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At least 127 records · Page 7

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NASA NTRS2013

A Leonard-Sanders-Budiansky-Koiter-Type Nonlinear Shell Theory with a Hierarchy of Transverse-Shearing Deformations

A detailed exposition on a refined nonlinear shell theory suitable for nonlinear buckling analyses of laminated-composite shell structures is presented. This shell theory includes the classical nonlinear shell theory attributed to Leonard, Sanders, Koiter, and Budiansky as an explicit proper subset. This approach is used in order to leverage the exisiting experience base and to make the theory attractive to industry. In addition, the formalism of general tensors is avoided in order to expose the details needed to fully understand and use the theory. The shell theory is based on "small" strains and "moderate" rotations, and no shell-thinness approximations are used. As a result, the strain-displacement relations are exact within the presumptions of "small" strains and "moderate" rotations. The effects of transverse-shearing deformations are included in the theory by using analyst-defined functions to describe the through-the-thickness distributions of transverse-shearing strains. Constitutive equations for laminated-composite shells are derived without using any shell-thinness approximations, and simplified forms and special cases are presented.

Nemeth, Michael P.↗

NASA NTRS2018

Information Theory Applied to Decision Making Structures

Decision making structures, such as control boards, process information on many topics as they select options for the system and project. The decisions are based on the information known to the board members and presenters (subject matter experts) and shared at the board during discussion. This information flow through this process can be modelled using information theory. Information theory provides a mathematical basis to understand the flow of information through the decision making process and the information needed for a particular decision. Information theory also provides the mathematical relationships on which to base the optimal decision making structure for a specific system development and organizational structure. Since decision making bodies provide control for the system or project, control theory can be used to construct a decision making model. This provides a starting point for adding cognitive science models. Information processing by each individual board participant can be represented through cognitive processes which are integrated across the board participants through information theory relationship. The set theory view of information theory provides a structure in which to look at the relationships between the participants in a decision making structure.

Watson, Michael D.↗

NASA NTRS2018

Information Theory Applied to Decision Making Structures

Watson, Michael D.↗

NASA NTRS1974

Modified Brans-Dicke gravitational theory with nonzero divergence of the energy-momentum tensor

The Brans-Dicke theory of gravitation is modified by assuming that the divergence of the energy-momentum tensor is proportional to the covariant derivative of the scalar curvature. No ad hoc additions to the usual Brans-Dicke field equations are required as in Rastall's modification of the Einstein theory or as in the steady-state theories, of which this is a natural possibility. Three parameters emerge from the theory - namely, the unnormalized gravitational constant, the usual Brans-Dicke parameter, and the proportionality constant. In the post-Newtonian approximation, these parameters can be fixed by experiment. However, there exists a certain choice of the parameters for which the theory reduces to an Einstein theory with constant scalar curvature.

Smalley, L. L.↗

NASA NTRS1974

Analytical satellite theories based on a new set of canonical elements

A new analytical satellite theory is presented. Instead of the 6 classical elements of Delaunay, a set of 8 canonical elements is used. Whereas the time is the independent variable in classical theory, the true anomaly is the independent variable in the new theory. The new approach has four features: (1) The amount of formulas in the solution is reduced considerably. (2) The first order results are almost as accurate as second order results in classical theory. (3) The theory is easier to understand from a didactical point of view. (4) The problems connected with the inaccuracy of the mean motion that are typical for classical satellite theory are no longer present. The new elements are applied to analytical solutions of the zonal oblateness problem and to the problem of the 24 hour satellite.

Scheifele, G.↗

NASA NTRS1975

Hybrid theory and calculation of e-N2 scattering

A theory of electron-molecule scattering was developed which was a synthesis of close coupling and adiabatic-nuclei theories. The theory is shown to be a close coupling theory with respect to vibrational degrees of freedom but is a adiabatic-nuclei theory with respect to rotation. It can be applied to any number of partial waves required, and the remaining ones can be calculated purely in one or the other approximation. A theoretical criterion based on fixed-nuclei calculations and not on experiment can be given as to which partial waves and energy domains require the various approximations. The theory allows all cross sections (i.e., pure rotational, vibrational, simultaneous vibration-rotation, differential and total) to be calculated. Explicit formulae for all the cross sections are presented.

Chandra, N.↗

NASA NTRS1976

A high order theory for uniform and laminated plates

A theory of plate deformation is derived which accounts for the effects of transverse shear deformation, transverse normal strain, and a nonlinear distribution of the in-plane displacements with respect to the thickness coordinate. The theory is compared with lower order plate theories through application to a particular problem involving a plate acted upon by a sinusoidal surface pressure. Comparison is also made with exact elasticity solution of this problem. It is found that when the ratio of the characteristic length of the load pattern to the plate thickness is of the order of unity, lower order theories are inadequate and the present high order theory is required to give meaningful results. Results are given for the bending of symmetric cross-ply and angle-ply laminates. Comparison with exact elasticity solutions indicates that the present plate theory is sufficiently accurate for predicting the behavior of thick laminates.

