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NASA NTRS1991

Integrated force method - Compatibility conditions of structural mechanics for finite element analysis

The equilibrium equations and the compatibility conditions are fundamental to the analyses of structures. However, anyone who undertakes even a cursory generic study of the compatibility conditions can discover, with little effort, that historically this facet of structural mechanics had not been adequately researched by the profession. Now the compatibility conditions (CC's) have been researched and are understood to a great extent. For finite element discretizations, the CC's are banded and can be divided into three distinct categories: (1) the interface CC's, (2) the cluster or field CC's, and (3) the external CC's. The generation of CC's requires the separating of a local region, then writing the deformation displacement relation (ddr) for the region, and finally, the eliminating of the displacements from the ddr. The procedure to generate all three types of CC's is presented and illustrated through examples of finite element models. The uniqueness of the CC's thus generated is shown. The utilization of CC's has resulted in the novel integrated force method (IFM). The solution that is obtained by the IFM converges with a significantly fewer number of elements, compared to the stiffness and the hybrid methods.

Patnaik, Surya N.↗

DOE OSTI2026

PDE-constrained high-order mesh optimization

Here, we present a novel framework for PDE-constrained r-adaptivity of high-order meshes. The proposed method formulates mesh movement as an optimization problem, with an objective function defined as a convex combination of a mesh quality metric and a measure of the accuracy of the PDE solution obtained via finite element discretization. The proposed formulation achieves optimized, well-defined high-order meshes by integrating mesh quality control, PDE solution accuracy, and robust gradient regularization. We adopt the Target-Matrix Optimization Paradigm to control geometric properties across the mesh, independent of the PDE of interest. To incorporate the accuracy of the PDE solution, we introduce error measures that control the finite element discretization error. The implicit dependence of these error measures on the mesh nodal positions is accurately captured by adjoint sensitivity analysis. Additionally, a convolution-based gradient regularization strategy is used to ensure stable and effective adaptation of high-order meshes. We demonstrate that the proposed framework can improve mesh quality and reduce the error by up to 10 times for the solution of Poisson and linear elasto-static problems. The approach is general with respect to the dimensionality, the order of the mesh, the types of mesh elements, and can be applied to any PDE that admits well-defined adjoint operators.

Computer science↗

DOE OSTI2018

Improved Models for Metallic Nanoparticle Cores from Atomic Pair Distribution Function (PDF) Analysis

X-ray atomic pair distribution functions (PDFs) were collected from a range of canonical metallic nanomaterials, both elemental and alloyed, prepared using different synthesis methods and exhibiting drastically different morphological properties. Widely applied shape-tuned attenuated crystal (AC) fcc models proved inadequate, yielding structured, coherent, and correlated fit residuals. However, equally simple discrete cluster models could account for the largest amplitude features in these difference signals. A hypothesis testing based approach to nanoparticle structure modeling systematically ruled out effects from crystallite size, composition, shape, and surface faceting as primary factors contributing to the AC misfit. On the other hand, decahedrally twinned cluster cores were found to be the origin of the AC structure misfits for a majority of the nanomaterials reported here. It is further motivated that the PDF can readily differentiate between the arrangement of domains in these multiply twinned motifs. Most of the nanomaterials surveyed also fall within the sub-5 nm size regime where traditional electron microscopy cannot easily detect and quantify domain structures, with sampling representative of the average nanocrystal synthesized. Here, the results demonstrate that PDF analysis is a powerful method for understanding internal atomic interfaces in small noble metallic nanomaterials. Such core cluster models, easily built algorithmically, should serve as starting structures for more advanced models able to capture atomic positional disorder, ligand induced or otherwise, near nanocrystal surfaces.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

NASA NTRS1986

Conforming versus non-conforming boundary elements in three-dimensional elastostatics

A critical comparison of two basic formulations in three-dimensional elastostatics, using conforming and nonconforming boundary elements, is presented. The basic structure of the boundary element method is developed. The peculiarities that both types of boundary elements present in relation to the numerical implementation are discussed. Through selected examples, key issues such as the computational advantages and disadvantages of both formulations, mesh discretization and accuracy questions, and optimal location of the collocation nodes in the case of nonconforming elements are addressed. It is shown that conforming elements are able to produce more accurate results than nonconforming ones, with substantial economy in the final size of the system equations.

