Finite element solution for axisymmetrical shells.
Finite element approach to analysis of axisymmetric thin elastic shells, employing matrix method
SHELL THEORY↗
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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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Theory of radiative transfer in inhomogeneous atmospheres. IV - Application of the matrix perturbation method to a semi-infinite atmosphere
Polarized radiation transfer through inhomogeneous semiinfinite atmosphere by matrix perturbation method, giving nonlinear singular integral equation
Abhyankar, K. D.↗
Software for Fault-Tolerant Matrix Multiplication
Formal Linear Algebra Recovery Environment is a computer program for high-performance, fault-tolerant matrix multiplication. The program is based on an extension of the prior theory and practice of fault-tolerant matrix matrix multiplication of the form C = AB. This extension provides low-overhead methods for detecting errors, not only in C, but also in A and/or B. These methods enable the detection of all errors as long as, in a given case, only one entry in A, B, or C is corrupted. The program also provides for following a low-overhead rollback approach to correct errors once detected. Results of computational experiments have demonstrated that the methods implemented in this program work well in practice while imposing an acceptably low level of overhead, relative to high-performance matrix-multiplication methods that do not afford fault tolerance.
Katz, Daniel↗
Inelastic deformation of metal matrix composites
A theoretical model capable of predicting the thermomechanical response of continuously reinforced metal matrix composite laminates subjected to multiaxial loading was developed. A micromechanical model is used in conjunction with nonlinear lamination theory to determine inelastic laminae response. Matrix viscoplasticity, residual stresses, and damage to the fiber/matrix interfacial zone are explicitly included in the model. The representative cell of the micromechanical model is considered to be in a state of generalized plane strain, enabling a quasi two-dimensional analysis to be performed. Constant strain finite elements are formulated with elastic-viscoplastic constitutive equations. Interfacial debonding is incorporated into the model through interface elements based on the interfacial debonding theory originally presented by Needleman, and modified by Tvergaard. Nonlinear interfacial constitutive equations relate interfacial tractions to displacement discontinuities at the interface. Theoretical predictions are compared with the results of an experimental program conducted on silicon carbide/titanium (SiC/Ti) unidirectional, (O4), and angle-ply, (+34)(sub s), tubular specimens. Multiaxial loading included increments of axial tension, compression, torque, and internal pressure. Loadings were chosen in an effort to distinguish inelastic deformation due to damage from matrix plasticity and separate time-dependent effects from time-independent effects. Results show that fiber/matrix debonding is nonuniform throughout the composite and is a major factor in the effective response. Also, significant creep behavior occurs at relatively low applied stress levels at room temperature.
Lissenden, C. J.↗
Backscattering by nonspherical particles - A review of methods and suggested new approaches
Scattering of electromagnetic radiation near the backward direction is more sensitive to particle shape than scattering near the forward direction. Mie theory is therefore of dubious applicability to predicting backscattering by atmospheric particles known to be irregular or to inverting measurements on such particles. An irregular particle is one with an uncertain shape. In the face of uncertainty one must adopt a statistical approach in which scattering properties of ensembles are determined. To obtain ensemble averages, a basis is needed for averaging over a set of electromagnetic microstates. Ensemble averages based on the Rayleigh theory for small ellipsoids and on the T matrix method for spheroids agree better with measurements than Mie theory does. The coupled-dipole method also provides a basis for ensemble averaging. This method also leads to a simple physical interpretation of why backscattering is so sensitive to particle shape and can be used to calculate scattering by one- and two-dimensional analogs to three-dimensional irregular particles.
