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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 37 records · Page 2
All sourcesNASA NTRSDOE OSTI
DOE OSTI2024

Image-based modeling of coupled electro-chemo-mechanical behavior of Li-ion battery cathode using an interface-modified reproducing kernel particle method

Abstract An interface-modified reproducing kernel particle method (IM-RKPM) is introduced in this work to allow for a direct model construction from image pixels of heterogeneous polycrystalline Li-ion battery microstructures. The interface-modified reproducing kernel (IM-RK) approximation is constructed through scaling of a kernel function by a regularized distance function in conjunction with strategic placement of interface node locations. This leads to RK shape functions with either weak or strong discontinuities across material interfaces, suitable for modeling various interface mechanics. With the placement of a triple junction node and distance-based scaling of kernel functions, the resulting IM-RK shape function also possesses proper discontinuities at the triple junctions. This IM-RK approximation effectively remedies the well-known Gibb’s oscillation in the smooth approximation of discontinuities. Different from the conventional meshfree approaches for interface discontinuities, this IM-RK approach is done without additional degrees of freedom associated with the enrichment functions, and it is formulated with the standard procedures in the RK shape function construction. This work focuses on identifying the accuracy and convergence properties of IM-RKPM for modeling the coupled electro-chemo-mechanical system. A linear patch test is formulated and numerically tested for the electro-chemo-mechanical coupled problem with a Butler–Volmer boundary condition representing the physical conditions in Li-ion battery microstructures. This is followed by verification of the optimal rates of convergence of IM-RKPM for solving the coupled problem with higher order solutions. The image-based modeling of Li-ion battery microstructures in the numerical examples demonstrates the applicability of the proposed method to realistic Li-ion battery materials modeling.

25 ENERGY STORAGE↗
NASA NTRS1988

Time-domain transient elastodynamic analysis of 3-D solids by BEM

The BEM algorithm developed by Banerjee and Ahmad (1985) and Banerjee et al. (1986) for the analysis of three-dimensional time-dependent elastodynamics problems is extended and refined to improve the accuracy of the internal stress predictions. A quadratic spatial shape function and a linear temporal shape function are employed, and the complete numerical implementation (as part of BEST3D) is outlined. Applications of the improved BEM to typical problems are presented graphically and briefly characterized. Included are spherical cavities subjected to sudden radial expansion, triangular or rectangular pulses of radial pressure, or ramp loading; a circular loaded area on a half space; and a flexible square plate foundation on an elastic half space.

Ahmad, S.↗
DOE OSTI2021

Independent normalization for γ -ray strength functions: The shape method

Here, the shape method, a novel approach to obtain the functional form of the γ-ray strength function (γSF), is introduced. In connection with the Oslo method the slope of the nuclear level density (NLD) and γSF can be obtained simultaneously even in the absence of neutron resonance spacing data. The foundation of the shape method lies in the primary γ-ray transitions which preserve information on the functional form of the γSF. The shape method has been applied to 56 Fe, 92 Zr, and 164 Dy, which are representative cases for the variety of situations encountered in typical NLD and γSF studies. The comparisons of results from the shape method to those from the Oslo method demonstrate that the functional form of the γSF is retained regardless of nuclear structure details or J π values of the states fed by the primary transitions.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
NASA NTRS2013

Large-Deformation Displacement Transfer Functions for Shape Predictions of Highly Flexible Slender Aerospace Structures

Large deformation displacement transfer functions were formulated for deformed shape predictions of highly flexible slender structures like aircraft wings. In the formulation, the embedded beam (depth wise cross section of structure along the surface strain sensing line) was first evenly discretized into multiple small domains, with surface strain sensing stations located at the domain junctures. Thus, the surface strain (bending strains) variation within each domain could be expressed with linear of nonlinear function. Such piecewise approach enabled piecewise integrations of the embedded beam curvature equations [classical (Eulerian), physical (Lagrangian), and shifted curvature equations] to yield closed form slope and deflection equations in recursive forms.

