Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “matrix multiplication”

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 271 records · Page 15
All sourcesNASA NTRSDOE OSTI
NASA NTRS1988

The effect of hydrogen on deformation substructure, flow and fracture in a nickel-base single crystal superalloy

The room temperature flow and fracture of a nickel-base single crystal gamma/gamma-/prime superalloy in the presence and absence of hydrogen is explored. The procedure of hydrogen-charging employed in this study provides a very high and uniform hydrogen concentration of the order of 5000 at.-ppm in the material. It is shown that the most compelling hydrogen-induced changes in deformation behavior are enhanced dislocation accumulation in the gamma matrix and extensive cross-slip of super-dislocations. The explanation of these changes is proposed. Both effects contribute to the increase of flow stress and the notable work hardening that occurs prior to fracture. Hydrogen enhanced strain localization in the gamma matrix leads to the dramatic loss of ductility and premature cracking, which manifests as failure macroscopically parallel to the 100-plane-oriented faces of gamma-prime precipitates. On the microscale, cracking, while limited to the gamma matrix, occurs parallel to multiple 111-plane-oriented slip systems.

Dollar, M.↗
NASA NTRS1993

An analytical/numerical correlation study of the multiple concentric cylinder model for the thermoplastic response of metal matrix composites

The utility of a recently developed analytical micromechanics model for the response of metal matrix composites under thermal loading is illustrated by comparison with the results generated using the finite-element approach. The model is based on the concentric cylinder assemblage consisting of an arbitrary number of elastic or elastoplastic sublayers with isotropic or orthotropic, temperature-dependent properties. The elastoplastic boundary-value problem of an arbitrarily layered concentric cylinder is solved using the local/global stiffness matrix formulation (originally developed for elastic layered media) and Mendelson's iterative technique of successive elastic solutions. These features of the model facilitate efficient investigation of the effects of various microstructural details, such as functionally graded architectures of interfacial layers, on the evolution of residual stresses during cool down. The available closed-form expressions for the field variables can readily be incorporated into an optimization algorithm in order to efficiently identify optimal configurations of graded interfaces for given applications. Comparison of residual stress distributions after cool down generated using finite-element analysis and the present micromechanics model for four composite systems with substantially different temperature-dependent elastic, plastic, and thermal properties illustrates the efficacy of the developed analytical scheme.

Pindera, Marek-Jerzy↗
NASA NTRS2012

Computational Modeling of Micro-Crack Induced Attenuation in CFRP Composites

A computational study is performed to determine the contribution to ultrasound attenuation in carbon fiber reinforced polymer composite laminates of linear elastic scattering by matrix micro-cracking. Multiple scattering approximations are benchmarked against exact computational approaches. Results support linear scattering as the source of observed increased attenuation in the presence of micro-cracking.

Roberts, R. A.↗
NASA NTRS1993

Extending substructure based iterative solvers to multiple load and repeated analyses

Direct solvers currently dominate commercial finite element structural software, but do not scale well in the fine granularity regime targeted by emerging parallel processors. Substructure based iterative solvers--often called also domain decomposition algorithms--lend themselves better to parallel processing, but must overcome several obstacles before earning their place in general purpose structural analysis programs. One such obstacle is the solution of systems with many or repeated right hand sides. Such systems arise, for example, in multiple load static analyses and in implicit linear dynamics computations. Direct solvers are well-suited for these problems because after the system matrix has been factored, the multiple or repeated solutions can be obtained through relatively inexpensive forward and backward substitutions. On the other hand, iterative solvers in general are ill-suited for these problems because they often must restart from scratch for every different right hand side. In this paper, we present a methodology for extending the range of applications of domain decomposition methods to problems with multiple or repeated right hand sides. Basically, we formulate the overall problem as a series of minimization problems over K-orthogonal and supplementary subspaces, and tailor the preconditioned conjugate gradient algorithm to solve them efficiently. The resulting solution method is scalable, whereas direct factorization schemes and forward and backward substitution algorithms are not. We illustrate the proposed methodology with the solution of static and dynamic structural problems, and highlight its potential to outperform forward and backward substitutions on parallel computers. As an example, we show that for a linear structural dynamics problem with 11640 degrees of freedom, every time-step beyond time-step 15 is solved in a single iteration and consumes 1.0 second on a 32 processor iPSC-860 system; for the same problem and the same parallel processor, a pair of forward/backward substitutions at each step consumes 15.0 seconds.

