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NASA NTRSDate not supplied

Experimental Calibration of Flow Rule Coefficients for LS-Dyna Mat_213

Composite materials have become a popular choice in aerospace engineering applications due to their low weight, high specific stiffness, high specific energy absorption, and economic synthesis. As use of composite materials has proliferated, the need for accurate simulation under extreme loading conditions is of increasing importance. *MAT_213 is a tabulated plasticity and damage material model in LS-DYNA designed for such use cases. To account for the nonlinear material response, a plasticity algorithm is used, which employs a non-associative flow rule with coefficients requiring experimental calibration. This work outlines an experimental methodology for calibrating these coefficients using the macroscopic stress-strain response and microscopic in-plane strain measurements from coupon scale experiments. The model material used for the development and demonstration of this methodology is a plain weave woven fabric with T300 carbon fiber tows in the warp direction and Kevlar© 49 fiber tows in the weft direction, and an Epon© 828/Epikure© 3223 thermoset epoxy matrix. Coupon-scale tensile testing performed at multiple fiber angles (carbon fibers oriented 0º, 22.5º, 45º, 67.5º, and 90º relative to the loading axis) provides data for multiple calibration processes. The measured plastic strain increments in the principal material coordinate are used to set limits for ratios between flow rule coefficients. The identified ranges are used to bound the search for a set of coefficients, leading to convergence of different coupon responses in the effective stress – effective plastic strain space. Flow rule coefficients found by this methodology are then used as (i) input for LS-DYNA simulations of uniaxial tension coupon tests at varying fiber angles, and (ii) comparison of predicted values for the plastic Poisson’s ratio in global coordinates with the experimentally measured one for all off-axis orientations. These results are quantitatively and qualitatively compared to macroscopic stress-strain curves and experimental strain components. The conformity of the experimentally measured quantities with those derived from the simulations provide a means for assessing the quality of calibrated coefficients.

Polymer Matrix Composites↗
NASA NTRS1985

Simulation of the temperature distribution in crystals grown by Czochralski method

Production of perfect crystals, free of residual strain and dislocations and with prescribed dopant concentration, by the Czochralski method is possible only if the complex, interacting phenomena that affect crystal growth in a Cz-puller are fully understood and quantified. Natural and forced convection in the melt, thermocapillary effect and heat transfer in and around the crystal affect its growth rate, the shape of the crystal-melt interface and the temperature gradients in the crystal. The heat transfer problem in the crystal and between the crystal and all other surfaces present in the crystal pulling apparatus are discussed at length. A simulation and computer algorithm are used, based on the following assumptions: (1) only conduction occurs in the crystal (experimentally determined conductivity as a function of temperature is used), (2) melt temperature and the melt-crystal heat transfer coefficient are available (either as constant values or functions of radial position), (3) pseudo-steady state is achieved with respect to temperature gradients, (4) crystal radius is fixed, and (5) both direct and reflected radiation exchange occurs among all surfaces at various temperatures in the crystal puller enclosure.

Dudokovic, M. P.↗
NASA NTRS2023

Quantifying the Agyrotropy of Proton and Electron Heating in Turbulent Plasmas

An important aspect of energy dissipation in weakly collisional plasmas is that of energy partitioning between different species (e.g., protons and electrons) and between different energy channels. Here we analyse pressure–strain interaction to quantify the fractions of isotropic compressive, gyrotropic, and nongyrotropic heating for each species. An analysis of kinetic turbulence simulations is compared and contrasted with corresponding observational results from Magnetospheric Multiscale Mission data in the magnetosheath. In assessing how protons and electrons respond to different ingredients of the pressure–strain interaction, we find that compressive heating is stronger than incompressive heating in the magnetosheath for both electrons and protons, while incompressive heating is stronger in kinetic plasma turbulence simulations. Concerning incompressive heating, the gyrotropic contribution for electrons is dominant over the nongyrotropic contribution, while for protons nongyrotropic heating is enhanced in both simulations and observations. Variations with plasma β are also discussed, and protons tend to gain more heating with increasing β.

