SEARCH · Search NASA

Results for “Applied Mathematics”

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 433 records · Page 24

All sources NASA NTRS DOE OSTI

NASA NTRS1983

Stress studies in EFG

Stress distributions were calculated for a creep law to predict a rate of plastic deformation. The expected reduction in stresses is obtained. Improved schemes for calculating growth system temperature distributions were evaluated. Temperature field modeling examined the possibility of using horizontal temperature gradients to influence stress distribution in ribbon. The defect structure of 10 cm wide ribbon grown in the cartridge system was examined. A new feature is identified from an examination of cross sectional micrographs. It consists of high density dislocation bands extending through the ribbon thickness. A four point bending apparatus was constructed for high temperature study of the creep response of silicon, to be used to generate defects for comparison with as grown defects in ribbon. The feasibility of laser interferometric techniques for sheet residual stress distribution measurement is examined. The mathematical formalism for calculating residual stress from changes in surface topology caused by an applied stress in a rectangular specimen was developed, and the system for laser interferometric measurement to obtain surface topology data was tested on CZ silicon.

Source record↗

NASA NTRS1985

Residue-Measure Model-Reduction Technique

New residue-measure criterion simplifies mathematical models of feedback-control systems. Although originally developed for flight control, approach applied to any flexible structural system involving dominantly linear dynamics.

Gluch, D. P.↗

NASA NTRS1984

In Search of a Visual-cortical Describing Function: a Summary of Work in Progress

The thrust of the present work is to explore the utility of using a sum of sinusoids (seven or more) to obtain an evoked response and, furthermore, to see if the response is sensitive to changes in cognitive processing. Within the field of automatic control system technology, a mathematical input/output relationship for a sinusoidally stimulated nonlinear system is defined as describing function. Applying this technology, sum of sines inputs to yield describing functions for the visual-cortical response have been designed. What follows is a description of the method used to obtain visual-cortical describing functions. A number of measurement system redesigns were necessary to achieve the desired frequency resolution. Results that guided and came out of the redesigns are presented. Preliminary results of stimulus parameter effects (average intensity and depth of modulation) are also shown.

Junker, A. M.↗

NASA NTRS1986

A simple nonlinear joint model

Hertzian contact theory is applied to a butt joint with specially mismatched bearing surfaces to devise a simple mathematical model of nonlinear axial force-displacement behavior in jointed members. Normalized tangent stiffness-force plots, for several values of a joint imperfection parameter, are presented for the sample case of solid structural members of circular section. The results illustrate the potential problem of high joint compliance at low axial-force levels, as well as the generally desirable stiffening and linearizing effects of preload. A nonlinear oscillator problem based on the static model is also formulated and solved to illustrate the effect of amplitude on natural frequency. As expected, natural frequency is low when amplitude is small. The results call attention to the important roles that tight tolerances and preload are expected to play in the design and fabrication of deployable and erectable truss-type space structures.

Fichter, W. B.↗

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 NTRS1988

Recursive forward dynamics for multiple robot arms moving a common task object

Recursive forward dynamics algorithms are developed for an arbitrary number of robot arms moving a commonly held object. The multiarm forward dynamics problem is to find the angular accelerations at the joints and the contact forces that the arms impart to the task object. The problem also involves finding the acceleration of this object. The multiarm forward dynamics solutions provide a thorough physical and mathematical understanding of the way several arms behave in response to a set of applied joint moments. Such an understanding simplifies and guides the subsequent control design and experimentation process. The forward dynamics algorithms also provide the necessary analytical foundation for conducting analysis and simulation studies. The multiarm algorithms are based on the filtering and smoothing approach recently advanced for single-arm dynamics, and they can be built up modularly from the single-arm algorithms. The algorithms compute recursively the joint-angle accelerations, the contact forces, and the task-object accelerations. Algorithms are also developed to evaluate in closed form the linear transformations from the active joint moments to the joint-angle accelerations, to the task-object accelerations., and to the task-object contact forces. A possible computing architecture is presented as a precursor to a more complete investigation of the computational performance of the dynamics algorithms.

