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Variational Coupled Loads Analysis using the Hybrid Parametric Variation Method

Time-domain coupled loads analysis (CLA)is used to determine the response of a launch vehicle and payload system to transient forces, such as liftoff, engine ignitions and shutdowns, jettison events, and atmospheric flight loads, such as buffet. CLA, using Hurty/Craig-Bampton (HCB)component models, is the accepted method for the establishment of design-level loads for launch systems. However, uncertainty in the component models flows into uncertainty in predicted system results. Uncertainty in the structural responses during launch is a significant concern because small variations in launch vehicle and payload mode shapes and their interactions can result in significant variations in system loads. Uncertainty quantification (UQ)is used to determine statistical bounds on prediction accuracy based on model uncertainty. In this paper uncertainty is treated at the HCB component-model level. In an effort to account for model uncertainties and statistically bound their effect on CLA predictions, this work combines CLA with UQ in a process termed variational coupled loads analysis (VCLA). The modeling of uncertainty using a parametric approach, in which input parameters are represented by random variables, is common, but its major drawback is the resulting uncertainty is limited to the form of the nominal model. Uncertainty in model form is one of the biggest contributors to uncertainty in complex built-up structures. Model-form uncertainty can be represented using a nonparametric approach based on random matrix theory (RMT). In this work, UQ is performed using the hybrid parametric variation (HPV)method, which combines parametric with nonparametric uncertainty at the HCB component model level. The HPV method requires the selection of dispersion values for the HCB fixed-interface (FI)eigenvalues, and the HCB mass and stiffness matrices. The dispersions are based upon component test-analysis modal correlation results. During VCLA, random component models are assembled into an ensemble of random systems using a Monte Carlo (MC)approach. CLA is applied to each of the ensemble members to produce an ensemble of system-level responses for statistical analysis. The proposed methodology is demonstrated through its application to a buffet loads analysis of NASA’s Space Launch System (SLS)during the transonic regime fifty seconds after liftoff. Core stage (CS)section shears and moments are recovered, and statistics are computed.

Uncertainty Quantification↗

NASA NTRS1993

Finite element large deflection random response of thermally buckled plates

The governing nonlinear equations of motion are derived for a rectangular isotropic plate subjected to a combined thermal-acoustic loading. The thermal loading is taken to be a steady state temperature distribution, and the acoustic loading is considered to be a stationary Gaussian pressure with zero mean and uniform magnitude and phase over the plate surface. With these types of loads, the thermal-acoustic analysis can be separated into two problems: (1) thermal post-buckling; and (2) random vibration of the thermally buckled plate. Since both analyses are nonlinear, iterative techniques are used to solve each. For the random vibration analysis, the method of equivalent linearization is used; both auto- and cross-correlation terms are included. Results obtained using the present formulation are compared with previous classical equivalent linearization results.

Locke, J. E.↗

NASA NTRS2009

Using Maximal Isometric Force to Determine the Optimal Load for Measuring Dynamic Muscle Power

Maximal power output occurs when subjects perform ballistic exercises using loads of ~30-50% of one-repetition maximum (1-RM). However, performing 1-RM testing prior to power measurement requires considerable time, especially when testing involves multiple exercises. Maximal isometric force (MIF), which requires substantially less time to measure than 1-RM, might be an acceptable alternative for determining the optimal load for power testing. PURPOSE: To determine the optimal load based on MIF for maximizing dynamic power output during leg press and bench press exercises. METHODS: Twenty healthy volunteers (12 men and 8 women; mean +/- SD age: 31+/-6 y; body mass: 72 +/- 15 kg) performed isometric leg press and bench press movements, during which MIF was measured using force plates. Subsequently, subjects performed ballistic leg press and bench press exercises using loads corresponding to 20%, 30%, 40%, 50%, and 60% of MIF presented in randomized order. Maximal instantaneous power was calculated during the ballistic exercise tests using force plates and position transducers. Repeated-measures ANOVA and Fisher LSD post hoc tests were used to determine the load(s) that elicited maximal power output. RESULTS: For the leg press power test, six subjects were unable to be tested at 20% and 30% MIF because these loads were less than the lightest possible load (i.e., the weight of the unloaded leg press sled assembly [31.4 kg]). For the bench press power test, five subjects were unable to be tested at 20% MIF because these loads were less than the weight of the unloaded aluminum bar (i.e., 11.4 kg). Therefore, these loads were excluded from analysis. A trend (p = 0.07) for a main effect of load existed for the leg press exercise, indicating that the 40% MIF load tended to elicit greater power output than the 60% MIF load (effect size = 0.38). A significant (p . 0.05) main effect of load existed for the bench press exercise; post hoc analysis indicated that the effect of load on power output was: 30% > 40% > 50% = 60%. CONCLUSION: Loads of 40% and 30% of MIF elicit maximal power output during dynamic leg presses and bench presses, respectively. These findings are similar to those obtained when loading is based on 1-RM.