Bohren, Craig F.↗
Space transportation vehicle design evaluation using saturated designs
An important objective in the preliminary design and evaluation of space transportation vehicles is to find the best values of design variables that optimize the performance characteristic (e.g. dry weight). For a given configuration, the vehicle performance can be determined by the use of complex sizing and performance evaluation computer programs. These complex computer programs utilize iterative algorithms and they are generally too expensive and/or difficult to use directly in multidisciplinary design optimization. An alternative is to use response surface methodology (RSM) and obtain quadratic polynomial approximations to the functional relationships between performance characteristics and design variables. In RSM, these approximation models are then used to determine optimum design parameter values and for rapid sensitivity studies. Constructing a second-order model requires that 'n' design parameters be studied at least at 3 levels (values) so that the coefficients in the model can be estimated. There, 3(n) factorial experiments (point designs or observations) may be necessary. For small values of 'n' such as two or three, this design works well. However, when a large number of design parameters are under study, the number of design points required for a full-factorial design may become excessive. Fortunately, these quadratic polynomial approximations can be obtained by selecting an efficient design matrix using central composite designs (CCD) from design of experiments theory. Each unique point design from the CCD matrix is then conducted using computerized analysis tools (e.g. POST, CONSIZ, etc.). In the next step, least squares regression analysis is used to calculate the quadratic polynomial coefficients from the data. However, in some multidisciplinary applications involving a large number of design variables and several disciplines, the computerized performance synthesis programs may get too time consuming and expensive to run even with the use of efficient central composite designs. In such cases, it may be preferable to keep the number of design points to an absolute minimum and trade some model accuracy with cost. For this purpose, another class of experimental designs, called saturated D-optimal designs may be utilized for generating a matrix of vehicle designs. A design is called saturated when the number of design points is exactly equal to the number of terms in the model to be fitted. As a result, saturated designs require the absolute minimum number of design points ((n+1)(n+2)/s) to estimate the quadratic polynomial model coefficients. Saturated designs can be generated using the D-optimality criterion. A good saturated design should give rise to least squares estimates with minimum generalized variance.
Unal, Resit↗
Multiscale Modeling of Ceramic Matrix Composites
Results of multiscale modeling simulations of the nonlinear response of SiC/SiC ceramic matrix composites are reported, wherein the microstructure of the ceramic matrix is captured. This micro scale architecture, which contains free Si material as well as the SiC ceramic, is responsible for residual stresses that play an important role in the subsequent thermo-mechanical behavior of the SiC/SiC composite. Using the novel Multiscale Generalized Method of Cells recursive micromechanics theory, the microstructure of the matrix, as well as the microstructure of the composite (fiber and matrix) can be captured.
ceramic matrix composites↗
Nonlinear mechanical behavior of thermoplastic matrix materials for advanced composites
Two recent theories of nonlinear mechanical response are quantitatively compared and related to experimental data. Computer techniques are formulated to handle the numerical integration and iterative procedures needed to solve the associated sets of coupled nonlinear differential equations. Problems encountered during these formulations are discussed and some open questions described. Bearing in mind these cautions, the consequences of changing parameters that appear in the formulations on the resulting engineering properties are discussed. Hence, engineering approaches to the analysis of thermoplastic matrix material can be suggested.
Arenz, R. J.↗
Polarimetric signatures of a layer of random nonspherical discrete scatterers overlying a homogeneous half-space based on first- and second-order vector radiative transfer theory
Complete polarimetric signatures of a layer of random, nonspherical discrete scatterers overlying a homogeneous half space are studied with the first- and second-order solutions of the vector radiative transfer theory. Some of the salient features of the numerical results are as follows: (1) the inclusion of the nondiagonal extinction matrix in the vector radiative transfer theory accounts for an appreciable phase difference between vv and hh polarizations, particularly for aligned scatterers; (2) the ensemble-averaged scattered Stokes vector is generally partially polarized, with the degree of polarization less than unity; (3) there generally exists a pedestal in the copolarization return when plotted as a function of ellipticity and orientation angles, which may be due to heterogeneity of scattering objects and/or multiple scattering effects; and (4) multiple scattering effects generally enhance the pedestal in copolarization return, decrease the degree of polarization, affect phase difference, and also enhance the depolarization return.
Tsang, Leung↗
Spinor representations for fields with any spin: Lorentz tensor basis for operators and covariant multipole decomposition
This paper discusses a framework to parametrize and decompose operator matrix elements for particles with higher spin (j > 1/2) using chiral representations of the Lorentz group, i.e. the (j, 0) and (0, j) representations and their parity-invariant direct sum. Unlike traditional approaches that require imposing constraints to eliminate spurious degrees of freedom, these chiral representations contain exactly the 2j + 1 components needed to describe a spin-j particle. The central objects in the construction are the t-tensors, which are generalizations of the Pauli four-vector σ μ for higher spin. For the generalized spinors of these representations, we demonstrate how the algebra of the t-tensors allows to formulate a generalization of the Dirac matrix basis for any spin. For on-shell bilinears, we show that a set consisting exclusively of covariant multipoles of order 0 ≤ m ≤ 2j forms a complete basis. We provide explicit expressions for all bilinears of the generalized Dirac matrix basis, which are valid for any spin value. As a byproduct of our derivations we present an efficient algorithm to compute the t-tensor matrix elements. The formalism presented here paves the way to use a more unified approach to analyze the non-perturbative QCD structure of hadrons and nuclei across different spin values, with clear physical interpretation of the resulting distributions as covariant multipoles.
