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NASA NTRS1988

Stress-intensity factors for small surface and corner cracks in plates

Three-dimensional finite-element and finite-alternating methods were used to obtain the stress-intensity factors for small surface and corner cracked plates subjected to remote tension and bending loads. The crack-depth-to-crack-length ratios (a/c) ranged from 0.2 to 1 and the crack-depth-to-plate-thickness ratios (a/t) ranged from 0.05 to 0.2. The performance of the finite-element alternating method was studied on these crack configurations. A study of the computational effort involved in the finite-element alternating method showed that several crack configurations could be analyzed with a single rectangular mesh idealization, whereas the conventional finite-element method requires a different mesh for each configuration. The stress-intensity factors obtained with the finite-element-alternating method agreed well (within 5 percent) with those calculated from the finite-element method with singularity elements.

Raju, I. S.↗

NASA NTRS1989

Stress-intensity factors for small surface and corner cracks in plates

Raju, Ivatury S.↗

DOE OSTI2021

Numerical and Analytical Modeling of the Effect of Cracks on the Self-Inductance of a COTS YJ-41003-TC Toroid

COTS inductors and transformers often contain partial cracks whose effect on inductance, a key performance parameter, have not been carefully studied. In this report, the effects of both partial and complete cracks on the self-inductance of a 100 turn square cross section COTS YJ-41003-TC toroid comprised of J Material was comprehensively investigated using both analytically derived closed form expressions and 3D computational techniques employing commercial codes. Both partial (half-penny) and complete (air gap) cracks of 10 and 25 μm were investigated. The crack is defined as the physical distance between two faces of the toroid's magnetic core, such that the surface normal of either face is along the Φ-direction, in alignment with the B-field. For the purposes of validation, two different approaches were incorporated for both the analytical and numerical models. The two analytical methods are comprised of a first principles approach based on the physics of electromagnetics, as well as linear circuit theory. The former directly utilizes the integral form of Maxwell's equations while the latter exploits the interchangeable relationship between electric and magnetic circuits. Validation within the computational scheme is realized through a code-to-code comparison between commercial solvers, COMSOL Multiphysics and CST, with the former employing the Finite Element Method (FEM) and the latter the Finite Difference Time Domain (FDTD) technique. Sound agreement between all four methods (ie., two analytical and two numerical) is observed, with results indicating that only a perturbation in self-inductance occurs for the half-penny cracks, while a substantial reduction takes place for the case of complete cracks. It is important to note that even though a static μ r is applied, representing the linear region of the BH curve (based on manufacturer specifications), the complete crack results still place a lower conservative bound on the inductance. This follows from the fact that even in the case of a half-penny crack, if the magnetic core portion of the crack approaches saturation, the crack begins to behave like an air gap, or complete crack. When an air gap is introduced into a magnetic core, a substantial reduction in inductance can occur due to the significant difference in permeabilities between the two mediums (ie., μ core >> μ air ). The once intact bulk magnetic core of the toroid essentially begins to behave like an air core.

36 MATERIALS SCIENCE↗

NASA NTRS1990

General Rotorcraft Aeromechanical Stability Program (GRASP): Theory manual

The general rotorcraft aeromechanical stability program (GRASP) was developed to calculate aeroelastic stability for rotorcraft in hovering flight, vertical flight, and ground contact conditions. GRASP is described in terms of its capabilities and its philosophy of modeling. The equations of motion that govern the physical system are described, as well as the analytical approximations used to derive them. The equations include the kinematical equation, the element equations, and the constraint equations. In addition, the solution procedures used by GRASP are described. GRASP is capable of treating the nonlinear static and linearized dynamic behavior of structures represented by arbitrary collections of rigid-body and beam elements. These elements may be connected in an arbitrary fashion, and are permitted to have large relative motions. The main limitation of this analysis is that periodic coefficient effects are not treated, restricting rotorcraft flight conditions to hover, axial flight, and ground contact. Instead of following the methods employed in other rotorcraft programs. GRASP is designed to be a hybrid of the finite-element method and the multibody methods used in spacecraft analysis. GRASP differs from traditional finite-element programs by allowing multiple levels of substructure in which the substructures can move and/or rotate relative to others with no small-angle approximations. This capability facilitates the modeling of rotorcraft structures, including the rotating/nonrotating interface and the details of the blade/root kinematics for various types. GRASP differs from traditional multibody programs by considering aeroelastic effects, including inflow dynamics (simple unsteady aerodynamics) and nonlinear aerodynamic coefficients.