Rodriguez, G.↗

NASA NTRS1988

Euler/Navier-Stokes zonal scheme with applications to separated and isolated-vortex flows

An Euler/Navier-Stokes zonal scheme with boundary-layer compatibility conditions is developed to economically compute separated and vortex flows. The scheme is based on dividing the flow region into zones, where different levels of mathematical approximations of the governing equations are used in each zone. The scheme is applied to two specific problems: the two dimensional flow over a blunt leading-edge plate and the quasi-axisymmetric flow of an isolated vortex core. In the first problem, the computational domain is divided into inner and outer zones where the Navier-Stokes and Euler equations are used, respectively. On the downstream boundary of the computational domain, boundary-layer compatibility conditions are used. In the second problem, boundary-layer-like equations for slender, compressible, vortex flows are developed. A compatibility condition has been used to ensure consistency of the boundary and initial conditions. The outer boundary conditions of the flow are derived from Euler equations for a stream surface.

Kandil, Osama A.↗

NASA NTRS1988

A three dimensional calculation of elastic equilibrium for composite materials

Lustman, Liviu R.↗

NASA NTRS1989

More On Scattering From Dirty Mirrors

Mathematical model of scattering expanded from visible to include infrared wavelengths. Paper describes extension of mathematical model of scattering from mirror slightly contaminated with particulates. Original version of model applies to scattering at visible wavelengths. Updated version used to predict scattering at wavelengths from visible through infrared, based on measurements in visible spectrum.

Wang, Yaujen↗

NASA NTRS1989

Recursive forward dynamics for multiple robot arms moving a common task object

Recursive forward dynamics algorithms are developed and presented for an arbitrary number of robot arms moving a commonly held object. The multiarm forward dynamics problem is to find the angular accelerations at the joints and the contact forces that the arms impart to the task object. The problem also involves finding the acceleration of this object. The multiarm forward dynamics solutions provide a thorough physical and mathematical understanding of the way several arms behave in response to a set of applied joint moments. Such an understanding simplifies and guides the subsequent control design and experimentation process. The forward dynamics algorithms also provide the necessary analytical foundation for conducting analysis and simulation studies. The multiarm algorithms are based on the filtering and smoothing approach recently advanced for single-arm dynamics, and they can be built up modularly from the single-arm algorithms. The algorithms compute recursively the joint angle accelerations, the contact forces, and the task-object accelerations. Algorithms are also developed to evaluate in closed form the linear transformations from the active joint moments to the joint angle accelerations, to the task object accelerations, and to the task-object contact forces. A possible computing architecture is presented as a precursor to a more complete investigation of the computational performance of the dynamics algorithms.

Rodriguez, Guillermo↗

NASA NTRS1991

An analytical and experimental study to investigate flutter suppression via piezoelectric actuation

The objective was to analytically and experimentally study the capabilities of adaptive material plate actuators for suppressing flutter. The validity of analytical modeling techniques for piezoelectric materials was also investigated. Piezoelectrics are materials which are characterized by their ability to produce voltage when subjected to a mechanical strain. The converse piezoelectric effect can be utilized to actuate a structure by applying a voltage. For this investigation, a two degree of freedom wind tunnel model was designed, analyzed, and tested. The model consisted of a rigid airfoil and a flexible mount system which permitted a translational and a rotational degree of freedom. It was designed such that flutter was encounted within the testing envelope of the wind tunnel. Actuators, made of piezoelectric material were affixed to leaf springs of the mount system. Each degree of freedom was controlled by a separate leaf spring. Command signals, applied to the piezoelectric actuators, exerted control over the damping and stiffness properties. A mathematical aeroservoelastic model was constructed using finite element methods, laminated plate theory, and aeroelastic analysis tools. Plant characteristics were determined from this model and verified by open loop experimental tests. A flutter suppression control law was designed and implemented on a digital control computer. Closed loop flutter testing was conducted. The experimental results represent the first time that adaptive materials have been used to actively suppress flutter. It demonstrates that small, carefully placed actuating plates can be used effectively to control aeroelastic response.

