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At least 19 records

A uniform geometrical optics and an extended uniform geometrical theory of diffraction for evaluating high frequency EM fields near smooth caustics and composite shadow boundaries

A uniform geometrical optics (UGO) and an extended uniform geometrical theory of diffraction (EUTD) are developed for evaluating high frequency electromagnetic (EM) fields within transition regions associated with a two and three dimensional smooth caustic of reflected rays and a composite shadow boundary formed by the caustic termination or the confluence of the caustic with the reflection shadow boundary (RSB). The UGO is a uniform version of the classic geometrical optics (GO). It retains the simple ray optical expressions of classic GO and employs a new set of uniform reflection coefficients. The UGO also includes a uniform version of the complex GO ray field that exists on the dark side of the smooth caustic. The EUTD is an extension of the classic uniform geometrical theory of diffraction (UTD) and accounts for the non-ray optical behavior of the UGO reflected field near caustics by using a two-variable transition function in the expressions for the edge diffraction coefficients. It also uniformly recovers the classic UTD behavior of the edge diffracted field outside the composite shadow boundary transition region. The approach employed for constructing the UGO/EUTD solution is based on a spatial domain physical optics (PO) radiation integral representation for the fields which is then reduced using uniform asymptotic procedures. The UGO/EUTD analysis is also employed to investigate the far-zone RCS problem of plane wave scattering from two and three dimensional polynomial defined surfaces, and uniform reflection, zero-curvature, and edge diffraction coefficients are derived. Numerical results for the scattering and diffraction from cubic and fourth order polynomial strips are also shown and the UGO/EUTD solution is validated by comparison to an independent moment method (MM) solution. The UGO/EUTD solution is also compared with the classic GO/UTD solution. The failure of the classic techniques near caustics and composite shadow boundaries is clearly demonstrated and it is shown that the UGO/EUTD results remain valid and uniformly reduce to the classic results away from the transition regions. Mathematical details on the asymptotic properties and efficient numerical evaluation of the canonical functions involved in the UGO/EUTD expressions are also provided.

Constantinides, E. D.↗

Assessing laser powder bed fusion system geometric errors through artifact-based methods

Additive manufacturing (AM) machines have developed more rapidly than standardized frameworks needed for the qualification of their geometric capabilities. While some manufacturer-specific methods exist to test capabilities and perform some calibration tasks, standardization efforts have only recently been undertaken in the form of ISO/ASTM 52902. In this study, the recommended methodology prescribed by the standard was implemented by building geometric artifacts with a laser powder bed fusion (LPBF) system and performing dimensional inspection with a coordinate measurement machine (CMM), amongst other methods. Typical dimensional capabilities of the LPBF system are identified and commentary is made on applying metrology methods, detecting geometric error, and diagnosing base causes in the LPBF system. In doing so, favored metrology practices and measurement analysis methods auxiliary to the standard are proposed. Artifact measurements were used to characterize beam positioning error and beam offset error. Methods for decoupling the effects of error sources are proposed. Difficulties in the inspection of AM components are identified, and the effects of various CMM measurement strategies are evaluated. Insights on the application of the new standard are presented, along with commentary as to its fitness for the LPBF process.

Berez, J.↗

Structural Manipulation of Phase Transitions by Self‐Induced Strain in Geometrically Confined Thin Films

Strain engineering is a well-known method often used to tune material properties in thin films. The most studied sources of strain are lattice mismatch and differential thermal contraction between the substrate and film. However, in materials which undergo a structural phase transition (SPT), a third and often overlooked source of strain may play a very significant role. If the substrate confines the area of the film, the SPT may induce stress which changes the evolution of the transition. This is a 2D analog of the isochoric phase transition between water and ice, where the freezing point drops below 0 °C. To illustrate this, the prototypical Mott insulator V 2 O 3 which has an SPT coupled to a metal–insulator transition is used to show how self-induced strain can drastically alter structural and electronic properties. This effect provides an elegant approach for mapping the phase diagram of the SPT and the transitions coupled to it. Moreover, the magnitude of self-straining is tunable by modifying the substrate morphology. Furthermore, this effect may be important for numerous materials which exhibit an SPT and are subjected to geometrical constraints.

