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DOE OSTI2026

Full-wave modeling of RF waves in fusion plasmas with finite element method: Progress in past decades and its future role

This paper reviews the progress in computing radio frequency (RF) wave fields in fusion plasmas, specifically focusing on simulations utilizing the finite element method (FEM) over the past few decades. Computing RF wave fields in fusion plasmas presents unique challenges due to large simulation domains, complex antenna structures, non-local dielectric properties, and wide ranges of spatial scales. It highlights key developments and outlines future directions, primarily addressing waves in the ion cyclotron (IC) to lower hybrid (LH) frequency range. We begin with briefly revisiting earlier developments before the widespread availability of modern computer-aided engineering (CAE) software based on FEM. This historical perspective illuminates early progress and the physics difficulties that motivated ongoing work within the community. Modern wave simulations for RF antennas based on FEM are characterized by the use of detailed 3D antenna model geometry generated from engineering CAD software and localized wave dielectric model. Significant advancements have also been made in improving physics models to include phenomena such as RF sheath rectification and wave scattering. FEM-based RF simulations have also been applied to compute wave propagation in the core region, where the inclusion of non-local dielectric response is crucial. This is a challenging goal, and several promising approaches have been proposed in this area. Additionally, RF simulation development initiatives based on open-source libraries have gained popularity, demonstrating scalability and flexibility in extending physics models. This paper will discuss the advantages and disadvantages of using such a publicly available FEM library.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2024

A Characteristics Approach to the Finite Element Method

Herein, we present a new method for solving the linear Boltzmann transport equation. Two commonly used and well-understood methods for solving partial differential equations are the method of characteristics (MOC) and the finite element method (FEM). We propose a new method that combines the fundamental concept of the FEM with the analytic solution from the MOC to obtain coefficients for the FEM basis function expansion. Traditionally, coefficients for the FEM basis function expansion are obtained via matrix inversion. Instead, we solve for the coefficients with the MOC and represent the underlying fields with the basis function expansion using these coefficients. We provide a convergence study for our method with results from two sets of FEM basis functions: Gauss-Legendre and Gauss-Lobatto sets. We also compare two different variations of our method categorized as short characteristics and intermediate characteristics.

42 ENGINEERING↗

NASA NTRS1992

Moessbauer Spectroscopy for Lunar Resource Assessment: Measurement of Mineralogy and Soil Maturity

First-order assessment of lunar soil as a resource includes measurement of its mineralogy and maturity. Soils in which the mineral ilmenite is present in high concentrations are desirable feedstock for the production of oxygen at a lunar base. The maturity of lunar soils is a measure of their relative residence time in the upper 1 mm of the lunar surface. Increasing maturity implies increasing load of solar wind species (e.g., N, H, and He-3), decreasing mean grain size, and increasing glass content. All these physicochemical properties that vary in a regular way with maturity are important parameters for assessing lunar soil as a resource. For example, He-3 can be extracted and potentially used for nuclear fusion. A commonly used index for lunar soil maturity is I(sub s)/FeO, which is the concentration of fine-grained metal determined by ferromagnetic resonance (I(sub s)) normalized to the total iron content (as FeO). I(sub s)/FeO has been measured for virtually every soil returned by the Apollo and Luna missions to the Moon. Because the technique is sensitive to both oxidation state and mineralogy, iron Moessbauer spectroscopy (FeMS) is a viable technique for in situ lunar resource assessment. Its utility for mineralogy is apparent from examination of published FeMS data for lunar samples. From the data published, it can be inferred that FeMS data can also be used to determine soil maturity. The use of FeMS to determine mineralogy and maturity and progress on development of a FeMS instrument for lunar surface use are discussed.

Morris, R. V.↗

NASA NTRS1994

Thermal emission measurements (5-25 microns) of palagonite/Fe-substituted montmorillonite intimate mixtures: Applications to Mars

The emissivity of a Mauna Kea palagonitic soil mixed with an Fe-substituted montmorillonite (FeM) was measured. The emission spectra of all samples were measured at the TES spectroscopy laboratory at Arizona State University. The data were converted to emissivity using blackbody measurements combined with measurements of each sample at different temperatures. This preliminary study has demonstrated that both naturally-occurring palagonites, thought to be good visible to near-IR spectral analogs for Mars, and FeM exhibit complex emissivity spectra at thermal wavelengths. FeM exhibits greater emissivity variations than palagonite, and emissivity peaks observed in the FeM spectrum allows its identification for abundances greater than or equal to 15 percent when mixed with palagonite. Smaller abundances of FeM are potentially identifiable when mixed with palagonite, but this remains to be determined.

