Vectorial finite elements for solving the radiative transfer equation

NASA Astrophysics Data System (ADS)

Badri, M. A.; Jolivet, P.; Rousseau, B.; Le Corre, S.; Digonnet, H.; Favennec, Y.

2018-06-01

The discrete ordinate method coupled with the finite element method is often used for the spatio-angular discretization of the radiative transfer equation. In this paper we attempt to improve upon such a discretization technique. Instead of using standard finite elements, we reformulate the radiative transfer equation using vectorial finite elements. In comparison to standard finite elements, this reformulation yields faster timings for the linear system assemblies, as well as for the solution phase when using scattering media. The proposed vectorial finite element discretization for solving the radiative transfer equation is cross-validated against a benchmark problem available in literature. In addition, we have used the method of manufactured solutions to verify the order of accuracy for our discretization technique within different absorbing, scattering, and emitting media. For solving large problems of radiation on parallel computers, the vectorial finite element method is parallelized using domain decomposition. The proposed domain decomposition method scales on large number of processes, and its performance is unaffected by the changes in optical thickness of the medium. Our parallel solver is used to solve a large scale radiative transfer problem of the Kelvin-cell radiation.

Multiscale Modeling for the Analysis for Grain-Scale Fracture Within Aluminum Microstructures

NASA Technical Reports Server (NTRS)

Glaessgen, Edward H.; Phillips, Dawn R.; Yamakov, Vesselin; Saether, Erik

2005-01-01

Multiscale modeling methods for the analysis of metallic microstructures are discussed. Both molecular dynamics and the finite element method are used to analyze crack propagation and stress distribution in a nanoscale aluminum bicrystal model subjected to hydrostatic loading. Quantitative similarity is observed between the results from the two very different analysis methods. A bilinear traction-displacement relationship that may be embedded into cohesive zone finite elements is extracted from the nanoscale molecular dynamics results.

The accuracy of the Gaussian-and-finite-element-Coulomb (GFC) method for the calculation of Coulomb integrals.

PubMed

Przybytek, Michal; Helgaker, Trygve

2013-08-07

We analyze the accuracy of the Coulomb energy calculated using the Gaussian-and-finite-element-Coulomb (GFC) method. In this approach, the electrostatic potential associated with the molecular electronic density is obtained by solving the Poisson equation and then used to calculate matrix elements of the Coulomb operator. The molecular electrostatic potential is expanded in a mixed Gaussian-finite-element (GF) basis set consisting of Gaussian functions of s symmetry centered on the nuclei (with exponents obtained from a full optimization of the atomic potentials generated by the atomic densities from symmetry-averaged restricted open-shell Hartree-Fock theory) and shape functions defined on uniform finite elements. The quality of the GF basis is controlled by means of a small set of parameters; for a given width of the finite elements d, the highest accuracy is achieved at smallest computational cost when tricubic (n = 3) elements are used in combination with two (γ(H) = 2) and eight (γ(1st) = 8) Gaussians on hydrogen and first-row atoms, respectively, with exponents greater than a given threshold (αmin (G)=0.5). The error in the calculated Coulomb energy divided by the number of atoms in the system depends on the system type but is independent of the system size or the orbital basis set, vanishing approximately like d(4) with decreasing d. If the boundary conditions for the Poisson equation are calculated in an approximate way, the GFC method may lose its variational character when the finite elements are too small; with larger elements, it is less sensitive to inaccuracies in the boundary values. As it is possible to obtain accurate boundary conditions in linear time, the overall scaling of the GFC method for large systems is governed by another computational step-namely, the generation of the three-center overlap integrals with three Gaussian orbitals. The most unfavorable (nearly quadratic) scaling is observed for compact, truly three-dimensional systems; however, this scaling can be reduced to linear by introducing more effective techniques for recognizing significant three-center overlap distributions.

Particle-based simulation of charge transport in discrete-charge nano-scale systems: the electrostatic problem

PubMed Central

2012-01-01

The fast and accurate computation of the electric forces that drive the motion of charged particles at the nanometer scale represents a computational challenge. For this kind of system, where the discrete nature of the charges cannot be neglected, boundary element methods (BEM) represent a better approach than finite differences/finite elements methods. In this article, we compare two different BEM approaches to a canonical electrostatic problem in a three-dimensional space with inhomogeneous dielectrics, emphasizing their suitability for particle-based simulations: the iterative method proposed by Hoyles et al. and the Induced Charge Computation introduced by Boda et al. PMID:22338640

Particle-based simulation of charge transport in discrete-charge nano-scale systems: the electrostatic problem.

PubMed

Berti, Claudio; Gillespie, Dirk; Eisenberg, Robert S; Fiegna, Claudio

2012-02-16

The fast and accurate computation of the electric forces that drive the motion of charged particles at the nanometer scale represents a computational challenge. For this kind of system, where the discrete nature of the charges cannot be neglected, boundary element methods (BEM) represent a better approach than finite differences/finite elements methods. In this article, we compare two different BEM approaches to a canonical electrostatic problem in a three-dimensional space with inhomogeneous dielectrics, emphasizing their suitability for particle-based simulations: the iterative method proposed by Hoyles et al. and the Induced Charge Computation introduced by Boda et al.

Finite Element Simulation of the Shear Effect of Ultrasonic on Heat Exchanger Descaling

NASA Astrophysics Data System (ADS)

Lu, Shaolv; Wang, Zhihua; Wang, Hehui

2018-03-01

The shear effect on the interface of metal plate and its attached scale is an important mechanism of ultrasonic descaling, which is caused by the different propagation speed of ultrasonic wave in two different mediums. The propagating of ultrasonic wave on the shell is simulated based on the ANSYS/LS-DYNA explicit dynamic analysis. The distribution of shear stress in different paths under ultrasonic vibration is obtained through the finite element analysis and it reveals the main descaling mechanism of shear effect. The simulation result is helpful and enlightening to the reasonable design and the application of the ultrasonic scaling technology on heat exchanger.

An Embedded Statistical Method for Coupling Molecular Dynamics and Finite Element Analyses

NASA Technical Reports Server (NTRS)

Saether, E.; Glaessgen, E.H.; Yamakov, V.

2008-01-01

The coupling of molecular dynamics (MD) simulations with finite element methods (FEM) yields computationally efficient models that link fundamental material processes at the atomistic level with continuum field responses at higher length scales. The theoretical challenge involves developing a seamless connection along an interface between two inherently different simulation frameworks. Various specialized methods have been developed to solve particular classes of problems. Many of these methods link the kinematics of individual MD atoms with FEM nodes at their common interface, necessarily requiring that the finite element mesh be refined to atomic resolution. Some of these coupling approaches also require simulations to be carried out at 0 K and restrict modeling to two-dimensional material domains due to difficulties in simulating full three-dimensional material processes. In the present work, a new approach to MD-FEM coupling is developed based on a restatement of the standard boundary value problem used to define a coupled domain. The method replaces a direct linkage of individual MD atoms and finite element (FE) nodes with a statistical averaging of atomistic displacements in local atomic volumes associated with each FE node in an interface region. The FEM and MD computational systems are effectively independent and communicate only through an iterative update of their boundary conditions. With the use of statistical averages of the atomistic quantities to couple the two computational schemes, the developed approach is referred to as an embedded statistical coupling method (ESCM). ESCM provides an enhanced coupling methodology that is inherently applicable to three-dimensional domains, avoids discretization of the continuum model to atomic scale resolution, and permits finite temperature states to be applied.

A New Concurrent Multiscale Methodology for Coupling Molecular Dynamics and Finite Element Analyses

NASA Technical Reports Server (NTRS)

Yamakov, Vesselin; Saether, Erik; Glaessgen, Edward H/.

2008-01-01

The coupling of molecular dynamics (MD) simulations with finite element methods (FEM) yields computationally efficient models that link fundamental material processes at the atomistic level with continuum field responses at higher length scales. The theoretical challenge involves developing a seamless connection along an interface between two inherently different simulation frameworks. Various specialized methods have been developed to solve particular classes of problems. Many of these methods link the kinematics of individual MD atoms with FEM nodes at their common interface, necessarily requiring that the finite element mesh be refined to atomic resolution. Some of these coupling approaches also require simulations to be carried out at 0 K and restrict modeling to two-dimensional material domains due to difficulties in simulating full three-dimensional material processes. In the present work, a new approach to MD-FEM coupling is developed based on a restatement of the standard boundary value problem used to define a coupled domain. The method replaces a direct linkage of individual MD atoms and finite element (FE) nodes with a statistical averaging of atomistic displacements in local atomic volumes associated with each FE node in an interface region. The FEM and MD computational systems are effectively independent and communicate only through an iterative update of their boundary conditions. With the use of statistical averages of the atomistic quantities to couple the two computational schemes, the developed approach is referred to as an embedded statistical coupling method (ESCM). ESCM provides an enhanced coupling methodology that is inherently applicable to three-dimensional domains, avoids discretization of the continuum model to atomic scale resolution, and permits finite temperature states to be applied.

Multi-Scale Computational Modeling of Two-Phased Metal Using GMC Method

NASA Technical Reports Server (NTRS)

Moghaddam, Masoud Ghorbani; Achuthan, A.; Bednacyk, B. A.; Arnold, S. M.; Pineda, E. J.

2014-01-01

A multi-scale computational model for determining plastic behavior in two-phased CMSX-4 Ni-based superalloys is developed on a finite element analysis (FEA) framework employing crystal plasticity constitutive model that can capture the microstructural scale stress field. The generalized method of cells (GMC) micromechanics model is used for homogenizing the local field quantities. At first, GMC as stand-alone is validated by analyzing a repeating unit cell (RUC) as a two-phased sample with 72.9% volume fraction of gamma'-precipitate in the gamma-matrix phase and comparing the results with those predicted by finite element analysis (FEA) models incorporating the same crystal plasticity constitutive model. The global stress-strain behavior and the local field quantity distributions predicted by GMC demonstrated good agreement with FEA. High computational saving, at the expense of some accuracy in the components of local tensor field quantities, was obtained with GMC. Finally, the capability of the developed multi-scale model linking FEA and GMC to solve real life sized structures is demonstrated by analyzing an engine disc component and determining the microstructural scale details of the field quantities.

Finite element meshing of ANSYS (trademark) solid models

NASA Technical Reports Server (NTRS)

Kelley, F. S.

1987-01-01

A large scale, general purpose finite element computer program, ANSYS, developed and marketed by Swanson Analysis Systems, Inc. is discussed. ANSYS was perhaps the first commercially available program to offer truly interactive finite element model generation. ANSYS's purpose is for solid modeling. This application is briefly discussed and illustrated.

Peridynamic Multiscale Finite Element Methods

DOE Office of Scientific and Technical Information (OSTI.GOV)

Costa, Timothy; Bond, Stephen D.; Littlewood, David John

The problem of computing quantum-accurate design-scale solutions to mechanics problems is rich with applications and serves as the background to modern multiscale science research. The prob- lem can be broken into component problems comprised of communicating across adjacent scales, which when strung together create a pipeline for information to travel from quantum scales to design scales. Traditionally, this involves connections between a) quantum electronic structure calculations and molecular dynamics and between b) molecular dynamics and local partial differ- ential equation models at the design scale. The second step, b), is particularly challenging since the appropriate scales of molecular dynamic andmore » local partial differential equation models do not overlap. The peridynamic model for continuum mechanics provides an advantage in this endeavor, as the basic equations of peridynamics are valid at a wide range of scales limiting from the classical partial differential equation models valid at the design scale to the scale of molecular dynamics. In this work we focus on the development of multiscale finite element methods for the peridynamic model, in an effort to create a mathematically consistent channel for microscale information to travel from the upper limits of the molecular dynamics scale to the design scale. In particular, we first develop a Nonlocal Multiscale Finite Element Method which solves the peridynamic model at multiple scales to include microscale information at the coarse-scale. We then consider a method that solves a fine-scale peridynamic model to build element-support basis functions for a coarse- scale local partial differential equation model, called the Mixed Locality Multiscale Finite Element Method. Given decades of research and development into finite element codes for the local partial differential equation models of continuum mechanics there is a strong desire to couple local and nonlocal models to leverage the speed and state of the art of local models with the flexibility and accuracy of the nonlocal peridynamic model. In the mixed locality method this coupling occurs across scales, so that the nonlocal model can be used to communicate material heterogeneity at scales inappropriate to local partial differential equation models. Additionally, the computational burden of the weak form of the peridynamic model is reduced dramatically by only requiring that the model be solved on local patches of the simulation domain which may be computed in parallel, taking advantage of the heterogeneous nature of next generation computing platforms. Addition- ally, we present a novel Galerkin framework, the 'Ambulant Galerkin Method', which represents a first step towards a unified mathematical analysis of local and nonlocal multiscale finite element methods, and whose future extension will allow the analysis of multiscale finite element methods that mix models across scales under certain assumptions of the consistency of those models.« less

System-Integrated Finite Element Analysis of a Full-Scale Helicopter Crash Test with Deployable Energy Absorbers

NASA Technical Reports Server (NTRS)

Annett, Martin S.; Polanco, Michael A.

2010-01-01

A full-scale crash test of an MD-500 helicopter was conducted in December 2009 at NASA Langley's Landing and Impact Research facility (LandIR). The MD-500 helicopter was fitted with a composite honeycomb Deployable Energy Absorber (DEA) and tested under vertical and horizontal impact velocities of 26-ft/sec and 40-ft/sec, respectively. The objectives of the test were to evaluate the performance of the DEA concept under realistic crash conditions and to generate test data for validation of a system integrated finite element model. In preparation for the full-scale crash test, a series of sub-scale and MD-500 mass simulator tests was conducted to evaluate the impact performances of various components, including a new crush tube and the DEA blocks. Parameters defined within the system integrated finite element model were determined from these tests. The objective of this paper is to summarize the finite element models developed and analyses performed, beginning with pre-test predictions and continuing through post-test validation.

The Penn State Safety Floor: Part I--Design parameters associated with walking deflections.

PubMed

Casalena, J A; Ovaert, T C; Cavanagh, P R; Streit, D A

1998-08-01

A new flooring system has been developed to reduce peak impact forces to the hips when humans fall. The new safety floor is designed to remain relatively rigid under normal walking conditions, but to deform elastically when impacted during a fall. Design objectives included minimizing peak force experienced by the femur during a fall-induced impact, while maintaining a maximum of 2 mm of floor deflection during walking. Finite Element Models (FEMs) were developed to capture the complex dynamics of impact response between two deformable bodies. Validation of the finite element models included analytical calculations of theoretical buckling column response, experimental quasi-static loading of full-scale flooring prototypes, and flooring response during walking trials. Finite Element Method results compared well with theoretical and experimental data. Both finite element and experimental data suggest that the proposed safety floor can effectively meet the design goal of 2 mm maximum deflection during walking, while effectively reducing impact forces during a fall.

A 2-D Interface Element for Coupled Analysis of Independently Modeled 3-D Finite Element Subdomains

NASA Technical Reports Server (NTRS)

Kandil, Osama A.

1998-01-01

Over the past few years, the development of the interface technology has provided an analysis framework for embedding detailed finite element models within finite element models which are less refined. This development has enabled the use of cascading substructure domains without the constraint of coincident nodes along substructure boundaries. The approach used for the interface element is based on an alternate variational principle often used in deriving hybrid finite elements. The resulting system of equations exhibits a high degree of sparsity but gives rise to a non-positive definite system which causes difficulties with many of the equation solvers in general-purpose finite element codes. Hence the global system of equations is generally solved using, a decomposition procedure with pivoting. The research reported to-date for the interface element includes the one-dimensional line interface element and two-dimensional surface interface element. Several large-scale simulations, including geometrically nonlinear problems, have been reported using the one-dimensional interface element technology; however, only limited applications are available for the surface interface element. In the applications reported to-date, the geometry of the interfaced domains exactly match each other even though the spatial discretization within each domain may be different. As such, the spatial modeling of each domain, the interface elements and the assembled system is still laborious. The present research is focused on developing a rapid modeling procedure based on a parametric interface representation of independently defined subdomains which are also independently discretized.

Full-Scale Crash Test and Finite Element Simulation of a Composite Prototype Helicopter

NASA Technical Reports Server (NTRS)

Jackson, Karen E.; Fasanella, Edwin L.; Boitnott, Richard L.; Lyle, Karen H.

2003-01-01

A full-scale crash test of a prototype composite helicopter was performed at the Impact Dynamics Research Facility at NASA Langley Research Center in 1999 to obtain data for validation of a finite element crash simulation. The helicopter was the flight test article built by Sikorsky Aircraft during the Advanced Composite Airframe Program (ACAP). The composite helicopter was designed to meet the stringent Military Standard (MIL-STD-1290A) crashworthiness criteria and was outfitted with two crew and two troop seats and four anthropomorphic dummies. The test was performed at 38-ft/s vertical and 32.5-ft/s horizontal velocity onto a rigid surface. An existing modal-vibration model of the Sikorsky ACAP helicopter was converted into a model suitable for crash simulation. A two-stage modeling approach was implemented and an external user-defined subroutine was developed to represent the complex landing gear response. The crash simulation was executed with a nonlinear, explicit transient dynamic finite element code. Predictions of structural deformation and failure, the sequence of events, and the dynamic response of the airframe structure were generated and the numerical results were correlated with the experimental data to validate the simulation. The test results, the model development, and the test-analysis correlation are described.

Telescoping Mechanics: A New Paradigm for Composite Behavior Simulation

NASA Technical Reports Server (NTRS)

Chamis, C. C.; Murthy, P. L. N.; Gotsis, P. K.; Mital. S. K.

2004-01-01

This report reviews the application of telescoping mechanics to composites using recursive laminate theory. The elemental scale is the fiber-matrix slice, the behavior of which propagates to laminate. The results from using applications for typical, hybrid, and smart composites and composite-enhanced reinforced concrete structures illustrate the versatility and generality of telescoping scale mechanics. Comparisons with approximate, single-cell, and two- and three-dimensional finite-element methods demonstrate the accuracy and computational effectiveness of telescoping scale mechanics for predicting complex composite behavior.

Numerical analysis of a main crack interactions with micro-defects/inhomogeneities using two-scale generalized/extended finite element method

NASA Astrophysics Data System (ADS)

Malekan, Mohammad; Barros, Felício B.

2017-12-01

Generalized or extended finite element method (G/XFEM) models the crack by enriching functions of partition of unity type with discontinuous functions that represent well the physical behavior of the problem. However, this enrichment functions are not available for all problem types. Thus, one can use numerically-built (global-local) enrichment functions to have a better approximate procedure. This paper investigates the effects of micro-defects/inhomogeneities on a main crack behavior by modeling the micro-defects/inhomogeneities in the local problem using a two-scale G/XFEM. The global-local enrichment functions are influenced by the micro-defects/inhomogeneities from the local problem and thus change the approximate solution of the global problem with the main crack. This approach is presented in detail by solving three different linear elastic fracture mechanics problems for different cases: two plane stress and a Reissner-Mindlin plate problems. The numerical results obtained with the two-scale G/XFEM are compared with the reference solutions from the analytical, numerical solution using standard G/XFEM method and ABAQUS as well, and from the literature.

A class of hybrid finite element methods for electromagnetics: A review

NASA Technical Reports Server (NTRS)

Volakis, J. L.; Chatterjee, A.; Gong, J.

1993-01-01

Integral equation methods have generally been the workhorse for antenna and scattering computations. In the case of antennas, they continue to be the prominent computational approach, but for scattering applications the requirement for large-scale computations has turned researchers' attention to near neighbor methods such as the finite element method, which has low O(N) storage requirements and is readily adaptable in modeling complex geometrical features and material inhomogeneities. In this paper, we review three hybrid finite element methods for simulating composite scatterers, conformal microstrip antennas, and finite periodic arrays. Specifically, we discuss the finite element method and its application to electromagnetic problems when combined with the boundary integral, absorbing boundary conditions, and artificial absorbers for terminating the mesh. Particular attention is given to large-scale simulations, methods, and solvers for achieving low memory requirements and code performance on parallel computing architectures.

On Multiscale Modeling: Preserving Energy Dissipation Across the Scales with Consistent Handshaking Methods

NASA Technical Reports Server (NTRS)

Pineda, Evan J.; Bednarcyk, Brett A.; Arnold, Steven M.; Waas, Anthony M.

2013-01-01

A mesh objective crack band model was implemented within the generalized method of cells micromechanics theory. This model was linked to a macroscale finite element model to predict post-peak strain softening in composite materials. Although a mesh objective theory was implemented at the microscale, it does not preclude pathological mesh dependence at the macroscale. To ensure mesh objectivity at both scales, the energy density and the energy release rate must be preserved identically across the two scales. This requires a consistent characteristic length or localization limiter. The effects of scaling (or not scaling) the dimensions of the microscale repeating unit cell (RUC), according to the macroscale element size, in a multiscale analysis was investigated using two examples. Additionally, the ramifications of the macroscale element shape, compared to the RUC, was studied.

TECHNICAL NOTE: Direct finite-element analysis of the frequency response of a Y-Z lithium niobate SAW filter

NASA Astrophysics Data System (ADS)

Xu, Guanshui

2000-12-01

A direct finite-element model is developed for the full-scale analysis of the electromechanical phenomena involved in surface acoustic wave (SAW) devices. The equations of wave propagation in piezoelectric materials are discretized using the Galerkin method, in which an implicit algorithm of the Newmark family with unconditional stability is implemented. The Rayleigh damping coefficients are included in the elements near the boundary to reduce the influence of the reflection of waves. The performance of the model is demonstrated by the analysis of the frequency response of a Y-Z lithium niobate filter with two uniform ports, with emphasis on the influence of the number of electrodes. The frequency response of the filter is obtained through the Fourier transform of the impulse response, which is solved directly from the finite-element simulation. It shows that the finite-element results are in good agreement with the characteristic frequency response of the filter predicted by the simple phase-matching argument. The ability of the method to evaluate the influence of the bulk waves at the high-frequency end of the filter passband and the influence of the number of electrodes on insertion loss is noteworthy. We conclude that the direct finite-element analysis of SAW devices can be used as an effective tool for the design of high-performance SAW devices. Some practical computational challenges of finite-element modeling of SAW devices are discussed.

Finite element structural redesign by large admissible perturbations

NASA Technical Reports Server (NTRS)

Bernitsas, Michael M.; Beyko, E.; Rim, C. W.; Alzahabi, B.

1991-01-01

In structural redesign, two structural states are involved; the baseline (known) State S1 with unacceptable performance, and the objective (unknown) State S2 with given performance specifications. The difference between the two states in performance and design variables may be as high as 100 percent or more depending on the scale of the structure. A Perturbation Approach to Redesign (PAR) is presented to relate any two structural states S1 and S2 that are modeled by the same finite element model and represented by different values of the design variables. General perturbation equations are derived expressing implicitly the natural frequencies, dynamic modes, static deflections, static stresses, Euler buckling loads, and buckling modes of the objective S2 in terms of its performance specifications, and S1 data and Finite Element Analysis (FEA) results. Large Admissible Perturbation (LEAP) algorithms are implemented in code RESTRUCT to define the objective S2 incrementally without trial and error by postprocessing FEA results of S1 with no additional FEAs. Systematic numerical applications in redesign of a 10 element 48 degree of freedom (dof) beam, a 104 element 192 dof offshore tower, a 64 element 216 dof plate, and a 144 element 896 dof cylindrical shell show the accuracy, efficiency, and potential of PAR to find an objective state that may differ 100 percent from the baseline design.

Finite Element Model for Failure Study of Two-Dimensional Triaxially Braided Composite

NASA Technical Reports Server (NTRS)

Li, Xuetao; Binienda, Wieslaw K.; Goldberg, Robert K.

2010-01-01

A new three-dimensional finite element model of two-dimensional triaxially braided composites is presented in this paper. This meso-scale modeling technique is used to examine and predict the deformation and damage observed in tests of straight sided specimens. A unit cell based approach is used to take into account the braiding architecture as well as the mechanical properties of the fiber tows, the matrix and the fiber tow-matrix interface. A 0 deg / plus or minus 60 deg. braiding configuration has been investigated by conducting static finite element analyses. Failure initiation and progressive degradation has been simulated in the fiber tows by use of the Hashin failure criteria and a damage evolution law. The fiber tow-matrix interface was modeled by using a cohesive zone approach to capture any fiber-matrix debonding. By comparing the analytical results to those obtained experimentally, the applicability of the developed model was assessed and the failure process was investigated.

Finite Element Simulation of Three Full-Scale Crash Tests for Cessna 172 Aircraft

NASA Technical Reports Server (NTRS)

Mason, Brian H.; Warren, Jerry E., Jr.

2017-01-01

The NASA Emergency Locator Transmitter Survivability and Reliability (ELT-SAR) project was initiated in 2013 to assess the crash performance standards for the next generation of emergency locator transmitter (ELT) systems. Three Cessna 172 aircraft were acquired to perform crash testing at NASA Langley Research Center's Landing and Impact Research Facility. Full-scale crash tests were conducted in the summer of 2015 and each test article was subjected to severe, but survivable, impact conditions including a flare-to-stall during emergency landing, and two controlled-flight-into-terrain scenarios. Full-scale finite element analyses were performed using a commercial explicit solver, ABAQUS. The first test simulated impacting a concrete surface represented analytically by a rigid plane. Tests 2 and 3 simulated impacting a dirt surface represented analytically by an Eulerian grid of brick elements using a Mohr-Coulomb material model. The objective of this paper is to summarize the test and analysis results for the three full-scale crash tests. Simulation models of the airframe which correlate well with the tests are needed for future studies of alternate ELT mounting configurations.

Simulating the Response of a Composite Honeycomb Energy Absorber. Part 2; Full-Scale Impact Testing

NASA Technical Reports Server (NTRS)

Fasanella, Edwin L.; Annett, Martin S.; Jackson, Karen E.; Polanco, Michael A.

2012-01-01

NASA has sponsored research to evaluate an externally deployable composite honeycomb designed to attenuate loads in the event of a helicopter crash. The concept, designated the Deployable Energy Absorber (DEA), is an expandable Kevlar(Registered TradeMark) honeycomb. The DEA has a flexible hinge that allows the honeycomb to be stowed collapsed until needed during an emergency. Evaluation of the DEA began with material characterization of the Kevlar(Registered TradeMark)-129 fabric/epoxy, and ended with a full-scale crash test of a retrofitted MD-500 helicopter. During each evaluation phase, finite element models of the test articles were developed and simulations were performed using the dynamic finite element code, LS-DYNA(Registered TradeMark). The paper will focus on simulations of two full-scale impact tests involving the DEA, a mass-simulator and a full-scale crash of an instrumented MD-500 helicopter. Isotropic (MAT24) and composite (MAT58) material models, which were assigned to DEA shell elements, were compared. Based on simulations results, the MAT58 model showed better agreement with test.

Full-scale locomotive dynamic crash testing and correlations : locomotive consist colliding with steel coil truck at grade crossing (test 3).

DOT National Transportation Integrated Search

2011-09-01

This report presents the test results and finite element correlations of a full-scale dynamic collision between a locomotive and a highway truck loaded with two heavy steel coils. The locomotive consist was moving at 58 miles per hour before it struc...

A numerical formulation and algorithm for limit and shakedown analysis of large-scale elastoplastic structures

NASA Astrophysics Data System (ADS)

Peng, Heng; Liu, Yinghua; Chen, Haofeng

2018-05-01

In this paper, a novel direct method called the stress compensation method (SCM) is proposed for limit and shakedown analysis of large-scale elastoplastic structures. Without needing to solve the specific mathematical programming problem, the SCM is a two-level iterative procedure based on a sequence of linear elastic finite element solutions where the global stiffness matrix is decomposed only once. In the inner loop, the static admissible residual stress field for shakedown analysis is constructed. In the outer loop, a series of decreasing load multipliers are updated to approach to the shakedown limit multiplier by using an efficient and robust iteration control technique, where the static shakedown theorem is adopted. Three numerical examples up to about 140,000 finite element nodes confirm the applicability and efficiency of this method for two-dimensional and three-dimensional elastoplastic structures, with detailed discussions on the convergence and the accuracy of the proposed algorithm.

A parallel finite element simulator for ion transport through three-dimensional ion channel systems.

PubMed

Tu, Bin; Chen, Minxin; Xie, Yan; Zhang, Linbo; Eisenberg, Bob; Lu, Benzhuo

2013-09-15

A parallel finite element simulator, ichannel, is developed for ion transport through three-dimensional ion channel systems that consist of protein and membrane. The coordinates of heavy atoms of the protein are taken from the Protein Data Bank and the membrane is represented as a slab. The simulator contains two components: a parallel adaptive finite element solver for a set of Poisson-Nernst-Planck (PNP) equations that describe the electrodiffusion process of ion transport, and a mesh generation tool chain for ion channel systems, which is an essential component for the finite element computations. The finite element method has advantages in modeling irregular geometries and complex boundary conditions. We have built a tool chain to get the surface and volume mesh for ion channel systems, which consists of a set of mesh generation tools. The adaptive finite element solver in our simulator is implemented using the parallel adaptive finite element package Parallel Hierarchical Grid (PHG) developed by one of the authors, which provides the capability of doing large scale parallel computations with high parallel efficiency and the flexibility of choosing high order elements to achieve high order accuracy. The simulator is applied to a real transmembrane protein, the gramicidin A (gA) channel protein, to calculate the electrostatic potential, ion concentrations and I - V curve, with which both primitive and transformed PNP equations are studied and their numerical performances are compared. To further validate the method, we also apply the simulator to two other ion channel systems, the voltage dependent anion channel (VDAC) and α-Hemolysin (α-HL). The simulation results agree well with Brownian dynamics (BD) simulation results and experimental results. Moreover, because ionic finite size effects can be included in PNP model now, we also perform simulations using a size-modified PNP (SMPNP) model on VDAC and α-HL. It is shown that the size effects in SMPNP can effectively lead to reduced current in the channel, and the results are closer to BD simulation results. Copyright © 2013 Wiley Periodicals, Inc.

A Novel Multiscale Physics Based Progressive Failure Methodology for Laminated Composite Structures

NASA Technical Reports Server (NTRS)

Pineda, Evan J.; Waas, Anthony M.; Bednarcyk, Brett A.; Collier, Craig S.; Yarrington, Phillip W.

2008-01-01

A variable fidelity, multiscale, physics based finite element procedure for predicting progressive damage and failure of laminated continuous fiber reinforced composites is introduced. At every integration point in a finite element model, progressive damage is accounted for at the lamina-level using thermodynamically based Schapery Theory. Separate failure criteria are applied at either the global-scale or the microscale in two different FEM models. A micromechanics model, the Generalized Method of Cells, is used to evaluate failure criteria at the micro-level. The stress-strain behavior and observed failure mechanisms are compared with experimental results for both models.

Structure and conformational dynamics of scaffolded DNA origami nanoparticles

DTIC Science & Technology

2017-05-08

all-atom molecular dynamics and coarse-grained finite element modeling to DX-based nanoparticles to elucidate their fine-scale and global conforma... finite element (FE) modeling approach CanDo is also routinely used to predict the 3D equilibrium conformation of programmed DNA assemblies based on a...model with both experimental cryo-electron microscopy (cryo-EM) data and all-atom modeling. MATERIALS AND METHODS Lattice-free finite element model

Finite element analysis of structural engineering problems using a viscoplastic model incorporating two back stresses

NASA Technical Reports Server (NTRS)

Arya, Vinod K.; Halford, Gary R.

1993-01-01

The feasibility of a viscoplastic model incorporating two back stresses and a drag strength is investigated for performing nonlinear finite element analyses of structural engineering problems. To demonstrate suitability for nonlinear structural analyses, the model is implemented into a finite element program and analyses for several uniaxial and multiaxial problems are performed. Good agreement is shown between the results obtained using the finite element implementation and those obtained experimentally. The advantages of using advanced viscoplastic models for performing nonlinear finite element analyses of structural components are indicated.

Predicting cell viability within tissue scaffolds under equiaxial strain: multi-scale finite element model of collagen-cardiomyocytes constructs.

PubMed

Elsaadany, Mostafa; Yan, Karen Chang; Yildirim-Ayan, Eda

2017-06-01

Successful tissue engineering and regenerative therapy necessitate having extensive knowledge about mechanical milieu in engineered tissues and the resident cells. In this study, we have merged two powerful analysis tools, namely finite element analysis and stochastic analysis, to understand the mechanical strain within the tissue scaffold and residing cells and to predict the cell viability upon applying mechanical strains. A continuum-based multi-length scale finite element model (FEM) was created to simulate the physiologically relevant equiaxial strain exposure on cell-embedded tissue scaffold and to calculate strain transferred to the tissue scaffold (macro-scale) and residing cells (micro-scale) upon various equiaxial strains. The data from FEM were used to predict cell viability under various equiaxial strain magnitudes using stochastic damage criterion analysis. The model validation was conducted through mechanically straining the cardiomyocyte-encapsulated collagen constructs using a custom-built mechanical loading platform (EQUicycler). FEM quantified the strain gradients over the radial and longitudinal direction of the scaffolds and the cells residing in different areas of interest. With the use of the experimental viability data, stochastic damage criterion, and the average cellular strains obtained from multi-length scale models, cellular viability was predicted and successfully validated. This methodology can provide a great tool to characterize the mechanical stimulation of bioreactors used in tissue engineering applications in providing quantification of mechanical strain and predicting cellular viability variations due to applied mechanical strain.

Creating physically-based three-dimensional microstructures: Bridging phase-field and crystal plasticity models.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Lim, Hojun; Owen, Steven J.; Abdeljawad, Fadi F.

In order to better incorporate microstructures in continuum scale models, we use a novel finite element (FE) meshing technique to generate three-dimensional polycrystalline aggregates from a phase field grain growth model of grain microstructures. The proposed meshing technique creates hexahedral FE meshes that capture smooth interfaces between adjacent grains. Three dimensional realizations of grain microstructures from the phase field model are used in crystal plasticity-finite element (CP-FE) simulations of polycrystalline a -iron. We show that the interface conformal meshes significantly reduce artificial stress localizations in voxelated meshes that exhibit the so-called "wedding cake" interfaces. This framework provides a direct linkmore » between two mesoscale models - phase field and crystal plasticity - and for the first time allows mechanics simulations of polycrystalline materials using three-dimensional hexahedral finite element meshes with realistic topological features.« less

First-Order System Least-Squares for Second-Order Elliptic Problems with Discontinuous Coefficients

NASA Technical Reports Server (NTRS)

Manteuffel, Thomas A.; McCormick, Stephen F.; Starke, Gerhard

1996-01-01

The first-order system least-squares methodology represents an alternative to standard mixed finite element methods. Among its advantages is the fact that the finite element spaces approximating the pressure and flux variables are not restricted by the inf-sup condition and that the least-squares functional itself serves as an appropriate error measure. This paper studies the first-order system least-squares approach for scalar second-order elliptic boundary value problems with discontinuous coefficients. Ellipticity of an appropriately scaled least-squares bilinear form of the size of the jumps in the coefficients leading to adequate finite element approximation results. The occurrence of singularities at interface corners and cross-points is discussed. and a weighted least-squares functional is introduced to handle such cases. Numerical experiments are presented for two test problems to illustrate the performance of this approach.

Generation of segmental chips in metal cutting modeled with the PFEM

NASA Astrophysics Data System (ADS)

Rodriguez Prieto, J. M.; Carbonell, J. M.; Cante, J. C.; Oliver, J.; Jonsén, P.

2018-06-01

The Particle Finite Element Method, a lagrangian finite element method based on a continuous Delaunay re-triangulation of the domain, is used to study machining of Ti6Al4V. In this work the method is revised and applied to study the influence of the cutting speed on the cutting force and the chip formation process. A parametric methodology for the detection and treatment of the rigid tool contact is presented. The adaptive insertion and removal of particles are developed and employed in order to sidestep the difficulties associated with mesh distortion, shear localization as well as for resolving the fine-scale features of the solution. The performance of PFEM is studied with a set of different two-dimensional orthogonal cutting tests. It is shown that, despite its Lagrangian nature, the proposed combined finite element-particle method is well suited for large deformation metal cutting problems with continuous chip and serrated chip formation.

Generation of segmental chips in metal cutting modeled with the PFEM

NASA Astrophysics Data System (ADS)

Rodriguez Prieto, J. M.; Carbonell, J. M.; Cante, J. C.; Oliver, J.; Jonsén, P.

2017-09-01

The Particle Finite Element Method, a lagrangian finite element method based on a continuous Delaunay re-triangulation of the domain, is used to study machining of Ti6Al4V. In this work the method is revised and applied to study the influence of the cutting speed on the cutting force and the chip formation process. A parametric methodology for the detection and treatment of the rigid tool contact is presented. The adaptive insertion and removal of particles are developed and employed in order to sidestep the difficulties associated with mesh distortion, shear localization as well as for resolving the fine-scale features of the solution. The performance of PFEM is studied with a set of different two-dimensional orthogonal cutting tests. It is shown that, despite its Lagrangian nature, the proposed combined finite element-particle method is well suited for large deformation metal cutting problems with continuous chip and serrated chip formation.

A new technique for simulating composite material

NASA Technical Reports Server (NTRS)

Volakis, John L.

1991-01-01

This project dealt with the development on new methodologies and algorithms for the multi-spectrum electromagnetic characterization of large scale nonmetallic airborne vehicles and structures. A robust, low memory, and accurate methodology was developed which is particularly suited for modern machine architectures. This is a hybrid finite element method that combines two well known numerical solution approaches. That of the finite element method for modeling volumes and the boundary integral method which yields exact boundary conditions for terminating the finite element mesh. In addition, a variety of high frequency results were generated (such as diffraction coefficients for impedance surfaces and material layers) and a class of boundary conditions were developed which hold promise for more efficient simulations. During the course of this project, nearly 25 detailed research reports were generated along with an equal number of journal papers. The reports, papers, and journal articles are listed in the appendices along with their abstracts.

Summary Report of Working Group 2: Computation

NASA Astrophysics Data System (ADS)

Stoltz, P. H.; Tsung, R. S.

2009-01-01

The working group on computation addressed three physics areas: (i) plasma-based accelerators (laser-driven and beam-driven), (ii) high gradient structure-based accelerators, and (iii) electron beam sources and transport [1]. Highlights of the talks in these areas included new models of breakdown on the microscopic scale, new three-dimensional multipacting calculations with both finite difference and finite element codes, and detailed comparisons of new electron gun models with standard models such as PARMELA. The group also addressed two areas of advances in computation: (i) new algorithms, including simulation in a Lorentz-boosted frame that can reduce computation time orders of magnitude, and (ii) new hardware architectures, like graphics processing units and Cell processors that promise dramatic increases in computing power. Highlights of the talks in these areas included results from the first large-scale parallel finite element particle-in-cell code (PIC), many order-of-magnitude speedup of, and details of porting the VPIC code to the Roadrunner supercomputer. The working group featured two plenary talks, one by Brian Albright of Los Alamos National Laboratory on the performance of the VPIC code on the Roadrunner supercomputer, and one by David Bruhwiler of Tech-X Corporation on recent advances in computation for advanced accelerators. Highlights of the talk by Albright included the first one trillion particle simulations, a sustained performance of 0.3 petaflops, and an eight times speedup of science calculations, including back-scatter in laser-plasma interaction. Highlights of the talk by Bruhwiler included simulations of 10 GeV accelerator laser wakefield stages including external injection, new developments in electromagnetic simulations of electron guns using finite difference and finite element approaches.

Summary Report of Working Group 2: Computation

DOE Office of Scientific and Technical Information (OSTI.GOV)

Stoltz, P. H.; Tsung, R. S.

2009-01-22

The working group on computation addressed three physics areas: (i) plasma-based accelerators (laser-driven and beam-driven), (ii) high gradient structure-based accelerators, and (iii) electron beam sources and transport [1]. Highlights of the talks in these areas included new models of breakdown on the microscopic scale, new three-dimensional multipacting calculations with both finite difference and finite element codes, and detailed comparisons of new electron gun models with standard models such as PARMELA. The group also addressed two areas of advances in computation: (i) new algorithms, including simulation in a Lorentz-boosted frame that can reduce computation time orders of magnitude, and (ii) newmore » hardware architectures, like graphics processing units and Cell processors that promise dramatic increases in computing power. Highlights of the talks in these areas included results from the first large-scale parallel finite element particle-in-cell code (PIC), many order-of-magnitude speedup of, and details of porting the VPIC code to the Roadrunner supercomputer. The working group featured two plenary talks, one by Brian Albright of Los Alamos National Laboratory on the performance of the VPIC code on the Roadrunner supercomputer, and one by David Bruhwiler of Tech-X Corporation on recent advances in computation for advanced accelerators. Highlights of the talk by Albright included the first one trillion particle simulations, a sustained performance of 0.3 petaflops, and an eight times speedup of science calculations, including back-scatter in laser-plasma interaction. Highlights of the talk by Bruhwiler included simulations of 10 GeV accelerator laser wakefield stages including external injection, new developments in electromagnetic simulations of electron guns using finite difference and finite element approaches.« less

Stability analysis and backward whirl investigation of cracked rotors with time-varying stiffness

NASA Astrophysics Data System (ADS)

AL-Shudeifat, Mohammad A.

2015-07-01

The dynamic stability of dynamical systems with time-periodic stiffness is addressed here. Cracked rotor systems with time-periodic stiffness are well-known examples of such systems. Time-varying area moments of inertia at the cracked element cross-section of a cracked rotor have been used to formulate the time-periodic finite element stiffness matrix. The semi-infinite coefficient matrix obtained by applying the harmonic balance (HB) solution to the finite element (FE) equations of motion is employed here to study the dynamic stability of the system. Consequently, the sign of the determinant of a scaled version of a sub-matrix of this semi-infinite coefficient matrix at a finite number of harmonics in the HB solution is found to be sufficient for identifying the major unstable zones of the system in the parameter plane. Specifically, it is found that the negative determinant always corresponds to unstable zones in all of the systems considered. This approach is applied to a parametrically excited Mathieu's equation, a two degree-of-freedom linear time-periodic dynamical system, a cracked Jeffcott rotor and a finite element model of the cracked rotor system. Compared to the corresponding results obtained by Floquet's theory, the sign of the determinant of the scaled sub-matrix is found to be an efficient tool for identifying the major unstable zones of the linear time-periodic parametrically excited systems, especially large-scale FE systems. Moreover, it is found that the unstable zones for a FE cracked rotor with an open transverse crack model only appear at the backward whirl. The theoretical and experimental results have been found to agree well for verifying that the open crack model excites the backward whirl amplitudes at the critical backward whirling rotational speeds.

The Coupling of Finite Element and Integral Equation Representations for Efficient Three-Dimensional Modeling of Electromagnetic Scattering and Radiation

NASA Technical Reports Server (NTRS)

Cwik, Tom; Zuffada, Cinzia; Jamnejad, Vahraz

1996-01-01

Finite element modeling has proven useful for accurtely simulating scattered or radiated fields from complex three-dimensional objects whose geometry varies on the scale of a fraction of a wavelength.

Load Testing, Finite Element Analysis, and Design of Steel Traffic-Signal Poles

DOT National Transportation Integrated Search

1993-07-01

At request of the Structures Design and Construction Division, the Engineering Research and Development Bureau performed full-scale testing and finite element analysis (FEA) of span-wire traffic-signal poles to evaluate their structural adequacy. Res...

The Relation of Finite Element and Finite Difference Methods

NASA Technical Reports Server (NTRS)

Vinokur, M.

1976-01-01

Finite element and finite difference methods are examined in order to bring out their relationship. It is shown that both methods use two types of discrete representations of continuous functions. They differ in that finite difference methods emphasize the discretization of independent variable, while finite element methods emphasize the discretization of dependent variable (referred to as functional approximations). An important point is that finite element methods use global piecewise functional approximations, while finite difference methods normally use local functional approximations. A general conclusion is that finite element methods are best designed to handle complex boundaries, while finite difference methods are superior for complex equations. It is also shown that finite volume difference methods possess many of the advantages attributed to finite element methods.

Wavelet and Multiresolution Analysis for Finite Element Networking Paradigms

NASA Technical Reports Server (NTRS)

Kurdila, Andrew J.; Sharpley, Robert C.

1999-01-01

This paper presents a final report on Wavelet and Multiresolution Analysis for Finite Element Networking Paradigms. The focus of this research is to derive and implement: 1) Wavelet based methodologies for the compression, transmission, decoding, and visualization of three dimensional finite element geometry and simulation data in a network environment; 2) methodologies for interactive algorithm monitoring and tracking in computational mechanics; and 3) Methodologies for interactive algorithm steering for the acceleration of large scale finite element simulations. Also included in this report are appendices describing the derivation of wavelet based Particle Image Velocity algorithms and reduced order input-output models for nonlinear systems by utilizing wavelet approximations.

Predicting Print-thru for the Sub-scale Beryllium Mirror Demonstrator (SBMD)

NASA Technical Reports Server (NTRS)

Craig, Larry; J. Kevin Russell (Technical Monitor)

2002-01-01

This document presents a finite element method for predicting print-thru or quilting for a lightweight mirror in a low temperature environment. The mirror is represented with quadrilateral and triangular plate finite elements. The SBMD (Sub-scale Beryllium Mirror Demonstrator) is circular with a diameter of 50 cm and one flat side. The mirror structure is a thin-wall triangular cell core with a single facesheet. There is a 4 mm radius fillet between the facesheet and cell walls. It is made entirely of Beryllium. It is assumed that polishing the mirror surface creates a thin surface layer with different material properties. Finite element results are compared with measured values at cryogenic temperatures.

Correlation of finite-element structural dynamic analysis with measured free vibration characteristics for a full-scale helicopter fuselage

NASA Technical Reports Server (NTRS)

Kenigsberg, I. J.; Dean, M. W.; Malatino, R.

1974-01-01

The correlation achieved with each program provides the material for a discussion of modeling techniques developed for general application to finite-element dynamic analyses of helicopter airframes. Included are the selection of static and dynamic degrees of freedom, cockpit structural modeling, and the extent of flexible-frame modeling in the transmission support region and in the vicinity of large cut-outs. The sensitivity of predicted results to these modeling assumptions are discussed. Both the Sikorsky Finite-Element Airframe Vibration analysis Program (FRAN/Vibration Analysis) and the NASA Structural Analysis Program (NASTRAN) have been correlated with data taken in full-scale vibration tests of a modified CH-53A helicopter.

A 3-D turbulent flow analysis using finite elements with k-ɛ model

NASA Astrophysics Data System (ADS)

Okuda, H.; Yagawa, G.; Eguchi, Y.

1989-03-01

This paper describes the finite element turbulent flow analysis, which is suitable for three-dimensional large scale problems. The k-ɛ turbulence model as well as the conservation equations of mass and momentum are discretized in space using rather low order elements. Resulting coefficient matrices are evaluated by one-point quadrature in order to reduce the computational storage and the CPU cost. The time integration scheme based on the velocity correction method is employed to obtain steady state solutions. For the verification of this FEM program, two-dimensional plenum flow is simulated and compared with experiment. As the application to three-dimensional practical problems, the turbulent flows in the upper plenum of the fast breeder reactor are calculated for various boundary conditions.

The Overshoot Phenomenon in Geodynamics Codes

NASA Astrophysics Data System (ADS)

Kommu, R. K.; Heien, E. M.; Kellogg, L. H.; Bangerth, W.; Heister, T.; Studley, E. H.

2013-12-01

The overshoot phenomenon is a common occurrence in numerical software when a continuous function on a finite dimensional discretized space is used to approximate a discontinuous jump, in temperature and material concentration, for example. The resulting solution overshoots, and undershoots, the discontinuous jump. Numerical simulations play an extremely important role in mantle convection research. This is both due to the strong temperature and stress dependence of viscosity and also due to the inaccessibility of deep earth. Under these circumstances, it is essential that mantle convection simulations be extremely accurate and reliable. CitcomS and ASPECT are two finite element based mantle convection simulations developed and maintained by the Computational Infrastructure for Geodynamics. CitcomS is a finite element based mantle convection code that is designed to run on multiple high-performance computing platforms. ASPECT, an adaptive mesh refinement (AMR) code built on the Deal.II library, is also a finite element based mantle convection code that scales well on various HPC platforms. CitcomS and ASPECT both exhibit the overshoot phenomenon. One attempt at controlling the overshoot uses the Entropy Viscosity method, which introduces an artificial diffusion term in the energy equation of mantle convection. This artificial diffusion term is small where the temperature field is smooth. We present results from CitcomS and ASPECT that quantify the effect of the Entropy Viscosity method in reducing the overshoot phenomenon. In the discontinuous Galerkin (DG) finite element method, the test functions used in the method are continuous within each element but are discontinuous across inter-element boundaries. The solution space in the DG method is discontinuous. FEniCS is a collection of free software tools that automate the solution of differential equations using finite element methods. In this work we also present results from a finite element mantle convection simulation implemented in FEniCS that investigates the effect of using DG elements in reducing the overshoot problem.

A comparative study on dynamic stiffness in typical finite element model and multi-body model of C6-C7 cervical spine segment.

PubMed

Wang, Yawei; Wang, Lizhen; Du, Chengfei; Mo, Zhongjun; Fan, Yubo

2016-06-01

In contrast to numerous researches on static or quasi-static stiffness of cervical spine segments, very few investigations on their dynamic stiffness were published. Currently, scale factors and estimated coefficients were usually used in multi-body models for including viscoelastic properties and damping effects, meanwhile viscoelastic properties of some tissues were unavailable for establishing finite element models. Because dynamic stiffness of cervical spine segments in these models were difficult to validate because of lacking in experimental data, we tried to gain some insights on current modeling methods through studying dynamic stiffness differences between these models. A finite element model and a multi-body model of C6-C7 segment were developed through using available material data and typical modeling technologies. These two models were validated with quasi-static response data of the C6-C7 cervical spine segment. Dynamic stiffness differences were investigated through controlling motions of C6 vertebrae at different rates and then comparing their reaction forces or moments. Validation results showed that both the finite element model and the multi-body model could generate reasonable responses under quasi-static loads, but the finite element segment model exhibited more nonlinear characters. Dynamic response investigations indicated that dynamic stiffness of this finite element model might be underestimated because of the absence of dynamic stiffen effect and damping effects of annulus fibrous, while representation of these effects also need to be improved in current multi-body model. Copyright © 2015 John Wiley & Sons, Ltd. Copyright © 2015 John Wiley & Sons, Ltd.

Predicting Rediated Noise With Power Flow Finite Element Analysis

DTIC Science & Technology

2007-02-01

Defence R&D Canada – Atlantic DEFENCE DÉFENSE & Predicting Rediated Noise With Power Flow Finite Element Analysis D. Brennan T.S. Koko L. Jiang J...PREDICTING RADIATED NOISE WITH POWER FLOW FINITE ELEMENT ANALYSIS D.P. Brennan T.S. Koko L. Jiang J.C. Wallace Martec Limited Martec Limited...model- or full-scale data before it is available for general use. Brennan, D.P., Koko , T.S., Jiang, L., Wallace, J.C. 2007. Predicting Radiated

H-P adaptive methods for finite element analysis of aerothermal loads in high-speed flows

NASA Technical Reports Server (NTRS)

Chang, H. J.; Bass, J. M.; Tworzydlo, W.; Oden, J. T.

1993-01-01

The commitment to develop the National Aerospace Plane and Maneuvering Reentry Vehicles has generated resurgent interest in the technology required to design structures for hypersonic flight. The principal objective of this research and development effort has been to formulate and implement a new class of computational methodologies for accurately predicting fine scale phenomena associated with this class of problems. The initial focus of this effort was to develop optimal h-refinement and p-enrichment adaptive finite element methods which utilize a-posteriori estimates of the local errors to drive the adaptive methodology. Over the past year this work has specifically focused on two issues which are related to overall performance of a flow solver. These issues include the formulation and implementation (in two dimensions) of an implicit/explicit flow solver compatible with the hp-adaptive methodology, and the design and implementation of computational algorithm for automatically selecting optimal directions in which to enrich the mesh. These concepts and algorithms have been implemented in a two-dimensional finite element code and used to solve three hypersonic flow benchmark problems (Holden Mach 14.1, Edney shock on shock interaction Mach 8.03, and the viscous backstep Mach 4.08).

Field-scale and wellbore modeling of compaction-induced casing failures

DOE Office of Scientific and Technical Information (OSTI.GOV)

Hilbert, L.B. Jr.; Gwinn, R.L.; Moroney, T.A.

1999-06-01

Presented in this paper are the results and verification of field- and wellbore-scale large deformation, elasto-plastic, geomechanical finite element models of reservoir compaction and associated casing damage. The models were developed as part of a multidisciplinary team project to reduce the number of costly well failures in the diatomite reservoir of the South Belridge Field near Bakersfield, California. Reservoir compaction of high porosity diatomite rock induces localized shearing deformations on horizontal weak-rock layers and geologic unconformities. The localized shearing deformations result in casing damage or failure. Two-dimensional, field-scale finite element models were used to develop relationships between field operations, surfacemore » subsidence, and shear-induced casing damage. Pore pressures were computed for eighteen years of simulated production and water injection, using a three-dimensional reservoir simulator. The pore pressures were input to the two-dimensional geomechanical field-scale model. Frictional contact surfaces were used to model localized shear deformations. To capture the complex casing-cement-rock interaction that governs casing damage and failure, three-dimensional models of a wellbore were constructed, including a frictional sliding surface to model localized shear deformation. Calculations were compared to field data for verification of the models.« less

An Automated Method for Landmark Identification and Finite-Element Modeling of the Lumbar Spine.

PubMed

Campbell, Julius Quinn; Petrella, Anthony J

2015-11-01

The purpose of this study was to develop a method for the automated creation of finite-element models of the lumbar spine. Custom scripts were written to extract bone landmarks of lumbar vertebrae and assemble L1-L5 finite-element models. End-plate borders, ligament attachment points, and facet surfaces were identified. Landmarks were identified to maintain mesh correspondence between meshes for later use in statistical shape modeling. 90 lumbar vertebrae were processed creating 18 subject-specific finite-element models. Finite-element model surfaces and ligament attachment points were reproduced within 1e-5 mm of the bone surface, including the critical contact surfaces of the facets. Element quality exceeded specifications in 97% of elements for the 18 models created. The current method is capable of producing subject-specific finite-element models of the lumbar spine with good accuracy, quality, and robustness. The automated methods developed represent advancement in the state of the art of subject-specific lumbar spine modeling to a scale not possible with prior manual and semiautomated methods.

Scaling in biomechanical experimentation: a finite similitude approach.

PubMed

Ochoa-Cabrero, Raul; Alonso-Rasgado, Teresa; Davey, Keith

2018-06-01

Biological experimentation has many obstacles: resource limitations, unavailability of materials, manufacturing complexities and ethical compliance issues; any approach that resolves all or some of these is of some interest. The aim of this study is applying the recently discovered concept of finite similitude as a novel approach for the design of scaled biomechanical experiments supported with analysis using a commercial finite-element package and validated by means of image correlation software. The study of isotropic scaling of synthetic bones leads to the selection of three-dimensional (3D) printed materials for the trial-space materials. These materials conforming to the theory are analysed in finite-element models of a cylinder and femur geometries undergoing compression, tension, torsion and bending tests to assess the efficacy of the approach using reverse scaling of the approach. The finite-element results show similar strain patterns in the surface for the cylinder with a maximum difference of less than 10% and for the femur with a maximum difference of less than 4% across all tests. Finally, the trial-space, physical-trial experimentation using 3D printed materials for compression and bending testing provides a good agreement in a Bland-Altman statistical analysis, providing good supporting evidence for the practicality of the approach. © 2018 The Author(s).

Coupled Finite Volume and Finite Element Method Analysis of a Complex Large-Span Roof Structure

NASA Astrophysics Data System (ADS)

Szafran, J.; Juszczyk, K.; Kamiński, M.

2017-12-01

The main goal of this paper is to present coupled Computational Fluid Dynamics and structural analysis for the precise determination of wind impact on internal forces and deformations of structural elements of a longspan roof structure. The Finite Volume Method (FVM) serves for a solution of the fluid flow problem to model the air flow around the structure, whose results are applied in turn as the boundary tractions in the Finite Element Method problem structural solution for the linear elastostatics with small deformations. The first part is carried out with the use of ANSYS 15.0 computer system, whereas the FEM system Robot supports stress analysis in particular roof members. A comparison of the wind pressure distribution throughout the roof surface shows some differences with respect to that available in the engineering designing codes like Eurocode, which deserves separate further numerical studies. Coupling of these two separate numerical techniques appears to be promising in view of future computational models of stochastic nature in large scale structural systems due to the stochastic perturbation method.

Energy and technology review: Engineering modeling

DOE Office of Scientific and Technical Information (OSTI.GOV)

Cabayan, H.S.; Goudreau, G.L.; Ziolkowski, R.W.

1986-10-01

This report presents information concerning: Modeling Canonical Problems in Electromagnetic Coupling Through Apertures; Finite-Element Codes for Computing Electrostatic Fields; Finite-Element Modeling of Electromagnetic Phenomena; Modeling Microwave-Pulse Compression in a Resonant Cavity; Lagrangian Finite-Element Analysis of Penetration Mechanics; Crashworthiness Engineering; Computer Modeling of Metal-Forming Processes; Thermal-Mechanical Modeling of Tungsten Arc Welding; Modeling Air Breakdown Induced by Electromagnetic Fields; Iterative Techniques for Solving Boltzmann's Equations for p-Type Semiconductors; Semiconductor Modeling; and Improved Numerical-Solution Techniques in Large-Scale Stress Analysis.

A high-order multiscale finite-element method for time-domain acoustic-wave modeling

NASA Astrophysics Data System (ADS)

Gao, Kai; Fu, Shubin; Chung, Eric T.

2018-05-01

Accurate and efficient wave equation modeling is vital for many applications in such as acoustics, electromagnetics, and seismology. However, solving the wave equation in large-scale and highly heterogeneous models is usually computationally expensive because the computational cost is directly proportional to the number of grids in the model. We develop a novel high-order multiscale finite-element method to reduce the computational cost of time-domain acoustic-wave equation numerical modeling by solving the wave equation on a coarse mesh based on the multiscale finite-element theory. In contrast to existing multiscale finite-element methods that use only first-order multiscale basis functions, our new method constructs high-order multiscale basis functions from local elliptic problems which are closely related to the Gauss-Lobatto-Legendre quadrature points in a coarse element. Essentially, these basis functions are not only determined by the order of Legendre polynomials, but also by local medium properties, and therefore can effectively convey the fine-scale information to the coarse-scale solution with high-order accuracy. Numerical tests show that our method can significantly reduce the computation time while maintain high accuracy for wave equation modeling in highly heterogeneous media by solving the corresponding discrete system only on the coarse mesh with the new high-order multiscale basis functions.

A high-order multiscale finite-element method for time-domain acoustic-wave modeling

DOE Office of Scientific and Technical Information (OSTI.GOV)

Gao, Kai; Fu, Shubin; Chung, Eric T.

Accurate and efficient wave equation modeling is vital for many applications in such as acoustics, electromagnetics, and seismology. However, solving the wave equation in large-scale and highly heterogeneous models is usually computationally expensive because the computational cost is directly proportional to the number of grids in the model. We develop a novel high-order multiscale finite-element method to reduce the computational cost of time-domain acoustic-wave equation numerical modeling by solving the wave equation on a coarse mesh based on the multiscale finite-element theory. In contrast to existing multiscale finite-element methods that use only first-order multiscale basis functions, our new method constructsmore » high-order multiscale basis functions from local elliptic problems which are closely related to the Gauss–Lobatto–Legendre quadrature points in a coarse element. Essentially, these basis functions are not only determined by the order of Legendre polynomials, but also by local medium properties, and therefore can effectively convey the fine-scale information to the coarse-scale solution with high-order accuracy. Numerical tests show that our method can significantly reduce the computation time while maintain high accuracy for wave equation modeling in highly heterogeneous media by solving the corresponding discrete system only on the coarse mesh with the new high-order multiscale basis functions.« less

A high-order multiscale finite-element method for time-domain acoustic-wave modeling

DOE PAGES

Gao, Kai; Fu, Shubin; Chung, Eric T.

2018-02-04

Accurate and efficient wave equation modeling is vital for many applications in such as acoustics, electromagnetics, and seismology. However, solving the wave equation in large-scale and highly heterogeneous models is usually computationally expensive because the computational cost is directly proportional to the number of grids in the model. We develop a novel high-order multiscale finite-element method to reduce the computational cost of time-domain acoustic-wave equation numerical modeling by solving the wave equation on a coarse mesh based on the multiscale finite-element theory. In contrast to existing multiscale finite-element methods that use only first-order multiscale basis functions, our new method constructsmore » high-order multiscale basis functions from local elliptic problems which are closely related to the Gauss–Lobatto–Legendre quadrature points in a coarse element. Essentially, these basis functions are not only determined by the order of Legendre polynomials, but also by local medium properties, and therefore can effectively convey the fine-scale information to the coarse-scale solution with high-order accuracy. Numerical tests show that our method can significantly reduce the computation time while maintain high accuracy for wave equation modeling in highly heterogeneous media by solving the corresponding discrete system only on the coarse mesh with the new high-order multiscale basis functions.« less

The Development of Directional Decohesion Finite Elements for Multiscale Failure Analysis of Metallic Polycrystals

NASA Technical Reports Server (NTRS)

Saether, Erik; Glaessgen, Edward H.