Angular momentum of light↗
Application of antiresonance theory to helicopters
Antiresonance theory is the principle underlying nonresonant nodes in a structure, and covers both nonresonant nodes occurring naturally and those introduced by devices such as dynamic absorbers and antiresonant isolators. The dynamic antiresonant vibration isolator (DAVI) and the nodale module are examples of the applications of transfer antiresonances. It is shown that antiresonances are eigenvalues, and that they can be determined by matrix iteration. Applications of antiresonance theory to helicopter engineering problems, using the antiresonant eigenvalue equation are suggested.
Bartlett, F. D., Jr.↗
Lifting surface theory for rectangular wings
A new incompressible lifting-surface theory is developed for thin rectangular wings. The solution requires the downwash equation to be in the form of Cauchy-type integrals. Lan's method is employed for the chordwise integrals since it properly accounts for the leading-edge singularity, Cauchy singularity and Kutta condition. The Cauchy singularity in the spanwise integral is also accounted for by using the midpoint trapezoidal rule and theory of Chebychev polynomials. The resulting matrix equation, formed by satisfying the boundary condition at control points, is simpler and quicker to compute than other lifting surface theories. Solutions were found to converge with only a small number of control points and to compare favorably with results from other methods.
Dejarnette, F. R.↗
Research and study in system optimization techniques Second quarterly progress report, Feb. 14 - May 14, 1965
Systems optimization for motion stability matrix problem - predictive guidance for Thor vehicle trajectory
PREDICTION THEORY↗
A continuum model for damage evolution in laminated composites
The accumulation of matrix cracking is examined using continuum damage mechanics lamination theory. A phenomenologically based damage evolutionary relationship is proposed for matrix cracking in continuous fiber reinforced laminated composites. The use of material dependent properties and damage dependent laminate averaged ply stresses in this evolutionary relationship permits its application independently of the laminate stacking sequence. Several load histories are applied to crossply laminates using this model, and the results are compared to published experimental data. The stress redistribution among the plies during the accumulation of matrix damage is also examined. It is concluded that characteristics of the stress redistribution process could assist in the analysis of the progressive failure process in laminated composites.
Lo, D. C.↗
High Temperature Composite Analyzer (HITCAN) theoretical manual, version 1.0
This manual outlines some of the theoretical aspects embedded in the computer code, HITCAN (High Temperature Composite ANalyzer). HITCAN is a general purpose computer program for predicting nonlinear global structural and local stress-strain response of arbitrarily oriented, multilayered high temperature metal matrix composite structures. This code combines composite mechanics and laminate theory with an internal data base of the constituents (matrix, fiber and interface) material properties. The thermal and mechanical properties of the constituents are considered to be nonlinearly dependent on several parameters including temperature, stress and stress rate. The computational procedure for the analysis of the composite structure uses the finite element method. HITCAN consists of three modules: COBSTRAN, METCAN and MHOST. COBSTRAN generates the geometry (pre-processor) and defines the layup of the different plies. METCAN computes the material behavior of the composite and of the constituents. Finally, MHOST is a finite element program based on the mixed iterative solution technique. MHOST has a library for 2D and 3D isoparametric elements. HITCAN is written in FORTRAN 77 computer language and has been configured and executed on the NASA Lewis Research Center CRAY XMP and YMP computers.
Lackney, J. J.↗
Recent Updates to the Los Alamos EDA 𝑅-Matrix Code
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73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
Measuring attitude with a gradiometer
This paper explores using a gravity gradiometer to measure the attitude of a satellite, given that the gravity field is accurately known. Since gradiometers actually measure a combination of the gradient and attitude rate and acceleration terms, the answer is far from obvious. The paper demonstrates that it can be done and at microradian accuracy. The technique employed is dynamic estimation, based on the momentum biased Euler equations. The satellite is assumed nominally planet pointed, and subject to control, gravity gradient, and partly radom drag torques. The attitude estimator is unusual. While the standard method of feeding back measurement residuals is used, the feedback gain matrix isn't derived from Kalman theory. instead, it's chosen to minimize a measure of the terminal covariance of the error in the estimate. This depends on the gain matrix and the power spectra of all the process and measurement noises. An integration is required over multiple solutions of Lyapunov equations.
Sonnabend, David↗
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.↗