Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “generalized functions”

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.

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

At least 757 records · Page 42
All sourcesNASA NTRSDOE OSTI
NASA NTRS1992

Mappings and accuracy for Chebyshev pseudo-spectral approximations

The effect of mappings on the approximation, by Chebyshev collocation, of functions which exhibit localized regions of rapid variation is studied. A general strategy is introduced whereby mappings are adaptively constructed which map specified classes of rapidly varying functions into low order polynomials which can be accurately approximated by Chebyshev polynomial expansions. A particular family of mappings constructed in this way is tested on a variety of rapidly varying functions similar to those occurring in approximations. It is shown that the mapped function can be approximated much more accurately by Chebyshev polynomial approximations than in physical space or where mappings constructed from other strategies are employed.

Bayliss, Alvin↗
NASA NTRS1979

Multi-level adaptive finite element methods. 1: Variation problems

A general numerical strategy for solving partial differential equations and other functional problems by cycling between coarser and finer levels of discretization is described. Optimal discretization schemes are provided together with very fast general solvers. It is described in terms of finite element discretizations of general nonlinear minimization problems. The basic processes (relaxation sweeps, fine-grid-to-coarse-grid transfers of residuals, coarse-to-fine interpolations of corrections) are directly and naturally determined by the objective functional and the sequence of approximation spaces. The natural processes, however, are not always optimal. Concrete examples are given and some new techniques are reviewed. Including the local truncation extrapolation and a multilevel procedure for inexpensively solving chains of many boundary value problems, such as those arising in the solution of time-dependent problems.

Brandt, A.↗
NASA NTRS1995

Satellite observations of zonal electric fields near sunrise in the equatorial ionosphere

We report here on a number of examples of anomalous enhancements of eastward electric fields near sunrise in the equatorial ionospheric F-region. These examples were selected from the data base of the equatorial satellite, San Marco D (1988), which measured ionospheric electric fields during a period of solar minimum. The eastward electric fields reported correspond to vertical plasma drifts. The examples studied here are similar in signature and polarity to the pre-reversal electric field enhancements seen near sunset from ground-based radar systems. The morphology of these sunrise events, which are observed on about 14% of the morning-side satellite passes, are studied as a function of local zonal velocity, magnetic activity, geographic longitude and altitude. The nine events studied occur at locations where the zonal plasma flow is generally measured to be eastward, but reducing as a function of local time and at satellite longitudes where the magnetic declination has the opposite polarity as the declination of the sunrise terminator.

Aggson, T. L.↗
NASA NTRS1990

Localized basis functions and other computational improvements in variational nonorthogonal basis function methods for quantum mechanical scattering problems involving chemical reactions

The Generalized Newton Variational Principle for 3D quantum mechanical reactive scattering is briefly reviewed. Then three techniques are described which improve the efficiency of the computations. First, the fact that the Hamiltonian is Hermitian is used to reduce the number of integrals computed, and then the properties of localized basis functions are exploited in order to eliminate redundant work in the integral evaluation. A new type of localized basis function with desirable properties is suggested. It is shown how partitioned matrices can be used with localized basis functions to reduce the amount of work required to handle the complex boundary conditions. The new techniques do not introduce any approximations into the calculations, so they may be used to obtain converged solutions of the Schroedinger equation.

Schwenke, David W.↗
NASA NTRS1987

Diagnosis and sensor validation through knowledge of structure and function

The liquid oxygen expert system 'LES' is proposed as the first capable of diagnostic reasoning from sensor data, using model-based knowledge of structure and function to find the expected state of all system objects, including sensors. The approach is generally algorithmic rather than heuristic, and represents uncertainties as sets of possibilities. Functional relationships are inverted to determine hypothetical values for potentially faulty objects, and may include conditional functions not normally considered to have inverses.

