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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 253 records · Page 14
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NASA NTRS1989

A few remarks concerning several refined theories of anisotropic composite laminated plates

An analysis and comparison of several shear deformable bending theories of composite laminated anisotropic plates currently encountered in the field literature are given in this paper. Although apparently different, it is shown in a unitary way, that these theories constitute in fact only different formulations of a single theory, generically designated to as the moderately thick plate theory. Their connection with the first order transverse shear deformation theory is also emphasized and some conclusions concerning its shortcomings and field applicability are presented.

Librescu, L.↗
NASA NTRS1989

Multilayer theory for delamination analysis of a composite curved bar subjected to end forces and end moments

A composite test specimen in the shape of a semicircular curved bar subjected to bending offers an excellent stress field for studying the open-mode delamination behavior of laminated composite materials. This is because the open-mode delamination nucleates at the midspan of the curved bar. The classical anisotropic elasticity theory was used to construct a multilayer theory for the calculations of the stress and deformation fields induced in the multilayered composite semicircular curved bar subjected to end forces and end moments. The radial location and intensity of the open-mode delamination stress were calculated and were compared with the results obtained from the anisotropic continuum theory and from the finite element method. The multilayer theory gave more accurate predictions of the location and the intensity of the open-mode delamination stress than those calculated from the anisotropic continuum theory.

Ko, William L.↗
NASA NTRS1989

Secular perturbations of the Uranian satellites - Theory and practice

A simple revised secular perturbation theory which incorporates the averaged secular effect of first-order near-resonances is derived. By including the effects of these near-resonances, the largest error in the secular frequencies is reduced from 16 percent to less than 3 percent. It is concluded that the revised secular perturbation theory is adequate for the quantitative modeling of the long-term perturbations in the Uranian satellite system. If incorporated within the general theory of Laskar (1986), this theory would lead to completely analytic theory.

Malhotra, R.↗
NASA NTRS1991

Unified aeroacoustics analysis for high speed turboprop aerodynamics and noise. Volume 3: Application of theory for blade loading, wakes, noise, and wing shielding

Results of the program for the generation of a computer prediction code for noise of advanced single rotation, turboprops (prop-fans) such as the SR3 model are presented. The code is based on a linearized theory developed at Hamilton Standard in which aerodynamics and acoustics are treated as a unified process. Both steady and unsteady blade loading are treated. Capabilities include prediction of steady airload distributions and associated aerodynamic performance, unsteady blade pressure response to gust interaction or blade vibration, noise fields associated with thickness and steady and unsteady loading, and wake velocity fields associated with steady loading. The code was developed on the Hamilton Standard IBM computer and has now been installed on the Cray XMP at NASA-Lewis. The work had its genesis in the frequency domain acoustic theory developed at Hamilton Standard in the late 1970s. It was found that the method used for near field noise predictions could be adapted as a lifting surface theory for aerodynamic work via the pressure potential technique that was used for both wings and ducted turbomachinery. In the first realization of the theory for propellers, the blade loading was represented in a quasi-vortex lattice form. This was upgraded to true lifting surface loading. Originally, it was believed that a purely linear approach for both aerodynamics and noise would be adequate. However, two sources of nonlinearity in the steady aerodynamics became apparent and were found to be a significant factor at takeoff conditions. The first is related to the fact that the steady axial induced velocity may be of the same order of magnitude as the flight speed and the second is the formation of leading edge vortices which increases lift and redistribute loading. Discovery and properties of prop-fan leading edge vortices were reported in two papers. The Unified AeroAcoustic Program (UAAP) capabilites are demonstrated and the theory verified by comparison with the predictions with data from tests at NASA-Lewis. Steady aerodyanmic performance, unsteady blade loading, wakes, noise, and wing and boundary layer shielding are examined.

Hanson, D. B.↗
NASA NTRS1989

Multilayer theory for delamination analysis of a composite curved bar subjected to end forces and end moments

A composite test specimen in the shape of a semicircular curved bar subjected to bending offers an excellent stress field for studying the open-mode delamination behavior of laminated composite materials. This is because the open-mode delamination nucleates at the midspan of the curved bar. The classical anisotropic elasticity theory was used to construct a 'multilayer' theory for the calculations of the stress and deformation fields induced in the multilayered composite semicircular curved bar subjected to end forces and end moments. The radial location and intensity of the open-mode delamination stress were calculated and were compared with the results obtained from the anisotropic continuum theory and from the finite element method. The multilayer theory gave more accurate predictions of the location and the intensity of the open-mode delamination stress than those calculated from the anisotropic continuum theory.

