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NASA NTRS2016

Characterization of the High-Albedo NEA 3691 Bede

Characterization of NEAs provides important inputs to models for atmospheric entry, risk assessment and mitigation. Diameter is a key parameter because diameter translates to kinetic energy in atmospheric entry. Diameters can be derived from the absolute magnitude, H(PA=0deg), and from thermal modeling of observed IR fluxes. For both methods, the albedo (pv) is important - high pv surfaces have cooler temperatures, larger diameters for a given Hmag, and shallower phase curves (larger slope parameter G). Thermal model parameters are coupled, however, so that a higher thermal inertia also results in a cooler surface temperature. Multiple parameters contribute to constraining the diameter. Observations made at multiple observing geometries can contribute to understanding the relationships between and potentially breaking some of the degeneracies between parameters. We present data and analyses on NEA 3691 Bede with the aim of best constraining the diameter and pv from a combination of thermal modeling and light curve analyses. We employ our UKIRT+Michelle mid-IR photometric observations of 3691 Bede's thermal emission at 2 phase angles (27&43 deg 2015-03-19 & 04-13), in addition to WISE data (33deg 2010-05-27, Mainzer+2011). Observing geometries differ by solar phase angles and by moderate changes in heliocentric distance (e.g., further distances produce somewhat cooler surface temperatures). With the NEATM model and for a constant IR beaming parameter (eta=constant), there is a family of solutions for (diameter, pv, G, eta) where G is the slope parameter from the H-G Relation. NEATM models employing Pravec+2012's choice of G=0.43, produce D=1.8 km and pv≈0.4, given that G=0.43 is assumed from studies of main belt asteroids (Warner+2009). We present an analysis of the light curve of 3691 Bede to constrain G from observations. We also investigate fitting thermophysical models (TPM, Rozitis+11) to constrain the coupled parameters of thermal inertia (Gamma) and surface roughness, which in turn affect diameter and pv. Surface composition can be related to pv. This study focuses on understanding and characterizing the dependency of parameters with the aim of constraining diameter, pv and thermal inertia for 3691 Bede.

Wooden, Diane H.↗

NASA NTRS2016

Characterization of the High-Albedo NEA 3691 Bede

magnitude↗

NASA NTRS1974

Analysis of multiple pulse NMR in solids. II

A systematic method, an extension of the average Hamiltonian formalism, is presented for calculating the effects of pulse errors and imperfections in the multiple pulse nuclear magnetic resonance experiments. Application of this method to account for effects of pulse nonidealities such as phase errors, phase transient effects, pulse size errors, and rf inhomogeneity is found to agree with experimental observation, and the results furnish a basis for understanding the complex couplings between the pulse errors and other interactions such as the dipolar and the chemical shift Hamiltonians.

Rhim, W.-K.↗

NASA NTRS2018

Design of a Modular Monolithic Implicit Solver for Multi-Physics Applications

The design of a modular multi-physics high-order space-time finite-element framework is presented together with its extension to allow monolithic coupling of different physics. One of the main objectives of the framework is to perform efficient high- fidelity simulations of capsule/parachute systems. This problem requires simulating multiple physics including, but not limited to, the compressible Navier-Stokes equations, the dynamics of a moving body with mesh deformations and adaptation, the linear shell equations, non-re effective boundary conditions and wall modeling. The solver is based on high-order space-time - finite element methods. Continuous, discontinuous and C1-discontinuous Galerkin methods are implemented, allowing one to discretize various physical models. Tangent and adjoint sensitivity analysis are also targeted in order to conduct gradient-based optimization, error estimation, mesh adaptation, and flow control, adding another layer of complexity to the framework. The decisions made to tackle these challenges are presented. The discussion focuses first on the "single-physics" solver and later on its extension to the monolithic coupling of different physics. The implementation of different physics modules, relevant to the capsule/parachute system, are also presented. Finally, examples of coupled computations are presented, paving the way to the simulation of the full capsule/parachute system.

