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At least 955 records · Page 53

TokaMaker: An open-source time-dependent Grad-Shafranov tool for the design and modeling of axisymmetric fusion devices

Here, in this paper, we present a new static and time-dependent MagnetoHydroDynamic (MHD) equilibrium code, TokaMaker, for axisymmetric configurations of magnetized plasmas, based on the well-known Grad-Shafranov equation. This code utilizes finite element methods on an unstructured triangular grid to enable capturing accurate machine geometry and simple mesh generation from engineering-like descriptions of present and future devices. The new code is designed for ease of use without sacrificing capability and speed through a combination of Python, Fortran, and C/C++ components. A detailed description of the numerical methods of the code, including a novel formulation of the boundary conditions for free-boundary equilibria, and validation of the implementation of those methods using both analytic test cases and cross-code validation is shown. Results show expected convergence across tested polynomial degree for analytic and cross-code test cases.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Illumination-induced modulation of conductivity and Gunn oscillation properties in epitaxial GaAs

In this work, we illuminate a gallium arsenide (GaAs) Gunn device and study the light-induced changes of Gunn oscillation properties. We observe that illumination leads to the modulation of the Gunn threshold voltage, the Gunn oscillation magnitude, and the coherency of Gunn oscillation, with the nature of the modulation being closely related to the position of illumination on the device. These effects are attributed to the generation of optically excited carriers, which results in the modulation of conductivity and the electric field profile along the device. The finite element method is used to simulate the change of the field profile of the Gunn device caused by illumination. We also report an unexpected phenomenon of Gunn oscillation property manipulation with an optical chopper. In addition, wavelength-dependent, power-dependent, and pulsed illumination measurements are performed to help with further understanding the observations.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

A posteriori error analysis of fluid–structure interactions: Time dependent error

A posteriori error analysis is a technique to quantify the error in particular simulations of a numerical approximation method. In this article, we use such an approach to analyze how various error components propagate in certain moving boundary problems. We study quasi-steady state simulations where slowly moving boundaries remain in mechanical equilibrium with a surrounding fluid. Such problems can be numerically approximated with the Method of Regularized Stokelets (MRS), a popular method used for studying viscous fluid–structure interactions, especially in biological applications. Our approach to monitoring the regularization error of the MRS is novel, along with the derivation of linearized adjoint equations to the governing equations of the MRS with a elastic elements. Our main numerical results provide a clear illustration of how the error evolves over time in several MRS simulations.

97 MATHEMATICS AND COMPUTING↗

A three dimensional field formulation, and isogeometric solutions to point and line defects using Toupin's theory of gradient elasticity at finite strains

In this study, we present a field formulation for defects that draws from the classical representation of the cores as force dipoles. We write these dipoles as singular distributions. Exploiting the key insight that the variational setting is the only appropriate one for the theory of distributions, we arrive at universally applicable weak forms for defects in nonlinear elasticity. Remarkably, the standard, Galerkin finite element method yields numerical solutions for the elastic fields of defects that, when parameterized suitably, match very well with classical, linearized elasticity solutions. The true potential of our approach, however, lies in its easy extension to generate solutions to elastic fields of defects in the regime of nonlinear elasticity, and even more notably for Toupin's theory of gradient elasticity at finite strains (Toupin Arch. Ration. Mech. Anal., 11 (1962) 385). In computing these solutions we adopt recent numerical work on an isogeometric analytic framework that enabled the first three-dimensional solutions to general boundary value problems of Toupin's theory (Rudraraju et al. Comput. Methods Appl. Mech. Eng., 278 (2014) 705). We first present exhaustive solutions to point defects, edge and screw dislocations, and a study on the energetics of interacting dislocations. Then, to demonstrate the generality and potential of our treatment, we apply it to other complex dislocation configurations, including loops and low-angle grain boundaries.

36 MATERIALS SCIENCE↗

Interface profile optimization for planar stress wave attenuation in bi-layered plates

Stress waves scatter upon entering a new medium. This occurs due to the reflection and transmission of the waves, which depends on the impedance mismatch between the two materials and the angle of incidence. For a bi-layered structure with finite dimensions and constant impedance ratio, the scattering and intensity of the stress waves may be varied by changing the interface profile between the two layers. In this study, a methodology is proposed for optimizing the interface profile between the layers of a finite bi-layered plate for the objective of planar stress wave attenuation. The bi-layered plates are subjected at one end to highly impulsive loadings with various durations, and the geometry of the internal interface is optimized for the purpose of minimizing the amplitude of the maximum reaction force at the opposite fixed end. The optimization methodology is based on a genetic algorithm, which is coupled with a finite element method for analyzing the wave propagation behavior of the plates. Finally, it is observed that the interface profile and the amount of stress wave attenuation depend on the duration of the applied impulsive loading, with higher amounts of attenuation obtained when the wavelength associated with the impulsive load is small compared to the dimensions of the bi-layered plates.

