A one-dimensional shock capturing finite element method and multi-dimensional generalizations
NASA Technical Reports Server (NTRS)
Hughes, T. J. R.; Mallet, M.; Zanutta, R.; Taki, Y.; Tezduyar, T. E.
1985-01-01
Multi-dimensional generalizations of a one-dimensional finite element shock capturing scheme are proposed. A scalar model problem is used to emphasize that 'preferred directions' are important in multi-dimensional applications. Schemes are developed for the two-dimensional Euler equations. One, based upon characteristics, employs the Mach lines and streamlines as preferred directions.
Finite Element Model to Study One Dimensional Calcium Dyanmics in Cardiac Myocytes
NASA Astrophysics Data System (ADS)
Pathak, Kunal B.; Adlakha, Neeru
2015-12-01
The multi physical process involving calcium ions regulate expansion and contraction of cardiac myocytes. This mechanism of expansion and contraction of cardiac myocytes is responsible for contraction and expansion of heart for pumping of blood into arteries and receiving blood into heart from vein. Thus calcium dynamics in cardiac myocytes is responsible for the activities of the myocytes cells and functioning of the heart. The specific spatiotemporal calcium ion dynamics is required to trigger, sustain and terminate activity of the cell. In this paper an attempt has been done to propose a model to study calcium dynamics in cardiac myocytes for a one-dimensional unsteady state case. The model incorporates the process like diffusion, reaction involving source and excess buffers. Appropriate boundary conditions and initial conditions have been framed. The finite element method has been employed to obtain the solution. The numerical results have been used to study the effect of buffers and source influx on calcium dynamics in cardiac myocytes.
Giunta, G.; Belouettar, S.
2015-03-10
In this paper, the static response of three-dimensional beams made of functionally graded materials is investigated through a family of hierarchical one-dimensional finite elements. A wide variety of elements is proposed differing by the kinematic formulation and the number of nodes per elements along the beam axis. Elements’ stiffness matrix and load vector are derived in a unified nuclear form that does not depend upon the a priori expansion order over the cross-section nor the finite element approximation along the beam axis. Results are validated towards three-dimensional finite element models as well as equivalent Navier-type analytical solutions. The numerical investigations show that accurate and efficient solutions (when compared with full three-dimensional FEM solutions) can be obtained by the proposed family of hierarchical one-dimensional elements’ family.
NASA Astrophysics Data System (ADS)
Robbins, Joshua; Voth, Thomas
2011-06-01
Material response to dynamic loading is often dominated by microstructure such as grain topology, porosity, inclusions, and defects; however, many models rely on assumptions of homogeneity. We use the probabilistic finite element method (WK Liu, IJNME, 1986) to introduce local uncertainty to account for material heterogeneity. The PFEM uses statistical information about the local material response (i.e., its expectation, coefficient of variation, and autocorrelation) drawn from knowledge of the microstructure, single crystal behavior, and direct numerical simulation (DNS) to determine the expectation and covariance of the system response (velocity, strain, stress, etc). This approach is compared to resolved grain-scale simulations of the equivalent system. The microstructures used for the DNS are produced using Monte Carlo simulations of grain growth, and a sufficient number of realizations are computed to ensure a meaningful comparison. Finally, comments are made regarding the suitability of one-dimensional PFEM for modeling material heterogeneity. Sandia National Laboratories is a multi-program laboratory managed and operated by Sandia Corporation, a wholly owned subsidiary of Lockheed Martin Corporation, for the U.S. Department of Energy's National Nuclear Security Administration under contract DE-AC04-94AL85000.
1DFEMWATER: A one-dimensional finite element model of WATER flow through saturated-unsaturated media
Yeh, G.T.
1988-08-01
This report presents the development and verification of a one- dimensional finite element model of water flow through saturated- unsaturated media. 1DFEMWATER is very flexible and capable of modeling a wide range of real-world problems. The model is designed to (1) treat heterogeneous media consisting of many geologic formations; (2) consider distributed and point sources/sinks that are spatially and temporally variable; (3) accept prescribed initial conditions or obtain them from steady state simulations; (4) deal with transient heads distributed over the Dirichlet boundary; (5) handle time-dependent fluxes caused by pressure gradient on the Neumann boundary; (6) treat time-dependent total fluxes (i.e., the sum of gravitational fluxes and pressure-gradient fluxes) on the Cauchy boundary; (7) automatically determine variable boundary conditions of evaporation, infiltration, or seepage on the soil-air interface; (8) provide two options for treating the mass matrix (consistent and lumping); (9) provide three alternatives for approximating the time derivative term (Crank-Nicolson central difference, backward difference, and mid-difference); (10) give three options (exact relaxation, underrelaxation, and overrelaxation) for estimating the nonlinear matrix; (11) automatically reset the time step size when boundary conditions or source/sinks change abruptly; and (12) check mass balance over the entire region for every time step. The model is verified with analytical solutions and other numerical models for three examples.
Approximate Approaches to the One-Dimensional Finite Potential Well
ERIC Educational Resources Information Center
Singh, Shilpi; Pathak, Praveen; Singh, Vijay A.
2011-01-01
The one-dimensional finite well is a textbook problem. We propose approximate approaches to obtain the energy levels of the well. The finite well is also encountered in semiconductor heterostructures where the carrier mass inside the well (m[subscript i]) is taken to be distinct from mass outside (m[subscript o]). A relevant parameter is the mass…
Carbyne with finite length: The one-dimensional sp carbon
Pan, Bitao; Xiao, Jun; Li, Jiling; Liu, Pu; Wang, Chengxin; Yang, Guowei
2015-01-01
Carbyne is the one-dimensional allotrope of carbon composed of sp-hybridized carbon atoms. Definitive evidence for carbyne has remained elusive despite its synthesis and preparation in the laboratory. Given the remarkable technological breakthroughs offered by other allotropes of carbon, including diamond, graphite, fullerenes, carbon nanotubes, and graphene, interest in carbyne and its unusual potential properties remains intense. We report the first synthesis of carbyne with finite length, which is clearly composed of alternating single bonds and triple bonds, using a novel process involving laser ablation in liquid. Spectroscopic analyses confirm that the product is the structure of sp hybridization with alternating carbon-carbon single bonds and triple bonds and capped by hydrogen. We observe purple-blue fluorescence emissions from the gap between the highest occupied molecular orbital and the lowest unoccupied molecular orbital of carbyne. Condensed-phase carbyne crystals have a hexagonal lattice and resemble the white crystalline powder produced by drying a carbyne solution. We also establish that the combination of gold and alcohol is crucial to carbyne formation because carbon-hydrogen bonds can be cleaved with the help of gold catalysts under the favorable thermodynamic environment provided by laser ablation in liquid and because the unique configuration of two carbon atoms in an alcohol molecule matches the elementary entity of carbyne. This laboratory synthesis of carbyne will enable the exploration of its properties and applications. PMID:26601318
Carbyne with finite length: The one-dimensional sp carbon.
Pan, Bitao; Xiao, Jun; Li, Jiling; Liu, Pu; Wang, Chengxin; Yang, Guowei
2015-10-01
Carbyne is the one-dimensional allotrope of carbon composed of sp-hybridized carbon atoms. Definitive evidence for carbyne has remained elusive despite its synthesis and preparation in the laboratory. Given the remarkable technological breakthroughs offered by other allotropes of carbon, including diamond, graphite, fullerenes, carbon nanotubes, and graphene, interest in carbyne and its unusual potential properties remains intense. We report the first synthesis of carbyne with finite length, which is clearly composed of alternating single bonds and triple bonds, using a novel process involving laser ablation in liquid. Spectroscopic analyses confirm that the product is the structure of sp hybridization with alternating carbon-carbon single bonds and triple bonds and capped by hydrogen. We observe purple-blue fluorescence emissions from the gap between the highest occupied molecular orbital and the lowest unoccupied molecular orbital of carbyne. Condensed-phase carbyne crystals have a hexagonal lattice and resemble the white crystalline powder produced by drying a carbyne solution. We also establish that the combination of gold and alcohol is crucial to carbyne formation because carbon-hydrogen bonds can be cleaved with the help of gold catalysts under the favorable thermodynamic environment provided by laser ablation in liquid and because the unique configuration of two carbon atoms in an alcohol molecule matches the elementary entity of carbyne. This laboratory synthesis of carbyne will enable the exploration of its properties and applications. PMID:26601318
NASA Technical Reports Server (NTRS)
Amar, Adam J.; Blackwell, Ben F.; Edwards, Jack R.
2007-01-01
The development and verification of a one-dimensional material thermal response code with ablation is presented. The implicit time integrator, control volume finite element spatial discretization, and Newton's method for nonlinear iteration on the entire system of residual equations have been implemented and verified for the thermochemical ablation of internally decomposing materials. This study is a continuation of the work presented in "One-Dimensional Ablation with Pyrolysis Gas Flow Using a Full Newton's Method and Finite Control Volume Procedure" (AIAA-2006-2910), which described the derivation, implementation, and verification of the constant density solid energy equation terms and boundary conditions. The present study extends the model to decomposing materials including decomposition kinetics, pyrolysis gas flow through the porous char layer, and a mixture (solid and gas) energy equation. Verification results are presented for the thermochemical ablation of a carbon-phenolic ablator which involves the solution of the entire system of governing equations.
On One-Dimensional Stretching Functions for Finite-Difference Calculations
NASA Technical Reports Server (NTRS)
Vinokur, M.
1980-01-01
The class of one dimensional stretching function used in finite difference calculations is studied. For solutions containing a highly localized region of rapid variation, simple criteria for a stretching function are derived using a truncation error analysis. These criteria are used to investigate two types of stretching functions. One is an interior stretching function, for which the location and slope of an interior clustering region are specified. The simplest such function satisfying the criteria is found to be one based on the inverse hyperbolic sine. The other type of function is a two sided stretching function, for which the arbitrary slopes at the two ends of the one dimensional interval are specified. The simplest such general function is found to be one based on the inverse tangent. The general two sided function has many applications in the construction of finite difference grids.
NASA Technical Reports Server (NTRS)
Wang, Xiao-Yen; Chow, Chuen-Yen; Chang, Sin-Chung
1999-01-01
Test problems are used to examine the performance of several one-dimensional numerical schemes based on the space-time conservation and solution element (CE/SE) method. Investigated in this paper are the CE/SE schemes constructed previously for solving the linear unsteady advection-diffusion equation and the schemes derived here for solving the nonlinear viscous and inviscid Burgers equations. In comparison with the numerical solutions obtained using several traditional finite-difference schemes with similar accuracy, the CE/SE solutions display much lower numerical dissipation and dispersion errors.
NASA Technical Reports Server (NTRS)
Vinokur, M.
1979-01-01
The class of one-dimensional stretching functions used in finite-difference calculations is studied. For solutions containing a highly localized region of rapid variation, simple criteria for a stretching function are derived using a truncation error analysis. These criteria are used to investigate two types of stretching functions. One is an interior stretching function, for which the location and slope of an interior clustering region are specified. The simplest such function satisfying the criteria is found to be one based on the inverse hyperbolic sine. The other type of function is a two-sided stretching function, for which the arbitrary slopes at the two ends of the one-dimensional interval are specified. The simplest such general function is found to be one based on the inverse tangent.
Correlation versus commensurability effects for finite bosonic systems in one-dimensional lattices
Brouzos, Ioannis; Schmelcher, Peter; Zoellner, Sascha
2010-05-15
We investigate few-boson systems in finite one-dimensional multiwell traps covering the full interaction crossover from uncorrelated to fermionized particles. Our treatment of the ground-state properties is based on the numerically exact multiconfigurational time-dependent Hartree method. For commensurate filling, we trace the fingerprints of localization as the interaction strength increases, in several observables like reduced-density matrices, fluctuations, and momentum distribution. For a filling factor larger than 1 we observe on-site repulsion effects in the densities and fragmentation of particles beyond the validity of the Bose-Hubbard model upon approaching the Tonks-Girardeau limit. The presence of an incommensurate fraction of particles induces incomplete localization and spatial modulations of the density profiles, taking into account the finite size of the system.
Finite-temperature charge transport in the one-dimensional Hubbard model
NASA Astrophysics Data System (ADS)
Jin, F.; Steinigeweg, R.; Heidrich-Meisner, F.; Michielsen, K.; De Raedt, H.
2015-11-01
We study the charge conductivity of the one-dimensional repulsive Hubbard model at finite temperature using the method of dynamical quantum typicality, focusing at half filling. This numerical approach allows us to obtain current autocorrelation functions from systems with as many as 18 sites, way beyond the range of standard exact diagonalization. Our data clearly suggest that the charge Drude weight vanishes with a power law as a function of system size. The low-frequency dependence of the conductivity is consistent with a finite dc value and thus with diffusion, despite large finite-size effects. Furthermore, we consider the mass-imbalanced Hubbard model for which the charge Drude weight decays exponentially with system size, as expected for a nonintegrable model. We analyze the conductivity and diffusion constant as a function of the mass imbalance and we observe that the conductivity of the lighter component decreases exponentially fast with the mass-imbalance ratio. While in the extreme limit of immobile heavy particles, the Falicov-Kimball model, there is an effective Anderson-localization mechanism leading to a vanishing conductivity of the lighter species, we resolve finite conductivities for an inverse mass ratio of η ≳0.25 .
Properties of a finite fully spin-polarized free homogeneous one-dimensional electron gas
Ciftja, Orion
2015-01-15
The homogeneous electron gas model has been quite successful to predict the bulk properties of systems of electrons at various densities. In many occasions, a simplified free homogeneous electron gas model represents a powerful first approximation to a real system. Despite our considerable knowledge on the bulk properties of a homogeneous electron gas, advances in nanoscience and nanotechnology call for a greater effort to understand the opposite limit of small finite systems of electrons with size-dependent properties. In this work, we provide a detailed description of the properties of a finite fully spin-polarized (spinless) free homogeneous one-dimensional electron gas, the simplest of the free homogeneous electron gases. We derive exact analytical results for various quantities such as the one-particle density function, two-particle density function, one-particle density matrix, pair correlation function and energy of finite systems with an arbitrary number of electrons. The results obtained provide a detailed view on how various quantities corresponding to a finite system approach their bulk (thermodynamic limit) value.
Thermal tuning of omnidirectional reflection bands in one-dimensional finite phononic crystals
NASA Astrophysics Data System (ADS)
Chen, Zhaojiang
2015-03-01
This study investigates the temperature-tuned omnidirectional reflection (ODR) bands in a one-dimensional (1D) finite phononic crystal (PnC), formed by alternating layers of nitinol and epoxy. An analytical model, based on the transfer matrix method, is developed to study reflection and transmission characteristics of the acoustic waves including shear and compressional waves in a 1D PnC. Existence criteria and the sensitive and continuous temperature-tunability of ODR bands in the nitinol/epoxy PnC are demonstrated using the analyses of projected-band structures and reflection spectra. The width and location of the ODR bands shift markedly with temperature variations of nitinol across the phase transition from martensite to austenite. The effects of temperature, filling fraction of nitinol layers, and the Si clad layer on ODR bands are considered. The results will be of benefit in the design and optimization of thermal tuning of omnidirectional acoustic mirrors.
Improved finite-difference computation of the van der Waals force: One-dimensional case
Pinto, Fabrizio
2009-10-15
We present an improved demonstration of the calculation of Casimir forces in one-dimensional systems based on the recently proposed numerical imaginary frequency Green's function computation approach. The dispersion force on two thick lossy dielectric slabs separated by an empty gap and placed within a perfectly conducting cavity is obtained from the Green's function of the modified Helmholtz equation by means of an ordinary finite-difference method. In order to demonstrate the possibility to develop algorithms to explore complex geometries in two and three dimensions to higher order in the mesh spacing, we generalize existing classical electromagnetism algebraic methods to generate the difference equations for dielectric boundaries not coinciding with any grid points. Diagnostic tests are presented to monitor the accuracy of our implementation of the method and follow-up applications in higher dimensions are introduced.
Lefschetz thimble structure in one-dimensional lattice Thirring model at finite density
NASA Astrophysics Data System (ADS)
Fujii, Hirotsugu; Kamata, Syo; Kikukawa, Yoshio
2015-11-01
We investigate Lefschetz thimble structure of the complexified path-integration in the one-dimensional lattice massive Thirring model with finite chemical potential. The lattice model is formulated with staggered fermions and a compact auxiliary vector boson (a link field), and the whole set of the critical points (the complex saddle points) are sorted out, where each critical point turns out to be in a one-to-one correspondence with a singular point of the effective action (or a zero point of the fermion determinant). For a subset of critical point solutions in the uniform-field subspace, we examine the upward and downward cycles and the Stokes phenomenon with varying the chemical potential, and we identify the intersection numbers to determine the thimbles contributing to the path-integration of the partition function. We show that the original integration path becomes equivalent to a single Lefschetz thimble at small and large chemical potentials, while in the crossover region multiple thimbles must contribute to the path integration. Finally, reducing the model to a uniform field space, we study the relative importance of multi-thimble contributions and their behavior toward continuum and low-temperature limits quantitatively, and see how the rapid crossover behavior is recovered by adding the multi-thimble contributions at low temperatures. Those findings will be useful for performing Monte-Carlo simulations on the Lefschetz thimbles.
NASA Astrophysics Data System (ADS)
Park, Sung-Been; Cha, Min-Chul
2015-11-01
We investigate the finite-size scaling properties of the quantum phase transition in the one-dimensional quantum Ising model with periodic boundary conditions by representing the ground state in matrix product state forms. The infinite time-evolving block decimation technique is used to optimize the states. A trace over a product of the matrices multiplied as many times as the number of sites yields the finite-size effects. For sufficiently large Schmidt ranks, the finite-size scaling behavior determines the critical point and the critical exponents whose values are consistent with the analytical results.
NASA Technical Reports Server (NTRS)
Lumsdaine, E.; Ragab, S.
1977-01-01
The general equation for the velocity potential of quasi-one-dimensional acoustic wave motion in a variable area, finite duct with one-dimensional flow is derived by using a perturbation technique. The nonlinear second-order partial differential equation is linearized and then solved, by either a power series expansion method or the Runge-Kutta fourth-order method, for harmonic time dependence. The boundary condition taken at the duct mouth is that of matching the impedance of the duct sound field to that of the radiation field at the duct opening. Three axial Mach number variations along the duct axis are considered and the results obtained are compared with those for the case of constant Mach number, to determine the influence of the axial velocity gradient on sound propagation. The effect of flow on the radiation impedance is also considered.
Equivalence of Fluctuation Splitting and Finite Volume for One-Dimensional Gas Dynamics
NASA Technical Reports Server (NTRS)
Wood, William A.
1997-01-01
The equivalence of the discretized equations resulting from both fluctuation splitting and finite volume schemes is demonstrated in one dimension. Scalar equations are considered for advection, diffusion, and combined advection/diffusion. Analysis of systems is performed for the Euler and Navier-Stokes equations of gas dynamics. Non-uniform mesh-point distributions are included in the analyses.
Wave transport in one-dimensional disordered systems with finite-size scatterers
NASA Astrophysics Data System (ADS)
Díaz, Marlos; Mello, Pier A.; Yépez, Miztli; Tomsovic, Steven
2015-05-01
We study the problem of wave transport in a one-dimensional disordered system, where the scatterers of the chain are n barriers and wells with statistically independent intensities and with a spatial extension lc which may contain an arbitrary number δ /2 π of wavelengths, where δ =k lc . We analyze the average Landauer resistance and transmission coefficient of the chain as a function of n and the phase parameter δ . For weak scatterers, we find: (i) a regime, to be called I, associated with an exponential behavior of the resistance with n ; (ii) a regime, to be called II, for δ in the vicinity of π , where the system is almost transparent and less localized; and (iii) right in the middle of regime II, for δ very close to π , the formation of a band gap, which becomes ever more conspicuous as n increases. In regime II, both the average Landauer resistance and the transmission coefficient show an oscillatory behavior with n and δ . These characteristics of the system are found analytically, some of them exactly and some others approximately. The agreement between theory and simulations is excellent, which suggests a strong motivation for the experimental study of these systems. We also present a qualitative discussion of the results.
Centini, M.; Sciscione, L.; Sibilia, C.; Bertolotti, M.; Perina, J. Jr.; Scalora, M.; Bloemer, M.J.
2005-09-15
A description of spontaneous parametric down-conversion in finite-length one-dimensional nonlinear photonic crystals is developed using semiclassical and quantum approaches. It is shown that if a suitable averaging is added to the semiclassical model, its results are in very good agreement with the quantum approach. We propose two structures made with GaN/AlN that generate both degenerate and nondegenerate entangled photon pairs. Both structures are designed so as to achieve a high efficiency of the nonlinear process.
WONDY V: a one-dimensional finite-difference wave-propagation code
Kipp, M.E.; Lawrence, R.J.
1982-06-01
WONDY V solves the finite difference analogs to the Lagrangian equations of motion in one spatial dimension (planar, cylindrical, or spherical). Simulations of explosive detonation, energy deposition, plate impact, and dynamic fracture are possible, using a variety of existing material models. In addition, WONDY has proven to be a powerful tool in the evaluation of new constitutive models. A preprocessor is available to allocate storage arrays commensurate with problem size, and automatic rezoning may be employed to improve resolution. This document provides a description of the equations solved, available material models, operating instructions, and sample problems.
One-dimensional transient finite difference model of an operational salinity gradient solar pond
NASA Technical Reports Server (NTRS)
Hicks, Michael C.; Golding, Peter
1992-01-01
This paper describes the modeling approach used to simulate the transient behavior of a salinity gradient solar pond. A system of finite difference equations are used to generate the time dependent temperature and salinity profiles within the pond. The stability of the pond, as determined by the capacity of the resulting salinity profile to suppress thermal convection within the primary gradient region of the pond, is continually monitored and when necessary adjustments are made to the thickness of the gradient zone. Results of the model are then compared to measurements taken during two representative seasonal periods at the University of Texas at El Paso's (UTEP's) research solar pond.
One-dimensional plasmons in ultrathin metallic silicide wires of finite width
NASA Astrophysics Data System (ADS)
Rugeramigabo, Eddy P.; Tegenkamp, Christoph; Pfnür, Herbert; Inaoka, Takeshi; Nagao, Tadaaki
2010-04-01
The acoustic dispersion of plasmons (PLs) in narrow (4 nm) and ultrathin (one unit cell) metallic DySi2 wires, grown by self-assembly on vicinal Si(100)-[011] 4° turns out to be unidirectional. We observed the lowest intersubband PL as well as the acoustic PL. These PLs are specific for narrow metallic strips of finite width. Our experimental and theoretical analysis suggests that only one of two electron pockets in the surface Brillouin zone makes a substantial contribution to the PLs because the other pocket has a much smaller conductive character due to a strong admixture of electronic states with d character.
Analytic solutions of the one-dimensional finite-coupling delta-function Bose gas
NASA Astrophysics Data System (ADS)
Forrester, P. J.; Frankel, N. E.; Makin, M. I.
2006-10-01
An intensive study for both the weak coupling and strong coupling limits of the ground state properties of this classic system is presented. Detailed results for specific values of finite N are given and from them results for general N are determined. We focus on the density matrix and concomitantly its Fourier transform, the occupation numbers, along with the pair correlation function and concomitantly its Fourier transform, the structure factor. These are the signature quantities of the Bose gas. One specific result is that for weak coupling a rational polynomial structure holds despite the transcendental nature of the Bethe equations. All these results are predicated on the Bethe ansatz and are built upon the seminal works of the past.
