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Results for “stable finite element method”

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 55 records · Page 3
All sourcesNASA NTRSDOE OSTI
NASA NTRS2001

The Use of Non-Standard Devices in Finite Element Analysis

A general mathematical description of the response behavior of thin-skin pneumatic envelopes and many other membrane and cable structures produces under-constrained systems that pose severe difficulties to analysis. These systems are mobile, and the general mathematical description exposes the mobility. Yet the response behavior of special under-constrained structures under special loadings can be accurately predicted using a constrained mathematical description. The static response behavior of systems that are infinitesimally mobile, such as a non-slack membrane subtended from a rigid or elastic boundary frame, can be easily analyzed using such general mathematical description as afforded by the non-linear, finite element method using an implicit solution scheme if the incremental uploading is guided through a suitable path. Similarly, if such structures are assembled with structural lack of fit that provides suitable self-stress, then dynamic response behavior can be predicted by the non-linear, finite element method and an implicit solution scheme. An explicit solution scheme is available for evolution problems. Such scheme can be used via the method of dynamic relaxation to obtain the solution to a static problem. In some sense, pneumatic envelopes and many other compliant structures can be said to have destiny under a specified loading system. What that means to the analyst is that what happens on the evolution path of the solution is irrelevant as long as equilibrium is achieved at destiny under full load and that the equilibrium is stable in the vicinity of that load. The purpose of this paper is to alert practitioners to the fact that non-standard procedures in finite element analysis are useful and can be legitimate although they burden their users with the requirement to use special caution. Some interesting findings that are useful to the US Scientific Balloon Program and that could not be obtained without non-standard techniques are presented.

Schur, Willi W.↗
NASA NTRS2001

Energy Stable Flux Formulas For The Discontinuous Galerkin Discretization Of First Order Nonlinear Conservation Laws

We consider the discontinuous Galerkin (DG) finite element discretization of first order systems of conservation laws derivable as moments of the kinetic Boltzmann equation. This includes well known conservation law systems such as the Euler For the class of first order nonlinear conservation laws equipped with an entropy extension, an energy analysis of the DG method for the Cauchy initial value problem is developed. Using this DG energy analysis, several new variants of existing numerical flux functions are derived and shown to be energy stable.

Barth, Timothy↗
NASA NTRS1983

Analyses of large quasistatic deformations of inelastic bodies by a new hybrid-stress finite element algorithm - Applications

A new hybrid-stress finite element algorithm suitable for analyzing large quasistatic deformations of inelastic solids is presented and its feasibility and performance are demonstrated with examples. The algorithm provides extremely accurate bifurcation analysis which is stable with respect to variation in the finite element mesh, so long as the same type of element is used in every mesh. When the mesh element is varied, the result changes in a predictable manner. The method does not necessarily lead to an upper or lower bound for the critical load. An explicit forward gradient scheme is used to improve stability and is shown to be useful also for elongation-dominated deformations. The application of the method to the onset of necking in plane extension and to deformation and stress in plane extension of an elasticoviscous fluid with an array of cylindrical voids is given in detail.

Reed, K. W.↗
NASA NTRS1989

Unconditionally stable concurrent procedures for transient finite-element analysis

A family of algorithms was outlined which would appear to be particularly well-suited for implementation in a parallel environment. This is due to the fact that for any partition of the mesh each subdomain in the partition can be processed over a time step simultaneously and independently of the rest. The method eliminates the need for assembling and factorizing large global arrays while retaining the unconditional stability properties of the algorithms used at the local level. To critically appraise the proposed methodology, two limiting cases were considered: element-by-element mesh partitions, and coarse mesh partitions. It was concluded that while the proposed methodology can be useful in sequential machines, it would appear to be promising as it bears on computation. It should also be emphasized that extensions of the method to nonlinear problems are possible.

Ortiz, Michael↗
NASA NTRS1992

Finite element developments for two dimensional multiple-interface phase change problems

Finite element developments for multiple phase change problems in two-dimensional models are presented for the first time. The enthalpy method is used to simulate latent heat release in conjunction with fixed grid techniques. An unconditionally stable implicit method is used for the time integration. The effects of boundary conditions and the different phase regions on the multiple phase front developments are examined for numerous examples. Discussions and conclusions are appropriately addressed.