Lo, K. H.↗

NASA NTRS1976

Theory of a cylindrical probe in a collisionless magnetoplasma

A theory is presented for a cylindrical electrostatic probe in a collisionless plasma in the case where the probe axis is inclined at an angle to a uniform magnetic field. The theory is applicable to electron collection, and under more restrictive conditions, to ion collection. For a probe at space potential, the theory is exact in the limit where probe radius is much less than Debye length. At attracting probe potentials, the theory yields an upper bound and an adiabatic limit for current collection. At repelling probe potentials, it provides a lower bound. The theory is valid if the ratios of probe radius to Debye length and probe radius to mean gyroradius are not simultaneously large enough to produce extrema in the probe sheath potential. The numerical current calculations are based on the approximation that particle orbits are helices near the probe, together with the use of kinetic theory to relate velocity distributions near the probe to those far from it. Probe characteristics are presented for inclination angles from 0 to 90 deg and for probe-radius mean-gyroradius ratios from 0.1 to infinity. For an angle of 0 deg, the end-effect current is calculated separately.

Laframboise, J. G.↗

NASA NTRS1977

Gravitational radiation from binary systems in alternative metric theories of gravity - Dipole radiation and the binary pulsar

The generation of gravitational radiation in several currently viable metric theories of gravitation (Brans-Dicke, Rosen, Ni, and Lightman-Lee) is analyzed, and it is shown that these theories predict the emission of dipole gravitational radiation from systems containing gravitationally bound objects. In the binary system PSR 1913 + 16, this radiation results in a secular change in the orbital period of the system with a nominal magnitude of 3 parts in 100,000 per year. The size of the effect is proportional to the reduced mass of the system, to the square of the difference in (self-gravitational energy)/(mass) between the two components of the system, and to a parameter, xi, whose value varies from theory to theory. In general relativity xi equals 0, in Rosen's (1973) theory xi equals -20/3, and in Ni's (1973) theory xi equals -400/3. The current upper limit on such a secular period change is one part in 1 million per year. It is shown that further observations of the binary system that tighten this limit and that establish the masses of the components and the identity of the companion may provide a crucial test of otherwise viable alternatives to general relativity.

Will, C. M.↗

NASA NTRS1977

Evaluation of the Tensor Polynomial and Hoffman strength theories for composite materials

The Hoffman theory and the Tensor Polynomial (Tsai-Wu) theory with the stress interaction term set equal to zero have been found to be preferred alternatives to the general Tensor Polynomial theory for predicting strength of filamentary composite laminae. These theories were used to predict failure of off-axis boron/epoxy and E-glass/epoxy test specimens and gave excellent agreement with available experimental results. A numerical experiment was also performed to estimate the errors for ten different composite systems under six different loadings. The maximum error in predicted failure loads among all cases was below 10 percent. These results suggest that the Hoffman failure theory and the Tensor Polynomial theory with the stress interaction term equal to zero can predict failure of practical filamentary composite materials under general biaxial loading with sufficient accuracy for engineering applications.

Narayanaswami, R.↗

NASA NTRS1978

A comparison of three classical analytical theories for the motion of artificial satellites

Motivated by the heavy reliance upon the analytic orbit theory in orbit determination operations at the Goddard Space Flight Center (GSFC), a comparison study is performed for three classical analytical theories of artificial satellite motion about an oblate earth. The three analytical theories are: (1) Brouwer, (2) a modified Brouwer, i.e., Brouwer-Lyddane and Cohen, and (3) Vinti. Comparison results for each theory are produced for a number of representative satellites of current or past interest which proved amenable to analytic theory application. The uniformity of these results has significant implications for current and future mission operations and planning activities. Subsidiary topics arising from the results of this study which relate to the optimum usage of the individual theories are also discussed

Gordon, R. A.↗

NASA NTRS1980

A comparison between an existing propeller noise theory and wind tunnel data

The noise of three supersonic helical tip speed propellers was compared with the noise predicted by an existing noise theory. Comparisons of the peak blade passage tones showed fairly good agreement beween theory and experiment at the lowest helical tip Mach numbers tested, 0.86 and 1.00, while at higher numbers, the theory predicted higher noise levels than measured. When the differences among the propellers were considered the theory and measurement showed fairly good agreement. Directivity measurements in general showed that the measured blade passage tone data peaked further downstream than the theory predicted. At the cruise design condition the harmonics appeared to fall off faster in the data than the theory indicated.