Manolis, G. D.↗

NASA NTRS1989

Propagation and scattering of elastic waves in fiber-reinforced plates

The objectives of this program are as follows: modelling of guided waves in fiber-reinforced plates in terms of different modes; and analysis of scattering by transverse cracks using modal representation. A hybrid numerical method combining the finite element representation of a region around the crack with the modal representation in the exterior region will be used in this program. Modes will be obtained using the through-the-thickness discretization of the displacement field.

Bratton, Robert L.↗

NASA NTRS1996

H Infinity Control of Magnetic Bearings to Ensure Both System and External Periodic Disturbance Robustness

Both self-excited and forced disturbances often lead to severe rotor vibrations in a magnetic bearing systems with long slender shafts. This problem has been studied using the H-infinity method, and stability with good robustness can be achieved for the linearized model of a magnetic bearing when small transient disturbances are applied. In this paper, the H-infinity control method for self-excited and forced disturbances is first reviewed. It is then applied to the control of a magnetic bearing rotor system. In modelling the system, the shaft is first discretized into 18 finite elements and then three levels of condensation are applied. This leads to a system with three masses and three compliant elements which can be described by six state variable coordinates. Simulation of the resultant system design has been performed at speeds up to 10,000 rpm. Disturbances in terms of different initial displacements, initial impulses, and external periodic inputs have been imposed. The simulation results show that good stability can be achieved under these different transient disturbances using the proposed controller while at the same time reducing the sensitivity to external periodic disturbances.

Jiang, Yuhong↗

NASA NTRS2021

Analysis of Nonlinear Shrinkage for the Bound Metal Deposition Manufacturing using Multi-scale Approach

We consider problem of nonlinear shrinkage of the metal part during bound metal deposition manufacturing on the ground and in zero-G. To analyze this problem we developed multi-scale physics-based approach that spans atomistic dynamics at the scale of nanoseconds and the full part shrinkage at the time scale of hours. Using this approach we estimated the key parameters of the problem including grain boundary width, coefficient of surface diffusion, initial redistribution of particles during debinding stage, micro-structure evolution from round particles to densely packed grains and corresponding change of the total and chemical free energy, and sintering stress. The introduced method was used to predict shrinkage at the level of two particles, filament cross-section, sub-model, and the whole green, brown, and metal parts. To further improve accuracy and reliability of the shrinkage predictions we propose concept of intelligent additive manufacturing of metal powders in space that combines the strengths of both physics-based and data-driven methods of analysis of AM.

bound metal deposition↗

NASA NTRSDate not supplied

Computational Study of Low-Speed Boundary-Layer Laminar-Turbulent Transition over a 30º Swept Plate in a Channel

Reliable boundary-layer laminar-turbulent transition predictions are critical for the design of aircraft that use natural or controlled laminar flow to achieve low drag and better fuel efficiency. During cruise flight through low turbulence, the three-dimensional boundary layer over swept surfaces can transition prematurely due to stationary crossflow instabilities induced by surface roughness. Parabolized stability equations analyses have been successfully used to explain the different phases of the transition process under well controlled perturbations such as steps or discrete roughness elements. However, methodologies are still lacking to model the boundary layer receptivity to distributed random roughness, and the following non-linear instability stages leading to transition. For engineering applications, several semi-empirical methods based on linear amplification factors or local helicity have found growing adoption, but their reliability is limited by their level of simplification and the sparsity of data they are based on. To address this gap, a new study of the effect of distributed random surface roughness on crossflow transition was started, using a 30◦ swept plate as a test vehicle. The plate, which is mounted in the 2 Foot × 3 Foot Low-Speed Boundary-Layer Channel at the NASA Langley Research Center, has been tested with micro-scale roughness of varied geometry near the leading edge. In order to analyze the flow in the test section and prepare Direct Numerical Simulations with resolved roughness, Reynolds-Averaged Navier-Stokes (RANS) simulations of the flow over the plate installed in the wind tunnel test section were performed using the Langtry-Menter transition model with stationary crossflow extension. This paper presents the results of these simulations, with comparison to the experiment.