Scarl, Ethan A.↗
NASA NTRS2004

A Meshless Method Using Radial Basis Functions for Beam Bending Problems

A meshless local Petrov-Galerkin (MLPG) method that uses radial basis functions (RBFs) as trial functions in the study of Euler-Bernoulli beam problems is presented. RBFs, rather than generalized moving least squares (GMLS) interpolations, are used to develop the trial functions. This choice yields a computationally simpler method as fewer matrix inversions and multiplications are required than when GMLS interpolations are used. Test functions are chosen as simple weight functions as they are in the conventional MLPG method. Compactly and noncompactly supported RBFs are considered. Noncompactly supported cubic RBFs are found to be preferable. Patch tests, mixed boundary value problems, and problems with complex loading conditions are considered. Results obtained from the radial basis MLPG method are either of comparable or better accuracy than those obtained when using the conventional MLPG method.

Raju, I. S.↗
NASA NTRSDate not supplied

Statistical Considerations for the Design and Execution of NASA's Community Noise Surveys

The World Health Organization defines community noise as noise emitted from all sources apart from noise at an industrial workplace. Example sources include neighborhood and construction noise, noise from road and rail, and air traffic noise. In particular, overland supersonic flights have been banned in the United States since the 1970s based on data accumulated during the 1960s; the degree of reported annoyance from the resulting sonic booms was a key factor leading to the prohibition. In subsequent years, scientific and engineering understanding has led to the potential to produce low amplitude sonic booms, or ‘sonic thumps’, during supersonic flight through aircraft design choices. Aircraft manufacturers have expressed renewed interest in producing supersonic commercial aircraft, but without appropriate changes to regulation, only overseas routes can be traveled supersonically. The National Aeronautics and Space Administration (NASA) will be flying the X-59 demonstrator aircraft in a series of community tests to begin in the 2024 fiscal year. In this presentation we provide some historical context for the current prohibitions on supersonic commercial flight. Using data collected during earlier NASA risk reduction tests, we demonstrate how generalized linear mixed models can be used to inform the functional dose-response response curve. Finally, we discuss some of the challenges in designing the future community studies and generalizing them to a nationally-representative dose-response curve. The study effort will be of national and international importance as the data and models prepared during the community tests will be provided to the International Civil Aviation Organization (ICAO) in order to help noise regulators determine if supersonic flight will be permitted over land once again and at what demonstrable noise levels.

Nathan B Cruze↗
NASA NTRS2018

Coupled Thermo-Mechanical Micromechanics Modeling of the Influence of Thermally Grown Oxide Layer in an Environmental Barrier Coating System

Environmental Barrier Coatings (EBCs) have emerged as a promising means of protecting silicon based ceramic matrix composite (CMC) components for high temperature applications (e.g., aircraft engines). EBCs are often used to protect an underlying material (substrate) such as silicon carbide from extreme thermal/chemical environments. In a typical CMC/EBC system, an EBC may or may not be adhered to an underlying substrate with a bond coat (e.g., silicon). Irrespective, systems that utilize EBCs are susceptible to a number of failure modes including oxidation/delamination, recession, chemical attack and dissolution, thermomechanical degradation, erosion, and foreign object damage. Current work at NASA Glenn Research Center is aimed at addressing these failure modes in EBC systems and developing robust analysis tools to aid in the design process. The Higher-Order Theory for Functionally Graded Materials (HOTFGM), a precursor to the High-Fidelity Generalized Method of Cells micromechanics approach, was developed to investigate the coupled thermo-mechanical behavior of functionally graded composites and will be used herein to assess the development and growth of a low-stiffness thermally grown oxide (TGO) layer in EBC/CMC systems without a silicon bond coat. To accomplish this a sensitivity study is conducted to examine the influence of uniformly and nonuniformly grown oxide layer on the associated driving forces leading to mechanical failure (spallation) of EBC layer when subjected to isothermal loading.

thermally grown oxide↗
NASA NTRSDate not supplied

Fracture Prediction of Epoxy Resin using Morse Bond Potential Embedded in GAFF using Molecular Dynamics Simulations