Carton De Wiart, Corentin↗

NASA NTRS2007

Finite Element Simulation of Solid Rocket Booster Separation Motors During Motor Firing

One of the toughest challenges facing Solid Rocket Booster (SRB) engineers is to ensure that any design changes made to the Shuttle-Derived Booster Separation Motors (BSM) for future space exploration vehicles is able to withstand the increasingly hostile motor firing environment without cracking its critical component - the graphite throat. This paper presents a critical analysis methodology and techniques for assessing effects of BSM design changes with great accuracy and precision. For current Space Shuttle operation, the motor firing occurs at SRB separation - approximately 125 seconds after Shuttle launch at an altitude of about 28 miles. The motor operation event lasts about two seconds, however, the surface temperature of the graphite throat increases approximately 3400 F in less than one second with a corresponding increase in surface pressure of approximately 2200 pounds per square inch (psi) in less than one-tenth of a second. To capture this process fully and accurately, a two-phase sequentially coupled thermal-mechanical finite element approach was developed. This method allows the time- and location-dependent pressure fields to interact with the spatial-temporal thermal fields throughout the operation. The material properties of graphite throat are orthotropic and temperature-dependent. The analysis involves preload and multiple body contacts.

Yu. Weiping↗

NASA NTRS2006

X-ray Mapping of Terrestrial and Extraterrestrial Materials Using the Electron Microprobe

Lunar samples returned from the Apollo program motivated development of the Bence-Albee algorithm for the rapid and accurate analysis of lunar materials, and established interlaboratory comparability through its common use. In the analysis of mineral and rock fragments it became necessary to combine micro- and macroscopic analysis by coupling electron-probe microanalysis (EPMA) with automated stage point counting. A coarse grid that included several thousand points was used, and initially wavelength-dispersive (WDS) and later energydispersive (EDS) data were acquired at discrete stage points using approx. 5 sec count times. A approx 50 micrometer beam diameter was used for WDS and up to 500 micrometer beam diameter for EDS analysis. Average analyses of discretely sampled phases were coupled with the point count data to calculate the bulk composition using matrix algebra. Use of a defocused beam resulted in a contribution from multiple phases to each analytical point, and the analytical data were deconvolved relative to end-member phase chemistry on the fly. Impressive agreement was obtained between WDS and EDS measurements as well as comparison with bulk chemistry obtained by other methods. In the 30 years since these methods were developed, significant improvements in EPMA automation and computer processing have taken place. Digital beam control allows routine collection of x-ray maps by EDS, and stage mapping for WDS is conducted continuously at slew speed and incrementally by sampling at discrete points. Digital pulse processing in EDS systems has significantly increased the throughput for EDS mapping, and the ongoing development of Si-drift detector systems promises mapping capabilities rivaling WDS systems. Spectrum imaging allows a data cube of EDS spectra to be acquired and sophisticated processing of the original data is possible using matrix algebra techniques. The study of lunar and meteoritic materials includes the need to conveniently: (1) Characterize the sample at microscopic and macroscopic scales with relatively high sensitivity, (2) Determine the modal abundance of minerals, and (3) Identify and relocate discrete features of interest in terms of size and chemistry. The coupled substitution of cations in minerals can result in significant variation in mineral chemistry, but at similar average Z, leading to poor backscattered-electron (BSE) contrast discrimination of mineralogy. It is necessary to discriminate phase chemistry at both the trace element level and the major element level. To date, the WDS of microprobe systems is preferred for mapping due to high throughput and the ability to obtain the necessary intensity to discriminate phases at both trace and major element concentrations. It is desirable to produce fully quantitative compositional maps of geological materials, which requires the acquisition of k-ratio maps that are background and dead-time corrected, and which have been corrected by phi(delta z> or an equivalent algorithm at each pixel. To date, turnkey systems do not allow the acquisition of k-ratio maps and the rigorous correction in this manner. X-ray maps of a chondrule from the Ourique meteorite, and a comb-layered xenolith from the San Francisco volcanic field, have been analyzed and processed to extract phase information. The Ourique meteorite presents a challenge due to relatively low BSE contrast, and has been studied using spectrum imaging. X-ray maps for Si, Mg, and FeK(alpha) were used to produce RGB images. The xenolith sample contains sector-zoned augite, olivine, plagioclase, and basaltic glass. X-ray maps were processed using Lispix and ImageJ software to produce mineral phase maps. The x-ray maps for Mg, Ca, and Ti were used with traceback to generate binary images that were converted to RGB images. These approaches are successful in discriminating phases, but it is desirable to achieve the methods that were used on lunar samples 30 years ago on current microprobe systems. Curnt research includes x-ray mapping analysis of the Dalgety Downs chondrite by micro x-ray fluorescence and spectrum imaging, in collaboration with Kenny Witherspoon of IXRF Systems and Dale Newbury of NIST.