Deflection equations↗
NASA NTRS2012

New Vary-Chap Profile of the Topside Ionosphere Electron Density Distribution for use with the IRI Model and the GIRO Real-Time Data

A new Vary-Chap function is introduced for the empirical modeling of the electron density N(h) profile in the topside ionosphere that uses a shape function S(h) in the generalized Chapman function. The Vary-Chap profile extends the bottomside profile that is specified by the IRI model or measured by the Global Ionospheric Radio Observatory (GIRO) to the altitude of the ISIS-2 satellite. Some 80,000 topside profiles, measured by the topside sounder on the ISIS-2 satellite were analyzed, and the shape function S(h) was calculated for each profile. A parameterized function S*(h), composed of two sub-functions S1(h) and S2(h), is fitted to the measured S(h) profile using three free parameters. At altitudes just above the F2 layer peak height hmF2, the shape function S1 controls S(h), and at greater altitudes S2 controls S(h). The height of the intersection of S1 and S2 is defined as the transition height h(sub T) indicating the transition from an O(+) to an H(+)-dominated profile shape. The observed transition heights range from approx.500 km to 800 km.

Nsumei, Patrick↗
DOE OSTI2024

Shape restricted additive hazards models: Monotone, unimodal, and U‐shape hazard functions

We consider estimation of the semiparametric additive hazards model with an unspecified baseline hazard function where the effect of a continuous covariate has a specific shape but otherwise unspecified. Such estimation is particularly useful for a unimodal hazard function, where the hazard is monotone increasing and monotone decreasing with an unknown mode. A popular approach of the proportional hazards model is limited in such setting due to the complicated structure of the partial likelihood. Our model defines a quadratic loss function, and its simple structure allows a global Hessian matrix that does not involve parameters. Thus, once the global Hessian matrix is computed, a standard quadratic programming method can be applicable by profiling all possible locations of the mode. However, the quadratic programming method may be inefficient to handle a large global Hessian matrix in the profiling algorithm due to a large dimensionality, where the dimension of the global Hessian matrix and number of hypothetical modes are the same order as the sample size. We propose the quadratic pool adjacent violators algorithm to reduce computational costs. The proposed algorithm is extended to the model with a time‐dependent covariate with monotone or U‐shape hazard function. In simulation studies, our proposed method improves computational speed compared to the quadratic programming method, with bias and mean square error reductions. We analyze data from a recent cardiovascular study.

Mathematical & Computational Biology↗
DOE OSTI2022

A symbolic framework to obtain mid-fidelity models of flexible multibody systems with application to horizontal-axis wind turbines

Abstract. The article presents a symbolic framework (also called computer algebra program) that is used to obtain, in symbolic mathematical form, the linear and nonlinear equations of motion of a mid-fidelity multibody system including rigid and flexible bodies. Our approach is based on Kane's method and a nonlinear shape function representation for flexible bodies. The shape function approach does not represent the state of the art for flexible multibody dynamics but is an effective trade-off to obtain mid-fidelity models with few degrees of freedom, taking advantage of the separation of space and time. The method yields compact symbolic equations of motion with implicit account of the constraints. The general and automatic framework facilitates the creation and manipulation of models with various levels of complexity by adding or removing degrees of freedom. The symbolic treatment allows for analytical gradients and linearized equations of motion. The linear and nonlinear equations can be exported to Python code or dedicated software. There are multiple applications, such as time domain simulation, stability analyses, frequency domain analyses, advanced controller design, state observers, and digital twins. In this article, we describe the method we used to systematically generate the equations of motion of multibody systems and present the implementation of the framework using the Python package SymPy. We apply the framework to generate illustrative land-based and offshore wind turbine models. We compare our results with OpenFAST simulations and discuss the advantages and limitations of the method. The Python implementation is provided as an open-source project.