Ouyang, Tianhong↗
NASA NTRS2000

Uncertainty Analysis of Decomposing Polyurethane Foam

Sensitivity/uncertainty analyses are necessary to determine where to allocate resources for improved predictions in support of our nation's nuclear safety mission. Yet, sensitivity/uncertainty analyses are not commonly performed on complex combustion models because the calculations are time consuming, CPU intensive, nontrivial exercises that can lead to deceptive results. To illustrate these ideas, a variety of sensitivity/uncertainty analyses were used to determine the uncertainty associated with thermal decomposition of polyurethane foam exposed to high radiative flux boundary conditions. The polyurethane used in this study is a rigid closed-cell foam used as an encapsulant. Related polyurethane binders such as Estane are used in many energetic materials of interest to the JANNAF community. The complex, finite element foam decomposition model used in this study has 25 input parameters that include chemistry, polymer structure, and thermophysical properties. The response variable was selected as the steady-state decomposition front velocity calculated as the derivative of the decomposition front location versus time. An analytical mean value sensitivity/uncertainty (MV) analysis was used to determine the standard deviation by taking numerical derivatives of the response variable with respect to each of the 25 input parameters. Since the response variable is also a derivative, the standard deviation was essentially determined from a second derivative that was extremely sensitive to numerical noise. To minimize the numerical noise, 50-micrometer element dimensions and approximately 1-msec time steps were required to obtain stable uncertainty results. As an alternative method to determine the uncertainty and sensitivity in the decomposition front velocity, surrogate response surfaces were generated for use with a constrained Latin Hypercube Sampling (LHS) technique. Two surrogate response surfaces were investigated: 1) a linear surrogate response surface (LIN) and 2) a quadratic response surface (QUAD). The LHS techniques do not require derivatives of the response variable and are subsequently relatively insensitive to numerical noise. To compare the LIN and QUAD methods to the MV method, a direct LHS analysis (DLHS) was performed using the full grid and timestep resolved finite element model. The surrogate response models (LIN and QUAD) are shown to give acceptable values of the mean and standard deviation when compared to the fully converged DLHS model.

Hobbs, Michael L.↗
NASA NTRS1995

Fracture analysis of stiffened panels under biaxial loading with widespread cracking

An elastic-plastic finite-element analysis with a critical crack-tip opening angle (CTOA) fracture criterion was used to model stable crack growth and fracture of 2024-T3 aluminum alloy (bare and clad) panels for several thicknesses. The panels had either single or multiple-site damage (MSD) cracks subjected to uniaxial or biaxial loading. Analyses were also conducted on cracked stiffened panels with single or MSD cracks. The critical CTOA value for each thickness was determined by matching the failure load on a middle-crack tension specimen. Comparisons were made between the critical angles determined from the finite-element analyses and those measured with photographic methods. Predicted load-against-crack extension and failure loads for panels under biaxial loading, panels with MSD cracks, and panels with various numbers of stiffeners were compared with test data whenever possible. The predicted results agreed well with the test data even for large-scale plastic deformations. The analyses were also able to predict stable tearing behavior of a large lead crack in the presence of MSD cracks. The analyses were then used to study the influence of stiffeners on residual strength in the presence of widespread fatigue cracking. Small MSD cracks were found to greatly reduce the residual strength for large lead cracks even for stiffened panels.

Newman, J. C., Jr.↗
NASA NTRS1995

Fracture analysis of stiffened panels under biaxial loading with widespread cracking

An elastic-plastic finite-element analysis with a critical crack-tip-opening angle (CTOA) fracture criterion was used to model stable crack growth and fracture of 2024-T3 aluminum alloy (bare and clad) panels for several thicknesses. The panels had either single or multiple-site damage (MSD) cracks subjected to uniaxial or biaxial loading. Analyses were also conducted on cracked stiffened panels with single or MSD cracks. The critical CTOA value for each thickness was determined by matching the failure load on a middle-crack tension specimen. Comparisons were made between the critical angles determined from the finite-element analyses and those measured with photographic methods. Predicted load-against-crack extension and failure loads for panels under biaxial loading, panels with MSD cracks, and panels with various number of stiffeners were compared with test data, whenever possible. The predicted results agreed well with the test data even for large-scale plastic deformations. The analyses were also able to predict stable tearing behavior of a large lead crack in the presence of MSD cracks. The analyses were then used to study the influence of stiffeners on residual strength in the presence of widespread fatigue cracking. Small MSD cracks were found to greatly reduce the residual strength for large lead cracks even for stiffened panels.

Newman, J. C., Jr.↗
DOE OSTI2024

Pressure-stabilized fixed-stress iterative solutions of compositional poromechanics

We consider the numerical behavior of the fixed-stress splitting method for coupled poromechanics as undrained regimes are approached. We explain that pressure stability is related to the splitting error of the scheme, not the fact that the discrete saddle point matrix never appears in the fixed-stress approach. This observation reconciles previous results regarding the pressure stability of the splitting method. Using examples of compositional poromechanics with application to geological CO sequestration, we see that solutions obtained using the fixed-stress scheme with a low order finite element-finite volume discretization which is not inherently inf-sup stable can exhibit the same pressure oscillations obtained with the corresponding fully implicit scheme. Moreover, pressure jump stabilization can effectively remove these spurious oscillations in the fixed-stress setting, while also improving the efficiency of the scheme in terms of the number of iterations required at every time step to reach convergence.

