Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “finite element expansion”

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.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 37 records · Page 2

An Integrated Computational Materials Engineering (ICME) Approach to Design Nonlinear Transition Zones Between Dissimilar Metals

Current approaches to designing graded transition joints (GTJs) between dissimilar metals often rely on linear changes in both composition profiles and thickness of each sublayer. This increases fabrication cost and may not be optimal with respect to residual stress or the formation of undesirable phases. Here, in this study, GTJs between P91 ferritic/martensitic steel and 347H austenitic stainless steel were designed using Integrated Computational Materials Engineering (ICME) principles with nonlinear composition and length profiles. Guided by inputs from classical mechanics and CALPHAD predictions of carbon chemical potential, a novel transition zone consisting of five discrete compositions was proposed, with the thickness of each sublayer varying according to a brachistochrone-inspired distribution. In addition to carbon potential gradients, CALPHAD was used to predict coefficients of thermal expansion, which were incorporated into finite element models to evaluate stress evolution. The proposed nonlinear design resulted in a smoother carbon potential gradient, lower carbon depletion at the P91 interface, and a comparable residual stress under long-term thermal exposure, compared to a conventional linear design using ten sublayers with equal thickness. This work introduces a brachistochrone-inspired distribution for GTJ design, offering a general framework for optimizing graded interfaces between dissimilar metals.

Directed Energy Deposition↗

RESIDUAL DEFORMATION ANALYSIS IN COMPOSITE SHELL STRUCTURES MANUFACTURED USING AUTOMATED FIBER PLACEMENT

The manufacturing of composites typically produces residual stresses that can significantly affect the final shape of the structure. The process of automated fiber placement (AFP) has become a prominent manufacturing technique in developing layups with tailored, variable stiffness morphology. The steered patterns of fiber tows with and without overlaps produce residual deformations that are distinctive from traditional layups. Digital image correlation was used to measure the AFP lamina coefficients of thermal expansion, which were incorporated into finite element analyses (FEA) to model the cooling phase of the cure cycle. The effects of nonlinear analysis and temperature-dependent lamina properties calculated using self-consistent field micromechanics, on the resulting residual deformation of shells, were also modeled. The predicted residual deformation was analyzed by considering out-of-roundness in cylindrical shells and compared to the experimental results. The shell FEA results were well-correlated with the overall deformed shape of the AFP cylinder with overlaps, while the shell FEA model of the AFP cylinder without overlaps did not show as good of qualitative match of the deformation pattern. Analytical correlation with measured results were insensitive to material softening at elevated temperatures, geometric nonlinearities, and variations in measured lamina thermal properties. To improve the accuracy of the residual deformation analysis, these results suggest that the thermo-chemical shrinkages preceding the cooldown should be considered, as well as possible variations in ply level microstructure due to the presence of the embedded fiber tow gaps and overlaps.

Composites↗

Improvements to the Griffin Transport Solvers

Griffin is a Multiphysics Object-Oriented Simulation Environment (MOOSE) based reactor multiphysics analysis application jointly developed by Idaho National Laboratory and Argonne National Laboratory. The code includes a variety of steady-state solvers for fixed-source, k-eigenvalue, adjoint, and subcritical multiplication, as well as transient solvers for point-kinetics, improved quasi-static, and spatial dynamics. This document summarizes the transport solver development efforts pursued during Fiscal Year 2022. We added the multiphysics transient capability for the coarse-mesh finite difference accelerated Richardson iteration for discontinuous finite element method discrete ordinates (DFEM-SN) scheme to support high-order heterogeneous transport simulations. HFEM (hybrid finite element method) - PN (spherical harmonics expansion) was completed and red-black iteration was added for solving the HFEM-PN system with both preconditioned Jacobian-free Newton Krylov and Richardson iteration solvers. The HFEM-PN scheme, as one of the low-order transport schemes, is expected for supporting routine design simulations. Pin power reconstruction capability was also designed and implemented with the Griffin ISOXML module to enhance all the low-order transport solvers for more accurate multiphysics simulations. Numerical results are presented for demonstrating the capabilities and verifying their performance, and future works are discussed.