NASA Astrophysics Data System (ADS)
Wang, Qian; Ren, Yu-Xin; Li, Wanai
2016-06-01
The large reconstruction stencil has been the major bottleneck problem in developing high order finite volume schemes on unstructured grids. This paper presents a compact reconstruction procedure for arbitrarily high order finite volume method on unstructured grids to overcome this shortcoming. In this procedure, a set of constitutive relations are constructed by requiring the reconstruction polynomial and its derivatives on the control volume of interest to conserve their averages on face-neighboring cells. These relations result in an over-determined linear equation system, which, in the sense of least-squares, can be reduced to a block-tridiagonal system in the one-dimensional case. The one-dimensional formulations of the reconstruction are discussed in detail and a Fourier analysis is presented to study the dispersion/dissipation and stability properties. The WBAP limiter based on the secondary reconstruction is used to suppress the non-physical oscillations near discontinuities while achieve high order accuracy in smooth regions of the solution. Numerical results demonstrate the method's high order accuracy, robustness and shock capturing capability.
NASA Astrophysics Data System (ADS)
Spiliotis, Konstantinos G.; Russo, Lucia; Aifantis, Elias C.
2016-06-01
We study the pattern formation in dislocation dynamics of solid materials through bifurcation analysis. The model under study is the celebrated Walgraef-Aifantis (W-A) model of dislocation patterning in one dimensional finite domain. The model describes the evolution of the patterns along the domain and it consists of a couple of partial diffusion equations. The system is a reaction diffusion type with two different diffusion coefficients, one for the mobile (free to move due to stress in the slip plane) dislocations and the second for the immobile dislocations (slow movement or trapped ones). We analytically study the onset of instabilities as the diffusion coefficients are varied. We finally construct the bifurcation diagram with respect to the diffusion coefficients.
NASA Astrophysics Data System (ADS)
Popov, Alexander P.; Gloria Pini, Maria; Rettori, Angelo
2016-03-01
The metastable states of a finite-size chain of N classical spins described by the chiral XY-model on a discrete one-dimensional lattice are calculated by means of a general theoretical method recently developed by one of us. This method allows one to determine all the possible equilibrium magnetic states in an accurate and systematic way. The ground state of a chain consisting of N classical XY spins is calculated in the presence of (i) a symmetric ferromagnetic exchange interaction, favoring parallel alignment of nearest neighbor spins, (ii) a uniaxial anisotropy, favoring a given direction in the film plane, and (iii) an antisymmetric Dzyaloshinskii-Moriya interaction (DMI), favoring perpendicular alignment of nearest neighbor spins. In addition to the ground state with a non-uniform helical spin arrangement, which originates from the energy competition in the finite-size chain with open boundary conditions, we have found a considerable number of higher-energy equilibrium states. In the investigated case of a chain with N=10 spins and a DMI much smaller than the in-plane uniaxial anisotropy, it turns out that a metastable (unstable) state of the finite chain is characterized by a configuration where none (at least one) of the inner spins is nearly parallel to the hard axis. The role of the DMI is to establish a unique rotational sense for the helical ground state. Moreover, the number of both metastable and unstable equilibrium states is doubled with respect to the case of zero DMI. This produces modifications in the Peierls-Nabarro potential encountered by a domain wall during its displacement along the discrete spin chain.
Automatic finite element generators
NASA Technical Reports Server (NTRS)
Wang, P. S.
1984-01-01
The design and implementation of a software system for generating finite elements and related computations are described. Exact symbolic computational techniques are employed to derive strain-displacement matrices and element stiffness matrices. Methods for dealing with the excessive growth of symbolic expressions are discussed. Automatic FORTRAN code generation is described with emphasis on improving the efficiency of the resultant code.
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 analyses is presented. New thermal finite elements which yield exact nodal and element temperature 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.
NASA Astrophysics Data System (ADS)
Arahata, Emiko; Nikuni, Tetsuro
2008-03-01
We study damping of the dipole oscillation in a Bose-condensed gas in a combined cigar-shaped harmonic trap and one-dimensional (1D) optical lattice potential at finite temperatures. In order to include the effect of thermal excitations in the radial direction, we derive a quasi-1D model of the Gross-Pitaevskii equation and the Bogoliubov equations. We use the Popov approximation to calculate the temperature dependence of the condensate fraction with varying lattice depth. We then calculate the Landau damping rate of the dipole oscillation as a function of the lattice depth and temperature. The damping rate increases with increasing lattice depth, which is consistent with experimental observations. The magnitude of the damping rate is in reasonable agreement with experimental data. We also find that the damping rate has a strong temperature dependence, showing a sharp increase with increasing temperature. Finally, we emphasize the importance of the radial thermal excitations in both equilibrium properties and the Landau damping.
NASA Astrophysics Data System (ADS)
Wei, Xiao-Kun; Shao, Wei; Shi, Sheng-Bing; Zhang, Yong; Wang, Bing-Zhong
2015-07-01
An efficient conformal locally one-dimensional finite-difference time-domain (LOD-CFDTD) method is presented for solving two-dimensional (2D) electromagnetic (EM) scattering problems. The formulation for the 2D transverse-electric (TE) case is presented and its stability property and numerical dispersion relationship are theoretically investigated. It is shown that the introduction of irregular grids will not damage the numerical stability. Instead of the staircasing approximation, the conformal scheme is only employed to model the curve boundaries, whereas the standard Yee grids are used for the remaining regions. As the irregular grids account for a very small percentage of the total space grids, the conformal scheme has little effect on the numerical dispersion. Moreover, the proposed method, which requires fewer arithmetic operations than the alternating-direction-implicit (ADI) CFDTD method, leads to a further reduction of the CPU time. With the total-field/scattered-field (TF/SF) boundary and the perfectly matched layer (PML), the radar cross section (RCS) of two 2D structures is calculated. The numerical examples verify the accuracy and efficiency of the proposed method. Project supported by the National Natural Science Foundation of China (Grant Nos. 61331007 and 61471105).
Finite element radiation transport in one dimension
Painter, J.F.
1997-05-09
A new physics package solves radiation transport equations in one space dimension, multiple energy groups and directions. A discontinuous finite element method discretizes radiation intensity with respect to space and angle, and a continuous finite element method discretizes electron temperature `in space. A splitting method solves the resulting linear equations. This is a one-dimensional analog of Kershaw and Harte`s two-dimensional package. This package has been installed in a two-dimensional inertial confinement fusion code, and has given excellent results for both thermal waves and highly directional radiation. In contrast, the traditional discrete ordinate and spherical harmonic methods show less accurate results in both cases.
Energy Science and Technology Software Center (ESTSC)
2006-03-08
MAPVAR-KD is designed to transfer solution results from one finite element mesh to another. MAPVAR-KD draws heavily from the structure and coding of MERLIN II, but it employs a new finite element data base, EXODUS II, and offers enhanced speed and new capabilities not available in MERLIN II. In keeping with the MERLIN II documentation, the computational algorithms used in MAPVAR-KD are described. User instructions are presented. Example problems are included to demonstrate the operationmore » of the code and the effects of various input options. MAPVAR-KD is a modification of MAPVAR in which the search algorithm was replaced by a kd-tree-based search for better performance on large problems.« less
Energy Science and Technology Software Center (ESTSC)
2005-05-07
CONEX is a code for joining sequentially in time multiple exodusll database files which all represent the same base mesh topology and geometry. It is used to create a single results or restart file from multiple results or restart files which typically arise as the result of multiple restarted analyses. CONEX is used to postprocess the results from a series of finite element analyses. It can join sequentially the data from multiple results databases intomore » a single database which makes it easier to postprocess the results data.« less
Energy Science and Technology Software Center (ESTSC)
2005-06-26
Exotxt is an analysis code that reads finite element results data stored in an exodusII file and generates a file in a structured text format. The text file can be edited or modified via a number of text formatting tools. Exotxt is used by analysis to translate data from the binary exodusII format into a structured text format which can then be edited or modified and then either translated back to exodusII format or tomore » another format.« less
Ablative Thermal Response Analysis Using the Finite Element Method
NASA Technical Reports Server (NTRS)
Dec John A.; Braun, Robert D.
2009-01-01
A review of the classic techniques used to solve ablative thermal response problems is presented. The advantages and disadvantages of both the finite element and finite difference methods are described. As a first step in developing a three dimensional finite element based ablative thermal response capability, a one dimensional computer tool has been developed. The finite element method is used to discretize the governing differential equations and Galerkin's method of weighted residuals is used to derive the element equations. A code to code comparison between the current 1-D tool and the 1-D Fully Implicit Ablation and Thermal Response Program (FIAT) has been performed.
Kempa, K.; Bakshi, P.; Gornik, E.
1996-09-01
We show theoretically that strong plasma mode generation is possible in a nonequilibrium steady-state quasi-one-dimensional bounded solid-state plasma, in which a nonequilibrium distribution is maintained by appropriate injection/extraction of carriers. We calculate the density response of realistic model systems using the random-phase approximation, determine the normal modes of the bounded carrier plasma, and show that strong plasma instabilities can be generated under suitable conditions. Such stimulated plasma oscillations could lead to sources of terahertz electromagnetic radiation. {copyright} {ital 1996 The American Physical Society.}
Probabilistic fracture finite elements
NASA Technical Reports Server (NTRS)
Liu, W. K.; Belytschko, T.; Lua, Y. J.
1991-01-01
The Probabilistic Fracture Mechanics (PFM) is a promising method for estimating the fatigue life and inspection cycles for mechanical and structural components. The Probability Finite Element Method (PFEM), which is based on second moment analysis, has proved to be a promising, practical approach to handle problems with uncertainties. As the PFEM provides a powerful computational tool to determine first and second moment of random parameters, the second moment reliability method can be easily combined with PFEM to obtain measures of the reliability of the structural system. The method is also being applied to fatigue crack growth. Uncertainties in the material properties of advanced materials such as polycrystalline alloys, ceramics, and composites are commonly observed from experimental tests. This is mainly attributed to intrinsic microcracks, which are randomly distributed as a result of the applied load and the residual stress.
Fourier analysis of finite element preconditioned collocation schemes
NASA Technical Reports Server (NTRS)
Deville, Michel O.; Mund, Ernest H.
1990-01-01
The spectrum of the iteration operator of some finite element preconditioned Fourier collocation schemes is investigated. The first part of the paper analyses one-dimensional elliptic and hyperbolic model problems and the advection-diffusion equation. Analytical expressions of the eigenvalues are obtained with use of symbolic computation. The second part of the paper considers the set of one-dimensional differential equations resulting from Fourier analysis (in the tranverse direction) of the 2-D Stokes problem. All results agree with previous conclusions on the numerical efficiency of finite element preconditioning schemes.
Yan, Yongli; Zhang, Chuang; Yao, Jiannian; Zhao, Yong Sheng
2013-07-19
Many recent activities in the use of one-dimensional nanostructures as photonic elements for optical information processing are explained by huge advantages that photonic circuits possess over traditional silicon-based electronic ones in bandwidth, heat dissipation, and resistance to electromagnetic wave interference. Organic materials are a promising candidate to support these optical-related applications, as they combine the properties of plastics with broad spectral tunability, high optical cross-section, easy fabrication, as well as low cost. Their outstanding compatibility allows organic composite structures which are made of two or more kinds of materials combined together, showing great superiority to single-component materials due to the introduced interactions among multiple constituents, such as energy transfer, electron transfer, exciton coupling, etc. The easy processability of organic 1D crystalline heterostructures enables a fine topological control of both composition and geometry, which offsets the intrinsic deficiencies of individual material. At the same time, the strong exciton-photon coupling and exciton-exciton interaction impart the excellent confinement of photons in organic microstructures, thus light can be manipulated according to our intention to realize specific functions. These collective properties indicate a potential utility of organic heterogeneous material for miniaturized photonic circuitry. Herein, focus is given on recent advances of 1D organic crystalline heterostructures, with special emphasis on the novel design, controllable construction, diverse performance, as well as wide applications in isolated photonic elements for integration. It is proposed that the highly coupled, hybrid optical networks would be an important material basis towards the creation of on-chip optical information processing. PMID:23703829
NASA Astrophysics Data System (ADS)
Pedrozo, Héctor A.; Rosenberger, Mario R.; Schvezov, Carlos E.
2016-06-01
The solution by the Finite Difference Method of the Richards equation written as a function of the degree of saturation of the domain and the matrix potential is obtained and the convergence of the solutions is analyzed. The necessary time and spatial sizes for convergence are obtained and established.
NASA Astrophysics Data System (ADS)
Sheikhan, A.; Snyman, I.
2012-08-01
We theoretically study a charge qubit interacting with electrons in a semi-infinite one-dimensional wire. The system displays the physics of the Fermi edge singularity. Our results generalize known results for the Fermi edge system to the regime where excitations induced by the qubit can resolve the spatial structure of the scattering region. We find resonant features in the qubit tunneling rate as a function of the qubit level splitting. They occur at integer multiples of hvF/l. Here vF is the Fermi velocity of the electrons in the wire, and l is the distance from the tip of the wire to the point where it interacts with the qubit. These features are due to the constructive interference of the amplitudes for creating single coherent left- or right-moving charge fluctuation (plasmon) in the electron gas. As the coupling between the qubit and the wire is increased, the resonances are washed out. This is a clear signature of the increasingly violent Fermi sea shake-up, associated with the creation of many plasmons whose individual energies are too low to meet the resonance condition.
NASA Technical Reports Server (NTRS)
Chang, Sin-Chung; Wang, Xiao-Yen; To, Wai-Ming
2000-01-01
In the space-time conservation element and solution element (CE/SE) method, the independent marching variables used comprise not only the mesh value of the physical dependent variables but also, in contrast to it typical numerical method, the Mesh values of the spatial derivatives of the physical variables The use of the extra marching variables results from the need to construct the two-level explicit and nondissipative schemes which are at the core of the CE/SE development. It also results from the need to minimize the stencil while maintaining accuracy. In this paper using the 1D(sub (alpha)-mu) scheme as an example, the effect of this added complication on consistency, accuracy and operation count is assessed. As part of this effort, an equivalent yet more efficient form of the alpha-mu scheme in which the independent marching variables are the local fluxes tied to each mesh point is introduced. Also, the intriguing relations that exist among the alpha-mu. Leapfrog, and DuFort-Frankel schemes are further explored. In addition, the redundance of the Leapfrog, DUFort-Frankel, and Lax scheme and the remedy for this redundance are discussed. This paper is concluded with the construction and evaluation of a CE/SE solver for the inviscid Burger equation.
Cherny, Alexander Yu.; Brand, Joachim
2006-02-15
Correlation functions related to the dynamic density response of the one-dimensional Bose gas in the model of Lieb and Liniger are calculated. An exact Bose-Fermi mapping is used to work in a fermionic representation with a pseudopotential Hamiltonian. The Hartree-Fock and generalized random phase approximations are derived and the dynamic polarizability is calculated. The results are valid to first order in 1/{gamma}, where {gamma} is Lieb-Liniger coupling parameter. Approximations for the dynamic and static structure factor at finite temperature are presented. The results preclude superfluidity at any finite temperature in the large-{gamma} regime due to the Landau criterion. Due to the exact Bose-Fermi duality, the results apply for spinless fermions with weak p-wave interactions as well as for strongly interacting bosons.
Finite element computational fluid mechanics
NASA Technical Reports Server (NTRS)
Baker, A. J.
1983-01-01
Finite element analysis as applied to the broad spectrum of computational fluid mechanics is analyzed. The finite element solution methodology is derived, developed, and applied directly to the differential equation systems governing classes of problems in fluid mechanics. The heat conduction equation is used to reveal the essence and elegance of finite element theory, including higher order accuracy and convergence. The algorithm is extended to the pervasive nonlinearity of the Navier-Stokes equations. A specific fluid mechanics problem class is analyzed with an even mix of theory and applications, including turbulence closure and the solution of turbulent flows.
NASA Astrophysics Data System (ADS)
Kubrak, Elżbieta; Kubrak, Janusz; Rowiński, Paweł
2013-02-01
One-dimensional model for vertical profiles of longitudinal velocities in open-channel flows is verified against laboratory data obtained in an open channel with artificial plants. Those plants simulate Canadian waterweed which in nature usually forms dense stands that reach all the way to the water surface. The model works particularly well for densely spaced plants.
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.
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.
Finite element error estimation and adaptivity based on projected stresses
Jung, J.
1990-08-01
This report investigates the behavior of a family of finite element error estimators based on projected stresses, i.e., continuous stresses that are a least squared error fit to the conventional Gauss point stresses. An error estimate based on element force equilibrium appears to be quite effective. Examples of adaptive mesh refinement for a one-dimensional problem are presented. Plans for two-dimensional adaptivity are discussed. 12 refs., 82 figs.
Probabilistic Finite Element: Variational Theory
NASA Technical Reports Server (NTRS)
Belytschko, T.; Liu, W. K.
1985-01-01
The goal of this research is to provide techniques which are cost-effective and enable the engineer to evaluate the effect of uncertainties in complex finite element models. Embedding the probabilistic aspects in a variational formulation is a natural approach. In addition, a variational approach to probabilistic finite elements enables it to be incorporated within standard finite element methodologies. Therefore, once the procedures are developed, they can easily be adapted to existing general purpose programs. Furthermore, the variational basis for these methods enables them to be adapted to a wide variety of structural elements and to provide a consistent basis for incorporating probabilistic features in many aspects of the structural problem. Tasks concluded include the theoretical development of probabilistic variational equations for structural dynamics, the development of efficient numerical algorithms for probabilistic sensitivity displacement and stress analysis, and integration of methodologies into a pilot computer code.
The NESSUS finite element code
NASA Technical Reports Server (NTRS)
Dias, J. B.; Nagiegaal, J. C.; Nakazawa, S.
1987-01-01
The objective of this development is to provide a new analysis tool which integrates the structural modeling versatility of a modern finite element code with the latest advances in the area of probabilistic modeling and structural reliability. Version 2.0 of the NESSUS finite element code was released last February, and is currently being exercised on a set of problems which are representative of typical Space Shuttle Main Engine (SSME) applications. NESSUS 2.0 allows linear elastostatic and eigenvalue analysis of structures with uncertain geometry, material properties and boundary conditions, which are subjected to a random mechanical and thermal loading environment. The NESSUS finite element code is a key component in a broader software system consisting of five major modules. NESSUS/EXPERT is an expert system under development at Southwest Research Institute, with the objective of centralizing all component-specific knowledge useful for conducting probabilistic analysis of typical Space Shuttle Main Engine (SSME) components. NESSUS/FEM contains the finite element code used for the structural analysis and parameter sensitivity evaluation of these components. The task of parametrizing a finite element mesh in terms of the random variables present is facilitated with the use of the probabilistic data preprocessor in NESSUS/PRE. An external database file is used for managing the bulk of the data generated by NESSUS/FEM.
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.
Adaptive finite-element method for diffraction gratings
NASA Astrophysics Data System (ADS)
Bao, Gang; Chen, Zhiming; Wu, Haijun
2005-06-01
A second-order finite-element adaptive strategy with error control for one-dimensional grating problems is developed. The unbounded computational domain is truncated to a bounded one by a perfectly-matched-layer (PML) technique. The PML parameters, such as the thickness of the layer and the medium properties, are determined through sharp a posteriori error estimates. The adaptive finite-element method is expected to increase significantly the accuracy and efficiency of the discretization as well as reduce the computation cost. Numerical experiments are included to illustrate the competitiveness of the proposed adaptive method.
Discontinuous Galerkin Finite Element Method for Parabolic Problems
NASA Technical Reports Server (NTRS)
Kaneko, Hideaki; Bey, Kim S.; Hou, Gene J. W.
2004-01-01
In this paper, we develop a time and its corresponding spatial discretization scheme, based upon the assumption of a certain weak singularity of parallel ut(t) parallel Lz(omega) = parallel ut parallel2, for the discontinuous Galerkin finite element method for one-dimensional parabolic problems. Optimal convergence rates in both time and spatial variables are obtained. A discussion of automatic time-step control method is also included.
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.
Nonlinear, finite deformation, finite element analysis
NASA Astrophysics Data System (ADS)
Nguyen, Nhung; Waas, Anthony M.
2016-06-01
The roles of the consistent Jacobian matrix and the material tangent moduli, which are used in nonlinear incremental finite deformation mechanics problems solved using the finite element method, are emphasized in this paper, and demonstrated using the commercial software ABAQUS standard. In doing so, the necessity for correctly employing user material subroutines to solve nonlinear problems involving large deformation and/or large rotation is clarified. Starting with the rate form of the principle of virtual work, the derivations of the material tangent moduli, the consistent Jacobian matrix, the stress/strain measures, and the objective stress rates are discussed and clarified. The difference between the consistent Jacobian matrix (which, in the ABAQUS UMAT user material subroutine is referred to as DDSDDE) and the material tangent moduli ( C e ) needed for the stress update is pointed out and emphasized in this paper. While the former is derived based on the Jaumann rate of the Kirchhoff stress, the latter is derived using the Jaumann rate of the Cauchy stress. Understanding the difference between these two objective stress rates is crucial for correctly implementing a constitutive model, especially a rate form constitutive relation, and for ensuring fast convergence. Specifically, the implementation requires the stresses to be updated correctly. For this, the strains must be computed directly from the deformation gradient and corresponding strain measure (for a total form model). Alternatively, the material tangent moduli derived from the corresponding Jaumann rate of the Cauchy stress of the constitutive relation (for a rate form model) should be used. Given that this requirement is satisfied, the consistent Jacobian matrix only influences the rate of convergence. Its derivation should be based on the Jaumann rate of the Kirchhoff stress to ensure fast convergence; however, the use of a different objective stress rate may also be possible. The error associated
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.
Infinite Possibilities for the Finite Element.
ERIC Educational Resources Information Center
Finlayson, Bruce A.
1981-01-01
Describes the uses of finite element methods in solving problems of heat transfer, fluid flow, etc. Suggests that engineers should know the general concepts and be able to apply the principles of finite element methods. (Author/WB)
Peridynamic Multiscale Finite Element Methods
Costa, Timothy; Bond, Stephen D.; Littlewood, David John; Moore, Stan Gerald
2015-12-01
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 and 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
NASA Astrophysics Data System (ADS)
1990-10-01
Topics presented include the finite element analysis of confined turbulent swirling flows, compressible viscous flow calculations using compatible finite element approximations, the equilibrium and stability of Tokamaks, and a coupled finite element solution of biharmonic problems for vector potentials. Also presented are the Godunov-mixed methods for immiscible displacement, the iterative adaptive implicit-explicit methods for flow problems, finite element methods for one-dimensional combustion problems, and a technique for analyzing finite element methods for viscous incompressible flow.
Xu, Li; Shi, Xiaohuo; Hu, Kaifeng
2014-12-01
One-dimensional (1D) quantitative NMR (qNMR) is a useful tool for concentration determination due to its experimental simplicity and the direct proportionality of the integrated signal area to the number of nuclei spin. For complex mixtures, however, signal overlapping often in one-dimensional quantitative (1) H NMR (1D (1) H qNMR) spectrum limits the accurate quantification of individual compound. Here, we introduced employing joint 1D qNMR methods of different nuclei, such as (1) H and (31) P (or/and (19) F), to quantify multiple compounds in a complex mixture using a single universal concentration reference. When the concentration ratio of several compounds containing different elements in a complex mixture is of interest, the result calculated from measured intensities from 1D qNMR of different nuclei is independent of the gravimetric error from the reference. In this case, the common reference also serves as a 'quantitative bridge' among these 1D qNMR of different nuclei. Quantitative analysis of choline, phosphocholine, and glycerophosphocholine mixture is given as an example using trimethylphosphine oxide ((CH(3))(3) P(O)) as concentration reference. Compounds containing multiple elements, such as tetramethylammonium hexafluorophosphate (N(+) (CH(3))(4 PF6 (-) are proposed as the common concentration reference for (1) H, (13) C, (15) N, (31) P, and (19) F qNMR for the quantitative analysis of complex mixture containing these different elements. We anticipate that the proposed joint 1D qNMR approach using a universal concentration reference will be a valuable alternative for simultaneous quantification of multiple compounds in a complex mixture due to its accuracy and single and simple sample preparation. PMID:25298349
One-Dimensional Czedli-Type Islands
ERIC Educational Resources Information Center
Horvath, Eszter K.; Mader, Attila; Tepavcevic, Andreja
2011-01-01
The notion of an island has surfaced in recent algebra and coding theory research. Discrete versions provide interesting combinatorial problems. This paper presents the one-dimensional case with finitely many heights, a topic convenient for student research.
