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Equations of motion of shell are solved using Houbolt's numerical procedure with nonlinear terms being moved to right-hand side of equilibrium equations and treated as generalized loads. Program was written in FORTRAN IV for IBM 360 or CDC 6000 series computers.
The reliability of a complex system was optimized by a new approach for implementing the sequential unconstrained minimization technique (SUMT) with the aid of Hooke and Jeeves pattern search and heuristic programming. Two optimization problems were considered. In the first, the system reliability was maximized subject to a nonlinear weight constraint. In the second, the weight of the system was minimized without violating the requirements of the minimal system reliability and the minimum reliability for each component. The sensitivities of the system reliability and that of the system weight to the reliability of each component were determined under optimal conditions.
A supersonic wing design concept that overcomes the problems associated with nonlinear inviscid pressure distribution is presented together with a summary of the supporting theoretical and experimental development program. The key design feature is a conical panel supporting a controlled supercritical conical camber (SC3) crossflow expansion and recompression which permits lift on the upper surface to be obtained without producing an adverse pressure gradient or crossflow shock wave strong enough to separate the boundary layer. The role of aerodynamics in the design implementation is discussed, as are the concept development, the initial design validation on a fabricated and tested SC3 design, and the body and canard interaction effect. The design and testing of an isolated wing with a planform and thickness distribution representative of a practical application are described. Wind-tunnel results show that significant performance gains can be obtained for fighter aircraft using this concept.
The CMC fluid mechanics program system was developed to transmit the theoretical solution of finite element numerical solution methodology, applied to nonlinear field problems into a versatile computer code for comprehensive flow field analysis. Data procedures for the CMC 3 dimensional Parabolic Navier-Stokes (PNS) algorithm are presented. General data procedures a juncture corner flow standard test case data deck is described. A listing of the data deck and an explanation of grid generation methodology are presented. Tabulations of all commands and variables available to the user are described. These are in alphabetical order with cross reference numbers which refer to storage addresses.
The objectives of this program were: to verify the model of off schedule compressor variable geometry in the T700 turboshaft engine nonlinear model; to evaluate the use of the pseudo-random binary noise (PRBN) technique for obtaining engine frequency response data; and to design a high performance power turbine speed governor using modern control methods. Reduction of T700 engine test data generated at NASA-Lewis indicated that the off schedule variable geometry effects were accurate as modeled. Analysis also showed that the PRBN technique combined with the maximum likelihood model identification method produced a Bode frequency response that was as accurate as the response obtained from standard sinewave testing methods. The frequency response verified the accuracy of linear models consisting of engine partial derivatives and used for design. A power turbine governor was designed using the Linear Quadratic Regulator (LQR) method of full state feedback control. A Kalman filter observer was used to estimate helicopter main rotor blade velocity. Compared to the baseline T700 power turbine speed governor, the LQR governor reduced droop up to 25 percent for a 490 shaft horsepower transient in 0.1 sec simulating a wind gust, and up to 85 percent for a 700 shaft horsepower transient in 0.5 sec simulating a large collective pitch angle transient.
Applications for unsteady aerodynamics analysis in this report are: (1) aeroelastic: blade flutter and forced vibration; (2) aeroacoustic: noise generation; (3) vibration and noise control; and (4) effects of unsteadiness on performance. This requires that the numerical simulations and analytical modeling be accurate and efficient and contain realistic operating conditions and arbitrary modes of unsteady excitation. The assumptions of this application contend that: (1) turbulence and transition can be modeled with the Reynolds averaged and using Navier-Stokes equations; (2) 'attached' flow with high Reynolds number will require thin-layer Navier-Stokes equations, or inviscid/viscid interaction analyses; (3) small-amplitude unsteady excitations will need nonlinear steady and linearized unsteady analyses; and (4) Re to infinity will concern inviscid flow. Several computer programs (LINFLO, CLT, UNSVIS, AND SFLOW-IVI) are utilized for these analyses. Results and computerized grid examples are shown. This report was given during NASA LeRC Workshop on Forced Response in Turbomachinery in August of 1993.