2009-01-01

Atomistic simulations of intergranular fracture have indicated that grain-scale crack growth in polycrystalline metals can be direction dependent. At these material length scales, the atomic environment greatly influences the nature of intergranular crack propagation, through either brittle or ductile mechanisms, that are a function of adjacent grain orientation and direction of crack propagation. Methods have been developed to obtain cohesive zone models (CZM) directly from molecular dynamics simulations. These CZMs may be incorporated into decohesion finite element formulations to simulate fracture at larger length scales. A new directional decohesion element is presented that calculates the direction of Mode I opening and incorporates a material criterion for dislocation emission based on the local crystallographic environment to automatically select the CZM that best represents crack growth. The simulation of fracture in 2-D and 3-D aluminum polycrystals is used to illustrate the effect of parameterized CZMs and the effectiveness of directional decohesion finite elements.

Parallel goal-oriented adaptive finite element modeling for 3D electromagnetic exploration

NASA Astrophysics Data System (ADS)

Zhang, Y.; Key, K.; Ovall, J.; Holst, M.

2014-12-01

We present a parallel goal-oriented adaptive finite element method for accurate and efficient electromagnetic (EM) modeling of complex 3D structures. An unstructured tetrahedral mesh allows this approach to accommodate arbitrarily complex 3D conductivity variations and a priori known boundaries. The total electric field is approximated by the lowest order linear curl-conforming shape functions and the discretized finite element equations are solved by a sparse LU factorization. Accuracy of the finite element solution is achieved through adaptive mesh refinement that is performed iteratively until the solution converges to the desired accuracy tolerance. Refinement is guided by a goal-oriented error estimator that uses a dual-weighted residual method to optimize the mesh for accurate EM responses at the locations of the EM receivers. As a result, the mesh refinement is highly efficient since it only targets the elements where the inaccuracy of the solution corrupts the response at the possibly distant locations of the EM receivers. We compare the accuracy and efficiency of two approaches for estimating the primary residual error required at the core of this method: one uses local element and inter-element residuals and the other relies on solving a global residual system using a hierarchical basis. For computational efficiency our method follows the Bank-Holst algorithm for parallelization, where solutions are computed in subdomains of the original model. To resolve the load-balancing problem, this approach applies a spectral bisection method to divide the entire model into subdomains that have approximately equal error and the same number of receivers. The finite element solutions are then computed in parallel with each subdomain carrying out goal-oriented adaptive mesh refinement independently. We validate the newly developed algorithm by comparison with controlled-source EM solutions for 1D layered models and with 2D results from our earlier 2D goal oriented adaptive refinement code named MARE2DEM. We demonstrate the performance and parallel scaling of this algorithm on a medium-scale computing cluster with a marine controlled-source EM example that includes a 3D array of receivers located over a 3D model that includes significant seafloor bathymetry variations and a heterogeneous subsurface.

Finite element modeling and analysis of tires

NASA Technical Reports Server (NTRS)

Noor, A. K.; Andersen, C. M.

1983-01-01

Predicting the response of tires under various loading conditions using finite element technology is addressed. Some of the recent advances in finite element technology which have high potential for application to tire modeling problems are reviewed. The analysis and modeling needs for tires are identified. Reduction methods for large-scale nonlinear analysis, with particular emphasis on treatment of combined loads, displacement-dependent and nonconservative loadings; development of simple and efficient mixed finite element models for shell analysis, identification of equivalent mixed and purely displacement models, and determination of the advantages of using mixed models; and effective computational models for large-rotation nonlinear problems, based on a total Lagrangian description of the deformation are included.

Development and Calibration of a System-Integrated Rotorcraft Finite Element Model for Impact Scenarios

NASA Technical Reports Server (NTRS)

Annett, Martin S.; Horta, Lucas G.; Jackson, Karen E.; Polanco, Michael A.; Littell, Justin D.

2012-01-01

Two full-scale crash tests of an MD-500 helicopter were conducted in 2009 and 2010 at NASA Langley's Landing and Impact Research Facility in support of NASA s Subsonic Rotary Wing Crashworthiness Project. The first crash test was conducted to evaluate the performance of an externally mounted composite deployable energy absorber (DEA) under combined impact conditions. In the second crash test, the energy absorber was removed to establish baseline loads that are regarded as severe but survivable. The presence of this energy absorbing device reduced the peak impact acceleration levels by a factor of three. Accelerations and kinematic data collected from the crash tests were compared to a system-integrated finite element model of the test article developed in parallel with the test program. In preparation for the full-scale crash test, a series of sub-scale and MD-500 mass simulator tests were conducted to evaluate the impact performances of various components and subsystems, including new crush tubes and the DEA blocks. Parameters defined for the system-integrated finite element model were determined from these tests. Results from 19 accelerometers placed throughout the airframe were compared to finite element model responses. The model developed for the purposes of predicting acceleration responses from the first crash test was inadequate when evaluating more severe conditions seen in the second crash test. A newly developed model calibration approach that includes uncertainty estimation, parameter sensitivity, impact shape orthogonality, and numerical optimization was used to calibrate model results for the full-scale crash test without the DEA. This combination of heuristic and quantitative methods identified modeling deficiencies, evaluated parameter importance, and proposed required model changes. The multidimensional calibration techniques presented here are particularly effective in identifying model adequacy. Acceleration results for the calibrated model were compared to test results and the original model results. There was a noticeable improvement in the pilot and copilot region, a slight improvement in the occupant model response, and an over-stiffening effect in the passenger region. One lesson learned was that this approach should be adopted early on, in combination with the building-block approaches that are customarily used, for model development and pretest predictions. Complete crash simulations with validated finite element models can be used to satisfy crash certification requirements, potentially reducing overall development costs.

LS-DYNA Analysis of a Full-Scale Helicopter Crash Test

NASA Technical Reports Server (NTRS)

Annett, Martin S.

2010-01-01

A full-scale crash test of an MD-500 helicopter was conducted in December 2009 at NASA Langley's Landing and Impact Research facility (LandIR). The MD-500 helicopter was fitted with a composite honeycomb Deployable Energy Absorber (DEA) and tested under vertical and horizontal impact velocities of 26 ft/sec and 40 ft/sec, respectively. The objectives of the test were to evaluate the performance of the DEA concept under realistic crash conditions and to generate test data for validation of a system integrated LS-DYNA finite element model. In preparation for the full-scale crash test, a series of sub-scale and MD-500 mass simulator tests was conducted to evaluate the impact performances of various components, including a new crush tube and the DEA blocks. Parameters defined within the system integrated finite element model were determined from these tests. The objective of this paper is to summarize the finite element models developed and analyses performed, beginning with pre-test and continuing through post test validation.

Newmark local time stepping on high-performance computing architectures

DOE Office of Scientific and Technical Information (OSTI.GOV)

Rietmann, Max, E-mail: max.rietmann@erdw.ethz.ch; Institute of Geophysics, ETH Zurich; Grote, Marcus, E-mail: marcus.grote@unibas.ch

In multi-scale complex media, finite element meshes often require areas of local refinement, creating small elements that can dramatically reduce the global time-step for wave-propagation problems due to the CFL condition. Local time stepping (LTS) algorithms allow an explicit time-stepping scheme to adapt the time-step to the element size, allowing near-optimal time-steps everywhere in the mesh. We develop an efficient multilevel LTS-Newmark scheme and implement it in a widely used continuous finite element seismic wave-propagation package. In particular, we extend the standard LTS formulation with adaptations to continuous finite element methods that can be implemented very efficiently with very strongmore » element-size contrasts (more than 100x). Capable of running on large CPU and GPU clusters, we present both synthetic validation examples and large scale, realistic application examples to demonstrate the performance and applicability of the method and implementation on thousands of CPU cores and hundreds of GPUs.« less

A general algorithm using finite element method for aerodynamic configurations at low speeds

NASA Technical Reports Server (NTRS)

Balasubramanian, R.

1975-01-01

A finite element algorithm for numerical simulation of two-dimensional, incompressible, viscous flows was developed. The Navier-Stokes equations are suitably modelled to facilitate direct solution for the essential flow parameters. A leap-frog time differencing and Galerkin minimization of these model equations yields the finite element algorithm. The finite elements are triangular with bicubic shape functions approximating the solution space. The finite element matrices are unsymmetrically banded to facilitate savings in storage. An unsymmetric L-U decomposition is performed on the finite element matrices to obtain the solution for the boundary value problem.

Adaptive finite element methods for two-dimensional problems in computational fracture mechanics

NASA Technical Reports Server (NTRS)

Min, J. B.; Bass, J. M.; Spradley, L. W.

1994-01-01

Some recent results obtained using solution-adaptive finite element methods in two-dimensional problems in linear elastic fracture mechanics are presented. The focus is on the basic issue of adaptive finite element methods for validating the new methodology by computing demonstration problems and comparing the stress intensity factors to analytical results.

Tools for Modeling & Simulation of Molecular and Nanoelectronics Devices

DTIC Science & Technology

2012-06-14

implemented a prototype DFT simulation software using two different open source Finite Element (FE) libraries: DEALII and FENICS . These two libraries have been...ATK. In the first part of this Phase I project we investigated two different candidate finite element libraries, DEAL II and FENICS . Although both...element libraries, Deal.II and FEniCS /dolfin, for use as back-ends to a finite element DFT in ATK, Quantum Insight and QuantumWise A/S, October 2011.

Development of technology for modeling of a 1/8-scale dynamic model of the shuttle Solid Rocket Booster (SRB)

NASA Technical Reports Server (NTRS)

Levy, A.; Zalesak, J.; Bernstein, M.; Mason, P. W.

1974-01-01

A NASTRAN analysis of the solid rocket booster (SRB) substructure of the space shuttle 1/8-scale structural dynamics model. The NASTRAN finite element modeling capability was first used to formulate a model of a cylinder 10 in. radius by a 200 in. length to investigate the accuracy and adequacy of the proposed grid point spacing. Results were compared with a shell analysis and demonstrated relatively accurate results for NASTRAN for the lower modes, which were of primary interest. A finite element model of the full SRB was then formed using CQUAD2 plate elements containing membrane and bending stiffness and CBAR offset bar elements to represent the longerons and frames. Three layers of three-dimensional CHEXAI elements were used to model the propellant. This model, consisting of 4000 degrees of freedom (DOF) initially, was reduced to 176 DOF using Guyan reduction. The model was then submitted for complex Eigenvalue analysis. After experiencing considerable difficulty with attempts to run the complete model, it was split into two substructres. These were run separately and combined into a single 116 degree of freedom A set which was successfully run. Results are reported.

Large-eddy simulation using the finite element method

DOE Office of Scientific and Technical Information (OSTI.GOV)

McCallen, R.C.; Gresho, P.M.; Leone, J.M. Jr.

1993-10-01

In a large-eddy simulation (LES) of turbulent flows, the large-scale motion is calculated explicitly (i.e., approximated with semi-empirical relations). Typically, finite difference or spectral numerical schemes are used to generate an LES; the use of finite element methods (FEM) has been far less prominent. In this study, we demonstrate that FEM in combination with LES provides a viable tool for the study of turbulent, separating channel flows, specifically the flow over a two-dimensional backward-facing step. The combination of these methodologies brings together the advantages of each: LES provides a high degree of accuracy with a minimum of empiricism for turbulencemore » modeling and FEM provides a robust way to simulate flow in very complex domains of practical interest. Such a combination should prove very valuable to the engineering community.« less

A new parallel-vector finite element analysis software on distributed-memory computers

NASA Technical Reports Server (NTRS)

Qin, Jiangning; Nguyen, Duc T.

1993-01-01

A new parallel-vector finite element analysis software package MPFEA (Massively Parallel-vector Finite Element Analysis) is developed for large-scale structural analysis on massively parallel computers with distributed-memory. MPFEA is designed for parallel generation and assembly of the global finite element stiffness matrices as well as parallel solution of the simultaneous linear equations, since these are often the major time-consuming parts of a finite element analysis. Block-skyline storage scheme along with vector-unrolling techniques are used to enhance the vector performance. Communications among processors are carried out concurrently with arithmetic operations to reduce the total execution time. Numerical results on the Intel iPSC/860 computers (such as the Intel Gamma with 128 processors and the Intel Touchstone Delta with 512 processors) are presented, including an aircraft structure and some very large truss structures, to demonstrate the efficiency and accuracy of MPFEA.

The application of super wavelet finite element on temperature-pressure coupled field simulation of LPG tank under jet fire

NASA Astrophysics Data System (ADS)

Zhao, Bin

2015-02-01

Temperature-pressure coupled field analysis of liquefied petroleum gas (LPG) tank under jet fire can offer theoretical guidance for preventing the fire accidents of LPG tank, the application of super wavelet finite element on it is studied in depth. First, review of related researches on heat transfer analysis of LPG tank under fire and super wavelet are carried out. Second, basic theory of super wavelet transform is studied. Third, the temperature-pressure coupled model of gas phase and liquid LPG under jet fire is established based on the equation of state, the VOF model and the RNG k-ɛ model. Then the super wavelet finite element formulation is constructed using the super wavelet scale function as interpolating function. Finally, the simulation is carried out, and results show that the super wavelet finite element method has higher computing precision than wavelet finite element method.

Radiation Heat Transfer Between Diffuse-Gray Surfaces Using Higher Order Finite Elements

NASA Technical Reports Server (NTRS)

Gould, Dana C.

2000-01-01

This paper presents recent work on developing methods for analyzing radiation heat transfer between diffuse-gray surfaces using p-version finite elements. The work was motivated by a thermal analysis of a High Speed Civil Transport (HSCT) wing structure which showed the importance of radiation heat transfer throughout the structure. The analysis also showed that refining the finite element mesh to accurately capture the temperature distribution on the internal structure led to very large meshes with unacceptably long execution times. Traditional methods for calculating surface-to-surface radiation are based on assumptions that are not appropriate for p-version finite elements. Two methods for determining internal radiation heat transfer are developed for one and two-dimensional p-version finite elements. In the first method, higher-order elements are divided into a number of sub-elements. Traditional methods are used to determine radiation heat flux along each sub-element and then mapped back to the parent element. In the second method, the radiation heat transfer equations are numerically integrated over the higher-order element. Comparisons with analytical solutions show that the integration scheme is generally more accurate than the sub-element method. Comparison to results from traditional finite elements shows that significant reduction in the number of elements in the mesh is possible using higher-order (p-version) finite elements.

Improving a complex finite-difference ground water flow model through the use of an analytic element screening model

USGS Publications Warehouse

Hunt, R.J.; Anderson, M.P.; Kelson, V.A.

1998-01-01

This paper demonstrates that analytic element models have potential as powerful screening tools that can facilitate or improve calibration of more complicated finite-difference and finite-element models. We demonstrate how a two-dimensional analytic element model was used to identify errors in a complex three-dimensional finite-difference model caused by incorrect specification of boundary conditions. An improved finite-difference model was developed using boundary conditions developed from a far-field analytic element model. Calibration of a revised finite-difference model was achieved using fewer zones of hydraulic conductivity and lake bed conductance than the original finite-difference model. Calibration statistics were also improved in that simulated base-flows were much closer to measured values. The improved calibration is due mainly to improved specification of the boundary conditions made possible by first solving the far-field problem with an analytic element model.This paper demonstrates that analytic element models have potential as powerful screening tools that can facilitate or improve calibration of more complicated finite-difference and finite-element models. We demonstrate how a two-dimensional analytic element model was used to identify errors in a complex three-dimensional finite-difference model caused by incorrect specification of boundary conditions. An improved finite-difference model was developed using boundary conditions developed from a far-field analytic element model. Calibration of a revised finite-difference model was achieved using fewer zones of hydraulic conductivity and lake bed conductance than the original finite-difference model. Calibration statistics were also improved in that simulated base-flows were much closer to measured values. The improved calibration is due mainly to improved specification of the boundary conditions made possible by first solving the far-field problem with an analytic element model.

Review of literature on the finite-element solution of the equations of two-dimensional surface-water flow in the horizontal plane

USGS Publications Warehouse

Lee, Jonathan K.; Froehlich, David C.

1987-01-01

Published literature on the application of the finite-element method to solving the equations of two-dimensional surface-water flow in the horizontal plane is reviewed in this report. The finite-element method is ideally suited to modeling two-dimensional flow over complex topography with spatially variable resistance. A two-dimensional finite-element surface-water flow model with depth and vertically averaged velocity components as dependent variables allows the user great flexibility in defining geometric features such as the boundaries of a water body, channels, islands, dikes, and embankments. The following topics are reviewed in this report: alternative formulations of the equations of two-dimensional surface-water flow in the horizontal plane; basic concepts of the finite-element method; discretization of the flow domain and representation of the dependent flow variables; treatment of boundary conditions; discretization of the time domain; methods for modeling bottom, surface, and lateral stresses; approaches to solving systems of nonlinear equations; techniques for solving systems of linear equations; finite-element alternatives to Galerkin's method of weighted residuals; techniques of model validation; and preparation of model input data. References are listed in the final chapter.

Finite Macro-Element Mesh Deformation in a Structured Multi-Block Navier-Stokes Code

NASA Technical Reports Server (NTRS)

Bartels, Robert E.

2005-01-01

A mesh deformation scheme is developed for a structured multi-block Navier-Stokes code consisting of two steps. The first step is a finite element solution of either user defined or automatically generated macro-elements. Macro-elements are hexagonal finite elements created from a subset of points from the full mesh. When assembled, the finite element system spans the complete flow domain. Macro-element moduli vary according to the distance to the nearest surface, resulting in extremely stiff elements near a moving surface and very pliable elements away from boundaries. Solution of the finite element system for the imposed boundary deflections generally produces smoothly varying nodal deflections. The manner in which distance to the nearest surface has been found to critically influence the quality of the element deformation. The second step is a transfinite interpolation which distributes the macro-element nodal deflections to the remaining fluid mesh points. The scheme is demonstrated for several two-dimensional applications.

Thermal Analysis of Small Re-Entry Probe

NASA Technical Reports Server (NTRS)

Agrawal, Parul; Prabhu, Dinesh K.; Chen, Y. K.

2012-01-01

The Small Probe Reentry Investigation for TPS Engineering (SPRITE) concept was developed at NASA Ames Research Center to facilitate arc-jet testing of a fully instrumented prototype probe at flight scale. Besides demonstrating the feasibility of testing a flight-scale model and the capability of an on-board data acquisition system, another objective for this project was to investigate the capability of simulation tools to predict thermal environments of the probe/test article and its interior. This paper focuses on finite-element thermal analyses of the SPRITE probe during the arcjet tests. Several iterations were performed during the early design phase to provide critical design parameters and guidelines for testing. The thermal effects of ablation and pyrolysis were incorporated into the final higher-fidelity modeling approach by coupling the finite-element analyses with a two-dimensional thermal protection materials response code. Model predictions show good agreement with thermocouple data obtained during the arcjet test.

Finite Element Multi-scale Modeling of Chemical Segregation in Steel Solidification Taking into Account the Transport of Equiaxed Grains

NASA Astrophysics Data System (ADS)

Nguyen, Thi-Thuy-My; Gandin, Charles-André; Combeau, Hervé; Založnik, Miha; Bellet, Michel

2018-02-01

The transport of solid crystals in the liquid pool during solidification of large ingots is known to have a significant effect on their final grain structure and macrosegregation. Numerical modeling of the associated physics is challenging since complex and strong interactions between heat and mass transfer at the microscopic and macroscopic scales must be taken into account. The paper presents a finite element multi-scale solidification model coupling nucleation, growth, and solute diffusion at the microscopic scale, represented by a single unique grain, while also including transport of the liquid and solid phases at the macroscopic scale of the ingots. The numerical resolution is based on a splitting method which sequentially describes the evolution and interaction of quantities into a transport and a growth stage. This splitting method reduces the non-linear complexity of the set of equations and is, for the first time, implemented using the finite element method. This is possible due to the introduction of an artificial diffusion in all conservation equations solved by the finite element method. Simulations with and without grain transport are compared to demonstrate the impact of solid phase transport on the solidification process as well as the formation of macrosegregation in a binary alloy (Sn-5 wt pct Pb). The model is also applied to the solidification of the binary alloy Fe-0.36 wt pct C in a domain representative of a 3.3-ton steel ingot.

Comparisons of external fixator combined with limited internal fixation and open reduction and internal fixation for Sanders type 2 calcaneal fractures: Finite element analysis and clinical outcome.

PubMed

Pan, M; Chai, L; Xue, F; Ding, L; Tang, G; Lv, B

2017-07-01

The aim of this study was to compare the biomechanical stability and clinical outcome of external fixator combined with limited internal fixation (EFLIF) and open reduction and internal fixation (ORIF) in treating Sanders type 2 calcaneal fractures. Two types of fixation systems were selected for finite element analysis and a dual cohort study. Two fixation systems were simulated to fix the fracture in a finite element model. The relative displacement and stress distribution were analysed and compared. A total of 71 consecutive patients with closed Sanders type 2 calcaneal fractures were enrolled and divided into two groups according to the treatment to which they chose: the EFLIF group and the ORIF group. The radiological and clinical outcomes were evaluated and compared. The relative displacement of the EFLIF was less than that of the plate (0.1363 mm to 0.1808 mm). The highest von Mises stress value on the plate was 33% higher than that on the EFLIF. A normal restoration of the Böhler angle was achieved in both groups. No significant difference was found in the clinical outcome on the American Orthopedic Foot and Ankle Society Ankle Hindfoot Scale, or on the Visual Analogue Scale between the two groups (p > 0.05). Wound complications were more common in those who were treated with ORIF (p = 0.028). Both EFLIF and ORIF systems were tested to 160 N without failure, showing the new construct to be mechanically safe to use. Both EFLIF and ORIF could be effective in treating Sanders type 2 calcaneal fractures. The EFLIF may be superior to ORIF in achieving biomechanical stability and less blood loss, shorter surgical time and hospital stay, and fewer wound complications. Cite this article : M. Pan, L. Chai, F. Xue, L. Ding, G. Tang, B. Lv. Comparisons of external fixator combined with limited internal fixation and open reduction and internal fixation for Sanders type 2 calcaneal fractures: Finite element analysis and clinical outcome. Bone Joint Res 2017;6:433-438. DOI: 10.1302/2046-3758.67.2000640. © 2017 Xue et al.

Improved finite element methodology for integrated thermal structural analysis

NASA Technical Reports Server (NTRS)

Dechaumphai, P.; Thornton, E. A.

1982-01-01

An integrated thermal-structural finite element approach for efficient coupling of thermal and structural analysis is presented. New thermal finite elements which yield exact nodal and element temperatures for one dimensional linear steady state heat transfer problems are developed. A nodeless variable formulation is used to establish improved thermal finite elements for one dimensional nonlinear transient and two dimensional linear transient heat transfer problems. The thermal finite elements provide detailed temperature distributions without using additional element nodes and permit a common discretization with lower order congruent structural finite elements. The accuracy of the integrated approach is evaluated by comparisons with analytical solutions and conventional finite element thermal structural analyses for a number of academic and more realistic problems. Results indicate that the approach provides a significant improvement in the accuracy and efficiency of thermal stress analysis for structures with complex temperature distributions.

TAP 1: A Finite Element Program for Steady-State Thermal Analysis of Convectively Cooled Structures

NASA Technical Reports Server (NTRS)

Thornton, E. A.

1976-01-01

The program has a finite element library of six elements: two conduction/convection elements to model heat transfer in a solid, two convection elements to model heat transfer in a fluid, and two integrated conduction/convection elements to represent combined heat transfer in tubular and plate/fin fluid passages. Nonlinear thermal analysis due to temperature dependent thermal parameters is performed using the Newton-Raphson iteration method. Program output includes nodal temperatures and element heat fluxes. Pressure drops in fluid passages may be computed as an option. A companion plotting program for displaying the finite element model and predicted temperature distributions is presented. User instructions and sample problems are presented in appendixes.

Progress in Computational Simulation of Earthquakes

NASA Technical Reports Server (NTRS)

Donnellan, Andrea; Parker, Jay; Lyzenga, Gregory; Judd, Michele; Li, P. Peggy; Norton, Charles; Tisdale, Edwin; Granat, Robert

2006-01-01

GeoFEST(P) is a computer program written for use in the QuakeSim project, which is devoted to development and improvement of means of computational simulation of earthquakes. GeoFEST(P) models interacting earthquake fault systems from the fault-nucleation to the tectonic scale. The development of GeoFEST( P) has involved coupling of two programs: GeoFEST and the Pyramid Adaptive Mesh Refinement Library. GeoFEST is a message-passing-interface-parallel code that utilizes a finite-element technique to simulate evolution of stress, fault slip, and plastic/elastic deformation in realistic materials like those of faulted regions of the crust of the Earth. The products of such simulations are synthetic observable time-dependent surface deformations on time scales from days to decades. Pyramid Adaptive Mesh Refinement Library is a software library that facilitates the generation of computational meshes for solving physical problems. In an application of GeoFEST(P), a computational grid can be dynamically adapted as stress grows on a fault. Simulations on workstations using a few tens of thousands of stress and displacement finite elements can now be expanded to multiple millions of elements with greater than 98-percent scaled efficiency on over many hundreds of parallel processors (see figure).

Experiments and Dynamic Finite Element Analysis of a Wire-Rope Rockfall Protective Fence

NASA Astrophysics Data System (ADS)

Tran, Phuc Van; Maegawa, Koji; Fukada, Saiji

2013-09-01

The imperative need to protect structures in mountainous areas against rockfall has led to the development of various protection methods. This study introduces a new type of rockfall protection fence made of posts, wire ropes, wire netting and energy absorbers. The performance of this rock fence was verified in both experiments and dynamic finite element analysis. In collision tests, a reinforced-concrete block rolled down a natural slope and struck the rock fence at the end of the slope. A specialized system of measuring instruments was employed to accurately measure the acceleration of the block without cable connection. In particular, the performance of two energy absorbers, which contribute also to preventing wire ropes from breaking, was investigated to determine the best energy absorber. In numerical simulation, a commercial finite element code having explicit dynamic capabilities was employed to create models of the two full-scale tests. To facilitate simulation, certain simplifying assumptions for mechanical data of each individual component of the rock fence and geometrical data of the model were adopted. Good agreement between numerical simulation and experimental data validated the numerical simulation. Furthermore, the results of numerical simulation helped highlight limitations of the testing method. The results of numerical simulation thus provide a deeper understanding of the structural behavior of individual components of the rock fence during rockfall impact. More importantly, numerical simulations can be used not only as supplements to or substitutes for full-scale tests but also in parametric study and design.

Stable finite element approximations of two-phase flow with soluble surfactant

NASA Astrophysics Data System (ADS)

Barrett, John W.; Garcke, Harald; Nürnberg, Robert

2015-09-01

A parametric finite element approximation of incompressible two-phase flow with soluble surfactants is presented. The Navier-Stokes equations are coupled to bulk and surfaces PDEs for the surfactant concentrations. At the interface adsorption, desorption and stress balances involving curvature effects and Marangoni forces have to be considered. A parametric finite element approximation for the advection of the interface, which maintains good mesh properties, is coupled to the evolving surface finite element method, which is used to discretize the surface PDE for the interface surfactant concentration. The resulting system is solved together with standard finite element approximations of the Navier-Stokes equations and of the bulk parabolic PDE for the surfactant concentration. Semidiscrete and fully discrete approximations are analyzed with respect to stability, conservation and existence/uniqueness issues. The approach is validated for simple test cases and for complex scenarios, including colliding drops in a shear flow, which are computed in two and three space dimensions.

On the existence and stability conditions for mixed-hybrid finite element solutions based on Reissner's variational principle

NASA Technical Reports Server (NTRS)

Karlovitz, L. A.; Atluri, S. N.; Xue, W.-M.

1985-01-01

The extensions of Reissner's two-field (stress and displacement) principle to the cases wherein the displacement field is discontinuous and/or the stress field results in unreciprocated tractions, at a finite number of surfaces ('interelement boundaries') in a domain (as, for instance, when the domain is discretized into finite elements), is considered. The conditions for the existence, uniqueness, and stability of mixed-hybrid finite element solutions based on such discontinuous fields, are summarized. The reduction of these global conditions to local ('element') level, and the attendant conditions on the ranks of element matrices, are discussed. Two examples of stable, invariant, least-order elements - a four-node square planar element and an eight-node cubic element - are discussed in detail.

Implementation of structural response sensitivity calculations in a large-scale finite-element analysis system

NASA Technical Reports Server (NTRS)

Giles, G. L.; Rogers, J. L., Jr.

1982-01-01

The methodology used to implement structural sensitivity calculations into a major, general-purpose finite-element analysis system (SPAR) is described. This implementation includes a generalized method for specifying element cross-sectional dimensions as design variables that can be used in analytically calculating derivatives of output quantities from static stress, vibration, and buckling analyses for both membrane and bending elements. Limited sample results for static displacements and stresses are presented to indicate the advantages of analytically calculating response derivatives compared to finite difference methods. Continuing developments to implement these procedures into an enhanced version of SPAR are also discussed.

Full-scale 3-D finite element modeling of a two-loop pressurized water reactor for heat transfer, thermal–mechanical cyclic stress analysis, and environmental fatigue life estimation

DOE Office of Scientific and Technical Information (OSTI.GOV)

Mohanty, Subhasish; Soppet, William K.; Majumdar, Saurindranath

This paper discusses a system-level finite element model of a two-loop pressurized water reactor (PWR). Based on this model, system-level heat transfer analysis and subsequent sequentially coupled thermal-mechanical stress analysis were performed for typical thermal-mechanical fatigue cycles. The in-air fatigue lives of example components, such as the hot and cold legs, were estimated on the basis of stress analysis results, ASME in-air fatigue life estimation criteria, and fatigue design curves. Furthermore, environmental correction factors and associated PWR environment fatigue lives for the hot and cold legs were estimated by using estimated stress and strain histories and the approach described inmore » US-NRC report: NUREG-6909.« less

FINITE ELEMENT MODEL FOR TIDES AND CURRENTS WITH FIELD APPLICATIONS.

USGS Publications Warehouse

Walters, Roy A.

1988-01-01

A finite element model, based upon the shallow water equations, is used to calculate tidal amplitudes and currents for two field-scale test problems. Because tides are characterized by line spectra, the governing equations are subjected to harmonic decomposition. Thus the solution variables are the real and imaginary parts of the amplitude of sea level and velocity rather than a time series of these variables. The time series is recovered through synthesis. This scheme, coupled with a modified form of the governing equations, leads to high computational efficiency and freedom from excessive numerical noise. Two test-cases are presented. The first is a solution for eleven tidal constituents in the English Channel and southern North Sea, and three constituents are discussed. The second is an analysis of the frequency response and tidal harmonics for south San Francisco Bay.

SUTRA (Saturated-Unsaturated Transport). A Finite-Element Simulation Model for Saturated-Unsaturated, Fluid-Density-Dependent Ground-Water Flow with Energy Transport or Chemically-Reactive Single-Species Solute Transport.

DTIC Science & Technology

1984-12-30

as three dimensional, when the assumption is made that all SUTRA parameters and coefficients have a constant value in the third space direction. A...finite element. The type of element employed by SUTRA for two-dimensional simulation is a quadrilateral which has a finite thickness in the third ... space dimension. This type of a quad- rilateral element and a typical two-dimensional mesh is shown in Figure 3.1. - All twelve edges of the two

A Simplified Finite Element Simulation for Straightening Process of Thin-Walled Tube

NASA Astrophysics Data System (ADS)

Zhang, Ziqian; Yang, Huilin

2017-12-01

The finite element simulation is an effective way for the study of thin-walled tube in the two cross rolls straightening process. To determine the accurate radius of curvature of the roll profile more efficiently, a simplified finite element model based on the technical parameters of an actual two cross roll straightening machine, was developed to simulate the complex straightening process. Then a dynamic simulation was carried out using ANSYS LS-DYNA program. The result implied that the simplified finite element model was reasonable for simulate the two cross rolls straightening process, and can be obtained the radius of curvature of the roll profile with the tube’s straightness 2 mm/m.

Edge-defined film-fed growth of thin silicon sheets

NASA Technical Reports Server (NTRS)

Ettouney, H. M.; Kalejs, J. P.

1984-01-01

Finite element analysis was used on two length scales to understand crystal growth of thin silicon sheets. Thermal-capillary models of entire ribbon growth systems were developed. Microscopic modeling of morphological structure of melt/solid interfaces beyond the point of linear instability was carried out. The application to silicon system is discussed.

Element-topology-independent preconditioners for parallel finite element computations

NASA Technical Reports Server (NTRS)

Park, K. C.; Alexander, Scott

1992-01-01

A family of preconditioners for the solution of finite element equations are presented, which are element-topology independent and thus can be applicable to element order-free parallel computations. A key feature of the present preconditioners is the repeated use of element connectivity matrices and their left and right inverses. The properties and performance of the present preconditioners are demonstrated via beam and two-dimensional finite element matrices for implicit time integration computations.

Finite element analyses of wood laminated composite poles

Treesearch

Cheng Piao; Todd F. Shupe; R.C. Tang; Chung Y. Hse

2005-01-01

Finite element analyses using ANSYS were conducted on orthotropic, polygonal, wood laminated composite poles subjected to a body force and a concentrated load at the free end. Deflections and stress distributions of small-scale and full-size composite poles were analyzed and compared to the results obtained in an experimental study. The predicted deflection for both...

Scaled boundary finite element simulation and modeling of the mechanical behavior of cracked nanographene sheets

NASA Astrophysics Data System (ADS)

Honarmand, M.; Moradi, M.

2018-06-01

In this paper, by using scaled boundary finite element method (SBFM), a perfect nanographene sheet or cracked ones were simulated for the first time. In this analysis, the atomic carbon bonds were modeled by simple bar elements with circular cross-sections. Despite of molecular dynamics (MD), the results obtained from SBFM analysis are quite acceptable for zero degree cracks. For all angles except zero, Griffith criterion can be applied for the relation between critical stress and crack length. Finally, despite the simplifications used in nanographene analysis, obtained results can simulate the mechanical behavior with high accuracy compared with experimental and MD ones.

Finite element methods on supercomputers - The scatter-problem

NASA Technical Reports Server (NTRS)

Loehner, R.; Morgan, K.

1985-01-01

Certain problems arise in connection with the use of supercomputers for the implementation of finite-element methods. These problems are related to the desirability of utilizing the power of the supercomputer as fully as possible for the rapid execution of the required computations, taking into account the gain in speed possible with the aid of pipelining operations. For the finite-element method, the time-consuming operations may be divided into three categories. The first two present no problems, while the third type of operation can be a reason for the inefficient performance of finite-element programs. Two possibilities for overcoming certain difficulties are proposed, giving attention to a scatter-process.

A Comparison of Spectral Element and Finite Difference Methods Using Statically Refined Nonconforming Grids for the MHD Island Coalescence Instability Problem

NASA Astrophysics Data System (ADS)

Ng, C. S.; Rosenberg, D.; Pouquet, A.; Germaschewski, K.; Bhattacharjee, A.

2009-04-01

A recently developed spectral-element adaptive refinement incompressible magnetohydrodynamic (MHD) code [Rosenberg, Fournier, Fischer, Pouquet, J. Comp. Phys. 215, 59-80 (2006)] is applied to simulate the problem of MHD island coalescence instability (\\ci) in two dimensions. \\ci is a fundamental MHD process that can produce sharp current layers and subsequent reconnection and heating in a high-Lundquist number plasma such as the solar corona [Ng and Bhattacharjee, Phys. Plasmas, 5, 4028 (1998)]. Due to the formation of thin current layers, it is highly desirable to use adaptively or statically refined grids to resolve them, and to maintain accuracy at the same time. The output of the spectral-element static adaptive refinement simulations are compared with simulations using a finite difference method on the same refinement grids, and both methods are compared to pseudo-spectral simulations with uniform grids as baselines. It is shown that with the statically refined grids roughly scaling linearly with effective resolution, spectral element runs can maintain accuracy significantly higher than that of the finite difference runs, in some cases achieving close to full spectral accuracy.

Nonlinear transient analysis by energy minimization: A theoretical basis for the ACTION computer code. [predicting the response of a lightweight aircraft during a crash

NASA Technical Reports Server (NTRS)

Kamat, M. P.

1980-01-01

The formulation basis for establishing the static or dynamic equilibrium configurations of finite element models of structures which may behave in the nonlinear range are provided. With both geometric and time independent material nonlinearities included, the development is restricted to simple one and two dimensional finite elements which are regarded as being the basic elements for modeling full aircraft-like structures under crash conditions. Representations of a rigid link and an impenetrable contact plane are added to the deformation model so that any number of nodes of the finite element model may be connected by a rigid link or may contact the plane. Equilibrium configurations are derived as the stationary conditions of a potential function of the generalized nodal variables of the model. Minimization of the nonlinear potential function is achieved by using the best current variable metric update formula for use in unconstrained minimization. Powell's conjugate gradient algorithm, which offers very low storage requirements at some slight increase in the total number of calculations, is the other alternative algorithm to be used for extremely large scale problems.

Phase-space finite elements in a least-squares solution of the transport equation

DOE Office of Scientific and Technical Information (OSTI.GOV)

Drumm, C.; Fan, W.; Pautz, S.

2013-07-01

The linear Boltzmann transport equation is solved using a least-squares finite element approximation in the space, angular and energy phase-space variables. The method is applied to both neutral particle transport and also to charged particle transport in the presence of an electric field, where the angular and energy derivative terms are handled with the energy/angular finite elements approximation, in a manner analogous to the way the spatial streaming term is handled. For multi-dimensional problems, a novel approach is used for the angular finite elements: mapping the surface of a unit sphere to a two-dimensional planar region and using a meshingmore » tool to generate a mesh. In this manner, much of the spatial finite-elements machinery can be easily adapted to handle the angular variable. The energy variable and the angular variable for one-dimensional problems make use of edge/beam elements, also building upon the spatial finite elements capabilities. The methods described here can make use of either continuous or discontinuous finite elements in space, angle and/or energy, with the use of continuous finite elements resulting in a smaller problem size and the use of discontinuous finite elements resulting in more accurate solutions for certain types of problems. The work described in this paper makes use of continuous finite elements, so that the resulting linear system is symmetric positive definite and can be solved with a highly efficient parallel preconditioned conjugate gradients algorithm. The phase-space finite elements capability has been built into the Sceptre code and applied to several test problems, including a simple one-dimensional problem with an analytic solution available, a two-dimensional problem with an isolated source term, showing how the method essentially eliminates ray effects encountered with discrete ordinates, and a simple one-dimensional charged-particle transport problem in the presence of an electric field. (authors)« less

Discrete maximum principle for the P1 - P0 weak Galerkin finite element approximations

NASA Astrophysics Data System (ADS)

Wang, Junping; Ye, Xiu; Zhai, Qilong; Zhang, Ran

2018-06-01

This paper presents two discrete maximum principles (DMP) for the numerical solution of second order elliptic equations arising from the weak Galerkin finite element method. The results are established by assuming an h-acute angle condition for the underlying finite element triangulations. The mathematical theory is based on the well-known De Giorgi technique adapted in the finite element context. Some numerical results are reported to validate the theory of DMP.

Prediction of shear critical behavior of high-strength reinforced concrete columns using finite element methods

NASA Astrophysics Data System (ADS)

Alrasyid, Harun; Safi, Fahrudin; Iranata, Data; Chen-Ou, Yu

2017-11-01

This research shows the prediction of shear behavior of High-Strength Reinforced Concrete Columns using Finite-Element Method. The experimental data of nine half scale high-strength reinforced concrete were selected. These columns using specified concrete compressive strength of 70 MPa, specified yield strength of longitudinal and transverse reinforcement of 685 and 785 MPa, respectively. The VecTor2 finite element software was used to simulate the shear critical behavior of these columns. The combination axial compression load and monotonic loading were applied at this prediction. It is demonstrated that VecTor2 finite element software provides accurate prediction of load-deflection up to peak at applied load, but provide similar behavior at post peak load. The shear strength prediction provide by VecTor 2 are slightly conservative compare to test result.

A multilevel correction adaptive finite element method for Kohn-Sham equation

NASA Astrophysics Data System (ADS)

Hu, Guanghui; Xie, Hehu; Xu, Fei

2018-02-01

In this paper, an adaptive finite element method is proposed for solving Kohn-Sham equation with the multilevel correction technique. In the method, the Kohn-Sham equation is solved on a fixed and appropriately coarse mesh with the finite element method in which the finite element space is kept improving by solving the derived boundary value problems on a series of adaptively and successively refined meshes. A main feature of the method is that solving large scale Kohn-Sham system is avoided effectively, and solving the derived boundary value problems can be handled efficiently by classical methods such as the multigrid method. Hence, the significant acceleration can be obtained on solving Kohn-Sham equation with the proposed multilevel correction technique. The performance of the method is examined by a variety of numerical experiments.

Finite elements and finite differences for transonic flow calculations

NASA Technical Reports Server (NTRS)

Hafez, M. M.; Murman, E. M.; Wellford, L. C.

1978-01-01

The paper reviews the chief finite difference and finite element techniques used for numerical solution of nonlinear mixed elliptic-hyperbolic equations governing transonic flow. The forms of the governing equations for unsteady two-dimensional transonic flow considered are the Euler equation, the full potential equation in both conservative and nonconservative form, the transonic small-disturbance equation in both conservative and nonconservative form, and the hodograph equations for the small-disturbance case and the full-potential case. Finite difference methods considered include time-dependent methods, relaxation methods, semidirect methods, and hybrid methods. Finite element methods include finite element Lax-Wendroff schemes, implicit Galerkin method, mixed variational principles, dual iterative procedures, optimal control methods and least squares.

Application of Interface Technology in Nonlinear Analysis of a Stitched/RFI Composite Wing Stub Box

NASA Technical Reports Server (NTRS)

Wang, John T.; Ransom, Jonathan B.

1997-01-01

A recently developed interface technology was successfully employed in the geometrically nonlinear analysis of a full-scale stitched/RFI composite wing box loaded in bending. The technology allows mismatched finite element models to be joined in a variationally consistent manner and reduces the modeling complexity by eliminating transition meshing. In the analysis, local finite element models of nonlinearly deformed wide bays of the wing box are refined without the need for transition meshing to the surrounding coarse mesh. The COMET-AR finite element code, which has the interface technology capability, was used to perform the analyses. The COMET-AR analysis is compared to both a NASTRAN analysis and to experimental data. The interface technology solution is shown to be in good agreement with both. The viability of interface technology for coupled global/local analysis of large scale aircraft structures is demonstrated.

Parallel Domain Decomposition Formulation and Software for Large-Scale Sparse Symmetrical/Unsymmetrical Aeroacoustic Applications

NASA Technical Reports Server (NTRS)

Nguyen, D. T.; Watson, Willie R. (Technical Monitor)

2005-01-01

The overall objectives of this research work are to formulate and validate efficient parallel algorithms, and to efficiently design/implement computer software for solving large-scale acoustic problems, arised from the unified frameworks of the finite element procedures. The adopted parallel Finite Element (FE) Domain Decomposition (DD) procedures should fully take advantages of multiple processing capabilities offered by most modern high performance computing platforms for efficient parallel computation. To achieve this objective. the formulation needs to integrate efficient sparse (and dense) assembly techniques, hybrid (or mixed) direct and iterative equation solvers, proper pre-conditioned strategies, unrolling strategies, and effective processors' communicating schemes. Finally, the numerical performance of the developed parallel finite element procedures will be evaluated by solving series of structural, and acoustic (symmetrical and un-symmetrical) problems (in different computing platforms). Comparisons with existing "commercialized" and/or "public domain" software are also included, whenever possible.

Finite Element Models and Properties of a Stiffened Floor-Equipped Composite Cylinder

NASA Technical Reports Server (NTRS)

Grosveld, Ferdinand W.; Schiller, Noah H.; Cabell, Randolph H.

2010-01-01

Finite element models were developed of a floor-equipped, frame and stringer stiffened composite cylinder including a coarse finite element model of the structural components, a coarse finite element model of the acoustic cavities above and below the beam-supported plywood floor, and two dense models consisting of only the structural components. The report summarizes the geometry, the element properties, the material and mechanical properties, the beam cross-section characteristics, the beam element representations and the boundary conditions of the composite cylinder models. The expressions used to calculate the group speeds for the cylinder components are presented.

Application of variational and Galerkin equations to linear and nonlinear finite element analysis

NASA Technical Reports Server (NTRS)

Yu, Y.-Y.

1974-01-01

The paper discusses the application of the variational equation to nonlinear finite element analysis. The problem of beam vibration with large deflection is considered. The variational equation is shown to be flexible in both the solution of a general problem and in the finite element formulation. Difficulties are shown to arise when Galerkin's equations are used in the consideration of the finite element formulation of two-dimensional linear elasticity and of the linear classical beam.

TAP 2: A finite element program for thermal analysis of convectively cooled structures

NASA Technical Reports Server (NTRS)

Thornton, E. A.

1980-01-01

A finite element computer program (TAP 2) for steady-state and transient thermal analyses of convectively cooled structures is presented. The program has a finite element library of six elements: two conduction/convection elements to model heat transfer in a solid, two convection elements to model heat transfer in a fluid, and two integrated conduction/convection elements to represent combined heat transfer in tubular and plate/fin fluid passages. Nonlinear thermal analysis due to temperature-dependent thermal parameters is performed using the Newton-Raphson iteration method. Transient analyses are performed using an implicit Crank-Nicolson time integration scheme with consistent or lumped capacitance matrices as an option. Program output includes nodal temperatures and element heat fluxes. Pressure drops in fluid passages may be computed as an option. User instructions and sample problems are presented in appendixes.

Dislocation dynamics in non-convex domains using finite elements with embedded discontinuities

NASA Astrophysics Data System (ADS)

Romero, Ignacio; Segurado, Javier; LLorca, Javier

2008-04-01

The standard strategy developed by Van der Giessen and Needleman (1995 Modelling Simul. Mater. Sci. Eng. 3 689) to simulate dislocation dynamics in two-dimensional finite domains was modified to account for the effect of dislocations leaving the crystal through a free surface in the case of arbitrary non-convex domains. The new approach incorporates the displacement jumps across the slip segments of the dislocations that have exited the crystal within the finite element analysis carried out to compute the image stresses on the dislocations due to the finite boundaries. This is done in a simple computationally efficient way by embedding the discontinuities in the finite element solution, a strategy often used in the numerical simulation of crack propagation in solids. Two academic examples are presented to validate and demonstrate the extended model and its implementation within a finite element program is detailed in the appendix.

Finite element area and line integral transforms for generalization of aperture function and geometry in Kirchhoff scalar diffraction theory

NASA Astrophysics Data System (ADS)

Kraus, Hal G.

1993-02-01

Two finite element-based methods for calculating Fresnel region and near-field region intensities resulting from diffraction of light by two-dimensional apertures are presented. The first is derived using the Kirchhoff area diffraction integral and the second is derived using a displaced vector potential to achieve a line integral transformation. The specific form of each of these formulations is presented for incident spherical waves and for Gaussian laser beams. The geometry of the two-dimensional diffracting aperture(s) is based on biquadratic isoparametric elements, which are used to define apertures of complex geometry. These elements are also used to build complex amplitude and phase functions across the aperture(s), which may be of continuous or discontinuous form. The finite element transform integrals are accurately and efficiently integrated numerically using Gaussian quadrature. The power of these methods is illustrated in several examples which include secondary obstructions, secondary spider supports, multiple mirror arrays, synthetic aperture arrays, apertures covered by screens, apodization, phase plates, and off-axis apertures. Typically, the finite element line integral transform results in significant gains in computational efficiency over the finite element Kirchhoff transform method, but is also subject to some loss in generality.

A majorized Newton-CG augmented Lagrangian-based finite element method for 3D restoration of geological models

NASA Astrophysics Data System (ADS)

Tang, Peipei; Wang, Chengjing; Dai, Xiaoxia

2016-04-01

In this paper, we propose a majorized Newton-CG augmented Lagrangian-based finite element method for 3D elastic frictionless contact problems. In this scheme, we discretize the restoration problem via the finite element method and reformulate it to a constrained optimization problem. Then we apply the majorized Newton-CG augmented Lagrangian method to solve the optimization problem, which is very suitable for the ill-conditioned case. Numerical results demonstrate that the proposed method is a very efficient algorithm for various large-scale 3D restorations of geological models, especially for the restoration of geological models with complicated faults.

Bearing-Load Modeling and Analysis Study for Mechanically Connected Structures

NASA Technical Reports Server (NTRS)

Knight, Norman F., Jr.

2006-01-01

Bearing-load response for a pin-loaded hole is studied within the context of two-dimensional finite element analyses. Pin-loaded-hole configurations are representative of mechanically connected structures, such as a stiffener fastened to a rib of an isogrid panel, that are idealized as part of a larger structural component. Within this context, the larger structural component may be idealized as a two-dimensional shell finite element model to identify load paths and high stress regions. Finite element modeling and analysis aspects of a pin-loaded hole are considered in the present paper including the use of linear and nonlinear springs to simulate the pin-bearing contact condition. Simulating pin-connected structures within a two-dimensional finite element analysis model using nonlinear spring or gap elements provides an effective way for accurate prediction of the local effective stress state and peak forces.

Nonlinear initial-boundary value solutions by the finite element method. [for Navier-Stokes equations of two dimensional flow

NASA Technical Reports Server (NTRS)

Baker, A. J.

1974-01-01

The finite-element method is used to establish a numerical solution algorithm for the Navier-Stokes equations for two-dimensional flows of a viscous compressible fluid. Numerical experiments confirm the advection property for the finite-element equivalent of the nonlinear convection term for both unidirectional and recirculating flowfields. For linear functionals, the algorithm demonstrates good accuracy using coarse discretizations and h squared convergence with discretization refinement.

Efficient Preconditioning for the p-Version Finite Element Method in Two Dimensions

DTIC Science & Technology

1989-10-01

paper, we study fast parallel preconditioners for systems of equations arising from the p-version finite element method. The p-version finite element...computations and the solution of a relatively small global auxiliary problem. We study two different methods. In the first (Section 3), the global...20], will be studied in the next section. Problem (3.12) is obviously much more easily solved than the original problem ,nd the procedure is highly

A blended continuous–discontinuous finite element method for solving the multi-fluid plasma model

DOE Office of Scientific and Technical Information (OSTI.GOV)

Sousa, E.M., E-mail: sousae@uw.edu; Shumlak, U., E-mail: shumlak@uw.edu

The multi-fluid plasma model represents electrons, multiple ion species, and multiple neutral species as separate fluids that interact through short-range collisions and long-range electromagnetic fields. The model spans a large range of temporal and spatial scales, which renders the model stiff and presents numerical challenges. To address the large range of timescales, a blended continuous and discontinuous Galerkin method is proposed, where the massive ion and neutral species are modeled using an explicit discontinuous Galerkin method while the electrons and electromagnetic fields are modeled using an implicit continuous Galerkin method. This approach is able to capture large-gradient ion and neutralmore » physics like shock formation, while resolving high-frequency electron dynamics in a computationally efficient manner. The details of the Blended Finite Element Method (BFEM) are presented. The numerical method is benchmarked for accuracy and tested using two-fluid one-dimensional soliton problem and electromagnetic shock problem. The results are compared to conventional finite volume and finite element methods, and demonstrate that the BFEM is particularly effective in resolving physics in stiff problems involving realistic physical parameters, including realistic electron mass and speed of light. The benefit is illustrated by computing a three-fluid plasma application that demonstrates species separation in multi-component plasmas.« less

Energy Finite Element Analysis for Computing the High Frequency Vibration of the Aluminum Testbed Cylinder and Correlating the Results to Test Data

NASA Technical Reports Server (NTRS)

Vlahopoulos, Nickolas

2005-01-01

The Energy Finite Element Analysis (EFEA) is a finite element based computational method for high frequency vibration and acoustic analysis. The EFEA solves with finite elements governing differential equations for energy variables. These equations are developed from wave equations. Recently, an EFEA method for computing high frequency vibration of structures either in vacuum or in contact with a dense fluid has been presented. The presence of fluid loading has been considered through added mass and radiation damping. The EFEA developments were validated by comparing EFEA results to solutions obtained by very dense conventional finite element models and solutions from classical techniques such as statistical energy analysis (SEA) and the modal decomposition method for bodies of revolution. EFEA results have also been compared favorably with test data for the vibration and the radiated noise generated by a large scale submersible vehicle. The primary variable in EFEA is defined as the time averaged over a period and space averaged over a wavelength energy density. A joint matrix computed from the power transmission coefficients is utilized for coupling the energy density variables across any discontinuities, such as change of plate thickness, plate/stiffener junctions etc. When considering the high frequency vibration of a periodically stiffened plate or cylinder, the flexural wavelength is smaller than the interval length between two periodic stiffeners, therefore the stiffener stiffness can not be smeared by computing an equivalent rigidity for the plate or cylinder. The periodic stiffeners must be regarded as coupling components between periodic units. In this paper, Periodic Structure (PS) theory is utilized for computing the coupling joint matrix and for accounting for the periodicity characteristics.

Multi-scale damage modelling in a ceramic matrix composite using a finite-element microstructure meshfree methodology

PubMed Central

2016-01-01

The problem of multi-scale modelling of damage development in a SiC ceramic fibre-reinforced SiC matrix ceramic composite tube is addressed, with the objective of demonstrating the ability of the finite-element microstructure meshfree (FEMME) model to introduce important aspects of the microstructure into a larger scale model of the component. These are particularly the location, orientation and geometry of significant porosity and the load-carrying capability and quasi-brittle failure behaviour of the fibre tows. The FEMME model uses finite-element and cellular automata layers, connected by a meshfree layer, to efficiently couple the damage in the microstructure with the strain field at the component level. Comparison is made with experimental observations of damage development in an axially loaded composite tube, studied by X-ray computed tomography and digital volume correlation. Recommendations are made for further development of the model to achieve greater fidelity to the microstructure. This article is part of the themed issue ‘Multiscale modelling of the structural integrity of composite materials’. PMID:27242308

Finite element based contact analysis of radio frequency MEMs switch membrane surfaces

NASA Astrophysics Data System (ADS)

Liu, Jin-Ya; Chalivendra, Vijaya; Huang, Wenzhen

2017-10-01

Finite element simulations were performed to determine the contact behavior of radio frequency (RF) micro-electro-mechanical (MEM) switch contact surfaces under monotonic and cyclic loading conditions. Atomic force microscopy (AFM) was used to capture the topography of RF-MEM switch membranes and later they were analyzed for multi-scale regular as well as fractal structures. Frictionless, non-adhesive contact 3D finite element analysis was carried out at different length scales to investigate the contact behavior of the regular-fractal surface using an elasto-plastic material model. Dominant micro-scale regular patterns were found to significantly change the contact behavior. Contact areas mainly cluster around the regular pattern. The contribution from the fractal structure is not significant. Under cyclic loading conditions, plastic deformation in the 1st loading/unloading cycle smooth the surface. The subsequent repetitive loading/unloading cycles undergo elastic contact without changing the morphology of the contacting surfaces. The work is expected to shed light on the quality of the switch surface contact as well as the optimum design of RF MEM switch surfaces.

Finite element modeling of small-scale tapered wood-laminated composite poles with biomimicry features

Treesearch

Cheng Piao; Todd F. Shupe; R.C. Tang; Chung Y. Hse

2008-01-01

Tapered composite poles with biomimicry features as in bamboo are a new generation of wood laminated composite poles that may some day be considered as an alternative to solid wood poles that are widely used in the transmission and telecommunication fields. Five finite element models were developed with ANSYS to predict and assess the performance of five types of...

Applications of FEM and BEM in two-dimensional fracture mechanics problems

NASA Technical Reports Server (NTRS)

Min, J. B.; Steeve, B. E.; Swanson, G. R.

1992-01-01

A comparison of the finite element method (FEM) and boundary element method (BEM) for the solution of two-dimensional plane strain problems in fracture mechanics is presented in this paper. Stress intensity factors (SIF's) were calculated using both methods for elastic plates with either a single-edge crack or an inclined-edge crack. In particular, two currently available programs, ANSYS for finite element analysis and BEASY for boundary element analysis, were used.

Dual-scale Galerkin methods for Darcy flow

NASA Astrophysics Data System (ADS)

Wang, Guoyin; Scovazzi, Guglielmo; Nouveau, Léo; Kees, Christopher E.; Rossi, Simone; Colomés, Oriol; Main, Alex

2018-02-01

The discontinuous Galerkin (DG) method has found widespread application in elliptic problems with rough coefficients, of which the Darcy flow equations are a prototypical example. One of the long-standing issues of DG approximations is the overall computational cost, and many different strategies have been proposed, such as the variational multiscale DG method, the hybridizable DG method, the multiscale DG method, the embedded DG method, and the Enriched Galerkin method. In this work, we propose a mixed dual-scale Galerkin method, in which the degrees-of-freedom of a less computationally expensive coarse-scale approximation are linked to the degrees-of-freedom of a base DG approximation. We show that the proposed approach has always similar or improved accuracy with respect to the base DG method, with a considerable reduction in computational cost. For the specific definition of the coarse-scale space, we consider Raviart-Thomas finite elements for the mass flux and piecewise-linear continuous finite elements for the pressure. We provide a complete analysis of stability and convergence of the proposed method, in addition to a study on its conservation and consistency properties. We also present a battery of numerical tests to verify the results of the analysis, and evaluate a number of possible variations, such as using piecewise-linear continuous finite elements for the coarse-scale mass fluxes.

Implementation of structural response sensitivity calculations in a large-scale finite-element analysis system

NASA Technical Reports Server (NTRS)

Giles, G. L.; Rogers, J. L., Jr.

1982-01-01

The implementation includes a generalized method for specifying element cross-sectional dimensions as design variables that can be used in analytically calculating derivatives of output quantities from static stress, vibration, and buckling analyses for both membrane and bending elements. Limited sample results for static displacements and stresses are presented to indicate the advantages of analytically calclating response derivatives compared to finite difference methods. Continuing developments to implement these procedures into an enhanced version of the system are also discussed.

Spatial Convergence of Three Dimensional Turbulent Flows

NASA Technical Reports Server (NTRS)

Park, Michael A.; Anderson, W. Kyle

2016-01-01

Finite-volume and finite-element schemes, both implemented within the FUN3D flow solver, are evaluated for several test cases described on the Turbulence-Modeling Resource (TMR) web site. The cases include subsonic flow over a hemisphere cylinder, subsonic flow over a swept bump configuration, and supersonic flow in a square duct. The finite- volume and finite-element schemes are both used to obtain solutions for the first two cases, whereas only the finite-volume scheme is used for the supersonic duct. For the hemisphere cylinder, finite-element solutions obtained on tetrahedral meshes are compared with finite- volume solutions on mixed-element meshes. For the swept bump, finite-volume solutions have been obtained for both hexahedral and tetrahedral meshes and are compared with finite-element solutions obtained on tetrahedral meshes. For the hemisphere cylinder and the swept bump, solutions are obtained on a series of meshes with varying grid density and comparisons are made between drag coefficients, pressure distributions, velocity profiles, and profiles of the turbulence working variable. The square duct shows small variation due to element type or the spatial accuracy of turbulence model convection. It is demonstrated that the finite-element scheme on tetrahedral meshes yields similar accuracy as the finite- volume scheme on mixed-element and hexahedral grids, and demonstrates less sensitivity to the mesh topology (biased tetrahedral grids) than the finite-volume scheme.

Solution-adaptive finite element method in computational fracture mechanics

NASA Technical Reports Server (NTRS)

Min, J. B.; Bass, J. M.; Spradley, L. W.

1993-01-01

Some recent results obtained using solution-adaptive finite element method in linear elastic two-dimensional fracture mechanics problems are presented. The focus is on the basic issue of adaptive finite element method for validating the applications of new methodology to fracture mechanics problems by computing demonstration problems and comparing the stress intensity factors to analytical results.

Evaluation of the use of a singularity element in finite element analysis of center-cracked plates

NASA Technical Reports Server (NTRS)

Mendelson, A.; Gross, B.; Srawley, J., E.

1972-01-01

Two different methods are applied to the analyses of finite width linear elastic plates with central cracks. Both methods give displacements as a primary part of the solution. One method makes use of Fourier transforms. The second method employs a coarse mesh of triangular second-order finite elements in conjunction with a single singularity element subjected to appropriate additional constraints. The displacements obtained by these two methods are in very good agreement. The results suggest considerable potential for the use of a cracked element for related crack problems, particularly in connection with the extension to nonlinear material behavior.

Finite-element analysis of dynamic fracture

NASA Technical Reports Server (NTRS)

Aberson, J. A.; Anderson, J. M.; King, W. W.

1976-01-01

Applications of the finite element method to the two dimensional elastodynamics of cracked structures are presented. Stress intensity factors are computed for two problems involving stationary cracks. The first serves as a vehicle for discussing lumped-mass and consistent-mass characterizations of inertia. In the second problem, the behavior of a photoelastic dynamic tear test specimen is determined for the time prior to crack propagation. Some results of a finite element simulation of rapid crack propagation in an infinite body are discussed.

Stress concentration investigations using NASTRAN

NASA Technical Reports Server (NTRS)

Gillcrist, M. C.; Parnell, L. A.

1986-01-01

Parametic investigations are performed using several two dimensional finite element formulations to determine their suitability for use in predicting extremum stresses in marine propellers. Comparisons are made of two NASTRAN elements (CTRIM6 and CTRAIA2) wherein elasticity properties have been modified to yield plane strain results. The accuracy of the elements is investigated by comparing finite element stress predictions with experimentally determined stresses in two classical cases: (1) tension in a flat plate with a circular hole; and (2) a filleted flat bar subjected to in-plane bending. The CTRIA2 element is found to provide good results. The displacement field from a three dimensional finite element model of a representative marine propeller is used as the boundary condition for the two dimensional plane strain investigations of stresses in the propeller blade and fillet. Stress predictions from the three dimensional analysis are compared with those from the two dimensional models. The validity of the plane strain modifications to the NASTRAN element is checked by comparing the modified CTRIA2 element stress predictions with those of the ABAQUS plane strain element, CPE4.