36 MATERIALS SCIENCE↗

Kernel methods for evolution of generalized parton distributions

Generalized parton distributions (GPDs) characterize the 3-dimensional structure of hadrons, combining information about their internal quark and gluon longitudinal momentum distributions and transverse position within the hadron. The dependence of GPDs on the factorization scale Q 2 allows one to connect hard exclusive processes involving GPDs at disparate energy and momentum scales, which is needed in global analyses of experimental data. Here, in this work, we explore how finite element methods can be used to construct fast and differentiable Q 2 evolution codes for GPDs in momentum space, which can be used in a machine learning framework. We show numerical benchmarks of the methods' accuracy, including a comparison to an existing evolution code from PARTONS/APFEL++, and provide a repository where the code can be accessed.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Smoothed Particle Hydrodynamics Continuous Boundary Force method for Navier-Stokes equations subject to Robin boundary condition

Robin boundary condition for the Navier-Stokes equations is used to model slip conditions at the fluid-solid boundaries. A novel Continuous Boundary Force (CBF) method is proposed for solving the Navier-Stokes equations subject to Robin boundary condition. In the CBF method, the Robin boundary condition at boundary is replaced by the homogeneous Neumann boundary condition at the boundary and a volumetric force term added to the momentum conservation equation. Smoothed Particle Hydrodynamics (SPH) method is used to solve the resulting Navier-Stokes equations. We present solutions for two-dimensional and three-dimensional flows in domains bounded by flat and curved boundaries subject to various forms of the Robin boundary condition. The numerical accuracy and convergence are examined through comparison of the SPH-CBF results with the solutions of finite difference or finite element method. Taken the no-slip boundary condition as a special case of slip boundary condition, we demonstrate that the SPH-CBF method describes accurately both no-slip and slip conditions.

Pan, Wenxiao↗

Adaptive Data-Driven Deep-Learning Surrogate Model for Frontal Polymerization in Dicyclopentadiene

Frontal polymerization (FP) is a self-sustaining curing process that enables rapid and energy-efficient manufacturing of thermoset polymers and composites. Computational methods conventionally used to simulate the FP process are time-consuming, and repeating simulations are required for sensitivity analysis, uncertainty quantification, or optimization of the manufacturing process. Here, in this work, we develop an adaptive surrogate deep-learning model for FP of dicyclopentadiene (DCPD), which predicts the evolution of temperature and degree of cure orders of magnitude faster than the finite-element method (FEM). The adaptive algorithm provides a strategy to select training samples efficiently and save computational costs by reducing the redundancy of FEM-based training samples. The adaptive algorithm calculates the residual error of the FP governing equations using automatic differentiation of the deep neural network. A probability density function expressed in terms of the residual error is used to select training samples from the Sobol sequence space. The temperature and degree of cure evolution of each training sample are obtained by a 2D FEM simulation. The adaptive method is more efficient and has a better prediction accuracy than the random sampling method. With the well-trained surrogate neural network, the FP characteristics (front speed, shape, and temperature) can be extracted quickly from the predicted temperature and degree-of-cure fields.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Overset meshing coupled with hybridizable discontinuous Galerkin finite elements

We introduce the use of hybridizable discontinuous Galerkin (HDG) finite element methods on overlapping (overset) meshes. Overset mesh methods are advantageous for solving problems on complex geometrical domains. We also combine geometric flexibility of overset methods with the advantages of HDG methods: arbitrarily high-order accuracy, reduced size of the global discrete problem, and the ability to solve elliptic, parabolic, and/or hyperbolic problems with a unified form of discretization. This approach to developing the ‘overset HDG’ method is to couple the global solution from one mesh to the local solution on the overset mesh. We present numerical examples for steady convection–diffusion and static elasticity problems. The examples demonstrate optimal order convergence in all primal fields for an arbitrary amount of overlap of the underlying meshes.

42 ENGINEERING↗

Computational Methods to Characterize Panel Loading Conditions for Accelerated Testing

Panel cracking and degradation due to wind loading are known to have a detrimental effect on power output. Recreating these damaging conditions in a controlled experimental setting requires an understanding of the loads being generated at the panel surface as a function of both wind speed, wind direction, and panel orientation. To better understand these relationships, a computational fluid dynamics (CFD) simulation package was constructed using an open-source Python library for solving partial differential equations with the finite element method. This CFD package allows the simulated wind speed and panel orientation of a multi-panel array to be easily changed and provides the capability to measure the traction forces at discrete points along the sun-facing and ground-facing surface of an interior panel residing in the wake of one or more upstream panels. A parameter exploration was performed in which the panel angle was varied in even increments from -70 deg to 70 deg and the wind speed was varied from 2 to 30 m/s. During post processing, the measured traction along the panel surface was averaged spatially and interpreted as a time-varying signal, where further processing of this signal yielded the root mean square amplitude and a characteristic frequency associated with the loading. This study found that higher wind speeds are generally associated with increased amplitude of loading and that the panel orientation angle can significantly exacerbate or mitigate this loading. These outcomes are presented along with current work on higher-fidelity verification simulations and recommendations for performing accelerated experimental testing.