Carpenter, P.↗

NASA NTRS1992

Multidisciplinary tailoring of hot composite structures

A computational simulation procedure is described for multidisciplinary analysis and tailoring of multilayered multimaterial hot composite engine structural components subjected to simultaneous multiple discipline-specific thermal, structural, vibration, and acoustic loadings including the effect of aggressive environments. The simulation is based on a 3D finite element analysis technique in conjunction with structural mechanics codes, thermal/acoustic analysis methods, and tailoring procedures. The integrated multidisciplinary simulation procedure is general-purpose including the coupled effects of nonlinearities in structure geometry, material, loading, and environmental complexities. The composite material behavior is assessed at all composite scales, i.e., the laminate/ply/constituents (fiber/matrix), via a nonlinear material characterization hygro-thermomechanical model. Sample tailoring cases exhibiting nonlinear material/loading/environmental behavior of aircraft engine fan blades, are presented. The various multidisciplinary loadings lead to different tailored designs, even those opposite of each other, as in the case of minimum material cost versus minimum structure weight and in the case of minimum vibration frequency versus minimum acoustic noise.

Singhal, Surendra N.↗

NASA NTRS2002

Turbopump Performance Improved by Evolutionary Algorithms

The development of design optimization technology for turbomachinery has been initiated using the multiobjective evolutionary algorithm under NASA's Intelligent Synthesis Environment and Revolutionary Aeropropulsion Concepts programs. As an alternative to the traditional gradient-based methods, evolutionary algorithms (EA's) are emergent design-optimization algorithms modeled after the mechanisms found in natural evolution. EA's search from multiple points, instead of moving from a single point. In addition, they require no derivatives or gradients of the objective function, leading to robustness and simplicity in coupling any evaluation codes. Parallel efficiency also becomes very high by using a simple master-slave concept for function evaluations, since such evaluations often consume the most CPU time, such as computational fluid dynamics. Application of EA's to multiobjective design problems is also straightforward because EA's maintain a population of design candidates in parallel. Because of these advantages, EA's are a unique and attractive approach to real-world design optimization problems.

Oyama, Akira↗

NASA NTRS2018

Intercomparison of Evapotranspiration Measurement Methods for Vegetable Crops in California

Recent drought events in California and legislation passed with the goal of increasing the sustainability of groundwater supplies have led to increased interest in tools to optimize irrigation schedules and increase on-farm water used efficiency. With more than 400 different crops produced in California, evapotranspiration-based irrigation scheduling is a promising and well-established approach. However, there is a need for accurate methods to estimate crop evapotranspiration (ET(sub c)) across the diverse range of crops grown, coupled with cost-effective methods for quantifying the accuracy of these tools. In this study, we evaluated remotely sensed estimates of ET(sub c) and associated crop water requirements from NASA's Satellite Irrigation Support (SIMS) system for two vegetable crops and measured crop evapotranspiration ET(sub c) using multiple methods, including weighing lysimeters, eddy covariance towers (EC), and surface renewal stations. We compared ET(sub c) data from these measurements with remotely sensed basal crop evapotranspiration (ET(sub cb)) data from SIMS as well as ET(sub c) data from a standard FAO-56 crop coefficient approach. Studies were conducted for sugar beets in Five Points, CA from 2014 to 2015 and studies are ongoing for fresh market tomatoes in Firebaugh, CA. We present results from these intercomparison studies and describe implications for future studies to quantify the accuracy of remotely sensed measures of ET(sub c). Highlights from results to date include strong correlations between ET measured with both surface renewal instrumentation and eddy covariance calculations using a 3D sonic anemometer and ET(sub c) data measured with the weighing lysimeter, with respective R2 values of 0.7964 (surface renewal) and 0.8034 (eddy covariance). This study provides insights into agreement between different approaches for monitoring evapotranspiration and provides another reference point for the community working to develop accurate and cost-effective tools that support growers in optimizing irrigation management.