Hodges, Dewey H.↗

DOE OSTI2020

Plate motion in sheared granular fault system

Plate motion near the fault gouge layer, and the elastic interplay between the gouge layer and the plate under stick-slip conditions, is key to understanding the dynamics of sheared granular fault systems. Here, a two-dimensional implementation of the combined finite-discrete element method (FDEM), which merges the finite element method (FEM) and the discrete element method (DEM), is used to explicitly simulate a sheared granular gouge fault system. In this work we focus on investigating the influence of normal load, driving shear velocity and plate stiffness on the velocities and displacements in the direction parallel to the shear direction (x-direction) measured at locations on the upper and lower plates just adjacent to the gouge. The simulations show that during slip phases the magnitudes of the measured velocities on the upper and lower plates are proportional to the normal load and may be inversely proportional to the square root of the plate's shear modulus. Whereas, the driving shear velocity does not show distinct influence on the measured velocities. Additionally, large slip velocities are generally associated with large macroscopic friction coefficient drops. For the models subjected to smaller normal loads, larger shear velocities and with stiffer shear plates, the same magnitude of slip velocity could cause a larger drop of macroscopic friction coefficient. During stick phases, the velocities of the upper and lower plates are respectively slightly greater and slightly smaller than half of the driving shear velocity and are both in the same direction of shear. The shear strain rate of the gouge is calculated from this velocity difference between the upper and lower plate during stick phases and thus the gouge effective shear modulus can be calculated. The results show that the gouge effective shear modulus increases proportionally with normal load, while the influence of shear velocity and plate stiffness on gouge effective shear modulus is minor. The simulations address the dynamics of a laboratory-scale fault gouge system and may aid in revealing the complexities of earthquake frictional dynamics.

58 GEOSCIENCES↗

DOE OSTI2021

A modular methodology for time-domain stochastic seismic wave propagation

Presented here is a modular methodology for time-domain stochastic seismic wave propagation analysis. Presented methodology is designed to analyse uncertain seismic motions as an input, propagating through uncertain material. Traditional approach for uncertain wave propagation relies on models that include deep bedrock, local soil site, and their random process and random field information. Such models can become quite large and computationally intractable. The modular approach proposed herein features two step approach that allows separate consideration of the deep bedrock and local site along with corresponding random field information. In this work, the first step considers an auxiliary stochastic motions problem in the bedrock. Stochastic local site response can then be simulated in a reduced domain within certain depth from the surface. Application of uncertain seismic motions at depth, for local uncertain site response is done using stochastic effective forces developed through the Domain Reduction Method. By using Hermite polynomial chaos expansion to represent the non-Gaussian random field of material parameters and non-stationary random process of seismic motion, the proposed modular methodology is formulated using intrusive stochastic Galerkin approach, as seen in the Stochastic Elastic–Plastic Finite Element Method (SEPFEM). Developed modular methodology is illustrated using a 1-D stochastic seismic wave propagation analysis with three cases, and simulation results are also verified with results from conventional approach.

