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All sourcesNASA NTRSDOE OSTI
NASA NTRS1972

Significance criteria for variance matrix applications.

A significance criterion is proposed that compares the strength parameter against the parameter expected from a random group of vectors in variance matrix applications. The variance matrix technique for determining preference or avoidance directions in space for a group of vectors gives only the parameter indicating the strength of the preference or avoidance, and the proposed criterion is shown to be of help in the achievement of reliability.

Siscoe, G. L.↗
NASA NTRS1998

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.↗
NASA NTRS2017

Electromagnetic Scattering by Spheroidal Volumes of Discrete Random Medium

We use the superposition T-matrix method to compare the far-field scattering matrices generated by spheroidal and spherical volumes of discrete random medium having the same volume and populated by identical spherical particles. Our results fully confirm the robustness of the previously identified coherent and diffuse scattering regimes and associated optical phenomena exhibited by spherical particulate volumes and support their explanation in terms of the interference phenomenon coupled with the order-of-scattering expansion of the far-field Foldy equations. We also show that increasing non-sphericity of particulate volumes causes discernible (albeit less pronounced) optical effects in forward and backscattering directions and explain them in terms of the same interference/multiple-scattering phenomenon.

Electromagnetic scattering; Multi-particle groups;↗
NASA NTRS1996

A Higher Harmonic Optimal Controller to Optimise Rotorcraft Aeromechanical Behaviour

Three methods to optimize rotorcraft aeromechanical behavior for those cases where the rotorcraft plant can be adequately represented by a linear model system matrix were identified and implemented in a stand-alone code. These methods determine the optimal control vector which minimizes the vibration metric subject to constraints at discrete time points, and differ from the commonly used non-optimal constraint penalty methods such as those employed by conventional controllers in that the constraints are handled as actual constraints to an optimization problem rather than as just additional terms in the performance index. The first method is to use a Non-linear Programming algorithm to solve the problem directly. The second method is to solve the full set of non-linear equations which define the necessary conditions for optimality. The third method is to solve each of the possible reduced sets of equations defining the necessary conditions for optimality when the constraints are pre-selected to be either active or inactive, and then to simply select the best solution. The effects of maneuvers and aeroelasticity on the systems matrix are modelled by using a pseudo-random pseudo-row-dependency scheme to define the systems matrix. Cases run to date indicate that the first method of solution is reliable, robust, and easiest to use, and that it was superior to the conventional controllers which were considered.

Leyland, Jane Anne↗
NASA NTRS1980

Light scattering by randomly oriented spheroidal particles

A study of the light scattering properties of randomly oriented, identical spheroidal particles is presented. A computation method was developed to integrate the Asano and Yamomoto solution (1975) for scattering from a homogeneous spheroid over all particle orientations; the extinction and scattering cross-sections, the asymmetry factor, and scattering matrix elements are calculated for randomly oriented prolate and oblate spheroids and compared with the calculations for spheres and laboratory measurements. The angular scattering behavior of spheroids is found to be different from that of the spheres for side scattering to backscattering directions, and prolate and oblate spheroids of the same shape parameter have similar angular scattering patterns.

Asano, S.↗
NASA NTRS1998

PCEMCAN - Probabilistic Ceramic Matrix Composites Analyzer: User's Guide, Version 1.0

PCEMCAN (Probabalistic CEramic Matrix Composites ANalyzer) is an integrated computer code developed at NASA Lewis Research Center that simulates uncertainties associated with the constituent properties, manufacturing process, and geometric parameters of fiber reinforced ceramic matrix composites and quantifies their random thermomechanical behavior. The PCEMCAN code can perform the deterministic as well as probabilistic analyses to predict thermomechanical properties. This User's guide details the step-by-step procedure to create input file and update/modify the material properties database required to run PCEMCAN computer code. An overview of the geometric conventions, micromechanical unit cell, nonlinear constitutive relationship and probabilistic simulation methodology is also provided in the manual. Fast probability integration as well as Monte-Carlo simulation methods are available for the uncertainty simulation. Various options available in the code to simulate probabilistic material properties and quantify sensitivity of the primitive random variables have been described. The description of deterministic as well as probabilistic results have been described using demonstration problems. For detailed theoretical description of deterministic and probabilistic analyses, the user is referred to the companion documents "Computational Simulation of Continuous Fiber-Reinforced Ceramic Matrix Composite Behavior," NASA TP-3602, 1996 and "Probabilistic Micromechanics and Macromechanics for Ceramic Matrix Composites", NASA TM 4766, June 1997.