Branlard, Emmanuel (ORCID:0000000277506128)↗
DOE OSTI2022

A deformation-dependent coupled Lagrangian/semi-Lagrangian meshfree hydromechanical formulation for landslide modeling

Abstract The numerical modelling of natural disasters such as landslides presents several challenges for conventional mesh-based methods such as the finite element method (FEM) due to the presence of numerically challenging phenomena such as severe material deformation and fragmentation. In contrast, meshfree methods such as the reproducing kernel particle method (RKPM) possess unique features conducive to modelling extreme events such as the absence of a structured mesh and the ease of adaptive refinement, among others. While the semi-Lagrangian reproducing kernel (SL-RK) shape functions of RKPM defined in the current configuration have proven to be effective in extreme event modelling, the computational cost for the re-evaluation of the shape functions at every time step is costly. In this work, a deformation-dependent coupling of the Lagrangian reproducing kernel (L-RK) and SL-RK approximations is proposed for the solution of a hydro-mechanical formulation for effective simulations of landslides. The ramp function is constructed based on an equivalent plastic strain as a deformation-dependent transition from L-RK shape functions to SL-RK ones as the deformation progresses. The particular focus of the paper will be on modelling seepage-induced landslides with a mixed $$u$$ u – $$p$$ p formulation to couple the solid and fluid phases. Examples are presented to examine the effectiveness of this coupled Lagrangian/semi-Lagrangian reproducing kernel (L–SL RK) formulation and to highlight its performance in landslide modelling.

Baek, Jonghyuk↗
DOE OSTI2021

Higher-order particle representation for particle-in-cell simulations

In this paper we present an alternative approach to the representation of simulation particles for unstructured electrostatic and electromagnetic PIC simulations. In our modified PIC algorithm we represent particles as having a smooth shape function limited by some specified finite radius, r 0 . A unique feature of our approach is the representation of this shape by surrounding simulation particles with a set of virtual particles with delta shape, with fixed offsets and weights derived from Gaussian quadrature rules and the value of r 0 . As the virtual particles are purely computational, they provide the additional benefit of increasing the arithmetic intensity of traditionally memory bound particle kernels. The modified algorithm is implemented within Sandia National Laboratories' unstructured EMPIRE-PIC code, for electrostatic and electromagnetic simulations, using periodic boundary conditions. We show results for a representative set of benchmark problems, including electron orbit, a transverse electromagnetic wave propagating through a plasma, numerical heating, and a plasma slab expansion. In this work, good error reduction across all of the chosen problems is achieved as the particles are made progressively smoother, with the optimal particle radius appearing to be problem-dependent.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2020

Regression Based Approach for Robust Finite Element Analysis on Arbitrary Grids. LDRD Final Report

This report summarizes the work performed under a one-year LDRD project aiming to enable accurate and robust numerical simulation of partial differential equations for meshes that are of poor quality. Traditional finite element methods use the mesh to both discretize the geometric domain and to define the finite element shape functions. The latter creates a dependence between the quality of the mesh and the properties of the finite element basis that may adversely affect the accuracy of the discretized problem. In this project, we propose a new approach for defining finite element shape functions that breaks this dependence and separates mesh quality from the discretization quality. At the core of the approach is a meshless definition of the shape functions, which limits the purpose of the mesh to representing the geometric domain and integrating the basis functions without having any role in their approximation quality. The resulting non-conforming space can be utilized within a standard discontinuous Galerkin framework providing a rigorous foundation for solving partial differential equations on low-quality meshes. We present a collection of numerical experiments demonstrating our approach in a wide range of settings: strongly coercive elliptic problems, linear elasticity in the compressible regime, and the stationary Stokes problem. We demonstrate convergence for all problems and stability for element pairs for problems which usually require inf-sup compatibility for conforming methods, also referring to a minor modification possible through the symmetric interior penalty Galerkin framework for stabilizing element pairs that would otherwise be traditionally unstable. Mesh robustness is particularly critical for elasticity, and we provide an example that our approach provides a greater than 5x improvement in accuracy and allows for taking an 8x larger stable timestep for a highly deformed mesh, compared to the continuous Galerkin finite element method. The report concludes with a brief summary of ongoing projects and collaborations that utilize or extend the products of this work.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

A discontinuous piecewise polynomial generalized moving least squares scheme for robust finite element analysis on arbitrary grids

