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Reliability Sensitivity Analysis and Design Optimization of Composite Structures Based on Response Surface Methodology

This report discusses the development and application of two alternative strategies in the form of global and sequential local response surface (RS) techniques for the solution of reliability-based optimization (RBO) problems. The problem of a thin-walled composite circular cylinder under axial buckling instability is used as a demonstrative example. In this case, the global technique uses a single second-order RS model to estimate the axial buckling load over the entire feasible design space (FDS) whereas the local technique uses multiple first-order RS models with each applied to a small subregion of FDS. Alternative methods for the calculation of unknown coefficients in each RS model are explored prior to the solution of the optimization problem. The example RBO problem is formulated as a function of 23 uncorrelated random variables that include material properties, thickness and orientation angle of each ply, cylinder diameter and length, as well as the applied load. The mean values of the 8 ply thicknesses are treated as independent design variables. While the coefficients of variation of all random variables are held fixed, the standard deviations of ply thicknesses can vary during the optimization process as a result of changes in the design variables. The structural reliability analysis is based on the first-order reliability method with reliability index treated as the design constraint. In addition to the probabilistic sensitivity analysis of reliability index, the results of the RBO problem are presented for different combinations of cylinder length and diameter and laminate ply patterns. The two strategies are found to produce similar results in terms of accuracy with the sequential local RS technique having a considerably better computational efficiency.

Rais-Rohani, Masoud↗

Approach for Input Uncertainty Propagation and Robust Design in CFD Using Sensitivity Derivatives

An implementation of the approximate statistical moment method for uncertainty propagation and robust optimization for quasi 3-D Euler CFD code is presented. Given uncertainties in statistically independent, random, normally distributed input variables, first- and second-order statistical moment procedures are performed to approximate the uncertainty in the CFD output. Efficient calculation of both first- and second-order sensitivity derivatives is required. In order to assess the validity of the approximations, these moments are compared with statistical moments generated through Monte Carlo simulations. The uncertainties in the CFD input variables are also incorporated into a robust optimization procedure. For this optimization, statistical moments involving first-order sensitivity derivatives appear in the objective function and system constraints. Second-order sensitivity derivatives are used in a gradient-based search to successfully execute a robust optimization. The approximate methods used throughout the analyses are found to be valid when considering robustness about input parameter mean values.

Putko, Michele M.↗

Standard random number generation for MBASIC

A machine-independent algorithm is presented and analyzed for generating pseudorandom numbers suitable for the standard MBASIC system. The algorithm used is the polynomial congruential or linear recurrence modulo 2 method. Numbers, formed as nonoverlapping adjacent 28-bit words taken from the bit stream produced by the formula a sub m + 532 = a sub m + 37 + a sub m (modulo 2), do not repeat within the projected age of the solar system, show no ensemble correlation, exhibit uniform distribution of adjacent numbers up to 19 dimensions, and do not deviate from random runs-up and runs-down behavior.

Tausworthe, R. C.↗

Statistical analysis of secondary particle distributions in relativistic nucleus-nucleus collisions

The use is described of several statistical techniques to characterize structure in the angular distributions of secondary particles from nucleus-nucleus collisions in the energy range 24 to 61 GeV/nucleon. The objective of this work was to determine whether there are correlations between emitted particle intensity and angle that may be used to support the existence of the quark gluon plasma. The techniques include chi-square null hypothesis tests, the method of discrete Fourier transform analysis, and fluctuation analysis. We have also used the method of composite unit vectors to test for azimuthal asymmetry in a data set of 63 JACEE-3 events. Each method is presented in a manner that provides the reader with some practical detail regarding its application. Of those events with relatively high statistics, Fe approaches 0 at 55 GeV/nucleon was found to possess an azimuthal distribution with a highly non-random structure. No evidence of non-statistical fluctuations was found in the pseudo-rapidity distributions of the events studied. It is seen that the most effective application of these methods relies upon the availability of many events or single events that possess very high multiplicities.

Mcguire, Stephen C.↗

Theory of thermal microwave emission from a two-layer medium

Thermal microwave emission from a scattering layer overlying a homogeneous half space is studied with the radiative transfer approach. Scattering models of random medium and discrete spherical scatterers are used. The radiative transfer equations are solved by both the classical method and the invariant imbedding method. The brightness temperatures of the two-layer model exhibit distinguishing features important to microwave passive remote sensing.

