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The Influence of Mesh Density on the Impact Response of a Shuttle Leading-Edge Panel Finite Element Simulation

A study was performed to examine the influence of varying mesh density on an LS-DYNA simulation of a rectangular-shaped foam projectile impacting the space shuttle leading edge Panel 6. The shuttle leading-edge panels are fabricated of reinforced carbon-carbon (RCC) material. During the study, nine cases were executed with all possible combinations of coarse, baseline, and fine meshes of the foam and panel. For each simulation, the same material properties and impact conditions were specified and only the mesh density was varied. In the baseline model, the shell elements representing the RCC panel are approximately 0.2-in. on edge, whereas the foam elements are about 0.5-in. on edge. The element nominal edge-length for the baseline panel was halved to create a fine panel (0.1-in. edge length) mesh and doubled to create a coarse panel (0.4-in. edge length) mesh. In addition, the element nominal edge-length of the baseline foam projectile was halved (0.25-in. edge length) to create a fine foam mesh and doubled (1.0- in. edge length) to create a coarse foam mesh. The initial impact velocity of the foam was 775 ft/s. The simulations were executed in LS-DYNA version 960 for 6 ms of simulation time. Contour plots of resultant panel displacement and effective stress in the foam were compared at five discrete time intervals. Also, time-history responses of internal and kinetic energy of the panel, kinetic and hourglass energy of the foam, and resultant contact force were plotted to determine the influence of mesh density. As a final comparison, the model with a fine panel and fine foam mesh was executed with slightly different material properties for the RCC. For this model, the average degraded properties of the RCC were replaced with the maximum degraded properties. Similar comparisons of panel and foam responses were made for the average and maximum degraded models.

Jackson, Karen E.↗

The RBE-LET relationship for rodent intestinal crypt cell survival, testes weight loss, and multicellular spheroid cell survival after heavy-ion irradiation

This report presents data for survival of mouse intestinal crypt cells, mouse testes weight loss as an indicator of survival of spermatogonial stem cells, and survival of rat 9L spheroid cells after irradiation in the plateau region of unmodified particle beams ranging in mass from 4He to 139La. The LET values range from 1.6 to 953 keV/microns. These studies examine the RBE-LET relationship for two normal tissues and for an in vitro tissue model, multicellular spheroids. When the RBE values are plotted as a function of LET, the resulting curve is characterized by a region in which RBE increases with LET, a peak RBE at an LET value of 100 keV/microns, and a region of decreasing RBE at LETs greater than 100 keV/microns. Inactivation cross sections (sigma) for these three biological systems have been calculated from the exponential terminal slope of the dose-response relationship for each ion. For this determination the dose is expressed as particle fluence and the parameter sigma indicates effect per particle. A plot of sigma versus LET shows that the curve for testes weight loss is shifted to the left, indicating greater radiosensitivity at lower LETs than for crypt cell and spheroid cell survival. The curves for cross section versus LET for all three model systems show similar characteristics with a relatively linear portion below 100 keV/microns and a region of lessened slope in the LET range above 100 keV/microns for testes and spheroids. The data indicate that the effectiveness per particle increases as a function of LET and, to a limited extent, Z, at LET values greater than 100 keV/microns. Previously published results for spread Bragg peaks are also summarized, and they suggest that RBE is dependent on both the LET and the Z of the particle.

Non-NASA Center↗

Neutron Diffraction Studies of the Atomic Vibrations of Bulk and Surface Atoms of Nanocrystalline SiC

Thermal atomic motions of nanocrystalline Sic were characterized by two temperature atomic factors B(sub core), and B(sub shell). With the use of wide angle neutron diffraction data it was shown that at the diffraction vector above 15A(exp -1) the Wilson plots gives directly the temperature factor of the grain interior (B(sub core)). At lower Q values the slope of the Wilson plot provides information on the relative amplitudes of vibrations of the core and shell atoms.

