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Probability techniques for reliability analysis of composite materials

Traditional design approaches for composite materials have employed deterministic criteria for failure analysis. New approaches are required to predict the reliability of composite structures since strengths and stresses may be random variables. This report will examine and compare methods used to evaluate the reliability of composite laminae. The two types of methods that will be evaluated are fast probability integration (FPI) methods and Monte Carlo methods. In these methods, reliability is formulated as the probability that an explicit function of random variables is less than a given constant. Using failure criteria developed for composite materials, a function of design variables can be generated which defines a 'failure surface' in probability space. A number of methods are available to evaluate the integration over the probability space bounded by this surface; this integration delivers the required reliability. The methods which will be evaluated are: the first order, second moment FPI methods; second order, second moment FPI methods; the simple Monte Carlo; and an advanced Monte Carlo technique which utilizes importance sampling. The methods are compared for accuracy, efficiency, and for the conservativism of the reliability estimation. The methodology involved in determining the sensitivity of the reliability estimate to the design variables (strength distributions) and importance factors is also presented.

Wetherhold, Robert C.↗

A fractal transition in the two dimensional shear layer

The dependence of product generation with the Peclet and Reynolds number in a numerically simulated, reacting, two dimensional, temporally growing mixing layer is used to compute the fractal dimension of passive scalar interfaces. A transition from a low dimension of 4/3 to a higher one of 5/3 is identified and shown to be associated to the kinematic distortion on the flow field during the first pairing interaction. It is suggested that the structures responsible for this transition are non-deterministic, non-random, inhomogeneous fractals. Only the large scales are involved. No further transition is found for Reynolds numbers up to 20,000.

Jimenez, Javier↗

Radiation-induced DNA damage and chromatin structure

DNA lesions induced by ionizing radiation in cells are clustered and not randomly distributed. For low linear energy transfer (LET) radiation this clustering occurs mainly on the small scales of DNA molecules and nucleosomes. For example, experimental evidence suggests that both strands of DNA on the nucleosomal surface can be damaged in single events and that this damage occurs with a 10-bp modulation because of protection by histones. For high LET radiation, clustering also occurs on a larger scale and depends on chromatin organization. A particularly significant clustering occurs when an ionizing particle traverses the 30 nm chromatin fiber with generation of heavily damaged DNA regions with an average size of about 2 kbp. On an even larger scale, high LET radiation can produce several DNA double-strand breaks in closer proximity than expected from randomness. It is suggested that this increases the probability of misrejoining of DNA ends and generation of lethal chromosome aberrations.

Review↗

Probabilistic analysis for fatigue strength degradation of materials

This report presents the results of the first year of a research program conducted for NASA-LeRC by the University of Texas at San Antonio. The research included development of methodology that provides a probabilistic treatment of lifetime prediction of structural components of aerospace propulsion systems subjected to fatigue. Material strength degradation models, based on primitive variables, include both a fatigue strength reduction model and a fatigue crack growth model. Linear elastic fracture mechanics is utilized in the latter model. Probabilistic analysis is based on simulation, and both maximum entropy and maximum penalized likelihood methods are used for the generation of probability density functions. The resulting constitutive relationships are included in several computer programs, RANDOM2, RANDOM3, and RANDOM4. These programs determine the random lifetime of an engine component, in mechanical load cycles, to reach a critical fatigue strength or crack size. The material considered was a cast nickel base superalloy, one typical of those used in the Space Shuttle Main Engine.

Royce, Lola↗

International Conference on Advances in Communication and Control Systems, 1st, Washington, DC, June 18-20, 1987, Proceedings

Theoretical models of communication and control systems are discussed in reviews and reports. Topics addressed include smoothing and identification for random fields, the information and coding capacities of mismatched Gaussian channels, recursive least-squares estimation and Kalman filtering by systolic arrays, Kemp echo digital filters, a periodic test-scheduling scheme for communication and queuing processes, and receivers for direct-sequence systems. Consideration is given to a distributed-parameter model for detecting cracks in rotors, active control of aeroelastic systems governed by functional differential equations, robust multivariable control of large space structures, finite-rank relatively bounded perturbations of semigroup generators, and sensitivity analysis of convex optimal-control problems.

