Bounds for the eigenvalues of a matrix
Mathematical models for determining eigenvalue bounds of matrix
Garren, K. R.↗
SEARCH · Search NASA
Results for “Matrix Models”
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.
Modeling Woven Polymer Matrix Composites with MAC/GMC
NASA's Micromechanics Analysis Code with Generalized Method of Cells (MAC/GMC) is used to predict the elastic properties of plain weave polymer matrix composites (PMCs). The traditional one step three-dimensional homogertization procedure that has been used in conjunction with MAC/GMC for modeling woven composites in the past is inaccurate due to the lack of shear coupling inherent to the model. However, by performing a two step homogenization procedure in which the woven composite repeating unit cell is homogenized independently in the through-thickness direction prior to homogenization in the plane of the weave, MAC/GMC can now accurately model woven PMCs. This two step procedure is outlined and implemented, and predictions are compared with results from the traditional one step approach and other models and experiments from the literature. Full coupling of this two step technique with MAC/ GMC will result in a widely applicable, efficient, and accurate tool for the design and analysis of woven composite materials and structures.
Bednarcyk, Brett A.↗
Application of Transfer Matrix Approach to Modeling and Decentralized Control of Lattice-Based Structures
This paper presents a modeling and control of aerostructure developed by lattice-based cellular materials/components. The proposed aerostructure concept leverages a building block strategy for lattice-based components which provide great adaptability to varying ight scenarios, the needs of which are essential for in- ight wing shaping control. A decentralized structural control design is proposed that utilizes discrete-time lumped mass transfer matrix method (DT-LM-TMM). The objective is to develop an e ective reduced order model through DT-LM-TMM that can be used to design a decentralized controller for the structural control of a wing. The proposed approach developed in this paper shows that, as far as the performance of overall structural system is concerned, the reduced order model can be as e ective as the full order model in designing an optimal stabilizing controller.
Transfer Matrix Method↗
Extension of a noninteractive reliability model for ceramic matrix composites
Developments in the processing of high temperature ceramic composites demand innovative and progressive design protocols that adequately predict the thermal and mechanical behavior of these materials. The focus here is the extension of a reliability model for orthotropic ceramic composites. The approach chosen to describe failures leads to a noninteractive formulation of reliability that is phenomenological. This particular criterion, which was constructed using tensorial invariant theory, allows six potential failure modes to emerge.
Duffy, Stephen F.↗
Global Influence of Organic Aerosol Volatility on Aerosol Microphysical Processes: Composition and Number
We present MATRIX-VBS, a new aerosol scheme that simulates organic partitioning in an aerosol microphysics model, as part of the NASA GISS ModelE Earth System Model. MATRIX-VBS builds on its predecessor aerosol microphysics model MATRIX (Bauer et al., 2008, https://doi.org/10.5194/acp-8-6003-2008) and was developed in the box model framework (Gao et al., 2017, https://doi.org/10.5194/gmd-10-751-2017). The scheme features the inclusion of organic partitioning between the gas and particle phases and the photochemical aging process using the volatility-basis set (Donahue et al., 2006, https://doi.org/10.1021/es052297c). To assess the performance of the new model, we compared its mass concentration, number concentration, and activated number concentration to the original scheme MATRIX, and evaluated its mass concentrations in four seasons against data from the NASA Atmospheric Tomography Mission (ATom) aircraft campaign. Results from MATRIX-VBS show that organics are transported further away from their source, and their mass concentration increases aloft and decreases at the surface compared to those in MATRIX. The mass concentration of organics at the surface agrees well with measurements, and there are discrepancies for vertical profiles aloft. In the new scheme, the global mass load of organic aerosols increased by 50%, there is also an increased number of particles at the surface and fewer activated ones in most regions. The new scheme presents advanced and more comprehensive capability in simulating aerosol processes.
aerosol modeling↗
Can Semi-Volatile Organic Aerosols Lead to Fewer Cloud Particles?
The impact of condensing organic aerosols on activated cloud number concentration is examined in a new aerosol microphysics box model, MATRIX-VBS. The model includes the volatility-basis set (VBS) framework coupled with the aerosol microphysical scheme MATRIX (Multiconfiguration Aerosol TRacker of mIXing state) that resolves aerosol mass and number concentrations and aerosol mixing state. By including the condensation of organic aerosols, the new model produces less activated particles compared to the original model, which treats organic aerosols as non-volatile. Parameters such as aerosol chemical composition, mass and number concentrations, and particle sizes which affect activated cloud number concentration are thoroughly tested via a suite of Monte-Carlo simulations. Results show that by considering semi-volatile organics in MATRIX-VBS, there is lower activated particle number concentration, except in cases with low cloud updrafts, in clean environment at above freezing temperatures, and in polluted environments at high temperature (310K) and extremely low humidity conditions.