Stelmakh, S.↗

Analysis of Buoyancy Effects in Helium Jets Using High-Speed Rainbow Schlieren Deflectometry

The flow phenomena of buoyant jets have been analyzed by many researchers in recent years. Few, however have studied jets in microgravity conditions, and the exact nature of the flow under these conditions has until recently been unknown. This study seeks to extend the work done by researchers at the university of Oklahoma in examining and documenting the behavior of helium jets in micro-gravity conditions. Quantitative rainbow schlieren deflectometry data have been obtained for helium jets discharging vertically into quiescent ambient air from tubes of several diameters at various flow rates using a high-speed digital camera. These data have obtained before, during and after the onset of microgravity conditions. High-speed rainbow schlieren deflectometry has been developed for this study with the installation and use of a high-speed digital camera and modifications to the optical setup. Higher temporal resolution of the transitional phase between terrestrial and micro-gravity conditions has been obtained which has reduced the averaging effect of longer exposure times used in all previous schlieren studies. Results include color schlieren images, color time-space images (temporal evolution images), frequency analyses, contour plots of hue and contour plots of helium mole fraction. The results, which focus primarily on the periods before and during the onset of microgravity conditions, show that the pulsation of the jets normally found in terrestrial gravity ("earth"-gravity) conditions cease, and the gradients in helium diminish to produce a widening of the jet in micro-gravity conditions. In addition, the results show that the disturbance propagate upstream from a downstream source.

Leptuch, Peter A.↗

Full Field Scalar Measurements in a Pulsating Helium Jet using Rainbow Schlieren Deflectometry

The flow structure of a pulsating helium jet was investigated using quantitative rainbow schlieren deflectometry. The operating parameters included the tube inside diameter, the jet Reynolds number and the jet Richardson number. The jet structure was characterized by the frequency spectrum, temporal evolution of the oscillations and mean and root-mean-square profiles of the species mole fraction, which in this case, was helium. Experiments were conducted using a variable nozzle facility. Angular deflection data were obtained using rainbow schlieren deflectometry across full field of color images taken at a temporal resolution of 60Hz. The flicker cycle was analyzed by instantaneous rainbow schlieren images, contour plots of deflection angle and helium mole fraction placed sequentially in time. Two observe the flow downstream, the tube was lowered with respect to the optical setup and images were taken at different axial planes. In this way, the laminar, transition and turbulent regions of the jet flow were observed. Abel inversion algorithm was utilized to reconstruct the refractive index field from the measurements of the beam deflection angle. The concentration field was then generated from the refractive index field. The phenomenon of vortex initiation and propagation in the flicker cycle was described by correlating the ray deflection angle and concentration contour plots. Experiments in the flickering jet reveal global oscillation in the flow field. The effect of jet exit Reynolds number and jet Richardson number on the flickering frequency was analyzed. The effect of jet Richardson number was more pronounced than that of the jet exit Reynolds number. The flow field was studies quantitatively in terms of temporal evolution and statistical description of helium mole fraction.

Pasumarthi, Kasyap S.↗

Characterizing Oscillatory Bursts in Single-Trial EEG Data

Oscillatory bursts in numerous bands ranging from low (theta) to high frequencies (e.g., gamma) undoubtedly play an important role in cortical dynamics. Largely because of the inadequacy of existing analytic techniques. however, oscillatory bursts and their role in cortical processing remains poorly understood. To study oscillatory bursts effectively one must be able to isolate them and characterize them in the single trial. We describe a series of straightforward analysis techniques that produce useful indices of burst characteristics. First, stimulus-evoked responses are estimated using Differentially Variable Component Analysis (dVCA), and are subtracted from the single-trial. The single-trial characteristics of the evoked responses are stored to identify possible correlations with burst activity. Time-frequency (T-F), or wavelet, analyses are then applied to the single trial residuals. While T-F plots have been used in recent studies to identify and isolate bursts, we go further by fitting each burst in the T-F plot with a two-dimensional Gaussian. This provides a set of burst characteristics, such as, center time. burst duration, center frequency. frequency dispersion. and amplitude, all of which contribute to the accurate characterization of the individual burst. The burst phase can also be estimated. Burst characteristics can be quantified with several standard techniques (e.g.. histogramming and clustering), as well as Bayesian techniques (e.g., blocking) to allow a more parametric description analysis of the characteristics of oscillatory bursts, and the relationships of specific parameters to cortical excitability and stimulus integration.