42 ENGINEERING↗
DOE OSTI2026

An implicit-explicit time splitting strategy for the far SOL plasma fluid model with DG-FEM discretization

We consider a far scrape-off layer (SOL) plasma fluid model of ions that is governed by a Braginskiitype model: a one-dimensional, nonlinear system of advection-diffusion equations coupled with a diffusion equation for neutral particles. Our motivation for studying this system arises from the coupling between the edge plasma and radio-frequency (RF) heating, where solving a far SOL plasma fluid model provides critical insights into edge plasma dynamics. Numerical simulations of plasma fluid models require advanced computational techniques to achieve both efficiency and accuracy, especially when resolving the boundary layer in magnetically confined plasmas. In this work, we propose an implicit-explicit time operator splitting strategy that allows for an efficient solution algorithm, where the diffusive terms are treated semi-implicitly requiring only a linear solve, while the advection part is handled explicitly using a strong-stability-preserving Runge-Kutta (SSP-RK3) scheme. This leads to a fully decoupled system in which the diffusion and advection sub-problems can be solved separately, simplifying the overall solution procedure and allowing for efficient parallelization, which is particularly relevant for exploring the impact of RF heating on the SOL plasma. The main challenge of the discretization is due to the strong coupling between diffusion and advection, particularly through the boundary conditions. This makes implementation of such a scheme in an accurate and stable manner nontrivial. We discuss in detail how to split the equations and manage boundary conditions to maintain stability and well-posedness for each subsystem. We also describe a spatial discretization approach, based on the discontinuous Galerkin finite element method (DG-FEM) and present numerical results for a one-dimensional system.

Burkovska, Olena [ORNL] (ORCID:0000000163101130)↗
NASA NTRS1995

Analysis and Development of Finite Element Methods for the Study of Nonlinear Thermomechanical Behavior of Structural Components

Underintegrated methods are investigated with respect to their stability and convergence properties. The focus was on identifying regions where they work and regions where techniques such as hourglass viscosity and hourglass control can be used. Results obtained show that underintegrated methods typically lead to finite element stiffness with spurious modes in the solution. However, problems exist (scalar elliptic boundary value problems) where underintegrated with hourglass control yield convergent solutions. Also, stress averaging in underintegrated stiffness calculations does not necessarily lead to stable or convergent stress states.

Oden, J. Tinsley↗
DOE OSTI2021

Analysis of the SBP-SAT Stabilization for Finite Element Methods Part II: Entropy Stability

In the hyperbolic research community, there exists the strong belief that a continuous Galerkin scheme is notoriously unstable and additional stabilization terms have to be added to guarantee stability. In the first part of the series, the application of simultaneous approximation terms for linear problems is investigated where the boundary conditions are imposed weakly. By applying this technique, the authors demonstrate that a pure continuous Galerkin scheme is indeed linearly stable if the boundary conditions are imposed in the correct way. In this work, we extend this investigation to the nonlinear case and focus on entropy conservation. Here, by switching to entropy variables, we provide an estimation of the boundary operators also for nonlinear problems, that guarantee conservation. In numerical simulations, we verify our theoretical analysis.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

A multiscale model to understand the interface chemistry, contacts, and dynamics during lithium stripping

A reversible Li-metal electrode, paired with a solid electrolyte, is critical for attaining higher energy density and safer batteries beyond the current lithium-ion cells. A stable stripping process may be even harder to attain as the stripping process will remove Li-atoms from the surface, and naturally reduce surface contact area, if not self-corrected by other mechanisms, such as diffusion and plastic deformation under an applied external stack pressure. Here, we capture these mechanisms occurring at multiple length- and time- scales, i.e., interface interactions, vacancy hopping, and plastic deformation, by integrating density functional theory (DFT) simulations, kinetic Monte Carlo (KMC), and continuum finite element method (FEM). By assuming the self-affine nature of multiscale contacts, we predict the steady-state contact area as a function of stripping current density, interface wettability, and stack pressure. We further estimate the exponential increase of overpotential due to contact area loss to maintain the same stripping current density. We demonstrate that a lithiophilic interface requires less stack pressure to reach the same steady-state contact area fraction than a lithiophobic interface. A “tolerable steady-state” contact area loss for maintaining stable stripping is estimated at 20 %, corresponding to a 10 % increase in overpotential. To constrain contact loss within the tolerance, the required stack pressure is 0.1, 0.5, and 2 times the yield strength of lithium metal for three distinct interfaces, lithiophilic Li/lithium oxide(Li2O), Li/lithium lanthanum zirconium oxide(LLZO), and lithiophoblic Li/lithium fluoride(LiF), respectively. The modeling results agree with experiments on the impact of the stack pressure quantitatively, while the discrepancy in stripping rate sensitivity is attributed to the simplifying interface interaction in our simulations. Overall, this multiscale simulation framework demonstrates the importance of electrochemical-mechanical coupling in understanding the dynamics of the Li/SE interface during stripping.

