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At least 199 records · Page 11

Predictor-corrector procedures for thermal buckling analysis of multilayered composite plates

A study is made of two predictor-corrector procedures for the accurate determination of global, as well as detailed, thermal buckling response characteristics of composite plates. Both procedures use first-order shear deformation theory in the predictor phase, but differ in the elements of the computational model being adjusted in the corrector phase. The first procedure calculates a posteriori estimates of the composite correction factors and uses them to adjust the transverse shear stiffnesses of the plate. The second procedure calculates a posteriori the functional dependence of the displacement components on the thickness coordinate. The corrected quantities are then used in conjunction with three-dimensional equations to obtain better estimates for the different response quantities. Extensive numerical results are presented, showing the effects of variation in the geometric and lamination parameters for antisymmetrically laminated composite plates subjected to uniform temperature rise, on the accuracy of the thermal buckling response obtained by predictor-corrector procedures.

Noor, A. K.↗

Trajectories of ballistic impact ejecta on a rotating Earth

On an airless, slowly rotating planetary body like the Moon, ejecta particles from an impact follow simple ballistic trajectories. If gaseous interactions in the fireball are ignored, ejecta particles follow elliptical orbits with the center of the planetary body at one focus until they encounter the surface at the point of reimpact. The partial elliptical orbit of the ejecta particle lies in a plane in inertial (galactic) coordinates. Because of the slow rotation rate (for example, 360 degrees/28 days for the Moon), the intersection of the orbital plane and the surface remains nearly a great circle during the flight time of the ejecta. For this reason, lunar rays, representing concentrations of ejecta with the same azimuth but different velocities and/or ejecta angles, lie essentially along great circles. Ejecta from airless but more rapidly rotating bodies will follow more complicated, curving trajectories when plotted in the coordinate frame of the rotating planet or viewed as rays on the planetary surface. The curvature of trajectories of ejecta particles can be treated as a manifestation of the Coriolis effect, with the particles being accelerated by Coriolis pseudoforces. However, it is more straightforward to calculate the elliptical orbit in inertial space and then determine how far the planet rotates beneath the orbiting ejecta particle before reimpact. The Earth's eastward rotation affects ballistic ejecta in two ways: (1) the eastward velocity component increases the velocity of eastbound ejecta and reduces the velocity of westbound ejecta; and (2) the Earth turns underneath inflight ejecta, so that although the latitude of reimpact is not changed, the longitude is displaced westward, with the displacement increasing as a function of the time the ejecta remains aloft.

Alvarez, W.↗

Effects of Restricted Launch Conditions for the Enhancement of Bandwidth-Distance Product of Multimode Fiber Links

Several techniques had been proposed to enhance multimode fiber bandwidth-distance product. Single mode-to-multimode offset launch condition technique had been experimented with at Kennedy Space Center. Significant enhancement in multimode fiber link bandwidth is achieved using this technique. It is found that close to three-fold bandwidth enhancement can be achieved compared to standard zero offset launch technique. Moreover, significant reduction in modal noise has been observed as a function of offset launch displacement. However, significant reduction in the overall signal-to-noise ratio is also observed due to signal attenuation due to mode radiation from fiber core to its cladding.