Shah, Ashwin R.↗
NASA NTRS2021

Micromechanics-based Modeling of Laminated SiC/SiC Ceramic Matrix Composites

The behavior and response of ceramic matrix composites (CMCs), in particular silicon carbide fiber reinforced silicon carbide matrix (SiC/SiC), is affected by many factors such as variation of fiber volume fraction, residual stresses resulting from processing of the composites at high temperature, random microstructures, and the presence of matrix flaws (e.g., voids, pores, cracks etc.) as well as general material nonlinearity and heterogeneity that occurs randomly in a composite. Residual stresses arising from the phase change of constituents are evaluated in this paper and it is shown that they do influence composite strength and need to be properly accounted for. Additionally, the microstructures (location of fiber centers, coating thickness etc.) of advanced CMCs are usually disordered (or random) and fiber diameter and strength typically have a distribution. They rarely resemble the ordered fiber packing (square, rectangular, or hexagonal) that is generally assumed in micromechanics-based models with periodic boundary conditions for computational expediency. These issues raise the question of how should one model such systems effectively? Can an ordered hexagonal packed repeating unit cell (RUC) accurately represent the random microstructure behavior? How many fibers need to be included to enable accurate representation? Clearly, the number of fibers within an RUC must be limited to insure a balance between accuracy and efficiency. NASA’s in-house micromechanics-based code MAC/GMC provides a framework to analyze such RUCs for the overall composite behavior and the FEAMAC computer code provides linkage of MAC/GMC to the commercial FEA code, ABAQUS. The appropriate level of discretization of the RUC as well as the analysis method employed, i.e., Generalized Method of Cells (GMC) or High Fidelity Generalized Method of Cells (HFGMC), is investigated in this paper in the context of a unidirectional as well as a cross-ply laminated CMC. Results including effective composite properties, proportional limit stress (an important design parameter) and fatigue are shown utilizing both GMC as well as HFGMC. Finally, a few multiscale analyses are performed on smooth bar test coupons as well as test coupons with features such as open-hole and double notches using FEAMAC. Best practices and guidance are provided to take these phenomena into account and keep a proper balance between fidelity (accuracy) and efficiency. Following these guidelines can account for important physics of the problem and provide significant advantages when performing large multiscale composite structural analyses.

Ceramic Matrix Composites↗
NASA NTRS2015

Elastic and Piezoelectric Properties of Boron Nitride Nanotube Composites: Finite Element Model - Part II

This paper is the second part of a two-part series where the first part presents a molecular dynamics model of a single Boron Nitride Nanotube (BNNT) and this paper scales up to multiple BNNTs in a polymer matrix. This paper presents finite element (FE) models to investigate the effective elastic and piezoelectric properties of (BNNT) nanocomposites. The nanocomposites studied in this paper are thin films of polymer matrix with aligned co-planar BNNTs. The FE modelling approach provides a computationally efficient way to gain an understanding of the material properties. We examine several FE models to identify the most suitable models and investigate the effective properties with respect to the BNNT volume fraction and the number of nanotube walls. The FE models are constructed to represent aligned and randomly distributed BNNTs in a matrix of resin using 2D and 3D hollow and 3D filled cylinders. The homogenisation approach is employed to determine the overall elastic and piezoelectric constants for a range of volume fractions. These models are compared with an analytical model based on Mori-Tanaka formulation suitable for finite length cylindrical inclusions. The model applies to primarily single-wall BNNTs but is also extended to multi-wall BNNTs, for which preliminary results will be presented. Results from the Part 1 of this series can help to establish a constitutive relationship for input into the finite element model to enable the modeling of multiple BNNTs in a polymer matrix.