Farhat, Charbel↗
NASA NTRS1973

Estimation and detection of signals in multiplicative noise

A class of detection-estimation problems on matrix Lie groups is defined in which the observation noise is multiplicative in nature. By examining the differential versions of the hypotheses, which are bilinear in nature, it is possible to derive the relevant likelihood ratio formula and the associated optimal estimation equations for the signal given the observations and the assumption that the signal is present. These estimation equations are of interest in their own right, in that they represent a finite dimensional optimal solution to a nonlinear estimation problem and can be viewed as consisting of a Kalman-Bucy filter along with the on-line computation of the solution of the associated Riccati equation, which is driven by the observations. The usefulness of these results is illustrated via an example concerning the detection of an actuator failure in a rigid body rotational control system.

Willsky, A. S.↗
NASA NTRS1974

Estimation and detection of signals in multiplicative noise

We define a class of detection-estimation problems on matrix Lie groups in which the observation noise is multiplicative in nature. By examining the differential versions of the hypotheses, which are bilinear, we are able to derive the relevant likelihood ratio formula and the associated optimal estimation equations for the signal given the observations and the assumption that the signal is present. These estimation equations are of interest in their own right, in that they represent a finite-dimensional optimal solution to a nonlinear estimation problem and consist of a Kalman-Bucy filter along with the on-line computation of the solution of the associated Riccati equation, which is driven by the observations. The usefulness of these results is illustrated via an example concerning the detection of an actuator failure in a rigid-body rotational control system.

Willsky, A. S.↗
DOE OSTI2022

Benefits of using multiple Raman laser wavelengths for characterizing defects in a UO 2 matrix

Abstract Raman spectroscopy is one of the most useful techniques for studying the structure of UO 2 and changes due to specific defects caused by doping, changes in stoichiometry, irradiation, or heating under oxidizing conditions. In this paper, we illustrate several aspects of the application of Raman techniques to the study of UO 2 , including the use of wavelength‐dependent excitation (455, 532, and 785 nm) to assess the effects of doping (Nd, Th, and Zr), ion irradiation, and in situ heating and oxidation (UO 2 to U 3 O 8 ). Additionally, we show examples of how correlative microscopy is possible using electron backscatter diffraction combined with Raman maps of specific vibration bands or of laser‐induced luminescence generated by rare‐earth dopants in the matrix. For each of these applications, we suggest optimal excitation wavelengths that vary depending on the desired data. Blue (455 nm) excitation tends to promote oxidation even at low powers, but because Raman spectra change little with doping, irradiation‐induced changes are easier to observe. Green (532 nm) excitation is optimal for observing electron–phonon resonance effects in UO 2 and offers a good compromise for high‐temperature oxidation experiments, delivering high‐quality spectra for both UO 2 and U 3 O 8 . Infrared (785 nm) excitation is best for observing “defect” bands associated with doping in UO 2 , as changes with irradiation are small. Raman spectroscopy is particularly suited for studying the stability of UO 2 towards oxidation in the presence of dopants simulating fission products, where electron–phonon resonant effects, dopant ion luminescence, and mapping can be used together to investigate structural rearrangement as a function of temperature. These techniques can offer insight into microstructural changes in UO 2 fuels at higher burnups envisioned in future reactors.

42 ENGINEERING↗
NASA NTRS2006

Dielectric relaxation behavior of poly(acrylonitri1e-co-methacrylonitrile) microcapsules dispersed in a silicone matrix

The dielectric relaxation behavior of poly(acry1onitrile-co-methacrylonitrile) dispersed in a cured polydimethyl siloxane (PDMS) matrix as microcapsules was investigated over multiple thermal cycles and at varying concentrations. The copolymer microcapsules contained an isopentane core. In the PDMS matrix this copolymer displayed a pronounced relaxation signal at temperatures above the glass transition of the copolymers due to Maxwell-Wagner-Sillars (MWS) relaxation. The mechanism of MWS relaxation interpreted by the Havriliak-Negami and Kohlrausch-Williams-Watts relaxation functions was found to be very similar to previous studies of neat polyacrylonitrile and its copolymer. The activation energy of the relaxation decreased over successive thermal cycling coincident with a decreasing strength of the relaxation. These observations were attributed to the decreasing concentration of nitrile groups due to intramolecular cyclizations.

Park, Taigyoo↗
NASA NTRS2006

Dielectric Relaxation Behavior of Poly(acrylonitrile-co-methacrylonitrile) Microcapsules Dispersed in a Silicone Matrix

The dielectric relaxation behavior of poly(acrylonitrile-co-methacrylonitrile) dispersed in a cured polydimethyl siloxane (PDMS) matrix as microcapsules was investigated over multiple thermal cycles and at varying concentrations. The copolymer microcapsules contained an isopentane core. In the PDMS matrix this copolymer displayed a pronounced relaxation signal at temperatures above the glass transition of the copolymers due to Maxwell-Wagner-Sillars (MWS) relaxation. The mechanism of MWS relaxation interpreted by the Havriliak-Negami and Kohlrausch-Williams-Watts relaxation functions was found to be very similar to previous studies of neat polyacrylonitrile and its copolymer. The activation energy of the relaxation decreased over successive thermal cycling coincident with a decreasing strength of the relaxation. These observations were attributed to the decreasing concentration of nitrile groups due to intramolecular cyclizations.