Tsang, L.↗

Direct measurement of transmission loss of aircraft structures using the acoustic intensity approach

A measurement technique is developed in order to obtain the sound transmission loss of an aircraft fuselage which obviates the need for the two-room transmission suite. The sound transmission paths were determined in tests on a light aircraft fuselage using a two-microphone acoustic intensity method for measuring the acoustic intensity transmitted to the interior when the fuselage was exposed to an external random incidence sound-field. The intensity transmitted through different sections of the fuselage can be estimated accurately using this new technique. Results of these tests show that the plexiglass window is the major transmission path in the high frequency range. In addition, the transmission losses through a single and a double layer window were predicted theoretically by using the Statistical Energy Analysis Model. Very good agreement is found between the predictions and the measurements.

Wang, Y. S.↗

Optimum structural sizing for gust induced response

The present paper describes an optimization capability for sizing airframe structures that are subjected to a combination of deterministic and random loads. Design constraints are implemented to prevent structural failure in fatigue and due to a single exceedance of the allowable stress. The random load is treated as a stationary, homogeneous process with a Gaussian probability distribution, and a frequency domain method is used for the computation of dynamic response parameters. An equal-probability-of-load-combination criterion is proposed in the formulation of strength constraints. This alleviates problems associated with the incomplete phase information available when using power spectral density methods. The optimization procedure is illustrated by examples using typical built-up structures.

Hajela, P.↗

A finite element formulation for the large deflection random response of thermally buckled plates

By using the linear mode shapes of a thermally buckled structure, a governing system of finite element equations for large-deflection random vibrations is reduced to a system of nonlinear modal equations. This system is then solved using the method of equivalent linearization. The methodology developed in this study is applicable to the design of aerospace vehicles subjected to combined thermal/acoustic loads.

Locke, James↗

Determination of the mean solid-liquid interface energy of pivalic acid

A high-confidence solid-liquid interfacial energy is determined for an anisotropic material. A coaxial composite having a cylindrical specimen chamber geometry provides a thermal gradient with an axial heating wire. The surface energy is derived from measurements of grain boundary groove shapes. Applying this method to pivalic acid, a surface energy of 2.84 erg/sq cm was determined with a total systematic and random error less than 10 percent. The value of interfacial energy corresponds to 24 percent of the latent heat of fusion per molecule.

Singh, N. B.↗

Particle image fields and partial coherence

The accuracy of Young's fringe method for reducing velocity field data is compromized by a spatially incoherent background field which originates in the random locations of the seeding particles. The probability density function for the spatial frequency cutoff of this background is derived as a function of the particle count, the distribution governing the power in each frequency interval is derived, and conditions are found under which the Van Cittert-Zernike theorem applies. The background field resembles the far field of a partially coherent source in the high particle count limit, but departs significantly at low and moderate counts.

Rubinstein, Robert↗

Idealized textile composites for experimental/analytical correlation

Textile composites are fiber reinforced materials produced by weaving, braiding, knitting, or stitching. These materials offer possible reductions in manufacturing costs compared to conventional laminated composites. Thus, they are attractive candidate materials for aircraft structures. To date, numerous experimental studies have been performed to characterize the mechanical performance of specific textile architectures. Since many materials and architectures are of interest, there is a need for analytical models to predict the mechanical properties of a specific textile composite material. Models of varying sophistication have been proposed based on mechanics of materials, classical laminated plate theory, and the finite element method. These modeling approaches assume an idealized textile architecture and generally consider a single unit cell. Due to randomness of the textile architectures produced using conventional processing techniques, experimental data obtained has been of limited use for verifying the accuracy of these analytical approaches. This research is focused on fabricating woven textile composites with highly aligned and accurately placed fiber tows that closely represent the idealized architectures assumed in analytical models. These idealized textile composites have been fabricated with three types of layer nesting configurations: stacked, diagonal, and split-span. Compression testing results have identified strength variations as a function of nesting. Moire interferometry experiments are being used to determine localized deformations for detailed correlation with model predictions.

