SEARCH · Search NASA

Results for “Mathematical Methods”

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.

SourceResearch connectionFrom yearThrough year

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 703 records · Page 39

All sources NASA NTRS DOE OSTI

NASA NTRS1974

Thermal analysis of M551 experiment for materials processing in space

Heat flow in a disc due to moving heat generated by electron beam was studied analytically. Computer programs based on the finite-element method were developed for the analysis of two and three dimensional mathematical models. The limited experimental data were compared with the analytical results, and factors which had influence on heat flow in the disc were studied. The computer programs were modified to consider the effects of metal melting and solidification as well as radiation. Temperature dependency of thermophysical properties was also considered.

Muraki, T.↗

NASA NTRS1975

Intermittent bonding for high toughness/high strength composites

An analysis of toughness and strength in intermittently bonded brittle filament/brittle matrix composites is presented that shows the importance of the coating material in achieving high toughness properties. Some observations are made on methods of measuring the components of toughness in composites. Both a mathematical model and experimental results are incorporated into the discussion.

Atkins, A. G.↗

NASA NTRS1979

Computation of aerodynamic interference effects on oscillating airfoils with controls in ventilated subsonic wind tunnels

Lift interference effects are discussed based on Bland's (1968) integral equation. A mathematical existence theory is utilized for which convergence of the numerical method has been proved for general (square-integrable) downwashes. Airloads are computed using orthogonal airfoil polynomial pairs in conjunction with a collocation method which is numerically equivalent to Galerkin's method and complex least squares. Convergence exhibits exponentially decreasing error with the number n of collocation points for smooth downwashes, whereas errors are proportional to 1/n for discontinuous downwashes. The latter can be reduced to 1/n to the m+1 power with mth-order Richardson extrapolation (by using m = 2, hundredfold error reductions were obtained with only a 13% increase of computer time). Numerical results are presented showing acoustic resonance, as well as the effect of Mach number, ventilation, height-to-chord ratio, and mode shape on wind-tunnel interference. Excellent agreement with experiment is obtained in steady flow, and good agreement is obtained for unsteady flow.

Fromme, J. A.↗

NASA NTRS1981

On the convergence of unsteady generalized aerodynamic forces

Variations in generalized forces calculated by different computer programs are traced to improper mathematical modeling techniques. Comparisons of generalized forces calculated by three theoretical methods are presented to illustrate difficulties involved in obtaining prediction convergence for increasing wave number. Use of a sufficiently dense chordwise paneling arrangement, in finite panel methods, results in predictions that are essentially identical to predictions of converged solutions. Procedural modifications are suggested for application in finite panel methods to increase prediction accuracy and reduce computer usage costs.

Rowe, W. S.↗

NASA NTRS1982

A Closer Look at Track/Train Dynamics

Report describes analytical approach to question of operational safety for six-axle locomotives. Essential mathematical elements are locomotive model with corresponding data on suspension characteristics, method of track-defect characterization, and quantitative measures for characterizing operational safety.

Marcotte, P. P.↗

NASA NTRS1982

The 1981 NASA/ASEE Summer Faculty Fellowship Program: Research reports

Research reports related to spacecraft industry technological advances, requirements, and applications were considered. Some of the topic areas addressed were: (1) Fabrication, evaluation, and use of high performance composites and ceramics, (2) antenna designs, (3) electronics and microcomputer applications and mathematical modeling and programming techniques, (4) design, fabrication, and failure detection methods for structural materials, components, and total systems, and (5) chemical studies of bindary organic mixtures and polymer synthesis. Space environment parameters were also discussed.

Karr, G. R.↗

NASA NTRS1982

Mathematical enhancement of data from scientific measuring instruments

The accuracy of any physical measurement is limited by the instruments performing it. The proposed activities of this grant are related to the study of and application of mathematical techniques of deconvolution. Two techniques are being investigated: an iterative method and a function continuation Fourier method. This final status report describes the work performed during the period July 1 to December 31, 1982.

Ioup, J. W.↗

NASA NTRS1983

Kinematic equations for resolved-rate control of an industrial robot arm

An operator can use kinematic, resolved-rate equations to dynamically control a robot arm by watching its response to commanded inputs. Known resolved-rate equations for the control of a particular six-degree-of-freedom industrial robot arm and proceeds to simplify the equations for faster computations are derived. Methods for controlling the robot arm in regions which normally cause mathematical singularities in the resolved-rate equations are discussed.