ARMD↗

NASA NTRSDate not supplied

Space-borne Doppler Weather Radar Modeling for Radar Design Evaluation

A model has been developed to predict the reflectivity and Doppler performance of a spaceborne weather radar for atmospheric aerosol and cloud monitoring. The goal is to predict radar sensitivity, resolution, uncertainties and other key performance metrics vs. radar design parameters and hardware nonidealities. Analytical formulas are readily available to predict key performance metrics of a space-borne radar system as a function of design parameters such as antenna size, spacecraft velocity, transmit power, and receive noise figure. Effects of some system nonidealities such as antenna pointing errors, power amplifier nonlinearity and phase noise can be estimated using idealized methods. These analytical formulas use idealized forms of the antenna radiation pattern and weather statistics to predict system performance. However, it is desirable to have a more physical model based on discretized weather volumes in which the particle size distribution, Doppler distribution, and other parameters can be varied to study how the radar hardware design parameters and nonidealities affect the measurement of the weather reflectivity and Doppler characteristics. This would allow the radar designers to have more insight into what is being measured and the hardware parameters and errors that need to be carefully controlled to achieve best radar performance, as well as potential methods to calibrate the system or correct errors. This presentation will demonstrate some proof-of-concept Ka-band simulations where the discretized model agrees with the analytical formulas for a simple case where the elements in the discretized weather volume are defined by a constant reflectivity and simple velocity vectors. In particular, the system sensitivity and Doppler uncertainty are evaluated by analytical formulas as well as the discretized model. Future work will expand on this to include more complex weather scenarios and the addition of system nonidealities.

Sara Tucker↗

NASA NTRS1993

Probabilistic finite elements for fatigue and fracture analysis

An overview of the probabilistic finite element method (PFEM) developed by the authors and their colleagues in recent years is presented. The primary focus is placed on the development of PFEM for both structural mechanics problems and fracture mechanics problems. The perturbation techniques are used as major tools for the analytical derivation. The following topics are covered: (1) representation and discretization of random fields; (2) development of PFEM for the general linear transient problem and nonlinear elasticity using Hu-Washizu variational principle; (3) computational aspects; (4) discussions of the application of PFEM to the reliability analysis of both brittle fracture and fatigue; and (5) a stochastic computational tool based on stochastic boundary element (SBEM). Results are obtained for the reliability index and corresponding probability of failure for: (1) fatigue crack growth; (2) defect geometry; (3) fatigue parameters; and (4) applied loads. These results show that initial defect is a critical parameter.

Belytschko, Ted↗

DOE OSTI2021

Evolution of microstructures in radiation fields using a coupled binary-collision Monte Carlo phase field approach

The simulation of radiation effects in materials broadly falls into two categories. At short time and length scales lies the modeling of primary radiation damage, such as point defect creation, energy deposition, and ballistic mixing. This is followed by the modeling at longer time scales of thermally activated microstructure evolution and defect reactions, such as recombination, clustering, and coarsening. The binary collision Monte Carlo method is an established, numerically efficient method for the computation of primary radiation damage. Conversely, the phase field method is a state of the art method for microstructure evolution on longer time and length scales. Here we present a concurrent coupling of these two methods, overcoming the difference between the discrete object Monte Carlo paradigm for primary radiation damage and the continuum field variable approach for microstructure evolution. The coupling is bidirectional, in which the microstructure evolution in the MOOSE finite element frame- work provides the spatial scattering data set for the charged particle trans- port and receives point defect, mass transport, and heat source terms from the simulated collision cascades that contribute to the field variable evolution. The concurrent coupling scheme is implemented in the code Magpie and demonstrated by investigating patterning for a model irradiated immiscible binary alloy. The results from the coupled binary collision Monte Carlo/phase field simulations reproduce the results of analytical models for phase separation, phase mixing, and patterning, supporting the approach and indicating its utility for modeling real materials systems.