Finite element modeling of the residual stress evolution in forged and direct-aged alloy 718 turbine disks during manufacturing and its experimental validation

NASA Astrophysics Data System (ADS)

Drexler, Andreas; Ecker, Werner; Hessert, Roland; Oberwinkler, Bernd; Gänser, Hans-Peter; Keckes, Jozef; Hofmann, Michael; Fischersworring-Bunk, Andreas

2017-10-01

In this work the evolution of the residual stress field in a forged and heat treated turbine disk of Alloy 718 and its subsequent relaxation during machining was simulated and measured. After forging at around 1000 °C the disks were natural air cooled to room temperature and direct aged in a furnace at 720 °C for 8 hours and at 620 °C for 8 hours. The machining of the Alloy 718 turbine disk was performed in two steps: The machining of the Alloy 718 turbine disk was performed in two steps: First, from the forging contour to a contour used for ultra-sonic testing. Second, from the latter to the final contour. The thermal boundary conditions in the finite element model for air cooling and furnace heating were estimated based on analytical equations from literature. A constitutive model developed for the unified description of rate dependent and rate independent mechanical material behavior of Alloy 718 under in-service conditions up to temperatures of 1000 °C was extended and parametrized to meet the manufacturing conditions with temperatures up to 1000 °C. The results of the finite element model were validated with measurements on real-scale turbine disks. The thermal boundary conditions were validated in-field with measured cooling curves. For that purpose holes were drilled at different positions into the turbine disk and thermocouples were mounted in these holes to record the time-temperature curves during natural cooling and heating. The simulated residual stresses were validated by using the hole drilling method and the neutron diffraction technique. The accuracy of the finite element model for the final manufacturing step investigated was ±50 MPa.

A Minimum-Residual Finite Element Method for the Convection-Diffusion Equation

DTIC Science & Technology

2013-05-01

4p . We note that these two choices of discretization for V are not mutually exclusive, and that novel choices for Vh are likely the key to yielding...the inside with the positive- definite operator A, which is precisely the discrete system that arises under the optimal test function framework of DPG...converts the fine-scale problem into a symmetric-positive definite one, allowing for a well-behaved subgrid model of fine scale behavior. We begin again

A progress report on estuary modeling by the finite-element method

USGS Publications Warehouse

Gray, William G.

1978-01-01

Various schemes are investigated for finite-element modeling of two-dimensional surface-water flows. The first schemes investigated combine finite-element spatial discretization with split-step time stepping schemes that have been found useful in finite-difference computations. Because of the large number of numerical integrations performed in space and the large sparse matrices solved, these finite-element schemes were found to be economically uncompetitive with finite-difference schemes. A very promising leapfrog scheme is proposed which, when combined with a novel very fast spatial integration procedure, eliminates the need to solve any matrices at all. Additional problems attacked included proper propagation of waves and proper specification of the normal flow-boundary condition. This report indicates work in progress and does not come to a definitive conclusion as to the best approach for finite-element modeling of surface-water problems. The results presented represent findings obtained between September 1973 and July 1976. (Woodard-USGS)

Application of laser ranging and VLBI data to a study of plate tectonic driving forces. [finite element method

NASA Technical Reports Server (NTRS)

Solomon, S. C.

1980-01-01

The measurability of changes in plate driving or resistive forces associated with plate boundary earthquakes by laser rangefinding or VLBI is considered with emphasis on those aspects of plate forces that can be characterized by such measurements. Topics covered include: (1) analytic solutions for two dimensional stress diffusion in a plate following earthquake faulting on a finite fault; (2) two dimensional finite-element solutions for the global state of stress at the Earth's surface for possible plate driving forces; and (3) finite-element solutions for three dimensional stress diffusion in a viscoelastic Earth following earthquake faulting.

Modelling of thick composites using a layerwise laminate theory

NASA Technical Reports Server (NTRS)

Robbins, D. H., Jr.; Reddy, J. N.

1993-01-01

The layerwise laminate theory of Reddy (1987) is used to develop a layerwise, two-dimensional, displacement-based, finite element model of laminated composite plates that assumes a piecewise continuous distribution of the tranverse strains through the laminate thickness. The resulting layerwise finite element model is capable of computing interlaminar stresses and other localized effects with the same level of accuracy as a conventional 3D finite element model. Although the total number of degrees of freedom are comparable in both models, the layerwise model maintains a 2D-type data structure that provides several advantages over a conventional 3D finite element model, e.g. simplified input data, ease of mesh alteration, and faster element stiffness matrix formulation. Two sample problems are provided to illustrate the accuracy of the present model in computing interlaminar stresses for laminates in bending and extension.

Toward automatic finite element analysis

NASA Technical Reports Server (NTRS)

Kela, Ajay; Perucchio, Renato; Voelcker, Herbert

1987-01-01

Two problems must be solved if the finite element method is to become a reliable and affordable blackbox engineering tool. Finite element meshes must be generated automatically from computer aided design databases and mesh analysis must be made self-adaptive. The experimental system described solves both problems in 2-D through spatial and analytical substructuring techniques that are now being extended into 3-D.

The Elastic Behaviour of Sintered Metallic Fibre Networks: A Finite Element Study by Beam Theory

PubMed Central

Bosbach, Wolfram A.

2015-01-01

Background The finite element method has complimented research in the field of network mechanics in the past years in numerous studies about various materials. Numerical predictions and the planning efficiency of experimental procedures are two of the motivational aspects for these numerical studies. The widespread availability of high performance computing facilities has been the enabler for the simulation of sufficiently large systems. Objectives and Motivation In the present study, finite element models were built for sintered, metallic fibre networks and validated by previously published experimental stiffness measurements. The validated models were the basis for predictions about so far unknown properties. Materials and Methods The finite element models were built by transferring previously published skeletons of fibre networks into finite element models. Beam theory was applied as simplification method. Results and Conclusions The obtained material stiffness isn’t a constant but rather a function of variables such as sample size and boundary conditions. Beam theory offers an efficient finite element method for the simulated fibre networks. The experimental results can be approximated by the simulated systems. Two worthwhile aspects for future work will be the influence of size and shape and the mechanical interaction with matrix materials. PMID:26569603

Finite element probabilistic risk assessment of transmission line insulation flashovers caused by lightning strokes

DOE Office of Scientific and Technical Information (OSTI.GOV)

Bacvarov, D.C.

1981-01-01

A new method for probabilistic risk assessment of transmission line insulation flashovers caused by lightning strokes is presented. The utilized approach of applying the finite element method for probabilistic risk assessment is demonstrated to be very powerful. The reasons for this are two. First, the finite element method is inherently suitable for analysis of three dimensional spaces where the parameters, such as three variate probability densities of the lightning currents, are non-uniformly distributed. Second, the finite element method permits non-uniform discretization of the three dimensional probability spaces thus yielding high accuracy in critical regions, such as the area of themore » low probability events, while at the same time maintaining coarse discretization in the non-critical areas to keep the number of grid points and the size of the problem to a manageable low level. The finite element probabilistic risk assessment method presented here is based on a new multidimensional search algorithm. It utilizes an efficient iterative technique for finite element interpolation of the transmission line insulation flashover criteria computed with an electro-magnetic transients program. Compared to other available methods the new finite element probabilistic risk assessment method is significantly more accurate and approximately two orders of magnitude computationally more efficient. The method is especially suited for accurate assessment of rare, very low probability events.« less

Finite element modelling of woven composite failure modes at the mesoscopic scale: deterministic versus stochastic approaches

NASA Astrophysics Data System (ADS)

Roirand, Q.; Missoum-Benziane, D.; Thionnet, A.; Laiarinandrasana, L.

2017-09-01

Textile composites are composed of 3D complex architecture. To assess the durability of such engineering structures, the failure mechanisms must be highlighted. Examinations of the degradation have been carried out thanks to tomography. The present work addresses a numerical damage model dedicated to the simulation of the crack initiation and propagation at the scale of the warp yarns. For the 3D woven composites under study, loadings in tension and combined tension and bending were considered. Based on an erosion procedure of broken elements, the failure mechanisms have been modelled on 3D periodic cells by finite element calculations. The breakage of one element was determined using a failure criterion at the mesoscopic scale based on the yarn stress at failure. The results were found to be in good agreement with the experimental data for the two kinds of macroscopic loadings. The deterministic approach assumed a homogeneously distributed stress at failure all over the integration points in the meshes of woven composites. A stochastic approach was applied to a simple representative elementary periodic cell. The distribution of the Weibull stress at failure was assigned to the integration points using a Monte Carlo simulation. It was shown that this stochastic approach allowed more realistic failure simulations avoiding the idealised symmetry due to the deterministic modelling. In particular, the stochastic simulations performed have shown several variations of the stress as well as strain at failure and the failure modes of the yarn.

Measured and calculated acoustic attenuation rates of tuned resonator arrays for two surface impedance distribution models with flow

NASA Technical Reports Server (NTRS)

Parrott, Tony L.; Abrahamson, A. Louis; Jones, Michael G.

1988-01-01

An experiment was performed to validate two analytical models for predicting low frequency attenuation of duct liner configurations built from an array of seven resonators that could be individually tuned via adjustable cavity depths. These analytical models had previously been developed for high frequency aero-engine inlet duct liner design. In the low frequency application, the liner surface impedance distribution is unavoidably spatially varying by virtue of available fabrication techniques. The characteristic length of this spatial variation may be a significant fraction of the acoustic wavelength. Comparison of measured and predicted attenuation rates and transmission losses for both modal decomposition and finite element propagation models were in good to excellent agreement for a test frequency range that included the first and second cavity resonance frequencies. This was true for either of two surface impedance distribution modeling procedures used to simplify the impedance boundary conditions. In the presence of mean flow, measurements revealed a fine scale structure of acoustic hot spots in the attenuation and phase profiles. These details were accurately predicted by the finite element model. Since no impedance changes due to mean flow were assumed, it is concluded that this fine scale structure was due to convective effects of the mean flow interacting with the surface impedance nonuniformities.

Calibration of Airframe and Occupant Models for Two Full-Scale Rotorcraft Crash Tests

NASA Technical Reports Server (NTRS)

Annett, Martin S.; Horta, Lucas G.; Polanco, Michael A.

2012-01-01

Two full-scale crash tests of an MD-500 helicopter were conducted in 2009 and 2010 at NASA Langley's Landing and Impact Research Facility in support of NASA s Subsonic Rotary Wing Crashworthiness Project. The first crash test was conducted to evaluate the performance of an externally mounted composite deployable energy absorber under combined impact conditions. In the second crash test, the energy absorber was removed to establish baseline loads that are regarded as severe but survivable. Accelerations and kinematic data collected from the crash tests were compared to a system integrated finite element model of the test article. Results from 19 accelerometers placed throughout the airframe were compared to finite element model responses. The model developed for the purposes of predicting acceleration responses from the first crash test was inadequate when evaluating more severe conditions seen in the second crash test. A newly developed model calibration approach that includes uncertainty estimation, parameter sensitivity, impact shape orthogonality, and numerical optimization was used to calibrate model results for the second full-scale crash test. This combination of heuristic and quantitative methods was used to identify modeling deficiencies, evaluate parameter importance, and propose required model changes. It is shown that the multi-dimensional calibration techniques presented here are particularly effective in identifying model adequacy. Acceleration results for the calibrated model were compared to test results and the original model results. There was a noticeable improvement in the pilot and co-pilot region, a slight improvement in the occupant model response, and an over-stiffening effect in the passenger region. This approach should be adopted early on, in combination with the building-block approaches that are customarily used, for model development and test planning guidance. Complete crash simulations with validated finite element models can be used to satisfy crash certification requirements, thereby reducing overall development costs.

Optimal least-squares finite element method for elliptic problems

NASA Technical Reports Server (NTRS)

Jiang, Bo-Nan; Povinelli, Louis A.

1991-01-01

An optimal least squares finite element method is proposed for two dimensional and three dimensional elliptic problems and its advantages are discussed over the mixed Galerkin method and the usual least squares finite element method. In the usual least squares finite element method, the second order equation (-Delta x (Delta u) + u = f) is recast as a first order system (-Delta x p + u = f, Delta u - p = 0). The error analysis and numerical experiment show that, in this usual least squares finite element method, the rate of convergence for flux p is one order lower than optimal. In order to get an optimal least squares method, the irrotationality Delta x p = 0 should be included in the first order system.

Finite Element A Posteriori Error Estimation for Heat Conduction. Degree awarded by George Washington Univ.

NASA Technical Reports Server (NTRS)

Lang, Christapher G.; Bey, Kim S. (Technical Monitor)

2002-01-01

This research investigates residual-based a posteriori error estimates for finite element approximations of heat conduction in single-layer and multi-layered materials. The finite element approximation, based upon hierarchical modelling combined with p-version finite elements, is described with specific application to a two-dimensional, steady state, heat-conduction problem. Element error indicators are determined by solving an element equation for the error with the element residual as a source, and a global error estimate in the energy norm is computed by collecting the element contributions. Numerical results of the performance of the error estimate are presented by comparisons to the actual error. Two methods are discussed and compared for approximating the element boundary flux. The equilibrated flux method provides more accurate results for estimating the error than the average flux method. The error estimation is applied to multi-layered materials with a modification to the equilibrated flux method to approximate the discontinuous flux along a boundary at the material interfaces. A directional error indicator is developed which distinguishes between the hierarchical modeling error and the finite element error. Numerical results are presented for single-layered materials which show that the directional indicators accurately determine which contribution to the total error dominates.

Finite Element Peen Forming Simulation

NASA Astrophysics Data System (ADS)

Gariépy, Alexandre; Larose, Simon; Perron, Claude; Bocher, Philippe; Lévesque, Martin

Shot peening consists of projecting multiple small particles onto a ductile part in order to induce compressive residual stresses near the surface. Peen forming, a derivative of shot peening, is a process that creates an unbalanced stress state which in turn leads to a deformation to shape thin parts. This versatile and cost-effective process is commonly used to manufacture aluminum wing skins and rocket panels. This paper presents the finite element modelling approach that was developed by the authors to simulate the process. The method relies on shell elements and calculated stress profiles and uses an approximation equation to take into account the incremental nature of the process. Finite element predictions were in good agreement with experimental results for small-scale tests. The method was extended to a hypothetical wing skin model to show its potential applications.

Supercomputer implementation of finite element algorithms for high speed compressible flows

NASA Technical Reports Server (NTRS)

Thornton, E. A.; Ramakrishnan, R.

1986-01-01

Prediction of compressible flow phenomena using the finite element method is of recent origin and considerable interest. Two shock capturing finite element formulations for high speed compressible flows are described. A Taylor-Galerkin formulation uses a Taylor series expansion in time coupled with a Galerkin weighted residual statement. The Taylor-Galerkin algorithms use explicit artificial dissipation, and the performance of three dissipation models are compared. A Petrov-Galerkin algorithm has as its basis the concepts of streamline upwinding. Vectorization strategies are developed to implement the finite element formulations on the NASA Langley VPS-32. The vectorization scheme results in finite element programs that use vectors of length of the order of the number of nodes or elements. The use of the vectorization procedure speeds up processing rates by over two orders of magnitude. The Taylor-Galerkin and Petrov-Galerkin algorithms are evaluated for 2D inviscid flows on criteria such as solution accuracy, shock resolution, computational speed and storage requirements. The convergence rates for both algorithms are enhanced by local time-stepping schemes. Extension of the vectorization procedure for predicting 2D viscous and 3D inviscid flows are demonstrated. Conclusions are drawn regarding the applicability of the finite element procedures for realistic problems that require hundreds of thousands of nodes.

Multi-Scale Modeling of Liquid Phase Sintering Affected by Gravity: Preliminary Analysis

NASA Technical Reports Server (NTRS)

Olevsky, Eugene; German, Randall M.

2012-01-01

A multi-scale simulation concept taking into account impact of gravity on liquid phase sintering is described. The gravity influence can be included at both the micro- and macro-scales. At the micro-scale, the diffusion mass-transport is directionally modified in the framework of kinetic Monte-Carlo simulations to include the impact of gravity. The micro-scale simulations can provide the values of the constitutive parameters for macroscopic sintering simulations. At the macro-scale, we are attempting to embed a continuum model of sintering into a finite-element framework that includes the gravity forces and substrate friction. If successful, the finite elements analysis will enable predictions relevant to space-based processing, including size and shape and property predictions. Model experiments are underway to support the models via extraction of viscosity moduli versus composition, particle size, heating rate, temperature and time.

A mesoscopic bridging scale method for fluids and coupling dissipative particle dynamics with continuum finite element method

PubMed Central

Kojic, Milos; Filipovic, Nenad; Tsuda, Akira

2012-01-01

A multiscale procedure to couple a mesoscale discrete particle model and a macroscale continuum model of incompressible fluid flow is proposed in this study. We call this procedure the mesoscopic bridging scale (MBS) method since it is developed on the basis of the bridging scale method for coupling molecular dynamics and finite element models [G.J. Wagner, W.K. Liu, Coupling of atomistic and continuum simulations using a bridging scale decomposition, J. Comput. Phys. 190 (2003) 249–274]. We derive the governing equations of the MBS method and show that the differential equations of motion of the mesoscale discrete particle model and finite element (FE) model are only coupled through the force terms. Based on this coupling, we express the finite element equations which rely on the Navier–Stokes and continuity equations, in a way that the internal nodal FE forces are evaluated using viscous stresses from the mesoscale model. The dissipative particle dynamics (DPD) method for the discrete particle mesoscale model is employed. The entire fluid domain is divided into a local domain and a global domain. Fluid flow in the local domain is modeled with both DPD and FE method, while fluid flow in the global domain is modeled by the FE method only. The MBS method is suitable for modeling complex (colloidal) fluid flows, where continuum methods are sufficiently accurate only in the large fluid domain, while small, local regions of particular interest require detailed modeling by mesoscopic discrete particles. Solved examples – simple Poiseuille and driven cavity flows illustrate the applicability of the proposed MBS method. PMID:23814322

Multi Length Scale Finite Element Design Framework for Advanced Woven Fabrics

NASA Astrophysics Data System (ADS)

Erol, Galip Ozan

Woven fabrics are integral parts of many engineering applications spanning from personal protective garments to surgical scaffolds. They provide a wide range of opportunities in designing advanced structures because of their high tenacity, flexibility, high strength-to-weight ratios and versatility. These advantages result from their inherent multi scale nature where the filaments are bundled together to create yarns while the yarns are arranged into different weave architectures. Their highly versatile nature opens up potential for a wide range of mechanical properties which can be adjusted based on the application. While woven fabrics are viable options for design of various engineering systems, being able to understand the underlying mechanisms of the deformation and associated highly nonlinear mechanical response is important and necessary. However, the multiscale nature and relationships between these scales make the design process involving woven fabrics a challenging task. The objective of this work is to develop a multiscale numerical design framework using experimentally validated mesoscopic and macroscopic length scale approaches by identifying important deformation mechanisms and recognizing the nonlinear mechanical response of woven fabrics. This framework is exercised by developing mesoscopic length scale constitutive models to investigate plain weave fabric response under a wide range of loading conditions. A hyperelastic transversely isotropic yarn material model with transverse material nonlinearity is developed for woven yarns (commonly used in personal protection garments). The material properties/parameters are determined through an inverse method where unit cell finite element simulations are coupled with experiments. The developed yarn material model is validated by simulating full scale uniaxial tensile, bias extension and indentation experiments, and comparing to experimentally observed mechanical response and deformation mechanisms. Moreover, mesoscopic unit cell finite elements are coupled with a design-of-experiments method to systematically identify the important yarn material properties for the macroscale response of various weave architectures. To demonstrate the macroscopic length scale approach, two new material models for woven fabrics were developed. The Planar Material Model (PMM) utilizes two important deformation mechanisms in woven fabrics: (1) yarn elongation, and (2) relative yarn rotation due to shear loads. The yarns' uniaxial tensile response is modeled with a nonlinear spring using constitutive relations while a nonlinear rotational spring is implemented to define fabric's shear stiffness. The second material model, Sawtooth Material Model (SMM) adopts the sawtooth geometry while recognizing the biaxial nature of woven fabrics by implementing the interactions between the yarns. Material properties/parameters required by both PMM and SMM can be directly determined from standard experiments. Both macroscopic material models are implemented within an explicit finite element code and validated by comparing to the experiments. Then, the developed macroscopic material models are compared under various loading conditions to determine their accuracy. Finally, the numerical models developed in the mesoscopic and macroscopic length scales are linked thus demonstrating the new systematic design framework involving linked mesoscopic and macroscopic length scale modeling approaches. The approach is demonstrated with both Planar and Sawtooth Material Models and the simulation results are verified by comparing the results obtained from meso and macro models.

A Modeling Approach for Burn Scar Assessment Using Natural Features and Elastic Property

DOE Office of Scientific and Technical Information (OSTI.GOV)

Tsap, L V; Zhang, Y; Goldgof, D B

2004-04-02

A modeling approach is presented for quantitative burn scar assessment. Emphases are given to: (1) constructing a finite element model from natural image features with an adaptive mesh, and (2) quantifying the Young's modulus of scars using the finite element model and the regularization method. A set of natural point features is extracted from the images of burn patients. A Delaunay triangle mesh is then generated that adapts to the point features. A 3D finite element model is built on top of the mesh with the aid of range images providing the depth information. The Young's modulus of scars ismore » quantified with a simplified regularization functional, assuming that the knowledge of scar's geometry is available. The consistency between the Relative Elasticity Index and the physician's rating based on the Vancouver Scale (a relative scale used to rate burn scars) indicates that the proposed modeling approach has high potentials for image-based quantitative burn scar assessment.« less

A combined registration and finite element analysis method for fast estimation of intraoperative brain shift; phantom and animal model study.

PubMed

Mohammadi, Amrollah; Ahmadian, Alireza; Rabbani, Shahram; Fattahi, Ehsan; Shirani, Shapour

2017-12-01

Finite element models for estimation of intraoperative brain shift suffer from huge computational cost. In these models, image registration and finite element analysis are two time-consuming processes. The proposed method is an improved version of our previously developed Finite Element Drift (FED) registration algorithm. In this work the registration process is combined with the finite element analysis. In the Combined FED (CFED), the deformation of whole brain mesh is iteratively calculated by geometrical extension of a local load vector which is computed by FED. While the processing time of the FED-based method including registration and finite element analysis was about 70 s, the computation time of the CFED was about 3.2 s. The computational cost of CFED is almost 50% less than similar state of the art brain shift estimators based on finite element models. The proposed combination of registration and structural analysis can make the calculation of brain deformation much faster. Copyright © 2016 John Wiley & Sons, Ltd.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Wight, L.; Zaslawsky, M.

Two approaches for calculating soil structure interaction (SSI) are compared: finite element and lumped mass. Results indicate that the calculations with the lumped mass method are generally conservative compared to those obtained by the finite element method. They also suggest that a closer agreement between the two sets of calculations is possible, depending on the use of frequency-dependent soil springs and dashpots in the lumped mass calculations. There is a total lack of suitable guidelines for implementing the lumped mass method of calculating SSI, which leads to the conclusion that the finite element method is generally superior for calculative purposes.

Efficient finite element simulation of slot spirals, slot radomes and microwave structures

NASA Technical Reports Server (NTRS)

Gong, J.; Volakis, J. L.

1995-01-01

This progress report contains the following two documents: (1) 'Efficient Finite Element Simulation of Slot Antennas using Prismatic Elements' - A hybrid finite element-boundary integral (FE-BI) simulation technique is discussed to treat narrow slot antennas etched on a planar platform. Specifically, the prismatic elements are used to reduce the redundant sampling rates and ease the mesh generation process. Numerical results for an antenna slot and frequency selective surfaces are presented to demonstrate the validity and capability of the technique; and (2) 'Application and Design Guidelines of the PML Absorber for Finite Element Simulations of Microwave Packages' - The recently introduced perfectly matched layer (PML) uniaxial absorber for frequency domain finite element simulations has several advantages. In this paper we present the application of PML for microwave circuit simulations along with design guidelines to obtain a desired level of absorption. Different feeding techniques are also investigated for improved accuracy.

Workshop on the Integration of Finite Element Modeling with Geometric Modeling

NASA Technical Reports Server (NTRS)

Wozny, Michael J.

1987-01-01

The workshop on the Integration of Finite Element Modeling with Geometric Modeling was held on 12 May 1987. It was held to discuss the geometric modeling requirements of the finite element modeling process and to better understand the technical aspects of the integration of these two areas. The 11 papers are presented except for one for which only the abstract is given.

Finite element analysis of elasto-plastic soils. Report no. 4: Finite element analysis of elasto-plastic frictional materials for application to lunar earth sciences

NASA Technical Reports Server (NTRS)

Marr, W. A., Jr.

1972-01-01

The behavior of finite element models employing different constitutive relations to describe the stress-strain behavior of soils is investigated. Three models, which assume small strain theory is applicable, include a nondilatant, a dilatant and a strain hardening constitutive relation. Two models are formulated using large strain theory and include a hyperbolic and a Tresca elastic perfectly plastic constitutive relation. These finite element models are used to analyze retaining walls and footings. Methods of improving the finite element solutions are investigated. For nonlinear problems better solutions can be obtained by using smaller load increment sizes and more iterations per load increment than by increasing the number of elements. Suitable methods of treating tension stresses and stresses which exceed the yield criteria are discussed.

Active earth pressure model tests versus finite element analysis

NASA Astrophysics Data System (ADS)

Pietrzak, Magdalena

2017-06-01

The purpose of the paper is to compare failure mechanisms observed in small scale model tests on granular sample in active state, and simulated by finite element method (FEM) using Plaxis 2D software. Small scale model tests were performed on rectangular granular sample retained by a rigid wall. Deformation of the sample resulted from simple wall translation in the direction `from the soil" (active earth pressure state. Simple Coulomb-Mohr model for soil can be helpful in interpreting experimental findings in case of granular materials. It was found that the general alignment of strain localization pattern (failure mechanism) may belong to macro scale features and be dominated by a test boundary conditions rather than the nature of the granular sample.

Dynamic and thermal response finite element models of multi-body space structural configurations

NASA Technical Reports Server (NTRS)

Edighoffer, Harold H.

1987-01-01

Presented is structural dynamics modeling of two multibody space structural configurations. The first configuration is a generic space station model of a cylindrical habitation module, two solar array panels, radiator panel, and central connecting tube. The second is a 15-m hoop-column antenna. Discussed is the special joint elimination sequence used for these large finite element models, so that eigenvalues could be extracted. The generic space station model aided test configuration design and analysis/test data correlation. The model consisted of six finite element models, one of each substructure and one of all substructures as a system. Static analysis and tests at the substructure level fine-tuned the finite element models. The 15-m hoop-column antenna is a truss column and structural ring interconnected with tension stabilizing cables. To the cables, pretensioned mesh membrane elements were attached to form four parabolic shaped antennae, one per quadrant. Imposing thermal preloads in the cables and mesh elements produced pretension in the finite element model. Thermal preload variation in the 96 control cables was adjusted to maintain antenna shape within the required tolerance and to give pointing accuracy.

A combined finite element-boundary element formulation for solution of axially symmetric bodies

NASA Technical Reports Server (NTRS)

Collins, Jeffrey D.; Volakis, John L.

1991-01-01

A new method is presented for the computation of electromagnetic scattering from axially symmetric bodies. To allow the simulation of inhomogeneous cross sections, the method combines the finite element and boundary element techniques. Interior to a fictitious surface enclosing the scattering body, the finite element method is used which results in a sparce submatrix, whereas along the enclosure the Stratton-Chu integral equation is enforced. By choosing the fictitious enclosure to be a right circular cylinder, most of the resulting boundary integrals are convolutional and may therefore be evaluated via the FFT with which the system is iteratively solved. In view of the sparce matrix associated with the interior fields, this reduces the storage requirement of the entire system to O(N) making the method attractive for large scale computations. The details of the corresponding formulation and its numerical implementation are described.

Arbitrary-Order Conservative and Consistent Remapping and a Theory of Linear Maps: Part II

DOE Office of Scientific and Technical Information (OSTI.GOV)

Ullrich, Paul A.; Devendran, Dharshi; Johansen, Hans

2016-04-01

The focus on this series of articles is on the generation of accurate, conservative, consistent, and (optionally) monotone linear offline maps. This paper is the second in the series. It extends on the first part by describing four examples of 2D linear maps that can be constructed in accordance with the theory of the earlier work. The focus is again on spherical geometry, although these techniques can be readily extended to arbitrary manifolds. The four maps include conservative, consistent, and (optionally) monotone linear maps (i) between two finite-volume meshes, (ii) from finite-volume to finite-element meshes using a projection-type approach, (iii)more » from finite-volume to finite-element meshes using volumetric integration, and (iv) between two finite-element meshes. Arbitrary order of accuracy is supported for each of the described nonmonotone maps.« less

Finite element analysis of three patterns of internal fixation of fractures of the mandibular condyle.

PubMed

Aquilina, Peter; Chamoli, Uphar; Parr, William C H; Clausen, Philip D; Wroe, Stephen

2013-06-01

The most stable pattern of internal fixation for fractures of the mandibular condyle is a matter for ongoing discussion. In this study we investigated the stability of three commonly used patterns of plate fixation, and constructed finite element models of a simulated mandibular condylar fracture. The completed models were heterogeneous in the distribution of bony material properties, contained about 1.2 million elements, and incorporated simulated jaw-adducting musculature. Models were run assuming linear elasticity and isotropic material properties for bone. This model was considerably larger and more complex than previous finite element models that have been used to analyse the biomechanical behaviour of differing plating techniques. The use of two parallel 2.0 titanium miniplates gave a more stable configuration with lower mean element stresses and displacements over the use of a single miniplate. In addition, a parallel orientation of two miniplates resulted in lower stresses and displacements than did the use of two miniplates in an offset pattern. The use of two parallel titanium plates resulted in a superior biomechanical result as defined by mean element stresses and relative movement between the fractured fragments in these finite element models. Copyright © 2012 The British Association of Oral and Maxillofacial Surgeons. Published by Elsevier Ltd. All rights reserved.

A mixed shear flexible finite element for the analysis of laminated plates

NASA Technical Reports Server (NTRS)

Putcha, N. S.; Reddy, J. N.

1984-01-01

A mixed shear flexible finite element based on the Hencky-Mindlin type shear deformation theory of laminated plates is presented and their behavior in bending is investigated. The element consists of three displacements, two rotations, and three moments as the generalized degrees of freedom per node. The numerical convergence and accuracy characteristics of the element are investigated by comparing the finite element solutions with the exact solutions. The present study shows that reduced-order integration of the stiffness coefficients due to shear is necessary to obtain accurate results for thin plates.

Application of the control volume mixed finite element method to a triangular discretization

USGS Publications Warehouse

Naff, R.L.

2012-01-01

A two-dimensional control volume mixed finite element method is applied to the elliptic equation. Discretization of the computational domain is based in triangular elements. Shape functions and test functions are formulated on the basis of an equilateral reference triangle with unit edges. A pressure support based on the linear interpolation of elemental edge pressures is used in this formulation. Comparisons are made between results from the standard mixed finite element method and this control volume mixed finite element method. Published 2011. This article is a US Government work and is in the public domain in the USA. ?? 2012 John Wiley & Sons, Ltd. This article is a US Government work and is in the public domain in the USA.

Second order tensor finite element

NASA Technical Reports Server (NTRS)

Oden, J. Tinsley; Fly, J.; Berry, C.; Tworzydlo, W.; Vadaketh, S.; Bass, J.

1990-01-01

The results of a research and software development effort are presented for the finite element modeling of the static and dynamic behavior of anisotropic materials, with emphasis on single crystal alloys. Various versions of two dimensional and three dimensional hybrid finite elements were implemented and compared with displacement-based elements. Both static and dynamic cases are considered. The hybrid elements developed in the project were incorporated into the SPAR finite element code. In an extension of the first phase of the project, optimization of experimental tests for anisotropic materials was addressed. In particular, the problem of calculating material properties from tensile tests and of calculating stresses from strain measurements were considered. For both cases, numerical procedures and software for the optimization of strain gauge and material axes orientation were developed.

Developing parallel GeoFEST(P) using the PYRAMID AMR library

NASA Technical Reports Server (NTRS)

Norton, Charles D.; Lyzenga, Greg; Parker, Jay; Tisdale, Robert E.

2004-01-01

The PYRAMID parallel unstructured adaptive mesh refinement (AMR) library has been coupled with the GeoFEST geophysical finite element simulation tool to support parallel active tectonics simulations. Specifically, we have demonstrated modeling of coseismic and postseismic surface displacement due to a simulated Earthquake for the Landers system of interacting faults in Southern California. The new software demonstrated a 25-times resolution improvement and a 4-times reduction in time to solution over the sequential baseline milestone case. Simulations on workstations using a few tens of thousands of stress displacement finite elements can now be expanded to multiple millions of elements with greater than 98% scaled efficiency on various parallel platforms over many hundreds of processors. Our most recent work has demonstrated that we can dynamically adapt the computational grid as stress grows on a fault. In this paper, we will describe the major issues and challenges associated with coupling these two programs to create GeoFEST(P). Performance and visualization results will also be described.

The Use of Sparse Direct Solver in Vector Finite Element Modeling for Calculating Two Dimensional (2-D) Magnetotelluric Responses in Transverse Electric (TE) Mode

NASA Astrophysics Data System (ADS)

Yihaa Roodhiyah, Lisa’; Tjong, Tiffany; Nurhasan; Sutarno, D.

2018-04-01

The late research, linear matrices of vector finite element in two dimensional(2-D) magnetotelluric (MT) responses modeling was solved by non-sparse direct solver in TE mode. Nevertheless, there is some weakness which have to be improved especially accuracy in the low frequency (10-3 Hz-10-5 Hz) which is not achieved yet and high cost computation in dense mesh. In this work, the solver which is used is sparse direct solver instead of non-sparse direct solverto overcome the weaknesses of solving linear matrices of vector finite element metod using non-sparse direct solver. Sparse direct solver will be advantageous in solving linear matrices of vector finite element method because of the matrix properties which is symmetrical and sparse. The validation of sparse direct solver in solving linear matrices of vector finite element has been done for a homogen half-space model and vertical contact model by analytical solution. Thevalidation result of sparse direct solver in solving linear matrices of vector finite element shows that sparse direct solver is more stable than non-sparse direct solver in computing linear problem of vector finite element method especially in low frequency. In the end, the accuracy of 2D MT responses modelling in low frequency (10-3 Hz-10-5 Hz) has been reached out under the efficient allocation memory of array and less computational time consuming.

Variational approach to probabilistic finite elements

NASA Technical Reports Server (NTRS)

Belytschko, T.; Liu, W. K.; Mani, A.; Besterfield, G.

1991-01-01

Probabilistic finite element methods (PFEM), synthesizing the power of finite element methods with second-moment techniques, are formulated for various classes of problems in structural and solid mechanics. Time-invariant random materials, geometric properties and loads are incorporated in terms of their fundamental statistics viz. second-moments. Analogous to the discretization of the displacement field in finite element methods, the random fields are also discretized. Preserving the conceptual simplicity, the response moments are calculated with minimal computations. By incorporating certain computational techniques, these methods are shown to be capable of handling large systems with many sources of uncertainties. By construction, these methods are applicable when the scale of randomness is not very large and when the probabilistic density functions have decaying tails. The accuracy and efficiency of these methods, along with their limitations, are demonstrated by various applications. Results obtained are compared with those of Monte Carlo simulation and it is shown that good accuracy can be obtained for both linear and nonlinear problems. The methods are amenable to implementation in deterministic FEM based computer codes.

Variational approach to probabilistic finite elements

NASA Astrophysics Data System (ADS)

Belytschko, T.; Liu, W. K.; Mani, A.; Besterfield, G.

1991-08-01

Probabilistic finite element methods (PFEM), synthesizing the power of finite element methods with second-moment techniques, are formulated for various classes of problems in structural and solid mechanics. Time-invariant random materials, geometric properties and loads are incorporated in terms of their fundamental statistics viz. second-moments. Analogous to the discretization of the displacement field in finite element methods, the random fields are also discretized. Preserving the conceptual simplicity, the response moments are calculated with minimal computations. By incorporating certain computational techniques, these methods are shown to be capable of handling large systems with many sources of uncertainties. By construction, these methods are applicable when the scale of randomness is not very large and when the probabilistic density functions have decaying tails. The accuracy and efficiency of these methods, along with their limitations, are demonstrated by various applications. Results obtained are compared with those of Monte Carlo simulation and it is shown that good accuracy can be obtained for both linear and nonlinear problems. The methods are amenable to implementation in deterministic FEM based computer codes.

Variational approach to probabilistic finite elements

NASA Technical Reports Server (NTRS)

Belytschko, T.; Liu, W. K.; Mani, A.; Besterfield, G.

1987-01-01

Probabilistic finite element method (PFEM), synthesizing the power of finite element methods with second-moment techniques, are formulated for various classes of problems in structural and solid mechanics. Time-invariant random materials, geometric properties, and loads are incorporated in terms of their fundamental statistics viz. second-moments. Analogous to the discretization of the displacement field in finite element methods, the random fields are also discretized. Preserving the conceptual simplicity, the response moments are calculated with minimal computations. By incorporating certain computational techniques, these methods are shown to be capable of handling large systems with many sources of uncertainties. By construction, these methods are applicable when the scale of randomness is not very large and when the probabilistic density functions have decaying tails. The accuracy and efficiency of these methods, along with their limitations, are demonstrated by various applications. Results obtained are compared with those of Monte Carlo simulation and it is shown that good accuracy can be obtained for both linear and nonlinear problems. The methods are amenable to implementation in deterministic FEM based computer codes.

Discontinuous dual-primal mixed finite elements for elliptic problems

NASA Technical Reports Server (NTRS)

Bottasso, Carlo L.; Micheletti, Stefano; Sacco, Riccardo

2000-01-01

We propose a novel discontinuous mixed finite element formulation for the solution of second-order elliptic problems. Fully discontinuous piecewise polynomial finite element spaces are used for the trial and test functions. The discontinuous nature of the test functions at the element interfaces allows to introduce new boundary unknowns that, on the one hand enforce the weak continuity of the trial functions, and on the other avoid the need to define a priori algorithmic fluxes as in standard discontinuous Galerkin methods. Static condensation is performed at the element level, leading to a solution procedure based on the sole interface unknowns. The resulting family of discontinuous dual-primal mixed finite element methods is presented in the one and two-dimensional cases. In the one-dimensional case, we show the equivalence of the method with implicit Runge-Kutta schemes of the collocation type exhibiting optimal behavior. Numerical experiments in one and two dimensions demonstrate the order accuracy of the new method, confirming the results of the analysis.

A mixed parallel strategy for the solution of coupled multi-scale problems at finite strains

NASA Astrophysics Data System (ADS)

Lopes, I. A. Rodrigues; Pires, F. M. Andrade; Reis, F. J. P.

2018-02-01

A mixed parallel strategy for the solution of homogenization-based multi-scale constitutive problems undergoing finite strains is proposed. The approach aims to reduce the computational time and memory requirements of non-linear coupled simulations that use finite element discretization at both scales (FE^2). In the first level of the algorithm, a non-conforming domain decomposition technique, based on the FETI method combined with a mortar discretization at the interface of macroscopic subdomains, is employed. A master-slave scheme, which distributes tasks by macroscopic element and adopts dynamic scheduling, is then used for each macroscopic subdomain composing the second level of the algorithm. This strategy allows the parallelization of FE^2 simulations in computers with either shared memory or distributed memory architectures. The proposed strategy preserves the quadratic rates of asymptotic convergence that characterize the Newton-Raphson scheme. Several examples are presented to demonstrate the robustness and efficiency of the proposed parallel strategy.

Application of Probability Methods to Assess Crash Modeling Uncertainty

NASA Technical Reports Server (NTRS)

Lyle, Karen H.; Stockwell, Alan E.; Hardy, Robin C.

2003-01-01

Full-scale aircraft crash simulations performed with nonlinear, transient dynamic, finite element codes can incorporate structural complexities such as: geometrically accurate models; human occupant models; and advanced material models to include nonlinear stress-strain behaviors, and material failure. Validation of these crash simulations is difficult due to a lack of sufficient information to adequately determine the uncertainty in the experimental data and the appropriateness of modeling assumptions. This paper evaluates probabilistic approaches to quantify the effects of finite element modeling assumptions on the predicted responses. The vertical drop test of a Fokker F28 fuselage section will be the focus of this paper. The results of a probabilistic analysis using finite element simulations will be compared with experimental data.

Application of Probability Methods to Assess Crash Modeling Uncertainty

NASA Technical Reports Server (NTRS)

Lyle, Karen H.; Stockwell, Alan E.; Hardy, Robin C.

2007-01-01

Full-scale aircraft crash simulations performed with nonlinear, transient dynamic, finite element codes can incorporate structural complexities such as: geometrically accurate models; human occupant models; and advanced material models to include nonlinear stress-strain behaviors, and material failure. Validation of these crash simulations is difficult due to a lack of sufficient information to adequately determine the uncertainty in the experimental data and the appropriateness of modeling assumptions. This paper evaluates probabilistic approaches to quantify the effects of finite element modeling assumptions on the predicted responses. The vertical drop test of a Fokker F28 fuselage section will be the focus of this paper. The results of a probabilistic analysis using finite element simulations will be compared with experimental data.

Numerical Methods for 2-Dimensional Modeling

DTIC Science & Technology

1980-12-01

high-order finite element methods, and a multidimensional version of the method of lines, both utilizing an optimized stiff integrator for the time...integration. The finite element methods have proved disappointing, but the method of lines has provided an unexpectedly large gain in speed. Two...diffusion problems with the same number of unknowns (a 21 x 41 grid), solved by second-order finite element methods, took over seven minutes on the Cray-i

Design synthesis and optimization of permanent magnet synchronous machines based on computationally-efficient finite element analysis

NASA Astrophysics Data System (ADS)

Sizov, Gennadi Y.

In this dissertation, a model-based multi-objective optimal design of permanent magnet ac machines, supplied by sine-wave current regulated drives, is developed and implemented. The design procedure uses an efficient electromagnetic finite element-based solver to accurately model nonlinear material properties and complex geometric shapes associated with magnetic circuit design. Application of an electromagnetic finite element-based solver allows for accurate computation of intricate performance parameters and characteristics. The first contribution of this dissertation is the development of a rapid computational method that allows accurate and efficient exploration of large multi-dimensional design spaces in search of optimum design(s). The computationally efficient finite element-based approach developed in this work provides a framework of tools that allow rapid analysis of synchronous electric machines operating under steady-state conditions. In the developed modeling approach, major steady-state performance parameters such as, winding flux linkages and voltages, average, cogging and ripple torques, stator core flux densities, core losses, efficiencies and saturated machine winding inductances, are calculated with minimum computational effort. In addition, the method includes means for rapid estimation of distributed stator forces and three-dimensional effects of stator and/or rotor skew on the performance of the machine. The second contribution of this dissertation is the development of the design synthesis and optimization method based on a differential evolution algorithm. The approach relies on the developed finite element-based modeling method for electromagnetic analysis and is able to tackle large-scale multi-objective design problems using modest computational resources. Overall, computational time savings of up to two orders of magnitude are achievable, when compared to current and prevalent state-of-the-art methods. These computational savings allow one to expand the optimization problem to achieve more complex and comprehensive design objectives. The method is used in the design process of several interior permanent magnet industrial motors. The presented case studies demonstrate that the developed finite element-based approach practically eliminates the need for using less accurate analytical and lumped parameter equivalent circuit models for electric machine design optimization. The design process and experimental validation of the case-study machines are detailed in the dissertation.

Generalizing the TRAPRG and TRAPAX finite elements

NASA Technical Reports Server (NTRS)

Hurwitz, M. M.

1983-01-01

The NASTRAN TRAPRG and TRAPAX finite elements are very restrictive as to shape and grid point numbering. The elements must be trapezoidal with two sides parallel to the radial axis. In addition, the ordering of the grid points on the element connection card must follow strict rules. The paper describes the generalization of these elements so that these restrictions no longer apply.

Evaluation of Test Methods for Triaxially Braided Composites using a Meso-Scale Finite Element Model

DOE Office of Scientific and Technical Information (OSTI.GOV)

Zhang, Chao

The characterization of triaxially braided composite is complicate due to the nonuniformity of deformation within the unit cell as well as the possibility of the freeedge effect related to the large size of the unit cell. Extensive experimental investigation has been conducted to develop more accurate test approaches in characterizing the actual mechanical properties of the material we are studying. In this work, a meso-scale finite element model is utilized to simulate two complex specimens: notched tensile specimen and tube tensile specimen, which are designed to avoid the free-edge effect and free-edge effect induced premature edge damage. The full fieldmore » strain data is predicted numerically and compared with experimental data obtained by Digit Image Correlation. The numerically predicted tensile strength values are compared with experimentally measured results. The discrepancy between numerically predicted and experimentally measured data, the capability of different test approaches are analyzed and discussed. The presented numerical model could serve as assistance to the evaluation of different test methods, and is especially useful in identifying potential local damage events.« less

A Method for Combining Experimentation and Molecular Dynamics Simulation to Improve Cohesive Zone Models for Metallic Microstructures

NASA Technical Reports Server (NTRS)

Hochhalter, J. D.; Glaessgen, E. H.; Ingraffea, A. R.; Aquino, W. A.

2009-01-01

Fracture processes within a material begin at the nanometer length scale at which the formation, propagation, and interaction of fundamental damage mechanisms occur. Physics-based modeling of these atomic processes quickly becomes computationally intractable as the system size increases. Thus, a multiscale modeling method, based on the aggregation of fundamental damage processes occurring at the nanoscale within a cohesive zone model, is under development and will enable computationally feasible and physically meaningful microscale fracture simulation in polycrystalline metals. This method employs atomistic simulation to provide an optimization loop with an initial prediction of a cohesive zone model (CZM). This initial CZM is then applied at the crack front region within a finite element model. The optimization procedure iterates upon the CZM until the finite element model acceptably reproduces the near-crack-front displacement fields obtained from experimental observation. With this approach, a comparison can be made between the original CZM predicted by atomistic simulation and the converged CZM that is based on experimental observation. Comparison of the two CZMs gives insight into how atomistic simulation scales.

Processor farming in two-level analysis of historical bridge

NASA Astrophysics Data System (ADS)

Krejčí, T.; Kruis, J.; Koudelka, T.; Šejnoha, M.

2017-11-01

This contribution presents a processor farming method in connection with a multi-scale analysis. In this method, each macro-scopic integration point or each finite element is connected with a certain meso-scopic problem represented by an appropriate representative volume element (RVE). The solution of a meso-scale problem provides then effective parameters needed on the macro-scale. Such an analysis is suitable for parallel computing because the meso-scale problems can be distributed among many processors. The application of the processor farming method to a real world masonry structure is illustrated by an analysis of Charles bridge in Prague. The three-dimensional numerical model simulates the coupled heat and moisture transfer of one half of arch No. 3. and it is a part of a complex hygro-thermo-mechanical analysis which has been developed to determine the influence of climatic loading on the current state of the bridge.

Coupling finite element and spectral methods: First results

NASA Technical Reports Server (NTRS)

Bernardi, Christine; Debit, Naima; Maday, Yvon

1987-01-01

A Poisson equation on a rectangular domain is solved by coupling two methods: the domain is divided in two squares, a finite element approximation is used on the first square and a spectral discretization is used on the second one. Two kinds of matching conditions on the interface are presented and compared. In both cases, error estimates are proved.

Convergence of an hp-Adaptive Finite Element Strategy in Two and Three Space-Dimensions

NASA Astrophysics Data System (ADS)

Bürg, Markus; Dörfler, Willy

2010-09-01

We show convergence of an automatic hp-adaptive refinement strategy for the finite element method on the elliptic boundary value problem. The strategy is a generalization of a refinement strategy proposed for one-dimensional situations to problems in two and three space-dimensions.

MOFAT: A TWO-DIMENSIONAL FINITE ELEMENT PROGRAM FOR MULTIPHASE FLOW AND MULTICOMPONENT TRANSPORT - PROGRAM DOCUMENTATION AND USER'S GUIDE

EPA Science Inventory

This manual describes a two-dimensional, finite element model for coupled multiphase flow and multicomponent transport in planar or radially symmetric vertical sections. low and transport of three fluid phases, including water, nonaqueous phase liquid (NAPL), and gas are consider...

A Mixed Finite Volume Element Method for Flow Calculations in Porous Media

NASA Technical Reports Server (NTRS)

Jones, Jim E.

1996-01-01

A key ingredient in the simulation of flow in porous media is the accurate determination of the velocities that drive the flow. The large scale irregularities of the geology, such as faults, fractures, and layers suggest the use of irregular grids in the simulation. Work has been done in applying the finite volume element (FVE) methodology as developed by McCormick in conjunction with mixed methods which were developed by Raviart and Thomas. The resulting mixed finite volume element discretization scheme has the potential to generate more accurate solutions than standard approaches. The focus of this paper is on a multilevel algorithm for solving the discrete mixed FVE equations. The algorithm uses a standard cell centered finite difference scheme as the 'coarse' level and the more accurate mixed FVE scheme as the 'fine' level. The algorithm appears to have potential as a fast solver for large size simulations of flow in porous media.

Finite elements: Theory and application

NASA Technical Reports Server (NTRS)

Dwoyer, D. L. (Editor); Hussaini, M. Y. (Editor); Voigt, R. G. (Editor)

1988-01-01

Recent advances in FEM techniques and applications are discussed in reviews and reports presented at the ICASE/LaRC workshop held in Hampton, VA in July 1986. Topics addressed include FEM approaches for partial differential equations, mixed FEMs, singular FEMs, FEMs for hyperbolic systems, iterative methods for elliptic finite-element equations on general meshes, mathematical aspects of FEMS for incompressible viscous flows, and gradient weighted moving finite elements in two dimensions. Consideration is given to adaptive flux-corrected FEM transport techniques for CFD, mixed and singular finite elements and the field BEM, p and h-p versions of the FEM, transient analysis methods in computational dynamics, and FEMs for integrated flow/thermal/structural analysis.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Candel, Arno; Li, Z.; Ng, C.

The Compact Linear Collider (CLIC) provides a path to a multi-TeV accelerator to explore the energy frontier of High Energy Physics. Its novel two-beam accelerator concept envisions rf power transfer to the accelerating structures from a separate high-current decelerator beam line consisting of power extraction and transfer structures (PETS). It is critical to numerically verify the fundamental and higher-order mode properties in and between the two beam lines with high accuracy and confidence. To solve these large-scale problems, SLAC's parallel finite element electromagnetic code suite ACE3P is employed. Using curvilinear conformal meshes and higher-order finite element vector basis functions, unprecedentedmore » accuracy and computational efficiency are achieved, enabling high-fidelity modeling of complex detuned structures such as the CLIC TD24 accelerating structure. In this paper, time-domain simulations of wakefield coupling effects in the combined system of PETS and the TD24 structures are presented. The results will help to identify potential issues and provide new insights on the design, leading to further improvements on the novel CLIC two-beam accelerator scheme.« less

Un-collided-flux preconditioning for the first order transport equation

DOE Office of Scientific and Technical Information (OSTI.GOV)

Rigley, M.; Koebbe, J.; Drumm, C.

2013-07-01

Two codes were tested for the first order neutron transport equation using finite element methods. The un-collided-flux solution is used as a preconditioner for each of these methods. These codes include a least squares finite element method and a discontinuous finite element method. The performance of each code is shown on problems in one and two dimensions. The un-collided-flux preconditioner shows good speedup on each of the given methods. The un-collided-flux preconditioner has been used on the second-order equation, and here we extend those results to the first order equation. (authors)

A method of selecting grid size to account for Hertz deformation in finite element analysis of spur gears

NASA Technical Reports Server (NTRS)

Coy, J. J.; Chao, C. H. C.

1981-01-01

A method of selecting grid size for the finite element analysis of gear tooth deflection is presented. The method is based on a finite element study of two cylinders in line contact, where the criterion for establishing element size was that there be agreement with the classical Hertzian solution for deflection. The results are applied to calculate deflection for the gear specimen used in the NASA spur gear test rig. Comparisons are made between the present results and the results of two other methods of calculation. The results have application in design of gear tooth profile modifications to reduce noise and dynamic loads.

Finite element analysis of two disk rotor system

DOE Office of Scientific and Technical Information (OSTI.GOV)

Dixit, Harsh Kumar

A finite element model of simple horizontal rotor system is developed for evaluating its dynamic behaviour. The model is based on Timoshenko beam element and accounts for the effect of gyroscopic couple and other rotational forces. Present rotor system consists of single shaft which is supported by bearings at both ends and two disks are mounted at different locations. The natural frequencies, mode shapes and orbits of rotating system for a specific range of rotation speed are obtained by developing a MATLAB code for solving the finite element equations of rotary system. Consequently, Campbell diagram is plotted for finding amore » relationship between natural whirl frequencies and rotation of the rotor.« less

An enriched finite element method to fractional advection-diffusion equation

NASA Astrophysics Data System (ADS)

Luan, Shengzhi; Lian, Yanping; Ying, Yuping; Tang, Shaoqiang; Wagner, Gregory J.; Liu, Wing Kam

2017-08-01

In this paper, an enriched finite element method with fractional basis [ 1,x^{α }] for spatial fractional partial differential equations is proposed to obtain more stable and accurate numerical solutions. For pure fractional diffusion equation without advection, the enriched Galerkin finite element method formulation is demonstrated to simulate the exact solution successfully without any numerical oscillation, which is advantageous compared to the traditional Galerkin finite element method with integer basis [ 1,x] . For fractional advection-diffusion equation, the oscillatory behavior becomes complex due to the introduction of the advection term which can be characterized by a fractional element Peclet number. For the purpose of addressing the more complex numerical oscillation, an enriched Petrov-Galerkin finite element method is developed by using a dimensionless fractional stabilization parameter, which is formulated through a minimization of the residual of the nodal solution. The effectiveness and accuracy of the enriched finite element method are demonstrated by a series of numerical examples of fractional diffusion equation and fractional advection-diffusion equation, including both one-dimensional and two-dimensional, steady-state and time-dependent cases.

Recent Progress in the p and h-p Version of the Finite Element Method.

DTIC Science & Technology

1987-07-01

code PROBE which was developed recently by NOETIC Technologies, St. Louis £54]. PROBE solves two dimensional problems of linear elasticity, stationary...of the finite element method was studied in detail from various point of view. We will mention here some essential illustrative results. In one...28) Bathe, K. J., Brezzi, F., Studies of finite element procedures - the INF-SUP condition, equivalent forms and applications in Reliability of

The Impact of Varying the Physics Grid Resolution Relative to the Dynamical Core Resolution in CAM-SE-CSLAM

NASA Astrophysics Data System (ADS)

Herrington, A. R.; Lauritzen, P. H.; Reed, K. A.

2017-12-01

The spectral element dynamical core of the Community Atmosphere Model (CAM) has recently been coupled to an approximately isotropic, finite-volume grid per implementation of the conservative semi-Lagrangian multi-tracer transport scheme (CAM-SE-CSLAM; Lauritzen et al. 2017). In this framework, the semi-Lagrangian transport of tracers are computed on the finite-volume grid, while the adiabatic dynamics are solved using the spectral element grid. The physical parameterizations are evaluated on the finite-volume grid, as opposed to the unevenly spaced Gauss-Lobatto-Legendre nodes of the spectral element grid. Computing the physics on the finite-volume grid reduces numerical artifacts such as grid imprinting, possibly because the forcing terms are no longer computed at element boundaries where the resolved dynamics are least smooth. The separation of the physics grid and the dynamics grid allows for a unique opportunity to understand the resolution sensitivity in CAM-SE-CSLAM. The observed large sensitivity of CAM to horizontal resolution is a poorly understood impediment to improved simulations of regional climate using global, variable resolution grids. Here, a series of idealized moist simulations are presented in which the finite-volume grid resolution is varied relative to the spectral element grid resolution in CAM-SE-CSLAM. The simulations are carried out at multiple spectral element grid resolutions, in part to provide a companion set of simulations, in which the spectral element grid resolution is varied relative to the finite-volume grid resolution, but more generally to understand if the sensitivity to the finite-volume grid resolution is consistent across a wider spectrum of resolved scales. Results are interpreted in the context of prior ideas regarding resolution sensitivity of global atmospheric models.

The Programming Language Python In Earth System Simulations

NASA Astrophysics Data System (ADS)

Gross, L.; Imranullah, A.; Mora, P.; Saez, E.; Smillie, J.; Wang, C.

2004-12-01

Mathematical models in earth sciences base on the solution of systems of coupled, non-linear, time-dependent partial differential equations (PDEs). The spatial and time-scale vary from a planetary scale and million years for convection problems to 100km and 10 years for fault systems simulations. Various techniques are in use to deal with the time dependency (e.g. Crank-Nicholson), with the non-linearity (e.g. Newton-Raphson) and weakly coupled equations (e.g. non-linear Gauss-Seidel). Besides these high-level solution algorithms discretization methods (e.g. finite element method (FEM), boundary element method (BEM)) are used to deal with spatial derivatives. Typically, large-scale, three dimensional meshes are required to resolve geometrical complexity (e.g. in the case of fault systems) or features in the solution (e.g. in mantel convection simulations). The modelling environment escript allows the rapid implementation of new physics as required for the development of simulation codes in earth sciences. Its main object is to provide a programming language, where the user can define new models and rapidly develop high-level solution algorithms. The current implementation is linked with the finite element package finley as a PDE solver. However, the design is open and other discretization technologies such as finite differences and boundary element methods could be included. escript is implemented as an extension of the interactive programming environment python (see www.python.org). Key concepts introduced are Data objects, which are holding values on nodes or elements of the finite element mesh, and linearPDE objects, which are defining linear partial differential equations to be solved by the underlying discretization technology. In this paper we will show the basic concepts of escript and will show how escript is used to implement a simulation code for interacting fault systems. We will show some results of large-scale, parallel simulations on an SGI Altix system. Acknowledgements: Project work is supported by Australian Commonwealth Government through the Australian Computational Earth Systems Simulator Major National Research Facility, Queensland State Government Smart State Research Facility Fund, The University of Queensland and SGI.

Full-Scale Direct Numerical Simulation of Two- and Three-Dimensional Instabilities and Rivulet Formulation in Heated Falling Films

NASA Technical Reports Server (NTRS)

Krishnamoorthy, S.; Ramaswamy, B.; Joo, S. W.

1995-01-01

A thin film draining on an inclined plate has been studied numerically using finite element method. Three-dimensional governing equations of continuity, momentum and energy with a moving boundary are integrated in an arbitrary Lagrangian Eulerian frame of reference. Kinematic equation is solved to precisely update interface location. Rivulet formation based on instability mechanism has been simulated using full-scale computation. Comparisons with long-wave theory are made to validate the numerical scheme. Detailed analysis of two- and three-dimensional nonlinear wave formation and spontaneous rupture forming rivulets under the influence of combined thermocapillary and surface-wave instabilities is performed.

Nonlinear solid finite element analysis of mitral valves with heterogeneous leaflet layers

NASA Astrophysics Data System (ADS)

Prot, V.; Skallerud, B.

2009-02-01

An incompressible transversely isotropic hyperelastic material for solid finite element analysis of a porcine mitral valve response is described. The material model implementation is checked in single element tests and compared with a membrane implementation in an out-of-plane loading test to study how the layered structures modify the stress response for a simple geometry. Three different collagen layer arrangements are used in finite element analysis of the mitral valve. When the leaflets are arranged in two layers with the collagen on the ventricular side, the stress in the fibre direction through the thickness in the central part of the anterior leaflet is homogenized and the peak stress is reduced. A simulation using membrane elements is also carried out for comparison with the solid finite element results. Compared to echocardiographic measurements, the finite element models bulge too much in the left atrium. This may be due to evidence of active muscle fibres in some parts of the anterior leaflet, whereas our constitutive modelling is based on passive material.

Identification of minute damage in composite bridge structures equipped with fiber optic sensors using the location of neutral axis and finite element analysis

NASA Astrophysics Data System (ADS)

Li, Xi; Glisic, Branko

2016-04-01

By definition, the neutral axis of a loaded composite beam structure is the curve along which the section experiences zero bending strain. When no axial loading is present, the location of the neutral axis passes through the centroid of stiffness of the beam cross-section. In the presence of damage, the centroid of stiffness, as well as the neutral axis, shift from the healthy position. The concept of neutral axis can be widely applied to all beam-like structures. According to literature, a change in location of the neutral axis can be associated with damage in the corresponding cross-section. In this paper, the movement of neutral axis near locations of minute damage in a composite bridge structure was studied using finite element analysis and experimental results. The finite element model was developed based on a physical scale model of a composite simply-supported structure with controlled minute damage in the reinforced concrete deck. The structure was equipped with long-gauge fiber optic strain and temperature sensors at a healthy reference location as well as two locations of damage. A total of 12 strain sensors were installed during construction and used to monitor the structure during various loading events. This paper aims to explain previous experimental results which showed that the observed positions of neutral axis near damage locations were higher than the predicted healthy locations in some loading events. Analysis has shown that finite element analysis has potential to simulate and explain the physical behavior of the test structure.

Finite element methods for the biomechanics of soft hydrated tissues: nonlinear analysis and adaptive control of meshes.