Yan Yang↗
NASA NTRS1997

Computational Simulation of Composite Behavior

Composite microfracture technique developed here is based on the concept of global strain energy release rate. Step-by-step procedures were outlined to evaluate composite microfracture. The technique can predict microfracture initiation/propagation, predict the "structural fracture toughness", and establish the hierarchy of fracture modes. Both unidirectional and cross-ply metal-matrix composite laminates were evaluated for microfracture, subjected to thermal and mechanical loads. Five NASA reports were published as shown in the bibliography and several presentations were made at the technical conferences/ symposia. Work was also performed to develop simplified micromechanics and macromechanics for ceramic matrix composites. A novel fiber sub-structuring technique was developed, which divides the fiber into several "slices" and applies the micromechanics equation at the "slice" level, which are then integrated upwards to get the ply and the laminate properties. It allows for a more accurate representation of interfacial conditions such as partial interface bond etc. It also predicts the stress-strain behavior of a composite up to failure by taking into account material properties dependence upon temperature as well as stress redistribution that occurs due to damage initiation and propagation. A computer code CEMCAN (Ceramic Matrix Composites Analyzer) which includes all these capabilities has been developed as a part of this research activity.

Keith, Theo G., Jr.↗
NASA NTRS1987

The structure of the vorticity field in homogeneous turbulent flows

The structures of the vorticity fields in several homogeneous irrotational straining flows and a homogeneous turbulent shear flow were examined using a database generated by direct numerical simulation of the unsteady Navier-Stokes equations. In all cases, strong evidence was found for the presence of coherent vortical structures. The initially isotropic vorticity fields were rapidly affected by imposed mean strain and the rotational component of mean shear and developed accordingly. In the homogeneous turbulent shear-flow cases, the roll-up of mean vorticity into characteristic hairpin vortices was clearly observed, supporting the view that hairpin vortices are an important vortical structure in all turbulent shear flows; the absence of mean shear in the homogeneous irrotational straining flows precludes the presence of hairpin-like vortices.

Rogers, Michael M.↗
NASA NTRS1986

Tectonic motions in California inferred from very long baseline interferometry observations, 1980-1984

Using VLBI, three baselines of 150-300 km length within California, and three baselines of 1500 km length between California and Texas, measured between 1980 and 1984, have been fitted to a steady plane/strain rotation model. The observed rate of displacement across the southern San Andreas fault is in agreement with other contemporary rate estimates near 3 cm/yr. Discrepancies between these rates and indicators of relative plate motion near 6 cm/yr seem to be related to local departures of the San Andreas system from the expected strike of the plate boundary. Results support a regional distribution of elastic strain that is offset in about the same sense and amount as the Big Bend of the San Andreas fault, and finite element simulations suggest that tractions on the base of the crust that accompany mantle downswelling beneath the Transverse Ranges could contribute to these strain inhomogeneities.

Lyzenga, Gregory A.↗
NASA NTRS2017

Zoledronate Prevents Simulated Weightlessness-Induced Bone Loss in the Cancellous Compartment While Blunting the Efficacy of a Mechanical Loading Countermeasure