Finite element methods in numerical relativity.
NASA Astrophysics Data System (ADS)
Mann, P. J.
The finite element method is very successful in Newtonian fluid simulations, and can be extended to relativitstic fluid flows. This paper describes the general method, and then outlines some preliminary results for spherically symmetric geometries. The mixed finite element - finite difference scheme is introduced, and used for the description of spherically symmetric collapse. Baker's (Newtonian) shock modelling method and Miller's moving finite element method are also mentioned. Collapse in double-null coordinates requires non-constant time slicing, so the full finite element method in space and time is described.
Finite element and finite difference methods in electromagnetic scattering
NASA Astrophysics Data System (ADS)
Morgan, Michael A.
Finite-difference and finite-element methods for the computational analysis of EM scattering phenomena are examined in chapters contributed by leading experts. Topics addressed include an FEM for composite scatterers, coupled finite- and boundary-element methods for EM scattering, absorbing boundary conditions for the direct solution PDEs arising in EM scattering problems, application of the control-region approximation to two-dimensional EM scattering, coupled potentials for EM fields in inhomogeneous media, the method of conforming boundary elements for transient electromagnetics, and the finite-difference time-domain method for numerical modeling of EM wave interactions with arbitrary structures. Extensive diagrams and graphs of typical results are provided.
Kerstein, A.R.
1996-12-31
One-Dimensional Turbulence is a new turbulence modeling strategy involving an unsteady simulation implemented in one spatial dimension. In one dimension, fine scale viscous and molecular-diffusive processes can be resolved affordably in simulations at high turbulence intensity. The mechanistic distinction between advective and molecular processes is thereby preserved, in contrast to turbulence models presently employed. A stochastic process consisting of mapping {open_quote}events{close_quote} applied to a one-dimensional velocity profile represents turbulent advection. The local event rate for given eddy size is proportional to the velocity difference across the eddy. These properties cause an imposed shear to induce an eddy cascade analogous in many respects to the eddy cascade in turbulent flow. Many scaling and fluctuation properties of self-preserving flows, and of passive scalars introduced into these flows, are reproduced.
Phase-space finite elements in a least-squares solution of the transport equation
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 meshing 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)
Probabilistic finite element analysis of a craniofacial finite element model.
Berthaume, Michael A; Dechow, Paul C; Iriarte-Diaz, Jose; Ross, Callum F; Strait, David S; Wang, Qian; Grosse, Ian R
2012-05-01
We employed a probabilistic finite element analysis (FEA) method to determine how variability in material property values affects stress and strain values in a finite model of a Macaca fascicularis cranium. The material behavior of cortical bone varied in three ways: isotropic homogeneous, isotropic non-homogeneous, and orthotropic non-homogeneous. The material behavior of the trabecular bone and teeth was always treated as isotropic and homogeneous. All material property values for the cranium were randomized with a Gaussian distribution with either coefficients of variation (CVs) of 0.2 or with CVs calculated from empirical data. Latin hypercube sampling was used to determine the values of the material properties used in the finite element models. In total, four hundred and twenty six separate deterministic FE simulations were executed. We tested four hypotheses in this study: (1) uncertainty in material property values will have an insignificant effect on high stresses and a significant effect on high strains for homogeneous isotropic models; (2) the effect of variability in material property values on the stress state will increase as non-homogeneity and anisotropy increase; (3) variation in the in vivo shear strain values reported by Strait et al. (2005) and Ross et al. (2011) is not only due to variations in muscle forces and cranial morphology, but also due to variation in material property values; (4) the assumption of a uniform coefficient of variation for the material property values will result in the same trend in how moderate-to-high stresses and moderate-to-high strains vary with respect to the degree of non-homogeneity and anisotropy as the trend found when the coefficients of variation for material property values are calculated from empirical data. Our results supported the first three hypotheses and falsified the fourth. When material properties were varied with a constant CV, as non-homogeneity and anisotropy increased the level of variability in
Dynamic finite element modeling of poroviscoelastic soft tissue.
Yang, Zhaochun; Smolinski, Patrick
2006-02-01
Clinical evidences relative to biomechanical factors have demonstrated their important contribution to the behaviour of soft tissues. Finite element (FE) analysis is used to study the mechanical behaviour of soft tissue because it can provide numerical solutions to problems that are intractable to analytic solutions. This study focuses on the development of a FE model of a poroelastic biological tissue, which incorporates the viscoelastic material behaviour, finite deformation and inertial effect. The FE formulation is based on the weak form derived from the governing equation, and Newmark-beta method as well as Newton's method is incorporated into the implicit non-linear solutions. One-dimensional analytical solutions were used to verify the theoretical formulation and the numerical implementation of the proposed model. This study was further extended to analyze two-dimensional biomechanical models and the results clearly demonstrate the importance of including finite deformation, viscoelasticity and inertial effects. PMID:16880152
Domain decomposition methods for mortar finite elements
Widlund, O.
1996-12-31
In the last few years, domain decomposition methods, previously developed and tested for standard finite element methods and elliptic problems, have been extended and modified to work for mortar and other nonconforming finite element methods. A survey will be given of work carried out jointly with Yves Achdou, Mario Casarin, Maksymilian Dryja and Yvon Maday. Results on the p- and h-p-version finite elements will also be discussed.
FEBio: finite elements for biomechanics.
Maas, Steve A; Ellis, Benjamin J; Ateshian, Gerard A; Weiss, Jeffrey A
2012-01-01
In the field of computational biomechanics, investigators have primarily used commercial software that is neither geared toward biological applications nor sufficiently flexible to follow the latest developments in the field. This lack of a tailored software environment has hampered research progress, as well as dissemination of models and results. To address these issues, we developed the FEBio software suite (http://mrl.sci.utah.edu/software/febio), a nonlinear implicit finite element (FE) framework, designed specifically for analysis in computational solid biomechanics. This paper provides an overview of the theoretical basis of FEBio and its main features. FEBio offers modeling scenarios, constitutive models, and boundary conditions, which are relevant to numerous applications in biomechanics. The open-source FEBio software is written in C++, with particular attention to scalar and parallel performance on modern computer architectures. Software verification is a large part of the development and maintenance of FEBio, and to demonstrate the general approach, the description and results of several problems from the FEBio Verification Suite are presented and compared to analytical solutions or results from other established and verified FE codes. An additional simulation is described that illustrates the application of FEBio to a research problem in biomechanics. Together with the pre- and postprocessing software PREVIEW and POSTVIEW, FEBio provides a tailored solution for research and development in computational biomechanics. PMID:22482660
Finite element coiled cochlea model
NASA Astrophysics Data System (ADS)
Isailovic, Velibor; Nikolic, Milica; Milosevic, Zarko; Saveljic, Igor; Nikolic, Dalibor; Radovic, Milos; Filipović, Nenad
2015-12-01
Cochlea is important part of the hearing system, and thanks to special structure converts external sound waves into neural impulses which go to the brain. Shape of the cochlea is like snail, so geometry of the cochlea model is complex. The simplified cochlea coiled model was developed using finite element method inside SIFEM FP7 project. Software application is created on the way that user can prescribe set of the parameters for spiral cochlea, as well as material properties and boundary conditions to the model. Several mathematical models were tested. The acoustic wave equation for describing fluid in the cochlea chambers - scala vestibuli and scala timpani, and Newtonian dynamics for describing vibrations of the basilar membrane are used. The mechanical behavior of the coiled cochlea was analyzed and the third chamber, scala media, was not modeled because it does not have a significant impact on the mechanical vibrations of the basilar membrane. The obtained results are in good agreement with experimental measurements. Future work is needed for more realistic geometry model. Coiled model of the cochlea was created and results are compared with initial simplified coiled model of the cochlea.
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.
Graphics for Finite-Element Analysis
NASA Technical Reports Server (NTRS)
Thornton, E. A.; Sawyer, L. M.
1982-01-01
ELPLOT program is a passive computer graphics system that could be utilized for display of models and responses of general finite-element analyses. Program includes: Wide range of view-orientation selections, number of alternative data-input formats, extensive family of finite-element types, and capabilities for both static and dynamic-response displays.
3-D Finite Element Code Postprocessor
Energy Science and Technology Software Center (ESTSC)
1996-07-15
TAURUS is an interactive post-processing application supporting visualization of finite element analysis results on unstructured grids. TAURUS provides the ability to display deformed geometries and contours or fringes of a large number of derived results on meshes consisting of beam, plate, shell, and solid type finite elements. Time history plotting is also available.
Finite-Element Composite-Analysis Program
NASA Technical Reports Server (NTRS)
Bowles, David E.
1990-01-01
Finite Element Composite Analysis Program, FECAP, special-purpose finite-element program for analyzing behavior of composite material with microcomputer. Procedure leads to set of linear simultaneous equations relating unknown nodal displacement to applied loads. Written in HP BASIC 3.0.
Finite element analysis of helicopter structures
NASA Technical Reports Server (NTRS)
Rich, M. J.
1978-01-01
Application of the finite element analysis is now being expanded to three dimensional analysis of mechanical components. Examples are presented for airframe, mechanical components, and composite structure calculations. Data are detailed on the increase of model size, computer usage, and the effect on reducing stress analysis costs. Future applications for use of finite element analysis for helicopter structures are projected.
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.
Will Finite Elements Replace Structural Mechanics?
NASA Astrophysics Data System (ADS)
Ojalvo, I. U.
1984-01-01
This paper presents a personal view regarding the need for a continued interest and activity in structural methods in general, while viewing finite elements and the computer as simply two specific tools for assisting in this endeavor. An attempt is made to provide some insight as to why finite element methods seem to have "won the war," and to give examples of their more (and less) intelligent use. Items addressed include a highlight of unnecessary limitations of many existing standard finite element codes and where it is felt that further development work is needed.
The finite element method in thermomechanics
Hsu, T.
1986-01-01
Thermal stress analysis is critical in the design and operation of energy-efficient power plant components and engines as well as in nuclear and aerospace systems. The Finite Element Method in Thermomechanics attempts to embrace a wide range of topics in the nonlinear thermomechanical analysis. The book covers the basic principles of the finite element method: the formulations for the base thermomechanical analysis, including thermoelastic-plastic-creep stress analysis; the use of Fourier series for nonaxisymmetric loadings, and stress waves in solids in thermal environments; and the base finite element code called TEPSAC.
Assignment Of Finite Elements To Parallel Processors
NASA Technical Reports Server (NTRS)
Salama, Moktar A.; Flower, Jon W.; Otto, Steve W.
1990-01-01
Elements assigned approximately optimally to subdomains. Mapping algorithm based on simulated-annealing concept used to minimize approximate time required to perform finite-element computation on hypercube computer or other network of parallel data processors. Mapping algorithm needed when shape of domain complicated or otherwise not obvious what allocation of elements to subdomains minimizes cost of computation.
Visualization of higher order finite elements.
Thompson, David C.; Pebay, Philippe Pierre; Crawford, Richard H.; Khardekar, Rahul Vinay
2004-04-01
Finite element meshes are used to approximate the solution to some differential equation when no exact solution exists. A finite element mesh consists of many small (but finite, not infinitesimal or differential) regions of space that partition the problem domain, {Omega}. Each region, or element, or cell has an associated polynomial map, {Phi}, that converts the coordinates of any point, x = ( x y z ), in the element into another value, f(x), that is an approximate solution to the differential equation, as in Figure 1(a). This representation works quite well for axis-aligned regions of space, but when there are curved boundaries on the problem domain, {Omega}, it becomes algorithmically much more difficult to define {Phi} in terms of x. Rather, we define an archetypal element in a new coordinate space, r = ( r s t ), which has a simple, axis-aligned boundary (see Figure 1(b)) and place two maps onto our archetypal element:
A survey of mixed finite element methods
NASA Technical Reports Server (NTRS)
Brezzi, F.
1987-01-01
This paper is an introduction to and an overview of mixed finite element methods. It discusses the mixed formulation of certain basic problems in elasticity and hydrodynamics. It also discusses special techniques for solving the discrete problem.
Finite element modeling of the human pelvis
Carlson, B.
1995-11-01
A finite element model of the human pelvis was created using a commercial wire frame image as a template. To test the final mesh, the model`s mechanical behavior was analyzed through finite element analysis and the results were displayed graphically as stress concentrations. In the future, this grid of the pelvis will be integrated with a full leg model and used in side-impact car collision simulations.
Finite-Element Modeling For Structural Analysis
NASA Technical Reports Server (NTRS)
Min, J. B.; Androlake, S. G.
1995-01-01
Report presents study of finite-element mathematical modeling as used in analyzing stresses and strains at joints between thin, shell-like components (e.g., ducts) and thicker components (e.g., flanges or engine blocks). First approach uses global/local model to evaluate system. Provides correct total response and correct representation of stresses away from any discontinuities. Second approach involves development of special transition finite elements to model transitions between shells and thicker structural components.
One-Dimensionality and Whiteness
ERIC Educational Resources Information Center
Calderon, Dolores
2006-01-01
This article is a theoretical discussion that links Marcuse's concept of one-dimensional society and the Great Refusal with critical race theory in order to achieve a more robust interrogation of whiteness. The author argues that in the context of the United States, the one-dimensionality that Marcuse condemns in "One-Dimensional Man" is best…
The perspectives, information and conclusions conveyed in research project abstracts, progress reports, final reports, journal abstracts and journal publications convey the viewpoints of the principal investigator and may not represent the views and policies of ORD and EPA. Concl...
NASA Astrophysics Data System (ADS)
Naik, Parvaiz Ahmad; Pardasani, Kamal Raj
2013-11-01
Oocyte is a female gametocyte or germ cell involved in reproduction. Calcium ions (Ca2+) impact nearly all aspects of cellular life as they play an important role in a variety of cellular functions. Calcium ions contributes to egg activation upon fertilization. Since it is the internal stores which provide most of the calcium signal, much attention has been focused on the intracellular channels. There are mainly two types of calcium channels which release calcium from the internal stores to the cytoplasm in many cell types. These channels are IP3-Receptor and Ryanodine Receptor (RyR). Further it is essential to maintain low cytosolic calcium concentration, the cell engages the Serco/Endoplasmic reticulum Ca2+ ATPases (SERCA) present on the ER or SR membrane for the re-uptake of cytosolic calcium at the expense of ATP hydrolysis. In view of above an attempt has been made to study the effect of the Ryanodine receptor (RyR) and the SERCA pump on the calcium distribution in oocytes. The main aim of this paper is to study the calcium concentration in absence and presence of these parameters. The FEM is used to solve the proposed Mathematical model under appreciate initial and boundary conditions. The program has been developed in MATLAB 7.10 for the entire problem to get numerical results.
Finite element analysis of flexible, rotating blades
NASA Technical Reports Server (NTRS)
Mcgee, Oliver G.
1987-01-01
A reference guide that can be used when using the finite element method to approximate the static and dynamic behavior of flexible, rotating blades is given. Important parameters such as twist, sweep, camber, co-planar shell elements, centrifugal loads, and inertia properties are studied. Comparisons are made between NASTRAN elements through published benchmark tests. The main purpose is to summarize blade modeling strategies and to document capabilities and limitations (for flexible, rotating blades) of various NASTRAN elements.
Finite Element Interface to Linear Solvers
Williams, Alan
2005-03-18
Sparse systems of linear equations arise in many engineering applications, including finite elements, finite volumes, and others. The solution of linear systems is often the most computationally intensive portion of the application. Depending on the complexity of problems addressed by the application, there may be no single solver capable of solving all of the linear systems that arise. This motivates the desire to switch an application from one solver librwy to another, depending on the problem being solved. The interfaces provided by solver libraries differ greatly, making it difficult to switch an application code from one library to another. The amount of library-specific code in an application Can be greatly reduced by having an abstraction layer between solver libraries and the application, putting a common "face" on various solver libraries. One such abstraction layer is the Finite Element Interface to Linear Solvers (EEl), which has seen significant use by finite element applications at Sandia National Laboratories and Lawrence Livermore National Laboratory.
Quadrilateral finite element mesh coarsening
Staten, Matthew L; Dewey, Mark W; Benzley, Steven E
2012-10-16
Techniques for coarsening a quadrilateral mesh are described. These techniques include identifying a coarsening region within the quadrilateral mesh to be coarsened. Quadrilateral elements along a path through the coarsening region are removed. Node pairs along opposite sides of the path are identified. The node pairs along the path are then merged to collapse the path.
Finite-element models of continental extension
NASA Technical Reports Server (NTRS)
Lynch, H. David; Morgan, Paul
1990-01-01
Numerical models of the initial deformation of extending continental lithosphere, computed to investigate the control of preexisting thermal and mechanical heterogeneities on the style of deformation, are presented. The finite element method is used to calculate deformation with a viscoelastic-plastic model for the lithosphere. Comparisons of the results of analytic models and finite-element models using this method show that good results may be obtained by the numerical technique, even with elements containing both brittle and viscoelastic sampling points. It is shown that the gross style of initial extensional deformation is controlled by the depth and width of the initial heterogeneity which localizes deformation.
Quadratic Finite Element Method for 1D Deterministic Transport
Tolar, Jr., D R; Ferguson, J M
2004-01-06
In the discrete ordinates, or SN, numerical solution of the transport equation, both the spatial ({und r}) and angular ({und {Omega}}) dependences on the angular flux {psi}{und r},{und {Omega}}are modeled discretely. While significant effort has been devoted toward improving the spatial discretization of the angular flux, we focus on improving the angular discretization of {psi}{und r},{und {Omega}}. Specifically, we employ a Petrov-Galerkin quadratic finite element approximation for the differencing of the angular variable ({mu}) in developing the one-dimensional (1D) spherical geometry S{sub N} equations. We develop an algorithm that shows faster convergence with angular resolution than conventional S{sub N} algorithms.
Hybrid finite element and Brownian dynamics method for charged particles
NASA Astrophysics Data System (ADS)
Huber, Gary A.; Miao, Yinglong; Zhou, Shenggao; Li, Bo; McCammon, J. Andrew
2016-04-01
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. A previous study introduced a new hybrid diffusion method that couples the strengths of each of these two methods, but was limited by the lack of interactions among the particles; the force on each particle had to be from an external field. This study further develops the method to allow charged particles. The method is derived for a general multidimensional system and is presented using a basic test case for a one-dimensional linear system with one charged species and a radially symmetric system with three charged species.
Verification of Orthogrid Finite Element Modeling Techniques
NASA Technical Reports Server (NTRS)
Steeve, B. E.
1996-01-01
The stress analysis of orthogrid structures, specifically with I-beam sections, is regularly performed using finite elements. Various modeling techniques are often used to simplify the modeling process but still adequately capture the actual hardware behavior. The accuracy of such 'Oshort cutso' is sometimes in question. This report compares three modeling techniques to actual test results from a loaded orthogrid panel. The finite element models include a beam, shell, and mixed beam and shell element model. Results show that the shell element model performs the best, but that the simpler beam and beam and shell element models provide reasonable to conservative results for a stress analysis. When deflection and stiffness is critical, it is important to capture the effect of the orthogrid nodes in the model.
Visualizing higher order finite elements. Final report
Thompson, David C; Pebay, Philippe Pierre
2005-11-01
This report contains an algorithm for decomposing higher-order finite elements into regions appropriate for isosurfacing and proves the conditions under which the algorithm will terminate. Finite elements are used to create piecewise polynomial approximants to the solution of partial differential equations for which no analytical solution exists. These polynomials represent fields such as pressure, stress, and momentum. In the past, these polynomials have been linear in each parametric coordinate. Each polynomial coefficient must be uniquely determined by a simulation, and these coefficients are called degrees of freedom. When there are not enough degrees of freedom, simulations will typically fail to produce a valid approximation to the solution. Recent work has shown that increasing the number of degrees of freedom by increasing the order of the polynomial approximation (instead of increasing the number of finite elements, each of which has its own set of coefficients) can allow some types of simulations to produce a valid approximation with many fewer degrees of freedom than increasing the number of finite elements alone. However, once the simulation has determined the values of all the coefficients in a higher-order approximant, tools do not exist for visual inspection of the solution. This report focuses on a technique for the visual inspection of higher-order finite element simulation results based on decomposing each finite element into simplicial regions where existing visualization algorithms such as isosurfacing will work. The requirements of the isosurfacing algorithm are enumerated and related to the places where the partial derivatives of the polynomial become zero. The original isosurfacing algorithm is then applied to each of these regions in turn.
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.
Finite-element methods for spatially resolved mesoscopic electron transport
NASA Astrophysics Data System (ADS)
Kramer, Stephan
2013-09-01
A finite-element method is presented for calculating the quantum conductance of mesoscopic two-dimensional electron devices of complex geometry attached to semi-infinite leads. For computational purposes, the leads must be cut off at some finite length. To avoid spurious, unphysical reflections, this is modeled by transparent boundary conditions. We introduce the Hardy space infinite-element technique from acoustic scattering as a way of setting up transparent boundary conditions for transport computations spanning the range from the quantum mechanical to the quasiclassical regime. These boundary conditions are exact even for wave packets and thus are especially useful in the limit of high energies with many excited modes. Yet, they possess a memory-friendly sparse matrix representation. In addition to unbounded domains, Hardy space elements allow us to truncate those parts of the computational domain which are irrelevant for the calculation of the transport properties. Thus, the computation can be done only on the region that is essential for a physically meaningful simulation of the scattering states. The benefits of the method are demonstrated by three examples. The convergence properties are tested on the transport through a quasi-one-dimensional quantum wire. It is shown that higher-order finite elements considerably improve current conservation and establish the correct phase shift between the real and the imaginary parts of the electron wave function. The Aharonov-Bohm effect demonstrates that characteristic features of quantum interference can be assessed. A simulation of electron magnetic focusing exemplifies the capability of the computational framework to study the crossover from quantum to quasiclassical behavior.
Slave finite elements: The temporal element approach to nonlinear analysis
NASA Technical Reports Server (NTRS)
Gellin, S.
1984-01-01
A formulation method for finite elements in space and time incorporating nonlinear geometric and material behavior is presented. The method uses interpolation polynomials for approximating the behavior of various quantities over the element domain, and only explicit integration over space and time. While applications are general, the plate and shell elements that are currently being programmed are appropriate to model turbine blades, vanes, and combustor liners.
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.
Quadrilateral/hexahedral finite element mesh coarsening
Staten, Matthew L; Dewey, Mark W; Scott, Michael A; Benzley, Steven E
2012-10-16
A technique for coarsening a finite element mesh ("FEM") is described. This technique includes identifying a coarsening region within the FEM to be coarsened. Perimeter chords running along perimeter boundaries of the coarsening region are identified. The perimeter chords are redirected to create an adaptive chord separating the coarsening region from a remainder of the FEM. The adaptive chord runs through mesh elements residing along the perimeter boundaries of the coarsening region. The adaptive chord is then extracted to coarsen the FEM.
Evolution of assumed stress hybrid finite element
NASA Technical Reports Server (NTRS)
Pian, T. H. H.
1984-01-01
Early versions of the assumed stress hybrid finite elements were based on the a priori satisifaction of stress equilibrium conditions. In the new version such conditions are relaxed but are introduced through additional internal displacement functions as Lagrange multipliers. A rational procedure is to choose the displacement terms such that the resulting strains are now of complete polynomials up to the same degree as that of the assumed stresses. Several example problems indicate that optimal element properties are resulted by this method.
Finite element modeling of nonisothermal polymer flows
NASA Technical Reports Server (NTRS)
Roylance, D.