PubMed

Spilker, R L; de Almeida, E S; Donzelli, P S

1992-01-01

This chapter addresses computationally demanding numerical formulations in the biomechanics of soft tissues. The theory of mixtures can be used to represent soft hydrated tissues in the human musculoskeletal system as a two-phase continuum consisting of an incompressible solid phase (collagen and proteoglycan) and an incompressible fluid phase (interstitial water). We first consider the finite deformation of soft hydrated tissues in which the solid phase is represented as hyperelastic. A finite element formulation of the governing nonlinear biphasic equations is presented based on a mixed-penalty approach and derived using the weighted residual method. Fluid and solid phase deformation, velocity, and pressure are interpolated within each element, and the pressure variables within each element are eliminated at the element level. A system of nonlinear, first-order differential equations in the fluid and solid phase deformation and velocity is obtained. In order to solve these equations, the contributions of the hyperelastic solid phase are incrementally linearized, a finite difference rule is introduced for temporal discretization, and an iterative scheme is adopted to achieve equilibrium at the end of each time increment. We demonstrate the accuracy and adequacy of the procedure using a six-node, isoparametric axisymmetric element, and we present an example problem for which independent numerical solution is available. Next, we present an automated, adaptive environment for the simulation of soft tissue continua in which the finite element analysis is coupled with automatic mesh generation, error indicators, and projection methods. Mesh generation and updating, including both refinement and coarsening, for the two-dimensional examples examined in this study are performed using the finite quadtree approach. The adaptive analysis is based on an error indicator which is the L2 norm of the difference between the finite element solution and a projected finite element solution. Total stress, calculated as the sum of the solid and fluid phase stresses, is used in the error indicator. To allow the finite difference algorithm to proceed in time using an updated mesh, solution values must be transferred to the new nodal locations. This rezoning is accomplished using a projected field for the primary variables. The accuracy and effectiveness of this adaptive finite element analysis is demonstrated using a linear, two-dimensional, axisymmetric problem corresponding to the indentation of a thin sheet of soft tissue. The method is shown to effectively capture the steep gradients and to produce solutions in good agreement with independent, converged, numerical solutions.

Semi-automatic sparse preconditioners for high-order finite element methods on non-uniform meshes

NASA Astrophysics Data System (ADS)

Austin, Travis M.; Brezina, Marian; Jamroz, Ben; Jhurani, Chetan; Manteuffel, Thomas A.; Ruge, John

2012-05-01

High-order finite elements often have a higher accuracy per degree of freedom than the classical low-order finite elements. However, in the context of implicit time-stepping methods, high-order finite elements present challenges to the construction of efficient simulations due to the high cost of inverting the denser finite element matrix. There are many cases where simulations are limited by the memory required to store the matrix and/or the algorithmic components of the linear solver. We are particularly interested in preconditioned Krylov methods for linear systems generated by discretization of elliptic partial differential equations with high-order finite elements. Using a preconditioner like Algebraic Multigrid can be costly in terms of memory due to the need to store matrix information at the various levels. We present a novel method for defining a preconditioner for systems generated by high-order finite elements that is based on a much sparser system than the original high-order finite element system. We investigate the performance for non-uniform meshes on a cube and a cubed sphere mesh, showing that the sparser preconditioner is more efficient and uses significantly less memory. Finally, we explore new methods to construct the sparse preconditioner and examine their effectiveness for non-uniform meshes. We compare results to a direct use of Algebraic Multigrid as a preconditioner and to a two-level additive Schwarz method.

Simulating Thin Sheets: Buckling, Wrinkling, Folding and Growth

NASA Astrophysics Data System (ADS)

Vetter, Roman; Stoop, Norbert; Wittel, Falk K.; Herrmann, Hans J.

2014-03-01

Numerical simulations of thin sheets undergoing large deformations are computationally challenging. Depending on the scenario, they may spontaneously buckle, wrinkle, fold, or crumple. Nature's thin tissues often experience significant anisotropic growth, which can act as the driving force for such instabilities. We use a recently developed finite element model to simulate the rich variety of nonlinear responses of Kirchhoff-Love sheets. The model uses subdivision surface shape functions in order to guarantee convergence of the method, and to allow a finite element description of anisotropically growing sheets in the classical Rayleigh-Ritz formalism. We illustrate the great potential in this approach by simulating the inflation of airbags, the buckling of a stretched cylinder, as well as the formation and scaling of wrinkles at free boundaries of growing sheets. Finally, we compare the folding of spatially confined sheets subject to growth and shrinking confinement to find that the two processes are equivalent.

Computational homogenisation for thermoviscoplasticity: application to thermally sprayed coatings

NASA Astrophysics Data System (ADS)

Berthelsen, Rolf; Denzer, Ralf; Oppermann, Philip; Menzel, Andreas

2017-11-01

Metal forming processes require wear-resistant tool surfaces in order to ensure a long life cycle of the expensive tools together with a constant high quality of the produced components. Thermal spraying is a relatively widely applied coating technique for the deposit of wear protection coatings. During these coating processes, heterogeneous coatings are deployed at high temperatures followed by quenching where residual stresses occur which strongly influence the performance of the coated tools. The objective of this article is to discuss and apply a thermo-mechanically coupled simulation framework which captures the heterogeneity of the deposited coating material. Therefore, a two-scale finite element framework for the solution of nonlinear thermo-mechanically coupled problems is elaborated and applied to the simulation of thermoviscoplastic material behaviour including nonlinear thermal softening in a geometrically linearised setting. The finite element framework and material model is demonstrated by means of numerical examples.

Simulation of axisymmetric jets with a finite element Navier-Stokes solver and a multilevel VOF approach

NASA Astrophysics Data System (ADS)

Cervone, A.; Manservisi, S.; Scardovelli, R.

2010-09-01

A multilevel VOF approach has been coupled to an accurate finite element Navier-Stokes solver in axisymmetric geometry for the simulation of incompressible liquid jets with high density ratios. The representation of the color function over a fine grid has been introduced to reduce the discontinuity of the interface at the cell boundary. In the refined grid the automatic breakup and coalescence occur at a spatial scale much smaller than the coarse grid spacing. To reduce memory requirements, we have implemented on the fine grid a compact storage scheme which memorizes the color function data only in the mixed cells. The capillary force is computed by using the Laplace-Beltrami operator and a volumetric approach for the two principal curvatures. Several simulations of axisymmetric jets have been performed to show the accuracy and robustness of the proposed scheme.

Static and fatigue testing of full-scale fuselage panels fabricated using a Therm-X(R) process

NASA Technical Reports Server (NTRS)

Dinicola, Albert J.; Kassapoglou, Christos; Chou, Jack C.

1992-01-01

Large, curved, integrally stiffened composite panels representative of an aircraft fuselage structure were fabricated using a Therm-X process, an alternative concept to conventional two-sided hard tooling and contour vacuum bagging. Panels subsequently were tested under pure shear loading in both static and fatigue regimes to assess the adequacy of the manufacturing process, the effectiveness of damage tolerant design features co-cured with the structure, and the accuracy of finite element and closed-form predictions of postbuckling capability and failure load. Test results indicated the process yielded panels of high quality and increased damage tolerance through suppression of common failure modes such as skin-stiffener separation and frame-stiffener corner failure. Finite element analyses generally produced good predictions of postbuckled shape, and a global-local modelling technique yielded failure load predictions that were within 7% of the experimental mean.

The effect of in situ/in vitro three-dimensional quantitative computed tomography image voxel size on the finite element model of human vertebral cancellous bone.

PubMed

Lu, Yongtao; Engelke, Klaus; Glueer, Claus-C; Morlock, Michael M; Huber, Gerd

2014-11-01

Quantitative computed tomography-based finite element modeling technique is a promising clinical tool for the prediction of bone strength. However, quantitative computed tomography-based finite element models were created from image datasets with different image voxel sizes. The aim of this study was to investigate whether there is an influence of image voxel size on the finite element models. In all 12 thoracolumbar vertebrae were scanned prior to autopsy (in situ) using two different quantitative computed tomography scan protocols, which resulted in image datasets with two different voxel sizes (0.29 × 0.29 × 1.3 mm(3) vs 0.18 × 0.18 × 0.6 mm(3)). Eight of them were scanned after autopsy (in vitro) and the datasets were reconstructed with two voxel sizes (0.32 × 0.32 × 0.6 mm(3) vs. 0.18 × 0.18 × 0.3 mm(3)). Finite element models with cuboid volume of interest extracted from the vertebral cancellous part were created and inhomogeneous bilinear bone properties were defined. Axial compression was simulated. No effect of voxel size was detected on the apparent bone mineral density for both the in situ and in vitro cases. However, the apparent modulus and yield strength showed significant differences in the two voxel size group pairs (in situ and in vitro). In conclusion, the image voxel size may have to be considered when the finite element voxel modeling technique is used in clinical applications. © IMechE 2014.

Generalized multiscale finite-element method (GMsFEM) for elastic wave propagation in heterogeneous, anisotropic media

DOE Office of Scientific and Technical Information (OSTI.GOV)

Gao, Kai; Fu, Shubin; Gibson, Richard L.

It is important to develop fast yet accurate numerical methods for seismic wave propagation to characterize complex geological structures and oil and gas reservoirs. However, the computational cost of conventional numerical modeling methods, such as finite-difference method and finite-element method, becomes prohibitively expensive when applied to very large models. We propose a Generalized Multiscale Finite-Element Method (GMsFEM) for elastic wave propagation in heterogeneous, anisotropic media, where we construct basis functions from multiple local problems for both the boundaries and interior of a coarse node support or coarse element. The application of multiscale basis functions can capture the fine scale mediummore » property variations, and allows us to greatly reduce the degrees of freedom that are required to implement the modeling compared with conventional finite-element method for wave equation, while restricting the error to low values. We formulate the continuous Galerkin and discontinuous Galerkin formulation of the multiscale method, both of which have pros and cons. Applications of the multiscale method to three heterogeneous models show that our multiscale method can effectively model the elastic wave propagation in anisotropic media with a significant reduction in the degrees of freedom in the modeling system.« less

Generalized Multiscale Finite-Element Method (GMsFEM) for elastic wave propagation in heterogeneous, anisotropic media

DOE Office of Scientific and Technical Information (OSTI.GOV)

Gao, Kai, E-mail: kaigao87@gmail.com; Fu, Shubin, E-mail: shubinfu89@gmail.com; Gibson, Richard L., E-mail: gibson@tamu.edu

It is important to develop fast yet accurate numerical methods for seismic wave propagation to characterize complex geological structures and oil and gas reservoirs. However, the computational cost of conventional numerical modeling methods, such as finite-difference method and finite-element method, becomes prohibitively expensive when applied to very large models. We propose a Generalized Multiscale Finite-Element Method (GMsFEM) for elastic wave propagation in heterogeneous, anisotropic media, where we construct basis functions from multiple local problems for both the boundaries and interior of a coarse node support or coarse element. The application of multiscale basis functions can capture the fine scale mediummore » property variations, and allows us to greatly reduce the degrees of freedom that are required to implement the modeling compared with conventional finite-element method for wave equation, while restricting the error to low values. We formulate the continuous Galerkin and discontinuous Galerkin formulation of the multiscale method, both of which have pros and cons. Applications of the multiscale method to three heterogeneous models show that our multiscale method can effectively model the elastic wave propagation in anisotropic media with a significant reduction in the degrees of freedom in the modeling system.« less

Generalized multiscale finite-element method (GMsFEM) for elastic wave propagation in heterogeneous, anisotropic media

DOE PAGES

Gao, Kai; Fu, Shubin; Gibson, Richard L.; ...

2015-04-14

It is important to develop fast yet accurate numerical methods for seismic wave propagation to characterize complex geological structures and oil and gas reservoirs. However, the computational cost of conventional numerical modeling methods, such as finite-difference method and finite-element method, becomes prohibitively expensive when applied to very large models. We propose a Generalized Multiscale Finite-Element Method (GMsFEM) for elastic wave propagation in heterogeneous, anisotropic media, where we construct basis functions from multiple local problems for both the boundaries and interior of a coarse node support or coarse element. The application of multiscale basis functions can capture the fine scale mediummore » property variations, and allows us to greatly reduce the degrees of freedom that are required to implement the modeling compared with conventional finite-element method for wave equation, while restricting the error to low values. We formulate the continuous Galerkin and discontinuous Galerkin formulation of the multiscale method, both of which have pros and cons. Applications of the multiscale method to three heterogeneous models show that our multiscale method can effectively model the elastic wave propagation in anisotropic media with a significant reduction in the degrees of freedom in the modeling system.« less

Functional Data Approximation on Bounded Domains using Polygonal Finite Elements.

PubMed

Cao, Juan; Xiao, Yanyang; Chen, Zhonggui; Wang, Wenping; Bajaj, Chandrajit

2018-07-01

We construct and analyze piecewise approximations of functional data on arbitrary 2D bounded domains using generalized barycentric finite elements, and particularly quadratic serendipity elements for planar polygons. We compare approximation qualities (precision/convergence) of these partition-of-unity finite elements through numerical experiments, using Wachspress coordinates, natural neighbor coordinates, Poisson coordinates, mean value coordinates, and quadratic serendipity bases over polygonal meshes on the domain. For a convex n -sided polygon, the quadratic serendipity elements have 2 n basis functions, associated in a Lagrange-like fashion to each vertex and each edge midpoint, rather than the usual n ( n + 1)/2 basis functions to achieve quadratic convergence. Two greedy algorithms are proposed to generate Voronoi meshes for adaptive functional/scattered data approximations. Experimental results show space/accuracy advantages for these quadratic serendipity finite elements on polygonal domains versus traditional finite elements over simplicial meshes. Polygonal meshes and parameter coefficients of the quadratic serendipity finite elements obtained by our greedy algorithms can be further refined using an L 2 -optimization to improve the piecewise functional approximation. We conduct several experiments to demonstrate the efficacy of our algorithm for modeling features/discontinuities in functional data/image approximation.

Unified control/structure design and modeling research

NASA Technical Reports Server (NTRS)

Mingori, D. L.; Gibson, J. S.; Blelloch, P. A.; Adamian, A.

1986-01-01

To demonstrate the applicability of the control theory for distributed systems to large flexible space structures, research was focused on a model of a space antenna which consists of a rigid hub, flexible ribs, and a mesh reflecting surface. The space antenna model used is discussed along with the finite element approximation of the distributed model. The basic control problem is to design an optimal or near-optimal compensator to suppress the linear vibrations and rigid-body displacements of the structure. The application of an infinite dimensional Linear Quadratic Gaussian (LQG) control theory to flexible structure is discussed. Two basic approaches for robustness enhancement were investigated: loop transfer recovery and sensitivity optimization. A third approach synthesized from elements of these two basic approaches is currently under development. The control driven finite element approximation of flexible structures is discussed. Three sets of finite element basic vectors for computing functional control gains are compared. The possibility of constructing a finite element scheme to approximate the infinite dimensional Hamiltonian system directly, instead of indirectly is discussed.

Finite element solutions for crack-tip behavior in small-scale yielding

NASA Technical Reports Server (NTRS)

Tracey, D. M.

1976-01-01

The subject considered is the stress and deformation fields in a cracked elastic-plastic power law hardening material under plane strain tensile loading. An incremental plasticity finite element formulation is developed for accurate analysis of the complete field problem including the extensively deformed near tip region, the elastic-plastic region, and the remote elastic region. The formulation has general applicability and was used to solve the small scale yielding problem for a set of material hardening exponents. Distributions of stress, strain, and crack opening displacement at the crack tip and through the elastic-plastic zone are presented as a function of the elastic stress intensity factor and material properties.

Scaling a Human Body Finite Element Model with Radial Basis Function Interpolation

DTIC Science & Technology

Human body models are currently used to evaluate the body’s response to a variety of threats to the Soldier. The ability to adjust the size of human...body models is currently limited because of the complex shape changes that are required. Here, a radial basis function interpolation method is used to...morph the shape on an existing finite element mesh. Tools are developed and integrated into the Blender computer graphics software to assist with

Finite element analysis of a micromechanical deformable mirror device

NASA Technical Reports Server (NTRS)

Sheerer, T. J.; Nelson, W. E.; Hornbeck, L. J.

1989-01-01

A monolithic spatial light modulator chip was developed consisting of a large number of micrometer-scale mirror cells which can be rotated through an angle by application of an electrostatic field. The field is generated by electronics integral to the chip. The chip has application in photoreceptor based non-impact printing technologies. Chips containing over 16000 cells were fabricated, and were tested to several billions of cycles. Finite Element Analysis (FEA) of the device was used to model both the electrical and mechanical characteristics.

Heat transfer model and finite element formulation for simulation of selective laser melting

NASA Astrophysics Data System (ADS)

Roy, Souvik; Juha, Mario; Shephard, Mark S.; Maniatty, Antoinette M.

2017-10-01

A novel approach and finite element formulation for modeling the melting, consolidation, and re-solidification process that occurs in selective laser melting additive manufacturing is presented. Two state variables are introduced to track the phase (melt/solid) and the degree of consolidation (powder/fully dense). The effect of the consolidation on the absorption of the laser energy into the material as it transforms from a porous powder to a dense melt is considered. A Lagrangian finite element formulation, which solves the governing equations on the unconsolidated reference configuration is derived, which naturally considers the effect of the changing geometry as the powder melts without needing to update the simulation domain. The finite element model is implemented into a general-purpose parallel finite element solver. Results are presented comparing to experimental results in the literature for a single laser track with good agreement. Predictions for a spiral laser pattern are also shown.

Finite element computation of a viscous compressible free shear flow governed by the time dependent Navier-Stokes equations

NASA Technical Reports Server (NTRS)

Cooke, C. H.; Blanchard, D. K.

1975-01-01

A finite element algorithm for solution of fluid flow problems characterized by the two-dimensional compressible Navier-Stokes equations was developed. The program is intended for viscous compressible high speed flow; hence, primitive variables are utilized. The physical solution was approximated by trial functions which at a fixed time are piecewise cubic on triangular elements. The Galerkin technique was employed to determine the finite-element model equations. A leapfrog time integration is used for marching asymptotically from initial to steady state, with iterated integrals evaluated by numerical quadratures. The nonsymmetric linear systems of equations governing time transition from step-to-step are solved using a rather economical block iterative triangular decomposition scheme. The concept was applied to the numerical computation of a free shear flow. Numerical results of the finite-element method are in excellent agreement with those obtained from a finite difference solution of the same problem.

The use of Galerkin finite-element methods to solve mass-transport equations

USGS Publications Warehouse

Grove, David B.

1977-01-01

The partial differential equation that describes the transport and reaction of chemical solutes in porous media was solved using the Galerkin finite-element technique. These finite elements were superimposed over finite-difference cells used to solve the flow equation. Both convection and flow due to hydraulic dispersion were considered. Linear and Hermite cubic approximations (basis functions) provided satisfactory results: however, the linear functions were computationally more efficient for two-dimensional problems. Successive over relaxation (SOR) and iteration techniques using Tchebyschef polynomials were used to solve the sparce matrices generated using the linear and Hermite cubic functions, respectively. Comparisons of the finite-element methods to the finite-difference methods, and to analytical results, indicated that a high degree of accuracy may be obtained using the method outlined. The technique was applied to a field problem involving an aquifer contaminated with chloride, tritium, and strontium-90. (Woodard-USGS)

Application of numerical methods to heat transfer and thermal stress analysis of aerospace vehicles

NASA Technical Reports Server (NTRS)

Wieting, A. R.

1979-01-01

The paper describes a thermal-structural design analysis study of a fuel-injection strut for a hydrogen-cooled scramjet engine for a supersonic transport, utilizing finite-element methodology. Applications of finite-element and finite-difference codes to the thermal-structural design-analysis of space transports and structures are discussed. The interaction between the thermal and structural analyses has led to development of finite-element thermal methodology to improve the integration between these two disciplines. The integrated thermal-structural analysis capability developed within the framework of a computer code is outlined.

Stress Distribution During Deformation of Polycrystalline Aluminum by Molecular-Dynamics and Finite-Element Modeling

NASA Technical Reports Server (NTRS)

Yamakov, V.; Saether, E.; Phillips, D.; Glaessgen, E. H.

2004-01-01

In this paper, a multiscale modelling strategy is used to study the effect of grain-boundary sliding on stress localization in a polycrystalline microstructure with an uneven distribution of grain size. The development of the molecular dynamics (MD) analysis used to interrogate idealized grain microstructures with various types of grain boundaries and the multiscale modelling strategies for modelling large systems of grains is discussed. Both molecular-dynamics and finite-element (FE) simulations for idealized polycrystalline models of identical geometry are presented with the purpose of demonstrating the effectiveness of the adapted finite-element method using cohesive zone models to reproduce grain-boundary sliding and its effect on the stress distribution in a polycrystalline metal. The yield properties of the grain-boundary interface, used in the FE simulations, are extracted from a MD simulation on a bicrystal. The models allow for the study of the load transfer between adjacent grains of very different size through grain-boundary sliding during deformation. A large-scale FE simulation of 100 grains of a typical microstructure is then presented to reveal that the stress distribution due to grain-boundary sliding during uniform tensile strain can lead to stress localization of two to three times the background stress, thus suggesting a significant effect on the failure properties of the metal.

A study on the uniqueness of the plastic flow direction for granular assemblies of ductile particles using discrete finite-element simulations

NASA Astrophysics Data System (ADS)

Abdelmoula, Nouha; Harthong, Barthélémy; Imbault, Didier; Dorémus, Pierre

2017-12-01

The multi-particle finite element method involving assemblies of meshed particles interacting through finite-element contact conditions is adopted to study the plastic flow of a granular material with highly deformable elastic-plastic grains. In particular, it is investigated whether the flow rule postulate applies for such materials. Using a spherical stress probing method, the influence of incremental stress on plastic strain increment vectors was assessed for numerical samples compacted along two different loading paths up to different values of relative density. Results show that the numerical samples studied behave reasonably well according to an associated flow rule, except in the vicinity of the loading point where the influence of the stress increment proved to be very significant. A plausible explanation for the non-uniqueness of the direction of plastic flow is proposed, based on the idea that the resistance of the numerical sample to plastic straining can vary by an order of magnitude depending on the direction of the accumulated stress. The above-mentioned dependency of the direction of plastic flow on the direction of the stress increment was related to the difference in strength between shearing and normal stressing at the scale of contact surfaces between particles.

Revisiting of Multiscale Static Analysis of Notched Laminates Using the Generalized Method of Cells

NASA Technical Reports Server (NTRS)

Naghipour Ghezeljeh, Paria; Arnold, Steven M.; Pineda, Evan J.

2016-01-01

Composite material systems generally exhibit a range of behavior on different length scales (from constituent level to macro); therefore, a multiscale framework is beneficial for the design and engineering of these material systems. The complex nature of the observed composite failure during experiments suggests the need for a three-dimensional (3D) multiscale model to attain a reliable prediction. However, the size of a multiscale three-dimensional finite element model can become prohibitively large and computationally costly. Two-dimensional (2D) models are preferred due to computational efficiency, especially if many different configurations have to be analyzed for an in-depth damage tolerance and durability design study. In this study, various 2D and 3D multiscale analyses will be employed to conduct a detailed investigation into the tensile failure of a given multidirectional, notched carbon fiber reinforced polymer laminate. Threedimensional finite element analysis is typically considered more accurate than a 2D finite element model, as compared with experiments. Nevertheless, in the absence of adequate mesh refinement, large differences may be observed between a 2D and 3D analysis, especially for a shear-dominated layup. This observed difference has not been widely addressed in previous literature and is the main focus of this paper.

Deformation analysis of rotary combustion engine housings

NASA Technical Reports Server (NTRS)

Vilmann, Carl

1991-01-01

This analysis of the deformation of rotary combustion engine housings targeted the following objectives: (1) the development and verification of a finite element model of the trochoid housing, (2) the prediction of the stress and deformation fields present within the trochoid housing during operating conditions, and (3) the development of a specialized preprocessor which would shorten the time necessary for mesh generation of a trochoid housing's FEM model from roughly one month to approximately two man hours. Executable finite element models were developed for both the Mazda and the Outboard Marine Corporation trochoid housings. It was also demonstrated that a preprocessor which would hasten the generation of finite element models of a rotary engine was possible to develop. The above objectives are treated in detail in the attached appendices. The first deals with finite element modeling of a Wankel engine center housing, and the second with the development of a preprocessor that generates finite element models of rotary combustion engine center housings. A computer program, designed to generate finite element models of user defined rotary combustion engine center housing geometries, is also included.

Finite-element simulation of blood perfusion in muscle tissue during compression and sustained contraction.

PubMed

Vankan, W J; Huyghe, J M; Slaaf, D W; van Donkelaar, C C; Drost, M R; Janssen, J D; Huson, A

1997-09-01

Mechanical interaction between tissue stress and blood perfusion in skeletal muscles plays an important role in blood flow impediment during sustained contraction. The exact mechanism of this interaction is not clear, and experimental investigation of this mechanism is difficult. We developed a finite-element model of the mechanical behavior of blood-perfused muscle tissue, which accounts for mechanical blood-tissue interaction in maximally vasodilated vasculature. Verification of the model was performed by comparing finite-element results of blood pressure and flow with experimental measurements in a muscle that is subject to well-controlled mechanical loading conditions. In addition, we performed simulations of blood perfusion during tetanic, isometric contraction and maximal vasodilation in a simplified, two-dimensional finite-element model of a rat calf muscle. A vascular waterfall in the venous compartment was identified as the main cause for blood flow impediment both in the experiment and in the finite-element simulations. The validated finite-element model offers possibilities for detailed analysis of blood perfusion in three-dimensional muscle models under complicated loading conditions.

The method of space-time and conservation element and solution element: A new approach for solving the Navier-Stokes and Euler equations

NASA Technical Reports Server (NTRS)

Chang, Sin-Chung

1995-01-01

A new numerical framework for solving conservation laws is being developed. This new framework differs substantially in both concept and methodology from the well-established methods, i.e., finite difference, finite volume, finite element, and spectral methods. It is conceptually simple and designed to overcome several key limitations of the above traditional methods. A two-level scheme for solving the convection-diffusion equation is constructed and used to illuminate the major differences between the present method and those previously mentioned. This explicit scheme, referred to as the a-mu scheme, has two independent marching variables.

Adaptive macro finite elements for the numerical solution of monodomain equations in cardiac electrophysiology.

PubMed

Heidenreich, Elvio A; Ferrero, José M; Doblaré, Manuel; Rodríguez, José F

2010-07-01

Many problems in biology and engineering are governed by anisotropic reaction-diffusion equations with a very rapidly varying reaction term. This usually implies the use of very fine meshes and small time steps in order to accurately capture the propagating wave while avoiding the appearance of spurious oscillations in the wave front. This work develops a family of macro finite elements amenable for solving anisotropic reaction-diffusion equations with stiff reactive terms. The developed elements are incorporated on a semi-implicit algorithm based on operator splitting that includes adaptive time stepping for handling the stiff reactive term. A linear system is solved on each time step to update the transmembrane potential, whereas the remaining ordinary differential equations are solved uncoupled. The method allows solving the linear system on a coarser mesh thanks to the static condensation of the internal degrees of freedom (DOF) of the macroelements while maintaining the accuracy of the finer mesh. The method and algorithm have been implemented in parallel. The accuracy of the method has been tested on two- and three-dimensional examples demonstrating excellent behavior when compared to standard linear elements. The better performance and scalability of different macro finite elements against standard finite elements have been demonstrated in the simulation of a human heart and a heterogeneous two-dimensional problem with reentrant activity. Results have shown a reduction of up to four times in computational cost for the macro finite elements with respect to equivalent (same number of DOF) standard linear finite elements as well as good scalability properties.

CONSTRUCTION OF SCALAR AND VECTOR FINITE ELEMENT FAMILIES ON POLYGONAL AND POLYHEDRAL MESHES

PubMed Central

GILLETTE, ANDREW; RAND, ALEXANDER; BAJAJ, CHANDRAJIT

2016-01-01

We combine theoretical results from polytope domain meshing, generalized barycentric coordinates, and finite element exterior calculus to construct scalar- and vector-valued basis functions for conforming finite element methods on generic convex polytope meshes in dimensions 2 and 3. Our construction recovers well-known bases for the lowest order Nédélec, Raviart-Thomas, and Brezzi-Douglas-Marini elements on simplicial meshes and generalizes the notion of Whitney forms to non-simplicial convex polygons and polyhedra. We show that our basis functions lie in the correct function space with regards to global continuity and that they reproduce the requisite polynomial differential forms described by finite element exterior calculus. We present a method to count the number of basis functions required to ensure these two key properties. PMID:28077939

CONSTRUCTION OF SCALAR AND VECTOR FINITE ELEMENT FAMILIES ON POLYGONAL AND POLYHEDRAL MESHES.

PubMed

Gillette, Andrew; Rand, Alexander; Bajaj, Chandrajit

2016-10-01

We combine theoretical results from polytope domain meshing, generalized barycentric coordinates, and finite element exterior calculus to construct scalar- and vector-valued basis functions for conforming finite element methods on generic convex polytope meshes in dimensions 2 and 3. Our construction recovers well-known bases for the lowest order Nédélec, Raviart-Thomas, and Brezzi-Douglas-Marini elements on simplicial meshes and generalizes the notion of Whitney forms to non-simplicial convex polygons and polyhedra. We show that our basis functions lie in the correct function space with regards to global continuity and that they reproduce the requisite polynomial differential forms described by finite element exterior calculus. We present a method to count the number of basis functions required to ensure these two key properties.

A quasi two-dimensional model for sound attenuation by the sonic crystals.

PubMed

Gupta, A; Lim, K M; Chew, C H

2012-10-01

Sound propagation in the sonic crystal (SC) along the symmetry direction is modeled by sound propagation through a variable cross-sectional area waveguide. A one-dimensional (1D) model based on the Webster horn equation is used to obtain sound attenuation through the SC. This model is compared with two-dimensional (2D) finite element simulation and experiment. The 1D model prediction of frequency band for sound attenuation is found to be shifted by around 500 Hz with respect to the finite element simulation. The reason for this shift is due to the assumption involved in the 1D model. A quasi 2D model is developed for sound propagation through the waveguide. Sound pressure profiles from the quasi 2D model are compared with the finite element simulation and the 1D model. The result shows significant improvement over the 1D model and is in good agreement with the 2D finite element simulation. Finally, sound attenuation through the SC is computed based on the quasi 2D model and is found to be in good agreement with the finite element simulation. The quasi 2D model provides an improved method to calculate sound attenuation through the SC.

Probabilistic finite elements

NASA Technical Reports Server (NTRS)

Belytschko, Ted; Wing, Kam Liu

1987-01-01

In the Probabilistic Finite Element Method (PFEM), finite element methods have been efficiently combined with second-order perturbation techniques to provide an effective method for informing the designer of the range of response which is likely in a given problem. The designer must provide as input the statistical character of the input variables, such as yield strength, load magnitude, and Young's modulus, by specifying their mean values and their variances. The output then consists of the mean response and the variance in the response. Thus the designer is given a much broader picture of the predicted performance than with simply a single response curve. These methods are applicable to a wide class of problems, provided that the scale of randomness is not too large and the probabilistic density functions possess decaying tails. By incorporating the computational techniques we have developed in the past 3 years for efficiency, the probabilistic finite element methods are capable of handling large systems with many sources of uncertainties. Sample results for an elastic-plastic ten-bar structure and an elastic-plastic plane continuum with a circular hole subject to cyclic loadings with the yield stress on the random field are given.

Elastic and Piezoelectric Properties of Boron Nitride Nanotube Composites. Part II; Finite Element Model

NASA Technical Reports Server (NTRS)

Kim, H. Alicia; Hardie, Robert; Yamakov, Vesselin; Park, Cheol

2015-01-01

This paper is the second part of a two-part series where the first part presents a molecular dynamics model of a single Boron Nitride Nanotube (BNNT) and this paper scales up to multiple BNNTs in a polymer matrix. This paper presents finite element (FE) models to investigate the effective elastic and piezoelectric properties of (BNNT) nanocomposites. The nanocomposites studied in this paper are thin films of polymer matrix with aligned co-planar BNNTs. The FE modelling approach provides a computationally efficient way to gain an understanding of the material properties. We examine several FE models to identify the most suitable models and investigate the effective properties with respect to the BNNT volume fraction and the number of nanotube walls. The FE models are constructed to represent aligned and randomly distributed BNNTs in a matrix of resin using 2D and 3D hollow and 3D filled cylinders. The homogenisation approach is employed to determine the overall elastic and piezoelectric constants for a range of volume fractions. These models are compared with an analytical model based on Mori-Tanaka formulation suitable for finite length cylindrical inclusions. The model applies to primarily single-wall BNNTs but is also extended to multi-wall BNNTs, for which preliminary results will be presented. Results from the Part 1 of this series can help to establish a constitutive relationship for input into the finite element model to enable the modeling of multiple BNNTs in a polymer matrix.

Evaluation of an improved finite-element thermal stress calculation technique

NASA Technical Reports Server (NTRS)

Camarda, C. J.

1982-01-01

A procedure for generating accurate thermal stresses with coarse finite element grids (Ojalvo's method) is described. The procedure is based on the observation that for linear thermoelastic problems, the thermal stresses may be envisioned as being composed of two contributions; the first due to the strains in the structure which depend on the integral of the temperature distribution over the finite element and the second due to the local variation of the temperature in the element. The first contribution can be accurately predicted with a coarse finite-element mesh. The resulting strain distribution can then be combined via the constitutive relations with detailed temperatures from a separate thermal analysis. The result is accurate thermal stresses from coarse finite element structural models even where the temperature distributions have sharp variations. The range of applicability of the method for various classes of thermostructural problems such as in-plane or bending type problems and the effect of the nature of the temperature distribution and edge constraints are addressed. Ojalvo's method is used in conjunction with the SPAR finite element program. Results are obtained for rods, membranes, a box beam and a stiffened panel.

Analysis of the transient behavior of rubbing components

NASA Technical Reports Server (NTRS)

Quezdou, M. B.; Mullen, R. L.

1986-01-01

Finite element equations are developed for studying deformations and temperatures resulting from frictional heating in sliding system. The formulation is done for linear steady state motion in two dimensions. The equations include the effect of the velocity on the moving components. This gives spurious oscillations in their solutions by Galerkin finite element methods. A method called streamline upwind scheme is used to try to deal with this deficiency. The finite element program is then used to investigate the friction of heating in gas path seal.

A Discontinuous Galerkin Finite Element Method for Hamilton-Jacobi Equations

NASA Technical Reports Server (NTRS)

Hu, Changqing; Shu, Chi-Wang

1998-01-01

In this paper, we present a discontinuous Galerkin finite element method for solving the nonlinear Hamilton-Jacobi equations. This method is based on the Runge-Kutta discontinuous Galerkin finite element method for solving conservation laws. The method has the flexibility of treating complicated geometry by using arbitrary triangulation, can achieve high order accuracy with a local, compact stencil, and are suited for efficient parallel implementation. One and two dimensional numerical examples are given to illustrate the capability of the method.

Experimental strain analysis of the high pressure strain gauge pressure transducer and verification by using a finite element method

NASA Astrophysics Data System (ADS)

Orhan, M. H.; Dogan, Ç.; Kocabas, H.; Tepehan, G.

2001-03-01

The finite element method (FEM) was used in this study for the analysis of the strain distribution of a strain gauge pressure transducer for hydrostatic pressure measurements up to 150 MPa. The pressure transducer, which we investigated, on the basis of `thick-walled cylindrical vessel' theory has a free steel active element. Pressure is applied to the inside and both open ends of this active element. The symmetrical shape of the transducer and all the design parameters of the active element were selected in such a way as to ensure that a symmetrical stress and strain distribution was obtained even at the maximum working pressure of the transducer. The FEM analysis was conducted by investigating one half of the element in three dimensions. This paper presents the FEM output strain values for the area where the strain gauges were bonded. The validity of those values was established by comparing them with the results obtained from the strain gauge measurements. The relative difference between the two sets of values determined to be lower than 13% of the full scale. The two kinds of measuring elements were made of two different materials; AISI 4340 steel and Invar steel, which work in the hydraulic gauge pressure ranges of up to 150 and 100 MPa respectively. The transducers were calibrated using piston pressure balance. The metrological specifications of a total of eight specimens were evaluated. Although the scope of the study is only an application of the FEM, this evaluation also suggests that this type of transducer can be used with an estimated uncertainty of up to 0.1% of the full scale. However, this uncertainty can be improved by a small modification in design, to reduce the reproducibility and hysteresis errors of the device, which are the main parameters in the evaluation of the uncertainty. The results presented in this paper will be helpful for practical static pressure measurements as well as for the appropriate design of this kind of pressure transducer using the FEM.

Measurement of Temperature and Soil Properties for Finite Element Model Verification

DOT National Transportation Integrated Search

2012-08-01

In recent years, ADOT&PF personnel have used TEMP/W, a commercially available two-dimensional finite element program, to conduct thermal modeling of various : embankment configurations in an effort to reduce the thawing of ice-rich permafrost through...

A finite-element model for moving contact line problems in immiscible two-phase flow

NASA Astrophysics Data System (ADS)

Kucala, Alec

2017-11-01

Accurate modeling of moving contact line (MCL) problems is imperative in predicting capillary pressure vs. saturation curves, permeability, and preferential flow paths for a variety of applications, including geological carbon storage (GCS) and enhanced oil recovery (EOR). The macroscale movement of the contact line is dependent on the molecular interactions occurring at the three-phase interface, however most MCL problems require resolution at the meso- and macro-scale. A phenomenological model must be developed to account for the microscale interactions, as resolving both the macro- and micro-scale would render most problems computationally intractable. Here, a model for the moving contact line is presented as a weak forcing term in the Navier-Stokes equation and applied directly at the location of the three-phase interface point. The moving interface is tracked with the level set method and discretized using the conformal decomposition finite element method (CDFEM), allowing for the surface tension and the wetting model to be computed at the exact interface location. A variety of verification test cases for simple two- and three-dimensional geometries are presented to validate the current MCL model, which can exhibit grid independence when a proper scaling for the slip length is chosen. Sandia National Laboratories is a multi-mission laboratory managed and operated by National Technology and Engineering Solutions of Sandia, LLC., a wholly owned subsidiary of Honeywell International, Inc., for the U.S. Department of Energy's National Nuclear Security Administration under contract DE-NA-0003525.

Users manual for AUTOMESH-2D: A program of automatic mesh generation for two-dimensional scattering analysis by the finite element method

NASA Technical Reports Server (NTRS)

Hua, Chongyu; Volakis, John L.

1990-01-01

AUTOMESH-2D is a computer program specifically designed as a preprocessor for the scattering analysis of two dimensional bodies by the finite element method. This program was developed due to a need for reproducing the effort required to define and check the geometry data, element topology, and material properties. There are six modules in the program: (1) Parameter Specification; (2) Data Input; (3) Node Generation; (4) Element Generation; (5) Mesh Smoothing; and (5) Data File Generation.

A computer program for anisotropic shallow-shell finite elements using symbolic integration

NASA Technical Reports Server (NTRS)

Andersen, C. M.; Bowen, J. T.

1976-01-01

A FORTRAN computer program for anisotropic shallow-shell finite elements with variable curvature is described. A listing of the program is presented together with printed output for a sample case. Computation times and central memory requirements are given for several different elements. The program is based on a stiffness (displacement) finite-element model in which the fundamental unknowns consist of both the displacement and the rotation components of the reference surface of the shell. Two triangular and four quadrilateral elements are implemented in the program. The triangular elements have 6 or 10 nodes, and the quadrilateral elements have 4 or 8 nodes. Two of the quadrilateral elements have internal degrees of freedom associated with displacement modes which vanish along the edges of the elements (bubble modes). The triangular elements and the remaining two quadrilateral elements do not have bubble modes. The output from the program consists of arrays corresponding to the stiffness, the geometric stiffness, the consistent mass, and the consistent load matrices for individual elements. The integrals required for the generation of these arrays are evaluated by using symbolic (or analytic) integration in conjunction with certain group-theoretic techniques. The analytic expressions for the integrals are exact and were developed using the symbolic and algebraic manipulation language.

Scale-Limited Lagrange Stability and Finite-Time Synchronization for Memristive Recurrent Neural Networks on Time Scales.

PubMed

Xiao, Qiang; Zeng, Zhigang

2017-10-01

The existed results of Lagrange stability and finite-time synchronization for memristive recurrent neural networks (MRNNs) are scale-free on time evolvement, and some restrictions appear naturally. In this paper, two novel scale-limited comparison principles are established by means of inequality techniques and induction principle on time scales. Then the results concerning Lagrange stability and global finite-time synchronization of MRNNs on time scales are obtained. Scaled-limited Lagrange stability criteria are derived, in detail, via nonsmooth analysis and theory of time scales. Moreover, novel criteria for achieving the global finite-time synchronization are acquired. In addition, the derived method can also be used to study global finite-time stabilization. The proposed results extend or improve the existed ones in the literatures. Two numerical examples are chosen to show the effectiveness of the obtained results.

Probabilistic finite elements for fatigue and fracture analysis

NASA Astrophysics Data System (ADS)

Belytschko, Ted; Liu, Wing Kam

Attenuation is focused on the development of Probabilistic Finite Element Method (PFEM), which combines the finite element method with statistics and reliability methods, and its application to linear, nonlinear structural mechanics problems and fracture mechanics problems. The computational tool based on the Stochastic Boundary Element Method is also given for the reliability analysis of a curvilinear fatigue crack growth. The existing PFEM's have been applied to solve for two types of problems: (1) determination of the response uncertainty in terms of the means, variance and correlation coefficients; and (2) determination the probability of failure associated with prescribed limit states.

Probabilistic finite elements for fatigue and fracture analysis

NASA Technical Reports Server (NTRS)

Belytschko, Ted; Liu, Wing Kam

1992-01-01

Attenuation is focused on the development of Probabilistic Finite Element Method (PFEM), which combines the finite element method with statistics and reliability methods, and its application to linear, nonlinear structural mechanics problems and fracture mechanics problems. The computational tool based on the Stochastic Boundary Element Method is also given for the reliability analysis of a curvilinear fatigue crack growth. The existing PFEM's have been applied to solve for two types of problems: (1) determination of the response uncertainty in terms of the means, variance and correlation coefficients; and (2) determination the probability of failure associated with prescribed limit states.

A Multifunctional Interface Method for Coupling Finite Element and Finite Difference Methods: Two-Dimensional Scalar-Field Problems

NASA Technical Reports Server (NTRS)

Ransom, Jonathan B.

2002-01-01

A multifunctional interface method with capabilities for variable-fidelity modeling and multiple method analysis is presented. The methodology provides an effective capability by which domains with diverse idealizations can be modeled independently to exploit the advantages of one approach over another. The multifunctional method is used to couple independently discretized subdomains, and it is used to couple the finite element and the finite difference methods. The method is based on a weighted residual variational method and is presented for two-dimensional scalar-field problems. A verification test problem and a benchmark application are presented, and the computational implications are discussed.

DOUAR: A new three-dimensional creeping flow numerical model for the solution of geological problems

NASA Astrophysics Data System (ADS)

Braun, Jean; Thieulot, Cédric; Fullsack, Philippe; DeKool, Marthijn; Beaumont, Christopher; Huismans, Ritske

2008-12-01

We present a new finite element code for the solution of the Stokes and energy (or heat transport) equations that has been purposely designed to address crustal-scale to mantle-scale flow problems in three dimensions. Although it is based on an Eulerian description of deformation and flow, the code, which we named DOUAR ('Earth' in Breton language), has the ability to track interfaces and, in particular, the free surface, by using a dual representation based on a set of particles placed on the interface and the computation of a level set function on the nodes of the finite element grid, thus ensuring accuracy and efficiency. The code also makes use of a new method to compute the dynamic Delaunay triangulation connecting the particles based on non-Euclidian, curvilinear measure of distance, ensuring that the density of particles remains uniform and/or dynamically adapted to the curvature of the interface. The finite element discretization is based on a non-uniform, yet regular octree division of space within a unit cube that allows efficient adaptation of the finite element discretization, i.e. in regions of strong velocity gradient or high interface curvature. The finite elements are cubes (the leaves of the octree) in which a q1- p0 interpolation scheme is used. Nodal incompatibilities across faces separating elements of differing size are dealt with by introducing linear constraints among nodal degrees of freedom. Discontinuities in material properties across the interfaces are accommodated by the use of a novel method (which we called divFEM) to integrate the finite element equations in which the elemental volume is divided by a local octree to an appropriate depth (resolution). A variety of rheologies have been implemented including linear, non-linear and thermally activated creep and brittle (or plastic) frictional deformation. A simple smoothing operator has been defined to avoid checkerboard oscillations in pressure that tend to develop when using a highly irregular octree discretization and the tri-linear (or q1- p0) finite element. A three-dimensional cloud of particles is used to track material properties that depend on the integrated history of deformation (the integrated strain, for example); its density is variable and dynamically adapted to the computed flow. The large system of algebraic equations that results from the finite element discretization and linearization of the basic partial differential equations is solved using a multi-frontal massively parallel direct solver that can efficiently factorize poorly conditioned systems resulting from the highly non-linear rheology and the presence of the free surface. The code is almost entirely parallelized. We present example results including the onset of a Rayleigh-Taylor instability, the indentation of a rigid-plastic material and the formation of a fold beneath a free eroding surface, that demonstrate the accuracy, efficiency and appropriateness of the new code to solve complex geodynamical problems in three dimensions.

3-d finite element model development for biomechanics: a software demonstration

DOE Office of Scientific and Technical Information (OSTI.GOV)

Hollerbach, K.; Hollister, A.M.; Ashby, E.

1997-03-01

Finite element analysis is becoming an increasingly important part of biomechanics and orthopedic research, as computational resources become more powerful, and data handling algorithms become more sophisticated. Until recently, tools with sufficient power did not exist or were not accessible to adequately model complicated, three-dimensional, nonlinear biomechanical systems. In the past, finite element analyses in biomechanics have often been limited to two-dimensional approaches, linear analyses, or simulations of single tissue types. Today, we have the resources to model fully three-dimensional, nonlinear, multi-tissue, and even multi-joint systems. The authors will present the process of developing these kinds of finite element models,more » using human hand and knee examples, and will demonstrate their software tools.« less

Flow Applications of the Least Squares Finite Element Method

NASA Technical Reports Server (NTRS)

Jiang, Bo-Nan

1998-01-01

The main thrust of the effort has been towards the development, analysis and implementation of the least-squares finite element method (LSFEM) for fluid dynamics and electromagnetics applications. In the past year, there were four major accomplishments: 1) special treatments in computational fluid dynamics and computational electromagnetics, such as upwinding, numerical dissipation, staggered grid, non-equal order elements, operator splitting and preconditioning, edge elements, and vector potential are unnecessary; 2) the analysis of the LSFEM for most partial differential equations can be based on the bounded inverse theorem; 3) the finite difference and finite volume algorithms solve only two Maxwell equations and ignore the divergence equations; and 4) the first numerical simulation of three-dimensional Marangoni-Benard convection was performed using the LSFEM.

Relativistic, model-independent, multichannel 2 → 2 transition amplitudes in a finite volume

DOE PAGES

Briceno, Raul A.; Hansen, Maxwell T.

2016-07-13

We derive formalism for determining 2 + J → 2 infinite-volume transition amplitudes from finite-volume matrix elements. Specifically, we present a relativistic, model-independent relation between finite-volume matrix elements of external currents and the physically observable infinite-volume matrix elements involving two-particle asymptotic states. The result presented holds for states composed of two scalar bosons. These can be identical or non-identical and, in the latter case, can be either degenerate or non-degenerate. We further accommodate any number of strongly-coupled two-scalar channels. This formalism will, for example, allow future lattice QCD calculations of themore » $$\\rho$$-meson form factor, in which the unstable nature of the $$\\rho$$ is rigorously accommodated. In conclusion, we also discuss how this work will impact future extractions of nuclear parity and hadronic long-range matrix elements from lattice QCD.« less

Finite Element Evaluation of Two Retrofit Options to Enhance the Performance of Cable Media Barriers.

DOT National Transportation Integrated Search

2009-06-30

This report summarizes the finite element modeling and simulation efforts on evaluating the performance of cable median barriers including the current and several proposed retrofit designs. It also synthesizes a literature review of the performance e...

Least-squares finite element methods for compressible Euler equations

NASA Technical Reports Server (NTRS)

Jiang, Bo-Nan; Carey, G. F.

1990-01-01

A method based on backward finite differencing in time and a least-squares finite element scheme for first-order systems of partial differential equations in space is applied to the Euler equations for gas dynamics. The scheme minimizes the L-sq-norm of the residual within each time step. The method naturally generates numerical dissipation proportional to the time step size. An implicit method employing linear elements has been implemented and proves robust. For high-order elements, computed solutions based on the L-sq method may have oscillations for calculations at similar time step sizes. To overcome this difficulty, a scheme which minimizes the weighted H1-norm of the residual is proposed and leads to a successful scheme with high-degree elements. Finally, a conservative least-squares finite element method is also developed. Numerical results for two-dimensional problems are given to demonstrate the shock resolution of the methods and compare different approaches.

Analysis of random structure-acoustic interaction problems using coupled boundary element and finite element methods

NASA Technical Reports Server (NTRS)

Mei, Chuh; Pates, Carl S., III

1994-01-01

A coupled boundary element (BEM)-finite element (FEM) approach is presented to accurately model structure-acoustic interaction systems. The boundary element method is first applied to interior, two and three-dimensional acoustic domains with complex geometry configurations. Boundary element results are very accurate when compared with limited exact solutions. Structure-interaction problems are then analyzed with the coupled FEM-BEM method, where the finite element method models the structure and the boundary element method models the interior acoustic domain. The coupled analysis is compared with exact and experimental results for a simplistic model. Composite panels are analyzed and compared with isotropic results. The coupled method is then extended for random excitation. Random excitation results are compared with uncoupled results for isotropic and composite panels.

Effects of Subscale Size and Shape on Global Energy Dissipation in a Multiscale Model of a Fiber-Reinforced Composite Exhibiting Post-Peak Strain Softening Using Abaqus and FEAMAC

NASA Technical Reports Server (NTRS)

Pineda, Evan, J.; Bednarcyk, Brett, A.; Arnold, Steven, M.

2012-01-01

A mesh objective crack band model is implemented in the generalized method of cells (GMC) micromechanics model to predict failure of a composite repeating unit cell (RUC). The micromechanics calculations are achieved using the MAC/GMC core engine within the ImMAC suite of micromechanics codes, developed at the NASA Glenn Research Center. The microscale RUC is linked to a macroscale Abaqus/Standard finite element model using the FEAMAC multiscale framework (included in the ImMAC suite). The effects of the relationship between the characteristic length of the finite element and the size of the microscale RUC on the total energy dissipation of the multiscale model are investigated. A simple 2-D composite square subjected to uniaxial tension is used to demonstrate the effects of scaling the dimensions of the RUC such that the length of the sides of the RUC are equal to the characteristic length of the finite element. These results are compared to simulations where the size of the RUC is fixed, independent of the element size. Simulations are carried out for a variety of mesh densities and element shapes, including square and triangular. Results indicate that a consistent size and shape must be used to yield preserve energy dissipation across the scales.

Analysis of Ninety Degree Flexure Tests for Characterization of Composite Transverse Tensile Strength

NASA Technical Reports Server (NTRS)

OBrien, T. Kevin; Krueger, Ronald

2001-01-01

Finite element (FE) analysis was performed on 3-point and 4-point bending test configurations of ninety degree oriented glass-epoxy and graphite-epoxy composite beams to identify deviations from beam theory predictions. Both linear and geometric non-linear analyses were performed using the ABAQUS finite element code. The 3-point and 4-point bending specimens were first modeled with two-dimensional elements. Three-dimensional finite element models were then performed for selected 4-point bending configurations to study the stress distribution across the width of the specimens and compare the results to the stresses computed from two-dimensional plane strain and plane stress analyses and the stresses from beam theory. Stresses for all configurations were analyzed at load levels corresponding to the measured transverse tensile strength of the material.

A Dual Super-Element Domain Decomposition Approach for Parallel Nonlinear Finite Element Analysis

NASA Astrophysics Data System (ADS)

Jokhio, G. A.; Izzuddin, B. A.

2015-05-01

This article presents a new domain decomposition method for nonlinear finite element analysis introducing the concept of dual partition super-elements. The method extends ideas from the displacement frame method and is ideally suited for parallel nonlinear static/dynamic analysis of structural systems. In the new method, domain decomposition is realized by replacing one or more subdomains in a "parent system," each with a placeholder super-element, where the subdomains are processed separately as "child partitions," each wrapped by a dual super-element along the partition boundary. The analysis of the overall system, including the satisfaction of equilibrium and compatibility at all partition boundaries, is realized through direct communication between all pairs of placeholder and dual super-elements. The proposed method has particular advantages for matrix solution methods based on the frontal scheme, and can be readily implemented for existing finite element analysis programs to achieve parallelization on distributed memory systems with minimal intervention, thus overcoming memory bottlenecks typically faced in the analysis of large-scale problems. Several examples are presented in this article which demonstrate the computational benefits of the proposed parallel domain decomposition approach and its applicability to the nonlinear structural analysis of realistic structural systems.

A modular finite-element model (MODFE) for areal and axisymmetric ground-water-flow problems, Part 1: Model Description and User's Manual

USGS Publications Warehouse

Torak, L.J.

1993-01-01

A MODular, Finite-Element digital-computer program (MODFE) was developed to simulate steady or unsteady-state, two-dimensional or axisymmetric ground-water flow. Geometric- and hydrologic-aquifer characteristics in two spatial dimensions are represented by triangular finite elements and linear basis functions; one-dimensional finite elements and linear basis functions represent time. Finite-element matrix equations are solved by the direct symmetric-Doolittle method or the iterative modified, incomplete-Cholesky, conjugate-gradient method. Physical processes that can be represented by the model include (1) confined flow, unconfined flow (using the Dupuit approximation), or a combination of both; (2) leakage through either rigid or elastic confining beds; (3) specified recharge or discharge at points, along lines, and over areas; (4) flow across specified-flow, specified-head, or bead-dependent boundaries; (5) decrease of aquifer thickness to zero under extreme water-table decline and increase of aquifer thickness from zero as the water table rises; and (6) head-dependent fluxes from springs, drainage wells, leakage across riverbeds or confining beds combined with aquifer dewatering, and evapotranspiration. The report describes procedures for applying MODFE to ground-water-flow problems, simulation capabilities, and data preparation. Guidelines for designing the finite-element mesh and for node numbering and determining band widths are given. Tables are given that reference simulation capabilities to specific versions of MODFE. Examples of data input and model output for different versions of MODFE are provided.

Nonlinear dynamics of planetary gears using analytical and finite element models

NASA Astrophysics Data System (ADS)

Ambarisha, Vijaya Kumar; Parker, Robert G.

2007-05-01

Vibration-induced gear noise and dynamic loads remain key concerns in many transmission applications that use planetary gears. Tooth separations at large vibrations introduce nonlinearity in geared systems. The present work examines the complex, nonlinear dynamic behavior of spur planetary gears using two models: (i) a lumped-parameter model, and (ii) a finite element model. The two-dimensional (2D) lumped-parameter model represents the gears as lumped inertias, the gear meshes as nonlinear springs with tooth contact loss and periodically varying stiffness due to changing tooth contact conditions, and the supports as linear springs. The 2D finite element model is developed from a unique finite element-contact analysis solver specialized for gear dynamics. Mesh stiffness variation excitation, corner contact, and gear tooth contact loss are all intrinsically considered in the finite element analysis. The dynamics of planetary gears show a rich spectrum of nonlinear phenomena. Nonlinear jumps, chaotic motions, and period-doubling bifurcations occur when the mesh frequency or any of its higher harmonics are near a natural frequency of the system. Responses from the dynamic analysis using analytical and finite element models are successfully compared qualitatively and quantitatively. These comparisons validate the effectiveness of the lumped-parameter model to simulate the dynamics of planetary gears. Mesh phasing rules to suppress rotational and translational vibrations in planetary gears are valid even when nonlinearity from tooth contact loss occurs. These mesh phasing rules, however, are not valid in the chaotic and period-doubling regions.

A modular finite-element model (MODFE) for areal and axisymmetric ground-water-flow problems; Part 1, Model description and user's manual

USGS Publications Warehouse

Torak, Lynn J.

1992-01-01

A MODular, Finite-Element digital-computer program (MODFE) was developed to simulate steady or unsteady-state, two-dimensional or axisymmetric ground-water flow. Geometric- and hydrologic-aquifer characteristics in two spatial dimensions are represented by triangular finite elements and linear basis functions; one-dimensional finite elements and linear basis functions represent time. Finite-element matrix equations are solved by the direct symmetric-Doolittle method or the iterative modified, incomplete-Cholesky, conjugate-gradient method. Physical processes that can be represented by the model include (1) confined flow, unconfined flow (using the Dupuit approximation), or a combination of both; (2) leakage through either rigid or elastic confining beds; (3) specified recharge or discharge at points, along lines, and over areas; (4) flow across specified-flow, specified-head, or head-dependent boundaries; (5) decrease of aquifer thickness to zero under extreme water-table decline and increase of aquifer thickness from zero as the water table rises; and (6) head-dependent fluxes from springs, drainage wells, leakage across riverbeds or confining beds combined with aquifer dewatering, and evapotranspiration.The report describes procedures for applying MODFE to ground-water-flow problems, simulation capabilities, and data preparation. Guidelines for designing the finite-element mesh and for node numbering and determining band widths are given. Tables are given that reference simulation capabilities to specific versions of MODFE. Examples of data input and model output for different versions of MODFE are provided.

Finite element analysis and genetic algorithm optimization design for the actuator placement on a large adaptive structure

NASA Astrophysics Data System (ADS)

Sheng, Lizeng

The dissertation focuses on one of the major research needs in the area of adaptive/intelligent/smart structures, the development and application of finite element analysis and genetic algorithms for optimal design of large-scale adaptive structures. We first review some basic concepts in finite element method and genetic algorithms, along with the research on smart structures. Then we propose a solution methodology for solving a critical problem in the design of a next generation of large-scale adaptive structures---optimal placements of a large number of actuators to control thermal deformations. After briefly reviewing the three most frequently used general approaches to derive a finite element formulation, the dissertation presents techniques associated with general shell finite element analysis using flat triangular laminated composite elements. The element used here has three nodes and eighteen degrees of freedom and is obtained by combining a triangular membrane element and a triangular plate bending element. The element includes the coupling effect between membrane deformation and bending deformation. The membrane element is derived from the linear strain triangular element using Cook's transformation. The discrete Kirchhoff triangular (DKT) element is used as the plate bending element. For completeness, a complete derivation of the DKT is presented. Geometrically nonlinear finite element formulation is derived for the analysis of adaptive structures under the combined thermal and electrical loads. Next, we solve the optimization problems of placing a large number of piezoelectric actuators to control thermal distortions in a large mirror in the presence of four different thermal loads. We then extend this to a multi-objective optimization problem of determining only one set of piezoelectric actuator locations that can be used to control the deformation in the same mirror under the action of any one of the four thermal loads. A series of genetic algorithms, GA Version 1, 2 and 3, were developed to find the optimal locations of piezoelectric actuators from the order of 1021 ˜ 1056 candidate placements. Introducing a variable population approach, we improve the flexibility of selection operation in genetic algorithms. Incorporating mutation and hill climbing into micro-genetic algorithms, we are able to develop a more efficient genetic algorithm. Through extensive numerical experiments, we find that the design search space for the optimal placements of a large number of actuators is highly multi-modal and that the most distinct nature of genetic algorithms is their robustness. They give results that are random but with only a slight variability. The genetic algorithms can be used to get adequate solution using a limited number of evaluations. To get the highest quality solution, multiple runs including different random seed generators are necessary. The investigation time can be significantly reduced using a very coarse grain parallel computing. Overall, the methodology of using finite element analysis and genetic algorithm optimization provides a robust solution approach for the challenging problem of optimal placements of a large number of actuators in the design of next generation of adaptive structures.

Three-dimensional Finite Element Formulation and Scalable Domain Decomposition for High Fidelity Rotor Dynamic Analysis

NASA Technical Reports Server (NTRS)

Datta, Anubhav; Johnson, Wayne R.

2009-01-01

This paper has two objectives. The first objective is to formulate a 3-dimensional Finite Element Model for the dynamic analysis of helicopter rotor blades. The second objective is to implement and analyze a dual-primal iterative substructuring based Krylov solver, that is parallel and scalable, for the solution of the 3-D FEM analysis. The numerical and parallel scalability of the solver is studied using two prototype problems - one for ideal hover (symmetric) and one for a transient forward flight (non-symmetric) - both carried out on up to 48 processors. In both hover and forward flight conditions, a perfect linear speed-up is observed, for a given problem size, up to the point of substructure optimality. Substructure optimality and the linear parallel speed-up range are both shown to depend on the problem size as well as on the selection of the coarse problem. With a larger problem size, linear speed-up is restored up to the new substructure optimality. The solver also scales with problem size - even though this conclusion is premature given the small prototype grids considered in this study.

Finite element method for optimal guidance of an advanced launch vehicle

NASA Technical Reports Server (NTRS)

Hodges, Dewey H.; Bless, Robert R.; Calise, Anthony J.; Leung, Martin

1992-01-01

A temporal finite element based on a mixed form of Hamilton's weak principle is summarized for optimal control problems. The resulting weak Hamiltonian finite element method is extended to allow for discontinuities in the states and/or discontinuities in the system equations. An extension of the formulation to allow for control inequality constraints is also presented. The formulation does not require element quadrature, and it produces a sparse system of nonlinear algebraic equations. To evaluate its feasibility for real-time guidance applications, this approach is applied to the trajectory optimization of a four-state, two-stage model with inequality constraints for an advanced launch vehicle. Numerical results for this model are presented and compared to results from a multiple-shooting code. The results show the accuracy and computational efficiency of the finite element method.

On finite element implementation and computational techniques for constitutive modeling of high temperature composites

NASA Technical Reports Server (NTRS)

Saleeb, A. F.; Chang, T. Y. P.; Wilt, T.; Iskovitz, I.