Astronauts using high-force resistance training while weightless show a high-turnover remodeling state within the skeletal system, with resorption and formation biomarkers being elevated. One countermeasure for the skeletal health of astronauts includes an antiresorptive of the bisphosphonate (BP) drug class. We asked, does the combination of an anti-resorptive and high-force exercise during weightlessness have negative effects on bone remodeling and strength? In this study, we developed an integrated model to mimic the mechanical strain of exercise via cyclical loading (CL) in mice treated with the BP Zoledronate (ZOL) combined with hind limb unloading (HU) to simulate weightlessness. We hypothesized that ZOL prevents structural degradation from simulated weightlessness and that CL and ZOL interact to render CL less effective. Thirty-two C57BL/6 mice (male, 16 weeks old, n=8/group) were exposed to 3 weeks of either HU or normal ambulation (NA). Cohorts of mice received one subcutaneous injection of ZOL (45μg/kg), or saline vehicle (VEH), prior to the start of HU. The right tibia was axially compressed in vivo 60x/day to 9N (+1200μstrain on the periosteal surface) and repeated 3x/week during HU. Left tibiae served as a within subject, non-compressed control. Ex vivo μCT was performed on all subjects to determine cancellous and cortical architectural parameters. Static and dynamic histomorphometry were carried out for the left and right tibiae to determine osteoclast- and osteoblast relevant surfaces. Further, micro damage was assessed in select groups by basic-fuchsin staining to test whether CL had an effect. For all assays, a multivariate (2x2x2) ANCOVA model was used to account for body weight changes. Additionally, for the tibiae, we incorporated a random effect for the subject (hence, a mixed model) to account for observations of both left and right tibiae within each subject. P < 0.05 was considered significant. In the cancellous compartment of the proximal tibial metaphysis, we observed a main effect from each independent variable, as determined by structural and histomorphometric assays. Specifically, as expected, ZOL showed an increase in the cancellous bone volume to total volume fraction (BV/TV, +32%) and trabecular number (+18%) compared to the VEH. As expected, ZOL decreased osteoclast surface (OC/BS) by -45% compared to VEH. Surprisingly, ZOL reduced mineralizing surface (MS/BS) and bone formation rate (BFR), indicators of osteoblast activity, by -40% and -54%, respectively, compared to VEH. Altogether, ZOL-treated mice displayed a low turnover state of remodeling in the metaphysis. In the context of skeletal aging, we speculate that ZOL prevented age-related cancellous strut loss during the experiment. As a main effect, as expected, HU decreased BV/TV by - 31% via reductions in both trabecular thickness (-11%) and number (-22%) compared to NA controls. Additionally, HU decreased MS/BS by -38% and bone formation rate (BFR) by -50% compared to NA controls. Altogether, these data are consistent with structural degradation resulting from imbalanced remodeling that favors resorption. As a main effect, CL increased BV/TV by +15% via increased trabecular thickness (+12%) compared to the noncompressed limb. As expected, CL increased MS/BS (+20%) and BFR (+24%), indicating osteoblast mineralization contributed to bone gains. These data show that CL provided an anabolic stimulus to the cancellous tissue. We observed unique interactions in ZOL*CL and HU*CL. First, ZOL prevented CL-induced increases in BV/TV and trabecular number, as compared to VEH. In the context of skeletal aging, these data suggest no added benefit from CL in the ZOL-treated mice. Interestingly, no microdamage was observed in mice that were unloaded and treated with ZOL (independent of CL). Secondly, HU prevented CL-induced increases in BFR, as compared to NA controls. These data suggest that either exercise is less effective or the kinetics of formation are slower during simulated weightlessness. Osteoclast surface was unchanged by either treatment. Thus, in contrast to exercising astronauts, these data do not suggest a high-turnover state in the metaphysis. To assess mechanical properties as a function of HU or ZOL, we tested the left femur in three-point bending ex vivo. As expected, HU decreased stiffness (-30%) compared to NA, and ZOL increased stiffness compared to VEH (+28%). Interestingly, HU increased the post-yield displacement, related to collagenous tensile loading, compared to NA (+20%). ZOL increased yield force (+11%) and ultimate force (+17%), which seems to explain the significant effect of ZOL increasing total energy (work-to-fracture, +15%), while not affecting the post yield displacement. Taken together, ZOL did not have detrimental affect on mechanical properties. Our integrated model simulates the combination of weightlessness, exercise-induced mechanical strain, and anti-resorptive treatment that astronauts experience during space missions. We conclude that Zoledronate was an effective countermeasure against weightlessness-induced bone loss, though zoledronate, as well as weightlessness, rendered exercise-related mechanical loading less effective.

bone↗
NASA NTRS1997

Formation of Carbon Nanotube Based Gears: Quantum Chemistry and Molecular Mechanics Study of the Electrophilic Addition of o-Benzyne to Fullerenes, Graphene, and Nanotubes

Considerable progress has been made in recent years in chemical functionalization of fullerene molecules. In some cases, the predominant reaction products are different from those obtained (using the same reactants) from polycyclic aromatic hydrocarbons (PAHs). One such example is the cycloaddition of o-benzyne to C60. It is well established that benzyne adds across one of the rings in naphthalene, anthracene and other PAHs forming the [2+4] cycloaddition product (benzobicyclo[2.2.2.]-octatriene with naphthalene and triptycene with anthracene). However, Hoke et al demonstrated that the only reaction path for o-benzyne with C60 leads to the [2+2] cycloaddition product in which benzyne adds across one of the interpentagonal bonds (forming a cyclobutene ring in the process). Either reaction product results in a loss of aromaticity and distortion of the PAH or fullerene substrate, and in a loss of strain in the benzyne. It is not clear, however, why different products are preferred in these cases. In the current paper, we consider the stability of benzyne-nanotube adducts and the ability of Brenner's potential energy model to describe the structure and stability of these adducts. The Brenner potential has been widely used for describing diamondoid and graphitic carbon. Recently it has also been used for molecular mechanics and molecular dynamics simulations of fullerenes and nanotubes. However, it has not been tested for the case of functionalized fullerenes (especially with highly strained geometries). We use the Brenner potential for our companion nanogear simulations and believe that it should be calibrated to insure that those simulations are physically reasonable. In the present work, Density Functional theory (DFT) calculations are used to determine the preferred geometric structures and energetics for this calibration. The DFT method is a kind of ab initio quantum chemistry method for determining the electronic structure of molecules. For a given basis set expansion, it is comparable in accuracy to the MP2 method (better than Hartree Fock, but less accurate than more extensive electron correlation methods such as MP4 or CCSD). However, for systems with large numbers of basis functions it more efficient than any other methods that include electron correlation effects. In this presentation we show the results of DFT calculations for the reaction of benzyne with naphthalene, C60, and nanotube models. We compare energies for [2+2] and [2+4] cycloaddition products. The preferred products for the naphthalene and C60 reactions have been determined by experiment and, thus, these cases serve as a validation of our quantum chemical approach. We also compare the DFT and Brenner potential results. Finally we can predict the likelihood of reaction between benzyne and nanotubes.