58 GEOSCIENCES↗

DOE OSTI2015

Entropy–viscosity method for the single material Euler equations in Lagrangian frame

In this work, a new finite element method for solving the Euler equations in Lagrangian coordinates is proposed. The method is stabilized by adding artificial diffusion terms compatible with positivity of mass and internal energy, a minimum principle on the specific entropy, and all generalized entropy inequalities. Two options of first-order artificial diffusion are considered. One is in the spirit of the Eulerian based method (Guermond et al., 2011 [23, 22]; Zingan et al., 2013) and the other is similar to existing viscosity stabilizations in Lagrangian frame, e.g., Dobrev et al. (2012). The method is verified to be high-order for smooth solutions even with active viscosity terms. This is achieved by using high-order finite element spaces and an entropy-based viscosity stabilization that degenerates the first-order viscous terms. This stabilization automatically distinguishes smooth and singular regions. The formal accuracy and convergence properties of the proposed methods are tested on a series of benchmark problems. This is the first result extending the entropy–viscosity methodology to the Lagrangian hydrodynamics.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2019

HTS Transformer Windings Design Using Distributive Ratios for Minimization of Short Circuit Forces

High-temperature superconducting (HTS) transformers have a promising feature in reduction of total weight, total size, and the losses of large-scale distribution transformers. However, the lower leakage reactance of HTS transformers results in a higher short-circuit fault currents and electromagnetic forces. Therefore, optimization of short-circuit electromagnetic forces is one of the crucial aspects in the design of HTS transformers. In this paper, a novel analytical method is proposed for determination of optimum distributive ratios resulting in minimization of these forces for asymmetrical multi-segment windings of an HTS transformer. Employing these distributive ratios, radial and axial components of short-circuit electromagnetic forces in an HTS transformer are significantly reduced. Two- and three-dimensional (2D and 3D) finite element method (FEM) simulations are employed to verify the analytical method results.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2021

Joint inversion of electromagnetic measurements for the determination of water saturation profiles in concrete structures

Highlights: • DC-electrical and dielectric data are combined to estimate concrete saturation degree. • A joint inversion approach of the electromagnetic measurements is proposed. • The sensitivity of the measurements to the saturation model parameters is analysed. • The new joint approach was developed and is applied to synthetic and real data. • The benefits of the joint approach over the inversion of one data type are highlighted. Water saturation profiles in concrete are essential to assess its durability and can be determined using non-destructive techniques, especially the electric and the capacitive methods. In this paper, we propose a new inversion scheme where both resistivity and permittivity measurements are inverted jointly to retrieve the saturation profile. The finite element method is used to model the measurements in 3D, the concrete having a saturation profile with depth, represented by a continuous model taking the form of a Weibull curve with four parameters. A non-linear least-squares optimization based on the Levenberg-Marquardt scheme is developed for the inversion of measurements. Results show that information gathered from both measurements enriches the reconstructed profile, leading to a more reliable estimation of saturation profiles. We believe that the joint inversion method herein developed could lead to the study of more complex phenomena, such as the coupled water-chloride ingress.

36 MATERIALS SCIENCE↗

DOE OSTI2015

Theoretical detection threshold of the proton-acoustic range verification technique

Purpose: Range verification in proton therapy using the proton-acoustic signal induced in the Bragg peak was investigated for typical clinical scenarios. The signal generation and detection processes were simulated in order to determine the signal-to-noise limits. Methods: An analytical model was used to calculate the dose distribution and local pressure rise (per proton) for beams of different energy (100 and 160 MeV) and spot widths (1, 5, and 10 mm) in a water phantom. In this method, the acoustic waves propagating from the Bragg peak were generated by the general 3D pressure wave equation implemented using a finite element method. Various beam pulse widths (0.1–10 μs) were simulated by convolving the acoustic waves with Gaussian kernels. A realistic PZT ultrasound transducer (5 cm diameter) was simulated with a Butterworth bandpass filter with consideration of random noise based on a model of thermal noise in the transducer. The signal-to-noise ratio on a per-proton basis was calculated, determining the minimum number of protons required to generate a detectable pulse. The maximum spatial resolution of the proton-acoustic imaging modality was also estimated from the signal spectrum. Results: The calculated noise in the transducer was 12–28 mPa, depending on the transducer central frequency (70–380 kHz). The minimum number of protons detectable by the technique was on the order of 3–30 × 10{sup 6} per pulse, with 30–800 mGy dose per pulse at the Bragg peak. Wider pulses produced signal with lower acoustic frequencies, with 10 μs pulses producing signals with frequency less than 100 kHz. Conclusions: The proton-acoustic process was simulated using a realistic model and the minimal detection limit was established for proton-acoustic range validation. These limits correspond to a best case scenario with a single large detector with no losses and detector thermal noise as the sensitivity limiting factor. Our study indicated practical proton-acoustic range verification may be feasible with approximately 5 × 10{sup 6} protons/pulse and beam current.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗

DOE OSTI2015

WE-AB-BRB-01: Development of a Probe-Format Graphite Calorimeter for Practical Clinical Dosimetry: Numerical Design Optimization, Prototyping, and Experimental Proof-Of-Concept

Purpose: In this work, the feasibility of performing absolute dose to water measurements using a constant temperature graphite probe calorimeter (GPC) in a clinical environment is established. Methods: A numerical design optimization study was conducted by simulating the heat transfer in the GPC resulting from irradiation using a finite element method software package. The choice of device shape, dimensions, and materials was made to minimize the heat loss in the sensitive volume of the GPC. The resulting design, which incorporates a novel aerogel-based thermal insulator, and 15 temperature sensitive resistors capable of both Joule heating and measuring temperature, was constructed in house. A software based process controller was developed to stabilize the temperatures of the GPC’s constituent graphite components to within a few 10’s of µK. This control system enables the GPC to operate in either the quasi-adiabatic or isothermal mode, two well-known, and independent calorimetry techniques. Absorbed dose to water measurements were made using these two methods under standard conditions in a 6 MV 1000 MU/min photon beam and subsequently compared against TG-51 derived values. Results: Compared to an expected dose to water of 76.9 cGy/100 MU, the average GPC-measured doses were 76.5 ± 0.5 and 76.9 ± 0.5 cGy/100 MU for the adiabatic and isothermal modes, respectively. The Monte Carlo calculated graphite to water dose conversion was 1.013, and the adiabatic heat loss correction was 1.003. With an overall uncertainty of about 1%, the most significant contributions were the specific heat capacity (type B, 0.8%) and the repeatability (type A, 0.6%). Conclusion: While the quasi-adiabatic mode of operation had been validated in previous work, this is the first time that the GPC has been successfully used isothermally. This proof-of-concept will serve as the basis for further study into the GPC’s application to small fields and MRI-linac dosimetry. This work has been supported in part by the CREATE Medical Physics Research Training Network of the Natural Sciences and Engineering Research Council (NSERC) grant 432290, NSERC grants RGPIN 298191 & 435608-13, Canadian Institutes of Health Research doctoral scholarship GSD-121793. This work has also been supported by Sun Nuclear Corporation.

60 APPLIED LIFE SCIENCES↗

DOE OSTI2016

SU-G-TeP1-15: Toward a Novel GPU Accelerated Deterministic Solution to the Linear Boltzmann Transport Equation

