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NASA NTRS1989

Composite Blade Structural Analyzer (COBSTRAN) theoretical/programmer's manual

This manual describes the organization and flow of data and analysis in the computer code, COBSTRAN (COmposite Blade STRuctural ANalyzer). This code combines composite mechanics and laminate theory with an internal data base of fiber and matrix properties and was developed for the design and analysis of composite turbofan and turboprop blades and composite wind turbine blades. Inputs to the code are constituent fiber and matrix material properties, factors reflecting the fabrication process, composite geometry and blade geometry. COBSTRAN performs the micromechanics and laminate analyses of these fiber composites and generates a NASTRAN finite element model of the blade. This manual describes the equations formulated and solved in the code and the function of each of the seventy-two subroutines. COBSTRAN is written in FORTRAN 77.

Aiello, Robert A.↗

NASA NTRS1994

Predicting Fatigue Lives Of Metal-Matrix/Fiber Composites

Method of prediction of fatigue lives of intermetallic-matrix/fiber composite parts at high temperatures styled after method of universal slopes. It suffices to perform relatively small numbers of fatigue tests. Data from fatigue tests correlated with tensile-test data by fitting universal-slopes equation to both sets of data. Thereafter, universal-slopes equation used to predict fatigue lives from tensile properties.

Bartolotta, Paul A.↗

NASA NTRS2003

Calculation of Free-Free Opacities

Free-free absorption is an important contribution to the opacity for radiation transport through hot materials Temperatures can be as high as several keV, such that it becomes a computational challenge to solve the Schrodinger equation efficiently for rapidly oscillating continuum functions for high angular momenta. Several groups\footnots, including ours, have studied the phase amplitude solution (PAS) of the Schrodinger equation, in which one solves equations for the wave function amplitude and phase, which are: smooth functions of the electron energy. It is also important to have an accurate Schroudinger benchmark for the development of the PAS method. We present results for dipole matrix elements, Gaunt factors, and cross sections for the absorption of radiation at various energies for Cs XIX at temperature=100 eV and density=0.187 g/cc for our newly developed PAS and Schrodinger benchmark.

Bhatia, A. K.↗

NASA NTRS1986

Higher-order flux difference splitting schemes for the Euler equations using upstream interpolations

A class of explicit two time-level, 2p + 1 space-point, (2p 1)-th order, upwind-biased flux difference splitting schemes are proposed for the numerical advection based on Lagrange's interpolation, and the method is an accord with the physical domain of dependence. A normalized Jacobian coefficient matrix is introduced to convert the schemes to hyperbolic systems of conservation laws, and approaches to make the higher-order schemes total variation stable are discussed. Accuracy and stability of the present schemes are examined, and implicit total variation diminishing schemes are developed for steady-state calculations.Application to gasdynamic problems for both steady and unsteady flows covering a wide range of Mach numbers is considered, and results for a blast wave passing a cylinder, and head-on collision of two blast waves over a circular arc, are presented. The flow patterns were found to be symmetric, and good resolution of flow structures was obtained.

Yang, J. Y.↗

NASA NTRS1973

Evaluation of control laws and actuator locations for control systems applicable to deformable astronomical telescope mirrors

Some of the major difficulties associated with large orbiting astronomical telescopes are the cost of manufacturing the primary mirror to precise tolerances and the maintaining of diffraction-limited tolerances while in orbit. One successfully demonstrated approach for minimizing these problem areas is the technique of actively deforming the primary mirror by applying discrete forces to the rear of the mirror. A modal control technique, as applied to active optics, has previously been developed and analyzed. The modal control technique represents the plant to be controlled in terms of its eigenvalues and eigenfunctions which are estimated via numerical approximation techniques. The report includes an extension of previous work using the modal control technique and also describes an optimal feedback controller. The equations for both control laws are developed in state-space differential form and include such considerations as stability, controllability, and observability. These equations are general and allow the incorporation of various mode-analyzer designs; two design approaches are presented. The report also includes a technique for placing actuator and sensor locations at points on the mirror based upon the flexibility matrix of the uncontrolled or unobserved modes of the structure. The locations selected by this technique are used in the computer runs which are described. The results are based upon three different initial error distributions, two mode-analyzer designs, and both the modal and optimal control laws.

Ostroff, A. J.↗

NASA NTRS1977

Vibrational and rotational transitions in low-energy electron-diatomic-molecule collisions. I - Close-coupling theory in the moving body-fixed frame. II - Hybrid theory and close-coupling theory: An /l subscript z-prime/-conserving close-coupling approximation

A detailed vibrational-rotational (V-R) close-coupling formulation of electron-diatomic-molecule scattering is developed in which the target molecular axis is chosen to be the z-axis and the resulting coupled differential equation is solved in the moving body-fixed frame throughout the entire interaction region. The coupled differential equation and asymptotic boundary conditions in the body-fixed frame are given for each parity, and procedures are outlined for evaluating V-R transition cross sections on the basis of the body-fixed transition and reactance matrix elements. Conditions are discussed for obtaining identical results from the space-fixed and body-fixed formulations in the case where a finite truncated basis set is used. The hybrid theory of Chandra and Temkin (1976) is then reformulated, relevant expressions and formulas for the simultaneous V-R transitions of the hybrid theory are obtained in the same forms as those of the V-R close-coupling theory, and distorted-wave Born-approximation expressions for the cross sections of the hybrid theory are presented. A close-coupling approximation that conserves the internuclear axis component of the incident electronic angular momentum (l subscript z-prime) is derived from the V-R close-coupling formulation in the moving body-fixed frame.