Spiering, Barry A.↗

NASA NTRS1989

An approximate methods approach to probabilistic structural analysis

A major research and technology program in Probabilistic Structural Analysis Methods (PSAM) is currently being sponsored by the NASA Lewis Research Center with Southwest Research Institute as the prime contractor. This program is motivated by the need to accurately predict structural response in an environment where the loadings, the material properties, and even the structure may be considered random. The heart of PSAM is a software package which combines advanced structural analysis codes with a fast probability integration (FPI) algorithm for the efficient calculation of stochastic structural response. The basic idea of PAAM is simple: make an approximate calculation of system response, including calculation of the associated probabilities, with minimal computation time and cost, based on a simplified representation of the geometry, loads, and material. The deterministic solution resulting should give a reasonable and realistic description of performance-limiting system responses, although some error will be inevitable. If the simple model has correctly captured the basic mechanics of the system, however, including the proper functional dependence of stress, frequency, etc. on design parameters, then the response sensitivities calculated may be of significantly higher accuracy.

Mcclung, R. C.↗

DOE OSTI2024

Ketone monoester plus high‐dose glucose supplementation before exercise does not affect immediate post‐exercise erythropoietin concentrations versus glucose alone

Abstract The objective of this study was to examine the effect of consuming ketone monoester plus a high dose of carbohydrate from glucose (KE + CHO) on the change in erythropoietin (EPO) concentrations during load carriage exercise compared with carbohydrate (CHO) alone. Using a randomized, crossover design, 12 males consumed KE + CHO (573 mg KE/kg body mass, 110 g glucose) or CHO (110 g glucose) 30 min before 4 miles of self‐paced treadmill exercise (KE + CHO:51 ± 13%, CHO: 52 ± 12% V̇O 2peak ) wearing a weighted vest (30% body mass; 25 ± 3 kg). Blood samples for analysis were obtained under resting fasted conditions before (Baseline) consuming the KE + CHO or CHO supplement and immediately after exercise (Post). βHB increased ( p < 0.05) from Baseline to Post in KE + CHO, with no change in CHO. Glucose and glycerol increased ( p < 0.05) from Baseline to Post in CHO, with no effect of time in KE + CHO. Insulin and lactate increased ( p < 0.05) from Baseline to Post independent of treatment. EPO increased ( p < 0.05) from Baseline to Post in KE + CHO and CHO with no difference between treatments. Although KE + CHO altered βHB, glucose, and glycerol concentrations, results from this study suggest that KE + CHO supplementation before load carriage exercise does not enhance immediate post‐exercise increases in EPO compared with CHO alone.

Howard, Emily E.↗

DOE OSTI2026

In-situ observations of cyclic deformation in an extruded Mg-2Nd-1Y-0.1Zr-0.1Ca alloy

In this study, the evolution of deformation mechanisms during cyclic loading in an extruded, solution-treated Mg–2Nd–1Y–0.1Zr–0.1Ca alloy was investigated using a combination of in-situ loading, scanning electron microscopy (SEM), electron backscatter diffraction (EBSD), and focused ion beam (FIB) nanofabrication. The initial microstructure exhibited a random crystallographic texture with no preferred grain orientation. Flat, rectangular dog-bone specimens were subjected to load-controlled, fully reversed fatigue for 50 cycles, during which the same region was sequentially mapped to track microstructural changes. After 10 cycles of loading deformation twins were observed. During tensile reloading detwinning or narrowing of those twinned regions occurred. After 20 cycles, detwinning ceased and residual twins remained in the material. SEM imaging revealed numerous surface slip traces after cyclic loading. EBSD-assisted slip trace analysis identified the activation of prismatic and pyramidal < c+a> slip systems during low-cycle fatigue. Site-specific scanning transmission electron microscopy (STEM) further revealed that deformation was also accommodated by basal < a> slip and the dissociation of < c+a> dislocations. Center-of-symmetry (COS) analysis confirmed that the dissociation of < c+a> dislocations resulted in the formation of I₁ intrinsic stacking faults after cyclic loading. These findings provide new insights into the complex interplay of dislocation mechanisms governing fatigue deformation in rare-earth-containing Mg alloys.

