Differential dynamic programming methods for solving bang-bang control problems.
Nonlinear bang-bang optimal control problems solution based on differential dynamic programming, noting use of Pontryagin adjoint variables
Jacobson, D. H.↗
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High-impact dynamic-response analysis of nonlinear structures
Program predicts expected deformations and stresses in nonlinear simple geometric structures subjected to high-impact loading. Technique is based on node-wise predictor-corrector approach and requires moderate computer storage and run time for most problems. Program extends to include physical and geometrical nonlinearities.
Gupta, K. K.↗
Solution of transient optimization problems by using an algorithm based on nonlinear programming
An algorithm is presented for solution of dynamic optimization problems which are nonlinear in the state variables and linear in the control variables. It is shown that the optimal control is bang-bang. A nominal bang-bang solution is found which satisfies the system equations and constraints, and influence functions are generated which check the optimality of the solution. Nonlinear optimization (gradient search) techniques are used to find the optimal solution. The algorithm is used to find a minimum time acceleration for a turbofan engine.
Teren, F.↗
Solution of transient optimization problems by using an algorithm based on nonlinear programming
A new algorithm is presented for solution of dynamic optimization problems which are nonlinear in the state variables and linear in the control variables. It is shown that the optimal control is bang-bang. A nominal bang-bang solution is found which satisfies the system equations and constraints, and influence functions are generated which check the optimality of the solution. Nonlinear optimization (gradient search) techniques are used to find the optimal solution. The algorithm is used to find a minimum time acceleration for a turbofan engine.
Teren, F.↗
Optimal control of nonlinear discrete time systems by mathematical programming
Nonlinear discrete time sampled systems optimal control by dynamic programming, with application to stochastic systems
Tabak, D.↗
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↗
Nonlinear structural crash dynamics analyses
Presented in this paper are the results of three nonlinear computer programs, KRASH, ACTION and DYCAST used to analyze the dynamic response of a twin-engine, low-wing airplane section subjected to a 8.38 m/s (27.5 ft/s) vertical impact velocity crash condition. This impact condition simulates the vertical sink rate in a shallow aircraft landing or takeoff accident. The three distinct analysis techniques for nonlinear dynamic response of aircraft structures are briefly examined and compared versus each other and the experimental data. The report contains brief descriptions of the three computer programs, the respective aircraft section mathematical models, pertinent data from the experimental test performed at NASA Langley, and a comparison of the analyses versus test results. Cost and accuracy comparisons between the three analyses are made to illustrate the possible uses of the different nonlinear programs and their future potential.
Hayduk, R. J.↗
A parallel trajectory optimization tool for aerospace plane guidance
A parallel trajectory optimization algorithm is being developed. One possible mission is to provide real-time, on-line guidance for the National Aerospace Plane. The algorithm solves a discrete-time problem via the augmented Lagrangian nonlinear programming algorithm. The algorithm exploits the dynamic programming structure of the problem to achieve parallelism in calculating cost functions, gradients, constraints, Jacobians, Hessian approximations, search directions, and merit functions. Special additions to the augmented Lagrangian algorithm achieve robust convergence, achieve (almost) superlinear local convergence, and deal with constraint curvature efficiency. The algorithm can handle control and state inequality constraints such as angle-of-attack and dynamic pressure constraints. Portions of the algorithm have been tested. The nonlinear programming core algorithm performs well on a variety of static test problems and on an orbit transfer problem. The parallel search direction algorithm can reduce wall clock time by a factor of 10 for this part of the computation task.
Psiaki, Mark L.↗
On a Class of Pursuit-Evasion Problems
Fixed time pursuit-evasion problems for dynamic systems solved with nonlinear programming algorithms
Jacob, J. P.↗
NASA automatic system for computer program documentation, volume 2
The DYNASOR 2 program is used for the dynamic nonlinear analysis of shells of revolution. The equations of motion of the shell are solved using Houbolt's numerical procedure. The displacements and stress resultants are determined for both symmetrical and asymmetrical loading conditions. Asymmetrical dynamic buckling can be investigated. Solutions can be obtained for highly nonlinear problems utilizing as many as five of the harmonics generated by SAMMSOR program. A restart capability allows the user to restart the program at a specified time. For Vol. 1, see N73-22129.