Barker, L. K.↗

NASA NTRS1984

NASA/Howard University Large Space Structures Institute

Basic research on the engineering behavior of large space structures is presented. Methods of structural analysis, control, and optimization of large flexible systems are examined. Topics of investigation include the Load Correction Method (LCM) modeling technique, stabilization of flexible bodies by feedback control, mathematical refinement of analysis equations, optimization of the design of structural components, deployment dynamics, and the use of microprocessors in attitude and shape control of large space structures. Information on key personnel, budgeting, support plans and conferences is included.

Broome, T. H., Jr.↗

NASA NTRS1984

Computation of solar magnetic fields from photospheric observations

The observational difficulties of obtaining the magnetic field distribution in the chromosphere and corona of the sun has led to methods of extending photospheric magnetic mesurements into the solar atmosphere by mathematical procedures. A new approach to this problem presented here is that a constant alpha force-free field can be uniquely determined from the tangential components of the measured photospheric flux alone. The vector magnetographs now provide measurements of both the solar photospheric tangential and the longitudinal magnetic field. This paper presents derivations for the computation of the solar magnetic field from these type of measurements. The fields considered are assumed to be a constant alpha force-free fields or equivalent, producing vanishing Lorentz forces. Consequently, magnetic field lines and currents are related by a constant and hence show an identical distribution. The magnetic field above simple solar regions are described from the solution of the field equations.

Hannakam, L.↗

NASA NTRS1986

A three dimensional calculation of elastic equilibrium for composite materials

A compact scheme is applied to three-dimensional elasticity problems for composite materials, involving simple geometries. The mathematical aspects of this approach are discussed, in particular the iteration method. A vector processor code implementing the compact scheme is presented, and several numerical experiments are summarized.

Lustman, Liviu R.↗

NASA NTRS1987

Theory of collapse and protostar formation

Interstellar clouds must increase in density by a factor of more than 10 to the 20th in order to form stars. Because observations of the phases intermediate between dense interstellar clouds and pre-main-sequence stars are difficult, theoretical solutions presently provide the primary means for exploring the collapse phase of protostellar formation. The mathematical formulation of the protostellar collapse problem is presented, and various methods employed in solving the equations are outlined. This tutorial emphasizes the numerical approach to the study of the nonlinear time-dependent evolution of collapsing interstellar clouds, including self-gravitation, rotation, and radiative transfer. Results are summarized for the restricted cases of spherical and axisymmetric symmetry, as well as for fully three-dimensional evolutions, and briefly compared to observations of star formation.

Boss, A. P.↗

NASA NTRS1988

A three dimensional calculation of elastic equilibrium for composite materials

Lustman, Liviu R.↗

NASA NTRS1989

Finite element simulations of thermosolutal convection in vertical solidification of binary alloys

Dendritic vertical solidification of a binary alloy is modeled using the finite element method to assess the effect of thermosolutal convection in macrosegregation. The mathematical model assumes steady-state solidification with a planar, undeformable surface defined by the dendrite tips and the eutectic isotherm. The dendritic region is assumed to advance at a constant solidification velocity v. The stability of the modeled system has been investigated and nonlinear calculations performed that show finger-like convection when the system is unstable. Results for lead-tin alloys show that when the system is unstable, convection is only significant in the uppermost part of the mush and is entirely driven by convection in the bulk fluid.

Heinrich, J. C.↗

NASA NTRS1992

Navier-Stokes analyses of flows over slender airframes

An account is given of the current development status of Navier-Stokes algorithms for the analysis of 3D viscous flows over slender airframes, emphasizing the design and analysis of practical configurations. The pacing items of the numerical algorithms used encompass grid generation, spatial and temporal differencing, and transition and turbulence modeling. Attention is given to the high angle-of-attack prediction capability of the various methods whose results are compared with experimental data; it is in that regime that Navier-Stokes methods surpass the prediction capabilities of flow solvers based on simpler mathematical models.