Measurement↗

NASA NTRS2016

Analysis and Characterization of Damage and Failure Utilizing a Generalized Composite Material Model Suitable for Use in Impact Problems

A material model which incorporates several key capabilities which have been identified by the aerospace community as lacking in state-of-the art composite impact models is under development. In particular, a next generation composite impact material model, jointly developed by the FAA and NASA, is being implemented into the commercial transient dynamic finite element code LS-DYNA. The material model, which incorporates plasticity, damage, and failure, utilizes experimentally based tabulated input to define the evolution of plasticity and damage and the initiation of failure as opposed to specifying discrete input parameters (such as modulus and strength). The plasticity portion of the orthotropic, three-dimensional, macroscopic composite constitutive model is based on an extension of the Tsai-Wu composite failure model into a generalized yield function with a non-associative flow rule. For the damage model, a strain equivalent formulation is utilized to allow for the uncoupling of the deformation and damage analyses. In the damage model, a semi-coupled approach is employed where the overall damage in a particular coordinate direction is assumed to be a multiplicative combination of the damage in that direction resulting from the applied loads in the various coordinate directions. Due to the fact that the plasticity and damage models are uncoupled, test procedures and methods to both characterize the damage model and to covert the material stress-strain curves from the true (damaged) stress space to the effective (undamaged) stress space have been developed. A methodology has been developed to input the experimentally determined composite failure surface in a tabulated manner. An analytical approach is then utilized to track how close the current stress state is to the failure surface.

Finite Element Method↗

NASA NTRS2016

On Holo-Hilbert Spectral Analysis: A Full Informational Spectral Representation for Nonlinear and Non-Stationary Data

The Holo-Hilbert spectral analysis (HHSA) method is introduced to cure the deficiencies of traditional spectral analysis and to give a full informational representation of nonlinear and non-stationary data. It uses a nested empirical mode decomposition and Hilbert-Huang transform (HHT) approach to identify intrinsic amplitude and frequency modulations often present in nonlinear systems. Comparisons are first made with traditional spectrum analysis, which usually achieved its results through convolutional integral transforms based on additive expansions of an a priori determined basis, mostly under linear and stationary assumptions. Thus, for non-stationary processes, the best one could do historically was to use the time- frequency representations, in which the amplitude (or energy density) variation is still represented in terms of time. For nonlinear processes, the data can have both amplitude and frequency modulations (intra-mode and inter-mode) generated by two different mechanisms: linear additive or nonlinear multiplicative processes. As all existing spectral analysis methods are based on additive expansions, either a priori or adaptive, none of them could possibly represent the multiplicative processes. While the earlier adaptive HHT spectral analysis approach could accommodate the intra-wave nonlinearity quite remarkably, it remained that any inter-wave nonlinear multiplicative mechanisms that include cross-scale coupling and phase-lock modulations were left untreated. To resolve the multiplicative processes issue, additional dimensions in the spectrum result are needed to account for the variations in both the amplitude and frequency modulations simultaneously. HHSA accommodates all the processes: additive and multiplicative, intra-mode and inter-mode, stationary and nonstationary, linear and nonlinear interactions. The Holo prefix in HHSA denotes a multiple dimensional representation with both additive and multiplicative capabilities.

Huang, Norden E.↗

NASA NTRS1992

A comparison of artificial compressibility and fractional step methods for incompressible flow computations

We have applied and compared the efficiency and accuracy of two commonly used numerical methods for the solution of Navier-Stokes equations. The artificial compressibility method augments the continuity equation with a transient pressure term and allows one to solve the modified equations as a coupled system. Due to its implicit nature, one can have the luxury of taking a large temporal integration step at the expense of higher memory requirement and larger operation counts per step. Meanwhile, the fractional step method splits the Navier-Stokes equations into a sequence of differential operators and integrates them in multiple steps. The memory requirement and operation count per time step are low, however, the restriction on the size of time marching step is more severe. To explore the strengths and weaknesses of these two methods, we used them for the computation of a two-dimensional driven cavity flow with Reynolds number of 100 and 1000, respectively. Three grid sizes, 41 x 41, 81 x 81, and 161 x 161 were used. The computations were considered after the L2-norm of the change of the dependent variables in two consecutive time steps has fallen below 10(exp -5).