Roush, Ted L.↗

NASA NTRS2008

New Developments in the Embedded Statistical Coupling Method: Atomistic/Continuum Crack Propagation

A concurrent multiscale modeling methodology that embeds a molecular dynamics (MD) region within a finite element (FEM) domain has been enhanced. The concurrent MD-FEM coupling methodology uses statistical averaging of the deformation of the atomistic MD domain to provide interface displacement boundary conditions to the surrounding continuum FEM region, which, in turn, generates interface reaction forces that are applied as piecewise constant traction boundary conditions to the MD domain. The enhancement is based on the addition of molecular dynamics-based cohesive zone model (CZM) elements near the MD-FEM interface. The CZM elements are a continuum interpretation of the traction-displacement relationships taken from MD simulations using Cohesive Zone Volume Elements (CZVE). The addition of CZM elements to the concurrent MD-FEM analysis provides a consistent set of atomistically-based cohesive properties within the finite element region near the growing crack. Another set of CZVEs are then used to extract revised CZM relationships from the enhanced embedded statistical coupling method (ESCM) simulation of an edge crack under uniaxial loading.

Saether, E.↗

NASA NTRS2007

Build-Up Approach to Updating the Mock Quiet Spike Beam Model

When a new aircraft is designed or a modification is done to an existing aircraft, the aeroelastic properties of the aircraft should be examined to ensure the aircraft is flight worthy. Evaluating the aeroelastic properties of a new or modified aircraft can include performing a variety of analyses, such as modal and flutter analyses. In order to produce accurate results from these analyses, it is imperative to work with finite element models (FEM) that have been validated by or correlated to ground vibration test (GVT) data, Updating an analytical model using measured data is a challenge in the area of structural dynamics. The analytical model update process encompasses a series of optimizations that match analytical frequencies and mode shapes to the measured modal characteristics of structure. In the past, the method used to update a model to test data was "trial and error." This is an inefficient method - running a modal analysis, comparing the analytical results to the GVT data, manually modifying one or more structural parameters (mass, CG, inertia, area, etc.), rerunning the analysis, and comparing the new analytical modal characteristics to the GVT modal data. If the match is close enough (close enough defined by analyst's updating requirements), then the updating process is completed. If the match does not meet updating-requirements, then the parameters are changed again and the process is repeated. Clearly, this manual optimization process is highly inefficient for large FEM's and/or a large number of structural parameters. NASA Dryden Flight Research Center (DFRC) has developed, in-house, a Mode Matching Code that automates the above-mentioned optimization process, DFRC's in-house Mode Matching Code reads mode shapes and frequencies acquired from GVT to create the target model. It also reads the current analytical model, as we11 as the design variables and their upper and lower limits. It performs a modal analysis on this model and modifies it to create an updated model that has similar mode shapes and frequencies as those of the target model. The Mode Matching Code output frequencies and modal assurance criteria (MAC) values that allow for the quantified comparison of the updated model versus the target model. A recent application of this code is the F453 supersonic flight testing platform, NASA DFRC possesses a modified F-15B that is used as a test bed aircraft for supersonic flight experiments. Traditionally, the finite element model of the test article is generated. A GVT is done on the test article ta validate and update its FEM. This FEM is then mated to the F-15B model, which was correlated to GVT data in fall of 2004, A GVT is conducted with the test article mated to the aircraft, and this mated F-15B/ test article FEM is correlated to this final GVT.

Herrera, Claudia Y.↗

NASA NTRS2012

Correlation Results for a Mass Loaded Vehicle Panel Test Article Finite Element Models and Modal Survey Tests

High-fidelity Finite Element Models (FEMs) were developed to support a recent test program at Marshall Space Flight Center (MSFC). The FEMs correspond to test articles used for a series of acoustic tests. Modal survey tests were used to validate the FEMs for five acoustic tests (a bare panel and four different mass-loaded panel configurations). An additional modal survey test was performed on the empty test fixture (orthogrid panel mounting fixture, between the reverb and anechoic chambers). Modal survey tests were used to test-validate the dynamic characteristics of FEMs used for acoustic test excitation. Modal survey testing and subsequent model correlation has validated the natural frequencies and mode shapes of the FEMs. The modal survey test results provide a basis for the analysis models used for acoustic loading response test and analysis comparisons