Park, Taigyoo↗
NASA NTRS1981

A high capacity satellite switched TDMA microwave switch matrix

A description is given of the conceptual design of a high-capacity satellite switched-time division multiple access (SS-TDMA) microwave switch matrix fabricated with GaAs monolithic microwave integrated circuits (MMICs), including integration of both microwave and control logic circuits into the monolithic design. The technology required for a 30/20 GHz communications system includes an on-board SS-TDMA switch matrix. A conceptual design study that has been completed for a wideband, high-capacity (typically 100 x 100) channel switch matrix using technology anticipated for 1987 is described, noting that the study resulted in a switch matrix design concept using a coupled crossbar architecture implemented with MMIC. The design involves basic building block MMIC, permitting flexible growth and efficient wraparound redundancy to increase reliability.

Cory, B. J.↗
NASA NTRS1989

Efficient eigenvalue assignment for large space structures

A novel and efficient approach for the eigenvalue assignment of large first-order time-invariant systems is developed using full-state feedback and output feedback. First, a Schur decomposition is applied to triangularize the state matrix. Second, a series of coordinate rotations (Givens rotations) are used to move the eigenvalue to be reassigned to the end of the diagonal of its Schur form. Third, the eigenvalue is moved to the desired location by a full-state feedback, without affecting the remaining eigenvalues. The second and third step can be repeated until all the assignable eigenvalues are moved to the desired locations. Given the freedom of multiple inputs, the feedback gain matrix is calculated to minimize an objective function composed of a gain matrix norm and/or a robustness index of the closed-loop system. Numerical examples are given to demonstrate the feasibility of the proposed approach.

Maghami, Peiman G.↗
DOE OSTI2023

Generalized Mercier stability criterion for stellarators

The Mercier criterion is a well-known stability criterion for tokamaks. It is derived from a 2 × 2 matrix eigenvalue problem arising from the expansion of resonant solutions about a singular surface where m−nq=0, with m and n being the poloidal and toroidal mode numbers, respectively, and q being the safety factor. The stability criterion is that the eigenvalues must be real, otherwise, the solution oscillates, violating the Newcomb crossing criterion. Because of the non-axisymmetry of stellarators, different toroidal as well as poloidal harmonics couple to each other. It follows that each singular surface can have multiple resonant harmonics, with multiplicity M≥1. The corresponding matrix eigenvalue problem involves a 2M×2M matrix, resulting in M pairs of positive and negative eigenvalues. The generalized stability criterion is that all eigenvalues must be real. While the original Mercier criterion can be expressed in terms of quadratures of equilibrium quantities over the singular surface, which can be evaluated anywhere, the generalized Mercier criterion can only be evaluated on rational q surfaces with a given set of resonant harmonics.

Physics↗
NASA NTRS1982

20 x 20 IF switch matrix for SS-TDMA systems

Satellite-switched TDMA, an effective means for the increasing of communication satellite channel capacity and the improvement of system flexibility, requires that the spacecraft carry an IF switch matrix in order to provide interconnectivity among multiple beam antennas. Attention is presently given to the development of a 20 x 20 IF switch matrix for the NASA 30/20 GHz communications satellite which will provide a 2.5 GHz bandwidth at C-band frequencies with a switching speed of 10 nsec. Switch matrix architecture, switching device characteristic, and distribution control unit design practices are discussed, together with switch matrix reliability.

Ho, P. T.↗
DOE OSTI2020

Dynamic and Programmable Cellular-Scale Granules Enable Tissue-like Materials

Living tissues are an integrated, multiscale architecture consisting of dense cellular ensembles and extracellular matrices (ECMs). The cells and ECMs cooperate to enable specialized mechanical properties and dynamic responsiveness. However, the mechanical properties of living tissues are difficult to replicate. A particular challenge is identification of a cell-like synthetic component, which is tightly integrated with its matrix and also responsive to external stimuli. Here, we demonstrate that cellular-scale hydrated starch granules, an underexplored component in materials science, can turn conventional hydrogels into tissue-like materials when composites are formed. By using several synchrotron-based X-ray techniques, we reveal the mechanically induced organization and training dynamics of the starch granules in the hydrogel matrix. These dynamic behaviors enable multiple tissue-like properties such as programmability, anisotropy, strain-stiffening, mechanochemistry, and self-healability.

36 MATERIALS SCIENCE↗