Knuth, K. H.↗

Aerodynamics of an Axisymmetric Missile Concept Having Cruciform Strakes and In-Line Tail Fins From Mach 0.60 to 4.63

An experimental study has been performed to develop a large force and moment aerodynamic data set on a slender axisymmetric missile configuration having cruciform strakes and in-line control tail fins. The data include six-component balance measurements of the configuration aerodynamics and three-component measurements on all four tail fins. The test variables include angle of attack, roll angle, Mach number, model buildup, strake length, nose size, and tail fin deflection angles to provide pitch, yaw, and roll control. Test Mach numbers ranged from 0.60 to 4.63. The entire data set is presented on a CD-ROM that is attached to this paper. The CD-ROM also includes extensive plots of both the six-component configuration data and the three-component tail fin data. Selected samples of these plots are presented in this paper to illustrate the features of the data and to investigate the effects of the test variables.

Jerry M Allen↗

The Influence of Clocking Angle of the Projectile on the Simulated Impact Response of a Shuttle Leading Edge Wing Panel

An analytical study was conducted to determine the influence of clocking angle of a foam projectile impacting a space shuttle leading edge wing panel. Four simulations were performed using LS-DYNA. The leading edge panels are fabricated of multiple layers of reinforced carbon-carbon (RCC) material. The RCC material was represented using Mat 58, which is a material property that can be used for laminated composite fabrics. Simulations were performed of a rectangular-shaped foam block, weighing 0.23-lb., impacting RCC Panel 9 on the top surface. The material properties of the foam were input using Mat 83. The impact velocity was 1,000 ft/s along the Orbiter X-axis. In two models, the foam impacted on a corner, in one model the foam impacted the panel initially on the 2-in.-long edge, and in the last model the foam impacted the panel on the 7-in.- long edge. The simulation results are presented as contour plots of first principal infinitesimal strain and time history plots of contact force and internal and kinetic energy of the foam and RCC panel.

Jackson, Karen E.↗

Aerodynamics of an Axisymmetric Missile Concept Having Cruciform Strakes and In-Line Tail Fins From Mach 0.60 to 4.63, Supplement

An experimental study has been performed to develop a large force and moment aerodynamic data set on a slender axisymmetric missile configuration having cruciform strakes and in-line control tail fins. The data include six-component balance measurements of the configuration aerodynamics and three-component measurements on all four tail fins. The test variables include angle of attack, roll angle, Mach number, model buildup, strake length, nose size, and tail fin deflection angles to provide pitch, yaw, and roll control. Test Mach numbers ranged from 0.60 to 4.63. The entire data set is presented on a CD-ROM that is attached to this paper. The CD-ROM also includes extensive plots of both the six-component configuration data and the three-component tail fin data. Selected samples of these plots are presented in this paper to illustrate the features of the data and to investigate the effects of the test variables.

Jerry M Allen↗

Apparent I-Xe Cooling Rates of Chondrules Compared with Silicates from the Colomera Iron Meteorite

In I-Xe dating, a regular pattern of increasing Xe-129/128Xe-128 ratio with increasing extraction temperature is often observed. If one makes the crude assumption that the temperatures at which the Xe is extracted in the laboratory is approximately the same as the temperature at which those sites closed 4.6 Ga ago, a (zeroth order) model cooling rate can be found. In order to test and refine this model we can apply the cooling theory of Dodson to those extraction steps approaching the I-Xe isochrons. Using an Arrhenius plot for these temperature fractions, and assuming that an only single phase is involved, the effective diffusion parameters can be estimated (frequency factor and activation energy). From the apparent (zeroth order) cooling rate, the closure temperature can be estimated from the Dodson equation. This model closure temperature can then be compared with the actual laboratory temperature at which the isochron begins. The ratio of the closure temperature and the temperature corresponding to the start of the isochron provides the ratio of the two temperature scales, incorporation and extraction. The actual cooling rate is then given by the apparent (zeroth order) cooling rate times the temperature scale factor. Figure 1 shows Arrhenius plots for I-Xe data

Hohenberg, C. M.↗

Rotordynamics on the PC: Transient Analysis With ARDS

Personal computers can now do many jobs that formerly required a large mainframe computer. An example is NASA Lewis Research Center's program Analysis of RotorDynamic Systems (ARDS), which uses the component mode synthesis method to analyze the dynamic motion of up to five rotating shafts. As originally written in the early 1980's, this program was considered large for the mainframe computers of the time. ARDS, which was written in Fortran 77, has been successfully ported to a 486 personal computer. Plots appear on the computer monitor via calls programmed for the original CALCOMP plotter; plots can also be output on a standard laser printer. The executable code, which uses the full array sizes of the mainframe version, easily fits on a high-density floppy disk. The program runs under DOS with an extended memory manager. In addition to transient analysis of blade loss, step turns, and base acceleration, with simulation of squeeze-film dampers and rubs, ARDS calculates natural frequencies and unbalance response.