97 MATHEMATICS AND COMPUTING↗

Computationally efficient models for aqueous organic redox flow batteries

The rising usage of intermittent energy has garnered the need for large scale energy storage systems. Redox flow batteries (RFB) based energy storage system shows promising potential. Numerical simulations and machine learning approaches have been widely used to study RFB performance. The development of autonomous material discovery framework and digital twin of energy storage system usually needs to query cell performance through fast response models. In this study, two computationally efficient models are introduced: a physics-based analytical flow battery model (EZBattery), and a machine learning operator model (Deep Operator Network, denoted by DeepONet). Both models can provide cell performance near instantly, and prediction accuracy was systematically examined on an application of evaluating the performances of a 780 cm 2 aqueous organic redox flow battery (AORFB), using potential anolyte candidates in dihydroxyphenazine (DHP)-based family of organic materials. A validated computationally expansive 3-dimensional multi-physics finite element model by COMSOL was used as the ground truth and provided the training data set for the DeepONet. 1280 samples were generated with 10 properties to mimic the different possible anolyte candidates, and the cell performances were evaluated under 10 different combined operating conditions. The accuracy comparisons for the two computationally efficient models show that both models can provide comparable accuracy in predicting cell charging/discharging voltage curves. DeepONet can provide slightly higher overall accuracy than EZBattery with faster calculation speed, but highly relies on the training dataset. EZBattery does not need a training dataset and can provide interpretable physics-based explanations of the results, while being more flexible to adjust to adapt any different cell designs, flow battery architectures, and electrolyte materials.

Analytical model↗

Microstructure-Sensitive Uncertainty Quantification for Crystal Plasticity Finite Element Constitutive Models Using Stochastic Collocation Methods

Uncertainty quantification (UQ) plays a major role in verification and validation for computational engineering models and simulations, and establishes trust in the predictive capability of computational models. In the materials science and engineering context, where the process-structure-property-performance linkage is well known to be the only road mapping from manufacturing to engineering performance, numerous integrated computational materials engineering (ICME) models have been developed across a wide spectrum of length-scales and time-scales to relieve the burden of resource-intensive experiments. Within the structure-property linkage, crystal plasticity finite element method (CPFEM) models have been widely used since they are one of a few ICME toolboxes that allows numerical predictions, providing the bridge from microstructure to materials properties and performances. Several constitutive models have been proposed in the last few decades to capture the mechanics and plasticity behavior of materials. While some UQ studies have been performed, the robustness and uncertainty of these constitutive models have not been rigorously established. In this work, we apply a stochastic collocation (SC) method, which is mathematically rigorous and has been widely used in the field of UQ, to quantify the uncertainty of three most commonly used constitutive models in CPFEM, namely phenomenological models (with and without twinning), and dislocation-density-based constitutive models, for three different types of crystal structures, namely face-centered cubic (fcc) copper (Cu), body-centered cubic (bcc) tungsten (W), and hexagonal close packing (hcp) magnesium (Mg). Our numerical results not only quantify the uncertainty of these constitutive models in stress-strain curve, but also analyze the global sensitivity of the underlying constitutive parameters with respect to the initial yield behavior, which may be helpful for robust constitutive model calibration works in the future.

36 MATERIALS SCIENCE↗

Applicability of Loads Estimation Techniques Using Sparse Acceleration Sensor Data to Spacecraft Structural Health Monitoring

The use of structural health monitoring systems on spacecraft structures can play a crucial role in ensuring the safety, reliability, and longevity of the structure by gathering and analyzing onboard sensor data. Of specific importance is monitoring for excessive loading at critical interfaces as any off-nominal structural excitations experienced by spacecraft structures can cause early unpredicted high structural life consumption or damage. The availability and cost of flight-certified sensors along with the size of spacecraft structures and allowable payload mass drives the need for a method to estimate loads using sparsely-located sensors. Numerous approaches such as physics-based, statistical learning, and physics-enhanced statistical learning algorithms have gained popularity among structural prognostics applications. However, developing noise-robust prediction models to assess loads and structural life predictions from a sparse multi-sensor data acquisition system can be a challenging task. This paper discusses the evaluation of physics-based versus machine-learning algorithms for predicting loads and structural life at mission critical locations on the spacecraft structure using a finite element loads analysis with the application of simulated noise and noise reduction techniques. To estimate the loads from accelerations, the physics-based algorithm leverages a loads transformation matrix from a Craig-Bampton reduced finite element model. A System Equivalent Reduction Expansion Process (SEREP) and a pseudo-inverse approach are considered to expand from the onboard sensor degrees of freedom to the Craig-Bampton model degrees of freedom. The machine learning algorithm provides a data driven solution/mapping of the sensor accelerations to the loads at the mission critical locations using a high dimensionality analysis. Although these strategies produce comparable loads prediction without noise, the limitations of these strategies with incorporating simulated noise and noise reduction techniques with low signal to noise ratio signals are evaluated. The study demonstrates the immense potential of statistical learning algorithms for sparse structural prognostic models and enhancing signal denoising techniques. These findings also highlight the need for noise-resilient prognostic models and low-noise data acquisition systems onboard spacecraft structures.