Improving aerodynamic models for adverse loss-of-control conditions in flight is an area being researched under the NASA Aviation Safety Program. Aerodynamic models appropriate for loss of control conditions require a more general mathematical representation to predict nonlinear unsteady behaviors. As more general aerodynamic models are studied that include nonlinear higher order effects, the possibility of measurements that confound aerodynamic and structural responses are probable. In this study an initial step is taken to look at including structural flexibility in analysis of rigid-body forced-oscillation testing that accounts for dynamic rig, sting and balance flexibility. Because of the significant testing required and associated costs in a general study, it makes sense to capitalize on low cost analytical methods where possible, especially where structural flexibility can be accounted for by a low cost method. This paper provides an initial look at using linear lifting surface theory applied to rigid-body aircraft roll forced-oscillation tests.
This study concentrates on results from probabilistic analysis and numerical simulation tools to identify parameter sensitivities and assess surrogate model suitability for a novel inflatable airlock concept, specifically the Non-Axisymmetric Inflatable Pressure Structure (NAIPS) under NASA's Minimalistic Advanced Softgoods Hatch (MASH) Program. The current studies extended the demonstration of probabilistic analysis tools to identify parameter sensitivities by: incorporating nonlinear material load-strain property curves and orthotropic representation of the fabric; and exploring the use of surrogate models to facilitate rapid evaluations as new information becomes available, as well as enable optimizations. The airlock model has been simplified to focus on the end dome section. Brief overviews of the finite element model and associated surrogate models are provided along with the probabilistic sensitivity analysis approaches. Responses of interest include the sensitivities of various loads in the structural elements of the NAIPS to material properties, cord lengths, inflation pressure and friction between softgoods components. The use of surrogate models was explored to facilitate rapid sensitivity evaluations as parameter ranges change. The completion of the sensitivity studies improved understanding of the dependence of load responses to several uncertain parameters and confidence in the ability to use surrogate models to represent the finite element simulations.
This paper describes an electrooptical flight-deflection measurement system (FDMS) developed for use on highly-maneuverable-aircraft-technology (HiMAT) RPV flight research program. The FDMS provides in-flight measurements of the aircraft structural deflections and magnetic-tape recordings for automated data processing. The capabilities and limitations, requirements for installation on an aircraft, analytical considerations, and typical flight data acquired from the HiMAT research program are examined. The flight data indicate that the background light is the major obstacle to acquiring high-quality data and that the relationship between the target displacement and the output of the FDMS is nonlinear; however, the nonlinear effects can be minimized with judicious planning of the installation of the FDMS on the aircraft. Excellent flight deflection data were obtained from both the HiMAT and X-29 A flight research program with very little data lost as a result of encounters with severe background light.
Here, a recently developed high-order implicit shock tracking (HOIST) framework for resolving discontinuous solutions of inviscid, steady conservation laws is extended to the unsteady case. Central to the framework is an optimization problem which simultaneously computes a discontinuity-aligned mesh and the corresponding high-order approximation to the flow, which provides nonlinear stabilization and a high-order approximation to the solution. This work extends the implicit shock tracking framework to the case of unsteady conservation laws using a method of lines discretization via a diagonally implicit Runge-Kutta method by “solving a steady problem at each timestep”. We formulate and solve an optimization problem that produces a feature-aligned mesh and solution at each Runge-Kutta stage of each timestep, and advance this solution in time by standard Runge-Kutta update formulas. A Rankine-Hugoniot based prediction of the shock location together with a high-order, untangling mesh smoothing procedure provides a high-quality initial guess for the optimization problem at each time, which results in rapid convergence of the sequential quadratic programing (SQP) optimization solver. This method is shown to deliver highly accurate solutions on coarse, high-order discretizations without nonlinear stabilization and recover the design accuracy of the Runge-Kutta scheme. We demonstrate this framework on a series of inviscid, unsteady conservation laws in both one- and two- dimensions. We also verify that our method is able to recover the design order of accuracy of our time integrator in the presence of a strong discontinuity.
This paper discusses the mathematical existence and the numerically-correct identification of linear and nonlinear aerodynamic impulse response functions. Differences between continuous-time and discrete-time system theories, which permit the identification and efficient use of these functions, will be detailed. Important input/output definitions and the concept of linear and nonlinear systems with memory will also be discussed. It will be shown that indicial (step or steady) responses (such as Wagner's function), forced harmonic responses (such as Tbeodorsen's function or those from doublet lattice theory), and responses to random inputs (such as gusts) can all be obtained from an aerodynamic impulse response function. This paper establishes the aerodynamic impulse response function as the most fundamental, and, therefore, the most computationally efficient, aerodynamic function that can be extracted from any given discrete-time, aerodynamic system. The results presented in this paper help to unify the understanding of classical two-dimensional continuous-time theories with modem three-dimensional, discrete-time theories. First, the method is applied to the nonlinear viscous Burger's equation as an example. Next the method is applied to a three-dimensional aeroelastic model using the CAP-TSD (Computational Aeroelasticity Program - Transonic Small Disturbance) code and then to a two-dimensional model using the CFL3D Navier-Stokes code. Comparisons of accuracy and computational cost savings are presented. Because of its mathematical generality, an important attribute of this methodology is that it is applicable to a wide range of nonlinear, discrete-time problems.