Andrawis, Alfred S.↗

High-Power Magnetoplasmadynamic Thruster Being Developed

High-power electromagnetic thrusters have been proposed as primary in-space propulsion options for several of the bold new interplanetary and deep space missions envisioned by the Human Exploration and Development of Space (HEDS) Strategic Enterprise. As the lead center for electric propulsion, the NASA Glenn Research Center is actively involved in the design, development, and testing of high-power electromagnetic technologies to meet these demanding mission requirements. One concept of particular interest is the magnetoplasmadynamic (MPD) thruster, shown schematically in the preceding figure. In its basic form, the MPD thruster consists of a central cathode surrounded by a concentric cylindrical anode. A high-current arc is struck between the anode and cathode, which ionizes and accelerates a gas (plasma) propellant. In the self-field version of the thruster, an azimuthal magnetic field generated by the current returning through the cathode interacts with the radial discharge current flowing through the plasma to produce an axial electromagnetic body force, providing thrust. In applied field-versions of the thruster, a magnetic field coil surrounding the anode is used to provide additional radial and axial magnetic fields that can help stabilize and accelerate the plasma propellant. The following figure shows an experimental megawatt-class MPD thruster developed at Glenn. The MPD thruster is fitted inside a magnetic field coil, which in turn is mounted on a thrust stand supported by thin metal flexures. A calibrated position transducer is used to determine the force provided by the thruster as a function of thrust stand displacement. Power to the thruster is supplied by a 250-kJ capacitor bank, which provides up to 30- MW to the thruster for a period of 2 msec. This short period of time is sufficient to establish thruster performance similar to steady-state operation, and it allows a number of thruster designs to be quickly and economically evaluated. In concert with this experimental research, Glenn is also developing and using advanced numerical simulations to predict the performance of self-field and applied-field MPD thrusters.

LaPointe, Michael R.↗

Symmetry-Based Structured Matrices for Efficient Approximately Equivariant Networks

There has been much recent interest in designing symmetry-aware neural networks (NNs) exhibiting relaxed equivariance. Such NNs aim to interpolate between being exactly equivariant and being fully flexible, affording consistent performance benefits. In a separate line of work, certain structured parameter matrices -- those with displacement structure, characterized by low displacement rank (LDR) -- have been used to design small-footprint NNs. Displacement structure enables fast function and gradient evaluation, but permits accurate approximations via compression primarily to classical convolutional neural networks (CNNs). In this work, we propose a general framework -- based on a novel construction of symmetry-based structured matrices -- to build approximately equivariant NNs with significantly reduced parameter counts. Our framework integrates the two aforementioned lines of work via the use of so-called Group Matrices (GMs), a forgotten precursor to the modern notion of regular representations of finite groups. GMs allow the design of structured matrices -- resembling LDR matrices -- which generalize the linear operations of a classical CNN from cyclic groups to general finite groups and their homogeneous spaces. We show that GMs can be employed to extend all the elementary operations of CNNs to general discrete groups. Further, the theory of structured matrices based on GMs provides a generalization of LDR theory focussed on matrices with cyclic structure, providing a tool for implementing approximate equivariance for discrete groups. We test GM-based architectures on a variety of tasks in the presence of relaxed symmetry. We report that our framework consistently performs competitively compared to approximately equivariant NNs, and other structured matrix-based compression frameworks, sometimes with a one or two orders of magnitude lower parameter count.

Samudre, Ashwin↗

Kinematics of Strong Discontinuities

Synthetic Aperture Radar (SAR) provides a detailed view of the Arctic ice cover. When processed with the RADARSAT Geophysical Processor System (RGPS), it provides estimates of sea ice motion and deformation over large regions of the Arctic for extended periods of time. The deformation is dominated by the appearance of linear kinematic features that have been associated with the presence of leads. The RGPS deformation products are based on the assumption that the displacement and velocity are smooth functions of the spatial coordinates. However, if the dominant deformation of multiyear ice results from the opening, closing and shearing of leads, then the displacement and velocity can be discontinuous. This presentation discusses the kinematics associated with strong discontinuities that describe possible jumps in displacement or velocity. Ice motion from SAR data are analyzed using this framework. It is assumed that RGPS cells deform due to the presence of a lead. The lead orientation is calculated to optimally account for the observed deformation. It is shown that almost all observed deformation can be represented by lead opening and shearing. The procedure used to reprocess motion data to account for leads will be described and applied to regions of the Beaufort Sea. The procedure not only provides a new view of ice deformation, it can be used to obtain information about the presence of leads for initialization and/or validation of numerical simulations.