Fleming, David P.↗

Jet Noise Reduction

The Acoustics Branch is responsible for reducing noise levels for jet and fan components on aircraft engines. To do this, data must be measured and calibrated accurately to ensure validity of test results. This noise reduction is accomplished by modifications to hardware such as jet nozzles, and by the use of other experimental hardware such as fluidic chevrons, elliptic cores, and fluidic shields. To insure validity of data calibration, a variety of software is used. This software adjusts the sound amplitude and frequency to be consistent with data taken on another day. Both the software and the hardware help make noise reduction possible. work properly. These software programs were designed to make corrections for atmosphere, shear, attenuation, electronic, and background noise. All data can be converted to a one-foot lossless condition, using the proper software corrections, making a reading independent of weather and distance. Also, data can be transformed from model scale to full scale for noise predictions of a real flight. Other programs included calculations of Over All Sound Pressure Level (OASPL), Effective Perceived Noise Level (EPNL). OASPL is the integration of sound with respect to frequency, and EPNL is weighted for a human s response to different sound frequencies and integrated with respect to time. With the proper software correction, data taken in the NATR are useful in determining ways to reduce noise. display any difference between two or more data files. Using this program and graphs of the data, the actual and predicted data can be compared. This software was tested on data collected at the Aero Acoustic Propulsion Laboratory (AAPL) using a variety of window types and overlaps. Similarly, short scripts were written to test each individual program in the software suite for verification. Each graph displays both the original points and the adjusted points connected with lines. During this summer, data points were taken during a live experiment at the AAPL to measure Nozzle Acoustic Test Rig (NATR) background noise levels. Six condenser microphones were placed in strategic locations around the dome and the inlet tunnel to measure different noise sources. From the control room the jet was monitored with the help of video cameras and other sensors. The data points were recorded, reduced, and plotted, and will be used to plan future modifications to the NATR. The primary goal to create data reduction test programs and provide verification was completed. As a result of the internship, I learned C/C++, UNIX/LINUX, Excel, and acoustic data processing methods. I also recorded data at the AAPL, then processed and plotted it. These data would be useful to compare against existing data. In addition, I adjusted software to work on the Mac OSX platform. And I used the available training resources.

Kenny, Patrick↗

Combustion Instabilities Modeled

NASA Lewis Research Center's Advanced Controls and Dynamics Technology Branch is investigating active control strategies to mitigate or eliminate the combustion instabilities prevalent in lean-burning, low-emission combustors. These instabilities result from coupling between the heat-release mechanisms of the burning process and the acoustic flow field of the combustor. Control design and implementation require a simulation capability that is both fast and accurate. It must capture the essential physics of the system, yet be as simple as possible. A quasi-one-dimensional, computational fluid dynamics (CFD) based simulation has been developed which may meet these requirements. The Euler equations of mass, momentum, and energy have been used, along with a single reactive species transport equation to simulate coupled thermoacoustic oscillations. A very simple numerical integration scheme was chosen to reduce computing time. Robust boundary condition procedures were incorporated to simulate various flow conditions (e.g., valves, open ends, and choked inflow) as well as to accommodate flow reversals that may arise during large flow-field oscillations. The accompanying figure shows a sample simulation result. A combustor with an open inlet, a choked outlet, and a large constriction approximately two thirds of the way down the length is shown. The middle plot shows normalized, time-averaged distributions of the relevant flow quantities, and the bottom plot illustrates the acoustic mode shape of the resulting thermoacoustic oscillation. For this simulation, the limit cycle peak-to-peak pressure fluctuations were 13 percent of the mean. The simulation used 100 numerical cells. The total normalized simulation time was 50 units (approximately 15 oscillations), which took 26 sec on a Sun Ultra2.