Maasha, Rumaasha↗

NASA NTRS2015

Integration of a Finite Element Model with the DAP Bone Remodeling Model to Characterize Bone Response to Skeletal Loading

NASA's Digital Astronaut Project (DAP) has developed a bone remodeling model that has been validated for predicting volumetric bone mineral density (vBMD) changes of trabecular and cortical bone in the absence of mechanical loading. The model was recently updated to include skeletal loading from exercise and free living activities to maintain healthy bone using a new daily load stimulus (DLS). This new formula was developed based on an extensive review of existing DLS formulas, as discussed in the abstract by Pennline et al. The DLS formula incorporated into the bone remodeling model utilizes strains and stress calculated from finite element model (FEM) of the bone region of interest. The proximal femur was selected for the initial application of the DLS formula, with a specific focus on the femoral neck. METHODS: The FEM was generated from CAD geometry of a femur using de-identified CT data. The femur was meshed using linear tetrahedral elements Figure (1) with higher mesh densities in the femoral neck region, which is the primary region of interest for the initial application of the DLS formula in concert with the DAP bone remodeling model. Nodal loads were applied to the femoral head and the greater trochanter and the base of the femur was held fixed. An L2 norm study was conducted to reduce the length of the femoral shaft without significantly impacting the stresses in the femoral neck. The material properties of the FEM of the proximal femur were separated between cortical and trabecular regions to work with the bone remodeling model. Determining the elements with cortical material properties in the FEM was based off of publicly available CT hip scans [4] that were segmented, cleaned, and overlaid onto the FEM.

Bone Remodeling↗

NASA NTRS2016

Structural Configuration Systems Analysis for Advanced Aircraft Fuselage Concepts

Structural configuration analysis of an advanced aircraft fuselage concept is investigated. This concept is characterized by a double-bubble section fuselage with rear mounted engines. Based on lessons learned from structural systems analysis of unconventional aircraft, high-fidelity finite-element models (FEM) are developed for evaluating structural performance of three double-bubble section configurations. Structural sizing and stress analysis are applied for design improvement and weight reduction. Among the three double-bubble configurations, the double-D cross-section fuselage design was found to have a relatively lower structural weight. The structural FEM weights of these three double-bubble fuselage section concepts are also compared with several cylindrical fuselage models. Since these fuselage concepts are different in size, shape and material, the fuselage structural FEM weights are normalized by the corresponding passenger floor area for a relative comparison. This structural systems analysis indicates that an advanced composite double-D section fuselage may have a relative structural weight ratio advantage over a conventional aluminum fuselage. Ten commercial and conceptual aircraft fuselage structural weight estimates, which are empirically derived from the corresponding maximum takeoff gross weight, are also presented and compared with the FEM- based estimates for possible correlation. A conceptual full vehicle FEM model with a double-D fuselage is also developed for preliminary structural analysis and weight estimation.

Mukhopadhyay, Vivek↗

NASA NTRS2019

European Service Module - Structural Test Article (E-STA) Building Block Test Approach and Model Correlation Observations

The Orion European Service Module - Structural Test Article (E-STA) underwent sine vibration testing in 2016 using the Mechanical Vibration Facility (MVF) multi-axis shaker system at NASA Glenn Research Center’s (GRC) Plum Brook Station (PBS) Space Power Facility (SPF). The main objective was to verify the structural integrity of the European Service Module (ESM) under sine sweep dynamic qualification vibration testing. A secondary objective was to perform a fixed-base modal survey, while E-STA was still mounted to MVF, in order to achieve a test correlate the finite element model (FEM). To facilitate the E-STA system level correlation effort, a building block test approach was implemented. Modal tests were performed on two major subassemblies, the crew module/launch abort structure (CM/LAS) and the crew module adapter (CMA) mass simulators. These subassembly FEMs were individually correlated and then integrated into the E-STA FEM prior to the start of the E-STA sine vibration test. This paper summarizes the modal testing and model correlation efforts of both of these subassemblies and how the building block approach assisted in the overall correlation of the E-STA FEM. This paper will also cover modeling practices that should be avoided, recommended instrumentation positioning on complex structures, and the importance of the FEM geometrically matching CAD in sufficient detail in order to adequately replicate internal load paths. The goal of this paper is to inform the reader of the hard earned lessons learned and pitfalls to avoid when applying a building block test approach.