36 MATERIALS SCIENCE↗

NASA NTRS1977

Finite-element methodology for thermal analysis of convectively cooled structures

A finite-element method for steady-state thermal analysis of convectively cooled structures is presented. The method is based on representing the coolant passages by finite elements with fluid bulk temperature nodes and fluid/structure interface modes. Four finite elements are described: two basic elements (mass transport and surface convection) and two integrated elements for applications to discrete tube and plate-fin convectively cooled structural configurations. Comparative finite-element and lumped-parameter thermal analyses of several convectively cooled structures demonstrate the practicality of utilizing finite-element methodology for thermal analysis of realistic convectively cooled structures.

Source record↗

NASA NTRS2016

Assessment of Preconditioner for a USM3D Hierarchical Adaptive Nonlinear Method (HANIM) (Invited)

Enhancements to the previously reported mixed-element USM3D Hierarchical Adaptive Nonlinear Iteration Method (HANIM) framework have been made to further improve robustness, efficiency, and accuracy of computational fluid dynamic simulations. The key enhancements include a multi-color line-implicit preconditioner, a discretely consistent symmetry boundary condition, and a line-mapping method for the turbulence source term discretization. The USM3D iterative convergence for the turbulent flows is assessed on four configurations. The configurations include a two-dimensional (2D) bump-in-channel, the 2D NACA 0012 airfoil, a three-dimensional (3D) bump-in-channel, and a 3D hemisphere cylinder. The Reynolds Averaged Navier Stokes (RANS) solutions have been obtained using a Spalart-Allmaras turbulence model and families of uniformly refined nested grids. Two types of HANIM solutions using line- and point-implicit preconditioners have been computed. Additional solutions using the point-implicit preconditioner alone (PA) method that broadly represents the baseline solver technology have also been computed. The line-implicit HANIM shows superior iterative convergence in most cases with progressively increasing benefits on finer grids.

Pandya, Mohagna J.↗

DOE OSTI2020

BISON Robustness and Performance Improvements

BISON is a modern finite-element based nuclear fuel performance code that has been under development at the Idaho National Laboratory (USA) since 2009 [1]. The code is applicable to both steady and transient fuel behavior and can be used to analyze 1D (spherically symmetric), 2D (axisymmetric and generalized plane strain) or 3D geometries. BISON is the fuel performance code used within CASL for LWR fuel under both normal operating and accident conditions. BISON is built using the INL Multiphysics ObjectOriented Simulation Environment, or MOOSE [2, 3]. MOOSE is a massively parallel, finite element-based framework to solve systems of coupled non-linear partial differential equations using the Jacobian-Free Newton Krylov (JFNK) method [4]. This enables investigation of computationally large problems, for example a full stack of discrete pellets in a LWR fuel rod, or every rod in a full reactor core. MOOSE supports the use of complex two and three-dimensional meshes and uses implicit time integration, important for the widely varied time scale in nuclear fuel simulation. An object-oriented architecture is employed which greatly minimizes the programming effort required to add new material and behavioral models. The flexibility of the implicit and fully coupled multiphysics approach comes with a need for constructing suitable approximations for the Jacobian matrix of the coupled system used for either preconditioning a Krylov solve or in a direct Newton solve. Preconditioning options for Bison problems need to be revisited with new preconditioning methods becoming available.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