1981-01-01
A finite element formulation designed to simulate polymer melt flows in which both conductive and convective heat transfer are important is described, and the numerical model is illustrated by means of computer experiments using extruder drag flow and entry flow as trial problems. Fluid incompressibility is enforced by a penalty treatment of the element pressures, and the thermal convective transport is modeled by conventional Galerkin and optimal upwind treatments.
A multidimensional finite element method for CFD
NASA Technical Reports Server (NTRS)
Pepper, Darrell W.; Humphrey, Joseph W.
1991-01-01
A finite element method is used to solve the equations of motion for 2- and 3-D fluid flow. The time-dependent equations are solved explicitly using quadrilateral (2-D) and hexahedral (3-D) elements, mass lumping, and reduced integration. A Petrov-Galerkin technique is applied to the advection terms. The method requires a minimum of computational storage, executes quickly, and is scalable for execution on computer systems ranging from PCs to supercomputers.
Finite Element Simulation of Smart Structures
NASA Technical Reports Server (NTRS)
Cui, Y. Lawrence; Panahandeh, M.
1996-01-01
Finite element equations representing the behavior of piezoelectric materials when bounded to a typical structure and used as sensors and actuators were developed. Emphasis was placed on generating sensor output equations of piezoelectric sensors and responses of a typical structure bonded with piezoelectric sensors and actuators on the basis of finite element formulation. The model can predict not only structural responses due to both mechanical and electrical loading but also electrical potential due to mechanical or thermal effects. The resulted finite element equations were then used for simple control design and performance evaluation. In the control algorithm, voltages coming out from piezoelectric sensors, which are proportional to strains at sensing locations, are taken as input. The voltages applied to the piezoelectric actuators are used as output. The feasibility of integrating control algorithm with the element routine developed herein and FEAP was demonstrated. In particular, optimal independent modal space control was implemented in a software package on the basis of finite element formulation. A rudimentary finite element-control algorithm package was also developed to evaluate the performance of candidate control laws. A few numerical simulations using the software package developed herein were given. The integrated software package will provide a design tool to address issues such as how adaptive smart systems will scale to a full size aircraft, the amount of piezoelectric materials and the powers needed to actuate it for desired performance. It will also provide a viable new structural control design concept for practical applications in large flexible structures such as aerospace vehicles and aircraft.
Gen Purpose 1-D Finite Element Network Fluid Flow Heat Transfer System Simulator
Energy Science and Technology Software Center (ESTSC)
1993-08-02
SAFSIM (System Analysis Flow Simulator) is a FORTRAN computer program to simulate the integrated performance of systems involving fluid mechanics, heat transfer, and reactor dynamics. SAFSIM provides sufficient versatility to allow the engineering simulation of almost any system, from a backyard sprinkler system to a clustered nuclear reactor propulsion system. In addition to versatility, speed and robustness are primary SAFSIM development goals. SAFSIM contains three basic physics modules: (1) a one-dimensional finite element fluid mechanicsmore » module with multiple flow network capability; (2) a one-dimensional finite element structure heat transfer module with multiple convection and radiation exchange capability; and (3) a point reactor dynamics module with reactivity feedback and decay heat capability. SAFSIM can be used for compressible and incompressible, single-phase, multicomponent flow systems.« less
Finite element displacement analysis of a lung.
NASA Technical Reports Server (NTRS)
Matthews, F. L.; West, J. B.
1972-01-01
A method is given based on the technique of finite elements which determines theoretically the mechanical behavior of a lung-shaped body loaded by its own weight. The results of this theoretical analysis have been compared with actual measurements of alveolar size and pleural pressures in animal lungs.
Animation of finite element models and results
NASA Technical Reports Server (NTRS)
Lipman, Robert R.
1992-01-01
This is not intended as a complete review of computer hardware and software that can be used for animation of finite element models and results, but is instead a demonstration of the benefits of visualization using selected hardware and software. The role of raw computational power, graphics speed, and the use of videotape are discussed.
One-dimensional immiscible displacement experiments
NASA Astrophysics Data System (ADS)
Thomson, N. R.; Graham, D. N.; Farquhar, G. J.
1992-08-01
In recent years, a great deal of attention has focused on the development of various methods to predict the fate of immiscible contaminants (NAPL's) in soils. In an attempt to satisfy this requirement, a host of numerical models has been developed. Unfortunately, there exist little experimental data to verify the assumptions used in the derivation of these immiscible flow models. One objective of this paper is to report on a non-destructive measurement technique which was used to capture the relative organic-phase saturation variations in a number of two-phase flow displacement experiments. The data obtained from these experiments were compared to results obtained from a one-dimensional, finite-element based, two-phase flow model. The experiments consisted of five separate trials using three different immiscible liquids (hydraulic oil, kerosene and hexane) in a water-saturated column. Irregular immiscible liquid infiltration fronts were observed in four of the five experiments, indicating that very small-scale heterogeneities control the infiltration of immiscible liquids into soil. Independent of the column experiments, saturation-capillary pressure curves were determined for the various liquids. In general, the simulated NAPL saturation vs. time profiles agreed very well with the observations for all five of the trials.
He, Xiao; Ryu, Shinsei; Hirata, So
2014-01-14
Finite-temperature extensions of ab initio Gaussian-basis-set spin-restricted Hartree–Fock (HF) and second-order many-body perturbation (MP2) theories are implemented for infinitely extended, periodic, one-dimensional solids and applied to the Peierls and charge-density-wave (CDW) transitions in polyyne and all-trans polyacetylene. The HF theory predicts insulating CDW ground states for both systems in their equidistant structures at low temperatures. In the same structures, they turn metallic at high temperatures. Starting from the “dimerized” low-temperature equilibrium structures, the systems need even higher temperatures to undergo a Peierls transition, which is accompanied by geometric as well as electronic distortions from dimerized to non-dimerized forms. The conventional finite-temperature MP2 theory shows a sign of divergence in any phase at any nonzero temperature and is useless. The renormalized finite-temperature MP2 (MP2R) theory is divergent only near metallic electronic structures, but is well behaved elsewhere. MP2R also predicts CDW and Peierls transitions occurring at two different temperatures. The effect of electron correlation is primarily to lower the Peierls transition temperature.
On Hybrid and mixed finite element methods
NASA Technical Reports Server (NTRS)
Pian, T. H. H.
1981-01-01
Three versions of the assumed stress hybrid model in finite element methods and the corresponding variational principles for the formulation are presented. Examples of rank deficiency for stiffness matrices by the hybrid stress model are given and their corresponding kinematic deformation modes are identified. A discussion of the derivation of general semi-Loof elements for plates and shells by the hybrid stress method is given. It is shown that the equilibrium model by Fraeijs de Veubeke can be derived by the approach of the hybrid stress model as a special case of semi-Loof elements.
Revolution in Orthodontics: Finite element analysis
Singh, Johar Rajvinder; Kambalyal, Prabhuraj; Jain, Megha; Khandelwal, Piyush
2016-01-01
Engineering has not only developed in the field of medicine but has also become quite established in the field of dentistry, especially Orthodontics. Finite element analysis (FEA) is a computational procedure to calculate the stress in an element, which performs a model solution. This structural analysis allows the determination of stress resulting from external force, pressure, thermal change, and other factors. This method is extremely useful for indicating mechanical aspects of biomaterials and human tissues that can hardly be measured in vivo. The results obtained can then be studied using visualization software within the finite element method (FEM) to view a variety of parameters, and to fully identify implications of the analysis. This is a review to show the applications of FEM in Orthodontics. It is extremely important to verify what the purpose of the study is in order to correctly apply FEM. PMID:27114948
Finite element computation with parallel VLSI
NASA Technical Reports Server (NTRS)
Mcgregor, J.; Salama, M.
1983-01-01
This paper describes a parallel processing computer consisting of a 16-bit microcomputer as a master processor which controls and coordinates the activities of 8086/8087 VLSI chip set slave processors working in parallel. The hardware is inexpensive and can be flexibly configured and programmed to perform various functions. This makes it a useful research tool for the development of, and experimentation with parallel mathematical algorithms. Application of the hardware to computational tasks involved in the finite element analysis method is demonstrated by the generation and assembly of beam finite element stiffness matrices. A number of possible schemes for the implementation of N-elements on N- or n-processors (N is greater than n) are described, and the speedup factors of their time consumption are determined as a function of the number of available parallel processors.
Finite Element Interface to Linear Solvers
Energy Science and Technology Software Center (ESTSC)
2005-03-18
Sparse systems of linear equations arise in many engineering applications, including finite elements, finite volumes, and others. The solution of linear systems is often the most computationally intensive portion of the application. Depending on the complexity of problems addressed by the application, there may be no single solver capable of solving all of the linear systems that arise. This motivates the desire to switch an application from one solver librwy to another, depending on themore » problem being solved. The interfaces provided by solver libraries differ greatly, making it difficult to switch an application code from one library to another. The amount of library-specific code in an application Can be greatly reduced by having an abstraction layer between solver libraries and the application, putting a common "face" on various solver libraries. One such abstraction layer is the Finite Element Interface to Linear Solvers (EEl), which has seen significant use by finite element applications at Sandia National Laboratories and Lawrence Livermore National Laboratory.« less
DENSITY-DEPENDENT FLOW IN ONE-DIMENSIONAL VARIABLY-SATURATED MEDIA
A one-dimensional finite element is developed to simulate density-dependent flow of saltwater in variably saturated media. The flow and solute equations were solved in a coupled mode (iterative), in a partially coupled mode (non-iterative), and in a completely decoupled mode. P...
Finite Element Heat & Mass Transfer Code
Energy Science and Technology Software Center (ESTSC)
1996-10-10
FEHM is a numerical simulation code for subsurface transport processes. It models 3-D, time-dependent, multiphase, multicomponent, non-isothermal, reactive flow through porous and fractured media. It can accurately represent complex 3-D geologic media and structures and their effects on subsurface flow and transport. Its capabilities include flow of gas, water, and heat; flow of air, water, and heat; multiple chemically reactive and sorbing tracers; finite element/finite volume formulation; coupled stress module; saturated and unsaturated media; andmore » double porosity and double porosity/double permeability capabilities.« less
Diagonal multisoliton matrix elements in finite volume
NASA Astrophysics Data System (ADS)
Pálmai, T.; Takács, G.
2013-02-01
We consider diagonal matrix elements of local operators between multisoliton states in finite volume in the sine-Gordon model and formulate a conjecture regarding their finite size dependence which is valid up to corrections exponential in the volume. This conjecture extends the results of Pozsgay and Takács which were only valid for diagonal scattering. In order to test the conjecture, we implement a numerical renormalization group improved truncated conformal space approach. The numerical comparisons confirm the conjecture, which is expected to be valid for general integrable field theories. The conjectured formula can be used to evaluate finite temperature one-point and two-point functions using recently developed methods.
Finite Element Analysis of Honeycomb Impact Attenuator
NASA Astrophysics Data System (ADS)
Yang, Seung-Yong; Choi, Seung-Kyu; Kim, Nohyu
To participate in Student Formula Society of Automotive Engineers (SAE) competitions, it is necessary to build an impact attenuator that would give an average deceleration not to exceed 20g when it runs into a rigid wall. Students can use numerical simulations or experimental test data to show that their car satisfies this safety requirement. A student group to study formula cars at the Korea University of Technology and Education has designed a vehicle to take part in a SAE competition, and a honeycomb structure was adopted as the impact attenuator. In this paper, finite element calculations were carried out to investigate the dynamic behavior of the honeycomb attenuator. Deceleration and deformation behaviors were studied. Effect of the yield strength was checked by comparing the numerical results. ABAQUS/Explicit finite element code was used.
Plasticity - Theory and finite element applications.
NASA Technical Reports Server (NTRS)
Armen, H., Jr.; Levine, H. S.
1972-01-01
A unified presentation is given of the development and distinctions associated with various incremental solution procedures used to solve the equations governing the nonlinear behavior of structures, and this is discussed within the framework of the finite-element method. Although the primary emphasis here is on material nonlinearities, consideration is also given to geometric nonlinearities acting separately or in combination with nonlinear material behavior. The methods discussed here are applicable to a broad spectrum of structures, ranging from simple beams to general three-dimensional bodies. The finite-element analysis methods for material nonlinearity are general in the sense that any of the available plasticity theories can be incorporated to treat strain hardening or ideally plastic behavior.
2-d Finite Element Code Postprocessor
Energy Science and Technology Software Center (ESTSC)
1996-07-15
ORION is an interactive program that serves as a postprocessor for the analysis programs NIKE2D, DYNA2D, TOPAZ2D, and CHEMICAL TOPAZ2D. ORION reads binary plot files generated by the two-dimensional finite element codes currently used by the Methods Development Group at LLNL. Contour and color fringe plots of a large number of quantities may be displayed on meshes consisting of triangular and quadrilateral elements. ORION can compute strain measures, interface pressures along slide lines, reaction forcesmore » along constrained boundaries, and momentum. ORION has been applied to study the response of two-dimensional solids and structures undergoing finite deformations under a wide variety of large deformation transient dynamic and static problems and heat transfer analyses.« less
Finite element analysis of human joints
Bossart, P.L.; Hollerbach, K.
1996-09-01
Our work focuses on the development of finite element models (FEMs) that describe the biomechanics of human joints. Finite element modeling is becoming a standard tool in industrial applications. In highly complex problems such as those found in biomechanics research, however, the full potential of FEMs is just beginning to be explored, due to the absence of precise, high resolution medical data and the difficulties encountered in converting these enormous datasets into a form that is usable in FEMs. With increasing computing speed and memory available, it is now feasible to address these challenges. We address the first by acquiring data with a high resolution C-ray CT scanner and the latter by developing semi-automated method for generating the volumetric meshes used in the FEM. Issues related to tomographic reconstruction, volume segmentation, the use of extracted surfaces to generate volumetric hexahedral meshes, and applications of the FEM are described.
Finite element based electric motor design optimization
NASA Technical Reports Server (NTRS)
Campbell, C. Warren
1993-01-01
The purpose of this effort was to develop a finite element code for the analysis and design of permanent magnet electric motors. These motors would drive electromechanical actuators in advanced rocket engines. The actuators would control fuel valves and thrust vector control systems. Refurbishing the hydraulic systems of the Space Shuttle after each flight is costly and time consuming. Electromechanical actuators could replace hydraulics, improve system reliability, and reduce down time.
Finite Element Analysis of Reverberation Chambers
NASA Technical Reports Server (NTRS)
Bunting, Charles F.; Nguyen, Duc T.
2000-01-01
The primary motivating factor behind the initiation of this work was to provide a deterministic means of establishing the validity of the statistical methods that are recommended for the determination of fields that interact in -an avionics system. The application of finite element analysis to reverberation chambers is the initial step required to establish a reasonable course of inquiry in this particularly data-intensive study. The use of computational electromagnetics provides a high degree of control of the "experimental" parameters that can be utilized in a simulation of reverberating structures. As the work evolved there were four primary focus areas they are: 1. The eigenvalue problem for the source free problem. 2. The development of a complex efficient eigensolver. 3. The application of a source for the TE and TM fields for statistical characterization. 4. The examination of shielding effectiveness in a reverberating environment. One early purpose of this work was to establish the utility of finite element techniques in the development of an extended low frequency statistical model for reverberation phenomena. By employing finite element techniques, structures of arbitrary complexity can be analyzed due to the use of triangular shape functions in the spatial discretization. The effects of both frequency stirring and mechanical stirring are presented. It is suggested that for the low frequency operation the typical tuner size is inadequate to provide a sufficiently random field and that frequency stirring should be used. The results of the finite element analysis of the reverberation chamber illustrate io-W the potential utility of a 2D representation for enhancing the basic statistical characteristics of the chamber when operating in a low frequency regime. The basic field statistics are verified for frequency stirring over a wide range of frequencies. Mechanical stirring is shown to provide an effective frequency deviation.
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.
ExodusII Finite Element Data Model
Energy Science and Technology Software Center (ESTSC)
2005-05-14
EXODUS II is a model developed to store and retrieve data for finite element analyses. It is used for preprocessing (problem definition), postprocessing (results visualization), as well as code to code data transfer. An EXODUS II data file is a random access, machine independent, binary file that is written and read via C, C++, or Fortran library routines which comprise the Application Programming Interface. (exodus II is based on netcdf)
Finite Element Results Visualization for Unstructured Grids
Speck, Douglas E.; Dovey, Donald J.
1996-07-15
GRIZ is a general-purpose post-processing application supporting interactive visualization of finite element analysis results on unstructured grids. In addition to basic pseudocolor renderings of state variables over the mesh surface, GRIZ provides modern visualization techniques such as isocontours and isosurfaces, cutting planes, vector field display, and particle traces. GRIZ accepts both command-line and mouse-driven input, and is portable to virtually any UNIX platform which provides Motif and OpenGl libraries.
Finite element model of needle electrode sensitivity
NASA Astrophysics Data System (ADS)
Høyum, P.; Kalvøy, H.; Martinsen, Ø. G.; Grimnes, S.
2010-04-01
We used the Finite Element (FE) Method to estimate the sensitivity of a needle electrode for bioimpedance measurement. This current conducting needle with insulated shaft was inserted in a saline solution and current was measured at the neutral electrode. FE model resistance and reactance were calculated and successfully compared with measurements on a laboratory model. The sensitivity field was described graphically based on these FE simulations.
FESDIF -- Finite Element Scalar Diffraction theory code
Kraus, H.G.
1992-09-01
This document describes the theory and use of a powerful scalar diffraction theory based computer code for calculation of intensity fields due to diffraction of optical waves by two-dimensional planar apertures and lenses. This code is called FESDIF (Finite Element Scalar Diffraction). It is based upon both Fraunhofer and Kirchhoff scalar diffraction theories. Simplified routines for circular apertures are included. However, the real power of the code comes from its basis in finite element methods. These methods allow the diffracting aperture to be virtually any geometric shape, including the various secondary aperture obstructions present in telescope systems. Aperture functions, with virtually any phase and amplitude variations, are allowed in the aperture openings. Step change aperture functions are accommodated. The incident waves are considered to be monochromatic. Plane waves, spherical waves, or Gaussian laser beams may be incident upon the apertures. Both area and line integral transformations were developed for the finite element based diffraction transformations. There is some loss of aperture function generality in the line integral transformations which are typically many times more computationally efficient than the area integral transformations when applicable to a particular problem.
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.
Enhancements to modal testing using finite elements
NASA Astrophysics Data System (ADS)
Jarvis, Brian
In calculating the natural frequencies and mode shapes from a finite element analysis, there are generally many more degrees of freedom than can be handled for the eigensolution. A reduction process is employed to reduce the number to a master set and chosen so that the modes of interest are well defined. By choosing those freedoms where the inertia terms are high or the stiffness terms are low then an automatic procedure for selecting the best freedoms can be defined. For modal testing, these master freedoms also indicate the best transducer locations for optimum low order mode identification. Having carried out the modal test, the mode shapes obtained can be forced onto the finite element model giving greatly enhanced results. By examining terms in all mode shapes from the finite element model in the frequency range of interest, the best reference or excitation position can be found. An example of the use of this technique to study the modal properties of an aero-engine compressor blade is given.
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.
Mixed Finite Element Method for Melt Migration
NASA Astrophysics Data System (ADS)
Taicher, A. L.; Hesse, M. A.; Arbogast, T.
2012-12-01
Multi-phase flow arises during partial melting in the earth mantle, where the porosity is small and material has the characteristics of a compacting porous medium. The equations governing multi-phase flow have been specialized to partially molten materials by McKenzie and Fowler. Their model, also called a Darcy-Stokes system, is highly coupled and non-linear. Melt flow is governed by Darcy's Law while the high temperature, ductile creep of the solid matrix is modeled using viscous non-Newtonian Stokes rheology. In addition, the melt and solid pressures are related through a compaction relation. This nearly elliptic mechanical problem is then coupled with both solute transport and thermal evolution according to the enthalpy method developed by Katz. A suitable numerical method must solve the Darcy-Stokes problem in a manner compatible with the transport problem. Moreover, unlike most porous media problems, partially molten materials transition dynamically from non-porous solid to porous medium. Therefore, a numerical method must also carefully account for the limit of zero porosity. The Darcy-Stokes system for modeling partial melting in the mantle is a novel problem. As far as we know, there currently does not exist a finite element solution in the literature solving these coupled equations. The finite element framework provides support for additional analysis of error and convergence. Moreover, both mesh refinement and anisotropy are naturally incorporated into finite elements. In particular, the mixed finite element method presents a good candidate because it works in both limiting cases: Darcy and incompressible Stokes flow. Mixed methods also produce discretely conservative fluxes that are required for the transport problem to remains stable without violating conservation of mass. Based preliminary investigations in 1D and derived energy estimates, we present a mixed formulation for the Darcy-Stokes system. Next, using novel elements of lowest order and
Modelling bucket excavation by finite element
NASA Astrophysics Data System (ADS)
Pecingina, O. M.
2015-11-01
Changes in geological components of the layers from lignite pits have an impact on the sustainability of the cup path elements and under the action of excavation force appear efforts leading to deformation of the entire assembly. Application of finite element method in the optimization of components leads to economic growth, to increase the reliability and durability of the studied machine parts thus the machine. It is obvious usefulness of knowledge the state of mechanical tensions that the designed piece or the assembly not to break under the action of tensions that must cope during operation. In the course of excavation work on all bucket cutting force components, the first coming into contact with the material being excavated cutting edge. Therefore in the study with finite element analysis is retained only cutting edge. To study the field of stress and strain on the cutting edge will be created geometric patterns for each type of cup this will be subject to static analysis. The geometric design retains the cutting edge shape and on this on the tooth cassette location will apply an areal force on the abutment tooth. The cutting edge real pattern is subjected to finite element study for the worst case of rock cutting by symmetrical and asymmetrical cups whose profile is different. The purpose of this paper is to determine the displacement and tensions field for both profiles considering the maximum force applied on the cutting edge and the depth of the cutting is equal with the width of the cutting edge of the tooth. It will consider the worst case when on the structure will act both the tangential force and radial force on the bucket profile. For determination of stress and strain field on the form design of cutting edge profile will apply maximum force assuming uniform distribution and on the edge surface force will apply a radial force. After geometric patterns discretization on the cutting knives and determining stress field, can be seen that at the
Hermes, Matthew R; Hirata, So
2015-09-14
One-dimensional (1D) solids exhibit a number of striking electronic structures including charge-density wave (CDW) and spin-density wave (SDW). Also, the Peierls theorem states that at zero temperature, a 1D system predicted by simple band theory to be a metal will spontaneously dimerize and open a finite fundamental bandgap, while at higher temperatures, it will assume the equidistant geometry with zero bandgap (a Peierls transition). We computationally study these unique electronic structures and transition in polyyne and all-trans polyacetylene using finite-temperature generalizations of ab initio spin-unrestricted Hartree-Fock (UHF) and spin-restricted coupled-cluster doubles (CCD) theories, extending upon previous work [He et al., J. Chem. Phys. 140, 024702 (2014)] that is based on spin-restricted Hartree-Fock (RHF) and second-order many-body perturbation (MP2) theories. Unlike RHF, UHF can predict SDW as well as CDW and metallic states, and unlike MP2, CCD does not diverge even if the underlying RHF reference wave function is metallic. UHF predicts a gapped SDW state with no dimerization at low temperatures, which gradually becomes metallic as the temperature is raised. CCD, meanwhile, confirms that electron correlation lowers the Peierls transition temperature. Furthermore, we show that the results from all theories for both polymers are subject to a unified interpretation in terms of the UHF solutions to the Hubbard-Peierls model using different values of the electron-electron interaction strength, U/t, in its Hamiltonian. The CCD wave function is shown to encompass the form of the exact solution of the Tomonaga-Luttinger model and is thus expected to describe accurately the electronic structure of Luttinger liquids. PMID:26374011
Hermes, Matthew R.; Hirata, So
2015-09-14
One-dimensional (1D) solids exhibit a number of striking electronic structures including charge-density wave (CDW) and spin-density wave (SDW). Also, the Peierls theorem states that at zero temperature, a 1D system predicted by simple band theory to be a metal will spontaneously dimerize and open a finite fundamental bandgap, while at higher temperatures, it will assume the equidistant geometry with zero bandgap (a Peierls transition). We computationally study these unique electronic structures and transition in polyyne and all-trans polyacetylene using finite-temperature generalizations of ab initio spin-unrestricted Hartree–Fock (UHF) and spin-restricted coupled-cluster doubles (CCD) theories, extending upon previous work [He et al., J. Chem. Phys. 140, 024702 (2014)] that is based on spin-restricted Hartree–Fock (RHF) and second-order many-body perturbation (MP2) theories. Unlike RHF, UHF can predict SDW as well as CDW and metallic states, and unlike MP2, CCD does not diverge even if the underlying RHF reference wave function is metallic. UHF predicts a gapped SDW state with no dimerization at low temperatures, which gradually becomes metallic as the temperature is raised. CCD, meanwhile, confirms that electron correlation lowers the Peierls transition temperature. Furthermore, we show that the results from all theories for both polymers are subject to a unified interpretation in terms of the UHF solutions to the Hubbard–Peierls model using different values of the electron-electron interaction strength, U/t, in its Hamiltonian. The CCD wave function is shown to encompass the form of the exact solution of the Tomonaga–Luttinger model and is thus expected to describe accurately the electronic structure of Luttinger liquids.