Choi, B. H.↗

NASA NTRS1989

Progress on a Taylor weak statement finite element algorithm for high-speed aerodynamic flows

A new finite element numerical Computational Fluid Dynamics (CFD) algorithm has matured to the point of efficiently solving two-dimensional high speed real-gas compressible flow problems in generalized coordinates on modern vector computer systems. The algorithm employs a Taylor Weak Statement classical Galerkin formulation, a variably implicit Newton iteration, and a tensor matrix product factorization of the linear algebra Jacobian under a generalized coordinate transformation. Allowing for a general two-dimensional conservation law system, the algorithm has been exercised on the Euler and laminar forms of the Navier-Stokes equations. Real-gas fluid properties are admitted, and numerical results verify solution accuracy, efficiency, and stability over a range of test problem parameters.

Baker, A. J.↗

NASA NTRS1992

MOM3D method of moments code theory manual

MOM3D is a FORTRAN algorithm that solves Maxwell's equations as expressed via the electric field integral equation for the electromagnetic response of open or closed three dimensional surfaces modeled with triangle patches. Two joined triangles (couples) form the vector current unknowns for the surface. Boundary conditions are for perfectly conducting or resistive surfaces. The impedance matrix represents the fundamental electromagnetic interaction of the body with itself. A variety of electromagnetic analysis options are possible once the impedance matrix is computed including backscatter radar cross section (RCS), bistatic RCS, antenna pattern prediction for user specified body voltage excitation ports, RCS image projection showing RCS scattering center locations, surface currents excited on the body as induced by specified plane wave excitation, and near field computation for the electric field on or near the body.

Shaeffer, John F.↗

NASA NTRS1993

Characterization of Asymmetric Coplanar Waveguide Discontinuities

A general technique to characterize asymmetric coplanar waveguide (CPW) discontinuities with air bridges where both the fundamental coplanar and slotline modes may be excited together is presented. First, the CPW discontinuity without air bridges is analyzed using the space-domain integral equation (SDIE) approach. Second, the parameters (phase, amplitude, and wavelength) of the coplanar and slotline modes are extracted from an amplitude modulated-like standing wave existing in the CPW feeding lines. Then a 2n x 2n generalized scattering matrix of the n-port discontinuity without air bridges is derived which includes the occurring mode conversion. Finally, this generalized scattering matrix is reduced to an n x n matrix by enforcing suitable conditions at the ports which correspond to the excited slotline mode. For the purpose of illustration, the method is applied to a shielded asymmetric short-end CPW shunt stub, the scattering parameters of which are compared with those of a symmetric one. Experiments are performed on both discontinuities and the results are in good agreement with theoretical data. The advantages of using air bridges in CPW circuits as opposed to bond wires are also discussed.

Dib, Nihad I.↗

NASA NTRS2020

An Overview of the Null-Field Method. I. Formulation and Basic Results

In this paper we revisit the fundamentals of the null-field method with discrete sources. We prove the unique solvability of the null-field equations for the total field inside the particle and the internal field outside the particle, at all wavenumbers. For this purpose, we use the equivalence between the null-field and surface integral equations methods. Furthermore, we discuss the completeness property of different systems of discrete sources for a surface field approximation, and derive an infinite set of integral equations for the surface fields in a variety of discrete sources. Finally, we formulate the null-field scheme as an approach aiming to construct an approximate solution to the scattering problem. The way in which we introduce the matrix of a particle is different from the standard approach relying on the assumption that the system of regular vector spherical wave functions for the interior problem is a basis.

Null-field method↗

NASA NTRS1974

A recurrence matrix method for the analysis of longitudinal and torsional vibrations in non-uniform multibranch beams with variable boundary conditions

An approximate method for calculating the longitudinal and torsional natural frequencies and associated modal data of a beamlike, variable cross section multibranch structure is presented. The procedure described is the numerical integration of the first order differential equations that characterize the beam element in longitudinal motion and that satisfy the appropriate boundary conditions.

Davis, R. B.↗

NASA NTRS1976

Comments on the role of diagonal dominance in implicit difference methods

Numerical tests were made for a model of the Navier-Stokes equations using a second-order accurate implicit scheme which guarantees diagonal dominance. The results suggest that the failure of implicit methods using large marching steps may not always be attributed to the lack of diagonal dominance in the coefficient matrix. In some cases the failure may be caused by a nonlinear instability associated with the solution method.