Declaris, Nicholas↗

STARS: A general-purpose finite element computer program for analysis of engineering structures

STARS (Structural Analysis Routines) is primarily an interactive, graphics-oriented, finite-element computer program for analyzing the static, stability, free vibration, and dynamic responses of damped and undamped structures, including rotating systems. The element library consists of one-dimensional (1-D) line elements, two-dimensional (2-D) triangular and quadrilateral shell elements, and three-dimensional (3-D) tetrahedral and hexahedral solid elements. These elements enable the solution of structural problems that include truss, beam, space frame, plane, plate, shell, and solid structures, or any combination thereof. Zero, finite, and interdependent deflection boundary conditions can be implemented by the program. The associated dynamic response analysis capability provides for initial deformation and velocity inputs, whereas the transient excitation may be either forces or accelerations. An effective in-core or out-of-core solution strategy is automatically employed by the program, depending on the size of the problem. Data input may be at random within a data set, and the program offers certain automatic data-generation features. Input data are formatted as an optimal combination of free and fixed formats. Interactive graphics capabilities enable convenient display of nodal deformations, mode shapes, and element stresses.

Gupta, K. K.↗

Correlation of finite element free vibration predictions using random vibration test data

Finite element analysis is regularly used during the engineering cycle of mechanical systems to predict the response to static, thermal, and dynamic loads. The finite element model (FEM) used to represent the system is often correlated with physical test results to determine the validity of analytical results provided. Results from dynamic testing provide one means for performing this correlation. One of the most common methods of measuring accuracy is by classical modal testing, whereby vibratory mode shapes are compared to mode shapes provided by finite element analysis. The degree of correlation between the test and analytical mode shapes can be shown mathematically using the cross orthogonality check. A great deal of time and effort can be exhausted in generating the set of test acquired mode shapes needed for the cross orthogonality check. In most situations response data from vibration tests are digitally processed to generate the mode shapes from a combination of modal parameters, forcing functions, and recorded response data. An alternate method is proposed in which the same correlation of analytical and test acquired mode shapes can be achieved without conducting the modal survey. Instead a procedure is detailed in which a minimum of test information, specifically the acceleration response data from a random vibration test, is used to generate a set of equivalent local accelerations to be applied to the reduced analytical model at discrete points corresponding to the test measurement locations. The static solution of the analytical model then produces a set of deformations that once normalized can be used to represent the test acquired mode shapes in the cross orthogonality relation. The method proposed has been shown to provide accurate results for both a simple analytical model as well as a complex space flight structure.

Chambers, Jeffrey A.↗

Vibration Testing of Stirling Power Convertors

The NASA John H. Glenn Research Center (GRC) and the U.S. Department of Energy (DOE) are currently developing a high efficient, long life, free piston Stirling convertor for use as an advanced spacecraft power system for future NASA missions. As part of this development, a Stirling Technology Demonstrator Convertor (TDC), developed by Stirling Technology Company (STC) for DOE, was vibration tested at GRC s Structural Dynamics Laboratory (SDU7735) in November- December 1999. This testing demonstrated that the Stirling TDC is able to withstand the harsh random vibration (20 to 2000 Hertz) seen during a typical spacecraft launch and survive with no structural damage or functional power performance degradation, thereby enabling its usage in future spacecraft power systems. The Stirling Vibration Test Team at NASA GRC and STC personnel conducted tests on a single 55 electric watt TDC. The purpose was to characterize the TDC s structural response to vibration and determine if the TDC could survive the vibration criteria established by the Jet Propulsion Laboratory (JPL) for launch environments. The TDC was operated at full-stroke and full power conditions during the vibration testing. The TDC was tested in two orientations, with the direction of vibration parallel and perpendicular to the TDC s moving components (displacer and piston). The TDC successfully passed a series of sine and random vibration tests. The most severe test was a 12.3 Grms random vibration test (peak vibration level of 0.2 g2/Hz from 50 to 250 Hertz) with test durations of 3 minutes per axis. The random vibration test levels were chosen to simulate, with margin, the maximum anticipated launch vibration conditions. As a result of this very successful vibration testing and successful evaluations in other key technical readiness areas, the Stirling power system is now considered a viable technology for future application for NASA spacecraft missions. Possible usage of the Stirling power system would be to supply on- board electric spacecraft power for future NASA Deep-Space Missions, performing as an attractive alternative to Radioisotope Thermoelectric Generators (RTG). Usage of the Stirling technology is also being considered as the electric power source for future Mars rovers, whose mission profiles may exclude the use of photovoltaic power systems (such as exploring at high Martian latitudes or for missions of lengthy durations). GRC s Thermo-Mechanical Systems Branch (5490) provides Stirling technology expertise under a Space Act Agreement with the DOE. Additional vibration testing, by GRC s Structural Systems Dynamics Branch (7733, is planned to continue to demonstrate the Stirling power system s vibration capability as its technology and flight system designs progress.