Kalcheim, Yoav↗

Au147(SPh)30(PPh3)12: A Geometrically Closed, but Electronically Open Triple‐Shell Icosahedral Gold Cluster and its Geometrically Open Counterpart

The aesthetic platonic solids have been known since ancient times, and the structure of all five platonic solids is also found in chemical compounds. While gold sub-nanometer clusters and gold nanoparticles with an icosahedral structure have been known for a long time to exist, a multi-shell icosahedral gold cluster at the intermediate size between 13 and thousands of atoms has been elusive. Here we present the synthesis and crystallographic characterization of the first triple-shell icosahedral metal cluster, Au147(SPh)30(PPh3)12 1. The gold core in 1 is stabilized by phosphines and thiolates, but surprisingly no staple motifs are formed. A second cluster, Au146(SPh)30(PPh3)12 2, cocrystallizes and is identified as having a closed electronic shell but can be considered as a geometrically open pendant of 1. The unique clusters are characterized experimentally by EDX, UV/vis, DLS, and EPR and theoretically by quantum chemical calculations.

Strienz, Markus↗

Geometric Optimization of an Electrochemical Purification Cell to Prevent Corrosion in CSP Plants During Operation

When exposed to moisture or oxygen, molten chloride salts produce corrosive impurities which degrade containment alloys. This can significantly decrease the lifetime and increase costs of molten-salt-based systems. To overcome this barrier, we designed and modeled an electrochemical purification cell to remove the corrosive impurity MgOH+. Various reactor architectures, including continuous stirred tank reactors (CSTRs) and plug flow reactors (PFRs) were investigated. Steady-state thermoelectric properties were evaluated using analytical methods, allowing assessment of the effects of structure and design parameters such as flow rate, cell length, and cross-sectional area of molten salt. The results suggest that our design could most effectively increase reliability and decrease costs of molten-chloride-salt-based systems by protecting them during continuous operation using an annular plug flow reactor.

analytical modeling↗

Method and apparatus for real time, in situ sensing and characterization of roughness, geometrical shapes, geometrical structures, composition, defects, and temperature in three-dimensional manufacturing systems

Methods and apparatuses for manufacturing are disclosed, including (a) providing an apparatus having: a laser; scanner; powder injection system; powder spreading system; dichroic filter; imager-and-processor; and computer; (b) programming the computer with specifications of a sample; (c) using the computer to set initial parameters based on the sample specifications; (d) adjusting a stage to position the sample; (e) focusing and scanning electromagnetic radiation onto the sample while powder is concurrently injected onto the sample in order to deposit a layer; (f) capturing two-dimensional images of the sample and probing the sample to determine whether the deposited layer was manufactured per the specifications; (g) use the computer to adjust the three-dimensional manufacturing parameters based on the determination made in step (f) prior to additively manufacturing a subsequent layer or making repairs; and (h) repeating steps (d), (e), (f), and (g) until the manufacture is complete. Other embodiments are described and claimed.

Liu, Jian↗

Developing Procedures to Implement Geometric Imperfections Beyond Right Circular Cylindrical Shells in Finite Element Method Models