Chan, Daniel C.↗

NASA NTRS1993

Dynamic-overlapped-grid simulation of aerodynamically determined relative motion

Currently, there is a need to develop a means of analyzing and studying unsteady flowfields which involve multiple component configurations with at least one of the components in relative motion with respect to the others. Two of the important phenomena that such analyses can help to understand are the unsteady aerodynamic interference and the boundary-induced component of the flowfield. With this motivation, a computational method is developed which couples the governing equations of the unsteady flowfield and the rigid-body dynamics in six degrees-of-freedom. These equations are solved on composite meshes of overlapped subdomain grids which can move with respect to each other. Initially, several measures that reduce the numerical error are studied and compared with the exact solution of a moving normal shock in a tube. It is concluded that a second-order accurate method, for spatial and temporal discretizations as well as for the moving subdomain interpolations, is needed as a minimum measure. Furthermore, the CFL numbers should be restricted to unity. Then, the method is used to simulate the flowfield history and predict the aerodynamically determined trajectory of a store dropped from its initial position under a wing.

Yen, Guan-Wei↗

NASA NTRS2014

Hindlimb Suspension as a Model to Study Ophthalmic Complications in Microgravity Status Report: Optimization of Rat Retina Flat Mounts Staining to Study Vascular Remodeling

Preliminary data from a prior tissue‐sharing experiment has suggested that early growth response protein‐1 (Egr1), a transcription factor involved in various stress responses in the vasculature, is induced in the rat retina after 14 days of hindlimb suspension (HS) and may be evidence that mechanical stress is occurring secondary to the cephalad fluid shift. This mechanical stress could cause changes in oxygenation of the retina, and the subsequent ischemia‐ or inflammation‐driven hypoxia may lead to microvascular remodeling. This microvascular remodeling process can be studied using image analysis of retinal vessels and can be then be quantified by the VESsel GENeration Analysis (VESGEN) software, a computational tool that quantifies remodeling patterns of branching vascular trees and capillary or vasculogenic networks. Our project investigates whether rodent HS is a valid model to study the effects of simulated‐weightlessness on ocular structures and their relationship with intracranial pressure (ICP). One of the hypotheses to be tested is that HS‐induced cephalad fluid shift is accompanied by vascular engorgement that produces changes in retinal oxygenation, leading to oxidative stress, hypoxia, microvascular remodeling, and cellular degeneration. We have optimized the procedure to obtain flat mounts of rat retina, staining of the endothelial lining in vasculature and acquisition of high quality images suitable for VESGEN analysis. Briefly, eyes were fixed in 4% paraformaldehyde for 24 hours and retinas were detached and then mounted flat on microscope slides. The microvascular staining was done with endothelial cell‐specific isolectin binding, coupled to Alexa‐488 fluorophore. Image acquisition at low magnification and high resolution was performed using a new Leica SP8 confocal microscope in a tile pattern across the X,Y plane and multiple sections along the Z‐axis. This new confocal microscope has the added capability of dye separation using the Linear Unmixing method and allows us to remove the autofluorescence originating from the photoreceptor layer. In summary, we have an improved method for studying the retinal microvasculature that will provide an increase in the quality of images captured and will be applied throughout the various animal cohorts of the recentlyinitiated study that will evaluate rodent HS as a model to study ophthalmic complications in microgravity.

Theriot, Corey A.↗

NASA NTRS2016

Identifying and Characterizing Impact Melt Outcrops in the Nectaris Basin

The Nectaris Basin is an 820-km diameter, multi-ring impact basin located on the near side of the Moon. Nectaris is a defining stratigraphic horizon based on relationships between ejecta units, giving its name to the Nectarian epoch of lunar history. Lunar basin chronology based on higher resolution LRO imagery and topography, while assigning some important basins like Serenitatis to pre-Nectarian time, were generally consistent with those previously derived. Based on this stratigraphy, at least 11 large basins formed in the time between Nectaris and Imbrium. The absolute age of Nectaris, therefore, is a crucial marker in the lunar time-stratigraphic sequence for understanding the impact flux on the Moon, and by extension, the entire inner solar system. For several decades, workers have attempted to constrain the age of the Nectaris basin through radiometric dating of lunar samples. However, there is little agreement on which samples in our collection represent Nectaris, if any, and what the correct radiometric age of such samples is. The importance of the age of Nectaris goes far beyond assigning a stratigraphic marker to lunar chronology. Several dynamical models use Nectaris as their pin date, so that this date becomes crucial in understanding the time-correlated effects in the rest of the solar system. The importance of the Nectaris basin age, coupled with its nearside, mid-latitude location, make remnants of the impact-melt sheet an attractive target for a future mission, either for in-situ dating or for sample return. We have started exploring this possibility. We have begun a consortium data-analysis effort bringing multiple datasets and analysis methods to bear on these putative impact-melt deposits to characterize their extent, elemental composition and mineralogy, maturity and geologic setting, and to identify potential landing sites that meet both operational safety and science requirements.

