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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 595 records · Page 33
All sourcesNASA NTRSDOE OSTI
NASA NTRS1974

Discrete optimal control approach to a four-dimensional guidance problem near terminal areas

Description of a computer-oriented technique to generate the necessary control inputs to guide an aircraft in a given time from a given initial state to a prescribed final state subject to the constraints on airspeed, acceleration, and pitch and bank angles of the aircraft. A discrete-time mathematical model requiring five state variables and three control variables is obtained, assuming steady wind and zero sideslip. The guidance problem is posed as a discrete nonlinear optimal control problem with a cost functional of Bolza form. A solution technique for the control problem is investigated, and numerical examples are presented. It is believed that this approach should prove to be useful in automated air traffic control schemes near large terminal areas.

Nagarajan, N.↗
NASA NTRS1975

Algorithm for nonlinear stationary Navier-Stokes problem

Results of applications of algorithm suggest that it has potential application to variety of related fluid flow problems, such as presently intractable separation problem of aerodynamics. Details of mathematical development, as well as computation of explicit error estimates, are available.

Gabrielsen, R. E.↗
NASA NTRS1974

The value of improved (ERS) information based on domestic distribution effects of U.S. agriculture crops

The value of improving information for forecasting future crop harvests was investigated. Emphasis was placed upon establishing practical evaluation procedures firmly based in economic theory. The analysis was applied to the case of U.S. domestic wheat consumption. Estimates for a cost of storage function and a demand function for wheat were calculated. A model of market determinations of wheat inventories was developed for inventory adjustment. The carry-over horizon is computed by the solution of a nonlinear programming problem, and related variables such as spot and future price at each stage are determined. The model is adaptable to other markets. Results are shown to depend critically on the accuracy of current and proposed measurement techniques. The quantitative results are presented parametrically, in terms of various possible values of current and future accuracies.

Bradford, D. F.↗
NASA NTRS1974

U.S. National Congress of Applied Mechanics, 7th, University of Colorado, Boulder, Colo., June 3-7, 1974, Proceedings

A series of experimental, theoretical, and review papers dealing with various aspects of applied mechanics, including structural analysis, mathematical methods, and fluid dynamics. Some of the topics covered are: the direct formulation of two-dimensional mechanics problems, the mechanical aspects of athletics, Laplace's tidal equations, cochlear mechanics, dynamic constitutive equations, optical techniques for the determination of displacement and strain fields, chemical and biochemical problems involving nonlinear diffusion processes, thermal stresses, the rotating rod viscometer, finite-element methods in plasticity, ships of minimum resistance, and wide-band random vibration of structures. Individual items are announced in this issue.

Source record↗
NASA NTRS1976

Four-dimensional guidance problem with control delays

This paper, assuming steady wind and zero sideslip, presents a discrete-time mathematical model to obtain a control law and three-dimensional flight path to guide an aircraft in a given time from a given initial state (position, velocity and heading) to a prescribed final state subject to the constraints on airspeed acceleration, and pitch and bank angles of the aircraft. For ease in implementing the control law, the control inputs are assumed to be delayed and are applied in a sequential fashion. The guidance problem is formulated as a discrete nonlinear optimal control problem with time delays in dynamics and a cost functional of Bolza form. With a quadratic penalty function to handle terminal constraints on velocity and heading, a solution technique to the control problem based on conjugate gradient algorithm is investigated. Numerical examples are presented to illustrate the applicability of this approach to solution of a terminal area guidance problem in an automated air traffic control environment.

Nagarajan, N.↗
NASA NTRS1975

Parameter adaptive estimation of random processes

This paper is concerned with the parameter adaptive least squares estimation of random processes. The main result is a general representation theorem for the conditional expectation of a random variable on a product probability space. Using this theorem along with the general likelihood ratio expression, the least squares estimate of the process is found in terms of the parameter conditioned estimates. The stochastic differential for the a posteriori probability and the stochastic differential equation for the a posteriori density are found by using simple stochastic calculus on the representations obtained. The results are specialized to the case when the parameter has a discrete distribution. The results can be used to construct an implementable recursive estimator for certain types of nonlinear filtering problems. This is illustrated by some simple examples.

Caglayan, A. K.↗
NASA NTRS1979

Generation of linear dynamic models from a digital nonlinear simulation

The results and methodology used to derive linear models from a nonlinear simulation are presented. It is shown that averaged positive and negative perturbations in the state variables can reduce numerical errors in finite difference, partial derivative approximations and, in the control inputs, can better approximate the system response in both directions about the operating point. Both explicit and implicit formulations are addressed. Linear models are derived for the F 100 engine, and comparisons of transients are made with the nonlinear simulation. The problem of startup transients in the nonlinear simulation in making these comparisons is addressed. Also, reduction of the linear models is investigated using the modal and normal techniques. Reduced-order models of the F 100 are derived and compared with the full-state models.

Daniele, C. J.↗
NASA NTRS1978

Research on an augmented Lagrangian penalty function algorithm for nonlinear programming

The augmented Lagrangian (ALAG) Penalty Function Algorithm for optimizing nonlinear mathematical models is discussed. The mathematical models of interest are deterministic in nature and finite dimensional optimization is assumed. A detailed review of penalty function techniques in general and the ALAG technique in particular is presented. Numerical experiments are conducted utilizing a number of nonlinear optimization problems to identify an efficient ALAG Penalty Function Technique for computer implementation.