A generic method is developed to investigate the fracture behavior of an epoxy resin using atomistic molecular (MD) dynamics simulations. The epoxy system consisted of the stoichiometric mixture of tetra-/tri-functional epoxies and di-functional hardener molecules and was cured with a step-growth crosslinking algorithm. A hybrid force field (hFF) in which Morse bond function were added in second generation-general Amber Force Field (GAFF2) was used to capture bond breaking of the crosslinked epoxy system under uniaxial deformation. The Morse bond parameters for covalent bonds in the crosslinked backbone were fit to dissociation curves computed by CASPT2/6-311+G**. After the systems in various crosslink densities were obtained and equilibrated, the full length of stress-strain (𝜎-𝜀) curve was produced including initial elastic regime, yielding, plastic flow, strain hardening, and progressive failure. We found that the hFF was effective in studying the dissociation of crosslinked polymers and understanding the failure mechanism. In the results, the hFF delivered the same elastic property obtained from the unmodified force field GAFF. The stress-strain curve, however, began to be distinct in the plastic regime due to broken covalent bonds capable of altering the tensile behavior. Once the stress reached maximum, it progressively decreased until the ultimate failure (𝜎=0). Since hFF employed the existing GAFF functions with including a minimal change of its bond potential, this approach is easier to perform and computationally more efficient for unveiling the fracture behavior of polymer materials at the molecular level than other approaches with reactive force fields. We expect this approach will be utilized to accelerate the material-by-design process for thermosets by incorporate data from molecular models.

Changwoon Jang↗
NASA NTRS1991

Deformation and stress response of composite laminated shells under internal pressure

This paper presents a theoretical study of the response of filament wound composite shells under internal pressure. Each layer of the material is generally cylindrically anisotropic. By using cylindrically anisotropic elasticity field equations and Lekhnitskii's stress functions, a system of sixth-order ordinary differential equations is obtained. The general expressions for the stresses and displacements in the laminated composite shells under internal pressure are discussed. Two composite systems, graphite/epoxy and glass/epoxy, are selected to demonstrate the influence of degree of material anisotropy and fiber orientations on the axial and induced twisting deformation. Stress distributions of (45/-45)s symmetric angle-ply fiber-reinforced laminated shells are shown to illustrate the effect of radius-to-thickness ratio.

Yuan, F. G.↗
NASA NTRS1981

Demonstration Advanced Avionics System (DAAS). Phase 1 report

An integrated avionics system which provides expanded functional capabilities that significantly enhance the utility and safety of general aviation at a cost commensurate with the general aviation market is discussed. Displays and control were designed so that the pilot can use the system after minimum training. Functional and hardware descriptions, operational evaluation and failure modes effects analysis are included.

Source record↗
NASA NTRS1976

Thermodynamics and statistical mechanics

The basic thermodynamic properties of gases are reviewed and the relations between them are derived from the first and second laws. The elements of statistical mechanics are then formulated and the partition function is derived. The classical form of the partition function is used to obtain the Maxwell-Boltzmann distribution of kinetic energies in the gas phase and the equipartition of energy theorem is given in its most general form. The thermodynamic properties are all derived as functions of the partition function. Quantum statistics are reviewed briefly and the differences between the Boltzmann distribution function for classical particles and the Fermi-Dirac and Bose-Einstein distributions for quantum particles are discussed.

Source record↗
NASA NTRS1920

The general theory of blade screws including propellers, fans, helicopter screws, helicoidal pumps, turbo-motors, and different kinds of helicoidal blades

Report presents a theory which gives a complete picture and an exact quantitative analysis of the whole phenomenon of the working of blade screws, but also unites in a continuous whole the entire scale of states of work conceivable for a blade screw. Chapter 1 is devoted to the establishment of the system of fundamental equations relating to the blade screw. Chapter 2 contains the general discussion of the 16 states of work which may establish themselves for a blade screw. The existence of the vortex ring state and the whirling phenomenon are established. All the fundamental functions which enter the blade-screw theory are submitted to a general analytical discussion. The general outline of the curve of the specific function is examined. Two limited cases of the work of the screw, the screw with a zero constructive pitch and the screw with an infinite constructive pitch, are pointed out. Chapter 3 is devoted to the study of the propulsive screw or propeller. (author)

De Bothezat, George↗
NASA NTRS1994

F2 peak electron density at Millstone Hill and Hobart: Comparsion of theory and measurement at solar maximum