Iterative methods for mixed finite element equations
NASA Technical Reports Server (NTRS)
Nakazawa, S.; Nagtegaal, J. C.; Zienkiewicz, O. C.
1985-01-01
Iterative strategies for the solution of indefinite system of equations arising from the mixed finite element method are investigated in this paper with application to linear and nonlinear problems in solid and structural mechanics. The augmented Hu-Washizu form is derived, which is then utilized to construct a family of iterative algorithms using the displacement method as the preconditioner. Two types of iterative algorithms are implemented. Those are: constant metric iterations which does not involve the update of preconditioner; variable metric iterations, in which the inverse of the preconditioning matrix is updated. A series of numerical experiments is conducted to evaluate the numerical performance with application to linear and nonlinear model problems.
Chemorheology of reactive systems: Finite element analysis
NASA Technical Reports Server (NTRS)
Douglas, C.; Roylance, D.
1982-01-01
The equations which govern the nonisothermal flow of reactive fluids are outlined, and the means by which finite element analysis is used to solve these equations for the sort of arbitrary boundary conditions encountered in industrial practice are described. The performance of the computer code is illustrated by several trial problems, selected more for their value in providing insight to polymer processing flows than as practical production problems. Although a good deal remains to be learned as to the performance and proper use of this numerical technique, it is undeniably useful in providing better understanding of today's complicated polymer processing problems.
Finite element solutions of free surface flows
NASA Technical Reports Server (NTRS)
Zarda, P. R.; Marcus, M. S.
1977-01-01
A procedure is presented for using NASTRAN to determine the flow field about arbitrarily shaped bodies in the presence of a free surface. The fundamental unknown of the problem is the velocity potential which must satisfy Laplace's equation in the fluid region. Boundary conditions on the free surface may involve second order derivatives in space and time. In cases involving infinite domains either a tractable radiation condition is applied at a truncated boundary or a series expansion is used and matched to the local finite elements. Solutions are presented for harmonic, transient, and steady state problems and compared to either exact solutions or other numerical solutions.
Algebraic surface design and finite element meshes
NASA Technical Reports Server (NTRS)
Bajaj, Chandrajit L.
1992-01-01
Some of the techniques are summarized which are used in constructing C sup 0 and C sup 1 continuous meshes of low degree, implicitly defined, algebraic surface patches in three dimensional space. These meshes of low degree algebraic surface patches are used to construct accurate computer models of physical objects. These meshes are also used in the finite element simulation of physical phenomena (e.g., heat dissipation, stress/strain distributions, fluid flow characteristics) required in the computer prototyping of both the manufacturability and functionality of the geometric design.
Finite element methods in probabilistic mechanics
NASA Technical Reports Server (NTRS)
Liu, Wing Kam; Mani, A.; Belytschko, Ted
1987-01-01
Probabilistic methods, synthesizing the power of finite element methods with second-order perturbation techniques, are formulated for linear and nonlinear problems. Random material, geometric properties and loads can be incorporated in these methods, in terms of their fundamental statistics. By construction, these methods are applicable when the scale of randomness is not too large and when the probabilistic density functions have decaying tails. By incorporating certain computational techniques, these methods are shown to be capable of handling large systems with many sources of uncertainties. Applications showing the effects of combined random fields and cyclic loading/stress reversal are studied and compared with Monte Carlo simulation results.
Shape optimization including finite element grid adaptation
NASA Technical Reports Server (NTRS)
Kikuchi, N.; Taylor, J. E.
1984-01-01
The prediction of optimal shape design for structures depends on having a sufficient level of precision in the computation of structural response. These requirements become critical in situations where the region to be designed includes stress concentrations or unilateral contact surfaces, for example. In the approach to shape optimization discussed here, a means to obtain grid adaptation is incorporated into the finite element procedures. This facility makes it possible to maintain a level of quality in the computational estimate of response that is surely adequate for the shape design problem.
2-D Finite Element Heat Conduction
Energy Science and Technology Software Center (ESTSC)
1989-10-30
AYER is a finite element program which implicitly solves the general two-dimensional equation of thermal conduction for plane or axisymmetric bodies. AYER takes into account the effects of time (transient problems), in-plane anisotropic thermal conductivity, a three-dimensional velocity distribution, and interface thermal contact resistance. Geometry and material distributions are arbitrary, and input is via subroutines provided by the user. As a result, boundary conditions, material properties, velocity distributions, and internal power generation may be mademore » functions of, e.g., time, temperature, location, and heat flux.« less
Dynamic analysis of mechanisms by finite elements
Botsali, F.M.; Uenuevar, A.
1996-11-01
The need to increase productivity in order to decrease manufacturing costs lead to an increase in the working speeds of machines and mechanical systems used in manufacturing. A method is presented for investigating the dynamics of mechanisms with elastic links. Finite element method is used in the formulation of the dynamic problem. Modal transformation is used in order to reduce the number of equations of motion. Using the presented technique, elastic and rigid body motions of mechanism links are solved simultaneously. The presented method may be applied to spatial and open loop mechanisms including robot manipulators as well.
Adaptive Finite Element Methods in Geodynamics
NASA Astrophysics Data System (ADS)
Davies, R.; Davies, H.; Hassan, O.; Morgan, K.; Nithiarasu, P.
2006-12-01
Adaptive finite element methods are presented for improving the quality of solutions to two-dimensional (2D) and three-dimensional (3D) convection dominated problems in geodynamics. The methods demonstrate the application of existing technology in the engineering community to problems within the `solid' Earth sciences. Two-Dimensional `Adaptive Remeshing': The `remeshing' strategy introduced in 2D adapts the mesh automatically around regions of high solution gradient, yielding enhanced resolution of the associated flow features. The approach requires the coupling of an automatic mesh generator, a finite element flow solver and an error estimator. In this study, the procedure is implemented in conjunction with the well-known geodynamical finite element code `ConMan'. An unstructured quadrilateral mesh generator is utilised, with mesh adaptation accomplished through regeneration. This regeneration employs information provided by an interpolation based local error estimator, obtained from the computed solution on an existing mesh. The technique is validated by solving thermal and thermo-chemical problems with known benchmark solutions. In a purely thermal context, results illustrate that the method is highly successful, improving solution accuracy whilst increasing computational efficiency. For thermo-chemical simulations the same conclusions can be drawn. However, results also demonstrate that the grid based methods employed for simulating the compositional field are not competitive with the other methods (tracer particle and marker chain) currently employed in this field, even at the higher spatial resolutions allowed by the adaptive grid strategies. Three-Dimensional Adaptive Multigrid: We extend the ideas from our 2D work into the 3D realm in the context of a pre-existing 3D-spherical mantle dynamics code, `TERRA'. In its original format, `TERRA' is computationally highly efficient since it employs a multigrid solver that depends upon a grid utilizing a clever
System software for the finite element machine
NASA Technical Reports Server (NTRS)
Crockett, T. W.; Knott, J. D.
1985-01-01
The Finite Element Machine is an experimental parallel computer developed at Langley Research Center to investigate the application of concurrent processing to structural engineering analysis. This report describes system-level software which has been developed to facilitate use of the machine by applications researchers. The overall software design is outlined, and several important parallel processing issues are discussed in detail, including processor management, communication, synchronization, and input/output. Based on experience using the system, the hardware architecture and software design are critiqued, and areas for further work are suggested.
NASA Technical Reports Server (NTRS)
Gelinas, R. J.; Doss, S. K.; Vajk, J. P.; Djomehri, J.; Miller, K.
1983-01-01
The mathematical background regarding the moving finite element (MFE) method of Miller and Miller (1981) is discussed, taking into account a general system of partial differential equations (PDE) and the amenability of the MFE method in two dimensions to code modularization and to semiautomatic user-construction of numerous PDE systems for both Dirichlet and zero-Neumann boundary conditions. A description of test problem results is presented, giving attention to aspects of single square wave propagation, and a solution of the heat equation.
One-Dimensional Grid Turbulence
NASA Astrophysics Data System (ADS)
Kerstein, Alan R.; Nilsen, Vebjørn
1998-11-01
To capture molecular mixing and other small scale phenomena such as chemical reactions and differential diffusion, it is essential to resolve all the length (and time) scales. For large Reynolds number flows this is impossible to do in three-dimensional turbulence simulations with the current and foreseeable future computer technology. To circumvent this problem the one-dimensional turbulence (ODT) model, as the name implies, considers only one spatial dimension in which all the length scales can be resolved even at very large Reynolds numbers. To incorporate the effect of advection on a one-dimensional domain, the evolution of the velocity and scalar profiles is randomly interrupted by a sequence of profile rearrangements representing the effect of turbulent eddies. Results obtained from ODT simulations of grid turbulence with a passive scalar are presented. The decay exponents for the velocity and passive scalar fluctuations, as predicted by ODT, compare favorably with experimental data.
An optimally blended finite-spectral element scheme with minimal dispersion for Maxwell equations
NASA Astrophysics Data System (ADS)
Wajid, Hafiz Abdul; Ayub, Sobia
2012-10-01
We study the dispersive properties of the time harmonic Maxwell equations for optimally blended finite-spectral element scheme using tensor product elements defined on rectangular grid in d-dimensions. We prove and give analytical expressions for the discrete dispersion relations for this scheme. We find that for a rectangular grid (a) the analytical expressions for the discrete dispersion error in higher dimensions can be obtained using one dimensional discrete dispersion error expressions; (b) the optimum value of the blending parameter is p/(p+1) for all p∈N and for any number of spatial dimensions; (c) analytical expressions for the discrete dispersion relations for finite element and spectral element schemes can be obtained when the value of blending parameter is chosen to be 0 and 1 respectively; (d) the optimally blended scheme guarantees two additional orders of accuracy compared with standard finite element and spectral element schemes; and (e) the absolute accuracy of the optimally blended scheme is O(p-2) and O(p-1) times better than that of the pure finite element and spectral element schemes respectively.
Finite element modeling of piezoelectric elements with complex electrode configuration
NASA Astrophysics Data System (ADS)
Paradies, R.; Schläpfer, B.
2009-02-01
It is well known that the material properties of piezoelectric materials strongly depend on the state of polarization of the individual element. While an unpolarized material exhibits mechanically isotropic material properties in the absence of global piezoelectric capabilities, the piezoelectric material properties become transversally isotropic with respect to the polarization direction after polarization. Therefore, for evaluating piezoelectric elements the material properties, including the coupling between the mechanical and the electromechanical behavior, should be addressed correctly. This is of special importance for the micromechanical description of piezoelectric elements with interdigitated electrodes (IDEs). The best known representatives of this group are active fiber composites (AFCs), macro fiber composites (MFCs) and the radial field diaphragm (RFD), respectively. While the material properties are available for a piezoelectric wafer with a homogeneous polarization perpendicular to its plane as postulated in the so-called uniform field model (UFM), the same information is missing for piezoelectric elements with more complex electrode configurations like the above-mentioned ones with IDEs. This is due to the inhomogeneous field distribution which does not automatically allow for the correct assignment of the material, i.e. orientation and property. A variation of the material orientation as well as the material properties can be accomplished by including the polarization process of the piezoelectric transducer in the finite element (FE) simulation prior to the actual load case to be investigated. A corresponding procedure is presented which automatically assigns the piezoelectric material properties, e.g. elasticity matrix, permittivity, and charge vector, for finite element models (FEMs) describing piezoelectric transducers according to the electric field distribution (field orientation and strength) in the structure. A corresponding code has been
Quantum algorithms and the finite element method
NASA Astrophysics Data System (ADS)
Montanaro, Ashley; Pallister, Sam
2016-03-01
The finite element method is used to approximately solve boundary value problems for differential equations. The method discretizes the parameter space and finds an approximate solution by solving a large system of linear equations. Here we investigate the extent to which the finite element method can be accelerated using an efficient quantum algorithm for solving linear equations. We consider the representative general question of approximately computing a linear functional of the solution to a boundary value problem and compare the quantum algorithm's theoretical performance with that of a standard classical algorithm—the conjugate gradient method. Prior work claimed that the quantum algorithm could be exponentially faster but did not determine the overall classical and quantum run times required to achieve a predetermined solution accuracy. Taking this into account, we find that the quantum algorithm can achieve a polynomial speedup, the extent of which grows with the dimension of the partial differential equation. In addition, we give evidence that no improvement of the quantum algorithm can lead to a superpolynomial speedup when the dimension is fixed and the solution satisfies certain smoothness properties.
Impeller deflection and modal finite element analysis.
Spencer, Nathan A.
2013-10-01
Deflections of an impeller due to centripetal forces are calculated using finite element analysis. The lateral, or out of plane, deflections are an important design consideration for this particular impeller because it incorporates an air bearing with critical gap tolerances. The target gap distance is approximately 10 microns at a rotational velocity of 2500 rpm. The centripetal forces acting on the impeller cause it deflect in a concave fashion, decreasing the initial gap distance as a function of radial position. This deflection is characterized for a previous and updated impeller design for comparative purposes. The impact of design options such as material selection, geometry dimensions, and operating rotational velocity are also explored, followed by a sensitivity study with these parameters bounded by specific design values. A modal analysis is also performed to calculate the impeller's natural frequencies which are desired to be avoided during operation. The finite element modeling techniques continue to be exercised by the impeller design team to address specific questions and evaluate conceptual designs, some of which are included in the Appendix.
Finite element analysis of multilayer coextrusion.
Hopkins, Matthew Morgan; Schunk, Peter Randall; Baer, Thomas A.; Mrozek, Randy A.; Lenhart, Joseph Ludlow; Rao, Rekha Ranjana; Collins, Robert; Mondy, Lisa Ann
2011-09-01
Multilayer coextrusion has become a popular commercial process for producing complex polymeric products from soda bottles to reflective coatings. A numerical model of a multilayer coextrusion process is developed based on a finite element discretization and two different free-surface methods, an arbitrary-Lagrangian-Eulerian (ALE) moving mesh implementation and an Eulerian level set method, to understand the moving boundary problem associated with the polymer-polymer interface. The goal of this work is to have a numerical capability suitable for optimizing and troubleshooting the coextrusion process, circumventing flow instabilities such as ribbing and barring, and reducing variability in layer thickness. Though these instabilities can be both viscous and elastic in nature, for this work a generalized Newtonian description of the fluid is used. Models of varying degrees of complexity are investigated including stability analysis and direct three-dimensional finite element free surface approaches. The results of this work show how critical modeling can be to reduce build test cycles, improve material choices, and guide mold design.
A finite element model for ultrasonic cutting.
Lucas, Margaret; MacBeath, Alan; McCulloch, Euan; Cardoni, Andrea
2006-12-22
Using a single-blade ultrasonic cutting device, a study of ultrasonic cutting of three very different materials is conducted using specimens of cheese, polyurethane foam and epoxy resin. Initial finite element models are created, based on the assumption that the ultrasonic blade causes a crack to propagate in a controlled mode 1 opening, and these are validated against experimental data from three point bend fracture tests and ultrasonic cutting experiments on the materials. Subsequently, the finite element model is developed to represent ultrasonic cutting of a multi-layered material. Materials are chosen whose properties allow a model to be developed that could represent a multi-layer food product or biological structure, to enable ultrasonic cutting systems to be designed for applications both in the field of food processing and surgical procedures. The model incorporates an estimation of the friction condition between the cutting blade and the material to be cut and allows adjustment of the frequency, cutting amplitude and cutting speed. PMID:16814351
Overcoming element erosion limitations within Lagrangian finite element codes
NASA Astrophysics Data System (ADS)
Vignjevic, Rade; Hughes, Kevin; Walker, Andrew; Taylor, Emma A.
2001-10-01
Lagrangian finite element methods have been used extensively in the past to study the non-linear transient behaviour of materials, ranging from crash test of cars to simulating bird strikes on planes.... However, as this type of space discretization does not allow for motion of the material through the mesh when modelling extremely large deformations, the mesh becomes highly distorted. This paper describes some limitations and applicability of this type of analysis for high velocity impacts. A method for dealing with this problem is by the erosion of elements is proposed where the main issue is the deformation of element failure strains. Results were compared with empirical perforation results and were found to be in good agreement. The results were then used to simulate high velocity impacts upon a multi-layered aluminium target, in order to predict a ballistic limit curve. LS-DYNA3D was used as the FE solver for all simulations. Meshes were generated with Truegrid.
Estimation of Thermoelectric Generator Performance by Finite Element Modeling
NASA Astrophysics Data System (ADS)
Ziolkowski, P.; Poinas, P.; Leszczynski, J.; Karpinski, G.; Müller, E.
2010-09-01
Prediction of thermoelectric performance parameters by numerical methods is an inherent part of thermoelectric generator (TEG) development and allows for time- and cost-saving assessment of material combinations and variations of crucial design parameters (e.g., shape, pellet length, and thermal coupling). Considering the complexity of a TEG system and its numerous affecting factors, the clarity and the flexibility of a mathematical treatment comes to the fore. Comfortable tools are provided by commercial finite element modeling (FEM) software offering powerful geometry interfaces, mesh generators, solvers, and postprocessing options. We describe the level of development and the simulation results of a three dimensional (3D) TEG FEM. Using ANSYS 11.0, we implemented and simulated a TEG module geometry under various conditions. Comparative analytical one dimensional (1D) results and a direct comparison with inhouse-developed TEG simulation software show the consistency of results. Several pellet aspect ratios and contact property configurations (thermal/electrical interface resistance) were evaluated for their impact on the TEG performance as well as parasitic effects such as convection, radiation, and conductive heat bypass. The scenarios considered revealed the highest efficiency decay for convectionally loaded setups (up to 4.8%pts), followed by the impacts of contact resistances (up to 4.8%pts), by radiation (up to 0.56%pts), and by thermal conduction of a solid filling material within the voids of the module construction (up to 0.14%pts).
A multigrid solution method for mixed hybrid finite elements
Schmid, W.
1996-12-31
We consider the multigrid solution of linear equations arising within the discretization of elliptic second order boundary value problems of the form by mixed hybrid finite elements. Using the equivalence of mixed hybrid finite elements and non-conforming nodal finite elements, we construct a multigrid scheme for the corresponding non-conforming finite elements, and, by this equivalence, for the mixed hybrid finite elements, following guidelines from Arbogast/Chen. For a rectangular triangulation of the computational domain, this non-conforming schemes are the so-called nodal finite elements. We explicitly construct prolongation and restriction operators for this type of non-conforming finite elements. We discuss the use of plain multigrid and the multilevel-preconditioned cg-method and compare their efficiency in numerical tests.
Mixed Finite Element Methods for Melt Migration
NASA Astrophysics Data System (ADS)
Taicher, A. L.
2013-12-01
Multi-phase flow arises during partial melting in the earth mantle, where the porosity is small and material has the characteristics of a compacting porous medium. The equations governing multi-phase flow have been specialized to partially molten materials by McKenzie and Fowler. Their model, also called a Darcy-Stokes system, is highly coupled and non-linear. Melt flow is governed by Darcy's Law while the high temperature, ductile creep of the solid matrix is modeled using viscous non-Newtonian Stokes rheology. In addition, the melt and solid pressures are related through a compaction relation. This nearly elliptic mechanical problem is then coupled with both solute transport and thermal evolution according to the enthalpy method developed by Katz. A suitable numerical method must solve the Darcy-Stokes problem in a manner compatible with the transport problem. Moreover, unlike most porous media problems, partially molten materials transition dynamically from non-porous solid to porous medium so must carefully account for the limit of zero porosity. The Darcy-Stokes system for modeling partial melting in the mantle is a novel problem. As far as we know, there currently does not exist a finite element solution in the literature solving these coupled equations. In particular, the mixed finite element method presents a good candidate because it works in both limiting cases: Darcy and incompressible Stokes flow. We present a mixed formulation for the Darcy-Stokes system. Next, we present novel elements of lowest order and compatible with both Darcy and Stokes flow Finally, we present our 2D mixed FEM code result for solving Stokes and Darcy flow as well as the coupled Darcy-Stokes system the mid-ocean ridge or corner flow problem.
Finite element analysis enhancement of cryogenic testing
NASA Astrophysics Data System (ADS)
Thiem, Clare D.; Norton, Douglas A.
1991-12-01
Finite element analysis (FEA) of large space optics enhances cryogenic testing by providing an analytical method by which to ensure that a test article survives proposed testing. The analyses presented in this paper were concerned with determining the reliability of a half meter mirror in an environment where the exact environmental profile was unknown. FEA allows the interaction between the test object and the environment to be simulated to detect potential problems prior to actual testing. These analyses examined worse case scenerios related to cooling the mirror, its structural integrity for the proposed test environment, and deformation of the reflective surface. The FEA was conducted in-house on the System's Reliability Division's VAX 11-750 and Decstation 3100 using Engineering Mechanics Research Corporation's numerically integrated elements for systems analysis finite element software. The results of the analyses showed that it would take at least 48 hours to cool the mirror to its desired testing temperature. It was also determined that the proposed mirror mount would not cause critical concentrated thermal stresses that would fracture the mirror. FEA and actual measurements of the front reflective face were compared and good agreement between computer simulation and physical tests were seen. Space deployment of large optics requires lightweight mirrors which can perform under the harsh conditions of space. The physical characteristics of these mirrors must be well understood in order that their deployment and operation are successful. Evaluating design approaches by analytical simulation, like FEA, verifies the reliability and structural integrity of a space optic during design prior to prototyping and testing. Eliminating an optic's poor design early in its life saves money, materials, and human resources while ensuring performance.