Ko, William L.↗
NASA NTRS1992

Practical theories for service life prediction of critical aerospace structural components

A new second-order theory was developed for predicting the service lives of aerospace structural components. The predictions based on this new theory were compared with those based on the Ko first-order theory and the classical theory of service life predictions. The new theory gives very accurate service life predictions. An equivalent constant-amplitude stress cycle method was proposed for representing the random load spectrum for crack growth calculations. This method predicts the most conservative service life. The proposed use of minimum detectable crack size, instead of proof load established crack size as an initial crack size for crack growth calculations, could give a more realistic service life.

Ko, William L.↗
NASA NTRS1992

Algorithmic information theory and the hidden variable question

The admissibility of certain nonlocal hidden-variable theories are explained via information theory. Consider a pair of Stern-Gerlach devices with fixed nonparallel orientations that periodically perform spin measurements on identically prepared pairs of electrons in the singlet spin state. Suppose the outcomes are recorded as binary strings l and r (with l sub n and r sub n denoting their n-length prefixes). The hidden-variable theories considered here require that there exists a recursive function which may be used to transform l sub n into r sub n for any n. This note demonstrates that such a theory cannot reproduce all the statistical predictions of quantum mechanics. Specifically, consider an ensemble of outcome pairs (l,r). From the associated probability measure, the Shannon entropies H sub n and H bar sub n for strings l sub n and pairs (l sub n, r sub n) may be formed. It is shown that such a theory requires that the absolute value of H bar sub n - H sub n be bounded - contrasting the quantum mechanical prediction that it grow with n.

Fuchs, Christopher↗
NASA NTRS1992

Vibration of thick composite laminates - Analytic theory and finite element approximations

Two versions of a (1,2) higher-order laminate plate theory are extended to elastodynamics, and their performance on free vibration problems for homogeneous and laminated plates is examined. Both versions are based on continuously varying through-the-thickness linear and parabolic distributions for the inplane and transverse displacements, respectively. They also use continuous parabolic distributions for the transverse shear strains. The theory is capable of providing an improved accuracy as compared to other approximate theories and accurately predicting the lowest thickness-stretch frequencies which cannot be obtained with shear-deformable theories. The theory is considered to be particularly well-suited for generating simple and efficient variationally-based displacement finite elements leading to C sup 0 elements with only five degrees of freedom per node.

Tessler, A.↗
NASA NTRS1992

Physics of pitch angle scattering and velocity diffusion. I - Theory

A general theory for the pitch angle scattering and velocity diffusion of particles in the field of a spectrum of waves in a magnetized plasma is presented. The test particle theory is used to analyze the particle motion. The form of diffusion surfaces is examined, and analytical expressions are given for the resonance width and bounce frequency. The resonance widths are found to vary strongly as a function of harmonic number. The resulting diffusion can be quite asymmetric with respect to pitch angle of 90 deg. The conditions for the onset of pitch angle scattering and energy diffusion are explained in detail. Some of the known shortcomings of the standard quasi-linear theory are also addressed, and ways to overcome them are shown. In particular, the often stated quasi-linear gap at 90 deg is found to exist only under very special cases. For instance, oblique wave propagation can easily remove the gap. The conditions for the existence of the gap are described in great detail. A new diffusion equation which takes into account the finite resonance widths is also discussed. The differences between this new theory and the standard resonance broadening theory is explained.

Karimabadi, H.↗
NASA NTRS1993

An open-shell restricted Hartree-Fock perturbation theory based on symmetric spin orbitals

A new open-shell perturbation theory is formulated in terms of symmetric spin orbitals. Only one set of spatial orbitals is required, thereby reducing the number of independent coefficients in the perturbed wavefunctions. For second order, the computational cost is shown to be similar to a closed-shell calculation. This formalism is therefore more efficient than the recently developed RMP, ROMP or RMP-MBPT theories. The perturbation theory described herein was designed to have a close correspondence with our recently proposed coupled-cluster theory based on symmetric spin orbitals. The first-order wavefunction contains contributions from only doubly excited determinants. Equilibrium structures and vibrational frequencies determined from second-order perturbation theory are presented for OH, NH, CH, 02, NH2 and CH2.

Lee, Timothy J.↗
NASA NTRS1951

Comparison Between Theory and Experiment for Wings at Supersonic Speeds

This paper presents a critical comparison made between experimental and theoretical results for the aerodynamic characteristics of wings at supersonic flight speeds. As a preliminary, a brief, nonmathematical review is given of the basic assumptions and general findings of supersonic wing theory in two and three dimensions. Published data from two-dimensional pressure-distribution tests are then used to illustrate the effects of fluid viscosity and to assess the accuracy of linear theory as compared with the more exact theories which are available in the two-dimensional case. Finally, an account is presented of an NACA study of the over-all force characteristics of three-dimensional wings at supersonic speed. In this study, the lift, pitching moment, and drag characteristics of several families of wings of varying plan form and section were measured in the wind tunnel and compared with values predicted by the three-dimensional linear theory. The regions of agreement and disagreement between experiment and theory are noted and discussed.