Rudy, D. H.↗

NASA NTRS1989

Kaon-nucleus scattering

The derivations of the Lippmann-Schwinger equation and Watson multiple scattering are given. A simple optical potential is found to be the first term of that series. The number density distribution models of the nucleus, harmonic well, and Woods-Saxon are used without t-matrix taken from the scattering experiments. The parameterized two-body inputs, which are kaon-nucleon total cross sections, elastic slope parameters, and the ratio of the real to the imaginary part of the forward elastic scattering amplitude, are presented. The eikonal approximation was chosen as our solution method to estimate the total and absorptive cross sections for the kaon-nucleus scattering.

Hong, Byungsik↗

NASA NTRS1990

Fundamental aspects and failure modes in high-temperature composites

Fundamental aspects and attendant failure mechanisms for high-temperature composites are summarized. These include in situ matrix behavior, load transfer, limits on matrix ductility to survive a given number of cyclic loadings, fundamental parameters which govern thermal stresses, vibration stresses and impact resistance, as well as their attendant failure mechanisms and failure sequences. The resulting guidelines are presented in terms of simple equations which are suitable for the preliminary assessment of the merits of a particular high-temperature composite in a specific application.

Chamis, C. C.↗

NASA NTRS1990

Vibration and wave propagation characteristics of multisegmented elastic beams

Closed form analytical solutions are derived for the vibration and wave propagation of multisegmented elastic beams. Each segment is modeled as a Timoshenko beam with possible inclusion of material viscosity, elastic foundation and axial forces. Solutions are obtained by using transfer matrix methods. According to these methods formal solutions are first constructed which relate the deflection, slope, moment and shear force of one end of the individual segment to those of the other. By satisfying appropriate continuity conditions at segment junctions, a global 4x4 matrix results which relates the deflection, slope, moment and shear force of one end of the beam to those of the other. If any boundary conditions are subsequently invoked on the ends of the beam one gets the appropriate characteristic equation for the natural frequencies. Furthermore, by invoking appropriate periodicity conditions the dispersion relation for a periodic system is obtained. A variety of numerical examples are included.

Nayfeh, Adnan H.↗

NASA NTRS1990

True covariance simulation of the EUVE (extreme ultra violet explorer) update filter

This paper presents a covariance analysis of the performance and sensitivity of the attitude determination Extended Kalman Filter (EKF) used by the onboard computer (OBC) of the Extreme Ultra Violet Explorer (EUVE) spacecraft. The linearized dynamics and measurement equations of the error states are used in formulating the 'truth model' describing the order of the systems involved. The 'design model' used by the OBC EKF is then obtained by reducing the order of the truth model. The covariance matrix of the EKF which uses the reduced order model is not the correct covariance of the EKF estimation error. A 'true covariance analysis' has to be carried out in order to evaluate the correct accuracy of the OBC generated estimates. The results of such analysis are presented which indicate both the performance and the sensitivity of the OBC EKF.

Bar-Itzhack, I. Y.↗

NASA NTRS1993

Preconditioning for the Navier-Stokes equations with finite-rate chemistry

The preconditioning procedure for generalized finite-rate chemistry and the proper preconditioning for the one-dimensional Navier-Stokes equations are presented. Eigenvalue stiffness is resolved and convergence-rate acceleration is demonstrated over the entire Mach-number range from the incompressible to the hypersonic. Specific benefits are realized at low and transonic flow speeds. The extended preconditioning matrix accounts for thermal and chemical non-equilibrium and its implementation is explained for both explicit and implicit time marching. The effect of higher-order spatial accuracy and various flux splittings is investigated. Numerical analysis reveals the possible theoretical improvements from using proconditioning at all Mach numbers. Numerical results confirm the expectations from the numerical analysis. Representative test cases include flows with previously troublesome embedded high-condition-number regions.

Godfrey, Andrew G.↗

NASA NTRS1994

Three-dimensional fully spectral numerical method for mantle convection with depth-dependent properties

A semi-implicit fully spectral collocation method for the simulation of three-dimensional mantle convection with depth-dependent thermo-dynamic and transport properties is presented. The variable property Navier-Stokes equation expressed in terms of the primitive variable velocity and pressure is solved with the mass continuity and temperature equations. The periodic horizontal boundary conditions allow a Fourier expansion for the two horizontal directions. The stress-free, impermeable isothermal boundary conditions along with the depth dependent coefficients are handled with a Chebyshev expansion in the vertical direction. In the limit of an infinite Prandtl number appropriate to mantle convection, the inertial terms in the momentum equation are unimportant. In this case an explicit solution of a Poisson equation for pressure can be avoided; instead a fourth-order equation for vertical velocity can be solved. Simultaneous imposition of both impermeable and continuity boundary conditions during the vertical velocity evaluation is discussed. The pressure distributions on the top and bottom bounding planes were determined by means of an influence matrix technique. The numerical method employed here avoids time-splitting errors and enforces velocity boundary conditions and continuity over the entire domain, including the boundaries, to machine accuracy. Strongly time-dependent three-dimensional solutions up to a surface Rayleigh number of 1 x 10(exp 7) have been obtained. Strong upwellings, pulsating chaotically, are formed by the collective merging of cylindrical plumes.

Balachandar, S.↗