Feng, Min↗
NASA NTRS1983

Unconditionally stable implicit-explicit algorithms for coupled thermal stress waves

An unconditionally stable implicit-explicit method is proposed for the analysis of transient coupled thermal stress waves, and the computer-implementation aspects of the method are discussed. In the method proposed here, the mechanical displacement and temperature are used as independent variables. The resulting coupled finite element matrix equations are symmetric.

Liu, W. K.↗
NASA NTRS2017

Development of an Input Suite for an Orthotropic Composite Material Model

An orthotropic three-dimensional material model suitable for use in modeling impact tests has been developed that has three major components elastic and inelastic deformations, damage and failure. The material model has been implemented as MAT213 into a special version of LS-DYNA and uses tabulated data obtained from experiments. The prominent features of the constitutive model are illustrated using a widely-used aerospace composite the T800S3900-2B[P2352W-19] BMS8-276 Rev-H-Unitape fiber resin unidirectional composite. The input for the deformation model consists of experimental data from 12 distinct experiments at a known temperature and strain rate: tension and compression along all three principal directions, shear in all three principal planes, and off axis tension or compression tests in all three principal planes, along with other material constants. There are additional input associated with the damage and failure models. The steps in using this model are illustrated composite characterization tests, verification tests and a validation test. The results show that the developed and implemented model is stable and yields acceptably accurate results.

finite element method↗
NASA NTRS2019

Experimental and Numerical Analysis of Skin-Stiffener Separation Using a Seven-Point Bend Configuration

Skin-stiffener separation in stiffened composite panels consists of a complex interaction between multiple scales of progressive damage and failure mechanisms. This work used a superposed cohesive element method of modeling resistance curve effects that represents the structural interface of a unidirectional tape skin and a fabric stiffener. Finite element models using cohesive elements with input properties obtained from tape-to-fabric interface characterization tests were compared to experimental results of a stable skin-stiffener separation characterization test using a seven-point bend fixture. This fixture deformed the stiffened panel specimens into a buckled configuration which induced mixed-mode interlaminar stress states at the skin-stiffener interface. The advantage of this fixture was the potential for more stable damage initiation and delamination growth compared to a stringer-stiffened panel under axial compression. Use of the superposed cohesive elements showed promise, but the characterization of interface material properties as input to the cohesive elements remains a crucial component to be investigated to ensure accurate prediction of skin-stiffener separation.

Kosztowny, Cyrus J. R.↗
NASA NTRS1990

Applicability and evaluation of an implicit self-starting unconditionally stable methodology for the dynamics of structures

The applicability and evaluation of a new self-starting, unconditionally stable, implicit methodology of computation for the dynamics of structures is described. The methodology offers different perspectives and architecture for structural dynamics compared with the traditional (widely advocated and commonly used) time integration methods. It is based on velocity representations and architecture and uses finite elements as the principal analysis tool for structural dynamic modeling/analysis. In particular, the dynamics of beam-type flexural models are considered, and comparative results validate and support the proposed use of the self-starting methodology of computation for the dynamics of linear/nonlinear structures. The overall effectiveness and elegance strongly support its use in most existing commercial codes.

Tamma, Kumar K.↗
NASA NTRS1982

Natural convection in melt crystal growth - The influence of flow pattern on solute segregation

The results of two lines of research aimed at calculating the structure of the flows driven by buoyancy in small-scale crystal growth systems and at understanding the coupling between these flows, the shape of the solidification interface, and dopant segregation in the crystal are reviewed. First, finite-element methods are combined with computer-aided methods for detecting multiple steady solutions to analyze the structure of the buoyancy-driven axisymmetric flows in a vertical cylinder heated from below. This system exhibits onset of convection, multiple steady flows, and loss of the primary stable flow beyond a critical value of the Rayleigh number. Second, results are presented for calculations of convection, melt/solid interface shape, and dopant segregation within a vertical ampoule with thermal boundary conditions that represent a prototype of the vertical Bridgman growth system.

Brown, R. A.↗