1989-01-01

The research work performed during the past year on finite element implementation and computational techniques pertaining to high temperature composites is outlined. In the present research, two main issues are addressed: efficient geometric modeling of composite structures and expedient numerical integration techniques dealing with constitutive rate equations. In the first issue, mixed finite elements for modeling laminated plates and shells were examined in terms of numerical accuracy, locking property and computational efficiency. Element applications include (currently available) linearly elastic analysis and future extension to material nonlinearity for damage predictions and large deformations. On the material level, various integration methods to integrate nonlinear constitutive rate equations for finite element implementation were studied. These include explicit, implicit and automatic subincrementing schemes. In all cases, examples are included to illustrate the numerical characteristics of various methods that were considered.

Solution of a tridiagonal system of equations on the finite element machine

NASA Technical Reports Server (NTRS)

Bostic, S. W.

1984-01-01

Two parallel algorithms for the solution of tridiagonal systems of equations were implemented on the Finite Element Machine. The Accelerated Parallel Gauss method, an iterative method, and the Buneman algorithm, a direct method, are discussed and execution statistics are presented.

CURVILINEAR FINITE ELEMENT MODEL FOR SIMULATING TWO-WELL TRACER TESTS AND TRANSPORT IN STRATIFIED AQUIFERS

EPA Science Inventory

The problem of solute transport in steady nonuniform flow created by a recharging and discharging well pair is investigated. Numerical difficulties encountered with the standard Galerkin formulations in Cartesian coordinates are illustrated. An improved finite element solution st...

A robust, finite element model for hydrostatic surface water flows

USGS Publications Warehouse

Walters, R.A.; Casulli, V.

1998-01-01

A finite element scheme is introduced for the 2-dimensional shallow water equations using semi-implicit methods in time. A semi-Lagrangian method is used to approximate the effects of advection. A wave equation is formed at the discrete level such that the equations decouple into an equation for surface elevation and a momentum equation for the horizontal velocity. The convergence rates and relative computational efficiency are examined with the use of three test cases representing various degrees of difficulty. A test with a polar-quadrant grid investigates the response to local grid-scale forcing and the presence of spurious modes, a channel test case establishes convergence rates, and a field-scale test case examines problems with highly irregular grids.A finite element scheme is introduced for the 2-dimensional shallow water equations using semi-implicit methods in time. A semi-Lagrangian method is used to approximate the effects of advection. A wave equation is formed at the discrete level such that the equations decouple into an equation for surface elevation and a momentum equation for the horizontal velocity. The convergence rates and relative computational efficiency are examined with the use of three test cases representing various degrees of difficulty. A test with a polar-quadrant grid investigates the response to local grid-scale forcing and the presence of spurious modes, a channel test case establishes convergence rates, and a field-scale test case examines problems with highly irregular grids.

Time-independent hybrid enrichment for finite element solution of transient conduction–radiation in diffusive grey media

DOE Office of Scientific and Technical Information (OSTI.GOV)

Mohamed, M. Shadi, E-mail: m.s.mohamed@durham.ac.uk; Seaid, Mohammed; Trevelyan, Jon

2013-10-15

We investigate the effectiveness of the partition-of-unity finite element method for transient conduction–radiation problems in diffusive grey media. The governing equations consist of a semi-linear transient heat equation for the temperature field and a stationary diffusion approximation to the radiation in grey media. The coupled equations are integrated in time using a semi-implicit method in the finite element framework. We show that for the considered problems, a combination of hyperbolic and exponential enrichment functions based on an approximation of the boundary layer leads to improved accuracy compared to the conventional finite element method. It is illustrated that this approach canmore » be more efficient than using h adaptivity to increase the accuracy of the finite element method near the boundary walls. The performance of the proposed partition-of-unity method is analyzed on several test examples for transient conduction–radiation problems in two space dimensions.« less

Multiphysics elastodynamic finite element analysis of space debris deorbit stability and efficiency by electrodynamic tethers

NASA Astrophysics Data System (ADS)

Li, Gangqiang; Zhu, Zheng H.; Ruel, Stephane; Meguid, S. A.

2017-08-01

This paper developed a new multiphysics finite element method for the elastodynamic analysis of space debris deorbit by a bare flexible electrodynamic tether. Orbital motion limited theory and dynamics of flexible electrodynamic tethers are discretized by the finite element method, where the motional electric field is variant along the tether and coupled with tether deflection and motion. Accordingly, the electrical current and potential bias profiles of tether are solved together with the tether dynamics by the nodal position finite element method. The newly proposed multiphysics finite element method is applied to analyze the deorbit dynamics of space debris by electrodynamic tethers with a two-stage energy control strategy to ensure an efficient and stable deorbit process. Numerical simulations are conducted to study the coupled effect between the motional electric field and the tether dynamics. The results reveal that the coupling effect has a significant influence on the tether stability and the deorbit performance. It cannot be ignored when the libration and deflection of the tether are significant.

Linear and Nonlinear Finite Elements.

DTIC Science & Technology

1983-12-01

Metzler. Con/ ugte rapdent solution of a finite element elastic problem with high Poson rato without scaling and once with the global stiffness matrix K...nonzero c, that makes u(0) = 1. According to the linear, small deflection theory of the membrane the central displacement given to the membrane is not... theory is possible based on the approximations (l-y 2 )t = +y’ 2 +y𔃾 , (1-y𔃼)’ 1-y’ 2 - y" (6) that change eq. (5) to V𔃺) = , [yŖ(1 + y") - Qy𔃼

Finite element modeling of frictionally restrained composite interfaces

NASA Technical Reports Server (NTRS)

Ballarini, Roberto; Ahmed, Shamim

1989-01-01

The use of special interface finite elements to model frictional restraint in composite interfaces is described. These elements simulate Coulomb friction at the interface, and are incorporated into a standard finite element analysis of a two-dimensional isolated fiber pullout test. Various interfacial characteristics, such as the distribution of stresses at the interface, the extent of slip and delamination, load diffusion from fiber to matrix, and the amount of fiber extraction or depression are studied for different friction coefficients. The results are compared to those obtained analytically using a singular integral equation approach, and those obtained by assuming a constant interface shear strength. The usefulness of these elements in micromechanical modeling of fiber-reinforced composite materials is highlighted.

Pretest predictions for the response of a 1:8-scale steel LWR containment building model to static overpressurization

DOE Office of Scientific and Technical Information (OSTI.GOV)

Clauss, D.B.

The analyses used to predict the behavior of a 1:8-scale model of a steel LWR containment building to static overpressurization are described and results are presented. Finite strain, large displacement, and nonlinear material properties were accounted for using finite element methods. Three-dimensional models were needed to analyze the penetrations, which included operable equipment hatches, personnel lock representations, and a constrained pipe. It was concluded that the scale model would fail due to leakage caused by large deformations of the equipment hatch sleeves. 13 refs., 34 figs., 1 tab.

Numerical Simulation of Two-Fluid Mingling Using the Particle Finite Element Method with Applications to Magmatic and Volcanic Processes

NASA Astrophysics Data System (ADS)

de Mier, M.; Costa, F.; Idelsohn, S.

2008-12-01

Many magmatic and volcanic processes (e.g., magma differentiation, mingling, transport in the volcanic conduit) are controlled by the physical properties and flow styles of high-temperature silicate melts. Such processes can be experimentally investigated using analog systems and scaling methods, but it is difficult to find the suitable material and it is generally not possible to quantitatively extrapolate the results to the natural system. An alternative means of studying fluid dynamics in volcanic systems is with numerical models. We have chosen the Particle Finite Element Method (PFEM), which is based on a Delaunay mesh that moves with the fluid velocity, the Navier-Stokes equations in Lagrangian formulation, and linear elements for velocity, pressure, and temperature. Remeshing is performed when the grid becomes too distorted [E. Oñate et al., 2004. The Particle Finite Element Method: An Overview. Int. J. Comput. Meth. 1, 267-307]. The method is ideal for tracking material interfaces between different fluids or media. Methods based on Eulerian reference frames need special techniques, such as level-set or volume-of-fluid, to capture the interface position, and these techniques add a significant numerical diffusion at the interface. We have performed a series of two-dimensional simulations of a classical problem of fluid dynamics in magmatic and volcanic systems: intrusion of a basaltic melt in a silica-rich magma reservoir. We have used realistic physical properties and equations of state for the silicate melts (e.g., temperature, viscosity, and density) and tracked the changes in the system for geologically relevant time scales (up to 100 years). The problem is modeled by the low-Mach-number equations derived from an asymptotic analysis of the compressible Navier-Stokes equations that removes shock waves from the flow but allows however large variations of density due to temperature variations. Non-constant viscosity and volume changes are taken into account in the momentum conservation equation through the full shear-stress tensor. The implications of different magma intrusion rates, volumes, and times will be discussed in the context of mafic-silicic magma mixing and eruption triggers.

Study of propellant dynamics in a shuttle type launch vehicle

NASA Technical Reports Server (NTRS)

Jones, C. E.; Feng, G. C.

1972-01-01

A method and an associated digital computer program for evaluating the vibrational characteristics of large liquid-filled rigid wall tanks of general shape are presented. A solution procedure was developed in which slosh modes and frequencies are computed for systems mathematically modeled as assemblages of liquid finite elements. To retain sparsity in the assembled system mass and stiffness matrices, a compressible liquid element formulation was incorporated in the program. The approach taken in the liquid finite element formulation is compatible with triangular and quadrilateral structural finite elements so that the analysis of liquid motion can be coupled with flexible tank wall motion at some future time. The liquid element repertoire developed during the course of this study consists of a two-dimensional triangular element and a three-dimensional tetrahedral element.

A comparison of two finite element models of tidal hydrodynamics using a North Sea data set

USGS Publications Warehouse

Walters, R.A.; Werner, F.E.

1989-01-01

Using the region of the English Channel and the southern bight of the North Sea, we systematically compare the results of two independent finite element models of tidal hydrodynamics. The model intercomparison provides a means for increasing our understanding of the relevant physical processes in the region in question as well as a means for the evaluation of certain algorithmic procedures of the two models. ?? 1989.

Reliability analysis of laminated CMC components through shell subelement techniques

NASA Technical Reports Server (NTRS)

Starlinger, A.; Duffy, S. F.; Gyekenyesi, J. P.

1992-01-01

An updated version of the integrated design program C/CARES (composite ceramic analysis and reliability evaluation of structures) was developed for the reliability evaluation of CMC laminated shell components. The algorithm is now split in two modules: a finite-element data interface program and a reliability evaluation algorithm. More flexibility is achieved, allowing for easy implementation with various finite-element programs. The new interface program from the finite-element code MARC also includes the option of using hybrid laminates and allows for variations in temperature fields throughout the component.

Adaptive finite element method for turbulent flow near a propeller

NASA Astrophysics Data System (ADS)

Pelletier, Dominique; Ilinca, Florin; Hetu, Jean-Francois

1994-11-01

This paper presents an adaptive finite element method based on remeshing to solve incompressible turbulent free shear flow near a propeller. Solutions are obtained in primitive variables using a highly accurate finite element approximation on unstructured grids. Turbulence is modeled by a mixing length formulation. Two general purpose error estimators, which take into account swirl and the variation of the eddy viscosity, are presented and applied to the turbulent wake of a propeller. Predictions compare well with experimental measurements. The proposed adaptive scheme is robust, reliable and cost effective.

Finite element validation of stress intensity factor calculation models for thru-thickness and thumb-nail cracks in double edge notch specimens

DOE Office of Scientific and Technical Information (OSTI.GOV)

Beres, W.; Koul, A.K.

1994-09-01

Stress intensity factors for thru-thickness and thumb-nail cracks in the double edge notch specimens, containing two different notch radius (R) to specimen width (W) ratios (R/W = 1/8 and 1/16), are calculated through finite element analysis. The finite element results are compared with predictions based on existing empirical models for SIF calculations. The effects of a change in R/W ratio on SIF of thru-thickness and thumb-nail cracks are also discussed. 34 refs.

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

NASA Technical Reports Server (NTRS)

Kim, Sang-Wook

1988-01-01

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

Scaling in two-fluid pinch-off

NASA Astrophysics Data System (ADS)

Pommer, Chris; Suryo, Ronald; Subramani, Hariprasad; Harris, Michael; Basaran, Osman

2009-11-01

Two-fluid pinch-off is encountered when drops or bubbles of one fluid are ejected from a nozzle into another fluid or when a compound jet breaks. While the breakup of a drop in a passive environment and that of a passive bubble in a liquid are well understood, the physics of pinch-off when both the inner and outer fluids are dynamically active is inadequately understood. In this talk, the breakup of a compound jet whose core and shell are both incompressible Newtonian fluids is analyzed computationally by a method of lines ALE algorithm which uses finite elements with elliptic mesh generation for spatial discretization and adaptive finite differences for time integration. Pinch-off dynamics are investigated well beyond the limit of experiments set by the wavelength of visible light and that of various algorithms used in the literature. Simulations show that the minimum neck radius r initially scales with time τ before breakup as &αcirc; where α varies over a certain range. However, depending on the values of the governing dimensionless groups, this initial scaling regime may be transitory and, closer to pinch-off, the dynamics may transition to a final asymptotic regime for which r ˜&βcirc;, where β!=α.

Large-scale computation of incompressible viscous flow by least-squares finite element method

NASA Technical Reports Server (NTRS)

Jiang, Bo-Nan; Lin, T. L.; Povinelli, Louis A.

1993-01-01

The least-squares finite element method (LSFEM) based on the velocity-pressure-vorticity formulation is applied to large-scale/three-dimensional steady incompressible Navier-Stokes problems. This method can accommodate equal-order interpolations and results in symmetric, positive definite algebraic system which can be solved effectively by simple iterative methods. The first-order velocity-Bernoulli function-vorticity formulation for incompressible viscous flows is also tested. For three-dimensional cases, an additional compatibility equation, i.e., the divergence of the vorticity vector should be zero, is included to make the first-order system elliptic. The simple substitution of the Newton's method is employed to linearize the partial differential equations, the LSFEM is used to obtain discretized equations, and the system of algebraic equations is solved using the Jacobi preconditioned conjugate gradient method which avoids formation of either element or global matrices (matrix-free) to achieve high efficiency. To show the validity of this scheme for large-scale computation, we give numerical results for 2D driven cavity problem at Re = 10000 with 408 x 400 bilinear elements. The flow in a 3D cavity is calculated at Re = 100, 400, and 1,000 with 50 x 50 x 50 trilinear elements. The Taylor-Goertler-like vortices are observed for Re = 1,000.

Multi-scale finite element modeling of strain localization in geomaterials with strong discontinuity

NASA Astrophysics Data System (ADS)

Lai, Timothy Yu

2002-01-01

Geomaterials such as soils and rocks undergo strain localization during various loading conditions. Strain localization manifests itself in the form of a shear band, a narrow zone of intense straining. It is now generally recognized that these localized deformations lead to an accelerated softening response and influence the response of structures at or near failure. In order to accurately predict the behavior of geotechnical structures, the effects of strain localization must be included in any model developed. In this thesis, a multi-scale Finite Element (FE) model has been developed that captures the macro- and micro-field deformation patterns present during strain localization. The FE model uses a strong discontinuity approach where a jump in the displacement field is assumed. The onset of strain localization is detected using bifurcation theory that checks when the governing equations lose ellipticity. Two types of bifurcation, continuous and discontinuous are considered. Precise conditions for plane strain loading conditions are reported for each type of bifurcation. Post-localization behavior is governed by the traction relations on the band. Different plasticity models such as Mohr-Coulomb, Drucker-Prager and a Modified Mohr-Coulomb yield were implemented together with cohesion softening and cutoff for the post-localization behavior. The FE model is implemented into a FORTRAN code SPIN2D-LOC using enhanced constant strain triangular (CST) elements. The model is formulated using standard Galerkin finite element method, applicable to problems under undrained conditions and small deformation theory. A band-tracing algorithm is implemented to track the propagation of the shear band. To validate the model, several simulations are performed from simple compression test of soft rock to simulation of a full-scale geosynthetic reinforced soil wall model undergoing strain localization. Results from both standard and enhanced FE method are included for comparison. The resulting load-displacement curves show that the model can represent the softening behavior of geomaterials once strain localization is detected. The orientation of the shear band is found to depend on both the friction and dilation angle of the geomaterial. For most practical problems, slight mesh dependency can be expected but is associated with the standard FE interpolation rather than the strong discontinuity enhancements.

Modal Substructuring of Geometrically Nonlinear Finite-Element Models

DOE PAGES

Kuether, Robert J.; Allen, Matthew S.; Hollkamp, Joseph J.

2015-12-21

The efficiency of a modal substructuring method depends on the component modes used to reduce each subcomponent model. Methods such as Craig–Bampton have been used extensively to reduce linear finite-element models with thousands or even millions of degrees of freedom down orders of magnitude while maintaining acceptable accuracy. A novel reduction method is proposed here for geometrically nonlinear finite-element models using the fixed-interface and constraint modes of the linearized system to reduce each subcomponent model. The geometric nonlinearity requires an additional cubic and quadratic polynomial function in the modal equations, and the nonlinear stiffness coefficients are determined by applying amore » series of static loads and using the finite-element code to compute the response. The geometrically nonlinear, reduced modal equations for each subcomponent are then coupled by satisfying compatibility and force equilibrium. This modal substructuring approach is an extension of the Craig–Bampton method and is readily applied to geometrically nonlinear models built directly within commercial finite-element packages. The efficiency of this new approach is demonstrated on two example problems: one that couples two geometrically nonlinear beams at a shared rotational degree of freedom, and another that couples an axial spring element to the axial degree of freedom of a geometrically nonlinear beam. The nonlinear normal modes of the assembled models are compared with those of a truth model to assess the accuracy of the novel modal substructuring approach.« less

Modal Substructuring of Geometrically Nonlinear Finite-Element Models

DOE Office of Scientific and Technical Information (OSTI.GOV)

Kuether, Robert J.; Allen, Matthew S.; Hollkamp, Joseph J.

The efficiency of a modal substructuring method depends on the component modes used to reduce each subcomponent model. Methods such as Craig–Bampton have been used extensively to reduce linear finite-element models with thousands or even millions of degrees of freedom down orders of magnitude while maintaining acceptable accuracy. A novel reduction method is proposed here for geometrically nonlinear finite-element models using the fixed-interface and constraint modes of the linearized system to reduce each subcomponent model. The geometric nonlinearity requires an additional cubic and quadratic polynomial function in the modal equations, and the nonlinear stiffness coefficients are determined by applying amore » series of static loads and using the finite-element code to compute the response. The geometrically nonlinear, reduced modal equations for each subcomponent are then coupled by satisfying compatibility and force equilibrium. This modal substructuring approach is an extension of the Craig–Bampton method and is readily applied to geometrically nonlinear models built directly within commercial finite-element packages. The efficiency of this new approach is demonstrated on two example problems: one that couples two geometrically nonlinear beams at a shared rotational degree of freedom, and another that couples an axial spring element to the axial degree of freedom of a geometrically nonlinear beam. The nonlinear normal modes of the assembled models are compared with those of a truth model to assess the accuracy of the novel modal substructuring approach.« less

Application of finite element substructuring to composite micromechanics. M.S. Thesis - Akron Univ., May 1984

NASA Technical Reports Server (NTRS)

Caruso, J. J.

1984-01-01

Finite element substructuring is used to predict unidirectional fiber composite hygral (moisture), thermal, and mechanical properties. COSMIC NASTRAN and MSC/NASTRAN are used to perform the finite element analysis. The results obtained from the finite element model are compared with those obtained from the simplified composite micromechanics equations. A unidirectional composite structure made of boron/HM-epoxy, S-glass/IMHS-epoxy and AS/IMHS-epoxy are studied. The finite element analysis is performed using three dimensional isoparametric brick elements and two distinct models. The first model consists of a single cell (one fiber surrounded by matrix) to form a square. The second model uses the single cell and substructuring to form a nine cell square array. To compare computer time and results with the nine cell superelement model, another nine cell model is constructed using conventional mesh generation techniques. An independent computer program consisting of the simplified micromechanics equation is developed to predict the hygral, thermal, and mechanical properties for this comparison. The results indicate that advanced techniques can be used advantageously for fiber composite micromechanics.

Applications of Taylor-Galerkin finite element method to compressible internal flow problems

NASA Technical Reports Server (NTRS)

Sohn, Jeong L.; Kim, Yongmo; Chung, T. J.

1989-01-01

A two-step Taylor-Galerkin finite element method with Lapidus' artificial viscosity scheme is applied to several test cases for internal compressible inviscid flow problems. Investigations for the effect of supersonic/subsonic inlet and outlet boundary conditions on computational results are particularly emphasized.

Advanced Electronic Structure Calculations For Nanoelectronics Using Finite Element Bases and Effective Mass Theory.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Gamble, John King; Nielsen, Erik; Baczewski, Andrew David

This paper describes our work over the past few years to use tools from quantum chemistry to describe electronic structure of nanoelectronic devices. These devices, dubbed "artificial atoms", comprise a few electrons, con ned by semiconductor heterostructures, impurities, and patterned electrodes, and are of intense interest due to potential applications in quantum information processing, quantum sensing, and extreme-scale classical logic. We detail two approaches we have employed: nite-element and Gaussian basis sets, exploring the interesting complications that arise when techniques that were intended to apply to atomic systems are instead used for artificial, solid-state devices.

Design feasibility study of a divertor component reinforced with fibrous metal matrix composite laminate

NASA Astrophysics Data System (ADS)

You, Jeong-Ha

2005-01-01

Fibrous metal matrix composites possess advanced mechanical properties compared to conventional alloys. It is expected that the application of these composites to a divertor component will enhance the structural reliability. A possible design concept would be a system consisting of tungsten armour, copper composite interlayer and copper heat sink where the composite interlayer is locally inserted into the highly stressed domain near the bond interface. For assessment of the design feasibility of the composite divertor concept, a non-linear multi-scale finite element analysis was performed. To this end, a micro-mechanics algorithm was implemented into a finite element code. A reactor-relevant heat flux load was assumed. Focus was placed on the evolution of stress state, plastic deformation and ductile damage on both macro- and microscopic scales. The structural response of the component and the micro-scale stress evolution of the composite laminate were investigated.

Two-dimensional finite element heat transfer model of softwood. Part II, Macrostructural effects

Treesearch

Hongmei Gu; John F. Hunt

2006-01-01

A two-dimensional finite element model was used to study the effects of structural features on transient heat transfer in softwood lumber with various orientations. Transient core temperature was modeled for lumber samples “cut” from various locations within a simulated log. The effects of ring orientation, earlywood to latewood (E/L) ratio, and ring density were...

Optimal mapping of irregular finite element domains to parallel processors

NASA Technical Reports Server (NTRS)

Flower, J.; Otto, S.; Salama, M.

1987-01-01

Mapping the solution domain of n-finite elements into N-subdomains that may be processed in parallel by N-processors is an optimal one if the subdomain decomposition results in a well-balanced workload distribution among the processors. The problem is discussed in the context of irregular finite element domains as an important aspect of the efficient utilization of the capabilities of emerging multiprocessor computers. Finding the optimal mapping is an intractable combinatorial optimization problem, for which a satisfactory approximate solution is obtained here by analogy to a method used in statistical mechanics for simulating the annealing process in solids. The simulated annealing analogy and algorithm are described, and numerical results are given for mapping an irregular two-dimensional finite element domain containing a singularity onto the Hypercube computer.

Transverse Tensile Properties of 3 Dimension-4 Directional Braided Cf/SiC Composite Based on Double-Scale Model

NASA Astrophysics Data System (ADS)

Niu, Xuming; Sun, Zhigang; Song, Yingdong

2017-11-01

In this thesis, a double-scale model for 3 Dimension-4 directional(3D-4d) braided C/SiC composites(CMCs) has been proposed to investigate mechanical properties of it. The double-scale model involves micro-scale which takes fiber/matrix/porosity in fibers tows into consideration and the unit cell scale which considers the 3D-4d braiding structure. Basing on the Micro-optical photographs of composite, we can build a parameterized finite element model that reflects structure of 3D-4d braided composites. The mechanical properties of fiber tows in transverse direction are studied by combining the crack band theory for matrix cracking and cohesive zone model for interface debonding. Transverse tensile process of 3D-4d CMCs can be simulated by introducing mechanical properties of fiber tows into finite element of 3D-4d braided CMCs. Quasi-static tensile tests of 3D-4d braided CMCs have been performed with PWS-100 test system. The predicted tensile stress-strain curve by the double scale model finds good agreement with the experimental results.

3D Finite Element Analysis of Yixing CFRD Built on Inclined Mountain Slope

NASA Astrophysics Data System (ADS)

Sun, Da Wei; Zhang, Liang; Qing Yao, Hui; Wang, Kang Ping

2018-05-01

There are few CFRDs built on steep slope with dam height more than 50 m. So does the relative design and construction experience. The 75 m-high Yixing CFRD was built on steep mountain slope and the 45.9m-high gravity retaining wall was used to against dam sliding. Since the excessive deformation of dam body and perimetric joints would lead to failure of seal materials and cause water leakage, 3D nonlinear finite element stress-deformation analysis was carried out. 3D finite element mesh with 63875 elements including retaining wall and surrounding mountain was established by use of advanced grid discreteness technique. Large scales of equations solving method were adopted in the computer procedure and the calculation time was greatly reduced from former 40 hours to now 45 minutes. Therefore the behavior of the dam, retaining wall and the joint was obtained in a short time, and the results would be helpful to the design and construction of Yixing dam.

A Statistical Approach for the Concurrent Coupling of Molecular Dynamics and Finite Element Methods

NASA Technical Reports Server (NTRS)

Saether, E.; Yamakov, V.; Glaessgen, E.

2007-01-01

Molecular dynamics (MD) methods are opening new opportunities for simulating the fundamental processes of material behavior at the atomistic level. However, increasing the size of the MD domain quickly presents intractable computational demands. A robust approach to surmount this computational limitation has been to unite continuum modeling procedures such as the finite element method (FEM) with MD analyses thereby reducing the region of atomic scale refinement. The challenging problem is to seamlessly connect the two inherently different simulation techniques at their interface. In the present work, a new approach to MD-FEM coupling is developed based on a restatement of the typical boundary value problem used to define a coupled domain. The method uses statistical averaging of the atomistic MD domain to provide displacement interface boundary conditions to the surrounding continuum FEM region, which, in return, generates interface reaction forces applied as piecewise constant traction boundary conditions to the MD domain. The two systems are computationally disconnected and communicate only through a continuous update of their boundary conditions. With the use of statistical averages of the atomistic quantities to couple the two computational schemes, the developed approach is referred to as an embedded statistical coupling method (ESCM) as opposed to a direct coupling method where interface atoms and FEM nodes are individually related. The methodology is inherently applicable to three-dimensional domains, avoids discretization of the continuum model down to atomic scales, and permits arbitrary temperatures to be applied.

Meso-Scale Finite Element Analysis of Mechanical Behavior of 3D Braided Composites Subjected to Biaxial Tension Loadings

NASA Astrophysics Data System (ADS)

Zhang, Chao; Curiel-Sosa, Jose L.; Bui, Tinh Quoc

2018-04-01

In many engineering applications, 3D braided composites are designed for primary loading-bearing structures, and they are frequently subjected to multi-axial loading conditions during service. In this paper, a unit-cell based finite element model is developed for assessment of mechanical behavior of 3D braided composites under different biaxial tension loadings. To predict the damage initiation and evolution of braiding yarns and matrix in the unit-cell, we thus propose an anisotropic damage model based on Murakami damage theory in conjunction with Hashin failure criteria and maximum stress criteria. To attain exact stress ratio, force loading mode of periodic boundary conditions which never been attempted before is first executed to the unit-cell model to apply the biaxial tension loadings. The biaxial mechanical behaviors, such as the stress distribution, tensile modulus and tensile strength are analyzed and discussed. The damage development of 3D braided composites under typical biaxial tension loadings is simulated and the damage mechanisms are revealed in the simulation process. The present study generally provides a new reference to the meso-scale finite element analysis (FEA) of multi-axial mechanical behavior of other textile composites.

Efficient evaluation of the Coulomb force in the Gaussian and finite-element Coulomb method.

PubMed

Kurashige, Yuki; Nakajima, Takahito; Sato, Takeshi; Hirao, Kimihiko

2010-06-28

We propose an efficient method for evaluating the Coulomb force in the Gaussian and finite-element Coulomb (GFC) method, which is a linear-scaling approach for evaluating the Coulomb matrix and energy in large molecular systems. The efficient evaluation of the analytical gradient in the GFC is not straightforward as well as the evaluation of the energy because the SCF procedure with the Coulomb matrix does not give a variational solution for the Coulomb energy. Thus, an efficient approximate method is alternatively proposed, in which the Coulomb potential is expanded in the Gaussian and finite-element auxiliary functions as done in the GFC. To minimize the error in the gradient not just in the energy, the derived functions of the original auxiliary functions of the GFC are used additionally for the evaluation of the Coulomb gradient. In fact, the use of the derived functions significantly improves the accuracy of this approach. Although these additional auxiliary functions enlarge the size of the discretized Poisson equation and thereby increase the computational cost, it maintains the near linear scaling as the GFC and does not affects the overall efficiency of the GFC approach.

Extension of the frequency-domain pFFT method for wave structure interaction in finite depth

NASA Astrophysics Data System (ADS)

Teng, Bin; Song, Zhi-jie

2017-06-01

To analyze wave interaction with a large scale body in the frequency domain, a precorrected Fast Fourier Transform (pFFT) method has been proposed for infinite depth problems with the deep water Green function, as it can form a matrix with Toeplitz and Hankel properties. In this paper, a method is proposed to decompose the finite depth Green function into two terms, which can form matrices with the Toeplitz and a Hankel properties respectively. Then, a pFFT method for finite depth problems is developed. Based on the pFFT method, a numerical code pFFT-HOBEM is developed with the discretization of high order elements. The model is validated, and examinations on the computing efficiency and memory requirement of the new method have also been carried out. It shows that the new method has the same advantages as that for infinite depth.

Adaptive Shape Functions and Internal Mesh Adaptation for Modelling Progressive Failure in Adhesively Bonded Joints

NASA Technical Reports Server (NTRS)

Stapleton, Scott; Gries, Thomas; Waas, Anthony M.; Pineda, Evan J.

2014-01-01

Enhanced finite elements are elements with an embedded analytical solution that can capture detailed local fields, enabling more efficient, mesh independent finite element analysis. The shape functions are determined based on the analytical model rather than prescribed. This method was applied to adhesively bonded joints to model joint behavior with one element through the thickness. This study demonstrates two methods of maintaining the fidelity of such elements during adhesive non-linearity and cracking without increasing the mesh needed for an accurate solution. The first method uses adaptive shape functions, where the shape functions are recalculated at each load step based on the softening of the adhesive. The second method is internal mesh adaption, where cracking of the adhesive within an element is captured by further discretizing the element internally to represent the partially cracked geometry. By keeping mesh adaptations within an element, a finer mesh can be used during the analysis without affecting the global finite element model mesh. Examples are shown which highlight when each method is most effective in reducing the number of elements needed to capture adhesive nonlinearity and cracking. These methods are validated against analogous finite element models utilizing cohesive zone elements.

An Optimal Order Nonnested Mixed Multigrid Method for Generalized Stokes Problems

NASA Technical Reports Server (NTRS)

Deng, Qingping

1996-01-01

A multigrid algorithm is developed and analyzed for generalized Stokes problems discretized by various nonnested mixed finite elements within a unified framework. It is abstractly proved by an element-independent analysis that the multigrid algorithm converges with an optimal order if there exists a 'good' prolongation operator. A technique to construct a 'good' prolongation operator for nonnested multilevel finite element spaces is proposed. Its basic idea is to introduce a sequence of auxiliary nested multilevel finite element spaces and define a prolongation operator as a composite operator of two single grid level operators. This makes not only the construction of a prolongation operator much easier (the final explicit forms of such prolongation operators are fairly simple), but the verification of the approximate properties for prolongation operators is also simplified. Finally, as an application, the framework and technique is applied to seven typical nonnested mixed finite elements.

The Effect of Scale Dependent Discretization on the Progressive Failure of Composite Materials Using Multiscale Analyses

NASA Technical Reports Server (NTRS)

Ricks, Trenton M.; Lacy, Thomas E., Jr.; Pineda, Evan J.; Bednarcyk, Brett A.; Arnold, Steven M.

2013-01-01

A multiscale modeling methodology, which incorporates a statistical distribution of fiber strengths into coupled micromechanics/ finite element analyses, is applied to unidirectional polymer matrix composites (PMCs) to analyze the effect of mesh discretization both at the micro- and macroscales on the predicted ultimate tensile (UTS) strength and failure behavior. The NASA code FEAMAC and the ABAQUS finite element solver were used to analyze the progressive failure of a PMC tensile specimen that initiates at the repeating unit cell (RUC) level. Three different finite element mesh densities were employed and each coupled with an appropriate RUC. Multiple simulations were performed in order to assess the effect of a statistical distribution of fiber strengths on the bulk composite failure and predicted strength. The coupled effects of both the micro- and macroscale discretizations were found to have a noticeable effect on the predicted UTS and computational efficiency of the simulations.

Novel numerical techniques for magma dynamics

NASA Astrophysics Data System (ADS)

Rhebergen, S.; Katz, R. F.; Wathen, A.; Alisic, L.; Rudge, J. F.; Wells, G.

2013-12-01

We discuss the development of finite element techniques and solvers for magma dynamics computations. These are implemented within the FEniCS framework. This approach allows for user-friendly, expressive, high-level code development, but also provides access to powerful, scalable numerical solvers and a large family of finite element discretisations. With the recent addition of dolfin-adjoint, FeniCS supports automated adjoint and tangent-linear models, enabling the rapid development of Generalised Stability Analysis. The ability to easily scale codes to three dimensions with large meshes, and/or to apply intricate adjoint calculations means that efficiency of the numerical algorithms is vital. We therefore describe our development and analysis of preconditioners designed specifically for finite element discretizations of equations governing magma dynamics. The preconditioners are based on Elman-Silvester-Wathen methods for the Stokes equation, and we extend these to flows with compaction. Our simulations are validated by comparison of results with laboratory experiments on partially molten aggregates.

Flexible Models for Solar Sail Control

NASA Technical Reports Server (NTRS)

Weaver Smith, Suzanne; Song, Haiping; Baker, John R.; Black, Jonathan; Muheim, Danniella M.

2005-01-01

Solar sails employ a unique form of propulsion, gaining momentum from incident and reflected photons. However, the momentum transferred by an individual photon is extremely small. Consequently, a solar sail must have an extremely large surface area and also be extremely light. The flexibility of the sail then must be considered when designing or evaluating control laws. In this paper, solar sail flexibility and its influence on control effectiveness is considered using idealized two-dimensional models to represent physical phenomena rather than a specific design. Differential equations of motion are derived for a distributed parameter model of a flexible solar sail idealized as a rotating central hub with two opposing flexible booms. This idealization is appropriate for solar sail designs in which the vibrational modes of the sail and supporting booms move together allowing the sail mass to be distributed along the booms in the idealized model. A reduced analytical model of the flexible response is considered. Linear feedback torque control is applied at the central hub. Two translational disturbances and a torque disturbance also act at the central hub representing the equivalent effect of deflecting sail shape about a reference line. Transient simulations explore different control designs and their effectiveness for controlling orientation, for reducing flexible motion and for disturbance rejection. A second model also is developed as a two-dimensional "pathfinder" model to calculate the effect of solar sail shape on the resultant thrust, in-plane force and torque at the hub. The analysis is then extended to larger models using the finite element method. The finite element modeling approach is verified by comparing results from a two-dimensional finite element model with those from the analytical model. The utility of the finite element modeling approach for this application is then illustrated through examples based on a full finite element model.

Homogenization-based interval analysis for structural-acoustic problem involving periodical composites and multi-scale uncertain-but-bounded parameters.

PubMed

Chen, Ning; Yu, Dejie; Xia, Baizhan; Liu, Jian; Ma, Zhengdong

2017-04-01

This paper presents a homogenization-based interval analysis method for the prediction of coupled structural-acoustic systems involving periodical composites and multi-scale uncertain-but-bounded parameters. In the structural-acoustic system, the macro plate structure is assumed to be composed of a periodically uniform microstructure. The equivalent macro material properties of the microstructure are computed using the homogenization method. By integrating the first-order Taylor expansion interval analysis method with the homogenization-based finite element method, a homogenization-based interval finite element method (HIFEM) is developed to solve a periodical composite structural-acoustic system with multi-scale uncertain-but-bounded parameters. The corresponding formulations of the HIFEM are deduced. A subinterval technique is also introduced into the HIFEM for higher accuracy. Numerical examples of a hexahedral box and an automobile passenger compartment are given to demonstrate the efficiency of the presented method for a periodical composite structural-acoustic system with multi-scale uncertain-but-bounded parameters.

Delamination Modeling of Composites for Improved Crash Analysis

NASA Technical Reports Server (NTRS)

Fleming, David C.

1999-01-01

Finite element crash modeling of composite structures is limited by the inability of current commercial crash codes to accurately model delamination growth. Efforts are made to implement and assess delamination modeling techniques using a current finite element crash code, MSC/DYTRAN. Three methods are evaluated, including a straightforward method based on monitoring forces in elements or constraints representing an interface; a cohesive fracture model proposed in the literature; and the virtual crack closure technique commonly used in fracture mechanics. Results are compared with dynamic double cantilever beam test data from the literature. Examples show that it is possible to accurately model delamination propagation in this case. However, the computational demands required for accurate solution are great and reliable property data may not be available to support general crash modeling efforts. Additional examples are modeled including an impact-loaded beam, damage initiation in laminated crushing specimens, and a scaled aircraft subfloor structures in which composite sandwich structures are used as energy-absorbing elements. These examples illustrate some of the difficulties in modeling delamination as part of a finite element crash analysis.

Analysis of wave motion in one-dimensional structures through fast-Fourier-transform-based wavelet finite element method

NASA Astrophysics Data System (ADS)

Shen, Wei; Li, Dongsheng; Zhang, Shuaifang; Ou, Jinping

2017-07-01

This paper presents a hybrid method that combines the B-spline wavelet on the interval (BSWI) finite element method and spectral analysis based on fast Fourier transform (FFT) to study wave propagation in One-Dimensional (1D) structures. BSWI scaling functions are utilized to approximate the theoretical wave solution in the spatial domain and construct a high-accuracy dynamic stiffness matrix. Dynamic reduction on element level is applied to eliminate the interior degrees of freedom of BSWI elements and substantially reduce the size of the system matrix. The dynamic equations of the system are then transformed and solved in the frequency domain through FFT-based spectral analysis which is especially suitable for parallel computation. A comparative analysis of four different finite element methods is conducted to demonstrate the validity and efficiency of the proposed method when utilized in high-frequency wave problems. Other numerical examples are utilized to simulate the influence of crack and delamination on wave propagation in 1D rods and beams. Finally, the errors caused by FFT and their corresponding solutions are presented.

Probabilistic structural analysis methods for select space propulsion system components

NASA Technical Reports Server (NTRS)

Millwater, H. R.; Cruse, T. A.

1989-01-01

The Probabilistic Structural Analysis Methods (PSAM) project developed at the Southwest Research Institute integrates state-of-the-art structural analysis techniques with probability theory for the design and analysis of complex large-scale engineering structures. An advanced efficient software system (NESSUS) capable of performing complex probabilistic analysis has been developed. NESSUS contains a number of software components to perform probabilistic analysis of structures. These components include: an expert system, a probabilistic finite element code, a probabilistic boundary element code and a fast probability integrator. The NESSUS software system is shown. An expert system is included to capture and utilize PSAM knowledge and experience. NESSUS/EXPERT is an interactive menu-driven expert system that provides information to assist in the use of the probabilistic finite element code NESSUS/FEM and the fast probability integrator (FPI). The expert system menu structure is summarized. The NESSUS system contains a state-of-the-art nonlinear probabilistic finite element code, NESSUS/FEM, to determine the structural response and sensitivities. A broad range of analysis capabilities and an extensive element library is present.

Poisson-Nernst-Planck equations for simulating biomolecular diffusion-reaction processes I: Finite element solutions

DOE Office of Scientific and Technical Information (OSTI.GOV)

Lu Benzhuo; Holst, Michael J.; Center for Theoretical Biological Physics, University of California San Diego, La Jolla, CA 92093

2010-09-20

In this paper we developed accurate finite element methods for solving 3-D Poisson-Nernst-Planck (PNP) equations with singular permanent charges for simulating electrodiffusion in solvated biomolecular systems. The electrostatic Poisson equation was defined in the biomolecules and in the solvent, while the Nernst-Planck equation was defined only in the solvent. We applied a stable regularization scheme to remove the singular component of the electrostatic potential induced by the permanent charges inside biomolecules, and formulated regular, well-posed PNP equations. An inexact-Newton method was used to solve the coupled nonlinear elliptic equations for the steady problems; while an Adams-Bashforth-Crank-Nicolson method was devised formore » time integration for the unsteady electrodiffusion. We numerically investigated the conditioning of the stiffness matrices for the finite element approximations of the two formulations of the Nernst-Planck equation, and theoretically proved that the transformed formulation is always associated with an ill-conditioned stiffness matrix. We also studied the electroneutrality of the solution and its relation with the boundary conditions on the molecular surface, and concluded that a large net charge concentration is always present near the molecular surface due to the presence of multiple species of charged particles in the solution. The numerical methods are shown to be accurate and stable by various test problems, and are applicable to real large-scale biophysical electrodiffusion problems.« less

Poisson-Nernst-Planck Equations for Simulating Biomolecular Diffusion-Reaction Processes I: Finite Element Solutions

PubMed Central

Lu, Benzhuo; Holst, Michael J.; McCammon, J. Andrew; Zhou, Y. C.

2010-01-01

In this paper we developed accurate finite element methods for solving 3-D Poisson-Nernst-Planck (PNP) equations with singular permanent charges for electrodiffusion in solvated biomolecular systems. The electrostatic Poisson equation was defined in the biomolecules and in the solvent, while the Nernst-Planck equation was defined only in the solvent. We applied a stable regularization scheme to remove the singular component of the electrostatic potential induced by the permanent charges inside biomolecules, and formulated regular, well-posed PNP equations. An inexact-Newton method was used to solve the coupled nonlinear elliptic equations for the steady problems; while an Adams-Bashforth-Crank-Nicolson method was devised for time integration for the unsteady electrodiffusion. We numerically investigated the conditioning of the stiffness matrices for the finite element approximations of the two formulations of the Nernst-Planck equation, and theoretically proved that the transformed formulation is always associated with an ill-conditioned stiffness matrix. We also studied the electroneutrality of the solution and its relation with the boundary conditions on the molecular surface, and concluded that a large net charge concentration is always present near the molecular surface due to the presence of multiple species of charged particles in the solution. The numerical methods are shown to be accurate and stable by various test problems, and are applicable to real large-scale biophysical electrodiffusion problems. PMID:21709855

Poisson-Nernst-Planck Equations for Simulating Biomolecular Diffusion-Reaction Processes I: Finite Element Solutions.

PubMed

Lu, Benzhuo; Holst, Michael J; McCammon, J Andrew; Zhou, Y C

2010-09-20

In this paper we developed accurate finite element methods for solving 3-D Poisson-Nernst-Planck (PNP) equations with singular permanent charges for electrodiffusion in solvated biomolecular systems. The electrostatic Poisson equation was defined in the biomolecules and in the solvent, while the Nernst-Planck equation was defined only in the solvent. We applied a stable regularization scheme to remove the singular component of the electrostatic potential induced by the permanent charges inside biomolecules, and formulated regular, well-posed PNP equations. An inexact-Newton method was used to solve the coupled nonlinear elliptic equations for the steady problems; while an Adams-Bashforth-Crank-Nicolson method was devised for time integration for the unsteady electrodiffusion. We numerically investigated the conditioning of the stiffness matrices for the finite element approximations of the two formulations of the Nernst-Planck equation, and theoretically proved that the transformed formulation is always associated with an ill-conditioned stiffness matrix. We also studied the electroneutrality of the solution and its relation with the boundary conditions on the molecular surface, and concluded that a large net charge concentration is always present near the molecular surface due to the presence of multiple species of charged particles in the solution. The numerical methods are shown to be accurate and stable by various test problems, and are applicable to real large-scale biophysical electrodiffusion problems.

Coupling Finite Element and Meshless Local Petrov-Galerkin Methods for Two-Dimensional Potential Problems

NASA Technical Reports Server (NTRS)

Chen, T.; Raju, I. S.

2002-01-01

A coupled finite element (FE) method and meshless local Petrov-Galerkin (MLPG) method for analyzing two-dimensional potential problems is presented in this paper. The analysis domain is subdivided into two regions, a finite element (FE) region and a meshless (MM) region. A single weighted residual form is written for the entire domain. Independent trial and test functions are assumed in the FE and MM regions. A transition region is created between the two regions. The transition region blends the trial and test functions of the FE and MM regions. The trial function blending is achieved using a technique similar to the 'Coons patch' method that is widely used in computer-aided geometric design. The test function blending is achieved by using either FE or MM test functions on the nodes in the transition element. The technique was evaluated by applying the coupled method to two potential problems governed by the Poisson equation. The coupled method passed all the patch test problems and gave accurate solutions for the problems studied.

Localized Overheating Phenomena and Optimization of Spark-Plasma Sintering Tooling Design

PubMed Central

Giuntini, Diletta; Olevsky, Eugene A.; Garcia-Cardona, Cristina; Maximenko, Andrey L.; Yurlova, Maria S.; Haines, Christopher D.; Martin, Darold G.; Kapoor, Deepak

2013-01-01

The present paper shows the application of a three-dimensional coupled electrical, thermal, mechanical finite element macro-scale modeling framework of Spark Plasma Sintering (SPS) to an actual problem of SPS tooling overheating, encountered during SPS experimentation. The overheating phenomenon is analyzed by varying the geometry of the tooling that exhibits the problem, namely by modeling various tooling configurations involving sequences of disk-shape spacers with step-wise increasing radii. The analysis is conducted by means of finite element simulations, intended to obtain temperature spatial distributions in the graphite press-forms, including punches, dies, and spacers; to identify the temperature peaks and their respective timing, and to propose a more suitable SPS tooling configuration with the avoidance of the overheating as a final aim. Electric currents-based Joule heating, heat transfer, mechanical conditions, and densification are imbedded in the model, utilizing the finite-element software COMSOL™, which possesses a distinguishing ability of coupling multiple physics. Thereby the implementation of a finite element method applicable to a broad range of SPS procedures is carried out, together with the more specific optimization of the SPS tooling design when dealing with excessive heating phenomena. PMID:28811398

Nonlinear transient analysis via energy minimization

NASA Technical Reports Server (NTRS)

Kamat, M. P.; Knight, N. F., Jr.

1978-01-01

The formulation basis for nonlinear transient analysis of finite element models of structures using energy minimization is provided. Geometric and material nonlinearities are included. The development is restricted to simple one and two dimensional finite elements which are regarded as being the basic elements for modeling full aircraft-like structures under crash conditions. The results indicate the effectiveness of the technique as a viable tool for this purpose.

On mathematical modelling of aeroelastic problems with finite element method

NASA Astrophysics Data System (ADS)

Sváček, Petr

2018-06-01

This paper is interested in solution of two-dimensional aeroelastic problems. Two mathematical models are compared for a benchmark problem. First, the classical approach of linearized aerodynamical forces is described to determine the aeroelastic instability and the aeroelastic response in terms of frequency and damping coefficient. This approach is compared to the coupled fluid-structure model solved with the aid of finite element method used for approximation of the incompressible Navier-Stokes equations. The finite element approximations are coupled to the non-linear motion equations of a flexibly supported airfoil. Both methods are first compared for the case of small displacement, where the linearized approach can be well adopted. The influence of nonlinearities for the case of post-critical regime is discussed.

A finite element beam propagation method for simulation of liquid crystal devices.

PubMed

Vanbrabant, Pieter J M; Beeckman, Jeroen; Neyts, Kristiaan; James, Richard; Fernandez, F Anibal

2009-06-22

An efficient full-vectorial finite element beam propagation method is presented that uses higher order vector elements to calculate the wide angle propagation of an optical field through inhomogeneous, anisotropic optical materials such as liquid crystals. The full dielectric permittivity tensor is considered in solving Maxwell's equations. The wide applicability of the method is illustrated with different examples: the propagation of a laser beam in a uniaxial medium, the tunability of a directional coupler based on liquid crystals and the near-field diffraction of a plane wave in a structure containing micrometer scale variations in the transverse refractive index, similar to the pixels of a spatial light modulator.

VLF Trimpi modelling on the path NWC-Dunedin using both finite element and 3D Born modelling

NASA Astrophysics Data System (ADS)

Nunn, D.; Hayakawa, K. B. M.

1998-10-01

This paper investigates the numerical modelling of VLF Trimpis, produced by a D region inhomogeneity on the great circle path. Two different codes are used to model Trimpis on the path NWC-Dunedin. The first is a 2D Finite Element Method Code (FEM), whose solutions are rigorous and valid in the strong scattering or non-Born limit. The second code is a 3D model that invokes the Born approximation. The predicted Trimpis from these codes compare very closely, thus confirming the validity of both models. The modal scattering matrices for both codes are analysed in some detail and are found to have a comparable structure. They indicate strong scattering between the dominant TM modes. Analysis of the scattering matrix from the FEM code shows that departure from linear Born behaviour occurs when the inhomogeneity has a horizontal scale size of about 100 km and a maximum electron density enhancement at 75 km altitude of about 6 electrons.

Potential of minicomputer/array-processor system for nonlinear finite-element analysis

NASA Technical Reports Server (NTRS)

Strohkorb, G. A.; Noor, A. K.

1983-01-01

The potential of using a minicomputer/array-processor system for the efficient solution of large-scale, nonlinear, finite-element problems is studied. A Prime 750 is used as the host computer, and a software simulator residing on the Prime is employed to assess the performance of the Floating Point Systems AP-120B array processor. Major hardware characteristics of the system such as virtual memory and parallel and pipeline processing are reviewed, and the interplay between various hardware components is examined. Effective use of the minicomputer/array-processor system for nonlinear analysis requires the following: (1) proper selection of the computational procedure and the capability to vectorize the numerical algorithms; (2) reduction of input-output operations; and (3) overlapping host and array-processor operations. A detailed discussion is given of techniques to accomplish each of these tasks. Two benchmark problems with 1715 and 3230 degrees of freedom, respectively, are selected to measure the anticipated gain in speed obtained by using the proposed algorithms on the array processor.

An automatic granular structure generation and finite element analysis of heterogeneous semi-solid materials

NASA Astrophysics Data System (ADS)

Sharifi, Hamid; Larouche, Daniel

2015-09-01

The quality of cast metal products depends on the capacity of the semi-solid metal to sustain the stresses generated during the casting. Predicting the evolution of these stresses with accuracy in the solidification interval should be highly helpful to avoid the formation of defects like hot tearing. This task is however very difficult because of the heterogeneous nature of the material. In this paper, we propose to evaluate the mechanical behaviour of a metal during solidification using a mesh generation technique of the heterogeneous semi-solid material for a finite element analysis at the microscopic level. This task is done on a two-dimensional (2D) domain in which the granular structure of the solid phase is generated surrounded by an intergranular and interdendritc liquid phase. Some basic solid grains are first constructed and projected in the 2D domain with random orientations and scale factors. Depending on their orientation, the basic grains are combined to produce larger grains or separated by a liquid film. Different basic grain shapes can produce different granular structures of the mushy zone. As a result, using this automatic grain generation procedure, we can investigate the effect of grain shapes and sizes on the thermo-mechanical behaviour of the semi-solid material. The granular models are automatically converted to the finite element meshes. The solid grains and the liquid phase are meshed properly using quadrilateral elements. This method has been used to simulate the microstructure of a binary aluminium-copper alloy (Al-5.8 wt% Cu) when the fraction solid is 0.92. Using the finite element method and the Mie-Grüneisen equation of state for the liquid phase, the transient mechanical behaviour of the mushy zone under tensile loading has been investigated. The stress distribution and the bridges, which are formed during the tensile loading, have been detected.

Efficient Computation of Atmospheric Flows with Tempest: Development of Next-Generation Climate and Weather Prediction Algorithms at Non-Hydrostatic Scales

NASA Astrophysics Data System (ADS)

Guerra, J. E.; Ullrich, P. A.

2015-12-01

Tempest is a next-generation global climate and weather simulation platform designed to allow experimentation with numerical methods at very high spatial resolutions. The atmospheric fluid equations are discretized by continuous / discontinuous finite elements in the horizontal and by a staggered nodal finite element method (SNFEM) in the vertical, coupled with implicit/explicit time integration. At global horizontal resolutions below 10km, many important questions remain on optimal techniques for solving the fluid equations. We present results from a suite of meso-scale test cases to validate the performance of the SNFEM applied in the vertical. Internal gravity wave, mountain wave, convective, and Cartesian baroclinic instability tests will be shown at various vertical orders of accuracy and compared with known results.

Vertical discretization with finite elements for a global hydrostatic model on the cubed sphere

NASA Astrophysics Data System (ADS)

Yi, Tae-Hyeong; Park, Ja-Rin

2017-06-01

A formulation of Galerkin finite element with basis-spline functions on a hybrid sigma-pressure coordinate is presented to discretize the vertical terms of global Eulerian hydrostatic equations employed in a numerical weather prediction system, which is horizontally discretized with high-order spectral elements on a cubed sphere grid. This replaces the vertical discretization of conventional central finite difference that is first-order accurate in non-uniform grids and causes numerical instability in advection-dominant flows. Therefore, a model remains in the framework of Galerkin finite elements for both the horizontal and vertical spatial terms. The basis-spline functions, obtained from the de-Boor algorithm, are employed to derive both the vertical derivative and integral operators, since Eulerian advection terms are involved. These operators are used to discretize the vertical terms of the prognostic and diagnostic equations. To verify the vertical discretization schemes and compare their performance, various two- and three-dimensional idealized cases and a hindcast case with full physics are performed in terms of accuracy and stability. It was shown that the vertical finite element with the cubic basis-spline function is more accurate and stable than that of the vertical finite difference, as indicated by faster residual convergence, fewer statistical errors, and reduction in computational mode. This leads to the general conclusion that the overall performance of a global hydrostatic model might be significantly improved with the vertical finite element.

High speed inviscid compressible flow by the finite element method

NASA Technical Reports Server (NTRS)

Zienkiewicz, O. C.; Loehner, R.; Morgan, K.

1984-01-01

The finite element method and an explicit time stepping algorithm which is based on Taylor-Galerkin schemes with an appropriate artificial viscosity is combined with an automatic mesh refinement process which is designed to produce accurate steady state solutions to problems of inviscid compressible flow in two dimensions. The results of two test problems are included which demonstrate the excellent performance characteristics of the proposed procedures.

Prediction of local proximal tibial subchondral bone structural stiffness using subject-specific finite element modeling: Effect of selected density-modulus relationship.

PubMed

Nazemi, S Majid; Amini, Morteza; Kontulainen, Saija A; Milner, Jaques S; Holdsworth, David W; Masri, Bassam A; Wilson, David R; Johnston, James D

2015-08-01

Quantitative computed tomography based subject-specific finite element modeling has potential to clarify the role of subchondral bone alterations in knee osteoarthritis initiation, progression, and pain initiation. Calculation of bone elastic moduli from image data is a basic step when constructing finite element models. However, different relationships between elastic moduli and imaged density (known as density-modulus relationships) have been reported in the literature. The objective of this study was to apply seven different trabecular-specific and two cortical-specific density-modulus relationships from the literature to finite element models of proximal tibia subchondral bone, and identify the relationship(s) that best predicted experimentally measured local subchondral structural stiffness with highest explained variance and least error. Thirteen proximal tibial compartments were imaged via quantitative computed tomography. Imaged bone mineral density was converted to elastic moduli using published density-modulus relationships and mapped to corresponding finite element models. Proximal tibial structural stiffness values were compared to experimentally measured stiffness values from in-situ macro-indentation testing directly on the subchondral bone surface (47 indentation points). Regression lines between experimentally measured and finite element calculated stiffness had R(2) values ranging from 0.56 to 0.77. Normalized root mean squared error varied from 16.6% to 337.6%. Of the 21 evaluated density-modulus relationships in this study, Goulet combined with Snyder and Schneider or Rho appeared most appropriate for finite element modeling of local subchondral bone structural stiffness. Though, further studies are needed to optimize density-modulus relationships and improve finite element estimates of local subchondral bone structural stiffness. Copyright © 2015 Elsevier Ltd. All rights reserved.

Influence of Finite Element Size in Residual Strength Prediction of Composite Structures

NASA Technical Reports Server (NTRS)

Satyanarayana, Arunkumar; Bogert, Philip B.; Karayev, Kazbek Z.; Nordman, Paul S.; Razi, Hamid

2012-01-01

The sensitivity of failure load to the element size used in a progressive failure analysis (PFA) of carbon composite center notched laminates is evaluated. The sensitivity study employs a PFA methodology previously developed by the authors consisting of Hashin-Rotem intra-laminar fiber and matrix failure criteria and a complete stress degradation scheme for damage simulation. The approach is implemented with a user defined subroutine in the ABAQUS/Explicit finite element package. The effect of element size near the notch tips on residual strength predictions was assessed for a brittle failure mode with a parametric study that included three laminates of varying material system, thickness and stacking sequence. The study resulted in the selection of an element size of 0.09 in. X 0.09 in., which was later used for predicting crack paths and failure loads in sandwich panels and monolithic laminated panels. Comparison of predicted crack paths and failure loads for these panels agreed well with experimental observations. Additionally, the element size vs. normalized failure load relationship, determined in the parametric study, was used to evaluate strength-scaling factors for three different element sizes. The failure loads predicted with all three element sizes provided converged failure loads with respect to that corresponding with the 0.09 in. X 0.09 in. element size. Though preliminary in nature, the strength-scaling concept has the potential to greatly reduce the computational time required for PFA and can enable the analysis of large scale structural components where failure is dominated by fiber failure in tension.

Full-scale locomotive dynamic collision testing and correlations : offset collisions between a locomotive and a covered hopper car (test 4).

DOT National Transportation Integrated Search

2011-09-01

This report presents the test results and finite element correlations of a full-scale dynamic collision test with rail vehicles as part of the Federal Railroad Administrations research program on improved crashworthiness of locomotive structures. ...

A two-layer multiple-time-scale turbulence model and grid independence study

NASA Technical Reports Server (NTRS)

Kim, S.-W.; Chen, C.-P.

1989-01-01

A two-layer multiple-time-scale turbulence model is presented. The near-wall model is based on the classical Kolmogorov-Prandtl turbulence hypothesis and the semi-empirical logarithmic law of the wall. In the two-layer model presented, the computational domain of the conservation of mass equation and the mean momentum equation penetrated up to the wall, where no slip boundary condition has been prescribed; and the near wall boundary of the turbulence equations has been located at the fully turbulent region, yet very close to the wall, where the standard wall function method has been applied. Thus, the conservation of mass constraint can be satisfied more rigorously in the two-layer model than in the standard wall function method. In most of the two-layer turbulence models, the number of grid points to be used inside the near-wall layer posed the issue of computational efficiency. The present finite element computational results showed that the grid independent solutions were obtained with as small as two grid points, i.e., one quadratic element, inside the near wall layer. Comparison of the computational results obtained by using the two-layer model and those obtained by using the wall function method is also presented.

Applications of finite-size scaling for atomic and non-equilibrium systems

NASA Astrophysics Data System (ADS)

Antillon, Edwin A.

We apply the theory of Finite-size scaling (FSS) to an atomic and a non-equilibrium system in order to extract critical parameters. In atomic systems, we look at the energy dependence on the binding charge near threshold between bound and free states, where we seek the critical nuclear charge for stability. We use different ab initio methods, such as Hartree-Fock, Density Functional Theory, and exact formulations implemented numerically with the finite-element method (FEM). Using Finite-size scaling formalism, where in this case the size of the system is related to the number of elements used in the basis expansion of the wavefunction, we predict critical parameters in the large basis limit. Results prove to be in good agreement with previous Slater-basis set calculations and demonstrate that this combined approach provides a promising first-principles approach to describe quantum phase transitions for materials and extended systems. In the second part we look at non-equilibrium one-dimensional model known as the raise and peel model describing a growing surface which grows locally and has non-local desorption. For a specific values of adsorption ( ua) and desorption (ud) the model shows interesting features. At ua = ud, the model is described by a conformal field theory (with conformal charge c = 0) and its stationary probability can be mapped to the ground state of a quantum chain and can also be related a two dimensional statistical model. For ua ≥ ud, the model shows a scale invariant phase in the avalanche distribution. In this work we study the surface dynamics by looking at avalanche distributions using FSS formalism and explore the effect of changing the boundary conditions of the model. The model shows the same universality for the cases with and with our the wall for an odd number of tiles removed, but we find a new exponent in the presence of a wall for an even number of avalanches released. We provide new conjecture for the probability distribution of avalanches with a wall obtained by using exact diagonalization of small lattices and Monte-Carlo simulations.

Modal element method for scattering of sound by absorbing bodies

NASA Technical Reports Server (NTRS)

Baumeister, Kenneth J.; Kreider, Kevin L.

1992-01-01

The modal element method for acoustic scattering from 2-D body is presented. The body may be acoustically soft (absorbing) or hard (reflecting). The infinite computational region is divided into two subdomains - the bounded finite element domain, which is characterized by complicated geometry and/or variable material properties, and the surrounding unbounded homogeneous domain. The acoustic pressure field is represented approximately in the finite element domain by a finite element solution, and is represented analytically by an eigenfunction expansion in the homogeneous domain. The two solutions are coupled by the continuity of pressure and velocity across the interface between the two subdomains. Also, for hard bodies, a compact modal ring grid system is introduced for which computing requirements are drastically reduced. Analysis for 2-D scattering from solid and coated (acoustically treated) bodies is presented, and several simple numerical examples are discussed. In addition, criteria are presented for determining the number of modes to accurately resolve the scattered pressure field from a solid cylinder as a function of the frequency of the incoming wave and the radius of the cylinder.