Vincenti, Walter G↗
NASA NTRS1993

A critical evaluation of theories for predicting microcracking in composite laminates

We present experimental results on 21 different layups of Hercules AS4 carbon fiber/3501-6 epoxy laminates. All laminates had 90 deg plies; some had them in the middle, while some had them on a free surface. During tensile loading, the first form of damage in all laminates was microcracking of the 90 deg plies. For each laminate, we recorded both the crack density and the complete distribution of crack spacings as a function of the applied load. By rearranging various microcracking theories, we developed a master-curve approach that permitted plotting the results from all laminates on a single plot. By comparing master-curve plots for different theories, it was possible to critically evaluate the quality of those theories. We found that a critical-energy-release-rate criterion calculated using a 2D variational stress analysis gave the best results. All microcracking theories based on a strength-failure criteria gave poor results. All microcracking theories using 1D stress analyses, regardless of the failure criterion, also gave poor results.

Nairn, John A.↗
NASA NTRS1993

Testing higher-order Lagrangian perturbation theory against numerical simulation. 1: Pancake models

We present results showing an improvement of the accuracy of perturbation theory as applied to cosmological structure formation for a useful range of quasi-linear scales. The Lagrangian theory of gravitational instability of an Einstein-de Sitter dust cosmogony investigated and solved up to the third order is compared with numerical simulations. In this paper we study the dynamics of pancake models as a first step. In previous work the accuracy of several analytical approximations for the modeling of large-scale structure in the mildly non-linear regime was analyzed in the same way, allowing for direct comparison of the accuracy of various approximations. In particular, the Zel'dovich approximation (hereafter ZA) as a subclass of the first-order Lagrangian perturbation solutions was found to provide an excellent approximation to the density field in the mildly non-linear regime (i.e. up to a linear r.m.s. density contrast of sigma is approximately 2). The performance of ZA in hierarchical clustering models can be greatly improved by truncating the initial power spectrum (smoothing the initial data). We here explore whether this approximation can be further improved with higher-order corrections in the displacement mapping from homogeneity. We study a single pancake model (truncated power-spectrum with power-spectrum with power-index n = -1) using cross-correlation statistics employed in previous work. We found that for all statistical methods used the higher-order corrections improve the results obtained for the first-order solution up to the stage when sigma (linear theory) is approximately 1. While this improvement can be seen for all spatial scales, later stages retain this feature only above a certain scale which is increasing with time. However, third-order is not much improvement over second-order at any stage. The total breakdown of the perturbation approach is observed at the stage, where sigma (linear theory) is approximately 2, which corresponds to the onset of hierarchical clustering. This success is found at a considerable higher non-linearity than is usual for perturbation theory. Whether a truncation of the initial power-spectrum in hierarchical models retains this improvement will be analyzed in a forthcoming work.

Buchert, T.↗
NASA NTRS1992

An improved plate theory of order (1,2) for thick composite laminates

A new (1,2)-order theory is proposed for the linear elasto-static analysis of laminated composite plates. The basic assumptions are those concerning the distribution through the laminate thickness of the displacements, transverse shear strains and the transverse normal stress, with these quantities regarded as some weighted averages of their exact elasticity theory representations. The displacement expansions are linear for the inplane components and quadratic for the transverse component, whereas the transverse shear strains and transverse normal stress are respectively quadratic and cubic through the thickness. The main distinguishing feature of the theory is that all strain and stress components are expressed in terms of the assumed displacements prior to the application of a variational principle. This is accomplished by an a priori least-square compatibility requirement for the transverse strains and by requiring exact stress boundary conditions at the top and bottom plate surfaces. Equations of equilibrium and associated Poisson boundary conditions are derived from the virtual work principle. It is shown that the theory is particularly suited for finite element discretization as it requires simple C(sup 0)- and C(sup -1)-continuous displacement interpolation fields. Analytic solutions for the problem of cylindrical bending are derived and compared with the exact elasticity solutions and those of our earlier (1,2)-order theory based on the assumed displacements and transverse strains.