Nectaris Basin↗

NASA NTRSDate not supplied

Conceptual Design of the Parallel Electric-Gas Architecture with Synergistic Utilization Scheme (PEGASUS) Concept

In this paper, a novel hybrid electric regional aircraft is presented that strategically locates multiple electric and hybrid electric propulsors to obtain aerodynamic benefits. This concept is called the Parallel Electric-Gas Architecture with Synergistic Utilization Scheme (PEGASUS) aircraft. The use of the alternative propulsive systems coupled with their potential aerodynamic benefits presents modeling challenges for conventional aircraft analysis tools. These challenges are addressed by two methods that quantify the potential benefits of the PEGASUS concept. The results of both methods suggest that when com-pared to other hybrid electric regional aircraft, the PEGASUS concept has the potential to decrease the total energy required to complete a mission while also reducing the vehicle gross weight

Kevin R. Antcliff↗

NASA NTRS2024

Accurate Assessment of Land-Atmosphere Coupling in Climate Models Requires High Frequency Data Output

Land-atmosphere (L-A) interactions are important for understanding convective processes, climate feedbacks, the development and perpetuation of droughts, heatwaves, pluvials, and other land-centred climate anomalies. Local L-A coupling (LoCo) metrics capture relevant L-A processes, highlighting the impact of soil and vegetation states on surface flux partitioning, and the impact of surface fluxes on boundary layer (BL) growth, development, and entrainment of air above the BL. A primary goal of the Climate Process Team on Coupling Land and Atmospheric Subgrid Parameterizations (CLASP) is parameterizing and characterizing the impact of subgrid heterogeneity in global and regional earth system models (ESMs) to improve the connection between land and atmospheric states and processes. A critical step in achieving that aim is the incorporation of L-A metrics, especially LoCo metrics, into climate model diagnostic process streams. However, because land-atmosphere interactions span time scales of minutes (e.g., turbulent fluxes), hours (e.g., BL growth and decay), days (e.g., soil moisture memory), and seasons (e.g., variability of behavioural regimes between soil moisture and latent heat flux), with multiple processes of interest happening in different geographic regions at different times of year, there is not a single metric that captures all the modes, means, and methods of interaction between the land and the atmosphere. And while monthly means of most of the LoCo-relevant variables are routinely saved from ESM simulations, data storage constraints typically preclude routine archival of the hourly data that would enable the calculation of all LoCo metrics. Here we outline a reasonable data request that would allow for adequate characterization of sub-daily coupling processes between the land and the atmosphere, preserving enough sub-daily output to describe, analyse, and better understand L-A coupling in modern climate models. A secondary request involves embedding calculations within the models to determine mean properties in and above the BL to further improve characterization of model behaviour. Higher-frequency model output will (i) allow for more direct comparison with observational field campaigns on process-relevant time scales, (ii) enable demonstration of inter-model spread in L-A coupling processes, and (iii) aid in targeted identification of sources of deficiencies and opportunities for improvement of the models.

Kirsten L. Findell↗

NASA NTRS1993

Multidisciplinary tailoring of hot composite structures

A computational simulation procedure is described for multidisciplinary analysis and tailoring of layered multi-material hot composite engine structural components subjected to simultaneous multiple discipline-specific thermal, structural, vibration, and acoustic loads. The effect of aggressive environments is also simulated. The simulation is based on a three-dimensional finite element analysis technique in conjunction with structural mechanics codes, thermal/acoustic analysis methods, and tailoring procedures. The integrated multidisciplinary simulation procedure is general-purpose including the coupled effects of nonlinearities in structure geometry, material, loading, and environmental complexities. The composite material behavior is assessed at all composite scales, i.e., laminate/ply/constituents (fiber/matrix), via a nonlinear material characterization hygro-thermo-mechanical model. Sample tailoring cases exhibiting nonlinear material/loading/environmental behavior of aircraft engine fan blades, are presented. The various multidisciplinary loads lead to different tailored designs, even those competing with each other, as in the case of minimum material cost versus minimum structure weight and in the case of minimum vibration frequency versus minimum acoustic noise.

Singhal, Surendra N.↗