A comparative study of an ABC and an artificial absorber for truncating finite element meshes

NASA Technical Reports Server (NTRS)

Oezdemir, T.; Volakis, John L.

1993-01-01

The type of mesh termination used in the context of finite element formulations plays a major role on the efficiency and accuracy of the field solution. The performance of an absorbing boundary condition (ABC) and an artificial absorber (a new concept) for terminating the finite element mesh was evaluated. This analysis is done in connection with the problem of scattering by a finite slot array in a thick ground plane. The two approximate mesh truncation schemes are compared with the exact finite element-boundary integral (FEM-BI) method in terms of accuracy and efficiency. It is demonstrated that both approximate truncation schemes yield reasonably accurate results even when the mesh is extended only 0.3 wavelengths away from the array aperture. However, the artificial absorber termination method leads to a substantially more efficient solution. Moreover, it is shown that the FEM-BI method remains quite competitive with the FEM-artificial absorber method when the FFT is used for computing the matrix-vector products in the iterative solution algorithm. These conclusions are indeed surprising and of major importance in electromagnetic simulations based on the finite element method.

Biomechanical Evaluation of Different Fixation Methods for Mandibular Anterior Segmental Osteotomy Using Finite Element Analysis, Part Two: Superior Repositioning Surgery With Bone Allograft.

PubMed

Kilinç, Yeliz; Erkmen, Erkan; Kurt, Ahmet

2016-01-01

In this study, the biomechanical behavior of different fixation methods used to fix the mandibular anterior segment following various amounts of superior repositioning was evaluated by using Finite Element Analysis (FEA). The three-dimensional finite element models representing 3 and 5 mm superior repositioning were generated. The gap in between segments was assumed to be filled by block bone allograft and resignated to be in perfect contact with the mandible and segmented bone. Six different finite element models with 2 distinct mobilization rate including 3 different fixation configurations, double right L (DRL), double left L (DLL), or double I (DI) miniplates with monocortical screws, correspondingly were created. A comparative evaluation has been made under vertical, horizontal and oblique loads. The von Mises and principal maximum stress (Pmax) values were calculated by finite element solver programme. The first part of our ongoing Finite Element Analysis research has been addressed to the mechanical behavior of the same fixation configurations in nongrafted models. In comparison with the findings of the first part of the study, it was concluded that bone graft offers superior mechanical stability without any limitation of mobilization and less stress on the fixative appliances as well as in the bone.

Surface cracks in a plate of finite width under tension or bending

NASA Technical Reports Server (NTRS)

Erdogan, F.; Boduroglu, H.

1984-01-01

The problem of a finite plate containing collinear surface cracks is considered and solved by using the line spring model with plane elasticity and Reissner's plate theory. The main focus is on the effect of interaction between two cracks or between cracks and stress-free plate boundaries on the stress intensity factors in an effort to provide extensive numerical results which may be useful in applications. Some sample results are obtained and are compared with the existing finite element results. Then the problem is solved for a single (internal) crack, two collinear cracks, and two corner cracks for wide range of relative dimensions. Particularly in corner cracks, the agreement with the finite element solution is surprisingly very good. The results are obtained for semi-elliptic and rectangular crack profiles which may, in practice, correspond to two limiting cases of the actual profile of a subcritically growing surface crack.

Surface cracks in a plate of finite width under extension or bending

NASA Technical Reports Server (NTRS)

Erdogan, F.; Boduroglu, H.

1984-01-01

In this paper the problem of a finite plate containing collinear surface cracks is considered. The problem is solved by using the line spring model with plane elasticity and Reissner's plate theory. The main purpose of the study is to investigate the effect of interaction between two cracks or between cracks and stress-free plate boundaries on the stress intensity factors and to provide extensive numerical results which may be useful in applications. First, some sample results are obtained and are compared with the existing finite element results. Then the problem is solved for a single (internal) crack, two collinear cracks and two corner cracks for wide range of relative dimensions. Particularly in corner cracks the agreement with the finite element solution is surprisingly very good. The results are obtained for semielliptic and rectangular crack profiles which may, in practice, correspond to two limiting cases of the actual profile of a subcritically growing surface crack.

Finite element analysis of low speed viscous and inviscid aerodynamic flows

NASA Technical Reports Server (NTRS)

Baker, A. J.; Manhardt, P. D.

1977-01-01

A weak interaction solution algorithm was established for aerodynamic flow about an isolated airfoil. Finite element numerical methodology was applied to solution of each of differential equations governing potential flow, and viscous and turbulent boundary layer and wake flow downstream of the sharp trailing edge. The algorithm accounts for computed viscous displacement effects on the potential flow. Closure for turbulence was accomplished using both first and second order models. The COMOC finite element fluid mechanics computer program was modified to solve the identified equation systems for two dimensional flows. A numerical program was completed to determine factors affecting solution accuracy, convergence and stability for the combined potential, boundary layer, and parabolic Navier-Stokes equation systems. Good accuracy and convergence are demonstrated. Each solution is obtained within the identical finite element framework of COMOC.

A Coupled/Uncoupled Computational Scheme for Deformation and Fatigue Damage Analysis of Unidirectional Metal-Matrix Composites

NASA Technical Reports Server (NTRS)

Wilt, Thomas E.; Arnold, Steven M.; Saleeb, Atef F.

1997-01-01

A fatigue damage computational algorithm utilizing a multiaxial, isothermal, continuum-based fatigue damage model for unidirectional metal-matrix composites has been implemented into the commercial finite element code MARC using MARC user subroutines. Damage is introduced into the finite element solution through the concept of effective stress that fully couples the fatigue damage calculations with the finite element deformation solution. Two applications using the fatigue damage algorithm are presented. First, an axisymmetric stress analysis of a circumferentially reinforced ring, wherein both the matrix cladding and the composite core were assumed to behave elastic-perfectly plastic. Second, a micromechanics analysis of a fiber/matrix unit cell using both the finite element method and the generalized method of cells (GMC). Results are presented in the form of S-N curves and damage distribution plots.

A finite element based method for solution of optimal control problems

NASA Technical Reports Server (NTRS)

Bless, Robert R.; Hodges, Dewey H.; Calise, Anthony J.

1989-01-01

A temporal finite element based on a mixed form of the Hamiltonian weak principle is presented for optimal control problems. The mixed form of this principle contains both states and costates as primary variables that are expanded in terms of elemental values and simple shape functions. Unlike other variational approaches to optimal control problems, however, time derivatives of the states and costates do not appear in the governing variational equation. Instead, the only quantities whose time derivatives appear therein are virtual states and virtual costates. Also noteworthy among characteristics of the finite element formulation is the fact that in the algebraic equations which contain costates, they appear linearly. Thus, the remaining equations can be solved iteratively without initial guesses for the costates; this reduces the size of the problem by about a factor of two. Numerical results are presented herein for an elementary trajectory optimization problem which show very good agreement with the exact solution along with excellent computational efficiency and self-starting capability. The goal is to evaluate the feasibility of this approach for real-time guidance applications. To this end, a simplified two-stage, four-state model for an advanced launch vehicle application is presented which is suitable for finite element solution.

Inversion of Robin coefficient by a spectral stochastic finite element approach

DOE Office of Scientific and Technical Information (OSTI.GOV)

Jin Bangti; Zou Jun

2008-03-01

This paper investigates a variational approach to the nonlinear stochastic inverse problem of probabilistically calibrating the Robin coefficient from boundary measurements for the steady-state heat conduction. The problem is formulated into an optimization problem, and mathematical properties relevant to its numerical computations are investigated. The spectral stochastic finite element method using polynomial chaos is utilized for the discretization of the optimization problem, and its convergence is analyzed. The nonlinear conjugate gradient method is derived for the optimization system. Numerical results for several two-dimensional problems are presented to illustrate the accuracy and efficiency of the stochastic finite element method.

Finite element formulation with embedded weak discontinuities for strain localization under dynamic conditions

DOE Office of Scientific and Technical Information (OSTI.GOV)

Jin, Tao; Mourad, Hashem M.; Bronkhorst, Curt A.

Here, we present an explicit finite element formulation designed for the treatment of strain localization under highly dynamic conditions. We also used a material stability analysis to detect the onset of localization behavior. Finite elements with embedded weak discontinuities are employed with the aim of representing subsequent localized deformation accurately. The formulation and its algorithmic implementation are described in detail. Numerical results are presented to illustrate the usefulness of this computational framework in the treatment of strain localization under highly dynamic conditions, and to examine its performance characteristics in the context of two-dimensional plane-strain problems.

Finite element formulation with embedded weak discontinuities for strain localization under dynamic conditions

DOE PAGES

Jin, Tao; Mourad, Hashem M.; Bronkhorst, Curt A.; ...

2017-09-13

Here, we present an explicit finite element formulation designed for the treatment of strain localization under highly dynamic conditions. We also used a material stability analysis to detect the onset of localization behavior. Finite elements with embedded weak discontinuities are employed with the aim of representing subsequent localized deformation accurately. The formulation and its algorithmic implementation are described in detail. Numerical results are presented to illustrate the usefulness of this computational framework in the treatment of strain localization under highly dynamic conditions, and to examine its performance characteristics in the context of two-dimensional plane-strain problems.

Thermal finite-element analysis of space shuttle main engine turbine blade

NASA Technical Reports Server (NTRS)

Abdul-Aziz, Ali; Tong, Michael T.; Kaufman, Albert

1987-01-01

Finite-element, transient heat transfer analyses were performed for the first-stage blades of the space shuttle main engine (SSME) high-pressure fuel turbopump. The analyses were based on test engine data provided by Rocketdyne. Heat transfer coefficients were predicted by performing a boundary-layer analysis at steady-state conditions with the STAN5 boundary-layer code. Two different peak-temperature overshoots were evaluated for the startup transient. Cutoff transient conditions were also analyzed. A reduced gas temperature profile based on actual thermocouple data was also considered. Transient heat transfer analyses were conducted with the MARC finite-element computer code.

Full-Scale Crash Tests and Analyses of Three High-Wing Single

NASA Technical Reports Server (NTRS)

Annett, Martin S.; Littell, Justin D.; Stimson, Chad M.; Jackson, Karen E.; Mason, Brian H.

2015-01-01

The NASA Emergency Locator Transmitter Survivability and Reliability (ELTSAR) project was initiated in 2014 to assess the crash performance standards for the next generation of ELT systems. Three Cessna 172 aircraft have been acquired to conduct crash testing at NASA Langley Research Center's Landing and Impact Research Facility. Testing is scheduled for the summer of 2015 and will simulate three crash conditions; a flare to stall while emergency landing, and two controlled flight into terrain scenarios. Instrumentation and video coverage, both onboard and external, will also provide valuable data of airframe response. Full-scale finite element analyses will be performed using two separate commercial explicit solvers. Calibration and validation of the models will be based on the airframe response under these varying crash conditions.

Multi-Scale Modeling of an Integrated 3D Braided Composite with Applications to Helicopter Arm

NASA Astrophysics Data System (ADS)

Zhang, Diantang; Chen, Li; Sun, Ying; Zhang, Yifan; Qian, Kun

2017-10-01

A study is conducted with the aim of developing multi-scale analytical method for designing the composite helicopter arm with three-dimensional (3D) five-directional braided structure. Based on the analysis of 3D braided microstructure, the multi-scale finite element modeling is developed. Finite element analysis on the load capacity of 3D five-directional braided composites helicopter arm is carried out using the software ABAQUS/Standard. The influences of the braiding angle and loading condition on the stress and strain distribution of the helicopter arm are simulated. The results show that the proposed multi-scale method is capable of accurately predicting the mechanical properties of 3D braided composites, validated by the comparison the stress-strain curves of meso-scale RVCs. Furthermore, it is found that the braiding angle is an important factor affecting the mechanical properties of 3D five-directional braided composite helicopter arm. Based on the optimized structure parameters, the nearly net-shaped composite helicopter arm is fabricated using a novel resin transfer mould (RTM) process.

Mechanics of low-dimensional carbon nanostructures: Atomistic, continuum, and multi-scale approaches

NASA Astrophysics Data System (ADS)

Mahdavi, Arash

A new multiscale modeling technique called the Consistent Atomic-scale Finite Element (CAFE) method is introduced. Unlike traditional approaches for linking the atomic structure to its equivalent continuum, this method directly connects the atomic degrees of freedom to a reduced set of finite element degrees of freedom without passing through an intermediate homogenized continuum. As a result, there is no need to introduce stress and strain measures at the atomic level. The Tersoff-Brenner interatomic potential is used to calculate the consistent tangent stiffness matrix of the structure. In this finite element formulation, all local and non-local interactions between carbon atoms are taken into account using overlapping finite elements. In addition, a consistent hierarchical finite element modeling technique is developed for adaptively coarsening and refining the mesh over different parts of the model. This process is consistent with the underlying atomic structure and, by refining the mesh to the scale of atomic spacing, molecular dynamic results can be recovered. This method is valid across the scales and can be used to concurrently model atomistic and continuum phenomena so, in contrast with most other multi-scale methods, there is no need to introduce artificial boundaries for coupling atomistic and continuum regions. Effect of the length scale of the nanostructure is also included in the model by building the hierarchy of elements from bottom up using a finite size atom cluster as the building block. To be consistent with the bravais multi-lattice structure of sp2-bonded carbon, two independent displacement fields are used for reducing the order of the model. Sparse structure of the stiffness matrix of these nanostructures is exploited to reduce the memory requirement and to speed up the formation of the system matrices and solution of the equilibrium equations. Applicability of the method is shown with several examples of the nonlinear mechanics of carbon nanotubes and carbon nanocones subject to different loadings and boundary conditions. This finite element technique is also used to study the natural frequencies of low-dimensional carbon nanostructures and comparing the results with those of a homogenized isotropic continuum shell. Conclusion is that, replacing the atomic lattice with an isotropic continuum shell for a graphene sheet does not significantly affect the vibration frequencies while in the case of carbon nanotubes and carbon nanocones there is a significant difference between the natural frequencies of the atomistic model and its continuum counterpart. In the case of the carbon nanotube, continuum model successfully captures the beam bending vibration modes while overestimating frequencies of the modes in which the cross-section undergoes significant deformation. Furthermore, in the case of carbon nanotubes, the continuum shell exhibits a torsional mode which appears to be an artifact resulting from the small nominal thickness typically used in the continuum shell approximation of these nanostructures. Results of this study indicate that isotropic continuum shell models, while simple and useful in static analysis, cannot accurately predict the vibration frequencies of these nanostructures. We have studied the bistable nature of single-walled carbon nanotubes by investigating the change in the tube's energy as it is compressed between flat rigid indenters of various widths. Assuming the nanotube deformed uniformly along its length and modeling the cross-section as an inextensible, non-linear beam we found that tubes with a radius greater than 12 A are bistable and that tubes with a radius greater than 25 A have a lower energy in the collapsed state than in the inflated state. The difference in energy between the collapsed and inflated states decreases nearly linearly with increasing tube radius. While the inflated state remains stable for tubes of all diameters, the energy barrier keeping the tube from collapsing approaches zero as the tube radius increases. We also demonstrate why collapse with a wide indenter may be difficult to observe in narrow tubes. A reduced-order model is developed for the dynamics of the carbon nanotube atomic force microscope probes. Bending behavior of the nanotube probe is modeled using Euler's elastica. A nonlinear moment-curvature relationship is implemeneted to account for the ovalization of the cross section of the nanotube during bending. Van der Waal forces acting between tube and the substrate is integrated over the surface of the tube and used as distributed follower forces acting on the equivalent elastica. Approximating the behavior of the nanotube with an elastica proved to be a very effiecient technique for modeling these nanostructures.

Three-dimensional finite element analysis for high velocity impact. [of projectiles from space debris

NASA Technical Reports Server (NTRS)

Chan, S. T. K.; Lee, C. H.; Brashears, M. R.

1975-01-01

A finite element algorithm for solving unsteady, three-dimensional high velocity impact problems is presented. A computer program was developed based on the Eulerian hydroelasto-viscoplastic formulation and the utilization of the theorem of weak solutions. The equations solved consist of conservation of mass, momentum, and energy, equation of state, and appropriate constitutive equations. The solution technique is a time-dependent finite element analysis utilizing three-dimensional isoparametric elements, in conjunction with a generalized two-step time integration scheme. The developed code was demonstrated by solving one-dimensional as well as three-dimensional impact problems for both the inviscid hydrodynamic model and the hydroelasto-viscoplastic model.

A Hybrid Numerical Analysis Method for Structural Health Monitoring

NASA Technical Reports Server (NTRS)

Forth, Scott C.; Staroselsky, Alexander

2001-01-01

A new hybrid surface-integral-finite-element numerical scheme has been developed to model a three-dimensional crack propagating through a thin, multi-layered coating. The finite element method was used to model the physical state of the coating (far field), and the surface integral method was used to model the fatigue crack growth. The two formulations are coupled through the need to satisfy boundary conditions on the crack surface and the external boundary. The coupling is sufficiently weak that the surface integral mesh of the crack surface and the finite element mesh of the uncracked volume can be set up independently. Thus when modeling crack growth, the finite element mesh can remain fixed for the duration of the simulation as the crack mesh is advanced. This method was implemented to evaluate the feasibility of fabricating a structural health monitoring system for real-time detection of surface cracks propagating in engine components. In this work, the authors formulate the hybrid surface-integral-finite-element method and discuss the mechanical issues of implementing a structural health monitoring system in an aircraft engine environment.

Coupled Structural, Thermal, Phase-change and Electromagnetic Analysis for Superconductors, Volume 2

NASA Technical Reports Server (NTRS)

Felippa, C. A.; Farhat, C.; Park, K. C.; Militello, C.; Schuler, J. J.

1996-01-01

Described are the theoretical development and computer implementation of reliable and efficient methods for the analysis of coupled mechanical problems that involve the interaction of mechanical, thermal, phase-change and electromag subproblems. The focus application has been the modeling of superconductivity and associated quantum-state phase change phenomena. In support of this objective the work has addressed the following issues: (1) development of variational principles for finite elements, (2) finite element modeling of the electromagnetic problem, (3) coupling of thermel and mechanical effects, and (4) computer implementation and solution of the superconductivity transition problem. The main accomplishments have been: (1) the development of the theory of parametrized and gauged variational principles, (2) the application of those principled to the construction of electromagnetic, thermal and mechanical finite elements, and (3) the coupling of electromagnetic finite elements with thermal and superconducting effects, and (4) the first detailed finite element simulations of bulk superconductors, in particular the Meissner effect and the nature of the normal conducting boundary layer. The theoretical development is described in two volumes. Volume 1 describes mostly formulation specific problems. Volume 2 describes generalization of those formulations.

Accurate traveltime computation in complex anisotropic media with discontinuous Galerkin method

NASA Astrophysics Data System (ADS)

Le Bouteiller, P.; Benjemaa, M.; Métivier, L.; Virieux, J.

2017-12-01

Travel time computation is of major interest for a large range of geophysical applications, among which source localization and characterization, phase identification, data windowing and tomography, from decametric scale up to global Earth scale.Ray-tracing tools, being essentially 1D Lagrangian integration along a path, have been used for their efficiency but present some drawbacks, such as a rather difficult control of the medium sampling. Moreover, they do not provide answers in shadow zones. Eikonal solvers, based on an Eulerian approach, have attracted attention in seismology with the pioneering work of Vidale (1988), while such approach has been proposed earlier by Riznichenko (1946). They have been used now for first-arrival travel-time tomography at various scales (Podvin & Lecomte (1991). The framework for solving this non-linear partial differential equation is now well understood and various finite-difference approaches have been proposed, essentially for smooth media. We propose a novel finite element approach which builds a precise solution for strongly heterogeneous anisotropic medium (still in the limit of Eikonal validity). The discontinuous Galerkin method we have developed allows local refinement of the mesh and local high orders of interpolation inside elements. High precision of the travel times and its spatial derivatives is obtained through this formulation. This finite element method also honors boundary conditions, such as complex topographies and absorbing boundaries for mimicking an infinite medium. Applications from travel-time tomography, slope tomography are expected, but also for migration and take-off angles estimation, thanks to the accuracy obtained when computing first-arrival times.References:Podvin, P. and Lecomte, I., 1991. Finite difference computation of traveltimes in very contrasted velocity model: a massively parallel approach and its associated tools, Geophys. J. Int., 105, 271-284.Riznichenko, Y., 1946. Geometrical seismics of layered media, Trudy Inst. Theor. Geophysics, Vol II, Moscow (in Russian).Vidale, J., 1988. Finite-difference calculation of travel times, Bull. seism. Soc. Am., 78, 2062-2076.

Single-trabecula building block for large-scale finite element models of cancellous bone.

PubMed

Dagan, D; Be'ery, M; Gefen, A

2004-07-01

Recent development of high-resolution imaging of cancellous bone allows finite element (FE) analysis of bone tissue stresses and strains in individual trabeculae. However, specimen-specific stress/strain analyses can include effects of anatomical variations and local damage that can bias the interpretation of the results from individual specimens with respect to large populations. This study developed a standard (generic) 'building-block' of a trabecula for large-scale FE models. Being parametric and based on statistics of dimensions of ovine trabeculae, this building block can be scaled for trabecular thickness and length and be used in commercial or custom-made FE codes to construct generic, large-scale FE models of bone, using less computer power than that currently required to reproduce the accurate micro-architecture of trabecular bone. Orthogonal lattices constructed with this building block, after it was scaled to trabeculae of the human proximal femur, provided apparent elastic moduli of approximately 150 MPa, in good agreement with experimental data for the stiffness of cancellous bone from this site. Likewise, lattices with thinner, osteoporotic-like trabeculae could predict a reduction of approximately 30% in the apparent elastic modulus, as reported in experimental studies of osteoporotic femora. Based on these comparisons, it is concluded that the single-trabecula element developed in the present study is well-suited for representing cancellous bone in large-scale generic FE simulations.

An extended algebraic variational multiscale-multigrid-multifractal method (XAVM4) for large-eddy simulation of turbulent two-phase flow

NASA Astrophysics Data System (ADS)

Rasthofer, U.; Wall, W. A.; Gravemeier, V.

2018-04-01

A novel and comprehensive computational method, referred to as the eXtended Algebraic Variational Multiscale-Multigrid-Multifractal Method (XAVM4), is proposed for large-eddy simulation of the particularly challenging problem of turbulent two-phase flow. The XAVM4 involves multifractal subgrid-scale modeling as well as a Nitsche-type extended finite element method as an approach for two-phase flow. The application of an advanced structural subgrid-scale modeling approach in conjunction with a sharp representation of the discontinuities at the interface between two bulk fluids promise high-fidelity large-eddy simulation of turbulent two-phase flow. The high potential of the XAVM4 is demonstrated for large-eddy simulation of turbulent two-phase bubbly channel flow, that is, turbulent channel flow carrying a single large bubble of the size of the channel half-width in this particular application.

Finite element simulation of structural performance on flexible pavements with stabilized base/treated sub-base materials under accelerated loading : research project capsule.

DOT National Transportation Integrated Search

2008-12-01

PROBLEM: The full-scale accelerated pavement testing (APT) provides a unique tool for pavement : engineers to directly collect pavement performance and failure data under heavy : wheel loading. However, running a full-scale APT experiment is very exp...

Cross-ply laminates with holes in compression - Straight free-edge stresses determined by two- to three-dimensional global/local finite element analysis

NASA Technical Reports Server (NTRS)

Thompson, Danniella Muheim; Griffin, O. Hayden, Jr.; Vidussoni, Marco A.

1990-01-01

A practical example of applying two- to three-dimensional (2- to 3-D) global/local finite element analysis to laminated composites is presented. Cross-ply graphite/epoxy laminates of 0.1-in. (0.254-cm) thickness with central circular holes ranging from 1 to 6 in. (2.54 to 15.2 cm) in diameter, subjected to in-plane compression were analyzed. Guidelines for full three-dimensional finite element analysis and two- to three-dimensional global/local analysis of interlaminar stresses at straight free edges of laminated composites are included. The larger holes were found to reduce substantially the interlaminar stresses at the straight free-edge in proximity to the hole. Three-dimensional stress results were obtained for thin laminates which require prohibitive computer resources for full three-dimensional analyses of comparative accuracy.

Determination of apparent coupling factors for adhesive bonded acrylic plates using SEAL approach

NASA Astrophysics Data System (ADS)

Pankaj, Achuthan. C.; Shivaprasad, M. V.; Murigendrappa, S. M.

2018-04-01

Apparent coupling loss factors (CLF) and velocity responses has been computed for two lap joined adhesive bonded plates using finite element and experimental statistical energy analysis like approach. A finite element model of the plates has been created using ANSYS software. The statistical energy parameters have been computed using the velocity responses obtained from a harmonic forced excitation analysis. Experiments have been carried out for two different cases of adhesive bonded joints and the results have been compared with the apparent coupling factors and velocity responses obtained from finite element analysis. The results obtained from the studies signify the importance of modeling of adhesive bonded joints in computation of the apparent coupling factors and its further use in computation of energies and velocity responses using statistical energy analysis like approach.

Stability and natural vibration analysis of laminated plates by using a mixed element based on a refined plate theory

NASA Technical Reports Server (NTRS)

Putcha, N. S.; Reddy, J. N.

1986-01-01

A mixed shear flexible finite element, with relaxed continuity, is developed for the geometrically linear and nonlinear analysis of layered anisotropic plates. The element formulation is based on a refined higher order theory which satisfies the zero transverse shear stress boundary conditions on the top and bottom faces of the plate and requires no shear correction coefficients. The mixed finite element developed herein consists of eleven degrees of freedom per node which include three displacements, two rotations and six moment resultants. The element is evaluated for its accuracy in the analysis of the stability and vibration of anisotropic rectangular plates with different lamination schemes and boundary conditions. The mixed finite element described here for the higher order theory gives very accurate results for buckling loads and natural frequencies.

Updating finite element dynamic models using an element-by-element sensitivity methodology

NASA Technical Reports Server (NTRS)

Farhat, Charbel; Hemez, Francois M.

1993-01-01

A sensitivity-based methodology for improving the finite element model of a given structure using test modal data and a few sensors is presented. The proposed method searches for both the location and sources of the mass and stiffness errors and does not interfere with the theory behind the finite element model while correcting these errors. The updating algorithm is derived from the unconstrained minimization of the squared L sub 2 norms of the modal dynamic residuals via an iterative two-step staggered procedure. At each iteration, the measured mode shapes are first expanded assuming that the model is error free, then the model parameters are corrected assuming that the expanded mode shapes are exact. The numerical algorithm is implemented in an element-by-element fashion and is capable of 'zooming' on the detected error locations. Several simulation examples which demonstate the potential of the proposed methodology are discussed.

User's guide for analysis of finite elastoplastic deformation: The FIPDEF and FIPAX programs for the CDC 6600

NASA Technical Reports Server (NTRS)

Osias, J. R.

1974-01-01

Computer programs are presented which provide incremental finite-element analysis capability for problems of quasi-static, finite, elastoplastic deformation in two spatial dimensions (plane strain, plane stress, axisymmetric). Monotonic or cyclic loading of isotropic hardening materials is considered. The only restriction on the form of the stress-strain curve is that the rate of work hardening exceed some small positive value. The user's guide assumes familiarity with both finite-element analysis and FORTRAN IV programming for the CDC 6600. Sufficient information is provided to support problem solving ultization of the programs.

Stress Recovery and Error Estimation for 3-D Shell Structures

NASA Technical Reports Server (NTRS)

Riggs, H. R.

2000-01-01

The C1-continuous stress fields obtained from finite element analyses are in general lower- order accurate than are the corresponding displacement fields. Much effort has focussed on increasing their accuracy and/or their continuity, both for improved stress prediction and especially error estimation. A previous project developed a penalized, discrete least squares variational procedure that increases the accuracy and continuity of the stress field. The variational problem is solved by a post-processing, 'finite-element-type' analysis to recover a smooth, more accurate, C1-continuous stress field given the 'raw' finite element stresses. This analysis has been named the SEA/PDLS. The recovered stress field can be used in a posteriori error estimators, such as the Zienkiewicz-Zhu error estimator or equilibrium error estimators. The procedure was well-developed for the two-dimensional (plane) case involving low-order finite elements. It has been demonstrated that, if optimal finite element stresses are used for the post-processing, the recovered stress field is globally superconvergent. Extension of this work to three dimensional solids is straightforward. Attachment: Stress recovery and error estimation for shell structure (abstract only). A 4-node, shear-deformable flat shell element developed via explicit Kirchhoff constraints (abstract only). A novel four-node quadrilateral smoothing element for stress enhancement and error estimation (abstract only).

A boundary element alternating method for two-dimensional mixed-mode fracture problems

NASA Technical Reports Server (NTRS)

Raju, I. S.; Krishnamurthy, T.

1992-01-01

A boundary element alternating method, denoted herein as BEAM, is presented for two dimensional fracture problems. This is an iterative method which alternates between two solutions. An analytical solution for arbitrary polynomial normal and tangential pressure distributions applied to the crack faces of an embedded crack in an infinite plate is used as the fundamental solution in the alternating method. A boundary element method for an uncracked finite plate is the second solution. For problems of edge cracks a technique of utilizing finite elements with BEAM is presented to overcome the inherent singularity in boundary element stress calculation near the boundaries. Several computational aspects that make the algorithm efficient are presented. Finally, the BEAM is applied to a variety of two dimensional crack problems with different configurations and loadings to assess the validity of the method. The method gives accurate stress intensity factors with minimal computing effort.

A Cellular Automaton / Finite Element model for predicting grain texture development in galvanized coatings

NASA Astrophysics Data System (ADS)

Guillemot, G.; Avettand-Fènoël, M.-N.; Iosta, A.; Foct, J.

2011-01-01

Hot-dipping galvanizing process is a widely used and efficient way to protect steel from corrosion. We propose to master the microstructure of zinc grains by investigating the relevant process parameters. In order to improve the texture of this coating, we model grain nucleation and growth processes and simulate the zinc solid phase development. A coupling scheme model has been applied with this aim. This model improves a previous two-dimensional model of the solidification process. It couples a cellular automaton (CA) approach and a finite element (FE) method. CA grid and FE mesh are superimposed on the same domain. The grain development is simulated at the micro-scale based on the CA grid. A nucleation law is defined using a Gaussian probability and a random set of nucleating cells. A crystallographic orientation is defined for each one with a choice of Euler's angle (Ψ,θ,φ). A small growing shape is then associated to each cell in the mushy domain and a dendrite tip kinetics is defined using the model of Kurz [2]. The six directions of basal plane and the two perpendicular directions develop in each mushy cell. During each time step, cell temperature and solid fraction are then determined at micro-scale using the enthalpy conservation relation and variations are reassigned at macro-scale. This coupling scheme model enables to simulate the three-dimensional growing kinetics of the zinc grain in a two-dimensional approach. Grain structure evolutions for various cooling times have been simulated. Final grain structure has been compared to EBSD measurements. We show that the preferentially growth of dendrite arms in the basal plane of zinc grains is correctly predicted. The described coupling scheme model could be applied for simulated other product or manufacturing processes. It constitutes an approach gathering both micro and macro scale models.

Remote sensing applied to numerical modelling. [water resources pollution

NASA Technical Reports Server (NTRS)

Sengupta, S.; Lee, S. S.; Veziroglu, T. N.; Bland, R.

1975-01-01

Progress and remaining difficulties in the construction of predictive mathematical models of large bodies of water as ecosystems are reviewed. Surface temperature is at present the only variable than can be measured accurately and reliably by remote sensing techniques, but satellite infrared data are of sufficient resolution for macro-scale modeling of oceans and large lakes, and airborne radiometers are useful in meso-scale analysis (of lakes, bays, and thermal plumes). Finite-element and finite-difference techniques applied to the solution of relevant coupled time-dependent nonlinear partial differential equations are compared, and the specific problem of the Biscayne Bay and environs ecosystem is tackled in a finite-differences treatment using the rigid-lid model and a rigid-line grid system.

Vibration Response Models of a Stiffened Aluminum Plate Excited by a Shaker

NASA Technical Reports Server (NTRS)

Cabell, Randolph H.

2008-01-01

Numerical models of structural-acoustic interactions are of interest to aircraft designers and the space program. This paper describes a comparison between two energy finite element codes, a statistical energy analysis code, a structural finite element code, and the experimentally measured response of a stiffened aluminum plate excited by a shaker. Different methods for modeling the stiffeners and the power input from the shaker are discussed. The results show that the energy codes (energy finite element and statistical energy analysis) accurately predicted the measured mean square velocity of the plate. In addition, predictions from an energy finite element code had the best spatial correlation with measured velocities. However, predictions from a considerably simpler, single subsystem, statistical energy analysis model also correlated well with the spatial velocity distribution. The results highlight a need for further work to understand the relationship between modeling assumptions and the prediction results.

Adaptive mixed finite element methods for Darcy flow in fractured porous media

NASA Astrophysics Data System (ADS)

Chen, Huangxin; Salama, Amgad; Sun, Shuyu

2016-10-01

In this paper, we propose adaptive mixed finite element methods for simulating the single-phase Darcy flow in two-dimensional fractured porous media. The reduced model that we use for the simulation is a discrete fracture model coupling Darcy flows in the matrix and the fractures, and the fractures are modeled by one-dimensional entities. The Raviart-Thomas mixed finite element methods are utilized for the solution of the coupled Darcy flows in the matrix and the fractures. In order to improve the efficiency of the simulation, we use adaptive mixed finite element methods based on novel residual-based a posteriori error estimators. In addition, we develop an efficient upscaling algorithm to compute the effective permeability of the fractured porous media. Several interesting examples of Darcy flow in the fractured porous media are presented to demonstrate the robustness of the algorithm.

Creating a Test Validated Structural Dynamic Finite Element Model of the Multi-Utility Technology Test Bed Aircraft

NASA Technical Reports Server (NTRS)

Pak, Chan-Gi; Truong, Samson S.

2014-01-01

Small modeling errors in the finite element model will eventually induce errors in the structural flexibility and mass, thus propagating into unpredictable errors in the unsteady aerodynamics and the control law design. One of the primary objectives of Multi Utility Technology Test Bed, X-56A, aircraft is the flight demonstration of active flutter suppression, and therefore in this study, the identification of the primary and secondary modes for the structural model tuning based on the flutter analysis of X-56A. The ground vibration test validated structural dynamic finite element model of the X-56A is created in this study. The structural dynamic finite element model of the X-56A is improved using a model tuning tool. In this study, two different weight configurations of the X-56A have been improved in a single optimization run.

POSTPROCESSING MIXED FINITE ELEMENT METHODS FOR SOLVING CAHN-HILLIARD EQUATION: METHODS AND ERROR ANALYSIS

PubMed Central

Wang, Wansheng; Chen, Long; Zhou, Jie

2015-01-01

A postprocessing technique for mixed finite element methods for the Cahn-Hilliard equation is developed and analyzed. Once the mixed finite element approximations have been computed at a fixed time on the coarser mesh, the approximations are postprocessed by solving two decoupled Poisson equations in an enriched finite element space (either on a finer grid or a higher-order space) for which many fast Poisson solvers can be applied. The nonlinear iteration is only applied to a much smaller size problem and the computational cost using Newton and direct solvers is negligible compared with the cost of the linear problem. The analysis presented here shows that this technique remains the optimal rate of convergence for both the concentration and the chemical potential approximations. The corresponding error estimate obtained in our paper, especially the negative norm error estimates, are non-trivial and different with the existing results in the literatures. PMID:27110063

Failure Behavior Characterization of Mo-Modified Ti Surface by Impact Test and Finite Element Analysis

NASA Astrophysics Data System (ADS)

Ma, Yong; Qin, Jianfeng; Zhang, Xiangyu; Lin, Naiming; Huang, Xiaobo; Tang, Bin

2015-07-01

Using the impact test and finite element simulation, the failure behavior of the Mo-modified layer on pure Ti was investigated. In the impact test, four loads of 100, 300, 500, and 700 N and 104 impacts were adopted. The three-dimensional residual impact dents were examined using an optical microscope (Olympus-DSX500i), indicating that the impact resistance of the Ti surface was improved. Two failure modes cohesive and wearing were elucidated by electron backscatter diffraction and energy-dispersive spectrometer performed in a field-emission scanning electron microscope. Through finite element forward analysis performed at a typical impact load of 300 N, stress-strain distributions in the Mo-modified Ti were quantitatively determined. In addition, the failure behavior of the Mo-modified layer was determined and an ideal failure model was proposed for high-load impact, based on the experimental and finite element forward analysis results.

ESCHER: An interactive mesh-generating editor for preparing finite-element input

NASA Technical Reports Server (NTRS)

Oakes, W. R., Jr.

1984-01-01

ESCHER is an interactive mesh generation and editing program designed to help the user create a finite-element mesh, create additional input for finite-element analysis, including initial conditions, boundary conditions, and slidelines, and generate a NEUTRAL FILE that can be postprocessed for input into several finite-element codes, including ADINA, ADINAT, DYNA, NIKE, TSAAS, and ABUQUS. Two important ESCHER capabilities, interactive geometry creation and mesh archival storge are described in detail. Also described is the interactive command language and the use of interactive graphics. The archival storage and restart file is a modular, entity-based mesh data file. Modules of this file correspond to separate editing modes in the mesh editor, with data definition syntax preserved between the interactive commands and the archival storage file. Because ESCHER was expected to be highly interactive, extensive user documentation was provided in the form of an interactive HELP package.

Life assessment of structural components using inelastic finite element analyses

NASA Technical Reports Server (NTRS)

Arya, Vinod K.; Halford, Gary R.

1993-01-01

The need for enhanced and improved performance of structural components subject to severe cyclic thermal/mechanical loadings, such as in the aerospace industry, requires development of appropriate solution technologies involving time-dependent inelastic analyses. Such analyses are mandatory to predict local stress-strain response and to assess more accurately the cyclic life time of structural components. The NASA-Lewis Research Center is cognizant of this need. As a result of concerted efforts at Lewis during the last few years, several such finite element solution technologies (in conjunction with the finite element program MARC) were developed and successfully applied to numerous uniaxial and multiaxial problems. These solution technologies, although developed for use with MARC program, are general in nature and can easily be extended for adaptation with other finite element programs such as ABAQUS, ANSYS, etc. The description and results obtained from two such inelastic finite element solution technologies are presented. The first employs a classical (non-unified) creep-plasticity model. An application of this technology is presented for a hypersonic inlet cowl-lip problem. The second of these technologies uses a unified creep-plasticity model put forth by Freed. The structural component for which this finite element solution technology is illustrated, is a cylindrical rocket engine thrust chamber. The advantages of employing a viscoplastic model for nonlinear time-dependent structural analyses are demonstrated. The life analyses for cowl-lip and cylindrical thrust chambers are presented. These analyses are conducted by using the stress-strain response of these components obtained from the corresponding finite element analyses.

Coupling of a 3D Finite Element Model of Cardiac Ventricular Mechanics to Lumped Systems Models of the Systemic and Pulmonic Circulation

PubMed Central

Kerckhoffs, Roy C. P.; Neal, Maxwell L.; Gu, Quan; Bassingthwaighte, James B.; Omens, Jeff H.; McCulloch, Andrew D.

2010-01-01

In this study we present a novel, robust method to couple finite element (FE) models of cardiac mechanics to systems models of the circulation (CIRC), independent of cardiac phase. For each time step through a cardiac cycle, left and right ventricular pressures were calculated using ventricular compliances from the FE and CIRC models. These pressures served as boundary conditions in the FE and CIRC models. In succeeding steps, pressures were updated to minimize cavity volume error (FE minus CIRC volume) using Newton iterations. Coupling was achieved when a predefined criterion for the volume error was satisfied. Initial conditions for the multi-scale model were obtained by replacing the FE model with a varying elastance model, which takes into account direct ventricular interactions. Applying the coupling, a novel multi-scale model of the canine cardiovascular system was developed. Global hemodynamics and regional mechanics were calculated for multiple beats in two separate simulations with a left ventricular ischemic region and pulmonary artery constriction, respectively. After the interventions, global hemodynamics changed due to direct and indirect ventricular interactions, in agreement with previously published experimental results. The coupling method allows for simulations of multiple cardiac cycles for normal and pathophysiology, encompassing levels from cell to system. PMID:17111210

Dynamic finite element analysis and moving particle simulation of human enamel on a microscale.

PubMed

Yamaguchi, Satoshi; Coelho, Paulo G; Thompson, Van P; Tovar, Nick; Yamauchi, Junpei; Imazato, Satoshi

2014-12-01

The study of biomechanics of deformation and fracture of hard biological tissues involving organic matrix remains a challenge as variations in mechanical properties and fracture mode may have time-dependency. Finite element analysis (FEA) has been widely used but the shortcomings of FEA such as the long computation time owing to re-meshing in simulating fracture mechanics have warranted the development of alternative computational methods with higher throughput. The aim of this study was to compare dynamic two-dimensional FEA and moving particle simulation (MPS) when assuming a plane strain condition in the modeling of human enamel on a reduced scale. Two-dimensional models with the same geometry were developed for MPS and FEA and tested in tension generated with a single step of displacement. The displacement, velocity, pressure, and stress levels were compared and Spearman׳s rank-correlation coefficients R were calculated (p<0.001). The MPS and FEA were significantly correlated for displacement, velocity, pressure, and Y-stress. The MPS may be further developed as an alternative approach without mesh generation to simulate deformation and fracture phenomena of dental and potentially other hard tissues with complex microstructure. Copyright © 2014 Elsevier Ltd. All rights reserved.

Ceramic component reliability with the restructured NASA/CARES computer program

NASA Technical Reports Server (NTRS)

Powers, Lynn M.; Starlinger, Alois; Gyekenyesi, John P.

1992-01-01

The Ceramics Analysis and Reliability Evaluation of Structures (CARES) integrated design program on statistical fast fracture reliability and monolithic ceramic components is enhanced to include the use of a neutral data base, two-dimensional modeling, and variable problem size. The data base allows for the efficient transfer of element stresses, temperatures, and volumes/areas from the finite element output to the reliability analysis program. Elements are divided to insure a direct correspondence between the subelements and the Gaussian integration points. Two-dimensional modeling is accomplished by assessing the volume flaw reliability with shell elements. To demonstrate the improvements in the algorithm, example problems are selected from a round-robin conducted by WELFEP (WEakest Link failure probability prediction by Finite Element Postprocessors).

A New Linearized Crank-Nicolson Mixed Element Scheme for the Extended Fisher-Kolmogorov Equation

PubMed Central

Wang, Jinfeng; Li, Hong; He, Siriguleng; Gao, Wei

2013-01-01

We present a new mixed finite element method for solving the extended Fisher-Kolmogorov (EFK) equation. We first decompose the EFK equation as the two second-order equations, then deal with a second-order equation employing finite element method, and handle the other second-order equation using a new mixed finite element method. In the new mixed finite element method, the gradient ∇u belongs to the weaker (L 2(Ω))2 space taking the place of the classical H(div; Ω) space. We prove some a priori bounds for the solution for semidiscrete scheme and derive a fully discrete mixed scheme based on a linearized Crank-Nicolson method. At the same time, we get the optimal a priori error estimates in L 2 and H 1-norm for both the scalar unknown u and the diffusion term w = −Δu and a priori error estimates in (L 2)2-norm for its gradient χ = ∇u for both semi-discrete and fully discrete schemes. PMID:23864831

A new linearized Crank-Nicolson mixed element scheme for the extended Fisher-Kolmogorov equation.

PubMed

Wang, Jinfeng; Li, Hong; He, Siriguleng; Gao, Wei; Liu, Yang

2013-01-01

We present a new mixed finite element method for solving the extended Fisher-Kolmogorov (EFK) equation. We first decompose the EFK equation as the two second-order equations, then deal with a second-order equation employing finite element method, and handle the other second-order equation using a new mixed finite element method. In the new mixed finite element method, the gradient ∇u belongs to the weaker (L²(Ω))² space taking the place of the classical H(div; Ω) space. We prove some a priori bounds for the solution for semidiscrete scheme and derive a fully discrete mixed scheme based on a linearized Crank-Nicolson method. At the same time, we get the optimal a priori error estimates in L² and H¹-norm for both the scalar unknown u and the diffusion term w = -Δu and a priori error estimates in (L²)²-norm for its gradient χ = ∇u for both semi-discrete and fully discrete schemes.

Application of a finite-element model to low-frequency sound insulation in dwellings.

PubMed

Maluski, S P; Gibbs, B M

2000-10-01

The sound transmission between adjacent rooms has been modeled using a finite-element method. Predicted sound-level difference gave good agreement with experimental data using a full-scale and a quarter-scale model. Results show that the sound insulation characteristics of a party wall at low frequencies strongly depend on the modal characteristics of the sound field of both rooms and of the partition. The effect of three edge conditions of the separating wall on the sound-level difference at low frequencies was examined: simply supported, clamped, and a combination of clamped and simply supported. It is demonstrated that a clamped partition provides greater sound-level difference at low frequencies than a simply supported. It also is confirmed that the sound-pressure level difference is lower in equal room than in unequal room configurations.

Least-squares finite element solution of 3D incompressible Navier-Stokes problems

NASA Technical Reports Server (NTRS)

Jiang, Bo-Nan; Lin, Tsung-Liang; Povinelli, Louis A.

1992-01-01

Although significant progress has been made in the finite element solution of incompressible viscous flow problems. Development of more efficient methods is still needed before large-scale computation of 3D problems becomes feasible. This paper presents such a development. The most popular finite element method for the solution of incompressible Navier-Stokes equations is the classic Galerkin mixed method based on the velocity-pressure formulation. The mixed method requires the use of different elements to interpolate the velocity and the pressure in order to satisfy the Ladyzhenskaya-Babuska-Brezzi (LBB) condition for the existence of the solution. On the other hand, due to the lack of symmetry and positive definiteness of the linear equations arising from the mixed method, iterative methods for the solution of linear systems have been hard to come by. Therefore, direct Gaussian elimination has been considered the only viable method for solving the systems. But, for three-dimensional problems, the computer resources required by a direct method become prohibitively large. In order to overcome these difficulties, a least-squares finite element method (LSFEM) has been developed. This method is based on the first-order velocity-pressure-vorticity formulation. In this paper the LSFEM is extended for the solution of three-dimensional incompressible Navier-Stokes equations written in the following first-order quasi-linear velocity-pressure-vorticity formulation.

Image-Based Macro-Micro Finite Element Models of a Canine Femur with Implant Design Implications

NASA Astrophysics Data System (ADS)

Ghosh, Somnath; Krishnan, Ganapathi; Dyce, Jonathan

2006-06-01

In this paper, a comprehensive model of a bone-cement-implant assembly is developed for a canine cemented femoral prosthesis system. Various steps in this development entail profiling the canine femur contours by computed tomography (CT) scanning, computer aided design (CAD) reconstruction of the canine femur from CT images, CAD modeling of the implant from implant blue prints and CAD modeling of the interface cement. Finite element analysis of the macroscopic assembly is conducted for stress analysis in individual components of the system, accounting for variation in density and material properties in the porous bone material. A sensitivity analysis is conducted with the macroscopic model to investigate the effect of implant design variables on the stress distribution in the assembly. Subsequently, rigorous microstructural analysis of the bone incorporating the morphological intricacies is conducted. Various steps in this development include acquisition of the bone microstructural data from histological serial sectioning, stacking of sections to obtain 3D renderings of void distributions, microstructural characterization and determination of properties and, finally, microstructural stress analysis using a 3D Voronoi cell finite element method. Generation of the simulated microstructure and analysis by the 3D Voronoi cell finite element model provides a new way of modeling complex microstructures and correlating to morphological characteristics. An inverse calculation of the material parameters of bone by combining macroscopic experiments with microstructural characterization and analysis provides a new approach to evaluating properties without having to do experiments at this scale. Finally, the microstructural stresses in the femur are computed using the 3D VCFEM to study the stress distribution at the scale of the bone porosity. Significant difference is observed between the macroscopic stresses and the peak microscopic stresses at different locations.

The least-squares finite element method for low-mach-number compressible viscous flows

NASA Technical Reports Server (NTRS)

Yu, Sheng-Tao

1994-01-01

The present paper reports the development of the Least-Squares Finite Element Method (LSFEM) for simulating compressible viscous flows at low Mach numbers in which the incompressible flows pose as an extreme. Conventional approach requires special treatments for low-speed flows calculations: finite difference and finite volume methods are based on the use of the staggered grid or the preconditioning technique; and, finite element methods rely on the mixed method and the operator-splitting method. In this paper, however, we show that such difficulty does not exist for the LSFEM and no special treatment is needed. The LSFEM always leads to a symmetric, positive-definite matrix through which the compressible flow equations can be effectively solved. Two numerical examples are included to demonstrate the method: first, driven cavity flows at various Reynolds numbers; and, buoyancy-driven flows with significant density variation. Both examples are calculated by using full compressible flow equations.

Efficient Computation Of Behavior Of Aircraft Tires

NASA Technical Reports Server (NTRS)

Tanner, John A.; Noor, Ahmed K.; Andersen, Carl M.

1989-01-01

NASA technical paper discusses challenging application of computational structural mechanics to numerical simulation of responses of aircraft tires during taxing, takeoff, and landing. Presents details of three main elements of computational strategy: use of special three-field, mixed-finite-element models; use of operator splitting; and application of technique reducing substantially number of degrees of freedom. Proposed computational strategy applied to two quasi-symmetric problems: linear analysis of anisotropic tires through use of two-dimensional-shell finite elements and nonlinear analysis of orthotropic tires subjected to unsymmetric loading. Three basic types of symmetry and combinations exhibited by response of tire identified.

Contact stresses in meshing spur gear teeth: Use of an incremental finite element procedure

NASA Technical Reports Server (NTRS)

Hsieh, Chih-Ming; Huston, Ronald L.; Oswald, Fred B.

1992-01-01

Contact stresses in meshing spur gear teeth are examined. The analysis is based upon an incremental finite element procedure that simultaneously determines the stresses in the contact region between the meshing teeth. The teeth themselves are modeled by two dimensional plain strain elements. Friction effects are included, with the friction forces assumed to obey Coulomb's law. The analysis assumes that the displacements are small and that the tooth materials are linearly elastic. The analysis procedure is validated by comparing its results with those for the classical two contacting semicylinders obtained from the Hertz method. Agreement is excellent.

Frequency response function (FRF) based updating of a laser spot welded structure

NASA Astrophysics Data System (ADS)

Zin, M. S. Mohd; Rani, M. N. Abdul; Yunus, M. A.; Sani, M. S. M.; Wan Iskandar Mirza, W. I. I.; Mat Isa, A. A.

2018-04-01

The objective of this paper is to present frequency response function (FRF) based updating as a method for matching the finite element (FE) model of a laser spot welded structure with a physical test structure. The FE model of the welded structure was developed using CQUAD4 and CWELD element connectors, and NASTRAN was used to calculate the natural frequencies, mode shapes and FRF. Minimization of the discrepancies between the finite element and experimental FRFs was carried out using the exceptional numerical capability of NASTRAN Sol 200. The experimental work was performed under free-free boundary conditions using LMS SCADAS. Avast improvement in the finite element FRF was achieved using the frequency response function (FRF) based updating with two different objective functions proposed.

Nonlinear static and dynamic finite element analysis of an eccentrically loaded graphite-epoxy beam

NASA Technical Reports Server (NTRS)

Fasanella, Edwin L.; Jackson, Karen E.; Jones, Lisa E.

1991-01-01

The Dynamic Crash Analysis of Structures (DYCAT) and NIKE3D nonlinear finite element codes were used to model the static and implulsive response of an eccentrically loaded graphite-epoxy beam. A 48-ply unidirectional composite beam was tested under an eccentric axial compressive load until failure. This loading configuration was chosen to highlight the capabilities of two finite element codes for modeling a highly nonlinear, large deflection structural problem which has an exact solution. These codes are currently used to perform dynamic analyses of aircraft structures under impact loads to study crashworthiness and energy absorbing capabilities. Both beam and plate element models were developed to compare with the experimental data using the DYCAST and NIKE3D codes.

Finite element simulation of crack depth measurements in concrete using diffuse ultrasound

NASA Astrophysics Data System (ADS)

Seher, Matthias; Kim, Jin-Yeon; Jacobs, Laurence J.

2012-05-01

This research simulates the measurements of crack depth in concrete using diffuse ultrasound. The finite element method is employed to simulate the ultrasonic diffusion process around cracks with different geometrical shapes, with the goal of gaining physical insight into the data obtained from experimental measurements. The commercial finite element software Ansys is used to implement the two-dimensional concrete model. The model is validated with an analytical solution and experimental results. It is found from the simulation results that preliminary knowledge of the crack geometry is required to interpret the energy evolution curves from measurements and to correctly determine the crack depth.

NASTRAN analysis for the Airmass Sunburst model 'C' Ultralight Aircraft

NASA Technical Reports Server (NTRS)

Verbestel, John; Smith, Howard W.

1993-01-01

The purpose of this project was to create a three dimensional NASTRAN model of the Airmass Sunburst Ultralight comparable to one made for finite element analysis. A two dimensional sample problem will be calculated by hand and by NASTRAN to make sure that NASTRAN finds similar results. A three dimensional model, similar to the one analyzed by the finite element program, will be run on NASTRAN. A comparison will be done between the NASTRAN results and the finite element program results. This study will deal mainly with the aerodynamic loads on the wing and surrounding support structure at an attack angle of 10 degrees.

Finite Element in Angle Unit Sphere Meshing for Charged Particle Transport.

DOE Office of Scientific and Technical Information (OSTI.GOV)

Ortega, Mario Ivan; Drumm, Clifton R.

Finite element in angle formulations of the charged particle transport equation require the discretization of the unit sphere. In Sceptre, a three-dimensional surface mesh of a sphere is transformed into a two-dimensional mesh. Projection of a sphere onto a two-dimensional surface is well studied with map makers spending the last few centuries attempting to create maps that preserve proportion and area. Using these techniques, various meshing schemes for the unit sphere were investigated.

Numerical Study of the Effect of Presence of Geometric Singularities on the Mechanical Behavior of Laminated Plates

NASA Astrophysics Data System (ADS)

Khechai, Abdelhak; Tati, Abdelouahab; Guettala, Abdelhamid

2017-05-01

In this paper, an effort is made to understand the effects of geometric singularities on the load bearing capacity and stress distribution in thin laminated plates. Composite plates with variously shaped cutouts are frequently used in both modern and classical aerospace, mechanical and civil engineering structures. Finite element investigation is undertaken to show the effect of geometric singularities on stress distribution. In this study, the stress concentration factors (SCFs) in cross-and-angle-ply laminated as well as in isotropic plates subjected to uniaxial loading are studied using a quadrilateral finite element of four nodes with thirty-two degrees-of-freedom per element. The varying parameters such as the cutout shape and hole sizes (a/b) are considered. The numerical results obtained by the present element are compared favorably with those obtained using the finite element software Freefem++ and the analytic findings published in literature, which demonstrates the accuracy of the present element. Freefem++ is open source software based on the finite element method, which could be helpful to study and improving the analyses of the stress distribution in composite plates with cutouts. The Freefem++ and the quadrilateral finite element formulations will be given in the beginning of this paper. Finally, to show the effect of the fiber orientation angle and anisotropic modulus ratio on the (SCF), number of figures are given for various ratio (a/b).

A geometrical multi-scale numerical method for coupled hygro-thermo-mechanical problems in photovoltaic laminates.

PubMed

Lenarda, P; Paggi, M

A comprehensive computational framework based on the finite element method for the simulation of coupled hygro-thermo-mechanical problems in photovoltaic laminates is herein proposed. While the thermo-mechanical problem takes place in the three-dimensional space of the laminate, moisture diffusion occurs in a two-dimensional domain represented by the polymeric layers and by the vertical channel cracks in the solar cells. Therefore, a geometrical multi-scale solution strategy is pursued by solving the partial differential equations governing heat transfer and thermo-elasticity in the three-dimensional space, and the partial differential equation for moisture diffusion in the two dimensional domains. By exploiting a staggered scheme, the thermo-mechanical problem is solved first via a fully implicit solution scheme in space and time, with a specific treatment of the polymeric layers as zero-thickness interfaces whose constitutive response is governed by a novel thermo-visco-elastic cohesive zone model based on fractional calculus. Temperature and relative displacements along the domains where moisture diffusion takes place are then projected to the finite element model of diffusion, coupled with the thermo-mechanical problem by the temperature and crack opening dependent diffusion coefficient. The application of the proposed method to photovoltaic modules pinpoints two important physical aspects: (i) moisture diffusion in humidity freeze tests with a temperature dependent diffusivity is a much slower process than in the case of a constant diffusion coefficient; (ii) channel cracks through Silicon solar cells significantly enhance moisture diffusion and electric degradation, as confirmed by experimental tests.

Combined tension and bending testing of tapered composite laminates

NASA Astrophysics Data System (ADS)

O'Brien, T. Kevin; Murri, Gretchen B.; Hagemeier, Rick; Rogers, Charles

1994-11-01

A simple beam element used at Bell Helicopter was incorporated in the Computational Mechanics Testbed (COMET) finite element code at the Langley Research Center (LaRC) to analyze the responce of tappered laminates typical of flexbeams in composite rotor hubs. This beam element incorporated the influence of membrane loads on the flexural response of the tapered laminate configurations modeled and tested in a combined axial tension and bending (ATB) hydraulic load frame designed and built at LaRC. The moments generated from the finite element model were used in a tapered laminated plate theory analysis to estimate axial stresses on the surface of the tapered laminates due to combined bending and tension loads. Surfaces strains were calculated and compared to surface strains measured using strain gages mounted along the laminate length. The strain distributions correlated reasonably well with the analysis. The analysis was then used to examine the surface strain distribution in a non-linear tapered laminate where a similarly good correlation was obtained. Results indicate that simple finite element beam models may be used to identify tapered laminate configurations best suited for simulating the response of a composite flexbeam in a full scale rotor hub.

Multi-scale modeling of multi-component reactive transport in geothermal aquifers

NASA Astrophysics Data System (ADS)

Nick, Hamidreza M.; Raoof, Amir; Wolf, Karl-Heinz; Bruhn, David

2014-05-01

In deep geothermal systems heat and chemical stresses can cause physical alterations, which may have a significant effect on flow and reaction rates. As a consequence it will lead to changes in permeability and porosity of the formations due to mineral precipitation and dissolution. Large-scale modeling of reactive transport in such systems is still challenging. A large area of uncertainty is the way in which the pore-scale information controlling the flow and reaction will behave at a larger scale. A possible choice is to use constitutive relationships relating, for example the permeability and porosity evolutions to the change in the pore geometry. While determining such relationships through laboratory experiments may be limited, pore-network modeling provides an alternative solution. In this work, we introduce a new workflow in which a hybrid Finite-Element Finite-Volume method [1,2] and a pore network modeling approach [3] are employed. Using the pore-scale model, relevant constitutive relations are developed. These relations are then embedded in the continuum-scale model. This approach enables us to study non-isothermal reactive transport in porous media while accounting for micro-scale features under realistic conditions. The performance and applicability of the proposed model is explored for different flow and reaction regimes. References: 1. Matthäi, S.K., et al.: Simulation of solute transport through fractured rock: a higher-order accurate finite-element finite-volume method permitting large time steps. Transport in porous media 83.2 (2010): 289-318. 2. Nick, H.M., et al.: Reactive dispersive contaminant transport in coastal aquifers: Numerical simulation of a reactive Henry problem. Journal of contaminant hydrology 145 (2012), 90-104. 3. Raoof A., et al.: PoreFlow: A Complex pore-network model for simulation of reactive transport in variably saturated porous media, Computers & Geosciences, 61, (2013), 160-174.

Implementation of a finite-amplitude method in a relativistic meson-exchange model

NASA Astrophysics Data System (ADS)

Sun, Xuwei; Lu, Dinghui

2017-08-01

The finite-amplitude method is a feasible numerical approach to large scale random phase approximation calculations. It avoids the storage and calculation of residual interaction elements as well as the diagonalization of the RPA matrix, which will be prohibitive when the configuration space is huge. In this work we finished the implementation of a finite-amplitude method in a relativistic meson exchange mean field model with axial symmetry. The direct variation approach makes our FAM scheme capable of being extended to the multipole excitation case.

Penalty-Based Interface Technology for Prediction of Delamination Growth in Laminated Structures

NASA Technical Reports Server (NTRS)

Averill, Ronald C.

2004-01-01

An effective interface element technology has been developed for connecting and simulating crack growth between independently modeled finite element subdomains (e.g., composite plies). This method has been developed using penalty constraints and allows coupling of finite element models whose nodes do not necessarily coincide along their common interface. Additionally, the present formulation leads to a computational approach that is very efficient and completely compatible with existing commercial software. The present interface element has been implemented in the commercial finite element code ABAQUS as a User Element Subroutine (UEL), making it easy to test the approach for a wide range of problems. The interface element technology has been formulated to simulate delamination growth in composite laminates. Thanks to its special features, the interface element approach makes it possible to release portions of the interface surface whose length is smaller than that of the finite elements. In addition, the penalty parameter can vary within the interface element, allowing the damage model to be applied to a desired fraction of the interface between the two meshes. Results for double cantilever beam DCB, end-loaded split (ELS) and fixed-ratio mixed mode (FRMM) specimens are presented. These results are compared to measured data to assess the ability of the present damage model to simulate crack growth.