Paxson, Daniel E.↗

Measurement and evaluation of the radiative properties of a thin solid fuel

Accurate modeling of combustion systems requires knowledge of the radiative properties of the system. Gas phase properties are well known, but detailed knowledge of surface properties is limited. Recent work has provided spectrally resolved data for some solid fuels, but only for the unburned material at room temperature, and for limited sets of previously burned and quenched samples. Due to lack of knowledge of the spectrally resolved properties at elevated temperatures, as well as processing limitations in the modeling effort, graybody values are typically used for the fuels surface radiative properties. However, the spectrally resolved properties for the fuels at room temperature can be used to give a first-order correction for temperature effects on the graybody values. Figure 1 shows a sample of the spectrally resolved emittance/absorptance for a thin solid fuel of the type commonly used in combustion studies, from approximately 2 to 20 microns. This plot clearly shows a strong spectral dependence across the entire range. By definition, the emittance is the ratio of the emitted energy to that of a blackbody at the same temperature. Therefore, to determine a graybody emittance for this material, the spectrally resolved data must be applied to a blackbody curve. The total area under the resulting curve is ratioed to the total area under the blackbody curve to yield the answer. Due to the asymmetry of the spectrally resolved emittance and the changing shape of the blackbody curve as the temperature increases, the relative importance of the emittance value at any given wavelength will change as a function of temperature. Therefore, the graybody emittance value for a given material will change as a function of temperature even if the spectral dependence of the radiative properties remains unchanged. This is demonstrated in Figures 2 and 3, which are plots of the spectrally resolved emittance for KimWipes (shown in Figure 1) multiplied by the blackbody curves for 300 K (Figure 2) and 800 K (Figure 3). Each figure also shows the blackbody curve for that temperature. Ratioing the areas under the curve for each of these figures give a graybody emittance of 0.64 at 300 K, and 0.46 at 800 K. It is recognized that materials undergoing pyrolysis will change in composition as they heat up, and that the radiative properties of the materials may have inherent temperature dependence. Both of these effects will contribute to changes in the radiative characteristics of a given material, and are not accounted for here. However, this paper demonstrates the temperature dependence of graybody radiative properties, and provides a method for a first-order correction (for temperature) to the graybody values if the spectrally resolved properties are known.

Pettegrew, Richard↗

Java-based Graphical User Interface for MAVERIC-II

A computer program entitled "Marshall Aerospace Vehicle Representation in C II, (MAVERIC-II)" is a vehicle flight simulation program written primarily in the C programming language. It is written by James W. McCarter at NASA/Marshall Space Flight Center. The goal of the MAVERIC-II development effort is to provide a simulation tool that facilitates the rapid development of high-fidelity flight simulations for launch, orbital, and reentry vehicles of any user-defined configuration for all phases of flight. MAVERIC-II has been found invaluable in performing flight simulations for various Space Transportation Systems. The flexibility provided by MAVERIC-II has allowed several different launch vehicles, including the Saturn V, a Space Launch Initiative Two-Stage-to-Orbit concept and a Shuttle-derived launch vehicle, to be simulated during ascent and portions of on-orbit flight in an extremely efficient manner. It was found that MAVERIC-II provided the high fidelity vehicle and flight environment models as well as the program modularity to allow efficient integration, modification and testing of advanced guidance and control algorithms. In addition to serving as an analysis tool for techno logy development, many researchers have found MAVERIC-II to be an efficient, powerful analysis tool that evaluates guidance, navigation, and control designs, vehicle robustness, and requirements. MAVERIC-II is currently designed to execute in a UNIX environment. The input to the program is composed of three segments: 1) the vehicle models such as propulsion, aerodynamics, and guidance, navigation, and control 2) the environment models such as atmosphere and gravity, and 3) a simulation framework which is responsible for executing the vehicle and environment models and propagating the vehicle s states forward in time and handling user input/output. MAVERIC users prepare data files for the above models and run the simulation program. They can see the output on screen and/or store in files and examine the output data later. Users can also view the output stored in output files by calling a plotting program such as gnuplot. A typical scenario of the use of MAVERIC consists of three-steps; editing existing input data files, running MAVERIC, and plotting output results.