loading↗

A three-dimensional meso-macroscopic model for Li-Ion intercalation batteries

Through this study, we present a three-dimensional computational formulation for electrode-electrolyte-electrode system of Li-Ion batteries. The physical consistency between electrical, thermal and chemical equations is enforced at each time increment by driving the residual of the resulting coupled system of nonlinear equations to zero. The formulation utilizes a rigorous volume averaging approach typical of multiphase formulations used in other fields and recently extended to modeling of supercapacitors [1]. Unlike existing battery modeling methods which use segregated solution of conservation equations and idealized geometries, our unified approach can model arbitrary battery and electrode configurations. The consistency of multi-physics solution also allows for consideration of a wide array of initial conditions and load cases. The formulation accounts for spatio-temporal variations of material and state properties such as electrode/void volume fractions and anisotropic conductivities. The governing differential equations are discretized using the finite element method and solved using a nonlinearly consistent approach that provides robust stability and convergence. The new formulation was validated for standard Li-ion cells and compared against experiments. Finally, its scope and ability to capture spatio-temporal variations of potential and lithium distribution is demonstrated on a prototypical three-dimensional electrode problem.

25 ENERGY STORAGE↗

Pressure Self-focusing Effect and Novel Methods for Increasing the Maximum Pressure in Traditional and Rotational Diamond Anvil Cells

The main principles of producing a region near the center of a sample, compressed in a diamond anvil cell (DAC), with a very high pressure gradient and, consequently, with high pressure are predicted theoretically. The revealed phenomenon of generating extremely high pressure gradient is called the pressure self-focusing effect. Initial analytical predictions utilized generalization of a simplified equilibrium equation. Then, the results are refined using our recent advanced model for elastoplastic material under high pressures in finite element method (FEM) simulations. The main points in producing the pressure self-focusing effect are to use beveled anvils and reach a very thin sample thickness at the center. We find that the superposition of torsion in a rotational DAC (RDAC) offers drastic enhancement of the pressure self-focusing effect and allows one to reach the same pressure under a much lower force and deformation of anvils.

42 ENGINEERING↗

Utilizing computer vision and artificial intelligence algorithms to predict and design the mechanical compression response of direct ink write 3D printed foam replacement structures

Additive Manufacturing (AM) of porous polymeric materials, such as foams, recently became a topic of intensive research due their unique combination of low density, impressive mechanical properties, and stress dissipation capabilities. Conventional methods for fabricating foams rely on complex and stochastic processes, making it challenging to achieve precise architectural control of structured porosity. In contrast, AM provides access to a wide range of printable materials, where precise spatial control over structured porosity can be modulated during the fabrication process enabling the production of foam replacement structures (FRS). Current approaches for designing FRS are based on intuitive understanding of their properties or an extensive number of finite element method (FEM) simulations. These approaches, however, are computationally expensive and time consuming. As such, in this work, we present a novel methodology for determining the mechanical compression response of direct ink write (DIW) 3D printed FRS using a simple cross-sectional image. By obtaining measurement data for a relatively small number of samples, an artificial neural network (ANN) was trained, and a computer vision algorithm was used to make inferences about foam compression characteristics from a single cross-sectional image. Finally, a genetic algorithm (GA) was used to solve the inverse design problem, generating the AM printing parameters that an engineer should use to achieve a desired compression response from a DIW printed FRS. The methods developed herein present an avenue for entirely autonomous design and analysis of additively manufactured structures using artificial intelligence.

36 MATERIALS SCIENCE↗

BISON: A Flexible Code for Advanced Simulation of the Performance of Multiple Nuclear Fuel Forms

BISON is a nuclear fuel performance application built using the Multiphysics Object-Oriented Simulation Environment (MOOSE) finite element library. One of its major goals is to have a great amount of flexibility in how it is used, including in the types of fuel it can analyze, the geometry of the fuel being modeled, the modeling approach employed, and the dimensionality and size of the models. Fuel forms that can be modeled include standard light water reactor fuel, emerging light water reactor fuels, tri-structural isotropic fuel particles, and metallic fuels. BISON is a platform for research in nuclear fuel performance modeling while simultaneously serving as a tool for the analysis of nuclear fuel designs. Recent research in BISON includes techniques such as the extended finite element method for fuel cracking, exploration of high-burnup light water reactor fuel behavior, swelling behavior of metallic fuels, and central void formation in mixed-oxide fuel. BISON includes integrated documentation for each of its capabilities, follows rigorous software quality assurance procedures, and has a growing set of rigorous verification and validation tests.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