This paper discusses the mathematical existence and the numerically-correct identification of linear and nonlinear aerodynamic impulse response functions. Differences between continuous-time and discrete-time system theories, which permit the identification and efficient use of these functions, will be detailed. Important input/output definitions and the concept of linear and nonlinear systems with memory will also be discussed. It will be shown that indicial (step or steady) responses (such as Wagner's function), forced harmonic responses (such as Theodorsen's function or those from doublet lattice theory), and responses to random inputs (such as gusts) can all be obtained from an aerodynamic impulse response function. This paper establishes the aerodynamic impulse response function as the most fundamental, and, therefore, the most computationally efficient, aerodynamic function that can be extracted from any given discrete-time, aerodynamic system. The results presented in this paper help to unify the understanding of classical two-dimensional continuous-time theories with modern three-dimensional, discrete-time theories. First, the method is applied to the nonlinear viscous Burger's equation as an example. Next the method is applied to a three-dimensional aeroelastic model using the CAP-TSD (Computational Aeroelasticity Program - Transonic Small Disturbance) code and then to a two-dimensional model using the CFL3D Navier-Stokes code. Comparisons of accuracy and computational cost savings are presented. Because of its mathematical generality, an important attribute of this methodology is that it is applicable to a wide range of nonlinear, discrete-time problems.
The use of linear rigid formats in COSMIC NASTRAN without DMAP procedures for the analysis of nonlinear propeller structures is described. Approaches for updating geometry and applying follower forces for incremental loading are demonstrated. The COSMIC NASTRAN rigid formats and other independent finite element programs are compared. The comparisons include results from the four approaches for updating the geometry using RIGID FORMAT 1, RIGID FORMATS 4 and 13, MARC and MSC/NASTRAN. It is shown that user friendly updating approaches can be used to predict the large displacements and instability of these nonlinear structures. The approaches are easily implemented by the user and predict conservative results.
Here we present a new algorithm for infinite-dimensional optimization with general constraints, called ALESQP. In short, ALESQP is an augmented Lagrangian method that penalizes inequality constraints and solves equality-constrained nonlinear optimization subproblems at every iteration. The subproblems are solved using a matrix-free trust-region sequential quadratic programming (SQP) method that takes advantage of iterative, i.e., inexact linear solvers, and is suitable for large-scale applications. A key feature of ALESQP is a constraint decomposition strategy that allows it to exploit problem-specific variable scalings and inner products. We analyze convergence of ALESQP under different assumptions. We show that strong accumulation points are stationary. Consequently, in finite dimensions ALESQP converges to a stationary point. In infinite dimensions we establish that weak accumulation points are feasible in many practical situations. Under additional assumptions we show that weak accumulation points are stationary. We present several infinite-dimensional examples where ALESQP shows remarkable discretization-independent performance in all of its iterative components, requiring a modest number of iterations to meet constraint tolerances at the level of machine precision. Also, we demonstrate a fully matrix-free solution of an infinite-dimensional problem with nonlinear inequality constraints.