Winkel, James P.↗

NASA NTRS2020

Occupant Response Analysis of a Full-Scale Crash Test of a Fokker F28 Fellowship Aircraft

In this report, the capability of component fuselage testing and finite element models (FEMs) to predict occupant injury risk when applied to full-scale aircraft crash testing was evaluated. Component level and full-scale crash tests of a Fokker-F28 aircraft were performed in conjunction with representative FEM simulations. Lumbar spine injury risk, calculated through Anthropomorphic Test Device (ATD) outputs measured in the full-scale test, was compared with predictions made by component level testing and simulations. A quantitative assessment of FEM prediction accuracy was made using the International Organization for Standardization (ISO) Technical Report (TR) 16250 curve comparison methodology. Lumbar load injury risk measured in the full-scale test configuration was found to be significantly higher than in the component tests performed. The FEM provided a closer prediction of occupant injury risk than component testing but exhibited limitations in the multi-axis load environment. This work will help inform the application of component testing and FEM simulation when used to evaluate aircraft crashworthiness.

Jacob B Putnam↗

NASA NTRSDate not supplied

Error Localization Examples: Looking for a Needle in a Hay-stack

Finite element models (FEM) are routinely developed and used during fabrication of high dollar-value hardware. NASA as part of the pre-flight certification of launch vehicles routinely conducts vibration and static tests to calibrate models used for flight-risk assessments. As part of the calibration process, certain areas in the model are modified, using engineering judgment and sensitivity analysis, to match the test results. Unfortunately, tools to identify problem areas in the FEM using test data directly are scarce. Over the years, Error Localization Algorithms (ELA) have been proposed with very limited success. Recently, the Analytical Dynamics Model Improvement (ADMI) algorithm, which computes closed-form mass and stiffness corrections to match the test data exactly, have been shown to be effective for error localization. The paper will present several FEM example problems where ELA is used with simulated test data to determine FEM problem areas. For each example, the correct answer is shown along with ELA results. It is shown that the ELA process is able to identify general problem areas in the FEM, which are consistent with known model perturbations. However, in most cases the ELA identified area of improvement is larger than the true answer. Nonetheless, with proper optimization tools, calibration results using the ELA identified areas provide excellent results.

error localization↗

NASA NTRSDate not supplied

Component Characterization of an eVTOL Reference Model for Crashworthiness Studies

Researchers at the National Aeronautics and Space Administration (NASA) Langley Research Center (LaRC) have conducted a series of structural component and seat level tests to improve finite element model (FEM) characterization of a representative vertical take-off and landing (eVTOL) test article developed by NASA. A full-scale dynamic test was conducted on the representative eVTOL test article in November of 2022. The test article represented a high wing, six passenger eVTOL design concept and is referred to as the lift plus cruise (LPC) test article. The full-scale test identified limitations in the analytical models used to predict aircraft structural response, in particular the composite material models did not effectively capture brittle failure of the structure which were measured during dynamic loading. To better understand the mechanism behind the composite material failure mechanisms observed and to improve the FEM, intact sample specimens of the composite airframe structure were recovered from the test article post-test and used in material characterization testing. In addition, the seat configurations used in the LPC test article were further studied using isolated seat and anthropomorphic test device (ATD) drop tower testing. Dynamic compression tests and three-point bend tests, conducted at varied impact speeds, were performed on the recovered frame section specimens. Additional testing was conducted to characterize the material properties of the forming foam, which remained in the frames after fabrication. These tests were used to improve characterization of the damage and failure parameters of the composite material model used in the FE model of the LPC test article. Seat level tests were conducted on the seats used in the LPC test article using acceleration pulses inclusive of current general aviation and rotorcraft certification load levels as well as conditions representative of those measured at the seat base during the LPC test. The structural material models and seat environment models of the LPC test article FEM were calibrated using the generated component test data. The updates made to these models were then integrated into the LPC FEM and simulated in the full-scale test condition. Results demonstrated the effectiveness of component testing to improve predictive capability of composite aerospace structural models within the crash and dynamic loading environments. Demonstration of the LPC FEM response across an accumulation of coupon, component, seat environment, and full-scale test levels provides confidence in the predictive capability of this model for future use in the study of occupant safety within eVTOL relevant crash environments.