This paper compares the observed behavior of the (F2) layer of the ionosphere at Millstone Hill and Hobart with calculations from the field line interhemispheric plasma (FLIP) model for solar maximum, solstice conditions in 1990. During the study period the daily F(sub 10.7) index varied by more than a factor of 2 (123 to 280), but the 81-day mean F(sub 10.7) (F(sub 10.7 A)) was almost constant near 190. Calculations were performed with and without the effects of vibrationally excited N2 (N(sup *)(sub 2) which affects the loss rate of atomic oxygen ions. In the case without N(sup *)(sub 2) there is generally good agreement between the model and measurement for the daytime, peak density of the F region (NmF2). Both the model and the measurement show a strong seasonal anomaly with the winter noon densities a factor of 3 to 4 greater than the summer noon densities at Millstone Hill and a factor of 2 greater at Hobart. The seasonal anomaly in the model is caused by changes in the neutral composition as given by the mass spectrometer and incoherent scatter (MSIS) 86 neutral density model. There is generally little or no increase in the observed noon NmF2 as a function of daily F(sub 10.7) except at Millstone Hill in winter. In contrast to the generally good agreement between model and data at noon, the model badly underestimates the density at night at Millstone Hill at all seasons. At Hobart the model reproduces the nighttime density variations well in both winter and summer. The international reference ionosphere (IRI) model generally provides a good representation of the average behavior of noon NmF2 and hmF2 but because the data show a lot of day-to-day variability, there are often large differences. The FLIP model is able to reproduce this variability when hmF2 is specified. The IRI model peak densities are better than the FLIP densities at night, but the IRI model does not represent the Millstone Hill summer data very well at night in 1990.

Richards, P. G.↗
NASA NTRS1996

Variational Methods in Sensitivity Analysis and Optimization for Aerodynamic Applications

Variational methods (VM) sensitivity analysis, which is the continuous alternative to the discrete sensitivity analysis, is employed to derive the costate (adjoint) equations, the transversality conditions, and the functional sensitivity derivatives. In the derivation of the sensitivity equations, the variational methods use the generalized calculus of variations, in which the variable boundary is considered as the design function. The converged solution of the state equations together with the converged solution of the costate equations are integrated along the domain boundary to uniquely determine the functional sensitivity derivatives with respect to the design function. The determination of the sensitivity derivatives of the performance index or functional entails the coupled solutions of the state and costate equations. As the stable and converged numerical solution of the costate equations with their boundary conditions are a priori unknown, numerical stability analysis is performed on both the state and costate equations. Thereafter, based on the amplification factors obtained by solving the generalized eigenvalue equations, the stability behavior of the costate equations is discussed and compared with the state (Euler) equations. The stability analysis of the costate equations suggests that the converged and stable solution of the costate equation is possible only if the computational domain of the costate equations is transformed to take into account the reverse flow nature of the costate equations. The application of the variational methods to aerodynamic shape optimization problems is demonstrated for internal flow problems at supersonic Mach number range. The study shows, that while maintaining the accuracy of the functional sensitivity derivatives within the reasonable range for engineering prediction purposes, the variational methods show a substantial gain in computational efficiency, i.e., computer time and memory, when compared with the finite difference sensitivity analysis.

Ibrahim, A. H.↗
NASA NTRS1985

Convergence of Newton's method for a single real equation

Newton's method for finding the zeroes of a single real function is investigated in some detail. Convergence is generally checked using the Contraction Mapping Theorem which yields sufficient but not necessary conditions for convergence of the general single point iteration method. The resulting convergence intervals are frequently considerably smaller than actual convergence zones. For a specific single point iteration method, such as Newton's method, better estimates of regions of convergence should be possible. A technique is described which, under certain conditions (frequently satisfied by well behaved functions) gives much larger zones where convergence is guaranteed.

Campbell, C. W.↗
NASA NTRS1963

A Hypergeometric Mean Value

Generalization of hypergeometric mean value from hypergeometric function without loss of homogeneity - derivation and properties of hypergeometric mean value

HYPERGEOMETRIC FUNCTION↗