Dittmar, J. H.↗

NASA NTRS1981

Comparison of theory and in situ observations for electron and ion distributions in the near wake of the Explorer 31 and AE-C satellites

Measurements of electron density, plasma potential, and mean ion mass from the Explorer 31 satellite, and measurements of ion current, plasma potential, and ion composition from the Atmosphere Explorer C satellite were used in a comparative study with Parker's theory regarding the charged particle distribution in the near wake of an ionospheric satellite (1976). It is shown that theory and experiment agree fairly well in the angle-of-attack range between 90 and 135 deg. In the maximum rarefaction zone (between 145 and 180 deg), however, the theoretical model overestimates the measured ion depletion by several orders of magnitude. A comparison between theory and the Explorer 31 electron measurements shows that the theory again overestimates the electron depletion. These discrepancies are mainly due to the use of a steady-state theory and a single ion equation (using a mean ion mass). Improved agreement between theory and experiment can be obtained by the use of the time-dependent Vlasov-Poisson equations with separate equations for the various ion species.

Samir, U.↗

NASA NTRS1983

Theory of hydromagnetic turbulence

The present state of MHD turbulence theory as a possible solar wind research tool is surveyed. The theory is statistical, and does not make statements about individual events. The ensembles considered typically have individual realizations which differ qualitatively, unlike equilibrium statistical mechanics. Most of the theory deals with highly symmetric situations; most of these symmetries have yet to be tested in the solar wind. The applicability of MHD itself to solar wind parameters is highly questionable; yet it has no competitors, as a potentially comprehensive dynamical description. The purpose of solar wind research require sharper articulation. If they are to understand radial turbulent plasma flows from spheres, laboratory experiments and numerical solution of equations of motion may be cheap alternative to spacecraft. If "real life" information is demanded, multiple spacecraft with variable separation may be necessary to go further. The principal emphasis in the theory so far has been on spectral behavior for spatial covariances in wave number space. There is no respectable theory of these for highly anisotropic situations. A rather slow development of theory acts as a brake on justifiable measurement, at this point.

Montgomery, D.↗

NASA NTRS1983

Magnetohydrodynamic and gasdynamic theories for planetary bow waves

A bow wave was previously observed in the solar wind upstream of each of the first six planets. The observed properties of these bow waves and the associated plasma flows are outlined, and those features identified that can be described by a continuum magnetohydrodynamic flow theory. An account of the fundamental concepts and current status of the magnetohydrodynamic and gas dynamic theories for solar wind flow past planetary bodies is provided. This includes a critical examination of: (1) the fundamental assumptions of the theories; (2) the various simplifying approximations introduced to obtain tractable mathematical problems; (3) the limitations they impose on the results; and (4) the relationship between the results of the simpler gas dynamic-frozen field theory and the more accurate but less completely worked out magnetohydrodynamic theory. Representative results of the various theories are presented and compared.

Spreiter, J. R.↗

NASA NTRS1984

A simple higher-order theory for laminated composite plates

A higher-order shear deformation theory of laminated composite plates is developed. The theory contains the same dependent unknowns as in the first-order shear deformation theory of Whitney and Pagano (1970), but accounts for parabolic distribution of the transverse shear strains through the thickness of the plate. Exact closed-form solutions of symmetric cross-ply laminates are obtained and the results are compared with three-dimensional elasticity solutions and first-order shear deformation theory solutions. The present theory predicts the deflections and stresses more accurately when compared to the first-order theory.

Reddy, J. N.↗

NASA NTRS1984

Rotary-wing aerodynamics. Volume 1 - Basic theories of rotor aerodynamics (With application to helicopters). Volume 2 Performance prediction of helicopters (2nd revised and enlarged edition)

Basic theories of rotor aerodynamics are presented and applied to the performance prediction of helicopters. The very simple physicomathematical model of the rotor offered by momentum theory is addressed first, followed by the combined blade-element and momentum theory. Vortex theory is discussed, and a rotor blade is modeled by means of a vortex filament or vorticity surface. Considerations of airfoil sections suitable for rotors are examined. Detailed performance techniques for a single-rotor helicopter in hover, vertical ascent, and forward flight are described, and winged and tandem-rotor helicopter performance calculations are presented as extensions and modifications of single-rotor methodology. Computer data based on the vortex theory are compared with approximate results obtained from the simplified momentum theory and the blade element solution.

Stepniewski, W. Z.↗

NASA NTRS1985

Theory of interparticle correlations in dense, high-temperature plasmas. V - Electric and thermal conductivities

Ichimaru et al. (1985) have developed a general theory in which the interparticle correlations in dense, high-temperature multicomponent plasmas were formulated systematically over a wide range of plasma parameters. The present paper is concerned with an extension of this theory, taking into account the problems of the electronic transport in such high-density plasmas. It is shown that the resulting theory is capable of describing the transport coefficients accurately over a wide range of the density and temperature parameters. Attention is given to electric and thermal conductivities, generalized Coulomb logarithms, a comparison of the considered theory with other theories, and a comparison of the theory with experimental results.

Ichimaru, S.↗