Kim, H. Alicia↗
NASA NTRS1981

Microstructure of Al2O3 scales formed on NiCrAl alloys

The structure of transient scales formed on pure and Y or Zr-doped Ni-15Cr-13Al alloys oxidized for 0.1 hr at 1100 C was studied by the use of transmission electron microscopy. Crystallographically oriented scales were found on all three alloys, but especially for the Zr-doped NiCrAl. The oriented scales consisted of alpha-(Al,Cr)2O3, Ni(Al,Cr)2O4 and gamma-Al2O3. They were often found in intimate contact with each other such that the close-packed planes and directions of one oxide phase were aligned with those of another. The prominent structural features of the oriented scales were approximately equal to micrometer subgrains; voids, antiphase domain boundaries and aligned precipitates were also prevalent. Randomly oriented alpha-Al2O3 was also found and was the only oxide ever observed at the immediate oxide metal interface. These approximately 0.15 micrometer grains were populated by intragranular voids which decreased in size and number towards the oxide metal interface. A sequence of oxidation was proposed in which the composition of the growing scale changed from oriented oxides rich in Ni and Cr to oriented oxides rich in Al. At the same time the structure changed from cubic spinels to hexagonal corundums with apparent precipitates of one phase in the matrix of the other. Eventually randomly oriented pure alpha-Al2O3 formed as the stable oxide with an abrupt transition: there was no gradual loss of orientation, no gradual compositional change or no gradual decrease in precipitate density.

Smialek, J. L.↗
NASA NTRS1966

Program ALLELE

Computer program to formulate matrix of relative deviations from random pairing of amino acids

COMPUTER PROGRAM↗
NASA NTRS1981

Multiobjective insensitive design of airplane control systems with uncertain parameters

A multiobjective computer-aided design algorithm has been developed which minimizes the sensitivity of the design objectives to uncertainties in system parameters. The more important uncertain parameters are described by a gaussian random vector with known covariance matrix, and a vector sensitivity objective function is defined as the probabilities that the design objectives will violate specified requirements constraints. Control system parameters are found which minimize the sensitivity vector in a Pareto-optimal sense, using constrained minimization algorithms. Example results are shown for lateral stability augmentation system (SAS) design for three Shuttle flight conditions.

Schy, A. A.↗
NASA NTRS1987

Response of discretely stiffened structures

This paper presents a theoretical study on dynamic response of complex discretely stiffened and interconnected structures to random loads. Modal and transfer matrix techniques are utilized to analyze these multidimensional structures. Application of this formulation for response and noise generation studies in space station and fuselage-wing design is discussed. The response spectral densities are calculated for several typical discretely stiffened and interconnected structural systems. It is found that this approach allows for easy parametric evaluation and that by proper selection of structural parameters and loading conditions, the vibration response can be reduced.

Vaicaitis, R.↗
NASA NTRS1991

Computational simulation of the creep-rupture process in filamentary composite materials

A computational simulation of the internal damage accumulation which causes the creep-rupture phenomenon in filamentary composite materials is developed. The creep-rupture process involves complex interactions between several damage mechanisms. A statistically-based computational simulation using a time-differencing approach is employed to model these progressive interactions. The finite element method is used to calculate the internal stresses. The fibers are modeled as a series of bar elements which are connected transversely by matrix elements. Flaws are distributed randomly throughout the elements in the model. Load is applied, and the properties of the individual elements are updated at the end of each time step as a function of the stress history. The simulation is continued until failure occurs. Several cases, with different initial flaw dispersions, are run to establish a statistical distribution of the time-to-failure. The calculations are performed on a supercomputer. The simulation results compare favorably with the results of creep-rupture experiments conducted at the Lawrence Livermore National Laboratory.