Discontinuous Galerkin Methods for NonLinear Differential Systems

NASA Technical Reports Server (NTRS)

Barth, Timothy; Mansour, Nagi (Technical Monitor)

2001-01-01

This talk considers simplified finite element discretization techniques for first-order systems of conservation laws equipped with a convex (entropy) extension. Using newly developed techniques in entropy symmetrization theory, simplified forms of the discontinuous Galerkin (DG) finite element method have been developed and analyzed. The use of symmetrization variables yields numerical schemes which inherit global entropy stability properties of the PDE (partial differential equation) system. Central to the development of the simplified DG methods is the Eigenvalue Scaling Theorem which characterizes right symmetrizers of an arbitrary first-order hyperbolic system in terms of scaled eigenvectors of the corresponding flux Jacobian matrices. A constructive proof is provided for the Eigenvalue Scaling Theorem with detailed consideration given to the Euler equations of gas dynamics and extended conservation law systems derivable as moments of the Boltzmann equation. Using results from kinetic Boltzmann moment closure theory, we then derive and prove energy stability for several approximate DG fluxes which have practical and theoretical merit.

Application of finite elements heterogeneous multi-scale method to eddy currents non destructive testing of carbon composites material

NASA Astrophysics Data System (ADS)

Khebbab, Mohamed; Feliachi, Mouloud; El Hadi Latreche, Mohamed

2018-03-01

In this present paper, a simulation of eddy current non-destructive testing (EC NDT) on unidirectional carbon fiber reinforced polymer is performed; for this magneto-dynamic formulation in term of magnetic vector potential is solved using finite element heterogeneous multi-scale method (FE HMM). FE HMM has as goal to compute the homogenized solution without calculating the homogenized tensor explicitly, the solution is based only on the physical characteristic known in micro domain. This feature is well adapted to EC NDT to evaluate defect in carbon composite material in microscopic scale, where the defect detection is performed by coil impedance measurement; the measurement value is intimately linked to material characteristic in microscopic level. Based on this, our model can handle different defects such as: cracks, inclusion, internal electrical conductivity changes, heterogeneities, etc. The simulation results were compared with the solution obtained with homogenized material using mixture law, a good agreement was found.

Efficient and robust compositional two-phase reservoir simulation in fractured media

NASA Astrophysics Data System (ADS)

Zidane, A.; Firoozabadi, A.

2015-12-01

Compositional and compressible two-phase flow in fractured media has wide applications including CO2 injection. Accurate simulations are currently based on the discrete fracture approach using the cross-flow equilibrium model. In this approach the fractures and a small part of the matrix blocks are combined to form a grid cell. The major drawback is low computational efficiency. In this work we use the discrete-fracture approach to model the fractures where the fracture entities are described explicitly in the computational domain. We use the concept of cross-flow equilibrium in the fractures (FCFE). This allows using large matrix elements in the neighborhood of the fractures. We solve the fracture transport equations implicitly to overcome the Courant-Freidricks-Levy (CFL) condition in the small fracture elements. Our implicit approach is based on calculation of the derivative of the molar concentration of component i in phase (cαi ) with respect to the total molar concentration (ci ) at constant volume V and temperature T. This contributes to significant speed up of the code. The hybrid mixed finite element method (MFE) is used to solve for the velocity in both the matrix and the fractures coupled with the discontinuous Galerkin (DG) method to solve the species transport equations in the matrix, and a finite volume (FV) discretization in the fractures. In large scale problems the proposed approach is orders of magnitude faster than the existing models.

An experimental and computational investigation of dynamic ductile fracture in stainless steel welds

NASA Astrophysics Data System (ADS)

Kothnur, Vasanth Srinivasa

The high strain rate viscoplastic flow and fracture behavior of NITRONIC-50 and AL6XN stainless steel weldments are studied under dynamic loading conditions. The study is primarily motivated by interest in modeling the micromechanics of dynamic ductile failure in heterogeneous weldments. The high strain rate response of specimens machined from the parent, weld and heat-affected zones of NITRONIC-50 and AL6XN weldments is reported here on the basis of experiments conducted in a compression Kolsky bar configuration. The failure response of specimens prepared from the various material zones is investigated under high rate loading conditions in a tension Kolsky bar set-up. The microstructure of voided fracture process zones in these weldments is studied using X-ray Computed Microtomography. To model the preferential evolution of damage near the heat-affected zone, a finite deformation elastic-viscoplastic constitutive model for porous materials is developed. The evolution of the macroscopic flow response and the porous microstructure have been analysed in two distinctive regimes: pre-coalescence and post-coalescence. The onset of void coalescence is analyzed on the basis of upper-bound models to obtain the limit-loads needed to sustain a localized mode of plastic flow in the inter-void ligament. A finite element framework for the integration of the porous material response under high rate loading conditions is implemented as a user-subroutine in ABAQUS/Explicit. To address the effect of mesh sensitivity of numerical simulations of ductile fracture, a microstructural length scale is used to discretize finite element models of test specimens. Results from a detailed finite element study of the deformation and damage evolution in AL6XN weldments are compared with experimental observations.

A Finite Element Framework for Studying the Mechanical Response of Macromolecules: Application to the Gating of the Mechanosensitive Channel MscL

PubMed Central

Tang, Yuye; Cao, Guoxin; Chen, Xi; Yoo, Jejoong; Yethiraj, Arun; Cui, Qiang

2006-01-01

The gating pathways of mechanosensitive channels of large conductance (MscL) in two bacteria (Mycobacterium tuberculosis and Escherichia coli) are studied using the finite element method. The phenomenological model treats transmembrane helices as elastic rods and the lipid membrane as an elastic sheet of finite thickness; the model is inspired by the crystal structure of MscL. The interactions between various continuum components are derived from molecular-mechanics energy calculations using the CHARMM all-atom force field. Both bacterial MscLs open fully upon in-plane tension in the membrane and the variation of pore diameter with membrane tension is found to be essentially linear. The estimated gating tension is close to the experimental value. The structural variations along the gating pathway are consistent with previous analyses based on structural models with experimental constraints and biased atomistic molecular-dynamics simulations. Upon membrane bending, neither MscL opens substantially, although there is notable and nonmonotonic variation in the pore radius. This emphasizes that the gating behavior of MscL depends critically on the form of the mechanical perturbation and reinforces the idea that the crucial gating parameter is lateral tension in the membrane rather than the curvature of the membrane. Compared to popular all-atom-based techniques such as targeted or steered molecular-dynamics simulations, the finite element method-based continuum-mechanics framework offers a unique alternative to bridge detailed intermolecular interactions and biological processes occurring at large spatial scales and long timescales. It is envisioned that such a hierarchical multiscale framework will find great value in the study of a variety of biological processes involving complex mechanical deformations such as muscle contraction and mechanotransduction. PMID:16731564

Dynamic Loads Generation for Multi-Point Vibration Excitation Problems

NASA Technical Reports Server (NTRS)

Shen, Lawrence

2011-01-01

A random-force method has been developed to predict dynamic loads produced by rocket-engine random vibrations for new rocket-engine designs. The method develops random forces at multiple excitation points based on random vibration environments scaled from accelerometer data obtained during hot-fire tests of existing rocket engines. This random-force method applies random forces to the model and creates expected dynamic response in a manner that simulates the way the operating engine applies self-generated random vibration forces (random pressure acting on an area) with the resulting responses that we measure with accelerometers. This innovation includes the methodology (implementation sequence), the computer code, two methods to generate the random-force vibration spectra, and two methods to reduce some of the inherent conservatism in the dynamic loads. This methodology would be implemented to generate the random-force spectra at excitation nodes without requiring the use of artificial boundary conditions in a finite element model. More accurate random dynamic loads than those predicted by current industry methods can then be generated using the random force spectra. The scaling method used to develop the initial power spectral density (PSD) environments for deriving the random forces for the rocket engine case is based on the Barrett Criteria developed at Marshall Space Flight Center in 1963. This invention approach can be applied in the aerospace, automotive, and other industries to obtain reliable dynamic loads and responses from a finite element model for any structure subject to multipoint random vibration excitations.

ANSYS duplicate finite-element checker routine

NASA Technical Reports Server (NTRS)

Ortega, R.

1995-01-01

An ANSYS finite-element code routine to check for duplicated elements within the volume of a three-dimensional (3D) finite-element mesh was developed. The routine developed is used for checking floating elements within a mesh, identically duplicated elements, and intersecting elements with a common face. A space shuttle main engine alternate turbopump development high pressure oxidizer turbopump finite-element model check using the developed subroutine is discussed. Finally, recommendations are provided for duplicate element checking of 3D finite-element models.

Adaptive implicit-explicit and parallel element-by-element iteration schemes

NASA Technical Reports Server (NTRS)

Tezduyar, T. E.; Liou, J.; Nguyen, T.; Poole, S.

1989-01-01

Adaptive implicit-explicit (AIE) and grouped element-by-element (GEBE) iteration schemes are presented for the finite element solution of large-scale problems in computational mechanics and physics. The AIE approach is based on the dynamic arrangement of the elements into differently treated groups. The GEBE procedure, which is a way of rewriting the EBE formulation to make its parallel processing potential and implementation more clear, is based on the static arrangement of the elements into groups with no inter-element coupling within each group. Various numerical tests performed demonstrate the savings in the CPU time and memory.

Analytical and experimental investigation of a 1/8-scale dynamic model of the shuttle orbiter. Volume 2: Technical report

NASA Technical Reports Server (NTRS)

Mason, P. W.; Harris, H. G.; Zalesak, J.; Bernstein, M.

1974-01-01

The methods and procedures used in the analysis and testing of the scale model are reported together with the correlation of the analytical and experimental results. The model, the NASTRAN finite element analysis, and results are discussed. Tests and analytical investigations are also reported.

Mesh Deformation Based on Fully Stressed Design: The Method and Two-Dimensional Examples

NASA Technical Reports Server (NTRS)

Hsu, Su-Yuen; Chang, Chau-Lyan

2007-01-01

Mesh deformation in response to redefined boundary geometry is a frequently encountered task in shape optimization and analysis of fluid-structure interaction. We propose a simple and concise method for deforming meshes defined with three-node triangular or four-node tetrahedral elements. The mesh deformation method is suitable for large boundary movement. The approach requires two consecutive linear elastic finite-element analyses of an isotropic continuum using a prescribed displacement at the mesh boundaries. The first analysis is performed with homogeneous elastic property and the second with inhomogeneous elastic property. The fully stressed design is employed with a vanishing Poisson s ratio and a proposed form of equivalent strain (modified Tresca equivalent strain) to calculate, from the strain result of the first analysis, the element-specific Young s modulus for the second analysis. The theoretical aspect of the proposed method, its convenient numerical implementation using a typical linear elastic finite-element code in conjunction with very minor extra coding for data processing, and results for examples of large deformation of two-dimensional meshes are presented in this paper. KEY WORDS: Mesh deformation, shape optimization, fluid-structure interaction, fully stressed design, finite-element analysis, linear elasticity, strain failure, equivalent strain, Tresca failure criterion

Conceptual Design and Structural Optimization of NASA Environmentally Responsible Aviation (ERA) Hybrid Wing Body Aircraft

NASA Technical Reports Server (NTRS)

Quinlan, Jesse R.; Gern, Frank H.

2016-01-01

Simultaneously achieving the fuel consumption and noise reduction goals set forth by NASA's Environmentally Responsible Aviation (ERA) project requires innovative and unconventional aircraft concepts. In response, advanced hybrid wing body (HWB) aircraft concepts have been proposed and analyzed as a means of meeting these objectives. For the current study, several HWB concepts were analyzed using the Hybrid wing body Conceptual Design and structural optimization (HCDstruct) analysis code. HCDstruct is a medium-fidelity finite element based conceptual design and structural optimization tool developed to fill the critical analysis gap existing between lower order structural sizing approaches and detailed, often finite element based sizing methods for HWB aircraft concepts. Whereas prior versions of the tool used a half-model approach in building the representative finite element model, a full wing-tip-to-wing-tip modeling capability was recently added to HCDstruct, which alleviated the symmetry constraints at the model centerline in place of a free-flying model and allowed for more realistic center body, aft body, and wing loading and trim response. The latest version of HCDstruct was applied to two ERA reference cases, including the Boeing Open Rotor Engine Integration On an HWB (OREIO) concept and the Boeing ERA-0009H1 concept, and results agreed favorably with detailed Boeing design data and related Flight Optimization System (FLOPS) analyses. Following these benchmark cases, HCDstruct was used to size NASA's ERA HWB concepts and to perform a related scaling study.

Modal Substructuring of Geometrically Nonlinear Finite Element Models with Interface Reduction

DOE Office of Scientific and Technical Information (OSTI.GOV)

Kuether, Robert J.; Allen, Matthew S.; Hollkamp, Joseph J.

Substructuring methods have been widely used in structural dynamics to divide large, complicated finite element models into smaller substructures. For linear systems, many methods have been developed to reduce the subcomponents down to a low order set of equations using a special set of component modes, and these are then assembled to approximate the dynamics of a large scale model. In this paper, a substructuring approach is developed for coupling geometrically nonlinear structures, where each subcomponent is drastically reduced to a low order set of nonlinear equations using a truncated set of fixedinterface and characteristic constraint modes. The method usedmore » to extract the coefficients of the nonlinear reduced order model (NLROM) is non-intrusive in that it does not require any modification to the commercial FEA code, but computes the NLROM from the results of several nonlinear static analyses. The NLROMs are then assembled to approximate the nonlinear differential equations of the global assembly. The method is demonstrated on the coupling of two geometrically nonlinear plates with simple supports at all edges. The plates are joined at a continuous interface through the rotational degrees-of-freedom (DOF), and the nonlinear normal modes (NNMs) of the assembled equations are computed to validate the models. The proposed substructuring approach reduces a 12,861 DOF nonlinear finite element model down to only 23 DOF, while still accurately reproducing the first three NNMs of the full order model.« less

Modal Substructuring of Geometrically Nonlinear Finite Element Models with Interface Reduction

DOE PAGES

Kuether, Robert J.; Allen, Matthew S.; Hollkamp, Joseph J.

2017-03-29

Substructuring methods have been widely used in structural dynamics to divide large, complicated finite element models into smaller substructures. For linear systems, many methods have been developed to reduce the subcomponents down to a low order set of equations using a special set of component modes, and these are then assembled to approximate the dynamics of a large scale model. In this paper, a substructuring approach is developed for coupling geometrically nonlinear structures, where each subcomponent is drastically reduced to a low order set of nonlinear equations using a truncated set of fixedinterface and characteristic constraint modes. The method usedmore » to extract the coefficients of the nonlinear reduced order model (NLROM) is non-intrusive in that it does not require any modification to the commercial FEA code, but computes the NLROM from the results of several nonlinear static analyses. The NLROMs are then assembled to approximate the nonlinear differential equations of the global assembly. The method is demonstrated on the coupling of two geometrically nonlinear plates with simple supports at all edges. The plates are joined at a continuous interface through the rotational degrees-of-freedom (DOF), and the nonlinear normal modes (NNMs) of the assembled equations are computed to validate the models. The proposed substructuring approach reduces a 12,861 DOF nonlinear finite element model down to only 23 DOF, while still accurately reproducing the first three NNMs of the full order model.« less

Biomechanical 3-Dimensional Finite Element Analysis of Obturator Protheses Retained with Zygomatic and Dental Implants in Maxillary Defects

PubMed Central

Akay, Canan; Yaluğ, Suat

2015-01-01

Background The objective of this study was to investigate the stress distribution in the bone around zygomatic and dental implants for 3 different implant-retained obturator prostheses designs in a Aramany class IV maxillary defect using 3-dimensional finite element analysis (FEA). Material\\Methods A 3-dimensional finite element model of an Aramany class IV defect was created. Three different implant-retained obturator prostheses were modeled: model 1 with 1 zygomatic implant and 1 dental implant, model 2 with 1 zygomatic implant and 2 dental implants, and model 3 with 2 zygomatic implants. Locator attachments were used as a superstructure. A 150-N load was applied 3 different ways. Qualitative analysis was based on the scale of maximum principal stress; values obtained through quantitative analysis are expressed in MPa. Results In all loading conditions, model 3 (when compared models 1 and 2) showed the lowest maximum principal stress value. Model 3 is the most appropirate reconstruction in Aramany class IV maxillary defects. Two zygomatic implants can reduce the stresses in model 3. The distribution of stresses on prostheses were more rational with the help of zygoma implants, which can distribute the stresses on each part of the maxilla. Conclusions Aramany class IV obturator prosthesis placement of 2 zygomatic implants in each side of the maxilla is more advantageous than placement of dental implants. In the non-defective side, increasing the number of dental implants is not as suitable as zygomatic implants. PMID:25714086

Crash Simulation of a Boeing 737 Fuselage Section Vertical Drop Test

NASA Technical Reports Server (NTRS)

Fasanella, Edwin L.; Jackson, Karen E.; Jones, Yvonne T.; Frings, Gary; Vu, Tong

2004-01-01

A 30-ft/s vertical drop test of a fuselage section of a Boeing 737 aircraft was conducted in October of 1999 at the FAA Technical Center in Atlantic City, NJ. This test was performed to evaluate the structural integrity of a conformable auxiliary fuel tank mounted beneath the floor and to determine its effect on the impact response of the airframe structure and the occupants. The test data were used to compare with a finite element simulation of the fuselage structure and to gain a better understanding of the impact physics through analytical/experimental correlation. To perform this simulation, a full-scale 3-dimensional finite element model of the fuselage section was developed using the explicit, nonlinear transient-dynamic finite element code, MSC.Dytran. The emphasis of the simulation was to predict the structural deformation and floor-level acceleration responses obtained from the drop test of the B737 fuselage section with the auxiliary fuel tank.

Parallelized modelling and solution scheme for hierarchically scaled simulations

NASA Technical Reports Server (NTRS)

Padovan, Joe

1995-01-01

This two-part paper presents the results of a benchmarked analytical-numerical investigation into the operational characteristics of a unified parallel processing strategy for implicit fluid mechanics formulations. This hierarchical poly tree (HPT) strategy is based on multilevel substructural decomposition. The Tree morphology is chosen to minimize memory, communications and computational effort. The methodology is general enough to apply to existing finite difference (FD), finite element (FEM), finite volume (FV) or spectral element (SE) based computer programs without an extensive rewrite of code. In addition to finding large reductions in memory, communications, and computational effort associated with a parallel computing environment, substantial reductions are generated in the sequential mode of application. Such improvements grow with increasing problem size. Along with a theoretical development of general 2-D and 3-D HPT, several techniques for expanding the problem size that the current generation of computers are capable of solving, are presented and discussed. Among these techniques are several interpolative reduction methods. It was found that by combining several of these techniques that a relatively small interpolative reduction resulted in substantial performance gains. Several other unique features/benefits are discussed in this paper. Along with Part 1's theoretical development, Part 2 presents a numerical approach to the HPT along with four prototype CFD applications. These demonstrate the potential of the HPT strategy.

Coupled Structural, Thermal, Phase-Change and Electromagnetic Analysis for Superconductors. Volume 1

NASA Technical Reports Server (NTRS)

Felippa, C. A.; Farhat, C.; Park, K. C.; Militello, C.; Schuler, J. J.

1996-01-01

Described are the theoretical development and computer implementation of reliable and efficient methods for the analysis of coupled mechanical problems that involve the interaction of mechanical, thermal, phase-change and electromagnetic subproblems. The focus application has been the modeling of superconductivity and associated quantum-state phase-change phenomena. In support of this objective the work has addressed the following issues: (1) development of variational principles for finite elements, (2) finite element modeling of the electromagnetic problem, (3) coupling of thermal and mechanical effects, and (4) computer implementation and solution of the superconductivity transition problem. The main accomplishments have been: (1) the development of the theory of parametrized and gauged variational principles, (2) the application of those principled to the construction of electromagnetic, thermal and mechanical finite elements, and (3) the coupling of electromagnetic finite elements with thermal and superconducting effects, and (4) the first detailed finite element simulations of bulk superconductors, in particular the Meissner effect and the nature of the normal conducting boundary layer. The theoretical development is described in two volumes. This volume, Volume 1, describes mostly formulations for specific problems. Volume 2 describes generalization of those formulations.

A three-dimensional thermal finite element analysis of AISI 304 stainless steel and copper dissimilar weldment

NASA Astrophysics Data System (ADS)

Singh, Gurdeep; Saxena, Ravindra K.; Pandey, Sunil

2018-04-01

The aim of this study to developed a 3-D thermal finite element model for dissimilar material welding of AISI-304 stainless steel and copper. Welding of similar material is widely studied using experimental and numerical methods but the problem becomes trivial for the welding of dissimilar materials especially in ferrous and nonferrous materials. Finite element analysis of dissimilar material welding is a cost-effective method for the understanding and analysis of the process. The finite element analysis has been performed to predict the heat affected zone and temperature distribution in AISI-304 stainless steel and copper dissimilar weldment using MSC Marc 2017®. Due to the difference in physical properties of these materials the behavior of heat affected zone and temperature distribution are perceived to be different. To verify the accuracy of the thermal finite element model, the welding process was simulated with butt-welded joints having same dimensions and parameters from Attarha and Far [1]. It is found from the study that the heat affected zone is larger in copper weld pads than in AISI 304 stainless steel due to large difference in thermal conductivity of these two weld pads.

Pore-scale modeling of moving contact line problems in immiscible two-phase flow.

NASA Astrophysics Data System (ADS)

Kucala, A.; Noble, D.; Martinez, M. J.

2016-12-01

Two immiscible fluids in static equilibrium form a common interface along a solid surface, characterized as the static contact (wetting) angle and is a function of surface geometry, intermolecular forces, and interfacial surface energies manifested as interfacial tension. This static configuration may become perturbed due to external force imbalances (mass injection, pressure gradients, buoyancy, etc.) and the contact line location and interface curvature becomes dynamic. Accurate modeling of moving contact line (MCL) problems is imperative in predicting capillary pressure vs. saturation curves, permeability, and preferential flow paths for a variety of applications, including geological carbon storage (GCS) and enhanced oil recovery (EOR). Here, we present a model for the moving contact line using pore-scale computational fluid dynamics (CFD) which solves the full, time-dependent Navier-Stokes equations using the Galerkin finite-element method. The MCL is modeled as a surface traction force proportional to the surface tension, dependent on the static properties of the immiscible fluid/solid system. The moving two-phase interface is tracked using the level set method and discretized with the conformal decomposition finite element method (CDFEM), allowing for surface tension effects to be computed at the exact interface location. We present a variety of verification test cases for simple two- and three-dimensional geometries to validate the current model, including threshold pressure predictions in flows through pore-throats for a variety of wetting angles. Simulations involving more complex geometries are also presented to be used in future simulations for GCS and EOR problems. Sandia is a multiprogram laboratory operated by Sandia Corporation, a Lockheed Martin Company, for the United States Department of Energy's National Nuclear Security Administration under contract DE-AC04-94AL85000

Numerical computation of transonic flows by finite-element and finite-difference methods

NASA Technical Reports Server (NTRS)

Hafez, M. M.; Wellford, L. C.; Merkle, C. L.; Murman, E. M.

1978-01-01

Studies on applications of the finite element approach to transonic flow calculations are reported. Different discretization techniques of the differential equations and boundary conditions are compared. Finite element analogs of Murman's mixed type finite difference operators for small disturbance formulations were constructed and the time dependent approach (using finite differences in time and finite elements in space) was examined.

On Two-Scale Modelling of Heat and Mass Transfer

NASA Astrophysics Data System (ADS)

Vala, J.; Št'astník, S.

2008-09-01

Modelling of macroscopic behaviour of materials, consisting of several layers or components, whose microscopic (at least stochastic) analysis is available, as well as (more general) simulation of non-local phenomena, complicated coupled processes, etc., requires both deeper understanding of physical principles and development of mathematical theories and software algorithms. Starting from the (relatively simple) example of phase transformation in substitutional alloys, this paper sketches the general formulation of a nonlinear system of partial differential equations of evolution for the heat and mass transfer (useful in mechanical and civil engineering, etc.), corresponding to conservation principles of thermodynamics, both at the micro- and at the macroscopic level, and suggests an algorithm for scale-bridging, based on the robust finite element techniques. Some existence and convergence questions, namely those based on the construction of sequences of Rothe and on the mathematical theory of two-scale convergence, are discussed together with references to useful generalizations, required by new technologies.

A combined molecular dynamics/micromechanics/finite element approach for multiscale constitutive modeling of nanocomposites with interface effects

NASA Astrophysics Data System (ADS)

Yang, B. J.; Shin, H.; Lee, H. K.; Kim, H.

2013-12-01

We introduce a multiscale framework based on molecular dynamic (MD) simulation, micromechanics, and finite element method (FEM). A micromechanical model, which considers influences of the interface properties, nanoparticle (NP) size, and microcracks, is developed. Then, we perform MD simulations to characterize the mechanical properties of the nanocomposite system (silica/nylon 6) with varying volume fraction and size of NPs. By comparing the MD with micromechanics results, intrinsic physical properties at interfacial region are derived. Finally, we implement the developed model in the FEM code with the derived interfacial parameters, and predict the mechanical behavior of the nanocomposite at the macroscopic scale.

Application of micropolar plasticity to post failure analysis in geomechanics

NASA Astrophysics Data System (ADS)

Manzari, Majid T.

2004-08-01

A micropolar elastoplastic model for soils is formulated and a series of finite element analyses are employed to demonstrate the use of a micropolar continuum in overcoming the numerical difficulties encountered in application of finite element method in standard Cauchy-Boltzmann continuum. Three examples of failure analysis involving a deep excavation, shallow foundation, and a retaining wall are presented. In all these cases, it is observed that the length scale introduced in the polar continuum regularizes the incremental boundary value problem and allows the numerical simulation to be continued until a clear collapse mechanism is achieved. The issue of grain size effect is also discussed. Copyright

Wakefield Computations for the CLIC PETS using the Parallel Finite Element Time-Domain Code T3P

DOE Office of Scientific and Technical Information (OSTI.GOV)

Candel, A; Kabel, A.; Lee, L.

In recent years, SLAC's Advanced Computations Department (ACD) has developed the high-performance parallel 3D electromagnetic time-domain code, T3P, for simulations of wakefields and transients in complex accelerator structures. T3P is based on advanced higher-order Finite Element methods on unstructured grids with quadratic surface approximation. Optimized for large-scale parallel processing on leadership supercomputing facilities, T3P allows simulations of realistic 3D structures with unprecedented accuracy, aiding the design of the next generation of accelerator facilities. Applications to the Compact Linear Collider (CLIC) Power Extraction and Transfer Structure (PETS) are presented.

On finite element methods for the Helmholtz equation

NASA Technical Reports Server (NTRS)

Aziz, A. K.; Werschulz, A. G.

1979-01-01

The numerical solution of the Helmholtz equation is considered via finite element methods. A two-stage method which gives the same accuracy in the computed gradient as in the computed solution is discussed. Error estimates for the method using a newly developed proof are given, and the computational considerations which show this method to be computationally superior to previous methods are presented.

Prediction of the thermal environment and thermal response of simple panels exposed to radiant heat

NASA Technical Reports Server (NTRS)

Turner, Travis L.; Ash, Robert L.

1989-01-01

A method of predicting the radiant heat flux distribution produced by a bank of tubular quartz heaters was applied to a radiant system consisting of a single unreflected lamp irradiating a flat metallic incident surface. In this manner, the method was experimentally verified for various radiant system parameter settings and used as a source of input for a finite element thermal analysis. Two finite element thermal analyses were applied to a thermal system consisting of a thin metallic panel exposed to radiant surface heating. A two-dimensional steady-state finite element thermal analysis algorithm, based on Galerkin's Method of Weighted Residuals (GFE), was formulated specifically for this problem and was used in comparison to the thermal analyzers of the Engineering Analysis Language (EAL). Both analyses allow conduction, convection, and radiation boundary conditions. Differences in the respective finite element formulation are discussed in terms of their accuracy and resulting comparison discrepancies. The thermal analyses are shown to perform well for the comparisons presented here with some important precautions about the various boundary condition models. A description of the experiment, corresponding analytical modeling, and resulting comparisons are presented.

Numerical simulations of earthquakes and the dynamics of fault systems using the Finite Element method.

NASA Astrophysics Data System (ADS)

Kettle, L. M.; Mora, P.; Weatherley, D.; Gross, L.; Xing, H.

2006-12-01

Simulations using the Finite Element method are widely used in many engineering applications and for the solution of partial differential equations (PDEs). Computational models based on the solution of PDEs play a key role in earth systems simulations. We present numerical modelling of crustal fault systems where the dynamic elastic wave equation is solved using the Finite Element method. This is achieved using a high level computational modelling language, escript, available as open source software from ACcESS (Australian Computational Earth Systems Simulator), the University of Queensland. Escript is an advanced geophysical simulation software package developed at ACcESS which includes parallel equation solvers, data visualisation and data analysis software. The escript library was implemented to develop a flexible Finite Element model which reliably simulates the mechanism of faulting and the physics of earthquakes. Both 2D and 3D elastodynamic models are being developed to study the dynamics of crustal fault systems. Our final goal is to build a flexible model which can be applied to any fault system with user-defined geometry and input parameters. To study the physics of earthquake processes, two different time scales must be modelled, firstly the quasi-static loading phase which gradually increases stress in the system (~100years), and secondly the dynamic rupture process which rapidly redistributes stress in the system (~100secs). We will discuss the solution of the time-dependent elastic wave equation for an arbitrary fault system using escript. This involves prescribing the correct initial stress distribution in the system to simulate the quasi-static loading of faults to failure; determining a suitable frictional constitutive law which accurately reproduces the dynamics of the stick/slip instability at the faults; and using a robust time integration scheme. These dynamic models generate data and information that can be used for earthquake forecasting.

Studies of finite element analysis of composite material structures

NASA Technical Reports Server (NTRS)

Douglas, D. O.; Holzmacher, D. E.; Lane, Z. C.; Thornton, E. A.

1975-01-01

Research in the area of finite element analysis is summarized. Topics discussed include finite element analysis of a picture frame shear test, BANSAP (a bandwidth reduction program for SAP IV), FEMESH (a finite element mesh generation program based on isoparametric zones), and finite element analysis of a composite bolted joint specimens.

An 8-node tetrahedral finite element suitable for explicit transient dynamic simulations

DOE Office of Scientific and Technical Information (OSTI.GOV)

Key, S.W.; Heinstein, M.W.; Stone, C.M.

1997-12-31

Considerable effort has been expended in perfecting the algorithmic properties of 8-node hexahedral finite elements. Today the element is well understood and performs exceptionally well when used in modeling three-dimensional explicit transient dynamic events. However, the automatic generation of all-hexahedral meshes remains an elusive achievement. The alternative of automatic generation for all-tetrahedral finite element is a notoriously poor performer, and the 10-node quadratic tetrahedral finite element while a better performer numerically is computationally expensive. To use the all-tetrahedral mesh generation extant today, the authors have explored the creation of a quality 8-node tetrahedral finite element (a four-node tetrahedral finite elementmore » enriched with four midface nodal points). The derivation of the element`s gradient operator, studies in obtaining a suitable mass lumping and the element`s performance in applications are presented. In particular, they examine the 80node tetrahedral finite element`s behavior in longitudinal plane wave propagation, in transverse cylindrical wave propagation, and in simulating Taylor bar impacts. The element only samples constant strain states and, therefore, has 12 hourglass modes. In this regard, it bears similarities to the 8-node, mean-quadrature hexahedral finite element. Given automatic all-tetrahedral meshing, the 8-node, constant-strain tetrahedral finite element is a suitable replacement for the 8-node hexahedral finite element and handbuilt meshes.« less

Hybrid finite element and Brownian dynamics method for diffusion-controlled reactions.

PubMed

Bauler, Patricia; Huber, Gary A; McCammon, J Andrew

2012-04-28

Diffusion is often the rate determining step in many biological processes. Currently, the two main computational methods for studying diffusion are stochastic methods, such as Brownian dynamics, and continuum methods, such as the finite element method. This paper proposes a new hybrid diffusion method that couples the strengths of each of these two methods. The method is derived for a general multidimensional system, and is presented using a basic test case for 1D linear and radially symmetric diffusion systems.

Design optimization of space structures

NASA Technical Reports Server (NTRS)

Felippa, Carlos

1991-01-01

The topology-shape-size optimization of space structures is investigated through Kikuchi's homogenization method. The method starts from a 'design domain block,' which is a region of space into which the structure is to materialize. This domain is initially filled with a finite element mesh, typically regular. Force and displacement boundary conditions corresponding to applied loads and supports are applied at specific points in the domain. An optimal structure is to be 'carved out' of the design under two conditions: (1) a cost function is to be minimized, and (2) equality or inequality constraints are to be satisfied. The 'carving' process is accomplished by letting microstructure holes develop and grow in elements during the optimization process. These holes have a rectangular shape in two dimensions and a cubical shape in three dimensions, and may also rotate with respect to the reference axes. The properties of the perforated element are obtained through an homogenization procedure. Once a hole reaches the volume of the element, that element effectively disappears. The project has two phases. In the first phase the method was implemented as the combination of two computer programs: a finite element module, and an optimization driver. In the second part, focus is on the application of this technique to planetary structures. The finite element part of the method was programmed for the two-dimensional case using four-node quadrilateral elements to cover the design domain. An element homogenization technique different from that of Kikuchi and coworkers was implemented. The optimization driver is based on an augmented Lagrangian optimizer, with the volume constraint treated as a Courant penalty function. The optimizer has to be especially tuned to this type of optimization because the number of design variables can reach into the thousands. The driver is presently under development.

NESSUS/NASTRAN Interface

NASA Technical Reports Server (NTRS)

Millwater, Harry; Riha, David

1996-01-01

The NESSUS probabilistic analysis computer program has been developed with a built-in finite element analysis program NESSUS/FEM. However, the NESSUS/FEM program is specialized for engine structures and may not contain sufficient features for other applications. In addition, users often become well acquainted with a particular finite element code and want to use that code for probabilistic structural analysis. For these reasons, this work was undertaken to develop an interface between NESSUS and NASTRAN such that NASTRAN can be used for the finite element analysis and NESSUS can be used for the probabilistic analysis. In addition, NESSUS was restructured such that other finite element codes could be more easily coupled with NESSUS. NESSUS has been enhanced such that NESSUS will modify the NASTRAN input deck for a given set of random variables, run NASTRAN and read the NASTRAN result. The coordination between the two codes is handled automatically. The work described here was implemented within NESSUS 6.2 which was delivered to NASA in September 1995. The code runs on Unix machines: Cray, HP, Sun, SGI and IBM. The new capabilities have been implemented such that a user familiar with NESSUS using NESSUS/FEM and NASTRAN can immediately use NESSUS with NASTRAN. In other words, the interface with NASTRAN has been implemented in an analogous manner to the interface with NESSUS/FEM. Only finite element specific input has been changed. This manual is written as an addendum to the existing NESSUS 6.2 manuals. We assume users have access to NESSUS manuals and are familiar with the operation of NESSUS including probabilistic finite element analysis. Update pages to the NESSUS PFEM manual are contained in Appendix E. The finite element features of the code and the probalistic analysis capabilities are summarized.

A finite element conjugate gradient FFT method for scattering

NASA Technical Reports Server (NTRS)

Collins, Jeffery D.; Zapp, John; Hsa, Chang-Yu; Volakis, John L.

1990-01-01

An extension of a two dimensional formulation is presented for a three dimensional body of revolution. With the introduction of a Fourier expansion of the vector electric and magnetic fields, a coupled two dimensional system is generated and solved via the finite element method. An exact boundary condition is employed to terminate the mesh and the fast fourier transformation (FFT) is used to evaluate the boundary integrals for low O(n) memory demand when an iterative solution algorithm is used. By virtue of the finite element method, the algorithm is applicable to structures of arbitrary material composition. Several improvements to the two dimensional algorithm are also described. These include: (1) modifications for terminating the mesh at circular boundaries without distorting the convolutionality of the boundary integrals; (2) the development of nonproprietary mesh generation routines for two dimensional applications; (3) the development of preprocessors for interfacing SDRC IDEAS with the main algorithm; and (4) the development of post-processing algorithms based on the public domain package GRAFIC to generate two and three dimensional gray level and color field maps.

Numerical Analysis of Stress Concentration in Isotropic and Laminated Plates with Inclined Elliptical Holes

NASA Astrophysics Data System (ADS)

Khechai, Abdelhak; Tati, Abdelouahab; Belarbi, Mohamed Ouejdi; Guettala, Abdelhamid

2018-03-01

The design of high-performance composite structures frequently includes discontinuities to reduce the weight and fastener holes for joining. Understanding the behavior of perforated laminates is necessary for structural design. In the current work, stress concentrations taking place in laminated and isotropic plates subjected to tensile load are investigated. The stress concentrations are obtained using a recent quadrilateral finite element of four nodes with 32 DOFs. The present finite element (PE) is a combination of two finite elements. The first finite element is a linear isoparametric membrane element and the second is a high precision Hermitian element. One of the essential objectives of the current investigation is to confirm the capability and efficiency of the PE for stress determination in perforated laminates. Different geometric parameters, such as the cutout form, sizes and cutout orientations, which have a considerable effect on the stress values, are studied. Using the present finite element formulation, the obtained results are found to be in good agreement with the analytical findings, which validates the capability and the efficiency of the proposed formulation. Finally, to understand the material parameters effect such as the orientation of fibers and degree of orthotropy ratio on the stress values, many figures are presented using different ellipse major to minor axis ratio. The stress concentration values are considerably affected by increasing the orientation angle of the fibers and degree of orthotropy.

Dispersion analysis of the Pn -Pn-1DG mixed finite element pair for atmospheric modelling

NASA Astrophysics Data System (ADS)

Melvin, Thomas

2018-02-01

Mixed finite element methods provide a generalisation of staggered grid finite difference methods with a framework to extend the method to high orders. The ability to generate a high order method is appealing for applications on the kind of quasi-uniform grids that are popular for atmospheric modelling, so that the method retains an acceptable level of accuracy even around special points in the grid. The dispersion properties of such schemes are important to study as they provide insight into the numerical adjustment to imbalance that is an important component in atmospheric modelling. This paper extends the recent analysis of the P2 - P1DG pair, that is a quadratic continuous and linear discontinuous finite element pair, to higher polynomial orders and also spectral element type pairs. In common with the previously studied element pair, and also with other schemes such as the spectral element and discontinuous Galerkin methods, increasing the polynomial order is found to provide a more accurate dispersion relation for the well resolved part of the spectrum but at the cost of a number of unphysical spectral gaps. The effects of these spectral gaps are investigated and shown to have a varying impact depending upon the width of the gap. Finally, the tensor product nature of the finite element spaces is exploited to extend the dispersion analysis into two-dimensions.

Multiscale Modeling of Intergranular Fracture in Aluminum: Constitutive Relation For Interface Debonding

NASA Technical Reports Server (NTRS)

Yamakov, V.; Saether, E.; Glaessgen, E. H.

2008-01-01

Intergranular fracture is a dominant mode of failure in ultrafine grained materials. In the present study, the atomistic mechanisms of grain-boundary debonding during intergranular fracture in aluminum are modeled using a coupled molecular dynamics finite element simulation. Using a statistical mechanics approach, a cohesive-zone law in the form of a traction-displacement constitutive relationship, characterizing the load transfer across the plane of a growing edge crack, is extracted from atomistic simulations and then recast in a form suitable for inclusion within a continuum finite element model. The cohesive-zone law derived by the presented technique is free of finite size effects and is statistically representative for describing the interfacial debonding of a grain boundary (GB) interface examined at atomic length scales. By incorporating the cohesive-zone law in cohesive-zone finite elements, the debonding of a GB interface can be simulated in a coupled continuum-atomistic model, in which a crack starts in the continuum environment, smoothly penetrates the continuum-atomistic interface, and continues its propagation in the atomistic environment. This study is a step towards relating atomistically derived decohesion laws to macroscopic predictions of fracture and constructing multiscale models for nanocrystalline and ultrafine grained materials.

Two-Level Hierarchical FEM Method for Modeling Passive Microwave Devices

NASA Astrophysics Data System (ADS)

Polstyanko, Sergey V.; Lee, Jin-Fa

1998-03-01

In recent years multigrid methods have been proven to be very efficient for solving large systems of linear equations resulting from the discretization of positive definite differential equations by either the finite difference method or theh-version of the finite element method. In this paper an iterative method of the multiple level type is proposed for solving systems of algebraic equations which arise from thep-version of the finite element analysis applied to indefinite problems. A two-levelV-cycle algorithm has been implemented and studied with a Gauss-Seidel iterative scheme used as a smoother. The convergence of the method has been investigated, and numerical results for a number of numerical examples are presented.

Atherosclerotic plaque delamination: Experiments and 2D finite element model to simulate plaque peeling in two strains of transgenic mice.

PubMed

Merei, Bilal; Badel, Pierre; Davis, Lindsey; Sutton, Michael A; Avril, Stéphane; Lessner, Susan M

2017-03-01

Finite element analyses using cohesive zone models (CZM) can be used to predict the fracture of atherosclerotic plaques but this requires setting appropriate values of the model parameters. In this study, material parameters of a CZM were identified for the first time on two groups of mice (ApoE -/- and ApoE -/- Col8 -/- ) using the measured force-displacement curves acquired during delamination tests. To this end, a 2D finite-element model of each plaque was solved using an explicit integration scheme. Each constituent of the plaque was modeled with a neo-Hookean strain energy density function and a CZM was used for the interface. The model parameters were calibrated by minimizing the quadratic deviation between the experimental force displacement curves and the model predictions. The elastic parameter of the plaque and the CZM interfacial parameter were successfully identified for a cohort of 11 mice. The results revealed that only the elastic parameter was significantly different between the two groups, ApoE -/- Col8 -/- plaques being less stiff than ApoE -/- plaques. Finally, this study demonstrated that a simple 2D finite element model with cohesive elements can reproduce fairly well the plaque peeling global response. Future work will focus on understanding the main biological determinants of regional and inter-individual variations of the material parameters used in the model. Copyright © 2016 Elsevier Ltd. All rights reserved.

Patient-specific finite element modeling of bones.

PubMed

Poelert, Sander; Valstar, Edward; Weinans, Harrie; Zadpoor, Amir A

2013-04-01

Finite element modeling is an engineering tool for structural analysis that has been used for many years to assess the relationship between load transfer and bone morphology and to optimize the design and fixation of orthopedic implants. Due to recent developments in finite element model generation, for example, improved computed tomography imaging quality, improved segmentation algorithms, and faster computers, the accuracy of finite element modeling has increased vastly and finite element models simulating the anatomy and properties of an individual patient can be constructed. Such so-called patient-specific finite element models are potentially valuable tools for orthopedic surgeons in fracture risk assessment or pre- and intraoperative planning of implant placement. The aim of this article is to provide a critical overview of current themes in patient-specific finite element modeling of bones. In addition, the state-of-the-art in patient-specific modeling of bones is compared with the requirements for a clinically applicable patient-specific finite element method, and judgment is passed on the feasibility of application of patient-specific finite element modeling as a part of clinical orthopedic routine. It is concluded that further development in certain aspects of patient-specific finite element modeling are needed before finite element modeling can be used as a routine clinical tool.

Exploiting symmetries in the modeling and analysis of tires

NASA Technical Reports Server (NTRS)

Noor, Ahmed K.; Andersen, C. M.; Tanner, John A.

1989-01-01

A computational procedure is presented for reducing the size of the analysis models of tires having unsymmetric material, geometry and/or loading. The two key elements of the procedure when applied to anisotropic tires are: (1) decomposition of the stiffness matrix into the sum of an orthotropic and nonorthotropic parts; and (2) successive application of the finite-element method and the classical Rayleigh-Ritz technique. The finite-element method is first used to generate few global approximation vectors (or modes). Then the amplitudes of these modes are computed by using the Rayleigh-Ritz technique. The proposed technique has high potential for handling practical tire problems with anisotropic materials, unsymmetric imperfections and asymmetric loading. It is also particularly useful for use with three-dimensional finite-element models of tires.

Development of Finite Elements for Two-Dimensional Structural Analysis Using the Integrated Force Method

NASA Technical Reports Server (NTRS)

Kaljevic, Igor; Patnaik, Surya N.; Hopkins, Dale A.

1996-01-01

The Integrated Force Method has been developed in recent years for the analysis of structural mechanics problems. This method treats all independent internal forces as unknown variables that can be calculated by simultaneously imposing equations of equilibrium and compatibility conditions. In this paper a finite element library for analyzing two-dimensional problems by the Integrated Force Method is presented. Triangular- and quadrilateral-shaped elements capable of modeling arbitrary domain configurations are presented. The element equilibrium and flexibility matrices are derived by discretizing the expressions for potential and complementary energies, respectively. The displacement and stress fields within the finite elements are independently approximated. The displacement field is interpolated as it is in the standard displacement method, and the stress field is approximated by using complete polynomials of the correct order. A procedure that uses the definitions of stress components in terms of an Airy stress function is developed to derive the stress interpolation polynomials. Such derived stress fields identically satisfy the equations of equilibrium. Moreover, the resulting element matrices are insensitive to the orientation of local coordinate systems. A method is devised to calculate the number of rigid body modes, and the present elements are shown to be free of spurious zero-energy modes. A number of example problems are solved by using the present library, and the results are compared with corresponding analytical solutions and with results from the standard displacement finite element method. The Integrated Force Method not only gives results that agree well with analytical and displacement method results but also outperforms the displacement method in stress calculations.

Fluid-structure interaction in fast breeder reactors

NASA Astrophysics Data System (ADS)

Mitra, A. A.; Manik, D. N.; Chellapandi, P. A.

2004-05-01

A finite element model for the seismic analysis of a scaled down model of Fast breeder reactor (FBR) main vessel is proposed to be established. The reactor vessel, which is a large shell structure with a relatively thin wall, contains a large volume of sodium coolant. Therefore, the fluid structure interaction effects must be taken into account in the seismic design. As part of studying fluid-structure interaction, the fundamental frequency of vibration of a circular cylindrical shell partially filled with a liquid has been estimated using Rayleigh's method. The bulging and sloshing frequencies of the first four modes of the aforementioned system have been estimated using the Rayleigh-Ritz method. The finite element formulation of the axisymmetric fluid element with Fourier option (required due to seismic loading) is also presented.

An Optimization Code for Nonlinear Transient Problems of a Large Scale Multidisciplinary Mathematical Model

NASA Astrophysics Data System (ADS)

Takasaki, Koichi

This paper presents a program for the multidisciplinary optimization and identification problem of the nonlinear model of large aerospace vehicle structures. The program constructs the global matrix of the dynamic system in the time direction by the p-version finite element method (pFEM), and the basic matrix for each pFEM node in the time direction is described by a sparse matrix similarly to the static finite element problem. The algorithm used by the program does not require the Hessian matrix of the objective function and so has low memory requirements. It also has a relatively low computational cost, and is suited to parallel computation. The program was integrated as a solver module of the multidisciplinary analysis system CUMuLOUS (Computational Utility for Multidisciplinary Large scale Optimization of Undense System) which is under development by the Aerospace Research and Development Directorate (ARD) of the Japan Aerospace Exploration Agency (JAXA).

Basilar membrane and reticular lamina motion in a multi-scale finite element model of the mouse cochlea

NASA Astrophysics Data System (ADS)

Soons, Joris; Dirckx, Joris; Steele, Charles; Puria, Sunil

2015-12-01

A multi-scale finite element (FE) model of the mouse cochlea, based on its anatomy and material properties is presented. The important feature in the model is a lattice of 400 Y-shaped structures in the longitudinal direction, each formed by Deiters cells, phalangeal processes and outer hair cells (OHC). OHC somatic motility is modeled by an expansion force proportional to the shear on the stereocilia, which in turn is proportional to the pressure difference between the scala vestibule and scala tympani. Basilar membrane (BM) and reticular lamina (RL) velocity compare qualitatively very well with recent in vivo measurements in guinea pig [2]. Compared to the BM, the RL is shown to have higher amplification and a shift to higher frequencies. This comes naturally from the realistic Y-shaped cell organization without tectorial membrane tuning.

Investigation of Micro-Scale Architectural Effects on Damage of Composites

NASA Technical Reports Server (NTRS)

Stier, Bertram; Bednarcyk, Brett A.; Simon, Jaan W.; Reese, Stefanie

2015-01-01

This paper presents a three-dimensional, energy based, anisotropic, stiffness reduction, progressive damage model for composite materials and composite material constituents. The model has been implemented as a user-defined constitutive model within the Abaqus finite element software package and applied to simulate the nonlinear behavior of a damaging epoxy matrix within a unidirectional composite material. Three different composite microstructures were considered as finite element repeating unit cells, with appropriate periodicity conditions applied at the boundaries. Results representing predicted transverse tensile, longitudinal shear, and transverse shear stress-strain curves are presented, along with plots of the local fields indicating the damage progression within the microstructure. It is demonstrated that the damage model functions appropriately at the matrix scale, enabling localization of the damage to simulate failure of the composite material. The influence of the repeating unit cell geometry and the effect of the directionality of the applied loading are investigated and discussed.

A finite-element method for large-amplitude, two-dimensional panel flutter at hypersonic speeds

NASA Technical Reports Server (NTRS)

Mei, Chuh; Gray, Carl E.

1989-01-01

The nonlinear flutter behavior of a two-dimensional panel in hypersonic flow is investigated analytically. An FEM formulation based unsteady third-order piston theory (Ashley and Zartarian, 1956; McIntosh, 1970) and taking nonlinear structural and aerodynamic phenomena into account is derived; the solution procedure is outlined; and typical results are presented in extensive tables and graphs. A 12-element finite-element solution obtained using an alternative method for linearizing the assumed limit-cycle time function is shown to give predictions in good agreement with classical analytical results for large-amplitude vibration in a vacuum and large-amplitude panel flutter, using linear aerodynamics.

Equivalent Linearization Analysis of Geometrically Nonlinear Random Vibrations Using Commercial Finite Element Codes

NASA Technical Reports Server (NTRS)

Rizzi, Stephen A.; Muravyov, Alexander A.

2002-01-01

Two new equivalent linearization implementations for geometrically nonlinear random vibrations are presented. Both implementations are based upon a novel approach for evaluating the nonlinear stiffness within commercial finite element codes and are suitable for use with any finite element code having geometrically nonlinear static analysis capabilities. The formulation includes a traditional force-error minimization approach and a relatively new version of a potential energy-error minimization approach, which has been generalized for multiple degree-of-freedom systems. Results for a simply supported plate under random acoustic excitation are presented and comparisons of the displacement root-mean-square values and power spectral densities are made with results from a nonlinear time domain numerical simulation.

Predictions of thermal buckling strengths of hypersonic aircraft sandwich panels using minimum potential energy and finite element methods

NASA Technical Reports Server (NTRS)

Ko, William L.

1995-01-01

Thermal buckling characteristics of hypersonic aircraft sandwich panels of various aspect ratios were investigated. The panel is fastened at its four edges to the substructures under four different edge conditions and is subjected to uniform temperature loading. Minimum potential energy theory and finite element methods were used to calculate the panel buckling temperatures. The two methods gave fairly close buckling temperatures. However, the finite element method gave slightly lower buckling temperatures than those given by the minimum potential energy theory. The reasons for this slight discrepancy in eigensolutions are discussed in detail. In addition, the effect of eigenshifting on the eigenvalue convergence rate is discussed.

Experimentally validated finite element model of electrocaloric multilayer ceramic structures

DOE Office of Scientific and Technical Information (OSTI.GOV)

Smith, N. A. S., E-mail: nadia.smith@npl.co.uk, E-mail: maciej.rokosz@npl.co.uk, E-mail: tatiana.correia@npl.co.uk; Correia, T. M., E-mail: nadia.smith@npl.co.uk, E-mail: maciej.rokosz@npl.co.uk, E-mail: tatiana.correia@npl.co.uk; Rokosz, M. K., E-mail: nadia.smith@npl.co.uk, E-mail: maciej.rokosz@npl.co.uk, E-mail: tatiana.correia@npl.co.uk

2014-07-28

A novel finite element model to simulate the electrocaloric response of a multilayer ceramic capacitor (MLCC) under real environment and operational conditions has been developed. The two-dimensional transient conductive heat transfer model presented includes the electrocaloric effect as a source term, as well as accounting for radiative and convective effects. The model has been validated with experimental data obtained from the direct imaging of MLCC transient temperature variation under application of an electric field. The good agreement between simulated and experimental data, suggests that the novel experimental direct measurement methodology and the finite element model could be used to supportmore » the design of optimised electrocaloric units and operating conditions.« less

Finite-element analysis of scattering parameters of surface acoustic wave bandpass filter formed on barium titanate thin film

NASA Astrophysics Data System (ADS)

Timoshenko; Kalinchuk; Shirokov

2018-04-01

The frequency dependence of scattering parameters of interdigital surface acoustic wave transducers placed on ferroelectric barium titanate (BaTiO3) epitaxial film in c-phase coated over magnesium oxide has been studied using the finite-element method (FEM) approach along with the perfectly matched layer (PML) technique. The interdigital transducer which has a comb-like structure with aluminum electrodes excites the mechanical wave. The distance between the fingers allows tuning the frequency properties of the wave propagation. The magnesium oxide is taken as the substrate. The two-dimensional model of two-port surface acoustic wave filter is created to calculate scattering parameters and to show how to design the fixture in COMSOLTM. Some practical computational challenges of finite element modeling of SAW devices in COMSOLTM are shown. The effect of lattice misfit strain on acoustic properties of heterostructures of BaTiO3 epitaxial film in c-phase at room temperature is discussed in present article for two low-frequency surface acoustic resonances.

A k-space method for large-scale models of wave propagation in tissue.

PubMed

Mast, T D; Souriau, L P; Liu, D L; Tabei, M; Nachman, A I; Waag, R C

2001-03-01

Large-scale simulation of ultrasonic pulse propagation in inhomogeneous tissue is important for the study of ultrasound-tissue interaction as well as for development of new imaging methods. Typical scales of interest span hundreds of wavelengths; most current two-dimensional methods, such as finite-difference and finite-element methods, are unable to compute propagation on this scale with the efficiency needed for imaging studies. Furthermore, for most available methods of simulating ultrasonic propagation, large-scale, three-dimensional computations of ultrasonic scattering are infeasible. Some of these difficulties have been overcome by previous pseudospectral and k-space methods, which allow substantial portions of the necessary computations to be executed using fast Fourier transforms. This paper presents a simplified derivation of the k-space method for a medium of variable sound speed and density; the derivation clearly shows the relationship of this k-space method to both past k-space methods and pseudospectral methods. In the present method, the spatial differential equations are solved by a simple Fourier transform method, and temporal iteration is performed using a k-t space propagator. The temporal iteration procedure is shown to be exact for homogeneous media, unconditionally stable for "slow" (c(x) < or = c0) media, and highly accurate for general weakly scattering media. The applicability of the k-space method to large-scale soft tissue modeling is shown by simulating two-dimensional propagation of an incident plane wave through several tissue-mimicking cylinders as well as a model chest wall cross section. A three-dimensional implementation of the k-space method is also employed for the example problem of propagation through a tissue-mimicking sphere. Numerical results indicate that the k-space method is accurate for large-scale soft tissue computations with much greater efficiency than that of an analogous leapfrog pseudospectral method or a 2-4 finite difference time-domain method. However, numerical results also indicate that the k-space method is less accurate than the finite-difference method for a high contrast scatterer with bone-like properties, although qualitative results can still be obtained by the k-space method with high efficiency. Possible extensions to the method, including representation of absorption effects, absorbing boundary conditions, elastic-wave propagation, and acoustic nonlinearity, are discussed.

An Investigation into the Postbuckling Response of a Single Blade-Stiffened Composite Panel

NASA Astrophysics Data System (ADS)

Spediacci, Alexander Daniel

The large strength reserves of stiffened composite structures in the postbuckling range appeal to the aerospace industry because of the high strength-to weight-ratio. Design and analysis of these large-scale, complex structures is technical, and requires major computational effort. Using the building-block approach, a smaller, single-stringer panel can be a useful and efficient tool for initial design, and can reveal critical behavior of a larger, multi-stringer panel. A characterization, through finite element modeling, of buckling and postbuckling response of a single blade-stiffened composite panel is proposed. Several factors affecting buckling and postbuckling behavior are investigated, including specimen length, initial imperfections, mode switching, and skin stringer separation. Two specimens are repeatedly tested under quasi- static compression loading well into the postbuckling range, showing no sign of damage. The test data from the specimens are used to compare and validate the nonlinear finite element models, show good correlation with the models. Ultimately, this work will serve to demonstrate the safety of stiffened structures operating in the postbuckling range and allow for thinner, lighter structures, which can increase the overall efficiency of aircraft.

Structural Analysis and Testing of an Erectable Truss for Precision Segmented Reflector Application

NASA Technical Reports Server (NTRS)

Collins, Timothy J.; Fichter, W. B.; Adams, Richard R.; Javeed, Mehzad

1995-01-01

This paper describes analysis and test results obtained at Langley Research Center (LaRC) on a doubly curved testbed support truss for precision reflector applications. Descriptions of test procedures and experimental results that expand upon previous investigations are presented. A brief description of the truss is given, and finite-element-analysis models are described. Static-load and vibration test procedures are discussed, and experimental results are shown to be repeatable and in generally good agreement with linear finite-element predictions. Truss structural performance (as determined by static deflection and vibration testing) is shown to be predictable and very close to linear. Vibration test results presented herein confirm that an anomalous mode observed during initial testing was due to the flexibility of the truss support system. Photogrammetric surveys with two 131-in. reference scales show that the root-mean-square (rms) truss-surface accuracy is about 0.0025 in. Photogrammetric measurements also indicate that the truss coefficient of thermal expansion (CTE) is in good agreement with that predicted by analysis. A detailed description of the photogrammetric procedures is included as an appendix.

A Large-scale Finite Element Model on Micromechanical Damage and Failure of Carbon Fiber/Epoxy Composites Including Thermal Residual Stress

NASA Astrophysics Data System (ADS)

Liu, P. F.; Li, X. K.

2018-06-01

The purpose of this paper is to study micromechanical progressive failure properties of carbon fiber/epoxy composites with thermal residual stress by finite element analysis (FEA). Composite microstructures with hexagonal fiber distribution are used for the representative volume element (RVE), where an initial fiber breakage is assumed. Fiber breakage with random fiber strength is predicted using Monte Carlo simulation, progressive matrix damage is predicted by proposing a continuum damage mechanics model and interface failure is simulated using Xu and Needleman's cohesive model. Temperature dependent thermal expansion coefficients for epoxy matrix are used. FEA by developing numerical codes using ANSYS finite element software is divided into two steps: 1. Thermal residual stresses due to mismatch between fiber and matrix are calculated; 2. Longitudinal tensile load is further exerted on the RVE to perform progressive failure analysis of carbon fiber/epoxy composites. Numerical convergence is solved by introducing the viscous damping effect properly. The extended Mori-Tanaka method that considers interface debonding is used to get homogenized mechanical responses of composites. Three main results by FEA are obtained: 1. the real-time matrix cracking, fiber breakage and interface debonding with increasing tensile strain is simulated. 2. the stress concentration coefficients on neighbouring fibers near the initial broken fiber and the axial fiber stress distribution along the broken fiber are predicted, compared with the results using the global and local load-sharing models based on the shear-lag theory. 3. the tensile strength of composite by FEA is compared with those by the shear-lag theory and experiments. Finally, the tensile stress-strain curve of composites by FEA is applied to the progressive failure analysis of composite pressure vessel.

A Large-scale Finite Element Model on Micromechanical Damage and Failure of Carbon Fiber/Epoxy Composites Including Thermal Residual Stress

NASA Astrophysics Data System (ADS)

Liu, P. F.; Li, X. K.

2017-09-01

The purpose of this paper is to study micromechanical progressive failure properties of carbon fiber/epoxy composites with thermal residual stress by finite element analysis (FEA). Composite microstructures with hexagonal fiber distribution are used for the representative volume element (RVE), where an initial fiber breakage is assumed. Fiber breakage with random fiber strength is predicted using Monte Carlo simulation, progressive matrix damage is predicted by proposing a continuum damage mechanics model and interface failure is simulated using Xu and Needleman's cohesive model. Temperature dependent thermal expansion coefficients for epoxy matrix are used. FEA by developing numerical codes using ANSYS finite element software is divided into two steps: 1. Thermal residual stresses due to mismatch between fiber and matrix are calculated; 2. Longitudinal tensile load is further exerted on the RVE to perform progressive failure analysis of carbon fiber/epoxy composites. Numerical convergence is solved by introducing the viscous damping effect properly. The extended Mori-Tanaka method that considers interface debonding is used to get homogenized mechanical responses of composites. Three main results by FEA are obtained: 1. the real-time matrix cracking, fiber breakage and interface debonding with increasing tensile strain is simulated. 2. the stress concentration coefficients on neighbouring fibers near the initial broken fiber and the axial fiber stress distribution along the broken fiber are predicted, compared with the results using the global and local load-sharing models based on the shear-lag theory. 3. the tensile strength of composite by FEA is compared with those by the shear-lag theory and experiments. Finally, the tensile stress-strain curve of composites by FEA is applied to the progressive failure analysis of composite pressure vessel.

Structural Evaluation of a Space Shuttle Main Engine (SSME) High Pressure Fuel Turbopump Turbine Blade

NASA Technical Reports Server (NTRS)

Abdul-Aziz, Ali

1996-01-01

Thermal and structural finite-element analyses were performed on the first high pressure fuel turbopump turbine blade of the space shuttle main engine (SSME). A two-dimensional (2-D) finite-element model of the blade and firtree disk attachment was analyzed using the general purpose MARC (finite-element) code. The loading history applied is a typical test stand engine cycle mission, which consists of a startup condition with two thermal spikes, a steady state and a shutdown transient. The blade material is a directionally solidified (DS) Mar-M 246 alloy, the blade rotor is forged with waspalloy material. Thermal responses under steady-state and transient conditions were calculated. The stresses and strains under the influence of mechanical and thermal loadings were also determined. The critical regions that exhibited high stresses and severe localized plastic deformation were the blade-rotor gaps.