Peterson, K.↗

Stress-intensity factors and crack-opening displacements for round compact specimens

A two dimensional, boundary collocation stress analysis was used to analyze various round compact specimens. The influence of the round external boundary and of pin-loaded holes on stress intensity factors and crack opening displacements was determined as a function of crack-length-to-specimen-width ratios. A wide-range equation for the stress intensity factors was developed. Equations for crack-surface displacements and load-point displacements were also developed. In addition, stress intensity factors were calculated from compliance methods to demonstrate that load-displacement records must be made at the loading points and not along the crack line for crack-length-to-specimen-width ratios less than about 0.4.

Newman, J. C., Jr.↗

Effect of Inductive Coil Geometry and Current Sheet Trajectory of a Conical Theta Pinch Pulsed Inductive Plasma Accelerator

Results are presented demonstrating the e ect of inductive coil geometry and current sheet trajectory on the exhaust velocity of propellant in conical theta pinch pulsed induc- tive plasma accelerators. The electromagnetic coupling between the inductive coil of the accelerator and a plasma current sheet is simulated, substituting a conical copper frustum for the plasma. The variation of system inductance as a function of plasma position is obtained by displacing the simulated current sheet from the coil while measuring the total inductance of the coil. Four coils of differing geometries were employed, and the total inductance of each coil was measured as a function of the axial displacement of two sep- arate copper frusta both having the same cone angle and length as the coil but with one compressed to a smaller size relative to the coil. The measured relationship between total coil inductance and current sheet position closes a dynamical circuit model that is used to calculate the resulting current sheet velocity for various coil and current sheet con gura- tions. The results of this model, which neglects the pinching contribution to thrust, radial propellant con nement, and plume divergence, indicate that in a conical theta pinch ge- ometry current sheet pinching is detrimental to thruster performance, reducing the kinetic energy of the exhausting propellant by up to 50% (at the upper bound for the parameter range of the study). The decrease in exhaust velocity was larger for coils and simulated current sheets of smaller half cone angles. An upper bound for the pinching contribution to thrust is estimated for typical operating parameters. Measurements of coil inductance for three di erent current sheet pinching conditions are used to estimate the magnetic pressure as a function of current sheet radial compression. The gas-dynamic contribution to axial acceleration is also estimated and shown to not compensate for the decrease in axial electromagnetic acceleration that accompanies the radial compression of the plasma in conical theta pinches.

Hallock, Ashley K.↗

Deformations and strains in adhesive joints by moire interferometry

Displacement fields in a thick adherend lap joint and a cracked lap shear specimen were measured by high sensitivity moire interferometry. Contour maps of in-plane U and V displacements were obtained across adhesive and adherent surfaces. Loading sequences ranged from modest loads to near-failure loads. Quantitative results are given for displacements and certain strains in the adhesive and along the adhesive/adherend boundary lines. The results show nonlinear displacements and strains as a function of loads or stresses and they show viscoelastic or time-dependent response. Moire interferometry is an excellent method for experimental studies of adhesive joint performance. Subwavelength displacement resolution of a few micro-inches, and spatial resolution corresponding to 1600 fringes/inch (64 fringes/mm), were obtained in these studies. The whole-field contour maps offer insights not available from local measurements made by high sensitivity gages.

Post, D.↗

Transient response of multidegree-of-freedom linear systems to forcing functions with inequality constraints

Optimal control theory is applied to analyze the transient response of discrete linear systems to forcing functions with unknown time dependence but having known bounds. Particular attention is given to forcing functions which include: (1) maximum displacement of any given mass element, (2) maximum relative displacement of any two adjacent masses, and (3) maximum acceleration of a given mass. Linear mechanical systems with an arbitrary number of degrees of freedom and only one forcing function acting are considered. In the general case, the desired forcing function is found to be a function that switches from the upper-to-lower bound and vice-versa at certain moments of time. A general procedure for finding such switching times is set forth.