Analysis of aerospace structures is frequently conducted using nominal dimensions and frequently assumes ideal conditions in loading, contact, constraints, et cetera. Off-nominal dimensions and nonideal conditions, however, are present in all structures. These are the result of widely ranging causes from coefficient of thermal expansion mismatches, manufacturing tooling anomalies, to assembly procedures that inadvertently alter the structure. Specifically, geometric imperfections can have potentially significant influence on the response of a structural test article observed in an experiment versus the response given by a numerical simulation. The Python Tool for Implementing Geometric Imperfections in Reduced Structures (Py_TIGIRS) was previously presented as a set of Python scripts to calculate and implement as-manufactured geometric midsurface and thickness imperfections into finite element method (FEM) shell models of nominally right circular cylinders. By taking advantage of the simple shape of a right circular cylinder, interpolations of the measured data points were able to be performed along directions that aligned to the cylindrical coordinate system axes of the entire structure. By taking advantage of the shell representation of the real structure as opposed to modeling using a continuum representation, the thickness variation was able to be implemented by shell section definitions instead of having to modify the position of multiple nodes in the thickness direction. Py_TIGIRS is a useful tool that established a procedural example on how to implement geometric imperfections in right circular cylindrical shell structures. Three new procedures, each expanded from concepts established in Py_TIGIRS, are proposed for various test-article designs and are intended to broaden the range of structures that can be modeled with measured geometric imperfections in the structural analysis community. Each test-article design introduces new challenges to successfully implement geometric imperfections into a FEM model. The first test-article design consists of a carbon fiber reinforced polymer square plate with a hat-shaped stiffener co-cured on one side. This test-article design was for a novel seven-point bend test that was also previously presented. Manufacturing and cure-cycle imperfections are observed using digital image correlation (DIC) techniques. As thermal expansion coefficient mismatches between the plate and stiffener materials were anticipated, a thermal analysis study with continuum shell and solid elements was conducted to capture the global shape observed prior to testing. The second test-article design is of a similar hat-stiffened plate configuration, but with a side length ratio near 3:1 with elongation in the stiffener direction. The test article was used to characterize the response to uniaxial compressive loading in the direction of the stiffener. Due to differing manufacturing steps, a thermal analysis like the one developed for the seven-point bend configuration was unable to mimic the observed geometric imperfections. Instead, a strategy based on applying deformations directly to the structure during analysis was developed for continuum shell and solid element representation of a stiffened panel.

Geometric imperfections↗

Titan-Like Exoplanets: Variations in Geometric Albedo and Effective Transit Height with Haze Production Rate

Extensive studies characterizing Titan present an opportunity to study the atmospheric properties of Titan-like exoplanets. Using an existing model of Titan's atmospheric haze, we computed geometric albedo spectra and effective transit height spectra for six values of the haze production rate (zero haze to twice present) over a wide range of wavelengths (0.2-2 microns). In the geometric albedo spectra, the slope in the UV-visible changes from blue to red when varying the haze production rate values from zero to twice the current Titan value. This spectral feature is the most effective way to characterize the haze production rates. Methane absorption bands in the visible-NIR compete with the absorbing haze, being more prominent for smaller haze production rates. The effective transit heights probe a region of the atmosphere where the haze and gas are optically thin and that is thus not effectively probed by the geometric albedo. The effective transit height decreases smoothly with increasing wavelength, from 376 km to 123 km at 0.2 and 2 microns, respectively. When decreasing the haze production rate, the methane absorption bands become more prominent, and the effective transit height decreases with a steeper slope with increasing wavelength. The slope of the geometric albedo in the UV-visible increases smoothly with increasing haze production rate, while the slope of the effective transit height spectra is not sensitive to the haze production rate other than showing a sharp rise when the haze production rate increases from zero. We conclude that geometric albedo spectra provide the most sensitive indicator of the haze production rate and the background Rayleigh gas. Our results suggest that important and complementary information can be obtained from the geometric albedo and motivates improvements in the technology for direct imaging of nearby exoplanets.

Geometric albedo↗

Implementing Geometric Surface Imperfections into Sandwich Composite Cylinder Finite Element Method Models

The buckling responses of certain cylindrical shell structures are extremely sensitive to geometric surface imperfections. The NASA Engineering and Safety Center (NESC) Shell Buckling Knockdown Factor Project (SBKF) is conducting research to develop analysis-based buckling design recommendations. Experiments are used to verify the analysis-based factors, but the sensitivity of the test articles to geometric imperfections requires implementing as-manufactured imperfections into high-fidelity finite element method models. Data collection methods such as structured light scanning are used for all geometric surface data used in this work. Common preprocessing and visualization steps used in SBKF are discussed, and steps on how surface scans are prepared for implementation into a finite element model is described. The Python Tool for Implementing Geometric Imperfections in Reduced Structures (Py_TIGIRS), written specifically for the use with SBKF, is briefly described and uses eight functions to extract, modify, and write geometric imperfections into Abaqus input files. Results of the pre-processing methods and results from Py_TIGIRS are provided and compared for Composite Test Article (CTA) 8.2B. Excellent agreement between the visualized scan data and the FEM-extracted geometry is demonstrated. A brief example of why geometric surface imperfections are significant in nonlinear numerical analyses for thin cylinders in axial compression is provided as motivation to use tools such as Py_TIGIRS. Future development of Py_TIGIRS including expansion to structures of arbitrary geometry is planned.