Seo, Suk Jai↗

Giovanni: A System for Rapid Access, Visualization and Analysis of Earth Science Data Online

Collecting data and understanding data structures traditionally are the first steps that a user must take, before the core investigation can begin. This is a time-consuming and challenging task, especially when science objectives require users to deal with large multi-sensor data that are usually in different formats and internal structures. The Goddard Earth Sciences Data and Information Services Center (GES DISC) has created the GES DISC Interactive Online Visualization and ANalysis Infrastructure, Giovanni, to enable Web-based visualization and analysis of satellite remotely sensed meteorological, oceanographic, and hydrologic data sets, without users having to download data. The current operational Giovanni interfaces provide the capability to process a number of important satellite measurements, such as (1) ozone and other trace gases from TOMS, OMI, HALOE, and MLS; (2) air temperature, water vapor, and geopotential height from AIRS; (3) aerosols from MODIS TerrdAqua, and GOCART model; (4) precipitation from TRMM and ground measurements; (5) chlorophyll and other ocean color products from SeaWiFS and MODIS Aqua; and (6) sea surface temperature from MODIS Aqua. Depending on the input data structure, the system provides simple statistical analysis and creates time-averaged area plot, area-averaged time series, animations, Hovmoller latitude vs. time and longitude vs. time plots, as well as vertical profiles. The inter-comparison interfaces allow a user to compare observations from different instruments, to conduct anomaly analysis, and to study basic relationships between physical parameters. Giovanni handles data with different temporal and spatial resolutions and, thus, enables both regional and global long-term climate research and short-term special events investigation, as well as data validations and assessments. Because of its simplicity of usage, Giovanni is powerful and versatile, able to assist a wide range of users, from the discipline scientists conducting preliminary research in various fields, to students in the classroom learning about weather, climate, and other natural phenomena. Giovanni can be accessed from: http://disc. esfc.nasa.gov/techlab/giovanni/index.shtml

Shen, S.↗

What Happens to bone health during and after spaceflight?

Weightless conditions of space flight accelerate bone loss. There are no reports to date that address whether the bone that is lost during spaceflight could ever be recovered. Spaceinduced bone loss in astronauts is evaluated at the Johnson Space Center (JSC) by measurement of bone mineral density (BMD) by Dual-energy x-ray absorptiometry (DXA) scans. Astronauts are routinely scanned preflight and at various time points postflight (greater than or equal to Return+2 days). Two sets of BMD data were used to model spaceflight-induced loss and skeletal recovery in crewmembers following long-duration spaceflight missions (4-6 months). Group I was from astronauts (n=7) who were systematically scanned at multiple time points during the postflight period as part of a research protocol to investigate skeletal recovery. Group II came from a total of 49 sets of preflight and postflight data obtained by different protocols. These data were from 39 different crewmembers some of whom served on multiple flights. Changes in BMD (between pre- and postflight BMD) were plotted as a function of time (days-after-landing); plotted data were fitted to an exponential equation which enabled estimations of i) BMD change at day 0 after landing and ii) the number of days by which 50% of the lost bone is recovered (half-life). These fits were performed for BMD of the lumbar spine, trochanter, pelvis, femoral neck and calcaneus. There was consistency between the models for BMD recovery. Based upon the exponential model of BMD restoration, recovery following long-duration missions appears to be substantially complete in crewmembers within 36 months following return to Earth.

Sibonga, Jean D.↗

A Mesh Refinement Study on the Impact Response of a Shuttle Leading-Edge Panel Finite Element Simulation

A study was performed to examine the influence of varying mesh density on an LS-DYNA simulation of a rectangular-shaped foam projectile impacting the space shuttle leading edge Panel 6. The shuttle leading-edge panels are fabricated of reinforced carbon-carbon (RCC) material. During the study, nine cases were executed with all possible combinations of coarse, baseline, and fine meshes of the foam and panel. For each simulation, the same material properties and impact conditions were specified and only the mesh density was varied. In the baseline model, the shell elements representing the RCC panel are approximately 0.2-in. on edge, whereas the foam elements are about 0.5-in. on edge. The element nominal edge-length for the baseline panel was halved to create a fine panel (0.1-in. edge length) mesh and doubled to create a coarse panel (0.4-in. edge length) mesh. In addition, the element nominal edge-length of the baseline foam projectile was halved (0.25-in. edge length) to create a fine foam mesh and doubled (1.0-in. edge length) to create a coarse foam mesh. The initial impact velocity of the foam was 775 ft/s. The simulations were executed in LS-DYNA for 6 ms of simulation time. Contour plots of resultant panel displacement and effective stress in the foam were compared at four discrete time intervals. Also, time-history responses of internal and kinetic energy of the panel, kinetic and hourglass energy of the foam, and resultant contact force were plotted to determine the influence of mesh density.

Fasanella, Edwin L.↗

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