Adams, Daniel O.↗

Bit Error Probability for Maximum Likelihood Decoding of Linear Block Codes

In this paper, the bit error probability P(sub b) for maximum likelihood decoding of binary linear codes is investigated. The contribution of each information bit to P(sub b) is considered. For randomly generated codes, it is shown that the conventional approximation at high SNR P(sub b) is approximately equal to (d(sub H)/N)P(sub s), where P(sub s) represents the block error probability, holds for systematic encoding only. Also systematic encoding provides the minimum P(sub b) when the inverse mapping corresponding to the generator matrix of the code is used to retrieve the information sequence. The bit error performances corresponding to other generator matrix forms are also evaluated. Although derived for codes with a generator matrix randomly generated, these results are shown to provide good approximations for codes used in practice. Finally, for decoding methods which require a generator matrix with a particular structure such as trellis decoding or algebraic-based soft decision decoding, equivalent schemes that reduce the bit error probability are discussed.

Lin, Shu↗

Flexible Ceramic-Metal Insulation Composite and Method of Making

A method for joining a woven flexible ceramic fabric and a thin metal sheet creating an integral metal surfaced flexible thermal protection article, which methods compress: placing multiple dots of high temperature metallic or fabric and the thin metal sheet in a random or organized pattern, with the proviso that the brazing material covers about 10% or less of the surface of one flat side of the metal sheet; heating the flexible ceramic fabric, brazing material and thin metal sheet for a predetermined period of time to integrally connect the same; and cooling the formed flexible article to ambient temperature. Preferably the flexible ceramic is selected from fibers comprising atoms of silicon, carbon, nitrogen, boron, oxygen or combinations thereof. The flexible thermal protection article produced is also part of the present invention. The thin metal sheet is comprised of titanium, aluminum, chromium, niobium or alloys or combinations thereof. The brazing material is selected from copper/silver or copper/gold or is a ceramic brazing or adhesive material.

Rasky, Daniel J.↗

Benefits of Force Limiting Vibration Testing

Force limited random vibration testing is used at NASA John Glenn Research Center (formerly NASA Lewis Research Center) for qualifying aerospace hardware for flight. The benefit of force limiting testing is that it limits overtesting of flight hardware, by controlling input force and acceleration from the shaker (dual control) to the test article. The purpose of force limiting is to replicate the test article resonant response for the actual flight mounting condition. The force limiting testing technology has been implemented at the Jet Propulsion Laboratory for the past 10 years on various spacecraft testing programs. The Cassini mission to Saturn, most notably, utilized force limiting vibration testing as part of the spacecraft system level vibration testing. NASA John Glenn Research Center is responsible for microgravity combustion and fluid science research on the Shuttle and the International Space Station. Qualification testing of delicate and vibration sensitive science instrumentation is particularly challenging to successfully qualify for flight. In order to facilitate the testing process, force limiting has been implemented to minimize overtesting of flight hardware. This paper will address recent flight camera testing (qualification random vibration and strength testing) for the Combustion Module-2 mission and the impact of Semi-empirical Method force limits.

McNelis, Mark E.↗

20 Meter Solar Sail Analysis and Correlation

This presentation discusses studies conducted to determine the element type and size that best represents a 20-meter solar sail under ground-test load conditions, the performance of test/Analysis correlation by using Static Shape Optimization Method for Q4 sail, and system dynamic. TRIA3 elements better represent wrinkle patterns than do QUAD3 elements Baseline, ten-inch elements are small enough to accurately represent sail shape, and baseline TRIA3 mesh requires a reasonable computation time of 8 min. 21 sec. In the test/analysis correlation by using Static shape optimization method for Q4 sail, ten parameters were chosen and varied during optimization. 300 sail models were created with random parameters. A response surfaces for each targets which were created based on the varied parameters. Parameters were optimized based on response surface. Deflection shape comparison for 0 and 22.5 degrees yielded a 4.3% and 2.1% error respectively. For the system dynamic study testing was done on the booms without the sails attached. The nominal boom properties produced a good correlation to test data the frequencies were within 10%. Boom dominated analysis frequencies and modes compared well with the test results.

Taleghani, B.↗

Processing Nanostructured Sensors Using Microfabrication Techniques

Standard microfabrication techniques can be implemented and scaled to help assemble nanoscale microsensors. Currently nanostructures are often deposited onto materials primarily by adding them to a solution, then applying the solution in a thin film. This results in random placement of the nanostructures with no controlled order, and no way to accurately reproduce the placement. This method changes the means by which microsensors with nanostructures are fabricated. The fundamental advantage to this approach is that it enables standard microfabrication techniques to be applied in the repeated manufacture of nanostructured sensors on a microplatform.

Hunter, Gary W.↗