Jaffe, Richard↗
NASA NTRS1989

Compression behavior of delaminated composite plates

The response of delaminated composite plates to compressive in-plane loads was investigated. The delaminated region may be either circular or elliptical, and may be located between any two plies of the laminate. For elliptical delaminations, the axes of the ellipse may be arbitrarily oriented with respect to the applied loads. A model was developed that describes the stresses, strains, and deformation of the sublaminate created by the delamination. The mathematical model is based on a two dimensional nonlinear plate theory that includes the effects of transverse shear deformation. The model takes into account thermal and moisture induced strains, transverse pressures acting on the sublaminate, and contact between the sublaminate and plate. The solution technique used is the Ritz method. A computationally efficient computer implementation of the model was developed. The code can be used to predict the nonlinear-load-strain behavior of the sublaminate including the buckling load, postbuckling behavior, and the onset of delamination growth. The accuracy of the code was evaluated by comparing the model results to benchmark analytical solutions. A series of experiments was conducted on Fiberite T300/976 graphite/epoxy laminates bonded to an aluminum honeycomb core forming a sandwich panel. Either circles or ellipses made from Teflon film were embedded in the laminates, simulating the presence of a delamination. Each specimen was loaded in compression and the strain history of the sublaminate was recorded far into the postbuckling regime. The extent of delamination growth was evaluated by C-scan examination of each specimen. The experimental data were compared to code predictions. The code was found to describe the data with reasonable accuracy. A sensitivity study examined the relative importance of various material properties, the delamination dimensions, the contact model, the transverse pressure differential, the critical strain energy release rate, and the relative growth direction on the buckling load, the postbuckling behavior, and the growth load of the sublaminate.

Peck, Scott O.↗
NASA NTRS2017

Integrated Model of the Eye/Optic Nerve Head Biomechanical Environment

Visual Impairment and Intracranial Pressure (VIIP) syndrome is a concern for long-duration space flight. Previously, it has been suggested that ocular changes observed in VIIP syndrome are related to the cephalad fluid shift that results in altered fluid pressures [1]. We are investigating the impact of changes in intracranial pressure (ICP) using a combination of numerical models, which simulate the effects of various environment conditions, including finite element (FE) models of the posterior eye. The specific interest is to understand how altered pressures due to gravitational changes affect the biomechanical environment of tissues of the posterior eye and optic nerve sheath. METHODS: Additional description of the numerical modeling is provided in the IWS abstract by Nelson et al. In brief, to simulate the effects of a cephalad fluid shift on the cardiovascular and ocular systems, we utilized a lumped-parameter compartment model of these systems. The outputs of this lumped-parameter model then inform boundary conditions (pressures) for a finite element model of the optic nerve head (Figure 1). As an example, we show here a simulation of postural change from supine to 15 degree head-down tilt (HDT), with primary outcomes being the predicted change in strains at the optic nerve head (ONH) region, specifically in the lamina cribrosa (LC), retrolaminar optic nerve, and prelaminar neural tissue (PLNT). The strain field can be decomposed into three orthogonal components, denoted as the first, second and third principal strains. We compare the peak tensile (first principal) and compressive (third principal) strains, since elevated strain alters cell phenotype and induces tissue remodeling. RESULTS AND CONCLUSIONS: Our lumped-parameter model predicted an IOP increase of c. 7 mmHg after 21 minutes of 15 degree HDT, which agreed with previous reports of IOP in HDT [1]. The corresponding FEM simulations predicted a relative increase in the magnitudes of the peak tensile and compressive strains in the lamina cribrosa of 42 and 43, respectively (Fig. 2). The corresponding changes in the optic nerve strains were 17 and 39, while in the PLNT they were 47 and 43. These magnitudes of relative elevations in peak strains may induce a phenotypic response in resident mechano-responsive resident cells [2]. This approach may be expanded to investigate other environmental changes (e.g. parabolic flight). Through our VIIP SCHOLAR project, we will validate and improve these integrated models by measuring patient-specific changes in optic nerve sheath geometry in patients with idiopathic intracranial hypertension before and after lumbar puncture and CSF removal.