Simmons, D. B.↗
In-space technology flight experiments: Middeck 0-gravity Dynamics Experiment (MODE) and Middeck Active Control Experiment (MACE)
The topics addressed are covered in viewgraph form. The objective of the Middeck 0-gravity Dynamics Experiment (MODE) programs is to study gravity dependent nonlinearities associated with fluid slosh and truss structure dynamics. MODE provides a reusable facility for on-orbit dynamics testing of small scale test articles in the shirt sleeve environment on the Shuttle middeck. Flight program objective of Middeck Active Control Experiment (MACE) is to study gravity effects on the performance and stability of controlled structures.
Venneri, Samuel L.↗
Application of Quasi-Static Modal Analysis to an Orion Multi-Purpose Crew Vehicle Test
Bolted structural joints often exhibit load-dependent stiffness and energy dissipation that leads to nonlinear, amplitude dependent frequency and damping in the structure. As an alternative to direct integration of the nonlinear equations of motion, quasi-static modal analysis (QSMA) determines the dependence of frequency and damping on response amplitude using loading behavior from nonlinear static analyses. QSMA has previously been demonstrated to substantially reduce computational cost and maintain accuracy relative to full nonlinear dynamic simulation. This work explores the applicability of QSMA to a complex, large-scale aerospace structure. QSMA is employed to analyze a nonlinear model of test hardware developed to support the Orion Multi-Purpose Crew Vehicle program, which exhibited nonlinear behavior during dynamic testing at flight-like load levels. In addition to the extraction of amplitude-dependent frequency and damping curves, a Bouc-Wen hysteresis model was used in conjunction with the quasi-static results to develop nonlinear, uncoupled, time-domain modal equations of motion for the structure. Excellent agreement was observed between the reduced and full-order nonlinear models, encouraging future employment of QSMA to support accurate and efficient model reduction of structures with bolted joint nonlinearities.
QSMA↗
Development of a moderately sized finite element program for nonlinear structural analysis
AGGIE 1 is a computer program for predicting the linear and nonlinear, static and dynamic structural response of two- and three-dimensional continuum solids. The program is based on isoparametric finite elements and allows for 2-D plane stress, plane strain, and axisymmetric analyses and general 3-D analyses. Large strain kinematics is based on the total Lagrangian formulation. Materially nonlinear models include several elastic-plastic work-hardening models as well as an incompressible Mooney-Rivlin model. Included in this report is a brief description of the theoretical bases of the program, the material models used, the element library and the overall program organization. Instructions for data input preparation are given in detail. Several sample problems are given along with the required program input and program generated solutions.
Haisler, W. E.↗
The NASTRAN computer program for structural analysis.
Discussion of a large NASA-sponsored digital computer program for static and dynamic analysis of structures with linear or nonlinear material properties. The program fits to perform buckling analysis, vibration mode analysis of conservative or damped systems, frequency response analysis, and transient response analysis on the IBM 360, UNIVAC 1108, and CDC 6600 computers. It also provides automatic generation of several types of loads such as gravity loads and thermal strain loads, plots of deformed and nondeformed structures, and the choice of alternate analysis methods such as direct or modal formulations of dynamic problems. The program is intended primarily for large problems involving hundreds of thousands of degrees of freedom. A flexible Executive System is provided to facilitate the addition of new functional capabilities to the program.