Elbow stress indices using finite element analysis
NASA Astrophysics Data System (ADS)
Yu, Lixin
Section III of the ASME Boiler and Pressure Vessel Code (the Code) specifies rules for the design of nuclear power plant components. NB-3600 of the Code presents a simplified design method using stress indices---Scalar Coefficients used the modify straight pipe stress equations so that they can be applied to elbows, tees and other piping components. The stress indices of piping components are allowed to be determined both analytically and experimentally. This study concentrates on the determination of B2 stress indices for elbow components using finite element analysis (FEA). First, the previous theoretical, numerical and experimental investigations on elbow behavior were comprehensively reviewed, as was the philosophy behind the use of stress indices. The areas of further research was defined. Then, a comprehensive investigation was carried out to determine how the finite element method should be used to correctly simulate an elbow's structural behavior. This investigation included choice of element type, convergence of mesh density, use of boundary restraint and a reconciliation study between FEA and laboratory experiments or other theoretical formulations in both elastic and elasto-plastic domain. Results from different computer programs were also compared. Reasonably good reconciliation was obtained. Appendix II of the Code describes the experimental method to determine B2 stress indices based on load-deflection curves. This procedure was used to compute the B2 stress indices for various loading modes on one particular elbow configuration. The B2 stress indices thus determined were found to be about half of the value calculated from the Code equation. Then the effect on B2 stress indices of those factors such as internal pressure and flange attachments were studied. Finally, the investigation was extended to other configurations of elbow components. A parametric study was conducted on different elbow sizes and schedules. Regression analysis was then used to
NASA Astrophysics Data System (ADS)
Beilina, Larisa
2016-08-01
We present domain decomposition finite element/finite difference method for the solution of hyperbolic equation. The domain decomposition is performed such that finite elements and finite differences are used in different subdomains of the computational domain: finite difference method is used on the structured part of the computational domain and finite elements on the unstructured part of the domain. Explicit discretizations for both methods are constructed such that the finite element and the finite difference schemes coincide on the common structured overlapping layer between computational subdomains. Then the resulting approach can be considered as a pure finite element scheme which avoids instabilities at the interfaces. We derive an energy estimate for the underlying hyperbolic equation with absorbing boundary conditions and illustrate efficiency of the domain decomposition method on the reconstruction of the conductivity function in three dimensions.
Finite element analysis of notch behavior using a state variable constitutive equation
NASA Technical Reports Server (NTRS)
Dame, L. T.; Stouffer, D. C.; Abuelfoutouh, N.
1985-01-01
The state variable constitutive equation of Bodner and Partom was used to calculate the load-strain response of Inconel 718 at 649 C in the root of a notch. The constitutive equation was used with the Bodner-Partom evolution equation and with a second evolution equation that was derived from a potential function of the stress and state variable. Data used in determining constants for the constitutive models was from one-dimensional smooth bar tests. The response was calculated for a plane stress condition at the root of the notch with a finite element code using constant strain triangular elements. Results from both evolution equations compared favorably with the observed experimental response. The accuracy and efficiency of the finite element calculations also compared favorably to existing methods.
A Viscoelastic Hybrid Shell Finite Element
NASA Technical Reports Server (NTRS)
Johnson, Arthur
1999-01-01
An elastic large displacement thick-shell hybrid finite element is modified to allow for the calculation of viscoelastic stresses. Internal strain variables are introduced at he element's stress nodes and are employed to construct a viscous material model. First order ordinary differential equations relate the internal strain variables to the corresponding elastic strains at the stress nodes. The viscous stresses are computed from the internal strain variables using viscous moduli which are a fraction of the elastic moduli. The energy dissipated by the action of the viscous stresses in included in the mixed variational functional. Nonlinear quasi-static viscous equilibrium equations are then obtained. Previously developed Taylor expansions of the equilibrium equations are modified to include the viscous terms. A predictor-corrector time marching solution algorithm is employed to solve the algebraic-differential equations. The viscous shell element is employed to numerically simulate a stair-step loading and unloading of an aircraft tire in contact with a frictionless surface.
Asymmetric quadrilateral shell elements for finite strains
NASA Astrophysics Data System (ADS)
Areias, P.; Dias-da-Costa, D.; Pires, E. B.; Van Goethem, N.
2013-07-01
Very good results in infinitesimal and finite strain analysis of shells are achieved by combining either the enhanced-metric technique or the selective-reduced integration for the in-plane shear energy and an assumed natural strain technique (ANS) in a non-symmetric Petrov-Galerkin arrangement which complies with the patch-test. A recovery of the original Wilson incompatible mode element is shown for the trial functions in the in-plane components. As a beneficial side-effect, Newton-Raphson convergence behavior for non-linear problems is improved with respect to symmetric formulations. Transverse-shear and in-plane patch tests are satisfied while distorted-mesh accuracy is higher than with symmetric formulations. Classical test functions with assumed-metric components are required for compatibility reasons. Verification tests are performed with advantageous comparisons being observed in all of them. Applications to large displacement elasticity and finite strain plasticity are shown with both low sensitivity to mesh distortion and (relatively) high accuracy. A equilibrium-consistent (and consistently linearized) updated-Lagrangian algorithm is proposed and tested. Concerning the time-step dependency, it was found that the consistent updated-Lagrangian algorithm is nearly time-step independent and can replace the multiplicative plasticity approach if only moderate elastic strains are present, as is the case of most metals.
Finite element or Galerkin type semidiscrete schemes
NASA Technical Reports Server (NTRS)
Durgun, K.
1983-01-01
A finite element of Galerkin type semidiscrete method is proposed for numerical solution of a linear hyperbolic partial differential equation. The question of stability is reduced to the stability of a system of ordinary differential equations for which Dahlquist theory applied. Results of separating the part of numerical solution which causes the spurious oscillation near shock-like response of semidiscrete scheme to a step function initial condition are presented. In general all methods produce such oscillatory overshoots on either side of shocks. This overshoot pathology, which displays a behavior similar to Gibb's phenomena of Fourier series, is explained on the basis of dispersion of separated Fourier components which relies on linearized theory to be satisfactory. Expository results represented.
Finite-element modeling of nanoindentation
Knapp, J.A.; Follstaedt, D.M.; Myers, S.M.; Barbour, J.C.; Friedmann, T.A.
1999-02-01
Procedures have been developed based on finite-element modeling of nanoindentation data to obtain the mechanical properties of thin films and ion-beam-modified layers independently of the properties of the underlying substrates. These procedures accurately deduce the yield strength, Young{close_quote}s elastic modulus, and layer hardness from indentations as deep as 50{percent} of the layer thickness or more. We have used these procedures to evaluate materials ranging from ion implanted metals to deposited, diamond-like carbon layers. The technique increases the applicability of indentation testing to very thin layers, composite layers, and modulated compositions. This article presents an overview of the procedures involved and illustrates them with selected examples. {copyright} {ital 1999 American Institute of Physics.}
Fuzzy finite element analysis of smart structures
NASA Astrophysics Data System (ADS)
Akpan, Unyime O.; Koko, Tamunoiyala S.; Orisamolu, Irewole R.; Gallant, B. Keith
2000-06-01
A fuzzy finite element based approach is developed for modelling smart structures with vague or imprecise uncertainties. Fuzzy sets are used to represent the uncertainties present in the piezoelectric, mechanical, thermal, and physical properties of the smart structure. In order to facilitate efficient computation, a sensitivity analysis procedure is used to streamline the number of input fuzzy variables, and the vertex fuzzy analysis technique is then used to compute the possibility distributions of the responses of the smart structural system. The methodology has been developed within the framework of the SMARTCOM computational tool for the design/analysis of smart composite structures. The methodology developed is found to be accurate and computationally efficient for solution of practical problems.
Continuation finite element analysis of viscoelastic fluids
NASA Astrophysics Data System (ADS)
Chow, Tai-Whang
A finite element procedure using a mixed formulation and a predictor-corrector type continuation algorithm for the analysis of two dimensional steady state flows of viscoelastic fluids is described. As a simple but nontrivial test example, radial flow immenating from a line by the numerical discretization and believed to be the cause for previous numerical failures, are shown and branch solution paths are followed by step length adjustment and by convergent tolerance relaxation. A technique for jumping over bifurcation points is presented and used to increase the Weissenberg number with no apparent limit for the radial flow problem. A second example related to extrusion of viscoelastic material is also analyzed. Steady state velocity fields, deviatoric stress distributions and pressure distributions for several different Weissenberg numbers are presented with bifurcation points and turning points noted.
Quality management of finite element analysis
NASA Astrophysics Data System (ADS)
Barlow, John
1991-09-01
A quality management system covering the use of finite element analysis is described. The main topics are as follows: acquisition, development and verification of software (including the software suppliers software quality control system), support, documentation, error control, internal software, software acceptance and release; development and qualification of analysis methods, including software evaluation, analysis procedure qualification and documentation, procedure quality checks, control of analysis procedure errors; product design and integrity analysis, including project quality assurance and analysis planning, task specification and allocation, analysis, execution, results checking and analysis records. Other issues include the commercial and business advantages of quality systems, project and technical management and the training and experience of personnel. The items are correlated with the requirements of International Standard Organization 9001.
Optimizing electroslag cladding with finite element modeling
Li, M.V.; Atteridge, D.G.; Meekisho, L.
1996-12-31
Electroslag cladding of nickel alloys onto carbon steel propeller shafts was optimized in terms of interpass temperatures. A two dimensional finite element model was used in this study to analyze the heat transfer induced by multipass electroslag cladding. Changes of interpass temperatures during a cladding experiment with uniform initial temperature distribution on a section of shaft were first simulated. It was concluded that uniform initial temperature distribution would lead to interpass temperatures out of the optimal range if continuous cladding is expected. The difference in the cooling conditions among experimental and full size shafts and its impact on interpass temperatures during the cladding were discussed. Electroslag cladding onto a much longer shaft, virtually an semi infinite long shaft, was analyzed with specific reference to the practical applications of electroslag cladding. Optimal initial preheating temperature distribution was obtained for continuous cladding on full size shafts which would keep the interpass temperatures within the required range.
Finite element simulation of pipe dynamic response
Slagis, G.C.; Litton, R.W.
1996-12-01
Nonlinear finite element dynamic analyses of the response of a pipe span to controlled-displacement, sinusoidal vibration have been performed. The objective of this preliminary study is to compare strain and acceleration response data to those generated by Beaney in the Berkeley Nuclear Laboratories experiments. Results for an unpressurized, 5 Hz, carbon steel pipe are in good agreement with the experiments. Hence, it appears that analytical simulation will be useful to assess seismic margins. Recommendations for additional studies are provided. The analyses confirm the test results--dynamic response is greatly attenuated by material plasticity. Analytical strains and accelerations are about 30% higher than test data. There are several possible explanations for the differences. To assess the effect of frequency on response, the length of the pipe span was increased. Analysis of the longer, 2 Hz, pipe span shows significantly greater cyclic strains than the 5 Hz span at the same input excitation levels.
3-D Finite Element Heat Transfer
Energy Science and Technology Software Center (ESTSC)
1992-02-01
TOPAZ3D is a three-dimensional implicit finite element computer code for heat transfer analysis. TOPAZ3D can be used to solve for the steady-state or transient temperature field on three-dimensional geometries. Material properties may be temperature-dependent and either isotropic or orthotropic. A variety of time-dependent and temperature-dependent boundary conditions can be specified including temperature, flux, convection, and radiation. By implementing the user subroutine feature, users can model chemical reaction kinetics and allow for any type of functionalmore » representation of boundary conditions and internal heat generation. TOPAZ3D can solve problems of diffuse and specular band radiation in an enclosure coupled with conduction in the material surrounding the enclosure. Additional features include thermal contact resistance across an interface, bulk fluids, phase change, and energy balances.« less
Finite element analysis: A boon to dentistry
Trivedi, Shilpa
2014-01-01
The finite element analysis (FEA) is an upcoming and significant research tool for biomechanical analyses in biological research. It is an ultimate method for modeling complex structures and analyzing their mechanical properties. In Implantology, FEA has been used to study the stress patterns in various implant components and also in the peri-implant bone. It is also useful for studying the biomechanical properties of implants as well as for predicting the success of implants in clinical condition. FEA of simulated traumatic loads can be used to understand the biomechanics of fracture. FEA has various advantages compared with studies on real models. The experiments are repeatable, there are no ethical considerations and the study designs may be modified and changed as per the requirement. There are certain limitations of FEA too. It is a computerized in vitro study in which clinical condition may not be completely replicated. So, further FEA research should be supplemented with clinical evaluation. PMID:25737944
Finite-element solutions for geothermal systems
NASA Technical Reports Server (NTRS)
Chen, J. C.; Conel, J. E.
1977-01-01
Vector potential and scalar potential are used to formulate the governing equations for a single-component and single-phase geothermal system. By assuming an initial temperature field, the fluid velocity can be determined which, in turn, is used to calculate the convective heat transfer. The energy equation is then solved by considering convected heat as a distributed source. Using the resulting temperature to compute new source terms, the final results are obtained by iterations of the procedure. Finite-element methods are proposed for modeling of realistic geothermal systems; the advantages of such methods are discussed. The developed methodology is then applied to a sample problem. Favorable agreement is obtained by comparisons with a previous study.
Boundary element and finite element coupling for aeroacoustics simulations
NASA Astrophysics Data System (ADS)
Balin, Nolwenn; Casenave, Fabien; Dubois, François; Duceau, Eric; Duprey, Stefan; Terrasse, Isabelle
2015-08-01
We consider the scattering of acoustic perturbations in the presence of a flow. We suppose that the space can be split into a zone where the flow is uniform and a zone where the flow is potential. In the first zone, we apply a Prandtl-Glauert transformation to recover the Helmholtz equation. The well-known setting of boundary element method for the Helmholtz equation is available. In the second zone, the flow quantities are space dependent, we have to consider a local resolution, namely the finite element method. Herein, we carry out the coupling of these two methods and present various applications and validation test cases. The source term is given through the decomposition of an incident acoustic field on a section of the computational domain's boundary. Validations against analytic, another numerical method and measurements on different test cases are presented.
Finite element analyses of CCAT preliminary design
NASA Astrophysics Data System (ADS)
Sarawit, Andrew T.; Kan, Frank W.
2014-07-01
This paper describes the development of the CCAT telescope finite element model (FEM) and the analyses performed to support the preliminary design work. CCAT will be a 25 m diameter telescope operating in the 0.2 to 2 mm wavelength range. It will be located at an elevation of 5600 m on Cerro Chajnantor in Northern Chile, near ALMA. The telescope will be equipped with wide-field cameras and spectrometers mounted at the two Nasmyth foci. The telescope will be inside an enclosure to protect it from wind buffeting, direct solar heating, and bad weather. The main structures of the telescope include a steel Mount and a carbon-fiber-reinforced-plastic (CFRP) primary truss. The finite element model developed in this study was used to perform modal, frequency response, seismic response spectrum, stress, and deflection analyses of telescope. Modal analyses of telescope were performed to compute the structure natural frequencies and mode shapes and to obtain reduced order modal output at selected locations in the telescope structure to support the design of the Mount control system. Modal frequency response analyses were also performed to compute transfer functions at these selected locations. Seismic response spectrum analyses of the telescope subject to the Maximum Likely Earthquake were performed to compute peak accelerations and seismic demand stresses. Stress analyses were performed for gravity load to obtain gravity demand stresses. Deflection analyses for gravity load, thermal load, and differential elevation drive torque were performed so that the CCAT Observatory can verify that the structures meet the stringent telescope surface and pointing error requirements.
One-Dimensional Heat Conduction
Sutton, Steven B.
1992-03-09
ICARUS-LLNL was developed to solve one-dimensional planar, cylindrical, or spherical conduction heat transfer problems. The IBM PC version is a family of programs including ICARUSB, an interactive BASIC heat conduction program; ICARUSF, a FORTRAN heat conduction program; PREICAR, a BASIC preprocessor for ICARUSF; and PLOTIC and CPLOTIC, interpretive BASIC and compiler BASIC plot postprocessor programs. Both ICARUSB and ICARUSF account for multiple material regions and complex boundary conditions, such as convection or radiation. In addition, ICARUSF accounts for temperature-dependent material properties and time or temperature-dependent boundary conditions. PREICAR is a user-friendly preprocessor used to generate or modify ICARUSF input data. PLOTIC and CPLOTIC generate plots of the temperature or heat flux profile at specified times, plots of the variation of temperature or heat flux with time at selected nodes, or plots of the solution grid. First developed in 1974 to allow easy modeling of complex one-dimensional systems, its original application was in the nuclear explosive testing program. Since then it has undergone extensive revision and been applied to problems dealing with laser fusion target fabrication, heat loads on underground tests, magnetic fusion switching tube anodes, and nuclear waste isolation canisters.
One-Dimensional Heat Conduction
Energy Science and Technology Software Center (ESTSC)
1992-03-09
ICARUS-LLNL was developed to solve one-dimensional planar, cylindrical, or spherical conduction heat transfer problems. The IBM PC version is a family of programs including ICARUSB, an interactive BASIC heat conduction program; ICARUSF, a FORTRAN heat conduction program; PREICAR, a BASIC preprocessor for ICARUSF; and PLOTIC and CPLOTIC, interpretive BASIC and compiler BASIC plot postprocessor programs. Both ICARUSB and ICARUSF account for multiple material regions and complex boundary conditions, such as convection or radiation. In addition,more » ICARUSF accounts for temperature-dependent material properties and time or temperature-dependent boundary conditions. PREICAR is a user-friendly preprocessor used to generate or modify ICARUSF input data. PLOTIC and CPLOTIC generate plots of the temperature or heat flux profile at specified times, plots of the variation of temperature or heat flux with time at selected nodes, or plots of the solution grid. First developed in 1974 to allow easy modeling of complex one-dimensional systems, its original application was in the nuclear explosive testing program. Since then it has undergone extensive revision and been applied to problems dealing with laser fusion target fabrication, heat loads on underground tests, magnetic fusion switching tube anodes, and nuclear waste isolation canisters.« less
One-dimensional Quantum Fluids
NASA Astrophysics Data System (ADS)
Gervais, Guillaume
2015-03-01
Fifty year ago, Joachim Mazdak Luttinger generalized the Tomonaga theory of interactions in a one-dimensional metal and show that the prior restrictions imposed by Tomonaga were not necessary. This model is now known as the Tomonaga- Luttinger liquid model (TLL) and most remarkably it does have mathematically exact solutions. In the case of electrons, it predicts that the spin and charge sector should separate, with each of them propagating with their own velocities. While there has been many attempts (some with great success) to observe TLL behaviour in clean quantum wires designed on an ultra-clean semiconductor platform, overall the Luttinger physics is experimentally still in its infancy. For instance, little is known regarding the 1D physics in a strongly-interacting neutral system, whether from the point-of-view of TLL theory or even localization physics. Helium-4, the paradigm superfluid, and Helium-3, the paradigm Fermi liquid, should in principleboth become Luttinger liquids if taken to the one-dimensional limit. In the bosonic case, this is supported by large-scale Quantum Monte Carlo simulations which found that a lengthscale of ~ 2 nm is sufficient for the system to crossover to the 1D regime and display universal Luttinger scaling. At McGill University, an experiment has been constructed to measure the liquid helium mass flow through a single nanopore. The technique consists of drilling a single nanopore in a SiN membrane using a TEM, and then applying a pressure gradient across the membrane. Previously published data in 45nm diameter hole determined the superfluid critical velocity to be close to the limit set by the Feynman vortex rings model. More recent work performed on nanopores with radii as small as 3 nm (and a length of 30nm) show the critical exponent for superfluid velocity to significantly deviate from its bulk value, 2/3. This is an important hint for the crossing over to the one-dimensional state in a strongly-correlated bosonic liquid.
One-dimensional wave turbulence
NASA Astrophysics Data System (ADS)
Zakharov, Vladimir; Dias, Frédéric; Pushkarev, Andrei
2004-08-01
The problem of turbulence is one of the central problems in theoretical physics. While the theory of fully developed turbulence has been widely studied, the theory of wave turbulence has been less studied, partly because it developed later. Wave turbulence takes place in physical systems of nonlinear dispersive waves. In most applications nonlinearity is small and dispersive wave interactions are weak. The weak turbulence theory is a method for a statistical description of weakly nonlinear interacting waves with random phases. It is not surprising that the theory of weak wave turbulence began to develop in connection with some problems of plasma physics as well as of wind waves. The present review is restricted to one-dimensional wave turbulence, essentially because finer computational grids can be used in numerical computations. Most of the review is devoted to wave turbulence in various wave equations, and in particular in a simple one-dimensional model of wave turbulence introduced by Majda, McLaughlin and Tabak in 1997. All the considered equations are model equations, but consequences on physical systems such as ocean waves are discussed as well. The main conclusion is that the range in which the theory of pure weak turbulence is valid is narrow. In general, wave turbulence is not completely weak. Together with the weak turbulence component, it can include coherent structures, such as solitons, quasisolitons, collapses or broad collapses. As a result, weak and strong turbulence coexist. In situations where coherent structures cannot develop, weak turbulence dominates. Even though this is primarily a review paper, new results are presented as well, especially on self-organized criticality and on quasisolitonic turbulence.
NASA Technical Reports Server (NTRS)
1976-01-01
The development of two new shell finite elements for applications to large deflection problems is considered. The elements in question are doubly curved and of triangular and quadrilateral planform. They are restricted to small strains of elastic materials, and can accommodate large rotations. The elements described, which are based on relatively simple linear elements, make use of a new displacement function approach specifically designed for strongly nonlinear problems. The displacement function development for nonlinear applications is based on certain beam element formulations, and the strain-displacement equations are of a shallow shell type. Additional terms were included in these equations in an attempt to avoid the large errors characteristic of shallow shell elements in certain types of problems. An incremental nonlinear solution procedure specifically adopted to the element formulation was developed. The solution procedure is of combined incremental and total Lagrangian type, and uses a new updating scheme. A computer program was written to evaluate the developed formulations. This program can accommodate small element groups in arbitrary arrangements. Two simple programs were successfully solved. The results indicate that this new type of element has definite promise and should be a fruitful area for further research.
Improved finite-element methods for rotorcraft structures
NASA Technical Reports Server (NTRS)
Hinnant, Howard E.
1991-01-01
An overview of the research directed at improving finite-element methods for rotorcraft airframes is presented. The development of a modification to the finite element method which eliminates interelement discontinuities is covered. The following subject areas are discussed: geometric entities, interelement continuity, dependent rotational degrees of freedom, and adaptive numerical integration. This new methodology is being implemented as an anisotropic, curvilinear, p-version, beam, shell, and brick finite element program.
Impact of new computing systems on finite element computations
NASA Technical Reports Server (NTRS)
Noor, A. K.; Storassili, O. O.; Fulton, R. E.
1983-01-01
Recent advances in computer technology that are likely to impact finite element computations are reviewed. The characteristics of supersystems, highly parallel systems, and small systems (mini and microcomputers) are summarized. The interrelations of numerical algorithms and software with parallel architectures are discussed. A scenario is presented for future hardware/software environment and finite element systems. A number of research areas which have high potential for improving the effectiveness of finite element analysis in the new environment are identified.
NASA Technical Reports Server (NTRS)
Fix, G. J.; Rose, M. E.
1983-01-01
A least squares formulation of the system divu = rho, curlu = zeta is surveyed from the viewpoint of both finite element and finite difference methods. Closely related arguments are shown to establish convergence estimates.
Finite element analysis in a minicomputer/mainframe environment
NASA Technical Reports Server (NTRS)
Storaasli, O. O.; Murphy, R. C.
1978-01-01
Design considerations were evaluated for general purpose finite element systems to maximize performance when installed on distributed computer hardware/software systems. It is shown how the features of current minicomputers complement those of a modular implementation of the finite element method for increasing the control, speed, and visibility (interactive graphics) in solving structural problems at reduced cost. The approach used is to implement a finite element system in a distributed computer environment to solve structural problems and to explore alternatives in distributing finite element computations.
A multi-microprocessor system for finite element structural analysis
NASA Technical Reports Server (NTRS)
Jordan, H. F.; Sawyer, P. L.
1978-01-01
During the last few years, advances in microprocessor technology have spurred a renewed interest in special-purpose computers. The microprocessor has become small, inexpensive, and powerful enough to be considered as a building block for special-purpose hardware. A description is presented of the architecture of a prototype 'finite element machine' currently being built. Attention is given to details regarding the finite element analysis problem, the arrangement of the processors as finite element nodes in the structural model, the influence of the architecture on the solution algorithm, interprocessor communication primitives, and the performance of the finite element machine.