Spacecraft Structural Health Monitoring↗

Calculation of skin-stiffener interface stresses in stiffened composite panels

A method for computing the skin-stiffener interface stresses in stiffened composite panels is developed. Both geometrically linear and nonlinear analyses are considered. Particular attention is given to the flange termination region where stresses are expected to exhibit unbounded characteristics. The method is based on a finite-element analysis and an elasticity solution. The finite-element analysis is standard, while the elasticity solution is based on an eigenvalue expansion of the stress functions. The eigenvalue expansion is assumed to be valid in the local flange termination region and is coupled with the finite-element analysis using collocation of stresses on the local region boundaries. Accuracy and convergence of the local elasticity solution are assessed using a geometrically linear analysis. Using this analysis procedure, the influence of geometric nonlinearities and stiffener parameters on the skin-stiffener interface stresses is evaluated.

Cohen, David↗

Finite element solutions of free surface flows

A procedure is presented for using NASTRAN to determine the flow field about arbitrarily shaped bodies in the presence of a free surface. The fundamental unknown of the problem is the velocity potential which must satisfy Laplace's equation in the fluid region. Boundary conditions on the free surface may involve second order derivatives in space and time. In cases involving infinite domains either a tractable radiation condition is applied at a truncated boundary or a series expansion is used and matched to the local finite elements. Solutions are presented for harmonic, transient, and steady state problems and compared to either exact solutions or other numerical solutions.

Zarda, P. R.↗

Crystal mechanics-based thermo-elastic constitutive modeling of orthorhombic uranium using generalized spherical harmonics and first-order bounding theories

In earlier works, a mathematical procedure for invertible microstructure-property linkages was developed using computationally efficient spectral methods for polycrystalline cubic and hexagonal metals. This paper formulates such invertible microstructure–property linkages for orthorhombic polycrystalline metals relying on the generalized spherical harmonics (GSH) spectral basis. The procedure is used to compute property closures of orthorhombic polycrystals. The closures represent the complete set of theoretically possible combinations of effective properties for a selected material. The procedure relies on the first-order bounding theories and considers orientation distribution functions (ODFs) as the main microstructural descriptor influencing homogenized properties. Numerous examples of these closures involving second-rank thermal expansion and fourth-rank elastic stiffness tensorial properties over a broad range of temperatures are presented for α-uranium (α-U). In doing so, certain key properties of these closures are exploited to facilitate their computation with drastically reduced computational effort. Along with the recently developed GSH-based interpolation procedure for ODFs from coarsely spaced experimental measurement grids to finely spaced finite element mesh resolution grids presented in Barrett et al., the developed computationally efficient ODF-effective property linkages are used to establish a crystal mechanics-based simulation framework coupled with the finite element method (FEM). The ODF dependent thermal expansion and elastic stiffness tensors are efficiently calculated at every integration point and used by the FEM to predict the overall distortion of a hemispherical part made of α-U during heating. In conclusion, it is shown that the developed framework can be used to simulate microstructurally heterogeneous components under thermo-mechanical loadings in a computationally efficient manner.

36 MATERIALS SCIENCE↗

Fiber shape effects on metal matrix composite behavior

The effects of different fiber shapes on the behavior of a SiC/Ti-15 metal matrix composite is computationally simulated. A three-dimensional finite element model consisting of a group of nine unidirectional fibers is used in the analysis. The model is employed to represent five different fiber shapes: a circle, an ellipse, a kidney, and two different cross shapes. The distribution of microstresses and the composite material properties, such as moduli, coefficients of thermal expansion, and Poisson's ratios, are obtained from the finite element analysis for the various fiber shapes. Comparisons of these results are used to determine the sensitivity of the composite behavior to the different fiber shapes and assess their potential benefits. No clear benefits result from different fiber shapes though there are some increases/decreases in isolated properties.

