy and enthalpy variations in the atmospheric layer and the gravitational effect. The program differs from the existing ones by accounting for non-axisymmetric terms. The asymmetry can be caused by the geometry of the body, the lift and also the fact that the variations in the atmospheric layer are two-dimensional. Numerical results demonstrate that the influence of these asymmetric effects tends to lower the pressure signature.

Ferri, A.↗

User's manual for GAMNAS: Geometric and Material Nonlinear Analysis of Structures

GAMNAS (Geometric and Material Nonlinear Analysis of Structures) is a two dimensional finite-element stress analysis program. Options include linear, geometric nonlinear, material nonlinear, and combined geometric and material nonlinear analysis. The theory, organization, and use of GAMNAS are described. Required input data and results for several sample problems are included.

Whitcomb, J. D.↗

Flexural fatigue life prediction of closed hat-section using materially nonlinear axial fatigue characteristics

Straight or curved hat-section members are often used as structural stiffeners in aircraft. For instance, they are employed as stiffeners for the dorsal skin as well as in the aerial refueling adjacent area structure in F-106 aircraft. The flanges of the hat-section are connected to the aircraft skin. Thus, the portion of the skin closing the hat-section interacts with the section itself when resisting the stresses due to service loads. The flexural fatigue life of such a closed section is estimated using materially nonlinear axial fatigue characteristics. It should be recognized that when a structural shape is subjected to bending, the fatigue life at the neutral axis is infinity since the normal stresses are zero at that location. Conversely, the fatigue life at the extreme fibers where the normal bending stresses are maximum can be expected to be finite. Thus, different fatigue life estimates can be visualized at various distances from the neural axis. The problem becomes compounded further when significant portions away from the neutral axis are stressed into plastic range. A theoretical analysis of the closed hat-section subjected to flexural cyclic loading is first conducted. The axial fatigue characteristics together with the related axial fatigue life formula and its inverted form given by Manson and Muralidharan are adopted for an aluminum alloy used in aircraft construction. A closed-form expression for predicting the flexural fatigue life is then derived for the closed hat-section including materially nonlinear action. A computer program is written to conduct a study of the variables such as the thicknesses of the hat-section and the skin, and the type of alloy used. The study has provided a fundamental understanding of the flexural fatigue life characteristics of a practical structural component used in aircraft when materially nonlinear action is present.

Razzaq, Zia↗

Numerical method for solution of systems of non-stationary spatially one-dimensional nonlinear differential equations

A computational scheme and a standard program is proposed for solving systems of nonstationary spatially one-dimensional nonlinear differential equations using Newton's method. The proposed scheme is universal in its applicability and its reduces to a minimum the work of programming. The program is written in the FORTRAN language and can be used without change on electronic computers of type YeS and BESM-6. The standard program described permits the identification of nonstationary (or stationary) solutions to systems of spatially one-dimensional nonlinear (or linear) partial differential equations. The proposed method may be used to solve a series of geophysical problems which take chemical reactions, diffusion, and heat conductivity into account, to evaluate nonstationary thermal fields in two-dimensional structures when in one of the geometrical directions it can take a small number of discrete levels, and to solve problems in nonstationary gas dynamics.

Morozov, S. K.↗

CIRCAL - On-line circuit design.

On-line nonlinear circuit design, discussing computer program for evaluating performance resulting from modifications

COMPUTER METHOD↗

Multispectrum measurements of spectral line parameters including temperature dependences of N2- and self-broadened half-width coefficients in the region of the v9 band of 12C2H6

Ethane is a prominent contributor to the spectrum of Titan, particularly in the region of the v9 band at 12μm. A multispectrum nonlinear least squares fitting program was applied to laboratory spectra of ethane to measure accurate positions, absolute intensities, N2- and selfbroadened half- width coefficients and their temperature dependences for a large number transitions. These measurements include several pQ and rQ sub-bands (and other sub-bands such as pP, rR) in the v9 fundamental band of 12C2H6 centered near 822 cm-1. Positions were measured for 2958 transitions and intensities for 3771 transitions. N2- and self-broadened half-width coefficients were determined for over 1700 transitions while temperature dependence exponents were retrieved for over 1350 of those transitions. Of these, many measurements (mostly line positions and intensities) belong to the v9+v4-v4 hot band, v9+2v4-2v4 hot band, 13C12CH6 v9 band and unidentified transitions. Forty-three high resolution (0.0016-0.005 cm-1) infrared laboratory absorption spectra recorded at temperatures between 148 and 298 K were fitted simultaneously to retrieve these parameters. Forty-one of these spectra were obtained in the temperature range of 211-298 K using the Bruker IFS 120HR interferometer located at the Pacific Northwest National Laboratory (PNNL) in Richland, Washington. Two additional spectra at 148 K were recorded using a new temperature stabilized cryogenic cell designed to work inside the sample compartment of the high resolution Bruker IFS 125HR interferometer of the Jet Propulsion Laboratory (JPL) in Pasadena California. The specialized cooling cell developed at Connecticut College and capable of achieving gas sample temperatures down to 70 K with a temperature stability and uniformity of better than ±0.05 K was employed to record the 148 K spectra. Constraints to intensity ratios, doublet separations, half-width coefficients and their temperature dependence exponents were required to determine these parameters for each of the two torsional split components. Similar to N2- and self-broadened half-width coefficients, their temperature dependence exponents were also found to follow distinctively different patterns. The variations of the observed half-width coefficients and their temperature dependences with respect to J, K quantum numbers are discussed. Because of the high density of torsionally split spectral lines, hot-band ransitions as well as blends, it was not possible to retrieve any information on the small pressure-induced shift coefficients. Present results are compared to other available measurements.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Discarding Information from Previous Iterations in an Optimal Way To Solve the Coupled Cluster Amplitude Equations

The direct inversion of the iterative subspace (DIIS) convergence acceleration algorithm is used in most electronic structure programs to solve the nonlinear coupled cluster amplitude equations. When the DIIS algorithm is used, the storage of previous trial vectors may become a bottleneck and the discarding of trial vectors may lead to a degradation of the convergence or even divergence. Here, we discuss an alternative way of storing information from trial vectors where only the last three trial vectors are needed to maintain the convergence of the full set of previous trial vectors, and which requires only minor modifications of an existing DIIS code

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