DOE OSTI2020

Optimal 1D Ly α forest power spectrum estimation – I. DESI-lite spectra

ABSTRACT The 1D Ly α forest flux power spectrum P1D is sensitive to scales smaller than a typical galaxy survey, and hence ties to the intergalactic medium’s thermal state, suppression from neutrino masses, and new dark matter models. It has emerged as a competitive framework to study new physics, but also has come with various challenges and systematic errors in analysis. In this work, we revisit the optimal quadratic estimator for P1D, which is robust against the relevant problems such as pixel masking, time evolution within spectrum, and quasar continuum errors. We further improve the estimator by introducing a fiducial power spectrum, which enables us to extract more information by alleviating the discreteness of band powers. We meticulously apply our method to synthetic Dark Energy Spectroscopic Instrument (DESI) spectra and demonstrate how the estimator overcomes each challenge. We further apply an optimization scheme that approximates the Fisher matrix to three elements per row and reduces computation time by 60 per cent. We show that we can achieve per cent precision in P1D with 5-yr DESI data in the absence of systematics and provide forecasts for different spectral qualities.

79 ASTRONOMY AND ASTROPHYSICS↗

NASA NTRS1993

Semi-discrete Galerkin solution of the compressible boundary-layer equations with viscous-inviscid interaction

A semi-discrete Galerkin (SDG) method is under development to model attached, turbulent, and compressible boundary layers for transonic airfoil analysis problems. For the boundary-layer formulation the method models the spatial variable normal to the surface with linear finite elements and the time-like variable with finite differences. A Dorodnitsyn transformed system of equations is used to bound the infinite spatial domain thereby providing high resolution near the wall and permitting the use of a uniform finite element grid which automatically follows boundary-layer growth. The second-order accurate Crank-Nicholson scheme is applied along with a linearization method to take advantage of the parabolic nature of the boundary-layer equations and generate a non-iterative marching routine. The SDG code can be applied to any smoothly-connected airfoil shape without modification and can be coupled to any inviscid flow solver. In this analysis, a direct viscous-inviscid interaction is accomplished between the Euler and boundary-layer codes through the application of a transpiration velocity boundary condition. Results are presented for compressible turbulent flow past RAE 2822 and NACA 0012 airfoils at various freestream Mach numbers, Reynolds numbers, and angles of attack.

Day, Brad A.↗

NASA NTRSDate not supplied

On the Representation of Through-The-Thickness Reinforcements in Finite Element Analysis of Stitched, Blade Stiffened Panels

Modern aircraft employ laminated composites for their tailorable in-plane properties, high specific strengths, and high specific stiffnesses. However, laminated composites exhibit relatively poor interlaminar properties without through-the-thickness reinforcements. Quantifying the necessary amount of through-the-thickness reinforcements is necessary to reduce cost and meet damage tolerance certification requirements. In this study, a discrete superposed cohesive element (DSCE) approach is applied to represent the mixed-mode delamination behavior of stitched stiffened panels subjected to seven-point bending. This approach is compared to a one-dimensional embedded spring element (ESE) method. The DSCE approach uses two superposed bilinear traction-separation laws to obtain a representative load-displacement response determined from interlaminar tensile and shear tests. Additionally, several stitch configurations (unstitched, stitched, and overstitched) are evaluated in terms of their load-displacement response and crack-arrestment capability. Results indicate that the DSCE and ESE approaches show good agreement with respect to the predicted load-displacement response, but the ESE method tends to overpredict the crack growth behavior by approximately 13%. Stitches were not observed to fail during skin-stringer separation. Using an overstitched laminate with stitches near the flange edge provides the greatest crack-arrestment capability. Furthermore, the skin retains 92% of its stiffness after skin-stringer separation occurs.

composites↗

NASA NTRSDate not supplied

On the Representation of Through-The-Thickness Reinforcements in Finite Element Analysis of Stitched, Blade Stiffened Panels

composites↗