Slattery, Kerry T.↗
NASA NTRS1993

Probabilistic assessment of composite structures

A general computational simulation methodology for an integrated probabilistic assessment of composite structures is discussed and demonstrated using aircraft fuselage (stiffened composite cylindrical shell) structures with rectangular cutouts. The computational simulation was performed for the probabilistic assessment of the structural behavior including buckling loads, vibration frequencies, global displacements, and local stresses. The scatter in the structural response is simulated based on the inherent uncertainties in the primitive (independent random) variables at the fiber matrix constituent, ply, laminate, and structural scales that describe the composite structures. The effect of uncertainties due to fabrication process variables such as fiber volume ratio, void volume ratio, ply orientation, and ply thickness is also included. The methodology has been embedded in the computer code IPACS (Integrated Probabilistic Assessment of Composite Structures). In addition to the simulated scatter, the IPACS code also calculates the sensitivity of the composite structural behavior to all the primitive variables that influence the structural behavior. This information is useful for assessing reliability and providing guidance for improvement. The results from the probabilistic assessment for the composite structure with rectangular cutouts indicate that the uncertainty in the longitudinal ply stress is mainly caused by the uncertainty in the laminate thickness, and the large overlap of the scatter in the first four buckling loads implies that the buckling mode shape for a specific buckling load can be either of the four modes.

Shiao, Michael E.↗
NASA NTRS2015

Scattering Properties of Heterogeneous Mineral Particles with Absorbing Inclusions

We analyze the results of numerically exact computer modeling of scattering and absorption properties of randomly oriented poly-disperse heterogeneous particles obtained by placing microscopic absorbing grains randomly on the surfaces of much larger spherical mineral hosts or by imbedding them randomly inside the hosts. These computations are paralleled by those for heterogeneous particles obtained by fully encapsulating fractal-like absorbing clusters in the mineral hosts. All computations are performed using the superposition T-matrix method. In the case of randomly distributed inclusions, the results are compared with the outcome of Lorenz-Mie computations for an external mixture of the mineral hosts and absorbing grains. We conclude that internal aggregation can affect strongly both the integral radiometric and differential scattering characteristics of the heterogeneous particle mixtures.

minerals↗
NASA NTRS1993

Intensity and polarization of light scattered by size distributions of randomly oriented nonspherical particles

Calculations of light scattering by small particles are important in many diverse fields of science and engineering. In many cases of practical interest, scattering particles are nonspherical and are distributed over sizes and orientations. However, accurate light scattering computations for ensembles of nonspherical particles are difficult and time-consuming, and the literature in which such calculations are reported is rather scarce. In this paper, the T-matrix approach, as extended recently to randomly oriented particles, is used to calculate rigorously light scattering by size distributions of randomly oriented axially symmetric particles. To model the variation of particle sizes in real ensembles, we use a power law distribution typical of some terrestrial aerosols. Contour plots of intensity and degree of linear polarization for polydisperse prolate and oblate spheroids of different aspect ratios and effective equivalent-sphere size parameters from 0 to 10 are calculated and compared with calculations for equivalent spheres. The angular scattering behavior of nonspherical polydispersions is found to be greatly different from that of spheres, while the scattering properties of oblate and prolate spheroids of the same aspect ratio are similar. With increasing particle size, both intensity and polarization become more shape-dependent. In general, nonspherical particles are stronger side scatterers and weaker backscatterers than equivalent spheres. With increasing aspect ratio of nonspherical particles polarization tends to be predominantly positive. Possible effects of particle nonsphericity on optical remote sensing of atmospheric aerosols are discussed.

Mishchenko, M. I.↗
NASA NTRS1992

Derivation of phase statistics from the Mueller matrix

Experimental observations show a strong dependence of phase differences of scattering matrix elements on the physical parameters of random media. Here, the statistical behavior of the phase differences is studied for distributed targets. The pdfs of the phase differences are derived from the Mueller matrix of the target. In deriving the density functions, it is assumed that the real and imaginary parts of the copolarized and cross-polarized terms of the scattering matrix are jointly Gaussian and their covariance matrices are found in terms of the Mueller matrix elements. The functional forms of the copolarized and cross-polarized density functions are similar and are obtained independently. It is shown that the density function of the phase difference is completely determined in terms of only two parameters.

Sarabandi, K.↗