Craswhorthiness↗

NASA NTRSDate not supplied

Component Characterization of an eVTOL Reference Model for Crashworthiness Studies

Craswhorthiness↗

DOE OSTI2024

Classifying topology in photonic crystal slabs with radiative environments

Abstract In the recent years, photonic Chern materials have attracted substantial interest as they feature topological edge states that are robust against disorder, promising to realize defect-agnostic integrated photonic crystal slab devices. However, the out-of-plane radiative losses in those photonic Chern slabs has been previously neglected, yielding limited accuracy for predictions of these systems’ topological protection. Here, we develop a general framework for measuring the topological protection in photonic systems, such as in photonic crystal slabs, while accounting for in-plane and out-of-plane radiative losses. Our approach relies on the spectral localizer that combines the position and Hamiltonian matrices of the system to draw a real-picture of the system’s topology. This operator-based approach to topology allows us to use an effective Hamiltonian directly derived from the full-wave Maxwell equations after discretization via finite-elements method (FEM), resulting in the full account of all the system’s physical processes. As the spectral FEM-localizer is constructed solely from FEM discretization of the system’s master equation, the proposed framework is applicable to any physical system and is compatible with commonly used FEM software. Moving forward, we anticipate the generality of the method to aid in the topological classification of a broad range of complex physical systems.

77 NANOSCIENCE AND NANOTECHNOLOGY↗

NASA NTRS1980

An approach to simulation of the finite element machine

The paper describes the simulation approach for the finite element machine (FEM), a special-purpose computer for structural analysis calculations under development at the NASA-Langley Research Center. The FEM consists of an array (1000 or more) of general-purpose microcomputers performing structural analysis in an asychronous parallel manner. A simulator of sufficient flexibility to model the behavior of the FEM on many levels has been designed and coded, and verification has begun using the experimental FEM hardware. The structure of the simulator is described, and preliminary simulation results are presented.

Sawyer, P. L.↗

NASA NTRS1987

Summary of the modeling and test correlations of a NASTRAN finite element vibrations model for the AH-1G helicopter, task 1

The AH-1G NASTRAN finite element model (FEM) is described and the correlations with measured data that were conducted to verify the model are summarized. Comparisons of the AH-1G NASTRAN FEM calculations with measured data include the following: (1) fuselage and tailboom static load deflection (stiffness) testing, (2) airframe ground vibration testing (0-30 H<), (3) airframe flight vibration testing (main rotor, 2,4, and 6/rev), and (4) tailboom effective skin static testing. A description of the modeling rationale and techniques used to develop the NASTRAN FEM is presented in conjunction with all previous correlation work. In general, the correlations show good agreement between analysis and test in stiffness and vibration response through 15 to 20 Hz. For higher frequencies (equal to or greater than 4/rev (21.6 Hz)), the vibration responses generally did not agree well. Also, the lateral (2/rev (10.8 Hz)) flight vibration responses were much lower in the FEM than test, indicating that there is a significant excitation source other than at the main rotor hub that is affecting the lateral vibrations, such as downwash impingement on the vertical tail.

Cronkhite, J. D.↗

NASA NTRS1989

Fatigue analysis of mini-mast space truss

The functional, structural adequacy of a 20 meter long generic space truss (Mini-Mast), subjected to fatigue loading, was examined with respect to the failure modes which are most likely to occur during services. The space truss is made of thin-walled tubes having unidirectional, zero degree layups of Celanese G50 graphite fibers/Narmco 5217 epoxy composites. The approach used to investigate the most probable failure mode of the truss under fatigue loading is to determine the stress level, including the types of stress, in the member first, then followed by failure mode analysis based on the stress level just determined. To begin, an approximate beam-parameter truss (BPT) model is analyzed first, followed by a detailed analysis of the truss using a finite element model (FEM) run with NASTRAN code. The response results of the BPT model are used to compare FEM results and to check any major deviation of trend derived from the FEM. The purpose of the work was to search available fatigue data of the tube material, to conduct approximate dynamical stress analysis of the BPT model, to run detailed dynamical stress analysis of the FEM model using NASTRAN code, and to predict the fatigue life of the truss member based on limited fatigue data.

Hwang, Shoi Y.↗