Quadrature rules for finite element approximations of 1D nonlocal problems
NASA Astrophysics Data System (ADS)
Zhang, Xiaoping; Gunzburger, Max; Ju, Lili
2016-04-01
It is well known that calculations of the entries of the stiffness matrix in the finite element approximations of nonlocal diffusion and mechanics models are often very time-consuming due to the double integration process over the domain and the singularities of the nonlocal kernel functions. In this paper, we propose some effective and accurate quadrature rules for computing these double integrals for one-dimensional nonlocal problems; in particular, for problems with highly singular kernels, the corresponding inner integrals can be first evaluated exactly in our method, and the outer one then will be approximated by some popular quadrature rules. With these quadrature rules, the assembly of the stiffness matrix in the finite element method for the nonlocal problems becomes similar to that for the classical partial differential equations and is thus quite efficient.
Gaussian and finite-element Coulomb method for the fast evaluation of Coulomb integrals
NASA Astrophysics Data System (ADS)
Kurashige, Yuki; Nakajima, Takahito; Hirao, Kimihiko
2007-04-01
The authors propose a new linear-scaling method for the fast evaluation of Coulomb integrals with Gaussian basis functions called the Gaussian and finite-element Coulomb (GFC) method. In this method, the Coulomb potential is expanded in a basis of mixed Gaussian and finite-element auxiliary functions that express the core and smooth Coulomb potentials, respectively. Coulomb integrals can be evaluated by three-center one-electron overlap integrals among two Gaussian basis functions and one mixed auxiliary function. Thus, the computational cost and scaling for large molecules are drastically reduced. Several applications to molecular systems show that the GFC method is more efficient than the analytical integration approach that requires four-center two-electron repulsion integrals. The GFC method realizes a near linear scaling for both one-dimensional alanine α-helix chains and three-dimensional diamond pieces.
An Integrated Magnetic Circuit Model and Finite Element Model Approach to Magnetic Bearing Design
NASA Technical Reports Server (NTRS)
Provenza, Andrew J.; Kenny, Andrew; Palazzolo, Alan B.
2003-01-01
A code for designing magnetic bearings is described. The code generates curves from magnetic circuit equations relating important bearing performance parameters. Bearing parameters selected from the curves by a designer to meet the requirements of a particular application are input directly by the code into a three-dimensional finite element analysis preprocessor. This means that a three-dimensional computer model of the bearing being developed is immediately available for viewing. The finite element model solution can be used to show areas of magnetic saturation and make more accurate predictions of the bearing load capacity, current stiffness, position stiffness, and inductance than the magnetic circuit equations did at the start of the design process. In summary, the code combines one-dimensional and three-dimensional modeling methods for designing magnetic bearings.
Gaussian and finite-element Coulomb method for the fast evaluation of Coulomb integrals.
Kurashige, Yuki; Nakajima, Takahito; Hirao, Kimihiko
2007-04-14
The authors propose a new linear-scaling method for the fast evaluation of Coulomb integrals with Gaussian basis functions called the Gaussian and finite-element Coulomb (GFC) method. In this method, the Coulomb potential is expanded in a basis of mixed Gaussian and finite-element auxiliary functions that express the core and smooth Coulomb potentials, respectively. Coulomb integrals can be evaluated by three-center one-electron overlap integrals among two Gaussian basis functions and one mixed auxiliary function. Thus, the computational cost and scaling for large molecules are drastically reduced. Several applications to molecular systems show that the GFC method is more efficient than the analytical integration approach that requires four-center two-electron repulsion integrals. The GFC method realizes a near linear scaling for both one-dimensional alanine alpha-helix chains and three-dimensional diamond pieces. PMID:17444700
Kim, S.
1994-12-31
Parallel iterative procedures based on domain decomposition techniques are defined and analyzed for the numerical solution of wave propagation by finite element and finite difference methods. For finite element methods, in a Lagrangian framework, an efficient way for choosing the algorithm parameter as well as the algorithm convergence are indicated. Some heuristic arguments for finding the algorithm parameter for finite difference schemes are addressed. Numerical results are presented to indicate the effectiveness of the methods.
Integrated finite element model of composite materials
NASA Astrophysics Data System (ADS)
Teply, Jan L.; Herbein, William C.
1989-05-01
Two problems traditionally addressed in the area of micromechanics of composite materials can be briefly summarized as follows: (1) for a macroscopically uniform volume of composite material, which is subjected to macroscopically uniform boundary tractions, displacements or heat influx, find overall thermomechanical properties in terms of the thermomechanical properties of the individual constituents; and (2) for the same material volume and boundary conditions as above, find the local stress, strain, and temperature fields in the constituents and on the interfaces. Two different types of micromechanical models are usually applied to the solutions of these two types of problems. For linear elastic materials, the micromechanical models to solve problem (1) offer simple solutions of overall thermomechanical properties either in terms of bound which are derived from periodic or random microstructures, or in terms of single estimates, which are derived from a solution of an isolated inclusion. The finite element variational approaches are applied to integrate the solutions of problems (1) and (2) into one model. The application of displacement and equilibrium variational approaches to the calculation of overall elastic-plastic properties, are extended to the solution of the second problem. The integrated model is then applied to calculate the overall properties and local stress and strain fields of boron-aluminum composites subjected to transverse tension, in-plane shear and bending.
Laterally displaced pipelines: Finite element analysis
Altaee, A.; Boivin, R.
1995-12-31
The rate effect of lateral soil movement against buried pipes in clay soils is investigated in finite element analyzes using two different computer programs, AGAC and CRISP. Rapid and slow ground movements are considered in ideal undrained and ideal drained analysis, respectively, which represent the two extreme boundaries with respect to rate of loading (rate of ground movement). The analyses address a typical full-scale buried pipe as described by Rizkalla et al. (1992). The pipe considered for the analysis has a diameter of 0.914 m and is placed in a backfilled 2.0 m wide and 1.8 m deep excavation. Results from both AGAC and CRISP analyzes are similar in terms of total lateral force versus lateral pipe movement. For example, both programs indicate the same clear difference in the resulting pipe movement for cases of rapid and slow ground movement, especially at large movement. When the ground movement is rapid, the pipe moves both laterally and upward. One the other hand, when the ground movement is slow, the pipe experiences only lateral movement and no noticeable vertical movement. The total force acting on the pipe (and stresses and strains within the pipe) is larger for the slow rate of loading. The results of analyzes presented herein agree with results of tests on a 5.5 m beam centrifuge performed by the Center for Cold Oceans Resources Engineering.
Finite Element Modeling of Human Placental Tissue
Yu, Mao; Manoogian, Sarah; Duma, Stefan M.; Stitzel, Joel D.
2009-01-01
Motor vehicle crashes account for a large portion of placental abruption and fetal losses. To better understand the material properties of the human placenta, a Finite Element (FE) model of human placenta tissue was created and verified using data from uniaxial tension tests. Sixty-four tensile tests at three different strain rates of 7% strain/s, 70% strain/s, and 700% strain/s from six whole human placentas were used for model development. Nominal stresses were calculated by dividing forces at the grips by the original cross-sectional area. Nominal strains were calculated by dividing cross-head displacement by the original gauge length. A detailed methodology for interpreting experimental data for application to material model development is presented. A model of the tension coupon was created in LS-DYNA and stretched in the same manner as the uniaxial tension tests. The behavior of the material was optimized to the uniaxial tension test using a multi-island genetic algorithm. The results demonstrate good correlation between experiments and the model, with an average difference of 2% between the optimized FE and experimental first principal stress at the termination state. The material parameters found in this study can be utilized in FE models of placental tissues for behavior under dynamic loading. PMID:20184849
Finite element modeling of retinal prosthesis mechanics
NASA Astrophysics Data System (ADS)
Basinger, B. C.; Rowley, A. P.; Chen, K.; Humayun, M. S.; Weiland, J. D.
2009-10-01
Epiretinal prostheses used to treat degenerative retina diseases apply stimulus via an electrode array fixed to the ganglion cell side of the retina. Mechanical pressure applied by these arrays to the retina, both during initial insertion and throughout chronic use, could cause sufficient retinal damage to reduce the device's effectiveness. In order to understand and minimize potential mechanical damage, we have used finite element analysis to model mechanical interactions between an electrode array and the retina in both acute and chronic loading configurations. Modeling indicates that an acute tacking force distributes stress primarily underneath the tack site and heel edge of the array, while more moderate chronic stresses are distributed more evenly underneath the array. Retinal damage in a canine model chronically implanted with a similar array occurred in correlating locations, and model predictions correlate well with benchtop eyewall compression tests. This model provides retinal prosthesis researchers with a tool to optimize the mechanical electrode array design, but the techniques used here represent a unique effort to combine a modifiable device and soft biological tissues in the same model and those techniques could be extended to other devices that come into mechanical contact with soft neural tissues.
TACO: a finite element heat transfer code
Mason, W.E. Jr.
1980-02-01
TACO is a two-dimensional implicit finite element code for heat transfer analysis. It can perform both linear and nonlinear analyses and can be used to solve either transient or steady state problems. Either plane or axisymmetric geometries can be analyzed. TACO has the capability to handle time or temperature dependent material properties and materials may be either isotropic or orthotropic. A variety of time and temperature dependent loadings and boundary conditions are available including temperature, flux, convection, and radiation boundary conditions and internal heat generation. Additionally, TACO has some specialized features such as internal surface conditions (e.g., contact resistance), bulk nodes, enclosure radiation with view factor calculations, and chemical reactive kinetics. A user subprogram feature allows for any type of functional representation of any independent variable. A bandwidth and profile minimization option is also available in the code. Graphical representation of data generated by TACO is provided by a companion post-processor named POSTACO. The theory on which TACO is based is outlined, the capabilities of the code are explained, the input data required to perform an analysis with TACO are described. Some simple examples are provided to illustrate the use of the code.
NASA Technical Reports Server (NTRS)
Meitner, Peter L.
2004-01-01
A calculation procedure is presented which allows the one-dimensional determination of flow distributions in arbitrarily connected (branching) flow passages having multiple inlets and exits. The procedure uses an adaptation of the finite element technique, iteratively coupled with an accurate one-dimensional flow solver. The procedure eliminates the usual restrictions inherent with finite element flow calculations. Unlike existing one-dimensional methods, which require simplifications to the flow equations (uncoupling the momentum and energy equations), to allow for arbitrary branching and multiple inlets and exits, the only limitation of the described methodology is that, at present, it can only accommodate non-rotating configurations (no pumping effects). The calculation procedure is robust, and will always converge for physically possible flow. The procedure is described, and its use is illustrated by an example.
Finite Element Analysis (FEA) in Design and Production.
ERIC Educational Resources Information Center
Waggoner, Todd C.; And Others
1995-01-01
Finite element analysis (FEA) enables industrial designers to analyze complex components by dividing them into smaller elements, then assessing stress and strain characteristics. Traditionally mainframe based, FEA is being increasingly used in microcomputers. (SK)
Aperiodicity in one-dimensional cellular automata
Jen, E.
1990-01-01
Cellular automata are a class of mathematical systems characterized by discreteness (in space, time, and state values), determinism, and local interaction. A certain class of one-dimensional, binary site-valued, nearest-neighbor automata is shown to generate infinitely many aperiodic temporal sequences from arbitrary finite initial conditions on an infinite lattice. The class of automaton rules that generate aperiodic temporal sequences are characterized by a particular form of injectivity in their interaction rules. Included are the nontrivial linear'' automaton rules (that is, rules for which the superposition principle holds); certain nonlinear automata that retain injectivity properties similar to those of linear automata; and a wider subset of nonlinear automata whose interaction rules satisfy a weaker form of injectivity together with certain symmetry conditions. A technique is outlined here that maps this last set of automata onto a linear automaton, and thereby establishes the aperiodicity of their temporal sequences. 12 refs., 3 figs.
One-dimensional silicone nanofilaments.
Artus, Georg R J; Seeger, Stefan
2014-07-01
A decade ago one-dimensional silicone nanofilaments (1D-SNF) such as fibres and wires were described for the first time. Since then, the exploration of 1D-SNF has led to remarkable advancements with respect to material science and surface science: one-, two- and three-dimensional nanostructures of silicone were unknown before. The discovery of silicone nanostructures marks a turning point in the research on the silicone material at the nanoscale. Coatings made of 1D-SNF are among the most superhydrophobic surfaces known today. They are free of fluorine, can be applied to a large range of technologically important materials and their properties can be modified chemically. This opens the way to many interesting applications such as water harvesting, superoleophobicity, separation of oil and water, patterned wettability and storage and manipulation of data on a surface. Because of their high surface area, coatings consisting of 1D-SNF are used for protein adsorption experiments and as carrier systems for catalytically active nanoparticles. This paper reviews the current knowledge relating to the broad development of 1D-SNF technologies. Common preparation and coating techniques are presented along with a comparison and discussion of the published coating parameters to provide an insight on how these affect the topography of the 1D-SNF or coating. The proposed mechanisms of growth are presented, and their potentials and shortcomings are discussed. We introduce all explored applications and finally identify future prospects and potentials of 1D-SNF with respect to applications in material science and surface science. PMID:24742356
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.
FINITE-ELEMENT ANALYSIS OF MULTIPHASE IMMISCIBLE FLOW THROUGH SOILS
A finite-element model is developed for multiphase flow through soil involving three immiscible fluids: namely, air, water, and a nonaqueous phase liquid (NAPL). A variational method is employed for the finite-element formulation corresponding to the coupled differential equation...
A computer graphics program for general finite element analyses
NASA Technical Reports Server (NTRS)
Thornton, E. A.; Sawyer, L. M.
1978-01-01
Documentation for a computer graphics program for displays from general finite element analyses is presented. A general description of display options and detailed user instructions are given. Several plots made in structural, thermal and fluid finite element analyses are included to illustrate program options. Sample data files are given to illustrate use of the program.
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.
Modular Finite Element Methods Library Version: 1.0
Energy Science and Technology Software Center (ESTSC)
2010-06-22
MFEM is a general, modular library for finite element methods. It provides a variety of finite element spaces and bilinear/linear forms in 2D and 3D. MFEM also includes classes for dealing with various types of meshes and their refinement.
Finite Element analyses of soil bioengineered slopes
NASA Astrophysics Data System (ADS)
Tamagnini, Roberto; Switala, Barbara Maria; Sudan Acharya, Madhu; Wu, Wei; Graf, Frank; Auer, Michael; te Kamp, Lothar
2014-05-01
Soil Bioengineering methods are not only effective from an economical point of view, but they are also interesting as fully ecological solutions. The presented project is aimed to define a numerical model which includes the impact of vegetation on slope stability, considering both mechanical and hydrological effects. In this project, a constitutive model has been developed that accounts for the multi-phase nature of the soil, namely the partly saturated condition and it also includes the effects of a biological component. The constitutive equation is implemented in the Finite Element (FE) software Comes-Geo with an implicit integration scheme that accounts for the collapse of the soils structure due to wetting. The mathematical formulation of the constitutive equations is introduced by means of thermodynamics and it simulates the growth of the biological system during the time. The numerical code is then applied in the analysis of an ideal rainfall induced landslide. The slope is analyzed for vegetated and non-vegetated conditions. The final results allow to quantitatively assessing the impact of vegetation on slope stability. This allows drawing conclusions and choosing whenever it is worthful to use soil bioengineering methods in slope stabilization instead of traditional approaches. The application of the FE methods show some advantages with respect to the commonly used limit equilibrium analyses, because it can account for the real coupled strain-diffusion nature of the problem. The mechanical strength of roots is in fact influenced by the stress evolution into the slope. Moreover, FE method does not need a pre-definition of any failure surface. FE method can also be used in monitoring the progressive failure of the soil bio-engineered system as it calculates the amount of displacements and strains of the model slope. The preliminary study results show that the formulated equations can be useful for analysis and evaluation of different soil bio
Nondestructive Evaluation Correlated with Finite Element Analysis
NASA Technical Reports Server (NTRS)
Abdul-Azid, Ali; Baaklini, George Y.
1999-01-01
Advanced materials are being developed for use in high-temperature gas turbine applications. For these new materials to be fully utilized, their deformation properties, their nondestructive evaluation (NDE) quality and material durability, and their creep and fatigue fracture characteristics need to be determined by suitable experiments. The experimental findings must be analyzed, characterized, modeled and translated into constitutive equations for stress analysis and life prediction. Only when these ingredients - together with the appropriate computational tools - are available, can durability analysis be performed in the design stage, long before the component is built. One of the many structural components being evaluated by the NDE group at the NASA Lewis Research Center is the flywheel system. It is being considered as an energy storage device for advanced space vehicles. Such devices offer advantages over electrochemical batteries in situations demanding high power delivery and high energy storage per unit weight. In addition, flywheels have potentially higher efficiency and longer lifetimes with proper motor-generator and rotor design. Flywheels made of fiber-reinforced polymer composite material show great promise for energy applications because of the high energy and power densities that they can achieve along with a burst failure mode that is relatively benign in comparison to those of flywheels made of metallic materials Therefore, to help improve durability and reduce structural uncertainties, we are developing a comprehensive analytical approach to predict the reliability and life of these components under these harsh loading conditions. The combination of NDE and two- and three-dimensional finite element analyses (e.g., stress analyses and fracture mechanics) is expected to set a standardized procedure to accurately assess the applicability of using various composite materials to design a suitable rotor/flywheel assembly.
Calculations for the one-dimensional soft Coulomb problem and the hard Coulomb limit
NASA Astrophysics Data System (ADS)
Gebremedhin, Daniel H.; Weatherford, Charles A.
2014-05-01
An efficient way of evolving a solution to an ordinary differential equation is presented. A finite element method is used where we expand in a convenient local basis set of functions that enforce both function and first derivative continuity across the boundaries of each element. We also implement an adaptive step-size choice for each element that is based on a Taylor series expansion. This algorithm is used to solve for the eigenpairs corresponding to the one-dimensional soft Coulomb potential, 1/√x2+β2 , which becomes numerically intractable (because of extreme stiffness) as the softening parameter (β) approaches zero. We are able to maintain near machine accuracy for β as low as β =10-8 using 16-digit precision calculations. Our numerical results provide insight into the controversial one-dimensional hydrogen atom, which is a limiting case of the soft Coulomb problem as β →0.
Three one-dimensional structural heating programs
NASA Technical Reports Server (NTRS)
Wing, L. D.
1978-01-01
Two computer programs for calculating profiles in a ten-element structure consisting of up to ten materials are presented, along with a third program for calculating the mean temperature for a payload container placed in an orbiting vehicle cargo bay. The three programs are related by the sharing of a common analytical technique; the energy balance is based upon one-dimensional heat transfer. The first program, NQLDW112, assumes a non-ablating surface. NQLDW117 is very similar but allows the outermost element to ablate. NQLDW040 calculates an average temperature profile through an idealized model of the real payload cannister and contents in the cargo bay of an orbiting vehicle.
NASA Technical Reports Server (NTRS)
Schuler, James J.; Felippa, Carlos A.
1994-01-01
The present work is part of a research program for the numerical simulation of electromagnetic (EM) fields within conventional Ginzburg-Landau (GL) superconductors. The final goal of this research is to formulate, develop and validate finite element (FE) models that can accurately capture electromagnetic thermal and material phase changes in a superconductor. The formulations presented here are for a time-independent Ginzburg-Landau superconductor and are derived from a potential-based variational principle. We develop an appropriate variational formulation of time-independent supercontivity for the general three-dimensional case and specialize it to the one-dimensional case. Also developed are expressions for the material-dependent parameters alpha and beta of GL theory and their dependence upon the temperature T. The one-dimensional formulation is then discretized for finite element purposes and the first variation of these equations is obtained. The resultant Euler equations contain nonlinear terms in the primary variables. To solve these equations, an incremental-iterative solution method is used. Expressions for the internal force vector, external force vector, loading vector and tangent stiffness matrix are therefore developed for use with the solution procedure.
Advances in 3D electromagnetic finite element modeling
Nelson, E.M.
1997-08-01
Numerous advances in electromagnetic finite element analysis (FEA) have been made in recent years. The maturity of frequency domain and eigenmode calculations, and the growth of time domain applications is briefly reviewed. A high accuracy 3D electromagnetic finite element field solver employing quadratic hexahedral elements and quadratic mixed-order one-form basis functions will also be described. The solver is based on an object-oriented C++ class library. Test cases demonstrate that frequency errors less than 10 ppm can be achieved using modest workstations, and that the solutions have no contamination from spurious modes. The role of differential geometry and geometrical physics in finite element analysis is also discussed.
STARS: A general-purpose finite element computer program for analysis of engineering structures
NASA Technical Reports Server (NTRS)
Gupta, K. K.
1984-01-01
STARS (Structural Analysis Routines) is primarily an interactive, graphics-oriented, finite-element computer program for analyzing the static, stability, free vibration, and dynamic responses of damped and undamped structures, including rotating systems. The element library consists of one-dimensional (1-D) line elements, two-dimensional (2-D) triangular and quadrilateral shell elements, and three-dimensional (3-D) tetrahedral and hexahedral solid elements. These elements enable the solution of structural problems that include truss, beam, space frame, plane, plate, shell, and solid structures, or any combination thereof. Zero, finite, and interdependent deflection boundary conditions can be implemented by the program. The associated dynamic response analysis capability provides for initial deformation and velocity inputs, whereas the transient excitation may be either forces or accelerations. An effective in-core or out-of-core solution strategy is automatically employed by the program, depending on the size of the problem. Data input may be at random within a data set, and the program offers certain automatic data-generation features. Input data are formatted as an optimal combination of free and fixed formats. Interactive graphics capabilities enable convenient display of nodal deformations, mode shapes, and element stresses.
Interpolation functions in the immersed boundary and finite element methods
NASA Astrophysics Data System (ADS)
Wang, Xingshi; Zhang, Lucy T.
2010-03-01
In this paper, we review the existing interpolation functions and introduce a finite element interpolation function to be used in the immersed boundary and finite element methods. This straightforward finite element interpolation function for unstructured grids enables us to obtain a sharper interface that yields more accurate interfacial solutions. The solution accuracy is compared with the existing interpolation functions such as the discretized Dirac delta function and the reproducing kernel interpolation function. The finite element shape function is easy to implement and it naturally satisfies the reproducing condition. They are interpolated through only one element layer instead of smearing to several elements. A pressure jump is clearly captured at the fluid-solid interface. Two example problems are studied and results are compared with other numerical methods. A convergence test is thoroughly conducted for the independent fluid and solid meshes in a fluid-structure interaction system. The required mesh size ratio between the fluid and solid domains is obtained.
ORMDIN: a finite element program for two-dimensional nonlinear inverse heat conduction analysis
Bass, B.R.; Drake, J.B.; Ott, L.J.
1980-12-01
The calculation of the surface temperature and surface heat flux from measured temperature transients at one or more interior points of a body is identified in the literature as the inverse heat conduction problem. Heretofore, analytical and computational methods of treating this problem have been limited to one-dimensional nonlinear or two-dimensional linear material models. This report presents, to the authors' knowledge, the first inverse solution technique applicable to the two-dimensional nonlinear model with temperature-dependent thermophysical properties. This technique, representing an extension of the one-dimensional formulation previously developed by one of the authors, utilizes a finite element heat conduction model and a generalization of Beck's one-dimensional nonlinear estimation procedure. A digital computer program ORMDIN (Oak Ridge Multi-Dimensional INverse) is developed from the formulation and applied to the cross section of a composite cylinder with temperature-dependent material properties. Results are presented to demonstrate that the inverse formulation is capable of successfully treating experimental data. An important feature of the method is that small time steps are permitted while avoiding severe oscillations or numerical instabilities due to experimental errors in measured data.
NASA Astrophysics Data System (ADS)
Kita, Takafumi; Takada, Yasutami
1990-09-01
A one-dimensional many-electron system with a repulsive δ-function interaction is studied by the application of the variational method developed in the preceding paper [Takada and Kita, Phys. Rev. A 42, 3242 (1990)] in order to illustrate its actual implementation. Our results on the grand potential, the entropy, and the specific heat are compared in detail with the exact ones that are calculated by the numerical solution of the coupled integral equations obtained by the Bethe ansatz.