Topics include: Simulation Testing of Embedded Flight Software; Improved Indentation Test for Measuring Nonlinear Elasticity; Ultraviolet-Absorption Spectroscopic Biofilm Monitor; Electronic Tongue for Quantitation of Contaminants in Water; Radar for Measuring Soil Moisture Under Vegetation; Modular Wireless Data-Acquisition and Control System; Microwave System for Detecting Ice on Aircraft; Routing Algorithm Exploits Spatial Relations; Two-Finger EKG Method of Detecting Evasive Responses; Updated System-Availability and Resource-Allocation Program; Routines for Computing Pressure Drops in Venturis; Software for Fault-Tolerant Matrix Multiplication; Reproducible Growth of High-Quality Cubic-SiC Layers; Nonlinear Thermoelastic Model for SMAs and SMA Hybrid Composites; Liquid-Crystal Thermosets, a New Generation of High-Performance Liquid-Crystal Polymers; Formulations for Stronger Solid Oxide Fuel-Cell Electrolytes; Simulation of Hazards and Poses for a Rocker-Bogie Rover; Autonomous Formation Flight; Expandable Purge Chambers Would Protect Cryogenic Fittings; Wavy-Planform Helicopter Blades Make Less Noise; Miniature Robotic Spacecraft for Inspecting Other Spacecraft; Miniature Ring-Shaped Peristaltic Pump; Compact Plasma Accelerator; Improved Electrohydraulic Linear Actuators; A Software Architecture for Semiautonomous Robot Control; Fabrication of Channels for Nanobiotechnological Devices; Improved Thin, Flexible Heat Pipes; Miniature Radioisotope Thermoelectric Power Cubes; Permanent Sequestration of Emitted Gases in the Form of Clathrate Hydrates; Electrochemical, H2O2-Boosted Catalytic Oxidation System; Electrokinetic In Situ Treatment of Metal-Contaminated Soil; Pumping Liquid Oxygen by Use of Pulsed Magnetic Fields; Magnetocaloric Pumping of Liquid Oxygen; Tailoring Ion-Thruster Grid Apertures for Greater Efficiency; and Lidar for Guidance of a Spacecraft or Exploratory Robot.
The algorithms that comprise the Variational Trajectory Optimization Tool Set (VTOTS) package are briefly described. The VTOTS is a software package for solving nonlinear constrained optimal control problems from a wide range of engineering and scientific disciplines. The VTOTS package was specifically designed to minimize the amount of user programming; in fact, for problems that may be expressed in terms of analytical functions, the user needs only to define the problem in terms of symbolic variables. This version of the VTOTS does not support tabular data; thus, problems must be expressed in terms of analytical functions. The VTOTS package consists of two methods for solving nonlinear optimal control problems: a time-domain finite-element algorithm and a multiple shooting algorithm. These two algorithms, under the VTOTS package, may be run independently or jointly. The finite-element algorithm generates approximate solutions, whereas the shooting algorithm provides a more accurate solution to the optimization problem. A user's manual, some examples with results, and a brief description of the individual subroutines are included.
A series of load tests was conducted on the HiMAT tailored composite wing. Coupon tests were also run on a series of unbalanced laminates, including the ply configuration of the wing, the purpose of which was to compare the measured and predicted behavior of unbalanced laminates, including - in the case of the wing - a comparison between the behavior of the full scale structure and coupon tests. Both linear and nonlinear finite element (NASTRAN) analyses were carried out on the wing. Both linear and nonlinear point-stress analyses were performed on the coupons. All test articles were instrumented with strain gages, and wing deflections measured. The leading and trailing edges were found to have no effect on the response of the wing to applied loads. A decrease in the stiffness of the wing box was evident over the 27-test program. The measured load-strain behavior of the wing was found to be linear, in contrast to coupon tests of the same laminate, which were nonlinear. A linear NASTRAN analysis of the wing generally correlated more favorably with measurements than did a nonlinear analysis. An examination of the predicted deflections in the wing root region revealed an anomalous behavior of the structural model that cannot be explained. Both hysteresis and creep appear to be less significant in the wing tests than in the corresponding laminate coupon tests.
Predictive mathematical models are a cornerstone of science and engineering. Yet selecting, calibrating, and validating said science-based models often remains an art in practice. Model-based design of experiments (MBDoE) provides a systematic framework to maximize information gain from experiments while minimizing time and resource costs. But MBDoE remains limited to niche application areas, in part because practitioners must integrate expertise in statistics, computational optimization, and modeling. To help reduce this barrier, we introduce Pyomo.DOE, an open-source package for MBDoE. Pyomo.DOE uses a nonlinear sensitivity analysis code k_aug to quickly approximate the Fisher information matrix and leverages a new stochastic programming abstraction. We demonstrate Pyomo.DOE with the first application of MBDoE to fixed-bed breakthrough experiments, which highlights the power of Pyomo.DOE to quantify the value of experimental modifications a priori for large-scale partial differential-algebraic equation (PDAE) models. Here we also provide a mathematical primer on MBDoE targeted at general chemical engineers.