Michalopoulos, C. D.↗

Delay of Turbulent Boundary Layer Detachment by Mechanical Excitation: Application to Rearward-facing Ramp

A vane oscillating about a fixed point at the inlet to a two-dimensional 20 deg rearward-facing ramp proved effective in delaying the detachment of a turbulent boundary layer. Flow-field, surface static pressure, and smoke-wire flow visualization measurements were made. Surface pressure coefficient distributions revealed that two different effects occurred with axial distance along the ramp surface. The surface pressure coefficient varied as a complex function of the vane oscillation frequency and its trailing edge displacement amplitude; that is, it varied as a function of the vane oscillation frequency throughout the entire range of frequencies covered during the test, but it varied over only a limited range of the trailing edge displacement amplitudes covered.The complexity of these findings prompted a detailed investigation, the results of which revealed a combination of phenomena that explain qualitatively how the mechanically generated, periodic, sinusoidal perturbing signal produced by the oscillating vane reacts with the fluid flow to delay the detachment of a turbulent boundary layer experiencing transitory detachment.

McKinzie, Daniel J., Jr.↗

Automated generation of influence functions for planar crack problems

A numerical procedure for the generation of influence functions for Mode I planar problems is described. The resulting influence functions are in a form for convenient evaluation of stress-intensity factors for complex stress distributions. Crack surface displacements are obtained by a least-squares solution of the Williams eigenfunction expansion for displacements in a cracked body. Discrete values of the influence function, evaluated using the crack surface displacements, are curve fit using an assumed functional form. The assumed functional form includes appropriate limit-behavior terms for very deep and very shallow cracks. Continuous representation of the influence function provides a convenient means for evaluating stress-intensity factors for arbitrary stress distributions by numerical integration. The procedure is demonstrated for an edge-cracked strip and a radially cracked disk. Comparisons with available published results demonstrate the accuracy of the procedure.

Sire, Robert A.↗

Prediction of stable tearing of 2024-T3 aluminum alloy using the crack-tip opening angle approach

In this study, the crack-tip opening angle (CTOA) approach was incorporated into a damage growth finite element program, MADGIC (Micromechanics Analysis and Damage Growth in Composites), and was used to predict stable tearing in a middle-crack tension 2024-T3 aluminum alloy specimen. The MADGIC code is a displacement based finite element program implemented with an incremental elastic-plastic algorithm used to model elastic-plastic behavior and a nodal splitting and nodal force relaxation algorithm used to generate crack surfaces. Predictions of the applied stress as a function of crack extension and applied stress as a function of load-line displacement were in good agreement with experiments and with similar predictions made using an existing finite element program, ZIP2D. In addition, path integrals, namely, the J-integral and T*-integral, were also evaluated and compared with the CTOA approach. There appears to be a weak relationship between the CTOA and the T*-integral evaluated on a specific integration path during crack extension beyond maximum applied stress. This study further verifies that the CTOA can be used as an effective elastic-plastic fracture mechanics parameter to predict crack growth.

Bakuckas, J. G., Jr.↗

Application of Papkovich-Neuber potentials to a crack problem.

The problem of an elastic solid containing a semi-infinite plane crack subjected to concentrated shears parallel to the edge of the crack is considered in this paper. A closed form solution using four harmonic functions is found to satisfy the finite displacement and inverse square root stress singularity at the edge of the crack. Explicit expressions in terms of elementary functions are given for the distribution of stress and displacement in the solid. These are obtained by employing Fourier and Kontorovich-Lebedev integral transforms and certain singular solutions of Laplace equations in three dimensions. The variations of the intensity of the local stress field along the crack border are shown graphically.