biomechanics↗
NASA NTRS1972

Experimental investigation of Mach 3 cruise heating simulations on a representative wing structure for flight loads measurement

Radiant heating experiments were performed in the laboratory on an instrumented multispar wing structure to investigate: (1) how accurately the structural temperatures of a Mach 3 cruise-flight profile could be simulated, (2) what the effects of the heating and heating inaccuracies would be on the responses of strain-gage bridges installed on the structure, and (3) how these responses would affect flight loads measurements. Test temperatures throughout the structure agreed well with temperatures calculated for a Mach 3 profile. In addition, temperatures produced by two identical tests were repeatable to less than + or -6 K deg. Thermally induced strain-gage-bridge responses were large enough to be detrimental to a high-speed flight loads program with a goal of establishing aerodynamic loads (exclusive of thermal loads). It was shown that heating simulation can be used effectively for thermal calibration (that is, to provide corrections for a high-temperature environment), and that thermal calibration may not be needed if the simulation data are used to carefully select bridges and load equations.

Fields, R. A.↗
NASA NTRS2002

Studies on Stress-Strain Relationships of Polymeric Materials Used in Space Applications

A two-year research plan was undertaken in association with Polymers Branch, NASA Glenn Research Center, to carry out experimental and modeling work relating stress and strain behavior of polymeric materials, especially elastomers and vulcanized rubber. An experimental system based on MTS (Mechanical Testing and Simulation) A/T-4 test facility environment has been developed for a broader range of polymeric materials in addition to a design of laser compatible temperature control chamber for online measurements of various strains. Necessary material processing has been accomplished including rubber compounding and thermoplastic elastomer processing via injection molding. A broad suite of testing methodologies has been identified to reveal the complex non-linear mechanical behaviors of rubbery materials when subjected to complex modes of deformation. This suite of tests required the conceptualization, design and development of new specimen geometries, test fixtures, and test systems including development of a new laser based technique to measure large multi-axial deformations. Test data has been generated for some of these new fixtures and has revealed some complex coupling effects generated during multi-axial deformations. In addition, fundamental research has been conducted concerning the foundation principles of rubber thermodynamics and resulting theories of rubber elasticity. Studies have been completed on morphological properties of several thermoplastic elastomers. Finally, a series of steps have been identified to further advance the goals of NASA's ongoing effort.

Jana, Sadhan C.↗
NASA NTRS1988

Predicted and observed effects of stacking sequence and delamination size on instability-related delamination growth

A three-dimensional, geometrically nonlinear finite element analysis was used to calculate strain-energy release rate distributions for several laminates which exhibited instability-related delamination growth. Two stacking sequences, (0/90/90/0)6 and (90/0/0/90)6 were considered. The specimens were fabricated with a double layer of 0.013 mm Kapton film located between the fourth and fifth plies, thereby simulating a delamination. Initial delamination sizes were 30, 40, or 60 mm in diameter. The static strain corresponding to delamination growth was determined experimentally. Comparison of the analytical and experimental results indicated that delamination growth was governed by the magnitude of GI.

Whitcomb, John D.↗
NASA NTRS1984

Delamination growth analysis in quasi-isotropic laminates under loads simulating low-velocity impact

A geometrically nonlinear finite-element analysis was developed to calculate the strain energy released by delamination plates during impact loading. Only the first mode of deformation, which is equivalent to static deflection, was treated. Both the impact loading and delamination in the plate were assumed to be axisymmetric. The strain energy release rate in peeling, G sub I, and shear sliding, G sub II, modes were calculated using the fracture mechanics crack closure technique. Energy release rates for various delamination sizes and locations and for various plate configurations and materials were compared. The analysis indicated that shear sliding (G sub II) was the primary mode of delamination growth. The analysis also indicated that the midplane (maximum transverse shear stress plane) delamination was more critical and would grow before any other delamination of the same size near the midplane region. The delamination growth rate was higher (neutrally stable) for a low toughness (brittle) matrix and slower (stable) for high toughness matrix. The energy release rate in the peeling mode, G sub I, for a near-surface delamination can be as high as 0.5G sub II and can contribute significantly to the delamination growth.

