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All sources NASA NTRS DOE OSTI

NASA NTRS1994

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.↗

NASA NTRS2002

MISR automatic geometric quality assessment and in-flight geometric calibration updates

An overview of the in-flight geometric calibrations and quality assessment along with the current status and discusion of the operational results is presented.

calibration geometric orthorectification photogram↗

DOE OSTI2025

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↗

NASA NTRSDate not supplied

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↗

NASA NTRS2016

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↗

NASA NTRSDate not supplied

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↗

NASA NTRSDate not supplied

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↗

NASA NTRSDate not supplied

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

Geometric imperfections↗

DOE OSTI2025

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↗

NASA NTRS2013

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.↗

NASA NTRS1985

An Intuitive Approach to Geometric Continuity for Parametric Curves and Surfaces (Extended Abstract)

The notion of geometric continuity is extended to an arbitrary order for curves and surfaces, and an intuitive development of constraints equations is presented that are necessary for it. The constraints result from a direct application of the univariate chain rule for curves, and the bivariate chain rule for surfaces. The constraints provide for the introduction of quantities known as shape parameters. The approach taken is important for several reasons: First, it generalizes geometric continuity to arbitrary order for both curves and surfaces. Second, it shows the fundamental connection between geometric continuity of curves and geometric continuity of surfaces. Third, due to the chain rule derivation, constraints of any order can be determined more easily than derivations based exclusively on geometric measures.

Derose, T. D.↗

NASA NTRS1987

Finite octree meshing through topologically driven geometric operators

The octree technique is developed into the finite octree, and an overview is given. Modeler requirements are given. The octree discretization is discussed along with geometric communication operators. Geometric communication operators returning topological associativity and geometric communication operators returning spatial data are also discussed and illustrated. The advantages are given of the boundary representation and of geometric communication operators. The implementation plays an important role in the integration with a variety of geometric modelers. The capabilities of closed loop processes within a complete finite element system are presented.

Grice, Kurt R.↗

NASA NTRS1990

A geometric representation scheme suitable for shape optimization

A geometric representation scheme is outlined which utilizes the natural design variable concept. A base configuration with distinct topological features is created. This configuration is then deformed to define components with similar topology but different geometry. The values of the deforming loads are the geometric entities used in the shape representation. The representation can be used for all geometric design studies; it is demonstrated here for structural optimization. This technique can be used in parametric design studies, where the system response is defined as functions of geometric entities. It can also be used in shape optimization, where the geometric entities of an original design are modified to maximize performance and satisfy constraints. Two example problems are provided. A cantilever beam is elongated to meet new design specifications and then optimized to reduce volume and satisfy stress constraints. A similar optimization problem is presented for an automobile crankshaft section. The finite element method is used to perform the analyses.

Tortorelli, Daniel A.↗

NASA NTRS1994

On the minimum of independent geometrically distributed random variables

The expectations E(X(sub 1)), E(Z(sub 1)), and E(Y(sub 1)) of the minimum of n independent geometric, modifies geometric, or exponential random variables with matching expectations differ. We show how this is accounted for by stochastic variability and how E(X(sub 1))/E(Y(sub 1)) equals the expected number of ties at the minimum for the geometric random variables. We then introduce the 'shifted geometric distribution' and show that there is a unique value of the shift for which the individual shifted geometric and exponential random variables match expectations both individually and in the minimums.

Ciardo, Gianfranco↗

NASA NTRS1999

Geometric Representations of Condition Queries on Three-Dimensional Vector Fields

Condition queries on distributed data ask where particular conditions are satisfied. It is possible to represent condition queries as geometric objects by plotting field data in various spaces derived from the data, and by selecting loci within these derived spaces which signify the desired conditions. Rather simple geometric partitions of derived spaces can represent complex condition queries because much complexity can be encapsulated in the derived space mapping itself A geometric view of condition queries provides a useful conceptual unification, allowing one to intuitively understand many existing vector field feature detection algorithms -- and to design new ones -- as variations on a common theme. A geometric representation of condition queries also provides a simple and coherent basis for computer implementation, reducing a wide variety of existing and potential vector field feature detection techniques to a few simple geometric operations.

Henze, Chris↗

NASA NTRS2018

JPSS-1/NOAA-20 VIIRS Early On-Orbit Geometric Performance

The first NOAA/NASA Join Polar Satellite System (JPSS-1) satellite was successfully launched on November 18, 2017,becoming NOAA-20. Instruments on-board the NOAA-20 satellite include the Visible Infrared Imaging RadiometerSuite (VIIRS). This instrument is the second build of VIIRS, with the first flight instrument on-board NASA/NOAASuomi National Polar-orbiting Partnership (SNPP) satellite operating since October 2011. The purpose of these VIIRSinstruments is to continue the long-term measurements of biogeophysical variables for multiple applications includingweather forecasting, rapid response and climate research. The geometric performance of VIIRS is essential to retrievingaccurate biogeophysical variables. This paper describes the early on-orbit geometric performance of the JPSS-1/NOAA-20 VIIRS. It first discusses the on-orbit orbit and attitude performance, a key input needed for accurate geolocation. Itthen discusses the on-orbit geometric characterization and calibration of VIIRS and an initial assessment of thegeometric accuracy. It follows with a discussion of an improvement in the instrument geometric model that correctssmall geometrical artifacts that appear in the along-scan direction. Finally, this paper discusses on-orbit measurements ofthe focal length and the impact of this on the scan-to-scan underlap/overlap.

Lin, Guoqing↗

NASA NTRSDate not supplied

Evaluation of Preliminary Buffet Forcing Function Development based on Wind-Tunnel Tests of Geometrically-similar Models

The current state-of-the-art for launch vehicle buffet load estimation involves wind tunnel testing of highly instrumented rigid models and data processing of experimental unsteady pressure measurements to estimate the fluctuating aerodynamic loads. The model and instrumentation requirements to accomplish this type of testing are significant. The rigid model, in particular, must be built with relatively high geometric fidelity to approximate similar aerodynamic phenomena that will occur during the full-scale vehicle flight. Due to this requirement, several iterative wind tunnel tests are often required during the design maturation of the vehicle. For preliminary buffet load estimation, however, data from previous launch vehicle wind tunnel tests of geometrically similar models can be used to provide initial buffet environment estimates before a high geometric fidelity wind tunnel test has been conducted. In this paper, two components of this preliminary buffet estimation process are described: (1) assembly of buffet forcing functions from multiple data sources and (2) scaling of these buffet forcing functions to geometrically-similar components of a target vehicle configuration. The impacts of these estimation methods on the full-vehicle buffet forcing functions, including their longitudinal distribution along the vehicle, frequency-content at individual stations, and station-to-station coherence, are investigated. Considerations for using these methods to extrapolate wind tunnel data to geometrically similar models are also discussed.

Patrick S Heaney↗

DOE OSTI2024

A Geometric Derivation of the Governing Equations of Motion of Nonholonomic Dynamic Systems

Here, in this paper, we present a Riemannian geometric derivation of the governing equations of motion of nonholonomic dynamic systems. A geometric form of the work-energy principle is first derived. The geometric form can be realized in appropriate generalized quantities, and the independent equations of motion can be obtained if the subspace of generalized speeds allowable by nonholonomic constraints can be determined. We provide a geometric perspective of the governing equations of motion and demonstrate its effectiveness in studying dynamic systems subjected to nonholonomic constraints.

42 ENGINEERING↗