Sandwich structures↗

Implementing Geometric Surface Imperfections into Sandwich Composite Cylinder Finite Element Method Models

The buckling responses of certain cylindrical shell structures are extremely sensitive to geometric imperfections. The NASA Engineering and Safety Center (NESC) Shell Buckling Knockdown Factor Project (SBKF) is conducting research to develop analysis-based buckling design recommendations. Experiments are used to verify the analysis-based factors, but the sensitivity of the test articles to geometric imperfections requires implementing as-manufactured imperfections into high-fidelity finite element method (FEM) models. Geometry measurement methods such as structured light scanning are used for all geometric surface data used in this work. Common preprocessing and visualization steps used in SBKF are discussed, and steps of how surface scans are prepared for implementation into a finite element model is described. The Python Tool for Implementing Geometric Imperfections in Reduced Structures (Py_TIGIRS), written specifically for the use with SBKF, is briefly described and uses eight functions to extract, modify, and write geometric imperfections into Abaqus input files. Results of the preprocessing methods and results from Py_TIGIRS are provided and compared for Composite Test Articles (CTA) 8.2, 8.2B, and 8.3. Excellent agreement between the visualized scan data and the FEM-extracted geometry is demonstrated. A brief example of why geometric surface imperfections are significant in nonlinear numerical analyses for thin cylinders in axial compression is provided as motivation to use tools such as Py_TIGIRS. Future developments of Py_TIGIRS including expansion to structures of arbitrary geometry is planned.

Geometric imperfections↗

Implementing Geometric Surface Imperfections into Sandwich Composite Cylinder Finite Element Method Models

The buckling responses of certain cylindrical shell structures are extremely sensitive to geometric imperfections. The NASA Engineering and Safety Center (NESC) Shell Buckling Knockdown Factor Project (SBKF) is conducting research to develop analysis-based buckling design recommendations. Experiments are used to verify the analysis-based factors, but the sensitivity of the test articles to geometric imperfections requires implementing as-manufactured imperfections into high-fidelity finite element method (FEM) models. Geometry measurement methods such as structured light scanning are used for all geometric surface data used in this work. Common preprocessing and visualization steps used in SBKF are discussed, and steps of how surface scans are prepared for implementation into a finite element model is described. The Python Tool for Implementing Geometric Imperfections in Reduced Structures (Py_TIGIRS), written specifically for the use with SBKF, is briefly described and uses eight functions to extract, modify, and write geometric imperfections into Abaqus input files. Results of the preprocessing methods and results from Py_TIGIRS are provided and compared for Composite Test Articles (CTA) 8.2, 8.2B, and 8.3. Excellent agreement between the visualized scan data and the FEM-extracted geometry is demonstrated. A brief example of why geometric surface imperfections are significant in nonlinear numerical analyses for thin cylinders in axial compression is provided as motivation to use tools such as Py_TIGIRS. Future developments of Py_TIGIRS including expansion to structures of arbitrary geometry is planned.

Geometric imperfections↗

Operational resilience of additively manufactured parts to stealthy cyberphysical attacks using geometric and process digital twins

Cyberphysical attacks on the digital backbone of Additive Manufacturing (AM) can compromise the printed part’s functionality. They can alter features in the digital geometry to introduce geometric defects (e.g., missing fillets) or alter process parameters to create local defects (e.g., voids). Addressing the downtime, waste, and quality deterioration associated with existing solutions requires operational resilience, i.e., rapid elimination or disruption of defect formation (to retain part function) without production stoppage or part disposal (to retain yield). This need is unmet due to the inherently unpredictable nature of attack-induced alterations, lack of access to the original geometric model for identification of altered geometric features, and in-process imposition of unknown process dynamics via attack-driven alteration of real-time-uncontrolled (or exogenous) parameters. This work establishes the above-mentioned operational resilience for the first time by creating two Digital Twins (DT). The Geometric DT (Geo-DT) is based on a unique physical-field-driven soft sensor and topology optimization method. The Process Digital Twin (Pro-DT) combines local defect quantification with a novel Reinforcement Learning formulation and training method. The importance of these methodological advances and the scalability of our approach are examined on a real AM testbed. It is shown that Geo-DT can correct geometric defects without access to the original digital geometry or explicit knowledge of attack-altered geometric features. Further, Pro-DT can accelerate real-time disruption of local defects despite attack-driven imposition of unknown process dynamics. We discuss how our framework goes beyond the contemporary focus on pre-attack security and in-attack detection towards resilience for AM and beyond.