Frair, L.↗
NASA NTRS1979

Nonlinear singularly perturbed optimal control problems with singular arcs

Singular perturbation techniques are studied for dealing with singular arc problems by analyzing a relatively low-order but otherwise general system. This system encompasses many flight mechanic problems including Goddard's problem and a version of the minimum time-to-climb problem. Boundary layer solutions are constructed which are stable and reach the outer solution in a finite time. A uniformly valid composite solution is then formed from the reduced and boundary layer solutions. The value of the approximate solution is that it is relatively easy to obtain and does not involve singular arcs. To illustrate the utility of the results, the technique is used to obtain an approximate solution of a simplified version of the aircraft minimum time-to-climb problem.

Ardema, M. D.↗
NASA NTRS1982

Profiles of electrified drops and bubbles

Axisymmetric equilibrium shapes of conducting drops and bubbles, (1) pendant or sessile on one face of a circular parallel-plate capacitor or (2) free and surface-charged, are found by solving simultaneously the free boundary problem consisting of the augmented Young-Laplace equation for surface shape and the Laplace equation for electrostatic field, given the surface potential. The problem is nonlinear and the method is a finite element algorithm employing Newton iteration, a modified frontal solver, and triangular as well as quadrilateral tessellations of the domain exterior to the drop in order to facilitate refined analysis of sharply curved drop tips seen in experiments. The stability limit predicted by this computer-aided theoretical analysis agrees well with experiments.

Basaran, O. A.↗
NASA NTRS1982

Utilization of normal mode initial conditions for detecting errors in the dynamics part of primitive equation global models

When a global atmospheric basic state has constant angular velocity and its temperature varies with altitude only, there exist normal mode solutions to the linearized global primitive equations. The use of these normal modes, which have known behavior in time, is superior to the use of the Rossby-Haurwitz wave as initial conditions for detecting errors in the dynamics part of primitive equation global models. With these initial conditions, integration through only one time step is sufficient to detect many formulation and coding errors. Other tests are still required for detecting problems of nonlinear instability and conservation of integral properties, however.

Chao, W. C.↗
NASA NTRS1982

Nonlinear optimization with linear constraints using a projection method

Nonlinear optimization problems that are encountered in science and industry are examined. A method of projecting the gradient vector onto a set of linear contraints is developed, and a program that uses this method is presented. The algorithm that generates this projection matrix is based on the Gram-Schmidt method and overcomes some of the objections to the Rosen projection method.

Fox, T.↗
NASA NTRS1982

Calculation of exact vibration modes for plane grillages by the dynamic stiffness method

A dynamic stiffness method is developed for the calculation of the exact modal parameters for plane grillages which consist of straight and uniform beams with coincident elastic and inertial axes. Elementary bending-torsion beam theory is utilized, and bending translation is restricted to one direction. The exact bending-torsion dynamic stiffness matrix is obtained for a straight and uniform beam element with coincident elastic and inertial axes. The element stiffness matrices are assembled using the standard procedure of the static stiffness method to form the dynamic stiffness matrix of the complete grillage. The exact natural frequencies, mode shapes, and generalized masses of the grillage are then calculated by solving a nonlinear eigenvalue problem based on the dynamic stiffness matrix. The exact modal solutions for an example grillage are calculated and compared with the approximate solutions obtained by using the finite element method.

Hallauer, W. L., Jr.↗
NASA NTRS1983

A refined finite element for vibration analysis of twisted blades based on beam theory

A finite element method of discretizing beam segments of pretwisted rotating blades is presented. Employing the matrix displacement method, stiffness and mass properties are developed from basic mechanics of a pretwisted beam theory. By introducing the proper displacement functions, the effect of rotor blade rotational motion on the stiffness matrix is obtained systematically from the kinetic energy expression. Comparing with other beam elements the derivation of this element is more fundamental. This allows one to apply the same approach to more complicated problems including nonlinear effects or complex dynamic motions. Illustrative examples are given comparing numerical results with available data and other numerical solutions from rotating and nonrotating force fields. These examples show that accurate prediction of vibration frequencies for pretwisted blades can be obtained by employing a quite modest number of degrees of freedom.

Sisto, F.↗
NASA NTRS1983

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.↗
NASA NTRS1983

Hybrid perturbation/Bubnov-Galerkin technique for nonlinear thermal analysis

A two step hybrid analysis technique to predict the nonlinear steady state temperature distribution in structures and solids is presented. The technique is based on the regular perturbation expansion and the classical Bubnov-Galerkin approximation. The functions are obtained by using the regular perturbation method. These functions are selected as coordinate functions and the classical Bubnov-Galerkin technique is used to compute their amplitudes. The potential of the proposed hybrid technique for the solution of nonlinear thermal problems is discussed. The effectiveness of this technique is demonstrated by the effects of conduction, convection, and radiation modes of heat transfer. It is indicated that the hybrid technique overcomes the two major drawbacks of the classical techniques: (1) the requirement of using a small parameter in the regular perturbation method; and (2) the arbitrariness in the choice of the coordinate functions in the Bubnov-Galerkin technique. The proposed technique extends the range of applicability of the regular perturbation method and enhances the effectiveness of the Bubnov-Galerkin technique.

Noor, A. K.↗
NASA NTRS1982

The CMC/3DPNS computer program for prediction of three-dimension, subsonic, turbulent aerodynamic juncture region flow. Volume 2: Users' manual

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.

Manhardt, P. D.↗