Heeg, Jennifer↗

NASA NTRS1991

Transient motion of thick anisotropic plates

Analyses are developed for the response of anisotropic plate strips to a transient load. The load is taken in the form of a line load of normal stress on the surface or within the body of the strip. The characteristic free vibrational modes of the strip are derived and used to derive the secular equation for this case in closed form and to isolate the mathematical conditions for symmetric and antisymmetric wave mode propagation in completely separate terms. The applied loads are expanded in terms of these normal modes and the response of the plate is obtained by superposition of the appropriate components. Material systems of higher symmetry are contained implicitly in the analysis.

Nayfeh, Adnan H.↗

NASA NTRS1993

Analytical and experimental investigation of flutter suppression by piezoelectric actuation

The objective of this research was to analytically and experimentally study the capabilities of piezoelectric plate actuators for suppressing flutter. Piezoelectric materials are characterized by their ability to produce voltage when subjected to a mechanical strain. The converse piezoelectric effect can be utilized to actuate a structure by applying a voltage. For this investigation, a two-degree-of-freedom wind tunnel model was designed, analyzed, and tested. The model consisted of a rigid wing and a flexible mount system that permitted a translational and a rotational degree of freedom. The model was designed such that flutter was encountered within the testing envelope of the wind tunnel. Actuators made of piezoelectric material were affixed to leaf springs of the mount system. Command signals, applied to the piezoelectric actuators, exerted control over the damping and stiffness properties. A mathematical aeroservoelastic model was constructed by using finite element methods, laminated plate theory, and aeroelastic analysis tools. Plant characteristics were determined from this model and verified by open loop experimental tests. A flutter suppression control law was designed and implemented on a digital control computer. Closed loop flutter testing was conducted. The experimental results represent the first time that adaptive materials have been used to actively suppress flutter. They demonstrate that small, carefully placed actuating plates can be used effectively to control aeroelastic response.

Heeg, Jennifer↗

NASA NTRS2004

A Six-Node Curved Triangular Element and a Four-Node Quadrilateral Element for Analysis of Laminated Composite Aerospace Structures

Mathematical development and some computed results are presented for Mindlin plate and shell elements, suitable for analysis of laminated composite and sandwich structures. These elements use the conventional 3 (plate) or 5 (shell) nodal degrees of freedom, have no communicable mechanisms, have no spurious shear energy (no shear locking), have no spurious membrane energy (no membrane locking) and do not require arbitrary reduction of out-of-plane shear moduli or under-integration. Artificial out-of-plane rotational stiffnesses are added at the element level to avoid convergence problems or singularity due to flat spots in shells. This report discusses a 6-node curved triangular element and a 4-node quadrilateral element. Findings show that in regular rectangular meshes, the Martin-Breiner 6-node triangular curved shell (MB6) is approximately equivalent to the conventional 8-node quadrilateral with integration. The 4-node quadrilateral (MB4) has very good accuracy for a 4-node element, and may be preferred in vibration analysis because of narrower bandwidth. The mathematical developments used in these elements, those discussed in the seven appendices, have been applied to elements with 3, 4, 6, and 10 nodes and can be applied to other nodal configurations.

Martin, C. Wayne↗

NASA NTRS2008

Nonstandard Analysis and Jump Conditions for Converging Shock Waves

Nonstandard analysis is an area of modern mathematics which studies abstract number systems containing both infinitesimal and infinite numbers. This article applies nonstandard analysis to derive jump conditions for one-dimensional, converging shock waves in a compressible, inviscid, perfect gas. It is assumed that the shock thickness occurs on an infinitesimal interval and the jump functions in the thermodynamic and fluid dynamic parameters occur smoothly across this interval. Predistributions of the Heaviside function and the Dirac delta measure are introduced to model the flow parameters across a shock wave. The equations of motion expressed in nonconservative form are then applied to derive unambiguous relationships between the jump functions for the flow parameters.