Cyclic deformation↗

NASA NTRS1995

Analysis of uncertainty in force balance calibration

In order to reduce errors encountered in the measurement and identification of loads using force balances, a third-order forward polynomial relation between loads and output voltages is proposed. This full third-order model represents an alternative to the second-order model currently in use at NASA Langley Research Center (LaRC) and many other installations worldwide. The new model requires the identification of 84 coefficients (including the 28 used presently) for each of the six outputs. The existing LaRC calibration loading sequence is insufficient for identification of many of these 504 coefficients because critical three-load combinations are absent. Accordingly, a new loading sequence that permits the identification of all 504 coefficients has been developed and is described fully. It is apparent from numerical tests that the new third-order model is clearly superior to second-order models in the presence of small amounts of random measurement noise, assuming that there are indeed higher-order interactions between loads. As the amount of noise increases, however, a third-order model becomes less attractive due to its ability to match the noise itself more faithfully than a second-order model. Numerical results suggest that the transition occurs when the magnitude of random noise becomes of the same order as that of the physical higher-order interactions.

Bursal, Faruk H.↗

NASA NTRS2004

Predicting the Influence of Nano-Scale Material Structure on the In-Plane Buckling of Orthotropic Plates

A multi-scale analysis of the structural stability of a carbon nanotube-polymer composite material is developed. The influence of intrinsic molecular structure, such as nanotube length, volume fraction, orientation and chemical functionalization, is investigated by assessing the relative change in critical, in-plane buckling loads. The analysis method relies on elastic properties predicted using the hierarchical, constitutive equations developed from the equivalent-continuum modeling technique applied to the buckling analysis of an orthotropic plate. The results indicate that for the specific composite materials considered in this study, a composite with randomly orientated carbon nanotubes consistently provides the highest values of critical buckling load and that for low volume fraction composites, the non-functionalized nanotube material provides an increase in critical buckling stability with respect to the functionalized system.

Gates, Thomas S.↗

NASA NTRS1997

A New Approach to Extreme Value Estimation Applicable to a Wide Variety of Random Variables

Designing reliable structures requires an estimate of the maximum and minimum values (i.e., strength and load) that may be encountered in service. Yet designs based on very extreme values (to insure safety) can result in extra material usage and hence, uneconomic systems. In aerospace applications, severe over-design cannot be tolerated making it almost mandatory to design closer to the assumed limits of the design random variables. The issue then is predicting extreme values that are practical, i.e. neither too conservative or non-conservative. Obtaining design values by employing safety factors is well known to often result in overly conservative designs and. Safety factor values have historically been selected rather arbitrarily, often lacking a sound rational basis. To answer the question of how safe a design needs to be has lead design theorists to probabilistic and statistical methods. The so-called three-sigma approach is one such method and has been described as the first step in utilizing information about the data dispersion. However, this method is based on the assumption that the random variable is dispersed symmetrically about the mean and is essentially limited to normally distributed random variables. Use of this method can therefore result in unsafe or overly conservative design allowables if the common assumption of normality is incorrect.

Holland, Frederic A., Jr.↗

NASA NTRS2018

Investigation of Multi-Input, Multi-Output (MIMO) Random Control Applied to Direct Field Acoustic Testing

Direct Field Acoustic Testing (DFAT) offers potential cost and time savings over reverberant chamber acoustic testing of spacecraft. The NASA Multi-Purpose Crew Vehicle (MPCV) Program recently directed a series of acoustic tests on Orion structural test articles comparing DFAT and reverberant testing of the same test article with a view to qualifying DFAT for manned space flight vehicles. The verification process compared four parameters noise level compliance with the one third octave test specification, spatial uniformity of the acoustic field, spatial correlation of the acoustic field and vibration response of vehicle structure, including representative solar array panels. While the results of the verification were encouraging, MPCV Loads and Dynamics engaged Quartus Engineering to investigate whether alternative MIMO random control strategies might improve the spatial uniformity and/or the spatial correlation of the DFAT acoustic field. This paper presents the results of acoustic field simulations of the DFAT test and provides a better understanding of how MIMO random control systems originally developed for vibration and structural durability testing can be expected to perform in DFAT testing.