Hughes, Bill↗

High-precision predictions of properties of chemically disordered crystals

Multiple scattering theory (MST) combined with density functional theory (DFT) allows to predict properties of chemically disordered materials from the first principles. However, such predictions often suffer from the systematic errors, which depend on crystal geometry. Each computed property of a particular crystal structure typically has a relatively small random error and a larger systematic error. Cancellation of systematic errors allows more accurate predictions. We propose a computational methodology based on the subtraction of the systematic errors in MST. To exemplify it, we apply it to the precipitated alloys. Considering precipitation strengthening in Ni superalloys, we compute the relative enthalpies of the competing Ni3(Al,Ti)1 crystal structures with a chemical disorder on the Al+Ti sublattice. Such predicted composition-structure-property dependencies are useful for the guided design of the next-generation alloys with improved strength. Our predictions are validated by comparison with the results of other DFT methods (having a higher computational cost) and with experiment. We acknowledge funding of the guided design of stronger superalloys for airspace by NASA Aeronautics Research Mission Directorate (ARMD) via Transformational Tools and Technologies (TTT) Project.

Computational↗

Integrated Structural Analysis and Test Program

An integrated structural-analysis and structure-testing computer program is being developed in order to: Automate repetitive processes in testing and analysis; Accelerate pre-test analysis; Accelerate reporting of tests; Facilitate planning of tests; Improve execution of tests; Create a vibration, acoustics, and shock test database; and Integrate analysis and test data. The software package includes modules pertaining to sinusoidal and random vibration, shock and time replication, acoustics, base-driven modal survey, and mass properties and static/dynamic balance. The program is commanded by use of ActiveX controls. There is minimal need to generate command lines. Analysis or test files are selected by opening a Windows Explorer display. After selecting the desired input file, the program goes to a so-called analysis data process or test data process, depending on the type of input data. The status of the process is given by a Windows status bar, and when processing is complete, the data are reported in graphical, tubular, and matrix form.

Kaufman, Daniel↗

High-precision predictions of properties of chemically disordered crystals

Multiple scattering theory (MST) combined with density functional theory (DFT) allows to predict properties of chemically disordered materials from the first principles. However, such predictions often suffer from the systematic errors, which depend on crystal geometry. Each computed property of a particular crystal structure typically has a relatively small random error and a larger systematic error. Cancellation of systematic errors allows more accurate predictions. We propose a computational methodology based on the subtraction of the systematic errors in MST. To exemplify it, we apply it to the precipitated alloys. Considering precipitation strengthening in Ni superalloys, we compute the relative enthalpies of the competing Ni_3(Al_{1-x}Ti_x)_1 crystal structures with a chemical disorder on the Al+Ti sublattice. Such predicted composition-structure-property dependencies are useful for the guided design of the next-generation alloys with improved strength. Our predictions are validated by comparison with the results of other DFT methods (having a higher computational cost) and with experiment.

density functional theory↗

Passive scalar entrainment and mixing in a forced, spatially-developing mixing layer

Numerical simulations are performed for the forced, spatially-developing plane mixing layer in two and three dimensions. Transport of a passive scalar field is included in the computation. This, together with the allowance for spatial development in the simulations, affords the opportunity for study of the asymmetric entrainment of irrotational fluid into the layer. The inclusion of a passive scalar field provides a means for simulating the effect of this entrainment asymmetry on the generation of 'products' from a 'fast' chemical reaction. Further, the three-dimensional simulations provide useful insight into the effect of streamwise structures on these entrainment and 'fast' reaction processes. Results from a two-dimensional simulation indicate 1.22 parts high-speed fluid are entrained for every one part low-speed fluid. Inclusion of streamwise vortices at the inlet plane of a three-dimensional simulation indicate a further increase in asymmetric entrainment - 1.44:1. Results from a final three-dimensional simulation are presented. In this case, a random velocity perturbation is imposed at the inlet plane. The results indicate the 'natural' development of the large spanwise structures characteristic of the mixing layer.

Lowery, P. S.↗

The relation of gravity waves and turbulence in the mesosphere

Since researchers couldn't prove that the mesospheric turbulence layers are generated by the simultaneously existing short-period gravity waves, they invoked other generation mechanisms than wave breaking. Possible mechanisms like lateral convection (Rottger 1980a), quasi-geostrophic flows at mesoscales (Lilly, 1983) or vortical modes of motion as seen in the ocean (Muller and Pujalet, 1984) could be candidates. Researchers are inclined to see a connection of these layers or laminae with very-long-period internal waves because of the periodicity in their vertical structure and their long mean persistency. Rottger (1980b) had proposed that such structures are due the modulation of the me an temperature and wind profiles by internal waves. The superposition of random or short-term wave-induced wind and temperature fluctuations with the background profile, modulated by very-long-period waves (quasi-inertia waves) then would yield the observed effects, and could explain the vertical periodicity, the long-term mean persistency as well as some short-term variability of their intensity.