Thomas, James L.↗

NASA NTRS2000

Validation of a "Kane's Dynamics" Model for the Active Rack Isolation System

Many microgravity space-science experiments require vibratory acceleration levels unachievable without active isolation. The Boeing Corporation's Active Rack Isolation System (ARIS) employs a novel combination of magnetic actuation and mechanical linkages, to address these isolation requirements on the International Space Station (ISS). ARIS provides isolation at the rack (international Standard Payload Rack, or ISPR) level. Effective model-based vibration isolation requires (1) an isolation device, (2) an adequate dynamic (i.e., mathematical) model of that isolator, and (3) a suitable, corresponding controller, ARIS provides the ISS response to the first requirement. In November 1999, the authors presented a response to the second ("A 'Kane's Dynamics' model for the Active Rack Isolation System", Hampton and Beech) intended to facilitate an optimal-controls approach to the third. This paper documents the validation of that high-fidelity dynamic model of ARIS. As before, this model contains the full actuator dynamics, however, the umbilical models are not included in this presentation. The validation of this dynamics model was achieved by utilizing two Commercial Off the Shelf (COTS) software tools: Deneb's ENVISION, and Online Dynamics' AUTOLEV. ENVISION is a robotics software package developed for the automotive industry that employs 3-dimensional (3-D) Computer Aided Design (CAD) models to facilitate both forward and inverse kinematics analyses. AUTOLEV is a DOS based interpreter that is designed in general to solve vector based mathematical problems and specifically to solve Dynamics problems using Kane's method.

Beech, Geoffrey S.↗

NASA NTRS2001

The Use of Non-Standard Devices in Finite Element Analysis

A general mathematical description of the response behavior of thin-skin pneumatic envelopes and many other membrane and cable structures produces under-constrained systems that pose severe difficulties to analysis. These systems are mobile, and the general mathematical description exposes the mobility. Yet the response behavior of special under-constrained structures under special loadings can be accurately predicted using a constrained mathematical description. The static response behavior of systems that are infinitesimally mobile, such as a non-slack membrane subtended from a rigid or elastic boundary frame, can be easily analyzed using such general mathematical description as afforded by the non-linear, finite element method using an implicit solution scheme if the incremental uploading is guided through a suitable path. Similarly, if such structures are assembled with structural lack of fit that provides suitable self-stress, then dynamic response behavior can be predicted by the non-linear, finite element method and an implicit solution scheme. An explicit solution scheme is available for evolution problems. Such scheme can be used via the method of dynamic relaxation to obtain the solution to a static problem. In some sense, pneumatic envelopes and many other compliant structures can be said to have destiny under a specified loading system. What that means to the analyst is that what happens on the evolution path of the solution is irrelevant as long as equilibrium is achieved at destiny under full load and that the equilibrium is stable in the vicinity of that load. The purpose of this paper is to alert practitioners to the fact that non-standard procedures in finite element analysis are useful and can be legitimate although they burden their users with the requirement to use special caution. Some interesting findings that are useful to the US Scientific Balloon Program and that could not be obtained without non-standard techniques are presented.

Schur, Willi W.↗

NASA NTRS1995

Scientific Visualization and Computational Science: Natural Partners

Scientific visualization is developing rapidly, stimulated by computational science, which is gaining acceptance as a third alternative to theory and experiment. Computational science is based on numerical simulations of mathematical models derived from theory. But each individual simulation is like a hypothetical experiment; initial conditions are specified, and the result is a record of the observed conditions. Experiments can be simulated for situations that can not really be created or controlled. Results impossible to measure can be computed.. Even for observable values, computed samples are typically much denser. Numerical simulations also extend scientific exploration where the mathematics is analytically intractable. Numerical simulations are used to study phenomena from subatomic to intergalactic scales and from abstract mathematical structures to pragmatic engineering of everyday objects. But computational science methods would be almost useless without visualization. The obvious reason is that the huge amounts of data produced require the high bandwidth of the human visual system, and interactivity adds to the power. Visualization systems also provide a single context for all the activities involved from debugging the simulations, to exploring the data, to communicating the results. Most of the presentations today have their roots in image processing, where the fundamental task is: Given an image, extract information about the scene. Visualization has developed from computer graphics, and the inverse task: Given a scene description, make an image. Visualization extends the graphics paradigm by expanding the possible input. The goal is still to produce images; the difficulty is that the input is not a scene description displayable by standard graphics methods. Visualization techniques must either transform the data into a scene description or extend graphics techniques to display this odd input. Computational science is a fertile field for visualization research because the results vary so widely and include things that have no known appearance. The amount of data creates additional challenges for both hardware and software systems. Evaluations of visualization should ultimately reflect the insight gained into the scientific phenomena. So making good visualizations requires consideration of characteristics of the user and the purpose of the visualization. Knowledge about human perception and graphic design is also relevant. It is this breadth of knowledge that stimulates proposals for multidisciplinary visualization teams and intelligent visualization assistant software. Visualization is an immature field, but computational science is stimulating research on a broad front.

Uselton, Samuel P.↗