Direct Field↗

NASA NTRS1989

Probabilistic modeling for simulation of aerodynamic uncertainties in propulsion systems

The numerical simulation of the probabilistic aerothermodynamic response of propulsion system components to randomness in their environment was explored. The reusable rocket engine turbopumps were selected as an example because of the severe cryogenic environment in which they operate. The thermal and combustion instabilities, coupled with the engine thrust requirements from start up to shut down, lead to randomness in the flow variables and uncertainties in the aerodynamic loading. The probabilistic modeling of the turbopumps aerodynamic response was accomplished using the panel method coupled with fast probability integration methods. The aerodynamic response in the form of probabilistic rotor blades and splitter loading were predicted and the results presented for specified flow coefficient and rotor preswirl variance. Possible future applications of the aerothermodynamic probabilistic modeling in engine transient simulation, condition monitoring and engine life prediction are briefly discussed.

Hamed, Awatef↗

NASA NTRS1990

Probabilistic modeling for simulation of aerodynamic uncertainties in propulsion systems

The numerical simulation of the probabilistic aerothermodynamic response of propulsion system components to randomness in their environment was explored. The reusable rocket engine turbopumps were selected as an example because of the severe cryogenic environment in which they operate. The thermal and combustion instabilities, coupled with the engine thrust requirements from start up to shut down, lead to randomness in the flow variables and uncertainties in the aerosynamic loading. The probabilistic modeling of the turbopumps' aerodynamic response was accomplished using the panel method coupled with fast probability integration methods. The aerodynamic response in the form of probabilistic rotor blades and splitter loading were predicted and the results presented for specified flow coefficient and rotor preswirl variance. Possible future applications of the aerothermodynamic probabilistic modeling in engine transient simulation, condition monitoring, and engine life prediction are briefly discussed.

Hamed, A.↗

NASA NTRS1996

Combining Acceleration and Displacement Dependent Modal Frequency Responses Using an MSC/NASTRAN DMAP Alter

Solving for dynamic responses of free-free launch vehicle/spacecraft systems acted upon by buffeting winds is commonly performed throughout the aerospace industry. Due to the unpredictable nature of this wind loading event, these problems are typically solved using frequency response random analysis techniques. To generate dynamic responses for spacecraft with statically-indeterminate interfaces, spacecraft contractors prefer to develop models which have response transformation matrices developed for mode acceleration data recovery. This method transforms spacecraft boundary accelerations and displacements into internal responses. Unfortunately, standard MSC/NASTRAN modal frequency response solution sequences cannot be used to combine acceleration- and displacement-dependent responses required for spacecraft mode acceleration data recovery. External user-written computer codes can be used with MSC/NASTRAN output to perform such combinations, but these methods can be labor and computer resource intensive. Taking advantage of the analytical and computer resource efficiencies inherent within MS C/NASTRAN, a DMAP Alter has been developed to combine acceleration- and displacement-dependent modal frequency responses for performing spacecraft mode acceleration data recovery. The Alter has been used successfully to efficiently solve a common aerospace buffeting wind analysis.