Purpose: To develop a Graphic Processor Unit (GPU) accelerated deterministic solution to the Linear Boltzmann Transport Equation (LBTE) for accurate dose calculations in radiotherapy (RT). A deterministic solution yields the potential for major speed improvements due to the sparse matrix-vector and vector-vector multiplications and would thus be of benefit to RT. Methods: In order to leverage the massively parallel architecture of GPUs, the first order LBTE was reformulated as a second order self-adjoint equation using the Least Squares Finite Element Method (LSFEM). This produces a symmetric positive-definite matrix which is efficiently solved using a parallelized conjugate gradient (CG) solver. The LSFEM formalism is applied in space, discrete ordinates is applied in angle, and the Multigroup method is applied in energy. The final linear system of equations produced is tightly coupled in space and angle. Our code written in CUDA-C was benchmarked on an Nvidia GeForce TITAN-X GPU against an Intel i7-6700K CPU. A spatial mesh of 30,950 tetrahedral elements was used with an S4 angular approximation. Results: To avoid repeating a full computationally intensive finite element matrix assembly at each Multigroup energy, a novel mapping algorithm was developed which minimized the operations required at each energy. Additionally, a parallelized memory mapping for the kronecker product between the sparse spatial and angular matrices, including Dirichlet boundary conditions, was created. Atomicity is preserved by graph-coloring overlapping nodes into separate kernel launches. The one-time mapping calculations for matrix assembly, kronecker product, and boundary condition application took 452±1ms on GPU. Matrix assembly for 16 energy groups took 556±3s on CPU, and 358±2ms on GPU using the mappings developed. The CG solver took 93±1s on CPU, and 468±2ms on GPU. Conclusion: Three computationally intensive subroutines in deterministically solving the LBTE have been formulated on GPU, resulting in two orders of magnitude speedup. Funding support from Natural Sciences and Engineering Research Council and Alberta Innovates Health Solutions. Dr. Fallone is a co-founder and CEO of MagnetTx Oncology Solutions (under discussions to license Alberta bi-planar linac MR for commercialization).

60 APPLIED LIFE SCIENCES↗

DOE OSTI2016

A Variational Nodal Approach to 2D/1D Pin Resolved Neutron Transport: II Spherical Harmonics

The variational nodal method (VNM) as implemented in the VARIANT code has found wide application to fast reactor problems where fuel assembly homogenization does not result in unacceptable errors. The objective of this research is to generalize VNM for application to PWR problems, where homogenization even at the pin-cell level often results in unacceptable errors. To accomplish this, we are developing the PANX code (Purdue - Argonne - Northwestern - Xi'an) to implement a 2D/1D VNM transport method without spatial homogenization employing spherical harmonics and diffusion theory, respectively, in the radial and axial directions. In the preceding paper, we employed diffusion theory in conjunction with finite element methods to implement heterogeneous VNM nodes, in which the problem of fuel-coolant smearing at axial interfaces, found in existing 2D/1D approximations, is eliminated. In this work, we generalize the resulting VNM nodes to couple spherical harmonics in the x-y plane with axial diffusion theory. We then apply the method to the three-dimensional C5G7 benchmark problem. (authors)

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

DOE OSTI2017

Enhancement of flow measurements using fluid-dynamic constraints

Novel experimental modalities acquire spatially resolved velocity measurements for steady state and transient flows which are of interest for engineering and biological applications. One of the drawbacks of such high resolution velocity data is their susceptibility to measurement errors. In this paper, we propose a novel filtering strategy that allows enhancement of the noisy measurements to obtain reconstruction of smooth divergence free velocity and corresponding pressure fields which together approximately comply to a prescribed flow model. The main step in our approach consists of the appropriate use of the velocity measurements in the design of a linearized flow model which can be shown to be well-posed and consistent with the true velocity and pressure fields up to measurement and modeling errors. The reconstruction procedure is then formulated as an optimal control problem for this linearized flow model. The resulting filter has analyzable smoothing and approximation properties. We briefly discuss the discretization of the approach by finite element methods and comment on the efficient solution by iterative methods. The capability of the proposed filter to significantly reduce data noise is demonstrated by numerical tests including the application to experimental data. In addition, we compare with other methods like smoothing and solenoidal filtering.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

NASA NTRS1992

Coupled finite-difference/finite-element approach for wing-body aeroelasticity

Computational methods using finite-difference approaches for fluids and finite-element approaches for structures have individually advanced to solve almost full-aircraft configurations. However, coupled approaches to solve fluid/structural interaction problems are still in their early stages of development, particularly for complex geometries using complete equations such as the Euler/Navier-Stokes equations. Earlier work demonstrated the success of coupling finite-difference and finite-element methods for simple wing configurations using the Euler/Navier-Stokes equations. In this paper, the same approach is extended for general wing-body configurations. The structural properties are represented by beam-type finite elements. The flow is modeled using the Euler/Navier-Stokes equations. A general procedure to fully couple structural finite-element boundary conditions with fluid finite-difference boundary conditions is developed for wing-body configurations. Computations are made using moving grids that adapt to wing-body structural deformations. Results are illustrated for a typical wing-body configuration.