Gao, Chloe Y.↗
Creep of Refractory Fibers and Modeling of Metal and Ceramic Matrix Composite Creep Behavior
Our concentration during this research was on the following subprograms. (1) Ultra high vacuum creep tests on 218, ST300 and WHfC tungsten and MoHfC molybdenum alloy wires, temperature range from 1100 K to 1500 K, creep time of 1 to 500 hours. (2) High temperature vacuum tensile tests on 218, ST300 and WHfC tungsten and MoHfC molybdenum alloy wires. (3) Air and vacuum tensile creep tests on polycrystalline and single crystal alumina fibers, such as alumina-mullite Nextel fiber, yttrium aluminum ganet (YAG) and Saphikon, temperature range from 1150 K to 1470 K, creep time of 2 to 200 hours. (4) Microstructural evaluation of crept fibers, TEM study on the crept metal wires, SEM study on the fracture surface of ceramic fibers. (5) Metal Matrix Composite creep models, based on the fiber creep properties and fiber-matrix interface zone formation.
Tewari, S.N.↗
A comparison of analytical results for 20 K LOX/hydrogen instabilities
Test data from NASA Lewis' Effect of Thrust Per Element on Combustion Stability Characteristics of Hydrogen-Oxygen Rocket Engines test program are used to validate two recently released stability analysis tools. The first tool is a design methodology called ROCCID (ROCket Combustor Interactive Design). ROCCID is an interactive design and analysis methodology that uses existing performance and combustion stability analysis codes. The second tool is HICCIP (High frequency Injection Coupled Combustion Instability Program). HICCIP is a recently developed combustion stability analysis model. Using a matrix of models, results from analytic comparisons with 20 K LOX/H2 experimental data are presented.
Klem, Mark D.↗
A comparison of analytical results for 20 K LOX/hydrogen instabilities
Test data from NASA Lewis' Effect of Thrust Per Element on Combustion Stability Characteristics of Hydrogen-Oxygen Rocket Engines test program are used to validate two recently released stability analysis tools. The first tool is a design methodology called ROCCID (ROCket Combustor Interactive Design). ROCCID is an interactive design and analysis methodology that uses existing performance and combustion stability analysis codes. The second tool is HICCIP (High frequency Injection Coupled Combustion Instability Program). HICCIP is a recently developed combustion stability analysis model. Using a matrix of models, results from analytic comparisons with 20 K LOX/H2 experimental data are presented.
Klem, Mark D.↗
Model of brittle matrix composite toughening based on discrete fiber reinforcement
An analytical approach for the analysis of the effectiveness of fiber reinforcement in brittle matrix composites is presented. The analytical method allows consideration of discrete fiber distribution and examination of the development of crack growth parameters on microscale. The problem associated with the bridging zone development is addressed here; therefore, the bridging zone is considered to be smaller than the main preexisting crack, and the small scale approach is used. The mechanics of the reinforcement is accurately accounted for in the process zone of a growing crack. Closed form solutions characterizing the initial failure process are presented for linear and nonlinear force - fiber pullout displacement relationships. The implicit exact solution for the extended bridging zone is presented as well.
Rubinstein, Asher A.↗
Probabilistic Modeling of Ceramic Matrix Composite Strength
Uncertainties associated with the primitive random variables such as manufacturing process (processing temperature, fiber volume ratio, void volume ratio), constituent properties (fiber, matrix and interface), and geometric parameters (ply thickness, interphase thickness) have been simulated to quantify the scatter in the first matrix cracking strength (FMCS) and the ultimate tensile strength of SCS-6/RBSN (SiC fiber (SCS-6) reinforced reaction-bonded silicon nitride composite) ceramic matrix composite laminate at room temperature. Cumulative probability distribution function for the FMCS and ultimate tensile strength at room temperature (RT) of (0)(sub 8), (0(sub 2)/90(sub 2), and (+/-45(sub 2))(sub S) laminates have been simulated and the sensitivity of primitive variables to the respective strengths have been quantified. Computationally predicted scatter of the strengths for a uniaxial laminate have been compared with those from limited experimental data. Also the experimental procedure used in the tests has been described briefly. Results show a very good agreement between the computational simulation and the experimental data. Dominating failure modes in (0)(sub 8), (0/90)(sub s) and (+/-45)(sub S) laminates have been identified. Results indicate that the first matrix cracking strength for the (0)(sub S), and (0/90)(sub S) laminates is sensitive to the thermal properties, modulus and strengths of both the fiber and matrix whereas the ultimate tensile strength is sensitive to the fiber strength and the fiber volume ratio. In the case of a (+/-45)(sub S), laminate, both the FMCS and the ultimate tensile strengths have a small scatter range and are sensitive to the fiber tensile strength as well as the fiber volume ratio.