A variational approach is developed with a meshless discretization to enable accurate and robust numerical simulation of partial differential equations for meshes that are of poor quality. Traditional finite element methods use the mesh to both discretize the geometric domain and to define the finite element shape functions. The latter creates a dependence between the quality of the mesh and the properties of the finite element basis that may adversely affect the accuracy of the discretized problem. Here, we propose a new approach for defining finite element shape functions that breaks this dependence and separates mesh quality from the discretization quality, which we call discontinuous piecewise polynomial generalized moving least squares (DPP-GMLS). At the core of the approach is a meshless definition of the shape functions, which limits the purpose of the mesh to representing the geometric domain and integrating the basis functions without having any role in their approximation quality. The resulting non-conforming space can be utilized within a standard discontinuous Galerkin framework, providing a rigorous foundation for solving partial differential equations on low-quality meshes. We present a collection of numerical experiments demonstrating our approach in a wide range of settings: strongly coercive elliptic problems, linear elasticity in the compressible regime, and the stationary Stokes problem. We demonstrate convergence for all problems and stability for element pairs for problems which usually require inf-sup compatibility for conforming methods, also referring to a minor modification possible through the symmetric interior penalty Galerkin framework for stabilizing element pairs that would otherwise be traditionally unstable. Mesh robustness is particularly critical for elasticity, and we provide an example that our approach provides a greater than 5 x improvement in accuracy and allows for taking an 8 x larger stable timestep for a highly deformed mesh, compared to the continuous Galerkin finite element method.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

A cohesive zone treatment for the material point method involving problems of large deformation and damage

A new algorithm is described that permits the use of cohesive zones in the material point method for problems involving large deformation and fracture. In contrast to previous cohesive zone implementations, this method does not utilize massless surface-element particles. Instead, cohesive tractions are computed using the shape function mappings from a reference grid configuration in combination with explicitly defined particle surface normals and surface positions. These normals and relative surface positions are updated each time step according to particle deformation. The tractions are converted to cohesive forces using the nodal areas and mapped back to particles using the same reference shape function mappings. These forces are then remapped by conventional particle-to-grid interpolation as external forces using the current-configuration shape-function mappings. This allows highly compliant cohesive zones to function over jump displacements larger than a grid cell. Upon damage, these interfaces can revert to conventional multi-field contact surfaces. This approach is general and readily applies to two and three dimensions as well as being compatible with damage-field gradient partitioning offering exceptional computational flexibility. The framework for this method enables other capabilities, such as improved contact precision using explicitly defined surface normals and positions, and a method to mitigate spurious material damage at weak discontinuities between stiff brittle materials and soft or compliant materials.

Cohesive zone↗
NASA NTRS1975

Spectral characteristics of digital phase-modulated signals

The power spectral density of two-level digital phase modulated signals is determined using various polar pulse shaping functions, the only restriction being that the pulses are independent and do not overlap. Rectangular pulses and pulses having finite rise and decay times are considered. It is shown that a substantial improvement in terms of minimizing spectral occupancy on a power basis over a given frequency band can be achieved by using linear and raised cosine pulse shaping functions. Further, the rate of decrease of the power spectral density is given for the asymptotic limit as f goes to infinity. The use of these and possibly other well chosen pulse shaping functions can then provide an additional aid to overall efficient spectrum utilization and management.

Mcgregor, D. N.↗
NASA NTRS2011

An Estimate of the Size and Shape of Sunspot Cycle 24 Based on its Early Cycle Behavior using the Hathaway-Wilson-Reichmann Shape-Fitting Function

On the basis of 12-month moving averages (12-mma) of monthly mean sunspot number (R), sunspot cycle 24 had its minimum amplitude (Rm = 1.7) in December 2008. At 12 mo past minimum, R measured 8.3, and at 18 mo past minimum, it measured 16.4. Thus far, the maximum month-to-month rate of rise in 12-mma values of monthly mean sunspot number (AR(t) max) has been 1.7, having occurred at elapsed times past minimum amplitude (t) of 14 and 15 mo. Compared to other sunspot cycles of the modern era, cycle 24?s Rm and AR(t) max (as observed so far) are the smallest on record, suggesting that it likely will be a slow-rising, long-period sunspot cycle of below average maximum amplitude (RM). Supporting this view is the now observed relative strength of cycle 24?s geomagnetic minimum amplitude as measured using the 12-mma value of the aa-geomagnetic index (aam = 8.4), which also is the smallest on record, having occurred at t equals 8 and 9 mo. From the method of Ohl (the inferred preferential association between RM and aam), one predicts RM = 55 +/- 17 (the ?1 se prediction interval) for cycle 24. Furthermore, from the Waldmeier effect (the inferred preferential association between the ascent duration (ASC) and RM) one predicts an ASC longer than 48 mo for cycle 24; hence, maximum amplitude occurrence should be after December 2012. Application of the Hathaway-Wilson-Reichmann shape-fitting function, using an RM = 70 and ASC = 56 mo, is found to adequately fit the early sunspot number growth of cycle 24.