Rottger, J.↗

Resonance absorption of Alfven waves at comet-solar wind interaction regions

The interaction of the low-frequency (0.01 Hz) MHD waves, observed upstream of comets, with the structured plasma near the cometary bow wave is examined. It is suggested that the waves undergo resonant absorption due to either ambient density gradients or localized shear in the background magnetic field. The absorption process can give rise to rapid heating of the solar wind protons, in agreement with observations from Comet Halley. Since the free energy for the generation of MHD waves came from deceleration (without accompanying heating) of the solar wind protons during the pick-up of cometary ions, the subsequent reabsorption of the energy is equivalent to a nonlocal transformation of ordered to random energy and can be described as nonlocal viscosity.

Sharma, A. S.↗

Coverage Metrics for Requirements-Based Testing: Evaluation of Effectiveness

In black-box testing, the tester creates a set of tests to exercise a system under test without regard to the internal structure of the system. Generally, no objective metric is used to measure the adequacy of black-box tests. In recent work, we have proposed three requirements coverage metrics, allowing testers to objectively measure the adequacy of a black-box test suite with respect to a set of requirements formalized as Linear Temporal Logic (LTL) properties. In this report, we evaluate the effectiveness of these coverage metrics with respect to fault finding. Specifically, we conduct an empirical study to investigate two questions: (1) do test suites satisfying a requirements coverage metric provide better fault finding than randomly generated test suites of approximately the same size?, and (2) do test suites satisfying a more rigorous requirements coverage metric provide better fault finding than test suites satisfying a less rigorous requirements coverage metric? Our results indicate (1) only one coverage metric proposed -- Unique First Cause (UFC) coverage -- is sufficiently rigorous to ensure test suites satisfying the metric outperform randomly generated test suites of similar size and (2) that test suites satisfying more rigorous coverage metrics provide better fault finding than test suites satisfying less rigorous coverage metrics.

Staats, Matt↗

Fragmented molecular complexes: The role of the magnetic field in feeding internal supersonic motions

A hierarchical structure for molecular complexes in their cold phase i.e., preceeding the formation of massive stars, was derived from extensive large scale CO(13)(J=1=0) observations: the mass is found to be distributed into virialized clouds which fill only a very low fraction approx. 01 of the volume of the complex and are supported against gravity by internal supersonic motions. An efficient mechanism was found to transfer kinetic energy from the orbital motions of the clouds to their internal random motions. The large perturbations of the magnetic field induced at the cloud boundaries by their interactions with their neighbors generate systems of hydromagnetic waves trapped inside the clouds. The magnetic field lines being closely coupled to the gas at the densities which prevail in the bulk of the clouds volume, internal velocity dispersion is thus generated. Some conclusions derived from this data are given.

Falgarone, E.↗

Probabilistic Analysis of Large-Scale Composite Structures Using the IPACS Code

An investigation was performed to ascertain the feasibility of using IPACS (Integrated Probabilistic Assessment of Composite Structures) for probabilistic analysis of a composite fan blade, the development of which is being pursued by various industries for the next generation of aircraft engines. A model representative of the class of fan blades used in the GE90 engine has been chosen as the structural component to be analyzed with IPACS. In this study, typical uncertainties are assumed in the level, and structural responses for ply stresses and frequencies are evaluated in the form of cumulative probability density functions. Because of the geometric complexity of the blade, the number of plies varies from several hundred at the root to about a hundred at the tip. This represents a extremely complex composites application for the IPACS code. A sensitivity study with respect to various random variables is also performed.

Lemonds, Jeffrey↗

Computation of vertical profiles of longwave radiative cooling over the equatorial Pacific

An important quantity whose magnitude has not been throughly examined is the vertical distribution of heating in the Tropics. The details of the vertical distribution of heating have a significant impact on a number of phenomena, including the 30-60 day oscillation, sometimes known as the intraseasonal oscillation. Prior attempts to establish the structure of the heating relied on limited field data or assimilated data, coupled with climatological radiative heating parameters. The availability of high quality global-scale datasets has made it possible to make more accurate calculations than were possible a few years ago. An important component of the apparent heat budget is the longwave radiative cooling, which in this paper is found by using the ECMWF/WCRP/TOGA Archive 2 and ISCCP C1 datasets, together with a well-established parameterization scheme. A method is developed that can be used to estimate the vertical structure of cloud amounts based on top-of-atmosphere cloud observations, and the results are used with a wide-band longwave parameterization to produce longwave cooling rates over the tropical Pacific Ocean. Outgoing longwave radiation is calculated and compared the ERBE results. The calculated values are generally higher than those from ERBE, though the spatial distributions are similar. Some significant problems exist with the ECMWF upper-tropospheric water vapor amounts, which could imply uncertainties of 0.5 C/day in the calculated cooling rates. This is comparable to the differences associated with the minimum or random overlap assumptions used to generate cloud profiles.

Ramsey, Perry G.↗