Integrated Nondestructive Evaluation and Finite Element Analysis Predicts Crack Location and Shape

NASA Technical Reports Server (NTRS)

Abdul-Azia, Ali; Baaklini, George Y.; Trudell, Jeffrey J.

2002-01-01

This study describes the finite-element analyses and the NDE modality undertaken on two flywheel rotors that were spun to burst speed. Computed tomography and dimensional measurements were used to nondestructively evaluate the rotors before and/or after they were spun to the first crack detection. Computed tomography data findings of two- and three-dimensional crack formation were used to conduct finite-element (FEA) and fracture mechanics analyses. A procedure to extend these analyses to estimate the life of these components is also outlined. NDE-FEA results for one of the rotors are presented in the figures. The stress results, which represent the radial stresses in the rim, clearly indicate that the maximum stress region is within the section defined by the computed tomography scan. Furthermore, the NDE data correlate well with the FEA results. In addition, the measurements reported show that the NDE and FEA data are in parallel.

Light refocusing with up-scalable resonant waveguide gratings in confocal prolate spheroid arrangements

NASA Astrophysics Data System (ADS)

Quaranta, Giorgio; Basset, Guillaume; Benes, Zdenek; Martin, Olivier J. F.; Gallinet, Benjamin

2018-01-01

Resonant waveguide gratings (RWGs) are thin-film structures, where coupled modes interfere with the diffracted incoming wave and produce strong angular and spectral filtering. The combination of two finite-length and impedance matched RWGs allows the creation of a passive beam steering element, which is compatible with up-scalable fabrication processes. Here, we propose a design method to create large patterns of such elements able to filter, steer, and focus the light from one point source to another. The method is based on ellipsoidal mirrors to choose a system of confocal prolate spheroids where the two focal points are the source point and observation point, respectively. It allows finding the proper orientation and position of each RWG element of the pattern, such that the phase is constructively preserved at the observation point. The design techniques presented here could be implemented in a variety of systems, where large-scale patterns are needed, such as optical security, multifocal or monochromatic lenses, biosensors, and see-through optical combiners for near-eye displays.

A collocation--Galerkin finite element model of cardiac action potential propagation.

PubMed

Rogers, J M; McCulloch, A D

1994-08-01

A new computational method was developed for modeling the effects of the geometric complexity, nonuniform muscle fiber orientation, and material inhomogeneity of the ventricular wall on cardiac impulse propagation. The method was used to solve a modification to the FitzHugh-Nagumo system of equations. The geometry, local muscle fiber orientation, and material parameters of the domain were defined using linear Lagrange or cubic Hermite finite element interpolation. Spatial variations of time-dependent excitation and recovery variables were approximated using cubic Hermite finite element interpolation, and the governing finite element equations were assembled using the collocation method. To overcome the deficiencies of conventional collocation methods on irregular domains, Galerkin equations for the no-flux boundary conditions were used instead of collocation equations for the boundary degrees-of-freedom. The resulting system was evolved using an adaptive Runge-Kutta method. Converged two-dimensional simulations of normal propagation showed that this method requires less CPU time than a traditional finite difference discretization. The model also reproduced several other physiologic phenomena known to be important in arrhythmogenesis including: Wenckebach periodicity, slowed propagation and unidirectional block due to wavefront curvature, reentry around a fixed obstacle, and spiral wave reentry. In a new result, we observed wavespeed variations and block due to nonuniform muscle fiber orientation. The findings suggest that the finite element method is suitable for studying normal and pathological cardiac activation and has significant advantages over existing techniques.

Eigensolution of finite element problems in a completely connected parallel architecture

NASA Technical Reports Server (NTRS)

Akl, F.; Morel, M.

1989-01-01

A parallel algorithm is presented for the solution of the generalized eigenproblem in linear elastic finite element analysis. The algorithm is based on a completely connected parallel architecture in which each processor is allowed to communicate with all other processors. The algorithm is successfully implemented on a tightly coupled MIMD parallel processor. A finite element model is divided into m domains each of which is assumed to process n elements. Each domain is then assigned to a processor or to a logical processor (task) if the number of domains exceeds the number of physical processors. The effect of the number of domains, the number of degrees-of-freedom located along the global fronts, and the dimension of the subspace on the performance of the algorithm is investigated. For a 64-element rectangular plate, speed-ups of 1.86, 3.13, 3.18, and 3.61 are achieved on two, four, six, and eight processors, respectively.

Penalty-Based Finite Element Interface Technology for Analysis of Homogeneous and Composite Structures

NASA Technical Reports Server (NTRS)

Averill, Ronald C.

2002-01-01

An effective and robust interface element technology able to connect independently modeled finite element subdomains has been developed. This method is based on the use of penalty constraints and allows coupling of finite element models whose nodes do not coincide along their common interface. Additionally, the present formulation leads to a computational approach that is very efficient and completely compatible with existing commercial software. A significant effort has been directed toward identifying those model characteristics (element geometric properties, material properties, and loads) that most strongly affect the required penalty parameter, and subsequently to developing simple 'formulae' for automatically calculating the proper penalty parameter for each interface constraint. This task is especially critical in composite materials and structures, where adjacent sub-regions may be composed of significantly different materials or laminates. This approach has been validated by investigating a variety of two-dimensional problems, including composite laminates.

PRELIMINARY PROGRESS IN THE DEVELOPMENT OF DUCTILE-PHASE TOUGHENED TUNGSTEN FOR PLASMA-FACING MATERIALS: DUAL-PHASE FINITE ELEMENT DAMAGE MODELS

DOE Office of Scientific and Technical Information (OSTI.GOV)

Henager, Charles H.; Nguyen, Ba Nghiep; Kurtz, Richard J.

The objective of this study is to develop a finite element continuum damage model suitable for modeling deformation, cracking, and crack bridging for W-Cu, W-Ni-Fe, and other ductile phase toughened W-composites, or more generally, any multi-phase composite structure where two or more phases undergo cooperative deformation in a composite system.

Comparisons of node-based and element-based approaches of assigning bone material properties onto subject-specific finite element models.

PubMed

Chen, G; Wu, F Y; Liu, Z C; Yang, K; Cui, F

2015-08-01

Subject-specific finite element (FE) models can be generated from computed tomography (CT) datasets of a bone. A key step is assigning material properties automatically onto finite element models, which remains a great challenge. This paper proposes a node-based assignment approach and also compares it with the element-based approach in the literature. Both approaches were implemented using ABAQUS. The assignment procedure is divided into two steps: generating the data file of the image intensity of a bone in a MATLAB program and reading the data file into ABAQUS via user subroutines. The node-based approach assigns the material properties to each node of the finite element mesh, while the element-based approach assigns the material properties directly to each integration point of an element. Both approaches are independent from the type of elements. A number of FE meshes are tested and both give accurate solutions; comparatively the node-based approach involves less programming effort. The node-based approach is also independent from the type of analyses; it has been tested on the nonlinear analysis of a Sawbone femur. The node-based approach substantially improves the level of automation of the assignment procedure of bone material properties. It is the simplest and most powerful approach that is applicable to many types of analyses and elements. Copyright © 2015 IPEM. Published by Elsevier Ltd. All rights reserved.

Posttest analysis of the 1:6-scale reinforced concrete containment

DOE Office of Scientific and Technical Information (OSTI.GOV)

Pfeiffer, P.A.; Kennedy, J.M.; Marchertas, A.H.

A prediction of the response of the Sandia National Laboratories 1:6- scale reinforced concrete containment model test was made by Argonne National Laboratory. ANL along with nine other organizations performed a detailed nonlinear response analysis of the 1:6-scale model containment subjected to overpressurization in the fall of 1986. The two-dimensional code TEMP-STRESS and the three-dimensional NEPTUNE code were utilized (1) to predict the global response of the structure, (2) to identify global failure sites and the corresponding failure pressures and (3) to identify some local failure sites and pressure levels. A series of axisymmetric models was studied with the two-dimensionalmore » computer program TEMP-STRESS. The comparison of these pretest computations with test data from the containment model has provided a test for the capability of the respective finite element codes to predict global failure modes, and hence serves as a validation of these codes. Only the two-dimensional analyses will be discussed in this paper. 3 refs., 10 figs.« less

Bolt clampup relaxation in a graphite/epoxy laminate

NASA Technical Reports Server (NTRS)

Shivakumar, K. N.; Crews, J. H., Jr.

1982-01-01

A simple bolted joint was analyzed to calculate bolt clampup relaxation for a graphite/epoxy (T300/5208) laminate. A viscoelastic finite element analysis of a double-lap joint with a steel bolt was conducted. Clampup forces were calculated for various steady-state temperature-moisture conditions using a 20-year exposure duration. The finite element analysis predicted that clampup forces relax even for the room-temperature-dry condition. The relaxations were 8, 13, 20, and 30 percent for exposure durations of 1 day, 1 month, 1 year, and 20 years, respectively. As expected, higher temperatures and moisture levels each increased the relaxation rate. The combined viscoelastic effects of steady-state temperature and moisture appeared to be additive. From the finite-element analysis, a simple equation was developed for clampup force relaxation. This generalized equation was used to calculate clampup forces for the same temperature-moisture conditions as used in the finite-element analysis. The two sets of calculated results agreed well.

Documentation of a graphical display program for the saturated- unsaturated transport (SUTRA) finite-element simulation model

USGS Publications Warehouse

Souza, W.R.

1987-01-01

This report documents a graphical display program for the U. S. Geological Survey finite-element groundwater flow and solute transport model. Graphic features of the program, SUTRA-PLOT (SUTRA-PLOT = saturated/unsaturated transport), include: (1) plots of the finite-element mesh, (2) velocity vector plots, (3) contour plots of pressure, solute concentration, temperature, or saturation, and (4) a finite-element interpolator for gridding data prior to contouring. SUTRA-PLOT is written in FORTRAN 77 on a PRIME 750 computer system, and requires Version 9.0 or higher of the DISSPLA graphics library. The program requires two input files: the SUTRA input data list and the SUTRA simulation output listing. The program is menu driven and specifications for individual types of plots are entered and may be edited interactively. Installation instruction, a source code listing, and a description of the computer code are given. Six examples of plotting applications are used to demonstrate various features of the plotting program. (Author 's abstract)

Finite element analysis of the end notched flexure specimen for measuring Mode II fracture toughness

NASA Technical Reports Server (NTRS)

Gillespie, J. W., Jr.; Carlsson, L. A.; Pipes, R. B.

1986-01-01

The paper presents a finite element analysis of the end-notched flexure (ENF) test specimen for Mode II interlaminar fracture testing of composite materials. Virtual crack closure and compliance techniques employed to calculate strain energy release rates from linear elastic two-dimensional analysis indicate that the ENF specimen is a pure Mode II fracture test within the constraints of small deflection theory. Furthermore, the ENF fracture specimen is shown to be relatively insensitive to process-induced cracks, offset from the laminate midplane. Frictional effects are investigated by including the contact problem in the finite element model. A parametric study investigating the influence of delamination length, span, thickness, and material properties assessed the accuracy of beam theory expressions for compliance and strain energy release rate, GII. Finite element results indicate that data reduction schemes based upon beam theory underestimate GII by approximately 20-40 percent for typical unidirectional graphite fiber composite test specimen geometries. Consequently, an improved data reduction scheme is proposed.

Applied mathematical problems in modern electromagnetics

NASA Astrophysics Data System (ADS)

Kriegsman, Gregory

1994-05-01

We have primarily investigated two classes of electromagnetic problems. The first contains the quantitative description of microwave heating of dispersive and conductive materials. Such problems arise, for example, when biological tissue are exposed, accidentally or purposefully, to microwave radiation. Other instances occur in ceramic processing, such as sintering and microwave assisted chemical vapor infiltration and other industrial drying processes, such as the curing of paints and concrete. The second class characterizes the scattering of microwaves by complex targets which possess two or more disparate length and/or time scales. Spatially complex scatterers arise in a variety of applications, such as large gratings and slowly changing guiding structures. The former are useful in developing microstrip energy couplers while the later can be used to model anatomical subsystems (e.g., the open guiding structure composed of two legs and the adjoining lower torso). Temporally complex targets occur in applications involving dispersive media whose relaxation times differ by orders of magnitude from thermal and/or electromagnetic time scales. For both cases the mathematical description of the problems gives rise to complicated ill-conditioned boundary value problems, whose accurate solutions require a blend of both asymptotic techniques, such as multiscale methods and matched asymptotic expansions, and numerical methods incorporating radiation boundary conditions, such as finite differences and finite elements.

A simple and efficient shear-flexible plate bending element

NASA Technical Reports Server (NTRS)

Chaudhuri, Reaz A.

1987-01-01

A shear-flexible triangular element formulation, which utilizes an assumed quadratic displacement potential energy approach and is numerically integrated using Gauss quadrature, is presented. The Reissner/Mindlin hypothesis of constant cross-sectional warping is directly applied to the three-dimensional elasticity theory to obtain a moderately thick-plate theory or constant shear-angle theory (CST), wherein the middle surface is no longer considered to be the reference surface and the two rotations are replaced by the two in-plane displacements as nodal variables. The resulting finite-element possesses 18 degrees of freedom (DOF). Numerical results are obtained for two different numerical integration schemes and a wide range of meshes and span-to-thickness ratios. These, when compared with available exact, series or finite-element solutions, demonstrate accuracy and rapid convergence characteristics of the present element. This is especially true in the case of thin to very thin plates, when the present element, used in conjunction with the reduced integration scheme, outperforms its counterpart, based on discrete Kirchhoff constraint theory (DKT).

A locally conservative non-negative finite element formulation for anisotropic advective-diffusive-reactive systems

NASA Astrophysics Data System (ADS)

Mudunuru, M. K.; Shabouei, M.; Nakshatrala, K.

2015-12-01

Advection-diffusion-reaction (ADR) equations appear in various areas of life sciences, hydrogeological systems, and contaminant transport. Obtaining stable and accurate numerical solutions can be challenging as the underlying equations are coupled, nonlinear, and non-self-adjoint. Currently, there is neither a robust computational framework available nor a reliable commercial package known that can handle various complex situations. Herein, the objective of this poster presentation is to present a novel locally conservative non-negative finite element formulation that preserves the underlying physical and mathematical properties of a general linear transient anisotropic ADR equation. In continuous setting, governing equations for ADR systems possess various important properties. In general, all these properties are not inherited during finite difference, finite volume, and finite element discretizations. The objective of this poster presentation is two fold: First, we analyze whether the existing numerical formulations (such as SUPG and GLS) and commercial packages provide physically meaningful values for the concentration of the chemical species for various realistic benchmark problems. Furthermore, we also quantify the errors incurred in satisfying the local and global species balance for two popular chemical kinetics schemes: CDIMA (chlorine dioxide-iodine-malonic acid) and BZ (Belousov--Zhabotinsky). Based on these numerical simulations, we show that SUPG and GLS produce unphysical values for concentration of chemical species due to the violation of the non-negative constraint, contain spurious node-to-node oscillations, and have large errors in local and global species balance. Second, we proposed a novel finite element formulation to overcome the above difficulties. The proposed locally conservative non-negative computational framework based on low-order least-squares finite elements is able to preserve these underlying physical and mathematical properties. Several representative numerical examples are discussed to illustrate the importance of the proposed numerical formulations to accurately describe various aspects of mixing process in chaotic flows and to simulate transport in highly heterogeneous anisotropic media.

A Dynamic Finite Element Method for Simulating the Physics of Faults Systems

NASA Astrophysics Data System (ADS)

Saez, E.; Mora, P.; Gross, L.; Weatherley, D.

2004-12-01

We introduce a dynamic Finite Element method using a novel high level scripting language to describe the physical equations, boundary conditions and time integration scheme. The library we use is the parallel Finley library: a finite element kernel library, designed for solving large-scale problems. It is incorporated as a differential equation solver into a more general library called escript, based on the scripting language Python. This library has been developed to facilitate the rapid development of 3D parallel codes, and is optimised for the Australian Computational Earth Systems Simulator Major National Research Facility (ACcESS MNRF) supercomputer, a 208 processor SGI Altix with a peak performance of 1.1 TFlops. Using the scripting approach we obtain a parallel FE code able to take advantage of the computational efficiency of the Altix 3700. We consider faults as material discontinuities (the displacement, velocity, and acceleration fields are discontinuous at the fault), with elastic behavior. The stress continuity at the fault is achieved naturally through the expression of the fault interactions in the weak formulation. The elasticity problem is solved explicitly in time, using the Saint Verlat scheme. Finally, we specify a suitable frictional constitutive relation and numerical scheme to simulate fault behaviour. Our model is based on previous work on modelling fault friction and multi-fault systems using lattice solid-like models. We adapt the 2D model for simulating the dynamics of parallel fault systems described to the Finite-Element method. The approach uses a frictional relation along faults that is slip and slip-rate dependent, and the numerical integration approach introduced by Mora and Place in the lattice solid model. In order to illustrate the new Finite Element model, single and multi-fault simulation examples are presented.

The influence of the lysimeter filling on the soil monolith inside

NASA Astrophysics Data System (ADS)

Puetz, T.; Schilling, J.; Vereecken, H.

2009-04-01

In general, lysimeters are vessels containing disturbed or undisturbed soil blocks, for the most realistic scenario with regard to real outdoor conditions an undisturbed soil block so called soil monolith is preferable. The lower boundary condition was realized in two different ways: as a zero-tension lysimeter with a perforated bottom plate or as controlled lower boundary condition with a suction plate. The optimal surface area and the lysimeter length depend mainly on the scientific question. For cropped lysimeter experiments the lysimeter length has to reflect to a maximum root length. The base area is strongly connected to the scale of observation, whereby small-scale heterogeneity will be averaged using large base areas. For our experiments lysimeters with 2.5 m length, 2 m2 base area and with a wall thickness of the round vessel of 10 mm were used. A base frame weighted down by 120 t of concrete weights is necessary to press a lysimeter cylinder into the ground by the aid of a hydraulic press. The hydraulic press is connected with the base frame via chains. Because of the control of the four hydraulic cylinders a very precise vertical pressing process is guaranteed. To visualize the impact of the lysimeter filling on the intactness of the soil monolith a finite element computation was conducted. The finite element package ANSYS Release 11 was used to execute a nonlinear static analysis on a 2D-axisymmetric finite element model, to simulate the pressing process starting from a soil initial stress state and ending with the full length of the vessel driven into the soil, after which the hydraulic press and the concrete weights are deactivated and the vessel-surrounding soil is excavated. The numerical model of the pressing process considers among other things, a cap non-associative plasticity model with shear and volumetric hardening, soil to soil contact with cohesive zone modelling, soil to vessel contact with high friction, soil excavation using element birth and death and a stagger-loop over the complete pressing process to determine the actual cutting plane

Simplified and refined finite element approaches for determining stresses and internal forces in geometrically nonlinear structural analysis

NASA Technical Reports Server (NTRS)

Robinson, J. C.

1979-01-01

Two methods for determining stresses and internal forces in geometrically nonlinear structural analysis are presented. The simplified approach uses the mid-deformed structural position to evaluate strains when rigid body rotation is present. The important feature of this approach is that it can easily be used with a general-purpose finite-element computer program. The refined approach uses element intrinsic or corotational coordinates and a geometric transformation to determine element strains from joint displacements. Results are presented which demonstrate the capabilities of these potentially useful approaches for geometrically nonlinear structural analysis.

Global-Local Finite Element Analysis for Thermo-Mechanical Stresses in Bonded Joints

NASA Technical Reports Server (NTRS)

Shkarayev, S.; Madenci, Erdogan; Camarda, C. J.

1997-01-01

An analysis of adhesively bonded joints using conventional finite elements does not capture the singular behavior of the stress field in regions where two or three dissimilar materials form a junction with or without free edges. However, these regions are characteristic of the bonded joints and are prone to failure initiation. This study presents a method to capture the singular stress field arising from the geometric and material discontinuities in bonded composites. It is achieved by coupling the local (conventional) elements with global (special) elements whose interpolation functions are constructed from the asymptotic solution.

MHOST version 4.2. Volume 1: Users' manual

NASA Technical Reports Server (NTRS)

Nakazawa, Shohei

1989-01-01

This manual describes the user options available for running the MHOST finite element analysis package. MHOST is a solid and structural analysis program based on mixed finite element technology, and is specifically designed for three-dimensional inelastic analysis. A family of two- and three-dimensional continuum elements along with beam and shell structural elements can be utilized. Many options are available in the constitutive equation library, the solution algorithms and the analysis capabilities. An overview of the algorithms, a general description of the input data formats, and a discussion of input data for selecting solution algorithms are given.

EIT Imaging Regularization Based on Spectral Graph Wavelets.

PubMed

Gong, Bo; Schullcke, Benjamin; Krueger-Ziolek, Sabine; Vauhkonen, Marko; Wolf, Gerhard; Mueller-Lisse, Ullrich; Moeller, Knut

2017-09-01

The objective of electrical impedance tomographic reconstruction is to identify the distribution of tissue conductivity from electrical boundary conditions. This is an ill-posed inverse problem usually solved under the finite-element method framework. In previous studies, standard sparse regularization was used for difference electrical impedance tomography to achieve a sparse solution. However, regarding elementwise sparsity, standard sparse regularization interferes with the smoothness of conductivity distribution between neighboring elements and is sensitive to noise. As an effect, the reconstructed images are spiky and depict a lack of smoothness. Such unexpected artifacts are not realistic and may lead to misinterpretation in clinical applications. To eliminate such artifacts, we present a novel sparse regularization method that uses spectral graph wavelet transforms. Single-scale or multiscale graph wavelet transforms are employed to introduce local smoothness on different scales into the reconstructed images. The proposed approach relies on viewing finite-element meshes as undirected graphs and applying wavelet transforms derived from spectral graph theory. Reconstruction results from simulations, a phantom experiment, and patient data suggest that our algorithm is more robust to noise and produces more reliable images.

Dynamic Shape Reconstruction of Three-Dimensional Frame Structures Using the Inverse Finite Element Method

NASA Technical Reports Server (NTRS)

Gherlone, Marco; Cerracchio, Priscilla; Mattone, Massimiliano; Di Sciuva, Marco; Tessler, Alexander

2011-01-01

A robust and efficient computational method for reconstructing the three-dimensional displacement field of truss, beam, and frame structures, using measured surface-strain data, is presented. Known as shape sensing , this inverse problem has important implications for real-time actuation and control of smart structures, and for monitoring of structural integrity. The present formulation, based on the inverse Finite Element Method (iFEM), uses a least-squares variational principle involving strain measures of Timoshenko theory for stretching, torsion, bending, and transverse shear. Two inverse-frame finite elements are derived using interdependent interpolations whose interior degrees-of-freedom are condensed out at the element level. In addition, relationships between the order of kinematic-element interpolations and the number of required strain gauges are established. As an example problem, a thin-walled, circular cross-section cantilevered beam subjected to harmonic excitations in the presence of structural damping is modeled using iFEM; where, to simulate strain-gauge values and to provide reference displacements, a high-fidelity MSC/NASTRAN shell finite element model is used. Examples of low and high-frequency dynamic motion are analyzed and the solution accuracy examined with respect to various levels of discretization and the number of strain gauges.

Coupled discrete element and finite volume solution of two classical soil mechanics problems

DOE Office of Scientific and Technical Information (OSTI.GOV)

Chen, Feng; Drumm, Eric; Guiochon, Georges A

One dimensional solutions for the classic critical upward seepage gradient/quick condition and the time rate of consolidation problems are obtained using coupled routines for the finite volume method (FVM) and discrete element method (DEM), and the results compared with the analytical solutions. The two phase flow in a system composed of fluid and solid is simulated with the fluid phase modeled by solving the averaged Navier-Stokes equation using the FVM and the solid phase is modeled using the DEM. A framework is described for the coupling of two open source computer codes: YADE-OpenDEM for the discrete element method and OpenFOAMmore » for the computational fluid dynamics. The particle-fluid interaction is quantified using a semi-empirical relationship proposed by Ergun [12]. The two classical verification problems are used to explore issues encountered when using coupled flow DEM codes, namely, the appropriate time step size for both the fluid and mechanical solution processes, the choice of the viscous damping coefficient, and the number of solid particles per finite fluid volume.« less

Advances in three-dimensional field analysis and evaluation of performance parameters of electrical machines

NASA Astrophysics Data System (ADS)

Sivasubramaniam, Kiruba

This thesis makes advances in three dimensional finite element analysis of electrical machines and the quantification of their parameters and performance. The principal objectives of the thesis are: (1)the development of a stable and accurate method of nonlinear three-dimensional field computation and application to electrical machinery and devices; and (2)improvement in the accuracy of determination of performance parameters, particularly forces and torque computed from finite elements. Contributions are made in two general areas: a more efficient formulation for three dimensional finite element analysis which saves time and improves accuracy, and new post-processing techniques to calculate flux density values from a given finite element solution. A novel three-dimensional magnetostatic solution based on a modified scalar potential method is implemented. This method has significant advantages over the traditional total scalar, reduced scalar or vector potential methods. The new method is applied to a 3D geometry of an iron core inductor and a permanent magnet motor. The results obtained are compared with those obtained from traditional methods, in terms of accuracy and speed of computation. A technique which has been observed to improve force computation in two dimensional analysis using a local solution of Laplace's equation in the airgap of machines is investigated and a similar method is implemented in the three dimensional analysis of electromagnetic devices. A new integral formulation to improve force calculation from a smoother flux-density profile is also explored and implemented. Comparisons are made and conclusions drawn as to how much improvement is obtained and at what cost. This thesis also demonstrates the use of finite element analysis to analyze torque ripples due to rotor eccentricity in permanent magnet BLDC motors. A new method for analyzing torque harmonics based on data obtained from a time stepping finite element analysis of the machine is explored and implemented.

Assessing a mini-application as a performance proxy for a finite element method engineering application

DOE Office of Scientific and Technical Information (OSTI.GOV)

Lin, Paul T.; Heroux, Michael A.; Barrett, Richard F.

The performance of a large-scale, production-quality science and engineering application (‘app’) is often dominated by a small subset of the code. Even within that subset, computational and data access patterns are often repeated, so that an even smaller portion can represent the performance-impacting features. If application developers, parallel computing experts, and computer architects can together identify this representative subset and then develop a small mini-application (‘miniapp’) that can capture these primary performance characteristics, then this miniapp can be used to both improve the performance of the app as well as provide a tool for co-design for the high-performance computing community.more » However, a critical question is whether a miniapp can effectively capture key performance behavior of an app. This study provides a comparison of an implicit finite element semiconductor device modeling app on unstructured meshes with an implicit finite element miniapp on unstructured meshes. The goal is to assess whether the miniapp is predictive of the performance of the app. Finally, single compute node performance will be compared, as well as scaling up to 16,000 cores. Results indicate that the miniapp can be reasonably predictive of the performance characteristics of the app for a single iteration of the solver on a single compute node.« less

On the use of finite difference matrix-vector products in Newton-Krylov solvers for implicit climate dynamics with spectral elements

DOE PAGES

Woodward, Carol S.; Gardner, David J.; Evans, Katherine J.

2015-01-01

Efficient solutions of global climate models require effectively handling disparate length and time scales. Implicit solution approaches allow time integration of the physical system with a step size governed by accuracy of the processes of interest rather than by stability of the fastest time scales present. Implicit approaches, however, require the solution of nonlinear systems within each time step. Usually, a Newton's method is applied to solve these systems. Each iteration of the Newton's method, in turn, requires the solution of a linear model of the nonlinear system. This model employs the Jacobian of the problem-defining nonlinear residual, but thismore » Jacobian can be costly to form. If a Krylov linear solver is used for the solution of the linear system, the action of the Jacobian matrix on a given vector is required. In the case of spectral element methods, the Jacobian is not calculated but only implemented through matrix-vector products. The matrix-vector multiply can also be approximated by a finite difference approximation which may introduce inaccuracy in the overall nonlinear solver. In this paper, we review the advantages and disadvantages of finite difference approximations of these matrix-vector products for climate dynamics within the spectral element shallow water dynamical core of the Community Atmosphere Model.« less

Assessing a mini-application as a performance proxy for a finite element method engineering application

DOE PAGES

Lin, Paul T.; Heroux, Michael A.; Barrett, Richard F.; ...

2015-07-30

The performance of a large-scale, production-quality science and engineering application (‘app’) is often dominated by a small subset of the code. Even within that subset, computational and data access patterns are often repeated, so that an even smaller portion can represent the performance-impacting features. If application developers, parallel computing experts, and computer architects can together identify this representative subset and then develop a small mini-application (‘miniapp’) that can capture these primary performance characteristics, then this miniapp can be used to both improve the performance of the app as well as provide a tool for co-design for the high-performance computing community.more » However, a critical question is whether a miniapp can effectively capture key performance behavior of an app. This study provides a comparison of an implicit finite element semiconductor device modeling app on unstructured meshes with an implicit finite element miniapp on unstructured meshes. The goal is to assess whether the miniapp is predictive of the performance of the app. Finally, single compute node performance will be compared, as well as scaling up to 16,000 cores. Results indicate that the miniapp can be reasonably predictive of the performance characteristics of the app for a single iteration of the solver on a single compute node.« less

Large-scale 3D geoelectromagnetic modeling using parallel adaptive high-order finite element method

DOE PAGES

Grayver, Alexander V.; Kolev, Tzanio V.

2015-11-01

Here, we have investigated the use of the adaptive high-order finite-element method (FEM) for geoelectromagnetic modeling. Because high-order FEM is challenging from the numerical and computational points of view, most published finite-element studies in geoelectromagnetics use the lowest order formulation. Solution of the resulting large system of linear equations poses the main practical challenge. We have developed a fully parallel and distributed robust and scalable linear solver based on the optimal block-diagonal and auxiliary space preconditioners. The solver was found to be efficient for high finite element orders, unstructured and nonconforming locally refined meshes, a wide range of frequencies, largemore » conductivity contrasts, and number of degrees of freedom (DoFs). Furthermore, the presented linear solver is in essence algebraic; i.e., it acts on the matrix-vector level and thus requires no information about the discretization, boundary conditions, or physical source used, making it readily efficient for a wide range of electromagnetic modeling problems. To get accurate solutions at reduced computational cost, we have also implemented goal-oriented adaptive mesh refinement. The numerical tests indicated that if highly accurate modeling results were required, the high-order FEM in combination with the goal-oriented local mesh refinement required less computational time and DoFs than the lowest order adaptive FEM.« less

Large-scale 3D geoelectromagnetic modeling using parallel adaptive high-order finite element method

DOE Office of Scientific and Technical Information (OSTI.GOV)

Grayver, Alexander V.; Kolev, Tzanio V.

Here, we have investigated the use of the adaptive high-order finite-element method (FEM) for geoelectromagnetic modeling. Because high-order FEM is challenging from the numerical and computational points of view, most published finite-element studies in geoelectromagnetics use the lowest order formulation. Solution of the resulting large system of linear equations poses the main practical challenge. We have developed a fully parallel and distributed robust and scalable linear solver based on the optimal block-diagonal and auxiliary space preconditioners. The solver was found to be efficient for high finite element orders, unstructured and nonconforming locally refined meshes, a wide range of frequencies, largemore » conductivity contrasts, and number of degrees of freedom (DoFs). Furthermore, the presented linear solver is in essence algebraic; i.e., it acts on the matrix-vector level and thus requires no information about the discretization, boundary conditions, or physical source used, making it readily efficient for a wide range of electromagnetic modeling problems. To get accurate solutions at reduced computational cost, we have also implemented goal-oriented adaptive mesh refinement. The numerical tests indicated that if highly accurate modeling results were required, the high-order FEM in combination with the goal-oriented local mesh refinement required less computational time and DoFs than the lowest order adaptive FEM.« less

Deformation of two-phase aggregates using standard numerical methods

NASA Astrophysics Data System (ADS)

Duretz, Thibault; Yamato, Philippe; Schmalholz, Stefan M.

2013-04-01

Geodynamic problems often involve the large deformation of material encompassing material boundaries. In geophysical fluids, such boundaries often coincide with a discontinuity in the viscosity (or effective viscosity) field and subsequently in the pressure field. Here, we employ popular implementations of the finite difference and finite element methods for solving viscous flow problems. On one hand, we implemented finite difference method coupled with a Lagrangian marker-in-cell technique to represent the deforming fluid. Thanks to it Eulerian nature, this method has a limited geometric flexibility but is characterized by a light and stable discretization. On the other hand, we employ the Lagrangian finite element method which offers full geometric flexibility at the cost of relatively heavier discretization. In order to test the accuracy of the finite difference scheme, we ran large strain simple shear deformation of aggregates containing either weak of strong circular inclusion (1e6 viscosity ratio). The results, obtained for different grid resolutions, are compared to Lagrangian finite element results which are considered as reference solution. The comparison is then used to establish up to which strain can finite difference simulations be run given the nature of the inclusions (dimensions, viscosity) and the resolution of the Eulerian mesh.

3D reconstruction of bony elements of the knee joint and finite element analysis of total knee prosthesis obtained from the reconstructed model.

PubMed

Djoudi, Farid

2013-01-01

Two separate themes are presented in this paper. The first theme is to present a graphical modeling approach of human anatomical structures namely, the femur and the tibia. The second theme involves making a finite element analysis of stresses, displacements and deformations in prosthetic implants (the femoral implant and the polyethylene insert). The graphical modeling approach comes in two parts. The first is the segmentation of MRI scanned images, retrieved in DICOM format for edge detection. In the second part, 3D-CAD models are generated from the results of the segmentation stage. The finite element analysis is done by first extracting the prosthetic implants from the reconstructed 3D-CAD model, then do a finite element analysis of these implants under objectively determined conditions such as; forces, allowed displacements, the materials composing implant, and the coefficient of friction. The objective of this work is to implement an interface for exchanging data between 2D MRI images obtained from a medical diagnosis of a patient and the 3D-CAD model used in various applications, such as; the extraction of the implants, stress analysis at the knee joint and can serve as an aid to surgery, also predict the behavior of the prosthetic implants vis-a-vis the forces acting on the knee joints.

Strain-energy-release rate analysis of the end-notched flexure specimen using the finite-element method

NASA Technical Reports Server (NTRS)

Salpekar, S. A.; Raju, I. S.; Obrien, T. K.

1987-01-01

Two-dimensional finite-element analysis of the end-notched flexure specimen was performed using 8-node isoparametric, parabolic elements to evaluate compliance and mode II strain energy release rates, G sub II. The G sub II values were computed using two different techniques: the virtural crack-closure technique (VCCT) and the rate of change of compliance with crack length (compliance derivative method). The analysis was performed for various crack-length-to-semi-span (a/L) ratios ranging from 0.2 to 0.9. Three material systems representing a wide range of material properties were analyzed. The compliance and strain energy release rates of the specimen calculated with the present finite-element analysis agree very well with beam theory equations including transverse shear. The G sub II values calculated using the compliance derivative method compared extremely well with those calculated using the VCCT. The G sub II values obtained by the compliance derivative method using the top or bottom beam deflections agreed closely with each other. The strain energy release rates from a plane-stress analysis were higher than the plane-strain values by only a small percentage, indicating that either assumption may be used in the analysis. The G sub II values for one material system calculated from the finite-element analysis agreed with one solution in the literature and disagreed with the other solution in the literature.

A forward-advancing wave expansion method for numerical solution of large-scale sound propagation problems

NASA Astrophysics Data System (ADS)

Rolla, L. Barrera; Rice, H. J.

2006-09-01

In this paper a "forward-advancing" field discretization method suitable for solving the Helmholtz equation in large-scale problems is proposed. The forward wave expansion method (FWEM) is derived from a highly efficient discretization procedure based on interpolation of wave functions known as the wave expansion method (WEM). The FWEM computes the propagated sound field by means of an exclusively forward advancing solution, neglecting the backscattered field. It is thus analogous to methods such as the (one way) parabolic equation method (PEM) (usually discretized using standard finite difference or finite element methods). These techniques do not require the inversion of large system matrices and thus enable the solution of large-scale acoustic problems where backscatter is not of interest. Calculations using FWEM are presented for two propagation problems and comparisons to data computed with analytical and theoretical solutions and show this forward approximation to be highly accurate. Examples of sound propagation over a screen in upwind and downwind refracting atmospheric conditions at low nodal spacings (0.2 per wavelength in the propagation direction) are also included to demonstrate the flexibility and efficiency of the method.

Shock Wave Propagation in Cementitious Materials at Micro/Meso Scales

NASA Astrophysics Data System (ADS)

Rajendran, Arunachalam

2015-06-01

The mechanical and constitutive response of materials like cement, and bio materials like fish scale and abalone shell is very complex due to heterogeneities that are inherently present in the nano and microstructures. The intrinsic constitutive behaviors are driven by the chemical composition and the molecular, micro, and meso structures. Therefore, it becomes important to identify the material genome as the building block for the material. For instance, in cementitious materials, the genome of C-S-H phase (the glue or the paste) that holds the various clinkers, such as the dicalcium silicate, tricalcium silicate, calcium ferroaluminates, and others is extremely complex. Often mechanical behaviors of C-S-H type materials are influenced by the chemistry and the structures at all nano to micro length scales. By explicitly modeling the molecular structures using appropriate potentials, it is then possible to compute the elastic tensor from molecular dynamics simulations using all atom method. The elastic tensors for the C-S-H gel and other clinkers are determined using the software suite ``Accelrys Materials Studio.'' A strain rate dependent, fracture mechanics based tensile damage model has been incorporated into ABAQUS finite element code to model spall evolution in the heterogeneous cementitious material with all constituents explicitly modeled through one micron element resolution. This paper presents results from nano/micro/meso scale analyses of shock wave propagation in a heterogeneous cementitious material using both molecular dynamic and finite element codes.

Finite element modeling of hyper-viscoelasticity of peripheral nerve ultrastructures.

PubMed

Chang, Cheng-Tao; Chen, Yu-Hsing; Lin, Chou-Ching K; Ju, Ming-Shaung

2015-07-16

The mechanical characteristics of ultrastructures of rat sciatic nerves were investigated through animal experiments and finite element analyses. A custom-designed dynamic testing apparatus was used to conduct in vitro transverse compression experiments on the nerves. The optical coherence tomography (OCT) was utilized to record the cross-sectional images of nerve during the dynamic testing. Two-dimensional finite element models of the nerves were built based on their OCT images. A hyper-viscoelastic model was employed to describe the elastic and stress relaxation response of each ultrastructure of the nerve, namely the endoneurium, the perineurium and the epineurium. The first-order Ogden model was employed to describe the elasticity of each ultrastructure and a generalized Maxwell model for the relaxation. The inverse finite element analysis was used to estimate the material parameters of the ultrastructures. The results show the instantaneous shear modulus of the ultrastructures in decreasing order is perineurium, endoneurium, and epineurium. The FE model combined with the first-order Ogden model and the second-order Prony series is good enough for describing the compress-and-hold response of the nerve ultrastructures. The integration of OCT and the nonlinear finite element modeling may be applicable to study the viscoelasticity of peripheral nerve down to the ultrastructural level. Copyright © 2015 Elsevier Ltd. All rights reserved.

Proper Generalized Decomposition (PGD) for the numerical simulation of polycrystalline aggregates under cyclic loading

NASA Astrophysics Data System (ADS)

Nasri, Mohamed Aziz; Robert, Camille; Ammar, Amine; El Arem, Saber; Morel, Franck

2018-02-01

The numerical modelling of the behaviour of materials at the microstructural scale has been greatly developed over the last two decades. Unfortunately, conventional resolution methods cannot simulate polycrystalline aggregates beyond tens of loading cycles, and they do not remain quantitative due to the plasticity behaviour. This work presents the development of a numerical solver for the resolution of the Finite Element modelling of polycrystalline aggregates subjected to cyclic mechanical loading. The method is based on two concepts. The first one consists in maintaining a constant stiffness matrix. The second uses a time/space model reduction method. In order to analyse the applicability and the performance of the use of a space-time separated representation, the simulations are carried out on a three-dimensional polycrystalline aggregate under cyclic loading. Different numbers of elements per grain and two time increments per cycle are investigated. The results show a significant CPU time saving while maintaining good precision. Moreover, increasing the number of elements and the number of time increments per cycle, the model reduction method is faster than the standard solver.

A fully coupled method for massively parallel simulation of hydraulically driven fractures in 3-dimensions: FULLY COUPLED PARALLEL SIMULATION OF HYDRAULIC FRACTURES IN 3-D

DOE PAGES

Settgast, Randolph R.; Fu, Pengcheng; Walsh, Stuart D. C.; ...

2016-09-18

This study describes a fully coupled finite element/finite volume approach for simulating field-scale hydraulically driven fractures in three dimensions, using massively parallel computing platforms. The proposed method is capable of capturing realistic representations of local heterogeneities, layering and natural fracture networks in a reservoir. A detailed description of the numerical implementation is provided, along with numerical studies comparing the model with both analytical solutions and experimental results. The results demonstrate the effectiveness of the proposed method for modeling large-scale problems involving hydraulically driven fractures in three dimensions.

A fully coupled method for massively parallel simulation of hydraulically driven fractures in 3-dimensions: FULLY COUPLED PARALLEL SIMULATION OF HYDRAULIC FRACTURES IN 3-D

DOE Office of Scientific and Technical Information (OSTI.GOV)

Settgast, Randolph R.; Fu, Pengcheng; Walsh, Stuart D. C.

This study describes a fully coupled finite element/finite volume approach for simulating field-scale hydraulically driven fractures in three dimensions, using massively parallel computing platforms. The proposed method is capable of capturing realistic representations of local heterogeneities, layering and natural fracture networks in a reservoir. A detailed description of the numerical implementation is provided, along with numerical studies comparing the model with both analytical solutions and experimental results. The results demonstrate the effectiveness of the proposed method for modeling large-scale problems involving hydraulically driven fractures in three dimensions.

2.5D Finite/infinite Element Approach for Simulating Train-Induced Ground Vibrations

NASA Astrophysics Data System (ADS)

Yang, Y. B.; Hung, H. H.; Kao, J. C.

2010-05-01

The 2.5D finite/infinite element approach for simulating the ground vibrations by surface or underground moving trains will be briefly summarized in this paper. By assuming the soils to be uniform along the direction of the railway, only a two-dimensional profile of the soil perpendicular to the railway need be considered in the modeling. Besides the two in-plane degrees of freedom (DOFs) per node conventionally used for plane strain elements, an extra DOF is introduced to account for the out-of-plane wave transmission. The profile of the half-space is divided into a near field and a semi-infinite far field. The near field containing the train loads and irregular structures is simulated by the finite elements, while the far field covering the soils with infinite boundary by the infinite elements, by which due account is taken of the radiation effects for the moving loads. Enhanced by the automated mesh expansion procedure proposed previously by the writers, the far field impedances for all the lower frequencies are generated repetitively from the mesh created for the highest frequency considered. Finally, incorporated with a proposed load generation mechanism that takes the rail irregularity and dynamic properties of trains into account, an illustrative case study was performed. This paper investigates the vibration isolation effect of the elastic foundation that separates the concrete slab track from the underlying soil or tunnel structure. In addition, the advantage of the 2.5D approach was clearly demonstrated in that the three-dimensional wave propagation effect can be virtually captured using a two-dimensional finite/infinite element mesh. Compared with the conventional 3D approach, the present approach appears to be simple, efficient and generally accurate.

Efficient and accurate two-scale FE-FFT-based prediction of the effective material behavior of elasto-viscoplastic polycrystals

NASA Astrophysics Data System (ADS)

Kochmann, Julian; Wulfinghoff, Stephan; Ehle, Lisa; Mayer, Joachim; Svendsen, Bob; Reese, Stefanie

2018-06-01

Recently, two-scale FE-FFT-based methods (e.g., Spahn et al. in Comput Methods Appl Mech Eng 268:871-883, 2014; Kochmann et al. in Comput Methods Appl Mech Eng 305:89-110, 2016) have been proposed to predict the microscopic and overall mechanical behavior of heterogeneous materials. The purpose of this work is the extension to elasto-viscoplastic polycrystals, efficient and robust Fourier solvers and the prediction of micromechanical fields during macroscopic deformation processes. Assuming scale separation, the macroscopic problem is solved using the finite element method. The solution of the microscopic problem, which is embedded as a periodic unit cell (UC) in each macroscopic integration point, is found by employing fast Fourier transforms, fixed-point and Newton-Krylov methods. The overall material behavior is defined by the mean UC response. In order to ensure spatially converged micromechanical fields as well as feasible overall CPU times, an efficient but simple solution strategy for two-scale simulations is proposed. As an example, the constitutive behavior of 42CrMo4 steel is predicted during macroscopic three-point bending tests.

Efficient and accurate two-scale FE-FFT-based prediction of the effective material behavior of elasto-viscoplastic polycrystals

NASA Astrophysics Data System (ADS)

Kochmann, Julian; Wulfinghoff, Stephan; Ehle, Lisa; Mayer, Joachim; Svendsen, Bob; Reese, Stefanie

2017-09-01

Recently, two-scale FE-FFT-based methods (e.g., Spahn et al. in Comput Methods Appl Mech Eng 268:871-883, 2014; Kochmann et al. in Comput Methods Appl Mech Eng 305:89-110, 2016) have been proposed to predict the microscopic and overall mechanical behavior of heterogeneous materials. The purpose of this work is the extension to elasto-viscoplastic polycrystals, efficient and robust Fourier solvers and the prediction of micromechanical fields during macroscopic deformation processes. Assuming scale separation, the macroscopic problem is solved using the finite element method. The solution of the microscopic problem, which is embedded as a periodic unit cell (UC) in each macroscopic integration point, is found by employing fast Fourier transforms, fixed-point and Newton-Krylov methods. The overall material behavior is defined by the mean UC response. In order to ensure spatially converged micromechanical fields as well as feasible overall CPU times, an efficient but simple solution strategy for two-scale simulations is proposed. As an example, the constitutive behavior of 42CrMo4 steel is predicted during macroscopic three-point bending tests.

An evaluation of solution algorithms and numerical approximation methods for modeling an ion exchange process

NASA Astrophysics Data System (ADS)

Bu, Sunyoung; Huang, Jingfang; Boyer, Treavor H.; Miller, Cass T.

2010-07-01

The focus of this work is on the modeling of an ion exchange process that occurs in drinking water treatment applications. The model formulation consists of a two-scale model in which a set of microscale diffusion equations representing ion exchange resin particles that vary in size and age are coupled through a boundary condition with a macroscopic ordinary differential equation (ODE), which represents the concentration of a species in a well-mixed reactor. We introduce a new age-averaged model (AAM) that averages all ion exchange particle ages for a given size particle to avoid the expensive Monte-Carlo simulation associated with previous modeling applications. We discuss two different numerical schemes to approximate both the original Monte-Carlo algorithm and the new AAM for this two-scale problem. The first scheme is based on the finite element formulation in space coupled with an existing backward difference formula-based ODE solver in time. The second scheme uses an integral equation based Krylov deferred correction (KDC) method and a fast elliptic solver (FES) for the resulting elliptic equations. Numerical results are presented to validate the new AAM algorithm, which is also shown to be more computationally efficient than the original Monte-Carlo algorithm. We also demonstrate that the higher order KDC scheme is more efficient than the traditional finite element solution approach and this advantage becomes increasingly important as the desired accuracy of the solution increases. We also discuss issues of smoothness, which affect the efficiency of the KDC-FES approach, and outline additional algorithmic changes that would further improve the efficiency of these developing methods for a wide range of applications.

Finite Element Analysis and Test Correlation of a 10-Meter Inflation-Deployed Solar Sail

NASA Technical Reports Server (NTRS)

Sleight, David W.; Michii, Yuki; Lichodziejewski, David; Derbes, Billy; Mann. Troy O.; Slade, Kara N.; Wang, John T.

2005-01-01

Under the direction of the NASA In-Space Propulsion Technology Office, the team of L Garde, NASA Jet Propulsion Laboratory, Ball Aerospace, and NASA Langley Research Center has been developing a scalable solar sail configuration to address NASA's future space propulsion needs. Prior to a flight experiment of a full-scale solar sail, a comprehensive phased test plan is currently being implemented to advance the technology readiness level of the solar sail design. These tests consist of solar sail component, subsystem, and sub-scale system ground tests that simulate the vacuum and thermal conditions of the space environment. Recently, two solar sail test articles, a 7.4-m beam assembly subsystem test article and a 10-m four-quadrant solar sail system test article, were tested in vacuum conditions with a gravity-offload system to mitigate the effects of gravity. This paper presents the structural analyses simulating the ground tests and the correlation of the analyses with the test results. For programmatic risk reduction, a two-prong analysis approach was undertaken in which two separate teams independently developed computational models of the solar sail test articles using the finite element analysis software packages: NEiNastran and ABAQUS. This paper compares the pre-test and post-test analysis predictions from both software packages with the test data including load-deflection curves from static load tests, and vibration frequencies and mode shapes from vibration tests. The analysis predictions were in reasonable agreement with the test data. Factors that precluded better correlation of the analyses and the tests were uncertainties in the material properties, test conditions, and modeling assumptions used in the analyses.

Development of a Aerothermoelastic-Acoustics Simulation Capability of Flight Vehicles

NASA Technical Reports Server (NTRS)

Gupta, K. K.; Choi, S. B.; Ibrahim, A.

2010-01-01

A novel numerical, finite element based analysis methodology is presented in this paper suitable for accurate and efficient simulation of practical, complex flight vehicles. An associated computer code, developed in this connection, is also described in some detail. Thermal effects of high speed flow obtained from a heat conduction analysis are incorporated in the modal analysis which in turn affects the unsteady flow arising out of interaction of elastic structures with the air. Numerical examples pertaining to representative problems are given in much detail testifying to the efficacy of the advocated techniques. This is a unique implementation of temperature effects in a finite element CFD based multidisciplinary simulation analysis capability involving large scale computations.

Simulation of CNT-AFM tip based on finite element analysis for targeted probe of the biological cell

DOE Office of Scientific and Technical Information (OSTI.GOV)

Yousefi, Amin Termeh, E-mail: at.tyousefi@gmail.com; Miyake, Mikio, E-mail: miyakejaist@gmail.com; Ikeda, Shoichiro, E-mail: sho16.ikeda@gmail.com

Carbon nanotubes (CNTs) are potentially ideal tips for atomic force microscopy (AFM) due to the robust mechanical properties, nano scale diameter and also their ability to be functionalized by chemical and biological components at the tip ends. This contribution develops the idea of using CNTs as an AFM tip in computational analysis of the biological cell’s. Finite element analysis employed for each section and displacement of the nodes located in the contact area was monitored by using an output database (ODB). This reliable integration of CNT-AFM tip process provides a new class of high performance nanoprobes for single biological cellmore » analysis.« less

Computational optical palpation: a finite-element approach to micro-scale tactile imaging using a compliant sensor

PubMed Central

Sampson, David D.; Kennedy, Brendan F.

2017-01-01

High-resolution tactile imaging, superior to the sense of touch, has potential for future biomedical applications such as robotic surgery. In this paper, we propose a tactile imaging method, termed computational optical palpation, based on measuring the change in thickness of a thin, compliant layer with optical coherence tomography and calculating tactile stress using finite-element analysis. We demonstrate our method on test targets and on freshly excised human breast fibroadenoma, demonstrating a resolution of up to 15–25 µm and a field of view of up to 7 mm. Our method is open source and readily adaptable to other imaging modalities, such as ultrasonography and confocal microscopy. PMID:28250098

The finite-element behaviour simulation of the rotary-type and frame-type solar sails on the geocentric orbits

NASA Astrophysics Data System (ADS)

Gorbunova, I.; Khabibullin, R.; Chernyakin, S.; Starinova, O.

2016-04-01

This paper discusses the research of functioning of different construction types for the spacecraft with a solar sail. Two types of the solar sail are considered, such as frame-type and rotary-type. The research is performed by means of application of the computer-assisted design system. The movement simulation of the spacecraft center mass and the forces acting on the solar sail is described. The finite element models of the two solar sail constructions are developed and compared.

On the accuracy of modelling the dynamics of large space structures

NASA Technical Reports Server (NTRS)

Diarra, C. M.; Bainum, P. M.

1985-01-01

Proposed space missions will require large scale, light weight, space based structural systems. Large space structure technology (LSST) systems will have to accommodate (among others): ocean data systems; electronic mail systems; large multibeam antenna systems; and, space based solar power systems. The structures are to be delivered into orbit by the space shuttle. Because of their inherent size, modelling techniques and scaling algorithms must be developed so that system performance can be predicted accurately prior to launch and assembly. When the size and weight-to-area ratio of proposed LSST systems dictate that the entire system be considered flexible, there are two basic modeling methods which can be used. The first is a continuum approach, a mathematical formulation for predicting the motion of a general orbiting flexible body, in which elastic deformations are considered small compared with characteristic body dimensions. This approach is based on an a priori knowledge of the frequencies and shape functions of all modes included within the system model. Alternatively, finite element techniques can be used to model the entire structure as a system of lumped masses connected by a series of (restoring) springs and possibly dampers. In addition, a computational algorithm was developed to evaluate the coefficients of the various coupling terms in the equations of motion as applied to the finite element model of the Hoop/Column.

Comparison of 2D Finite Element Modeling Assumptions with Results From 3D Analysis for Composite Skin-Stiffener Debonding

NASA Technical Reports Server (NTRS)

Krueger, Ronald; Paris, Isbelle L.; OBrien, T. Kevin; Minguet, Pierre J.

2004-01-01

The influence of two-dimensional finite element modeling assumptions on the debonding prediction for skin-stiffener specimens was investigated. Geometrically nonlinear finite element analyses using two-dimensional plane-stress and plane-strain elements as well as three different generalized plane strain type approaches were performed. The computed skin and flange strains, transverse tensile stresses and energy release rates were compared to results obtained from three-dimensional simulations. The study showed that for strains and energy release rate computations the generalized plane strain assumptions yielded results closest to the full three-dimensional analysis. For computed transverse tensile stresses the plane stress assumption gave the best agreement. Based on this study it is recommended that results from plane stress and plane strain models be used as upper and lower bounds. The results from generalized plane strain models fall between the results obtained from plane stress and plane strain models. Two-dimensional models may also be used to qualitatively evaluate the stress distribution in a ply and the variation of energy release rates and mixed mode ratios with delamination length. For more accurate predictions, however, a three-dimensional analysis is required.

Influence of 2D Finite Element Modeling Assumptions on Debonding Prediction for Composite Skin-stiffener Specimens Subjected to Tension and Bending

NASA Technical Reports Server (NTRS)

Krueger, Ronald; Minguet, Pierre J.; Bushnell, Dennis M. (Technical Monitor)

2002-01-01

The influence of two-dimensional finite element modeling assumptions on the debonding prediction for skin-stiffener specimens was investigated. Geometrically nonlinear finite element analyses using two-dimensional plane-stress and plane strain elements as well as three different generalized plane strain type approaches were performed. The computed deflections, skin and flange strains, transverse tensile stresses and energy release rates were compared to results obtained from three-dimensional simulations. The study showed that for strains and energy release rate computations the generalized plane strain assumptions yielded results closest to the full three-dimensional analysis. For computed transverse tensile stresses the plane stress assumption gave the best agreement. Based on this study it is recommended that results from plane stress and plane strain models be used as upper and lower bounds. The results from generalized plane strain models fall between the results obtained from plane stress and plane strain models. Two-dimensional models may also be used to qualitatively evaluate the stress distribution in a ply and the variation of energy release rates and mixed mode ratios with lamination length. For more accurate predictions, however, a three-dimensional analysis is required.

Transient Finite Element Computations on a Variable Transputer System

NASA Technical Reports Server (NTRS)

Smolinski, Patrick J.; Lapczyk, Ireneusz

1993-01-01

A parallel program to analyze transient finite element problems was written and implemented on a system of transputer processors. The program uses the explicit time integration algorithm which eliminates the need for equation solving, making it more suitable for parallel computations. An interprocessor communication scheme was developed for arbitrary two dimensional grid processor configurations. Several 3-D problems were analyzed on a system with a small number of processors.

Finite Element Approach for the Design of Control Algorithms for Vertical Fin Buffeting Using Strain Actuation

DTIC Science & Technology

2001-06-01

Algorithms for Vertical Fin Buffeting Using Strain Actuation DISTRIBUTION: Approved for public release, distribution unlimited This paper is part of the...UNCLASSIFIED 8-1 Finite Element Approach for the Design of Control Algorithms for Vertical Fin Buffeting Using Strain Actuation Fred Nitzsche...groups), the disturbance (buffet load), and the two output variables (a choice among four Introduction accelerometers and five strain - gauge positions

Finite element analysis of wrinkling membranes

NASA Technical Reports Server (NTRS)

Miller, R. K.; Hedgepeth, J. M.; Weingarten, V. I.; Das, P.; Kahyai, S.

1984-01-01

The development of a nonlinear numerical algorithm for the analysis of stresses and displacements in partly wrinkled flat membranes, and its implementation on the SAP VII finite-element code are described. A comparison of numerical results with exact solutions of two benchmark problems reveals excellent agreement, with good convergence of the required iterative procedure. An exact solution of a problem involving axisymmetric deformations of a partly wrinkled shallow curved membrane is also reported.

Biomechanical Property of a Newly Designed Assembly Locking Compression Plate: Three-Dimensional Finite Element Analysis

PubMed Central

Liu, Da

2017-01-01

In this study, we developed and validated a refined three-dimensional finite element model of middle femoral comminuted fracture to compare the biomechanical stability after two kinds of plate fixation: a newly designed assembly locking compression plate (NALCP) and a locking compression plate (LCP). CT data of a male volunteer was converted to middle femoral comminuted fracture finite element analysis model. The fracture was fixated by NALCP and LCP. Stress distributions were observed. Under slow walking load and torsion load, the stress distribution tendency of the two plates was roughly uniform. The anterolateral femur was the tension stress area, and the bone block shifted toward the anterolateral femur. Maximum stress was found on the lateral border of the number 5 countersink of the plate. Under a slow walking load, the NALCP maximum stress was 2.160e+03 MPa and the LCP was 8.561e+02 MPa. Under torsion load, the NALCP maximum stress was 2.260e+03 MPa and the LCP was 6.813e+02 MPa. Based on those results of finite element analysis, the NALCP can provide adequate mechanical stability for comminuted fractures, which would help fixate the bone block and promote bone healing. PMID:29065654

[Finite Element Modelling of the Eye for the Investigation of Accommodation].

PubMed

Martin, H; Stachs, O; Guthoff, R; Grabow, N

2016-12-01

Background: Accommodation research increasingly uses engineering methods. This article presents the use of the finite element method in accommodation research. Material and Methods: Geometry, material data and boundary conditions are prerequisites for the application of the finite element method. Published data on geometry and materials are reviewed. It is shown how boundary conditions are important and how they influence the results. Results: Two dimensional and three dimensional models of the anterior chamber of the eye are presented. With simple two dimensional models, it is shown that realistic results for the accommodation amplitude can always be achieved. More complex three dimensional models of the accommodation mechanism - including the ciliary muscle - require further investigations of the material data and of the morphology of the ciliary muscle, if they are to achieve realistic results for accommodation. Discussion and Conclusion: The efficiency and the limitations of the finite element method are especially clear for accommodation. Application of the method requires extensive preparation, including acquisition of geometric and material data and experimental validation. However, a validated model can be used as a basis for parametric studies, by systematically varying material data and geometric dimensions. This allows systematic investigation of how essential input parameters influence the results. Georg Thieme Verlag KG Stuttgart · New York.

Guided waves dispersion equations for orthotropic multilayered pipes solved using standard finite elements code.

PubMed

Predoi, Mihai Valentin

2014-09-01

The dispersion curves for hollow multilayered cylinders are prerequisites in any practical guided waves application on such structures. The equations for homogeneous isotropic materials have been established more than 120 years ago. The difficulties in finding numerical solutions to analytic expressions remain considerable, especially if the materials are orthotropic visco-elastic as in the composites used for pipes in the last decades. Among other numerical techniques, the semi-analytical finite elements method has proven its capability of solving this problem. Two possibilities exist to model a finite elements eigenvalue problem: a two-dimensional cross-section model of the pipe or a radial segment model, intersecting the layers between the inner and the outer radius of the pipe. The last possibility is here adopted and distinct differential problems are deduced for longitudinal L(0,n), torsional T(0,n) and flexural F(m,n) modes. Eigenvalue problems are deduced for the three modes classes, offering explicit forms of each coefficient for the matrices used in an available general purpose finite elements code. Comparisons with existing solutions for pipes filled with non-linear viscoelastic fluid or visco-elastic coatings as well as for a fully orthotropic hollow cylinder are all proving the reliability and ease of use of this method. Copyright © 2014 Elsevier B.V. All rights reserved.

Parallel, adaptive finite element methods for conservation laws

NASA Technical Reports Server (NTRS)

Biswas, Rupak; Devine, Karen D.; Flaherty, Joseph E.

1994-01-01

We construct parallel finite element methods for the solution of hyperbolic conservation laws in one and two dimensions. Spatial discretization is performed by a discontinuous Galerkin finite element method using a basis of piecewise Legendre polynomials. Temporal discretization utilizes a Runge-Kutta method. Dissipative fluxes and projection limiting prevent oscillations near solution discontinuities. A posteriori estimates of spatial errors are obtained by a p-refinement technique using superconvergence at Radau points. The resulting method is of high order and may be parallelized efficiently on MIMD computers. We compare results using different limiting schemes and demonstrate parallel efficiency through computations on an NCUBE/2 hypercube. We also present results using adaptive h- and p-refinement to reduce the computational cost of the method.