Wilson, Robert M.↗
NASA NTRS1987

A finite element computational method for high Reynolds number laminar flows

A velocity-pressure integrated, mixed interpolation, Galerkin finite element method for the Navier-Stokes equations is presented. In the method, the velocity variables are interpolated using complete quadratic shape functions, and the pressure is interpolated using linear shape functions which are defined on a triangular element for the two-dimensional case and on a tetrahedral element for the three-dimensional case. The triangular element and the tetrahedral element are contained inside the complete bi- and tri-quadratic elements for velocity variables for two and three dimensional cases, respectively, so that the pressure is discontinuous across the element boundaries. Example problems considered include: a cavity flow of Reynolds numbers 400 through 10,000; a laminar backward facing step flow; and a laminar flow in a square duct of strong curvature. The computational results compared favorably with the finite difference computational results and/or experimental data available. It was found that the present method can capture the delicate pressure driven recirculation zones, that the method did not yield any spurious pressure modes, and that the method requires fewer grid points than the finite difference methods to obtain comparable computational results.

Kim, Sang-Wook↗
NASA NTRS1988

A velocity-pressure integrated, mixed interpolation, Galerkin finite element method for high Reynolds number laminar flows

A velocity-pressure integrated, mixed interpolation, Galerkin finite element method for the Navier-Stokes equations is presented. In the method, the velocity variables were interpolated using complete quadratic shape functions and the pressure was interpolated using linear shape functions. For the two dimensional case, the pressure is defined on a triangular element which is contained inside the complete biquadratic element for velocity variables; and for the three dimensional case, the pressure is defined on a tetrahedral element which is again contained inside the complete tri-quadratic element. Thus the pressure is discontinuous across the element boundaries. Example problems considered include: a cavity flow for Reynolds number of 400 through 10,000; a laminar backward facing step flow; and a laminar flow in a square duct of strong curvature. The computational results compared favorable with those of the finite difference methods as well as experimental data available. A finite elememt computer program for incompressible, laminar flows is presented.

Kim, Sang-Wook↗
NASA NTRS1988

A fine grid finite element computation of two-dimensional high Reynolds number flows

A velocity-pressure-integrated mixed-interpolation Galerkin finite-element computation of the Navier-Stokes equations using the grids is presented. The velocity variables are interpolated using complete quadratic shape functions, and the pressure was interpolated using linear shape functions defined on a triangular element which is contained inside the quadratic element for velocity variables. Comprehensive computational results for a cavity flow at Reynolds number Re = 400-10,000 and a laminar backward-facing step flow at Re = 100-900 are presented. Many high-Re flows involve convection-dominated motion as well as diffusion-dominated motion in the flow domain. The computational results for both of the fluid motions compared favorably with high-accuracy finite-difference computational results and/or experimental data.

Kim, Sang-Wook↗
NASA NTRS1989

Neural networks for data compression and invariant image recognition

An approach to invariant image recognition (I2R), based upon a model of biological vision in the mammalian visual system (MVS), is described. The complete I2R model incorporates several biologically inspired features: exponential mapping of retinal images, Gabor spatial filtering, and a neural network associative memory. In the I2R model, exponentially mapped retinal images are filtered by a hierarchical set of Gabor spatial filters (GSF) which provide compression of the information contained within a pixel-based image. A neural network associative memory (AM) is used to process the GSF coded images. We describe a 1-D shape function method for coding of scale and rotationally invariant shape information. This method reduces image shape information to a periodic waveform suitable for coding as an input vector to a neural network AM. The shape function method is suitable for near term applications on conventional computing architectures equipped with VLSI FFT chips to provide a rapid image search capability.

Gardner, Sheldon↗