Tessler, A.↗
NASA NTRS1994

Towards an MHD theory for the standoff distance of Earth's bow shock

An MHD theory is developed for the stand-off distance a(sub s) of the bow shock and the thickness delta(sub ms) of the magnetosheath, using the empirical Spreiter et al. relation delta(sub ms) = kX and the MHD density ratio X across the shock. The theory includes as special cases the well-known gasdynamic theory and associated phenomenological MHD-like models for delta(sub ms) and a(sub s). In general, however, MHD effects produce major differences from previous models, especially at low Alfven (M(sub A)) and sonic (M(sub S)) Mach numbers. The magnetic field orientation, M(sub A), M(sub S) and the ratio of specific heats gamma are all important variables of the theory. Three principal conclusions are reached. First, the gasdynamic and phenomenological models miss important dependances on field orientation and M(sub S) and generally provide poor approximations to the MHD results. Second, changes in field orientation and M(sub S) are predicted to cause factor of approximately 4 changes in delta(sub ms) at low M(sub A). Third, using Spreiter et al.'s value for k in the MHD theory leads to maximum a(sub s) values at low M(sub A) and nominal M(sub S) that are much smaller than observations and MHD simulations require. Resolving this problem requires either the modified Spreiter-like relation and larger k found in recent MHD simulations and/or breakdown in the Spreiter-like relation at very low M(sub A).

Cairns, Iver H.↗
NASA NTRS1996

A Note on Multigrid Theory for Non-nested Grids and/or Quadrature

We provide a unified theory for multilevel and multigrid methods when the usual assumptions are not present. For example, we do not assume that the solution spaces or the grids are nested. Further, we do not assume that there is an algebraic relationship between the linear algebra problems on different levels. What we provide is a computationally useful theory for adaptively changing levels. Theory is provided for multilevel correction schemes, nested iteration schemes, and one way (i.e., coarse to fine grid with no correction iterations) schemes. We include examples showing the applicability of this theory: finite element examples using quadrature in the matrix assembly and finite volume examples with non-nested grids. Our theory applies directly to other discretizations as well.

Douglas, C. C.↗
NASA NTRS1994

Towards an MHD Theory for the Standoff Distance of Earth's Bow Shock

A magnetohydrodynamic (MHD) theory is developed for the standoff distance a(s) of the bow shock and the thickness Delta(ms) of the magnetosheath, using the empirical Spreiter et al. relation Delta(ms) = kX and the MHD density ratio X across the shock. The theory includes as special cases the well-known gasdynamic theory and associated phenomenological MHD-like models for Delta(ms) and As. In general, however, MHD effects produce major differences from previous models, especially at low Alfev (Ma) and Sonic (Ms) Mach numbers. The magnetic field orientation Ma, Ms and the ratio of specific heats gamma are all important variables of the theory. In contrast, the fast mode Mach number need play no direct role. Three principle conclusions are reached. First the gasdynamic and phenomenological models miss important dependences of field orientation and Ms generally provide poor approximations to the MHD results. Second, changes in field orientation and Ms are predicted to cause factor of approximately 4 changes in Delta(ms) at low Ma. These effects should be important when predicting the shock's location or calculating gramma from observations. Third, using Spreiter et al.'s value for k in the MHD theory leads to maxima a(s) values at low Ma and nominal Ms that are much smaller than observations and MHD simulations require. Resolving this problem requires either the modified Spreiter-like relation and larger k found in recent MHD simulations and/or a breakdown in the Spreiter-like relation at very low Ma.

Carins, Iver H.↗
NASA NTRS1997

A Viscoplastic Constitutive Theory for Monolithic Ceramic Materials

With increasing use of ceramic materials in high temperature structural applications such as advanced heat engine components, the need arises to accurately predict thermomechanical behavior. This paper, which is the first of two in a series, will focus on inelastic deformation behavior associated with these service conditions by providing an overview of a viscoplastic constitutive model that accounts for time-dependent hereditary material deformation (e.g., creep, stress relaxation, etc.) in monolithic structural ceramics. Early work in the field of metal plasticity indicated that inelastic deformations are essentially unaffected by hydrostatic stress. This is not the case, however, for ceramic-based material systems, unless the ceramic is fully dense. The theory presented here allows for fully dense material behavior as a limiting case. In addition, ceramic materials exhibit different time-dependent behavior in tension and compression. Thus, inelastic deformation models for ceramics must be constructed in a fashion that admits both sensitivity to hydrostatic stress and differing behavior in tension and compression. A number of constitutive theories for materials that exhibit sensitivity to the hydrostatic component of stress have been proposed that characterize deformation using time-independent classical plasticity as a foundation. However, none of these theories allow different behavior in tension and compression. In addition, these theories are somewhat lacking in that they are unable to capture creep, relaxation, and rate-sensitive phenomena exhibited by ceramic materials at high temperature. When subjected to elevated service temperatures, ceramic materials exhibit complex thermomechanical behavior that is inherently time-dependent, and hereditary in the sense that current behavior depends not only on current conditions, but also on thermo-mechanical history. The objective of this work is to present the formulation of a macroscopic continuum theory that captures these time-dependent phenomena. Specifically, the overview contained in this paper focuses on the multiaxial derivation of the constitutive model, and examines the scalar threshold function and its attending geometrical implications.

Janosik, Lesley A.↗