Guruswamy, Guru P.↗

DOE OSTI2022

Efficient co-solution of time step size and independent state in simulations of fluid-driven fracture propagation with embedded meshes

Here we present an efficient time-continuation scheme for fluid-driven fracture propagation problems in the extended finite element method framework. The approach applies a monolithic solution strategy to a fully coupled and implicit approximation of hydro-mechanical systems in conjunction with simultaneous linear elastic propagation of multiple fractures. At the end of each time step, the process ensures that the weakest fracture tip is in an equilibrium propagation regime. Furthermore, the solution process provides an initialization procedure for the newly created fracture spaces and an a priori estimate of the stress intensity factor growth rate, improving simulation robustness, and efficiency. The solution process is validated using the Kristianovich-Geertsma-de Klerk analytical solution under the toughness- and viscosity-dominated regimes. It is also extended to and demonstrated on problems with multiple fractures undergoing simultaneous propagation with stress shadow interactions. Numerical examples demonstrate that the solution process can reduce the required computational cost by one order of magnitude compared to other existing methods.

42 ENGINEERING↗

NASA NTRS1994

Thermocryogenic buckling and stress analyses of a partially filled cryogenic tank subjected to cylindrical strip heating

Thermocryogenic buckling and stress analyses were conducted on a horizontally oriented cryogenic tank using the finite element method. The tank is a finite-length circular cylindrical shell with its two ends capped with hemispherical shells. The tank is subjected to cylindrical strip heating in the region above the liquid-cryogen fill level and to cryogenic cooling below the fill level (i.e., under thermocryogenic loading). The effects of cryogen fill level on the buckling temperature and thermocryogenic stress field were investigated in detail. Both the buckling temperature and stress magnitudes were relatively insensitive to the cryogen fill level. The buckling temperature, however, was quite sensitive to the radius-to-thickness ratio. A mechanical stress analysis of the tank also was conducted when the tank was under: (1) cryogen liquid pressure loading; (2) internal pressure loading; and (3) tank-wall inertia loading. Deformed shapes of the cryogenic tanks under different loading conditions were shown, and high-stress domains were mapped on the tank wall for the strain-gage installations. The accuracies of solutions from different finite element models were compared.

Ko, William L.↗

DOE OSTI2017

Preliminary Study on the Suitability of a Second-Order Reconstructed Discontinuous Galerkin Method for RELAP-7 Thermal-Hydraulic Modeling

This document presents a preliminary study on the suitability of a second-order reconstructed discontinuous Galerkin (rDG) method for RELAP-7 thermal-hydraulic modeling. The document begins with a brief description of the governing equations for compressible, two-phase vapor and liquid flow, with a presentation of the seven-equation formulation details. A comparative study between the second-order rDG method and the RELAP-7's finite element method (FEM) with a entropy viscosity method (EVM) based numerical stabilization scheme (namely FEM-EVM) over a series of benchmark test problems is demonstrated. The intent for this suite of test problems is to provide baseline comparison data that demonstrate the performance of 1) the rDG solution and 2) the RELAP-7's FEM-EVM solution (with RELAP-7 code version dated August 15, 2017), on problems from single- to specific, limited two-phase flows. For all the test problems in this document, the rDG solutions were obtained with a second-order, two-step, explicit strong stability preserving Runge-Kutta time integration method. The computational results clearly indicate that the performance of the rDG method is superior to that of the RELAP-7's FEM-EVM method in all the test problems presented. Therefore, as far as the test problems in this document are considered, the second-order rDG method is recommended as an improved solution method option for RELAP-7.

97 MATHEMATICS AND COMPUTING↗