Macneal, R. H.↗
Parallel and vector computation for stochastic optimal control applications
A general method for parallel and vector numerical solutions of stochastic dynamic programming problems is described for optimal control of general nonlinear, continuous time, multibody dynamical systems, perturbed by Poisson as well as Gaussian random white noise. Possible applications include lumped flight dynamics models for uncertain environments, such as large scale and background random atmospheric fluctuations. The numerical formulation is highly suitable for a vector multiprocessor or vectorizing supercomputer, and results exhibit high processor efficiency and numerical stability. Advanced computing techniques, data structures, and hardware help alleviate Bellman's curse of dimensionality in dynamic programming computations.
Hanson, F. B.↗
Algorithms and software for nonlinear structural dynamics
The objective of this research is to develop efficient methods for explicit time integration in nonlinear structural dynamics for computers which utilize both concurrency and vectorization. As a framework for these studies, the program WHAMS, which is described in Explicit Algorithms for the Nonlinear Dynamics of Shells (T. Belytschko, J. I. Lin, and C.-S. Tsay, Computer Methods in Applied Mechanics and Engineering, Vol. 42, 1984, pp 225 to 251), is used. There are two factors which make the development of efficient concurrent explicit time integration programs a challenge in a structural dynamics program: (1) the need for a variety of element types, which complicates the scheduling-allocation problem; and (2) the need for different time steps in different parts of the mesh, which is here called mixed delta t integration, so that a few stiff elements do not reduce the time steps throughout the mesh.
Belytschko, Ted↗
Generic Kalman Filter Software
The Generic Kalman Filter (GKF) software provides a standard basis for the development of application-specific Kalman-filter programs. Historically, Kalman filters have been implemented by customized programs that must be written, coded, and debugged anew for each unique application, then tested and tuned with simulated or actual measurement data. Total development times for typical Kalman-filter application programs have ranged from months to weeks. The GKF software can simplify the development process and reduce the development time by eliminating the need to re-create the fundamental implementation of the Kalman filter for each new application. The GKF software is written in the ANSI C programming language. It contains a generic Kalman-filter-development directory that, in turn, contains a code for a generic Kalman filter function; more specifically, it contains a generically designed and generically coded implementation of linear, linearized, and extended Kalman filtering algorithms, including algorithms for state- and covariance-update and -propagation functions. The mathematical theory that underlies the algorithms is well known and has been reported extensively in the open technical literature. Also contained in the directory are a header file that defines generic Kalman-filter data structures and prototype functions and template versions of application-specific subfunction and calling navigation/estimation routine code and headers. Once the user has provided a calling routine and the required application-specific subfunctions, the application-specific Kalman-filter software can be compiled and executed immediately. During execution, the generic Kalman-filter function is called from a higher-level navigation or estimation routine that preprocesses measurement data and post-processes output data. The generic Kalman-filter function uses the aforementioned data structures and five implementation- specific subfunctions, which have been developed by the user on the basis of the aforementioned templates. The GKF software can be used to develop many different types of unfactorized Kalman filters. A developer can choose to implement either a linearized or an extended Kalman filter algorithm, without having to modify the GKF software. Control dynamics can be taken into account or neglected in the filter-dynamics model. Filter programs developed by use of the GKF software can be made to propagate equations of motion for linear or nonlinear dynamical systems that are deterministic or stochastic. In addition, filter programs can be made to operate in user-selectable "covariance analysis" and "propagation-only" modes that are useful in design and development stages.
Lisano, Michael E., II↗
Dynamic Discharge Arc Driver
A computer program using nonlinear RLC circuit analysis was developed to accurately model the electrical discharge performance of the Ames 1-MJ energy storage and arc-driver system. Solutions of circuit parameters are compared with experimental circuit data and related to shock speed measurements. Computer analysis led to the concept of a Dynamic Discharge Arc Driver (DDAD) capable of increasing the range of operation of shock-driven facilities. Utilization of mass addition of the driver gas offers a unique means of improving driver performance. Mass addition acts to increase the arc resistance, which results in better electrical circuit damping with more efficient Joule heating, producing stronger shock waves. Preliminary tests resulted in an increase in shock Mach number from 34 to 39 in air at an initial pressure of 2.5 torr.
Dannenberg, R. E.↗