Additive Manufacturing↗

Differential geometric approaches to momentum-based formulations for fluids [Slides]

This SAND report documents CIS Late Start LDRD Project 22-0311, "Differential geometric approaches to momentum-based formulations for fluids". The project primarily developed geometric mechanics formulations for momentum-based descriptions of nonrelativistic fluids, utilizing a differential geometry/exterior calculus treatment of momentum and a space+time splitting. Specifically, the full suite of geometric mechanics formulations (variational/Lagrangian, Lie-Poisson Hamiltonian and Curl-Form Hamiltonian) were developed in terms of exterior calculus using vector-bundle valued differential forms. This was done for a fairly general version of semi-direct product theory sufficient to cover a wide range of both neutral and charged fluid models, including compressible Euler, magnetohydrodynamics and Euler-Maxwell. As a secondary goal, this project also explored the connection between geometric mechanics formulations and the more traditional Godunov form (a hyperbolic system of conservation laws). Unfortunately, this stage did not produce anything particularly interesting, due to unforeseen technical difficulties. There are two publications related to this work currently in preparation, and this work will be presented at SIAM CSE 23, at which the PI is organizing a mini-symposium on geometric mechanics formulations and structure-preserving discretizations for fluids. The logical next step is to utilize the exterior calculus based understanding of momentum coupled with geometric mechanics formulations to develop (novel) structure-preserving discretizations of momentum. This is the main subject of a successful FY23 CIS LDRD "Structure-preserving discretizations for momentum-based formulations of fluids".

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

An empirical method for geometric calibration of a photon counting detector-based cone beam CT system

BACKGROUND: Geometric calibration is essential in developing a reliable computed tomography (CT) system. It involves estimating the geometry under which the angular projections are acquired. Geometric calibration of cone beam CTs employing small area detectors, such as currently available photon counting detectors (PCDs), is challenging when using traditional-based methods due to detectors’ limited areas. OBJECTIVE: This study presented an empirical method for the geometric calibration of small area PCD-based cone beam CT systems. METHODS: Unlike the traditional methods, we developed an iterative optimization procedure to determine geometric parameters using the reconstructed images of small metal ball bearings (BBs) embedded in a custom-built phantom. An objective function incorporating the sphericities and symmetries of the embedded BBs was defined to assess performance of the reconstruction algorithm with the given initial estimated set of geometric parameters. The optimal parameter values were those which minimized the objective function. The TIGRE toolbox was employed for fast tomographic reconstruction. To evaluate the proposed method, computer simulations were carried out using various numbers of spheres placed in various locations. Furthermore, efficacy of the method was experimentally assessed using a custom-made benchtop PCD-based cone beam CT. RESULTS: Computer simulations validated the accuracy and reproducibility of the proposed method. The precise estimation of the geometric parameters of the benchtop revealed high-quality imaging in CT reconstruction of a breast phantom. Within the phantom, the cylindrical holes, fibers, and speck groups were imaged in high fidelity. The CNR analysis further revealed the quantitative improvements of the reconstruction performed with the estimated parameters using the proposed method. CONCLUSION: Apart from the computational cost, we concluded that the method was easy to implement and robust.

Instruments & Instrumentation↗

Antenna with Dielectric Having Geometric Patterns

An antenna includes a ground plane, a dielectric disposed on the ground plane, and an electrically-conductive radiator disposed on the dielectric. The dielectric includes at least one layer of a first dielectric material and a second dielectric material that collectively define a dielectric geometric pattern, which may comprise a fractal geometry. The radiator defines a radiator geometric pattern, and the dielectric geometric pattern is geometrically identical, or substantially geometrically identical, to the radiator geometric pattern.

Dudley, Kenneth L.↗