Shan, Ashwin R.↗
Design Tool Developed for Probabilistic Modeling of Ceramic Matrix Composite Strength
Ceramic matrix composites are being evaluated as candidate materials for many high temperature applications such as engine combustor liners for the High-Speed Civil Transport (HSCT). They are required to have an assured life of several thousand hours. Estimating the reliability of these components is quite a complex process and requires knowledge of the uncertainties that occur at various scales. The properties of ceramic matrix composites (CMC) are known to display a considerable amount of scatter due to variations in fiber/matrix properties, interphase/coating properties, bonding, amount of matrix voids, and many geometry- and fabrication-related parameters such as ply thickness and ply orientations. The objective of this research effort is to account for these uncertainties in a formal way by probabilistically analyzing both the stiffness- and strength related properties of CMC's. In current deterministic approaches, uncertainties are usually accounted for by safety factors. This approach often yields overly conservative designs, thereby reducing the potential of many advanced composite materials.
Murthy, Pappu L. N.↗
A probabilistic model for the evaluation of fault-tolerant multiprocessor systems using concurrent error detection
A probabilistic model to evaluate fault-tolerant multiprocessor systems has been developed. The matrix-based model and the analysis algorihtms based on it are described. Various probabilities associated with an algorithm-based fault tolerance system are discussed and the fault coverage of a given check is derived analytically and illustrated with examples. The probability matrices that are formed by introducing the spatial probabilities into the matrix model are considered. Based on these matrices, a technique is developed to determine the combined coverage of multiple numbers of checks. Examples of the analysis of systems using the model are given.
Nair, V. S. S.↗
Comparison Of Models Of Metal-Matrix Composites
Report presents comparative review of four mathematical models of micromechanical behaviors of fiber/metal-matrix composite materials. Models differ in various details, all based on properties of fiber and matrix constituent materials, all involve square arrays of fibers continuous and parallel and all assume complete bonding between constituents. Computer programs implementing models used to predict properties and stress-vs.-strain behaviors of unidirectional- and cross-ply laminated composites made of boron fibers in aluminum matrices and silicon carbide fibers in titanium matrices. Stresses in fiber and matrix constituent materials also predicted.
Bigelow, C. A.↗
Micromechanics Fatigue Damage Analysis Modeling for Fabric Reinforced Ceramic Matrix Composites
A micromechanics analysis modeling method was developed to analyze the damage progression and fatigue failure of fabric reinforced composite structures, especially for the brittle ceramic matrix material composites. A repeating unit cell concept of fabric reinforced composites was used to represent the global composite structure. The thermal and mechanical properties of the repeating unit cell were considered as the same as those of the global composite structure. The three-phase micromechanics, the shear-lag, and the continuum fracture mechanics models were integrated with a statistical model in the repeating unit cell to predict the progressive damages and fatigue life of the composite structures. The global structure failure was defined as the loss of loading capability of the repeating unit cell, which depends on the stiffness reduction due to material slice failures and nonlinear material properties in the repeating unit cell. The present methodology is demonstrated with the analysis results evaluated through the experimental test performed with carbon fiber reinforced silicon carbide matrix plain weave composite specimens.
Min, J. B.↗
A penny-shaped crack in a filament reinforced matrix. 1: The filament model
The electrostatic problem of a penny-shaped crack in an elastic matrix which reinforced by filaments or fibers perpendicular to the plane of the crack was studied. The elastic filament model was developed for application to evaluation studies of the stress intensity factor along the periphery of the crack, the stresses in the filaments or fibers, and the interface shear between the matrix and the filaments or fibers. The requirements expected of the model are a sufficiently accurate representation of the filament and applicability to the interaction problems involving a cracked elastic continuum with multi-filament reinforcements. The technique for developing the model and numerical examples of it are shown.
Erdogan, F.↗