A modified finite element procedure for underwater shock analysis
Chan, S.K.
1990-12-31
Using the regular finite element method for analyzing wave propagation problems presents difficulties: (a) The finite element mesh gives spurious reflection of the traveling wave and (b) Since a finite element model has to have a finite boundary, the wave is reflected by the outside boundary. However, for underwater shock problems, only the response of the structure is of major interest, not the behavior of the wave itself, and the shock wave can be assumed to be spherical. By taking advantage of the limited scope of the underwater shock problem, a finite element procedure can be developed that eliminates the above difficulties. This procedure not only can give very accurate solutions but it may also include structural nonlinearities and effect of cavitation.
Transport in a one-dimensional hyperconductor
NASA Astrophysics Data System (ADS)
Plamadeala, Eugeniu; Mulligan, Michael; Nayak, Chetan
2016-03-01
We define a "hyperconductor" to be a material whose electrical and thermal dc conductivities are infinite at zero temperature and finite at any nonzero temperature. The low-temperature behavior of a hyperconductor is controlled by a quantum critical phase of interacting electrons that is stable to all potentially gap-generating interactions and potentially localizing disorder. In this paper, we compute the low-temperature dc and ac electrical and thermal conductivities in a one-dimensional hyperconductor, studied previously by the present authors, in the presence of both disorder and umklapp scattering. We identify the conditions under which the transport coefficients are finite, which allows us to exhibit examples of violations of the Wiedemann-Franz law. The temperature dependence of the electrical conductivity, which is characterized by the parameter ΔX, is a power law, σ ∝1 /T1 -2 (2 -ΔX) when ΔX≥2 , down to zero temperature when the Fermi surface is commensurate with the lattice. There is a surface in parameter space along which ΔX=2 and ΔX≈2 for small deviations from this surface. In the generic (incommensurate) case with weak disorder, such scaling is seen at high temperatures, followed by an exponential increase of the conductivity lnσ ˜1 /T at intermediate temperatures and, finally, σ ∝1 /T2 -2 (2 -ΔX) at the lowest temperatures. In both cases, the thermal conductivity diverges at low temperatures.
Sanchez, R.
2012-07-01
Nonlinear acceleration of a continuous finite element (CFE) discretization of the transport equation requires a modification of the transport solution in order to achieve local conservation, a condition used in nonlinear acceleration to define the stopping criterion. In this work we implement a coarse-mesh finite difference acceleration for a CFE discretization of the second-order self adjoint angular flux (SAAF) form of the transport equation and use a post processing to enforce local conservation. Numerical results are given for one-group source calculations of one-dimensional slabs. We also give a formal derivation of the boundary conditions for the SAAF. (authors)
Richard Sanchez; Cristian Rabiti; Yaqi Wang
2013-11-01
Nonlinear acceleration of a continuous finite element (CFE) discretization of the transport equation requires a modification of the transport solution in order to achieve local conservation, a condition used in nonlinear acceleration to define the stopping criterion. In this work we implement a coarse-mesh finite difference acceleration for a CFE discretization of the second-order self-adjoint angular flux (SAAF) form of the transport equation and use a postprocessing to enforce local conservation. Numerical results are given for one-group source calculations of one-dimensional slabs. We also give a novel formal derivation of the boundary conditions for the SAAF.
Application of the Finite Element Method to Rotary Wing Aeroelasticity
NASA Technical Reports Server (NTRS)
Straub, F. K.; Friedmann, P. P.
1982-01-01
A finite element method for the spatial discretization of the dynamic equations of equilibrium governing rotary-wing aeroelastic problems is presented. Formulation of the finite element equations is based on weighted Galerkin residuals. This Galerkin finite element method reduces algebraic manipulative labor significantly, when compared to the application of the global Galerkin method in similar problems. The coupled flap-lag aeroelastic stability boundaries of hingeless helicopter rotor blades in hover are calculated. The linearized dynamic equations are reduced to the standard eigenvalue problem from which the aeroelastic stability boundaries are obtained. The convergence properties of the Galerkin finite element method are studied numerically by refining the discretization process. Results indicate that four or five elements suffice to capture the dynamics of the blade with the same accuracy as the global Galerkin method.
NASA Technical Reports Server (NTRS)
Gerhard, Craig Steven; Gurdal, Zafer; Kapania, Rakesh K.
1996-01-01
Layerwise finite element analyses of geodesically stiffened cylindrical shells are presented. The layerwise laminate theory of Reddy (LWTR) is developed and adapted to circular cylindrical shells. The Ritz variational method is used to develop an analytical approach for studying the buckling of simply supported geodesically stiffened shells with discrete stiffeners. This method utilizes a Lagrange multiplier technique to attach the stiffeners to the shell. The development of the layerwise shells couples a one-dimensional finite element through the thickness with a Navier solution that satisfies the boundary conditions. The buckling results from the Ritz discrete analytical method are compared with smeared buckling results and with NASA Testbed finite element results. The development of layerwise shell and beam finite elements is presented and these elements are used to perform the displacement field, stress, and first-ply failure analyses. The layerwise shell elements are used to model the shell skin and the layerwise beam elements are used to model the stiffeners. This arrangement allows the beam stiffeners to be assembled directly into the global stiffness matrix. A series of analytical studies are made to compare the response of geodesically stiffened shells as a function of loading, shell geometry, shell radii, shell laminate thickness, stiffener height, and geometric nonlinearity. Comparisons of the structural response of geodesically stiffened shells, axial and ring stiffened shells, and unstiffened shells are provided. In addition, interlaminar stress results near the stiffener intersection are presented. First-ply failure analyses for geodesically stiffened shells utilizing the Tsai-Wu failure criterion are presented for a few selected cases.
Nonlinear finite element modeling of THUNDER piezoelectric actuators
NASA Astrophysics Data System (ADS)
Taleghani, Barmac K.; Campbell, Joel F.
1999-06-01
A NASTRAN non-linear finite element model has been developed for predicting the dome heights of THUNDER (Thin Layer Unimorph Ferroelectric Driver) piezoelectric actuators. To analytically validate the finite element model, a comparison was made with a non-linear plate solution using Von Karmen's approximation. A 500 volt input was used to examine the actuator deformation. The NASTRAN finite element model was also compared with experimental results. Four groups of specimens were fabricated and tested. Four different input voltages, which included 120, 160, 200, and 240 Vp-p with a 0 volts offset, were used for this comparison.
Quality assessment and control of finite element solutions
NASA Technical Reports Server (NTRS)
Noor, Ahmed K.; Babuska, Ivo
1987-01-01
Status and some recent developments in the techniques for assessing the reliability of finite element solutions are summarized. Discussion focuses on a number of aspects including: the major types of errors in the finite element solutions; techniques used for a posteriori error estimation and the reliability of these estimators; the feedback and adaptive strategies for improving the finite element solutions; and postprocessing approaches used for improving the accuracy of stresses and other important engineering data. Also, future directions for research needed to make error estimation and adaptive movement practical are identified.
P-Finite-Element Program For Analysis Of Plates
NASA Technical Reports Server (NTRS)
Smith, James P.
1995-01-01
BUCKY is p-finite-element computer program for highly accurate analysis of structures. Used to analyze buckling, bending, and in-plane stress-and-strain behaviors of plates. Provides elastic-plastic solutions for isotropic plates in states of plane stress, and axisymmetric solution sequence used to treat three-dimensional problems. Computes response of plate to variety of loading and boundary conditions by use of higher-order displacement function in p-finite-element method. Enables user to obtain results more accurate than obtained by use of traditional h-finite elements. Written in FORTRAN 77.
A finite element conjugate gradient FFT method for scattering
NASA Technical Reports Server (NTRS)
Collins, Jeffery D.; Ross, Dan; Jin, J.-M.; Chatterjee, A.; Volakis, John L.
1991-01-01
Validated results are presented for the new 3D body of revolution finite element boundary integral code. A Fourier series expansion of the vector electric and mangnetic fields is employed to reduce the dimensionality of the system, and the exact boundary condition is employed to terminate the finite element mesh. The mesh termination boundary is chosen such that is leads to convolutional boundary operatores of low O(n) memory demand. Improvements of this code are discussed along with the proposed formulation for a full 3D implementation of the finite element boundary integral method in conjunction with a conjugate gradiant fast Fourier transformation (CGFFT) solution.
Non-Linear Finite Element Modeling of THUNDER Piezoelectric Actuators
NASA Technical Reports Server (NTRS)
Taleghani, Barmac K.; Campbell, Joel F.
1999-01-01
A NASTRAN non-linear finite element model has been developed for predicting the dome heights of THUNDER (THin Layer UNimorph Ferroelectric DrivER) piezoelectric actuators. To analytically validate the finite element model, a comparison was made with a non-linear plate solution using Von Karmen's approximation. A 500 volt input was used to examine the actuator deformation. The NASTRAN finite element model was also compared with experimental results. Four groups of specimens were fabricated and tested. Four different input voltages, which included 120, 160, 200, and 240 Vp-p with a 0 volts offset, were used for this comparison.
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.
Higher-Order Finite Elements for Computing Thermal Radiation
NASA Technical Reports Server (NTRS)
Gould, Dana C.
2004-01-01
Two variants of the finite-element method have been developed for use in computational simulations of radiative transfers of heat among diffuse gray surfaces. Both variants involve the use of higher-order finite elements, across which temperatures and radiative quantities are assumed to vary according to certain approximations. In this and other applications, higher-order finite elements are used to increase (relative to classical finite elements, which are assumed to be isothermal) the accuracies of final numerical results without having to refine computational meshes excessively and thereby incur excessive computation times. One of the variants is termed the radiation sub-element (RSE) method, which, itself, is subject to a number of variations. This is the simplest and most straightforward approach to representation of spatially variable surface radiation. Any computer code that, heretofore, could model surface-to-surface radiation can incorporate the RSE method without major modifications. In the basic form of the RSE method, each finite element selected for use in computing radiative heat transfer is considered to be a parent element and is divided into sub-elements for the purpose of solving the surface-to-surface radiation-exchange problem. The sub-elements are then treated as classical finite elements; that is, they are assumed to be isothermal, and their view factors and absorbed heat fluxes are calculated accordingly. The heat fluxes absorbed by the sub-elements are then transferred back to the parent element to obtain a radiative heat flux that varies spatially across the parent element. Variants of the RSE method involve the use of polynomials to interpolate and/or extrapolate to approximate spatial variations of physical quantities. The other variant of the finite-element method is termed the integration method (IM). Unlike in the RSE methods, the parent finite elements are not subdivided into smaller elements, and neither isothermality nor other
Updating finite element dynamic models using an element-by-element sensitivity methodology
NASA Astrophysics Data System (ADS)
Farhat, Charbel; Hemez, Francois M.
1993-09-01
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.
North Atlantic Finite Element Ocean Modeling
NASA Astrophysics Data System (ADS)
Veluthedathekuzhiyil, Praveen
This thesis presents a modified version of the Finite Element Ocean Model (FEOM) developed at Alfred Wegener Institute for Polar and Marine Research (AWI) for the North Atlantic Ocean. A reasonable North Atlantic Ocean simulation is obtained against the observational data sets in a Control simulation (CS) where the surface boundary conditions are relaxed to a climatology. The vertical mixing in the model was tuned to represent convection in the model, also the horizontal mixing and diffusion coefficients to represent the changes in the resolution of the model’s unstructured grid. In addition, the open boundaries in the model are treated with a sponge layer where tracers are relaxed to climatology. The model is then further modified to accept the atmospheric flux forcing at the surface boundary with an added net heat flux correction and freshwater forcing from major rivers that are flowing into the North Atlantic Ocean. The impact of this boundary condition on the simulation results is then analyzed and shows many improvements albeit the drift in tracer properties around the Gulf Stream region remains as that of the CS case. However a comparison of the vertical sections at Cape Desolation and Cape Farewell with the available observational data sets shows many improvements in this simulation compared to that of the CS case. But the freshwater content in the Labrador Sea interior shows a continued drift as that of the CS case with an improvement towards the 10th model year. A detailed analysis of the boundary currents around the Labrador Sea shows the weak offshore transport of freshwater from the West Greenland Current (WGC) as one of the causes. To further improve the model and reasonably represent the boundary currents and associated sub-grid scale eddies in the model, a modified sub-grid scale parameterization based on Gent and McWilliams, (1990) is adopted. The sensitivity of using various approaches in the thickness diffusion parameter ( Kgm) for this
Application of Mass Lumped Higher Order Finite Elements
Chen, J.; Strauss, H. R.; Jardin, S. C.; Park, W.; Sugiyama, L. E.; G. Fu; Breslau, J.
2005-11-01
There are many interesting phenomena in extended-MHD such as anisotropic transport, mhd, 2-fluid effects stellarator and hot particles. Any one of them challenges numerical analysts, and researchers are seeking for higher order methods, such as higher order finite difference, higher order finite elements and hp/spectral elements. It is true that these methods give more accurate solution than their linear counterparts. However, numerically they are prohibitively expensive. Here we give a successful solution of this conflict by applying mass lumped higher order finite elements. This type of elements not only keep second/third order accuracy but also scale closely to linear elements by doing mass lumping. This is especially true for second order lump elements. Full M3D and anisotropic transport models are studied.
Error analysis of finite element solutions for postbuckled cylinders
NASA Technical Reports Server (NTRS)
Sistla, Rajaram; Thurston, Gaylen A.
1989-01-01
A general method of error analysis and correction is investigated for the discrete finite-element results for cylindrical shell structures. The method for error analysis is an adaptation of the method of successive approximation. When applied to the equilibrium equations of shell theory, successive approximations derive an approximate continuous solution from the discrete finite-element results. The advantage of this continuous solution is that it contains continuous partial derivatives of an order higher than the basis functions of the finite-element solution. Preliminary numerical results are presented in this paper for the error analysis of finite-element results for a postbuckled stiffened cylindrical panel modeled by a general purpose shell code. Numerical results from the method have previously been reported for postbuckled stiffened plates. A procedure for correcting the continuous approximate solution by Newton's method is outlined.
Generalized multiscale finite element method. Symmetric interior penalty coupling
NASA Astrophysics Data System (ADS)
Efendiev, Y.; Galvis, J.; Lazarov, R.; Moon, M.; Sarkis, M.
2013-12-01
Motivated by applications to numerical simulations of flows in highly heterogeneous porous media, we develop multiscale finite element methods for second order elliptic equations. We discuss a multiscale model reduction technique in the framework of the discontinuous Galerkin finite element method. We propose two different finite element spaces on the coarse mesh. The first space is based on a local eigenvalue problem that uses an interior weighted L2-norm and a boundary weighted L2-norm for computing the “mass” matrix. The second choice is based on generation of a snapshot space and subsequent selection of a subspace of a reduced dimension. The approximation with these multiscale spaces is based on the discontinuous Galerkin finite element method framework. We investigate the stability and derive error estimates for the methods and further experimentally study their performance on a representative number of numerical examples.
The finite element machine: An experiment in parallel processing
NASA Technical Reports Server (NTRS)
Storaasli, O. O.; Peebles, S. W.; Crockett, T. W.; Knott, J. D.; Adams, L.
1982-01-01
The finite element machine is a prototype computer designed to support parallel solutions to structural analysis problems. The hardware architecture and support software for the machine, initial solution algorithms and test applications, and preliminary results are described.
An enhanced finite element technique for diffuse phase transition
NASA Astrophysics Data System (ADS)
Münch, I.; Krauß, M.
2015-10-01
We propose a finite element technique to enhance phase-field simulations. As adaptive p-method it and can be generally applied to finite element formulations. However, diffuse interfaces have non-linear gradients within regions typically smaller compared to the size of the overall model. Thus, enhanced field interpolation with higher polynomial functions on demand allows for coarser meshing or lower regularization length for the phase transition. Our method preserves continuity of finite elements and is particularly advantageous in the context of parallelized computing. An analytical solution for the evolution of a phase-field variable governed by the Allen-Cahn equation is used to define an error measure and to investigate the proposed method. Several examples demonstrate the capability of this finite element technique.
Validation of high displacement piezoelectric actuator finite element models
NASA Astrophysics Data System (ADS)
Taleghani, Barmac K.
2000-08-01
The paper presents the results obtained by using NASTRAN and ANSYS finite element codes to predict doming of the THUNDER piezoelectric actuators during the manufacturing process and subsequent straining due to an applied input voltage. To effectively use such devices in engineering applications, modeling and characterization are essential. Length, width, dome height, and thickness and important parameters for users of such devices. Therefore, finite element models were used to assess the effects of these parameters. NASTRAN and ANSYS used different methods for modeling piezoelectric effects. In NASTRAN, a thermal analogy was used to represent voltage at nodes as equivalent temperatures, while ANSYS processed the voltage directly using piezoelectric finite elements. The results of finite element models were validated by using the experimental results.
Adaptive Finite-Element Computation In Fracture Mechanics
NASA Technical Reports Server (NTRS)
Min, J. B.; Bass, J. M.; Spradley, L. W.
1995-01-01
Report discusses recent progress in use of solution-adaptive finite-element computational methods to solve two-dimensional problems in linear elastic fracture mechanics. Method also shown extensible to three-dimensional problems.
Scalable, Finite Element Analysis of Electromagnetic Scattering and Radiation
NASA Technical Reports Server (NTRS)
Cwik, T.; Lou, J.; Katz, D.
1997-01-01
In this paper a method for simulating electromagnetic fields scattered from complex objects is reviewed; namely, an unstructured finite element code that does not use traditional mesh partitioning algorithms.
Validation of High Displacement Piezoelectric Actuator Finite Element Models
NASA Technical Reports Server (NTRS)
Taleghani, B. K.
2000-01-01
The paper presents the results obtained by using NASTRAN(Registered Trademark) and ANSYS(Regitered Trademark) finite element codes to predict doming of the THUNDER piezoelectric actuators during the manufacturing process and subsequent straining due to an applied input voltage. To effectively use such devices in engineering applications, modeling and characterization are essential. Length, width, dome height, and thickness are important parameters for users of such devices. Therefore, finite element models were used to assess the effects of these parameters. NASTRAN(Registered Trademark) and ANSYS(Registered Trademark) used different methods for modeling piezoelectric effects. In NASTRAN(Registered Trademark), a thermal analogy was used to represent voltage at nodes as equivalent temperatures, while ANSYS(Registered Trademark) processed the voltage directly using piezoelectric finite elements. The results of finite element models were validated by using the experimental results.
Comparison of different precondtioners for nonsymmtric finite volume element methods
Mishev, I.D.
1996-12-31
We consider a few different preconditioners for the linear systems arising from the discretization of 3-D convection-diffusion problems with the finite volume element method. Their theoretical and computational convergence rates are compared and discussed.
Finite element analysis of vibration and damping of laminated composites
NASA Astrophysics Data System (ADS)
Rikards, Rolands
Simple finite elements are used to form a special laminated beam and plate superelements excluding all degrees of freedom in the nodes of the middle layer, and the finite element analysis of this structure is performed. To estimate damping of structures, modal loss factors are calculated, using two methods: the 'exact' method of complex eigenvalues and the approximate energy method. It was found that both methods give satisfactory results. However, the energy method needs less computer time than the exact method.
Mathematical aspects of finite element methods for incompressible viscous flows
NASA Technical Reports Server (NTRS)
Gunzburger, M. D.
1986-01-01
Mathematical aspects of finite element methods are surveyed for incompressible viscous flows, concentrating on the steady primitive variable formulation. The discretization of a weak formulation of the Navier-Stokes equations are addressed, then the stability condition is considered, the satisfaction of which insures the stability of the approximation. Specific choices of finite element spaces for the velocity and pressure are then discussed. Finally, the connection between different weak formulations and a variety of boundary conditions is explored.
Evaluation of a hybrid, anisotropic, multilayered, quadrilateral finite element
NASA Technical Reports Server (NTRS)
Robinson, J. C.; Blackburn, C. L.
1978-01-01
A multilayered finite element with bending-extensional coupling is evaluated for: (1) buckling of general laminated plates; (2) thermal stresses of laminated plates cured at elevated temperatures; (3) displacements of a bimetallic beam; and (4) displacement and stresses of a single-cell box beam with warped cover panels. Also, displacements and stresses for flat and spherical orthotropic and anisotropic segments are compared with results from higher order plate and shell finite-element analyses.
Mixed finite elements for the Richards' equation: linearization procedure
NASA Astrophysics Data System (ADS)
Pop, I. S.; Radu, F.; Knabner, P.
2004-07-01
We consider mixed finite element discretization for a class of degenerate parabolic problems including the Richards' equation. After regularization, time discretization is achieved by an Euler implicit scheme, while mixed finite elements are employed for the discretization in space. Based on the results obtained in (Radu et al. RANA Preprint 02-06, Eindhoven University of Technology, 2002), this paper considers a simple iterative scheme to solve the emerging nonlinear elliptic problems.
Finite element analysis of a composite wheelchair wheel design
NASA Technical Reports Server (NTRS)
Ortega, Rene
1994-01-01
The finite element analysis of a composite wheelchair wheel design is presented. The design is the result of a technology utilization request. The designer's intent is to soften the riding feeling by incorporating a mechanism attaching the wheel rim to the spokes that would allow considerable deflection upon compressive loads. A finite element analysis was conducted to verify proper structural function. Displacement and stress results are presented and conclusions are provided.
Examples of finite element mesh generation using SDRC IDEAS
NASA Technical Reports Server (NTRS)
Zapp, John; Volakis, John L.
1990-01-01
IDEAS (Integrated Design Engineering Analysis Software) offers a comprehensive package for mechanical design engineers. Due to its multifaceted capabilities, however, it can be manipulated to serve the needs of electrical engineers, also. IDEAS can be used to perform the following tasks: system modeling, system assembly, kinematics, finite element pre/post processing, finite element solution, system dynamics, drafting, test data analysis, and project relational database.
Simulation of two-dimensional waterflooding using mixed finite elements
Chavent, G.; Jaffre, J.; Cohen, G.; Dupuy, M.; Dieste, I.
1982-01-01
A new method for the simulation of incompressible diphasic flows in two dimensions is presented, the distinctive features of which are: (1) reformation of the basic equation and specific choices of the finite element approximation of the same; (11) use of a mixed finite elements method, approximating both scalar and vector functions. Several test examples are shown, including gravity and capillary effects. The use of discontinuous basis functions proved successful for an accurate representation of sharp fronts. 16 refs.
Integration of geometric modeling and advanced finite element preprocessing
NASA Technical Reports Server (NTRS)
Shephard, Mark S.; Finnigan, Peter M.
1987-01-01
The structure to a geometry based finite element preprocessing system is presented. The key features of the system are the use of geometric operators to support all geometric calculations required for analysis model generation, and the use of a hierarchic boundary based data structure for the major data sets within the system. The approach presented can support the finite element modeling procedures used today as well as the fully automated procedures under development.
Azimuthally-dependent Finite Element Solution to the Cylindrical Resonator
NASA Technical Reports Server (NTRS)
Osegueda, R.; Pierluissi, J.; Gil, L.; Revilla, A.; Villalva, G.; Dick, G.; Wang, D. SantiagoR.
1994-01-01
The cylindrical cavity resonator loaded with an anisotropic dielectric is analyzed as a two-dimensional problem using a finite element approach that assumes sinusoidal dependence in azimuth. This methodology allows the first finite element treatment of the technically important case of a resonator containing a sapphire element with a cylindrically aligned c axis. Second order trial functions together with quadrilateral elements are adopted in the calculations. The method was validated through comparisons with the analytical solutions for the hollow metal cavity and a coaxial cavity, as well as through measurements on a shielded sapphire resonator.