Design-order, non-conformal low-Mach fluid algorithms using a hybrid CVFEM/DG approach

Here, a hybrid, design-order sliding mesh algorithm, which uses a control volume finite element method (CVFEM), in conjunction with a discontinuous Galerkin (DG) approach at non-conformal interfaces, is outlined in the context of a low-Mach fluid dynamics equation set. This novel hybrid DG approach is also demonstrated to be compatible with a classic edge-based vertex centered (EBVC) scheme. For the CVFEM, element polynomial, P , promotion is used to extend the low-order P = 1 CVFEM method to higher-order, i.e., P = 2. An equal-order low-Mach pressure-stabilized methodology, with emphasis on the non-conformal interface boundary condition, is presented. A fully implicit matrix solver approach that accounts for the full stencil connectivity across the non-conformal interface is employed. A complete suite of formal verification studies using the method of manufactured solutions (MMS) is performed to verify the order of accuracy of the underlying methodology. The chosen suite of analytical verification cases range from a simple steady diffusion system to a traveling viscous vortex across mixed-order non-conformal interfaces. Results from all verification studies demonstrate either second- or third-order spatial accuracy and, for transient solutions, second-order temporal accuracy.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

A method to generate conformal finite-element meshes from 3D measurements of microstructurally small fatigue-crack propagation [A method to generate conformal finite-element meshes from 3D measurements of microstructurally small fatigue-crack propagation: 3D Meshes of Microstructurally Small Crack Growth]

In an effort to reproduce computationally the observed evolution of microstructurally small fatigue cracks (MSFCs), a method is presented for generating conformal, finite-element (FE), volume meshes from 3D measurements of MSFC propagation. The resulting volume meshes contain traction-free surfaces that conform to incrementally measured 3D crack shapes. Grain morphologies measured using near-field high-energy X-ray diffraction microscopy are also represented within the FE volume meshes. Proof-of-concept simulations are performed to demonstrate the utility of the mesh-generation method. The proof-of-concept simulations employ a crystal-plasticity constitutive model and are performed using the conformal FE meshes corresponding to successive crack-growth increments. Although the simulations for each crack increment are currently independent of one another, they need not be, and transfer of material-state information among successive crack-increment meshes is discussed. The mesh-generation method was developed using post-mortem measurements, yet it is general enough that it can be applied to in-situ measurements of 3D MSFC propagation.

36 MATERIALS SCIENCE↗

Optimization of Air-Gap Profile in Interior Permanent-Magnet Synchronous Motors for Torque Ripple Mitigation

Interior permanent magnet synchronous motors (IPMSMs) have been widely used due to their high efficiency and high power density. Minimization of torque pulsation resulting in vibration and acoustic noise is one of the important design considerations for IPMSMs. In this paper, a grid on/off search method for the rotor profile is proposed to mitigate torque pulsation. Selection of the rotor profile is due to the fact that air-gap is the most sensitive parameter in electric machines wherein changes in flux densities can cause substantial differences in the distribution of forces. A layer comprised of 20 partitions with a 0.1 mm thickness and 3 degrees wide grids have been introduced to the rotor surface for each pole and the possible geometries have been analyzed using finite element method (FEM) in ANSYS Maxwell. An optimal design was found that has the lowest torque ripple with a higher average torque compared to the original design. Genetic algorithm (GA) has also been applied to the method to automate the coupling between Maxwell and Matlab thereby saving the simulation time. Finally, complete structural analysis has been done for both of the original and optimal designs to verify the superiority and feasibility of the proposed design.

42 ENGINEERING↗

Delamination imaging in composites using cross-correlation method by non-contact air-coupled Lamb waves

Abstract This paper presents a cross-correlation damage detection technique using damage scattered waves of all directions cross-correlate with the incident waves for delamination imaging in carbon fiber reinforced polymer (CFRP) composite plate. The presented imaging can not only detect the delamination but also precisely quantify the damage with locations and sizes. First, a CFRP composite sample with interlaminar delamination by inserting the Teflon layer is designed and manufactured in house using the hot-press machine. And a three-dimensional model of composite sample is simulated using the finite element method. Next, the cross-correlation imaging algorithm is introduced in detail, and the cross-correlation imaging proof-of-concept study is conducted with the simulated Lamb waves in the composite sample. Finally, a fully non-contact air-coupled transducer and scanning laser Doppler vibrometer system with a single-mode Lamb wave method is established to actuate and sense the interrogating Lamb waves in the structure. The imaging method is experimentally implemented for the one delamination and two delaminations imaging and quantification.

Instruments & Instrumentation↗