Shivakumar, K. N.↗
NASA NTRSDate not supplied

Uncertainty Reduction With Multi-Model Monte Carlo for Crystal Plasticity Simulations of Additively Manufactured Metals

In this work, multi-model Monte Carlo estimators are developed to reduce uncertainty in quantities of interest (QoIs) extracted from crystal plasticity simulations of additively manufactured (AM) metals. A significant concern in AM parts is uncertainty in mechanical properties caused in part by complex microstructures that arise from the AM process. Quantifying uncertainty in microstructure-sensitive behavior using experiments alone is costly, especially when mechanical allowables must be established. Quantitative relationships among microstructure, micromechanical metrics like slip accumulation, crack initiation, and failure are also difficult to capture with limited experiments. Crystal plasticity material models instead enable computational prediction of micromechanical stress and strain fields given a discretized microstructure. However, high-fidelity finely discretized crystal plasticity simulations are computationally expensive, while lower-fidelity models are less accurate and generally biased, making uncertainty quantification and reduction computationally difficult as well. Multi-model Monte Carlo methods leverage correlations between high- and low-fidelity models to produce unbiased estimators for QoIs with reduced uncertainty relative to standard Monte Carlo. Crystal plasticity QoIs considered in this work include yield strength and the mean and extreme values of micromechanical fields that are relevant to crack initiation. Multi-model Monte Carlo estimators are developed for each individual QoI and several groups of QoIs. The results of this work establish relationships among model correlations, sample allocation, and uncertainty reduction for different combinations of QoIs and demonstrate a trend of less uncertainty reduction as QoIs become more sensitive to local microstructure. Limitations from using pilot samples to estimate model covariances and train low-fidelity models are also addressed. The uncertainty reduction achieved by multi-model Monte Carlo is an important step toward using computational mechanics models to predict microstructure-sensitive crack initiation and failure in AM parts.

uncertainty quantification↗
NASA NTRS1977

An ILLIAC program for the numerical simulation of homogeneous incompressible turbulence

An algorithm and ILLIAC computer program, developed for the simulation of homogeneous incompressible turbulence in the presence of an applied mean strain, are described. The turbulence field is represented spatially by a truncated triple Fourier series (spectral method) and followed in time using a fourth-order Runge-Kutta algorithm. These include: (1) transformation of variables suggested by Taylor's sudden-distortion theory; (2) implicit viscous diffusion by use of an integrating factor; (3) implicit pressure calculation suggested by Taylor's sudden-distortion theory, and (4) inexpensive control of aliasing by random and phased coordinate shifts.

Rogallo, R. S.↗
NASA NTRS1987

Estimation of blade airloads from rotor blade bending moments

A method is developed to estimate the blade normal airloads by using measured flap bending moments; that is, the rotor blade is used as a force balance. The blade's rotation is calculated in vacuum modes and the airloads are then expressed as an algebraic sum of the mode shapes, modal amplitudes, mass distribution, and frequency properties. The modal amplitudes are identified from the blade bending moments using the Strain Pattern Analysis Method. The application of the method is examined using simulated flap bending moment data that have been calculated for measured airloads for a full-scale rotor in a wind tunnel. The estimated airloads are compared with the wind tunnel measurements. The effects of the number of measurements, the number of modes, and errors in the measurements and the blade properties are examined, and the method is shown to be robust.

Bousman, William G.↗
NASA NTRS1989

Enhanced element-specific modal formulations for flexible multibody dynamics

The accuracy of current flexible multibody formalisms based on assumed modes is examined in the context of standard spacecraft motions involving structural components undergoing both slow and fast overall translational and rotational motions as well as small deformations. Limitations of current techniques in treating: (1) element-specific coupling behavior of large motion and small deformation, and (2) motion-induced structural stiffness variations, are noted. The roles of nonlinear and linear elastic structural theories in accurately predicting transient large-displacement dynamic behavior of flexible multibody systems are examined in detail. Coupling effects between deformation and overall motion are carefully scrutinized in the context of assumed-mode discretization techniques. Consistently linearized beam, plate, and shell formulations involving in-plane stretch variables are proposed and shown to yield very accurate simulation results and extremely fast modal convergence for most motions involving small strains. In some particular cases, however, in which membrane stiffness dominates bending stiffness, a nonlinear strain formulation is required in order to capture proper coupling between deformation and overall motion.

Ryan, Robert R.↗