Barnett, Alan R.↗

NASA NTRS1999

Vibration and Acoustic Testing for Mars Micromission Spacecraft

The objective of the Mars Micromission program being managed by the Jet Propulsion Laboratory (JPL) for NASA is to develop a common spacecraft that can carry telecommunications equipment and a variety of science payloads for exploration of Mars. The spacecraft will be capable of carrying robot landers and rovers, cameras, probes, balloons, gliders or aircraft, and telecommunications equipment to Mars at much lower cost than recent NASA Mars missions. The lightweight spacecraft (about 220 Kg mass) will be launched in a cooperative venture with CNES as a TWIN auxiliary payload on the Ariane 5 launch vehicle. Two or more Mars Micromission launches are planned for each Mars launch opportunity, which occur every 26 months. The Mars launch window for the first mission is November 1, 2002 through April 2003, which is planned to be a Mars airplane technology demonstration mission to coincide with the 100 year anniversary of the Kittyhawk flight. Several subsequent launches will create a telecommunications network orbiting Mars, which will provide for continuous communication with lenders and rovers on the Martian surface. Dedicated science payload flights to Mars are slated to start in 2005. This new cheaper and faster approach to Mars exploration calls for innovative approaches to the qualification of the Mars Micromission spacecraft for the Ariane 5 launch vibration and acoustic environments. JPL has in recent years implemented new approaches to spacecraft testing that may be effectively applied to the Mars Micromission. These include 1) force limited vibration testing, 2) combined loads, vibration and modal testing, and 3) direct acoustic testing. JPL has performed nearly 200 force limited vibration tests in the past 9 years; several of the tests were on spacecraft and large instruments, including the Cassini and Deep Space One spacecraft. Force limiting, which measures and limits the spacecraft base reaction force using triaxial force gages sandwiched between the spacecraft and the test fixture, alleviates the severe overtest at spacecraft resonances inherent in rigid fixture vibration tests. It has the distinct advantage over response limiting that the method is not dependent on the accuracy of a detailed dynamic model of the spacecraft. Combined loads, vibration, and modal testing were recently performed on the QuikSCAT spacecraft. The combined tests were performed in a single test setup per axis on a vibration shaker, reducing test time by a factor of two or three. Force gages were employed to measure the true c.g. acceleration of the spacecraft for structural loads verification using a sine burst test, to automatically notch random vibration test input accelerations at spacecraft resonances based on predetermined force limits, and to directly measure modal masses in a base drive modal test. In addition to these combined tests on the shaker, the QuikSCAT spacecraft was subjected to a direct field acoustic test by surrounding the spacecraft, still on the vibration shaker, with rock concert type acoustic speakers. Since the spacecraft contractor does not have a reverberant field acoustic test facility, performing a direct field acoustic test -saved the program nearly two weeks schedule time that would have been required for packing / unpacking and shipping of the spacecraft. This paper discusses the rationale behind and advantages of the above test approaches and provides examples of their actual implementation and comparisons to flight data. The applicability of the test approaches to Mars Micromission spacecraft qualification is discussed.

Kern, Dennis L.↗

NASA NTRS1993

The application of structural reliability techniques to plume impingement loading of the Space Station Freedom Photovoltaic Array

A new aerospace application of structural reliability techniques is presented, where the applied forces depend on many probabilistic variables. This application is the plume impingement loading of the Space Station Freedom Photovoltaic Arrays. When the space shuttle berths with Space Station Freedom it must brake and maneuver towards the berthing point using its primary jets. The jet exhaust, or plume, may cause high loads on the photovoltaic arrays. The many parameters governing this problem are highly uncertain and random. An approach, using techniques from structural reliability, as opposed to the accepted deterministic methods, is presented which assesses the probability of failure of the array mast due to plume impingement loading. A Monte Carlo simulation of the berthing approach is used to determine the probability distribution of the loading. A probability distribution is also determined for the strength of the array. Structural reliability techniques are then used to assess the array mast design. These techniques are found to be superior to the standard deterministic dynamic transient analysis, for this class of problem. The results show that the probability of failure of the current array mast design, during its 15 year life, is minute.

Yunis, Isam S.↗

NASA NTRS1993

The Application of Structural Reliability Techniques to Plume Impingement Loading of the Space Station Freedom Photovoltaic Array

Yunis, Isam S.↗

NASA NTRS2012

New Approaches in Force-Limited Vibration Testing of Flight Hardware

To qualify flight hardware for random vibration environments the following methods are used to limit the loads in the aerospace industry: (1) Response limiting and notching (2) Simple TDOF model (3) Semi-empirical force limits (4) Apparent mass, etc. and (5) Impedance method. In all these methods attempts are made to remove conservatism due to the mismatch in impedances between the test and the flight configurations of the hardware that are being qualified. Assumption is the hardware interfaces have correlated responses. A new method that takes into account the un-correlated hardware interface responses are described in this presentation.

Random Vibration↗

NASA NTRS1973

Nonlinear response of boron/aluminum angleplied laminates under cyclic tensile loading: Contributing mechanisms and their effects

The nonlinear response of boron/aluminum angleplied laminates subjected to cyclic loads was investigated. A procedure is outlined and criteria are proposed which can be used to assess the nonlinear response. The procedure consists of testing strategically selected laminate configurations and analyzing the results using composite mechanics. Results from the investigation show the contributions to nonlinear behavior are from: premature random fiber breaks where the ply orientation angle is small relative to the load direction, ply relative rotation at intermediate values of the ply orientation angle, and nonlinear aluminum matrix behavior at large values of the orientation angle. Premature fiber breaks result in progressively more compliant material; large ply relative rotations result in progressively stiffer material; and pronounced matrix nonlinear behavior results in no significant change in the stiffness of the initial load portion.

Chamis, C. C.↗