Kassir, M. K.↗

Active Control of the Forced and Transient Response of a Finite Beam

When studying structural vibrations resulting from a concentrated source, many structures may be modelled as a finite beam excited by a point source. The theoretical limit on cancelling the resulting beam vibrations by utilizing another point source as an active controller is explored. Three different types of excitation are considered, harmonic, random, and transient. In each case, a cost function is defined and minimized for numerous parameter variations. For the case of harmonic excitation, the cost function is obtained by integrating the mean squared displacement over a region of the beam in which control is desired. A controller is then found to minimize this cost function in the control interval. The control interval and controller location are continuously varied for several frequencies of excitation. The results show that control over the entire beam length is possible only when the excitation frequency is near a resonant frequency of the beam, but control over a subregion may be obtained even between resonant frequencies at the cost of increasing the vibration outside of the control region. For random excitation, the cost function is realized by integrating the expected value of the displacement squared over the interval of the beam in which control is desired. This is shown to yield the identical cost function as obtained by integrating the cost function for harmonic excitation over all excitation frequencies. As a result, it is always possible to reduce the cost function for random excitation whether controlling the entire beam or just a subregion, without ever increasing the vibration outside the region in which control is desired. The last type of excitation considered is a single, transient pulse. A cost function representative of the beam vibration is obtained by integrating the transient displacement squared over a region of the beam and over all time. The form of the controller is chosen a priori as either one or two delayed pulses. Delays constrain the controller to be causal. The best possible control is then examined while varying the region of control and the controller location. It is found that control is always possible using either one or two control pulses. The two pulse controller gives better performance than a single pulse controller, but finding the optimal delay time for the additional controllers increases as the square of the number of control pulses.

Post, John Theodore↗

Thermostructural evolution of boron carbide characterized using in-situ x-ray diffraction

Boron carbide, with a nominal stoichiometry of B 4 C, is a highly desired ceramic candidate for armor applications due to its high hardness derived from the complex crystal structure. However, stress-induced local amorphization can lead to failure and is a known challenge for this material which must be addressed for applications in ballistic environments. Understanding boron carbide's atomic structural behavior and bonding environment is critical in determining effective strategies to mitigate these issues. Here, in this work, the thermo-structural behavior of B 4 C has been studied in detail using a conical nozzle levitator system coupled with in-situ synchrotron X-ray diffraction. Lattice expansion and the resulting thermal expansion coefficients (CTEs) were determined from 25-2100 °C. Rietveld refinements showed anisotropic atomic displacement for each of the 4 unique sites as a function of temperature. An exceptionally large z-axis displacement for the boron chain center is linked to bond weakness and may be linked to faster expansion of the α 33 relative to α 11 CTEs. Thermally induced lattice changes can inform the use of boron carbide at elevated temperatures as well as help develop strategies for mitigating structural failure for armor applications.

36 MATERIALS SCIENCE↗

Optically and thermally driven huge lattice orbital and spin angular momenta from spinning fullerenes

Lattice vibration in solids may carry angular momentum. But unlike the intrinsic spin of electrons, the lattice vibration is rarely rotational. To induce angular momentum, one needs to find a material that can accommodate a twisted normal mode, two orthogonal modes, or excitation of magnons. If excitation is too strong, one may exceed the Lindemann limit, so the material melts. Therefore these methods are not ideal. Here, we theoretically propose a route to phonon angular momentum in a molecular crystal C 60 . We find that a single laser pulse is able to inject a significant amount of angular momentum to C 60 , and the momentum transfer is helicity dependent. Changing from right-circularly polarized light to left-circularly polarized light switches the direction of phonon angular momentum. On the ultrafast timescale, the orbital angular momentum change closely resembles the displacive excitation of coherent phonons, with a cosine-function dependence on time, different from the spin counterpart. Atomic displacements, even under strong laser excitation, remain far below the Lindemann criterion. Under thermal excitation, spinning C 60 even at room temperature generates a huge angular momentum close to several hundred h¯. Our finding opens the door to a large group of fullerenes, from C 60 , C 70 to their endohedral derivatives, where angular momentum can be generated through light or temperature. Furthermore, this paves the way to the phononic control electronic spin and harvesting thermal energy through phonon angular momentum.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Vacancy-Vacancy Interaction in Copper

The binding energy of two vacancies in a static lattice as a function of their separation and the positions of their displaced neighboring atoms has been calculated using a Morse potential function model for copper. It was found that two vacancies attract one another at separation less than about 7 A. At separations greater than 7 A the vacancies do not interact appreciably. The most stable separation was found to be the first nearest- neighbor separation or the divacancy configuration, for which the binding energy was found to be 0.64 ev. Based on these calculations, it is shown that third-stage annealing in irradiated copper may be accounted for by divacancy migration. The role of the divacancy in copper self-diffusion is also explained.

Girifalco, L. A.↗