Baty, Roy S.↗

NASA NTRS2012

Rapid Parameterization Schemes for Aircraft Shape Optimization

A rapid shape parameterization tool called PROTEUS is developed for aircraft shape optimization. This tool can be applied directly to any aircraft geometry that has been defined in PLOT3D format, with the restriction that each aircraft component must be defined by only one data block. PROTEUS has eight types of parameterization schemes: planform, wing surface, twist, body surface, body scaling, body camber line, shifting/scaling, and linear morphing. These parametric schemes can be applied to two types of components: wing-type surfaces (e.g., wing, canard, horizontal tail, vertical tail, and pylon) and body-type surfaces (e.g., fuselage, pod, and nacelle). These schemes permit the easy setup of commonly used shape modification methods, and each customized parametric scheme can be applied to the same type of component for any configuration. This paper explains the mathematics for these parametric schemes and uses two supersonic configurations to demonstrate the application of these schemes.

Li, Wu↗

NASA NTRS2016

Cryovolcanic Emplacement of Domes on Europa

Here we explore the hypothesis that certain domes on Europa may have been produced by the extrusion of viscous cryolavas. A new mathematical method for the emplacement and relaxation of viscous lava domes is presented and applied to putative cryovolcanic domes on Europa. A similarity solution approach is applied to the governing equation for fluid flow in a cylindrical geometry, and dome relaxation is explored assuming a volume of cryolava has been rapidly emplaced onto the surface. Nonphysical sin- gularities inherent in previous models for dome relaxation have been eliminated, and cryolava cooling is represented by a time-variable viscosity. We find that at the onset of relaxation, bulk kinematic viscosities may lie in the range between 10(exp 3) and 10(exp 6) sq m/s, while the actual fluid lava viscosity may be much lower. Plausible relaxation times to form the domes, which are linked to bulk cryolava rheology, are found to range from 3.6 days to 7.5 years. We find that cooling of the cryolava, while dominated by conduction through an icy skin, should not prevent fluids from advancing and relaxing to form domes within the timescales considered. Determining the range of emplacement conditions for putative cryolava domes will shed light on Europa's resurfacing history. In addition, the rheologies and compositions of erupted cryolavas have implications for subsurface cryomagma ascent and local surface stress conditions on Europa.

volcanism↗

NASA NTRS2016

New Approaches to Inferences for Steep-Sided Domes on Venus

New mathematical approaches for the relaxation and emplacement of viscous lava domes are presented and applied to steep-sided domes on Venus. A similarity solution approach is applied to the governing equation for fluid flow in a cylindrical geometry for two distinct scenarios. In the first scenario, dome relaxation is explored assuming a constant volume of fluid (i.e. lava) has been rapidly emplaced onto the surface. Cooling of lava is represented by a time-variable viscosity and singularities inherent in previous models for dome relaxation have been eliminated. At the onset of relaxation, bulk dynamic viscosities lie in the range between 10(exp 10) - 10(exp 16) Pa s, consistent with basaltic-andesite to rhyolitic compositions. Plausible relaxation times range from 5 to 5000 years, depending on initial lava viscosity. The first scenario, however, is only valid during the final stages of dome relaxation and does not consider the time taken for lava to be extruded onto the surface. In the second scenario, emplacement and growth of a steep-sided dome is considered when the volume of lava on the surface increases over time (i.e. time-variable volume approach). The volumetric flow rate may depend on an arbitrary power of the dome thickness, thus embracing Newtonian as well as other rheologies for describing terrestrial and planetary mass flows. The approach can be used to distinguish between basic flow rate models for fluid emplacement. The formalism results in radial expansion of a dome proportional to t(sup 1/2), consistent with the diffusive nature of the governing equation. The flow at the front is shown to thicken as the front advances for a constant rate of lava supply. Emplacement times are intimately correlated with the bulk rheology. Comparison of the theoretical profiles with the shape of a typical dome on Venus indicates that a Newtonian bulk rheology is most appropriate, consistent with prior studies. However, results here suggest a bulk dynamic viscosity of 10(exp 12) - 10(exp 13) Pa s and emplacement times of approximately 2-16 years. Both scenarios investigated give emplacement times significantly less than prior estimates and compositions consistent with basaltic andesite.

steep-sided domes↗