Brown, H. C.↗

Calculation of stresses and forces between the skin and stiffener in composite panels

A methodology for computing the stresses at the interface between the skin and stiffener in stiffened composite panels is described. The methodology is based on finite-element analyses and on elasticity solution. The finite-element analyses are standard, while the elasticity solution is based on eigenvalue expansions of the stress function. The eigenvalue expansions are assumed to be valid in the local region where the stiffener flange terminates. The local elasticity solution is coupled to the global finite-element analysis using collocation on the boundary of the local region. Accuracy and convergence of the method are discussed and several examples of its utility are presented.

Hyer, M. W.↗

A finite element approach for solution of the 3D Euler equations

Prediction of thermal deformations and stresses has prime importance in the design of the next generation of high speed flight vehicles. Aerothermal load computations for complex three-dimensional shapes necessitate development of procedures to solve the full Navier-Stokes equations. This paper details the development of a three-dimensional inviscid flow approach which can be extended for three-dimensional viscous flows. A finite element formulation, based on a Taylor series expansion in time, is employed to solve the compressible Euler equations. Model generation and results display are done using a commercially available program, PATRAN, and vectorizing strategies are incorporated to ensure computational efficiency. Sample problems are presented to demonstrate the validity of the approach for analyzing high speed compressible flows.

Thornton, E. A.↗

Scattering Cross Section of Sound Waves by the Modal Element Method

#he modal element method has been employed to determine the scattered field from a plane acoustic wave impinging on a two dimensional body. In the modal element method, the scattering body is represented by finite elements, which are coupled to an eigenfunction expansion representing the acoustic pressure in the infinite computational domain surrounding the body. The present paper extends the previous work by developing the algorithm necessary to calculate the acoustics scattering cross section by the modal element method. The scattering cross section is the acoustical equivalent to the Radar Cross Section (RCS) in electromagnetic theory. Since the scattering cross section is evaluated at infinite distance from the body, an asymptotic approximation is used in conjunction with the standard modal element method. For validation, the scattering cross section of the rigid circular cylinder is computed for the frequency range 0.1 is less than or equal to ka is less than or equal to 100. Results show excellent agreement with the analytic solution.

Baumeister, Kenneth J.↗

Fiber shape effects on metal matrix composite behavior

The effects of different fiber shapes on the behavior of metal matrix composites is computationally simulated. A three-dimensional finite element model consisting of a group of nine unidirectional fibers in a three by three unit cell array of a SiC/Ti-15-3 metal matrix composite is used in the analysis. The model is employed to represent five fiber shapes that include a circle, an ellipse, a kidney, and two different cross shapes. The distribution of stresses and the composite material properties, such as moduli, coefficients of thermal expansion, and Poisson's ratios, are obtained from the finite element analysis using the various fiber shapes. Comparisons of these results are used to determine the sensitivity of the composite behavior to the different fiber shapes. In general, fiber dominated properties are not affected by fiber geometry and matrix dominated properties are only moderately affected.

Brown, H. C.↗

Modal element method for potential flow in non-uniform ducts: Combining closed form analysis with CFD

An analytical procedure is presented, called the modal element method, that combines numerical grid based algorithms with eigenfunction expansions developed by separation of variables. A modal element method is presented for solving potential flow in a channel with two-dimensional cylindrical like obstacles. The infinite computational region is divided into three subdomains; the bounded finite element domain, which is characterized by the cylindrical obstacle and the surrounding unbounded uniform channel entrance and exit domains. The velocity potential is represented approximately in the grid based domain by a finite element solution and is represented analytically by an eigenfunction expansion in the uniform semi-infinite entrance and exit domains. The calculated flow fields are in excellent agreement with exact analytical solutions. By eliminating the grid surrounding the obstacle, the modal element method reduces the numerical grid size, employs a more precise far field boundary condition, as well as giving theoretical insight to the interaction of the obstacle with the mean flow. Although the analysis focuses on a specific geometry, the formulation is general and can be applied to a variety of problems as seen by a comparison to companion theories in aeroacoustics and electromagnetics.

Baumeister, Kenneth J.↗