Quantum Finite Elements for Lattice Field Theory
Brower, Richard C; Gasbarro, Andrew; Raben, Timothy; Tan, Chung-I; Weinberg, Evan
2016-01-01
Viable non-perturbative methods for lattice quantum field theories on curved manifolds are difficult. By adapting features from the traditional finite element methods (FEM) and Regge Calculus, a new simplicial lattice Quantum Finite Element (QFE) Lagrangian is constructed for fields on a smooth Riemann manifold. To reach the continuum limit additional counter terms must be constructed to cancel the ultraviolet distortions. This is tested by the comparison of phi 4-th theory at the Wilson-Fisher fixed point with the exact Ising (c =1/2) CFT on a 2D Riemann sphere. The Dirac equation is also constructed on a simplicial lattice approximation to a Riemann manifold by introducing a lattice vierbein and spin connection on each link. Convergence of the QFE Dirac equation is tested against the exact solution for the 2D Riemann sphere. Future directions and applications to Conformal Field Theories are suggested.
Partitions of nonzero elements of a finite field into pairs
Karasev, R N
2010-01-01
In this paper we prove two theorems. Informally, they claim that the nonzero elements of a finite field with odd characteristic can be partitioned into pairs with prescribed difference (maybe, with some alternatives) in each pair. We also consider some generalizations of these results to packing translates in a finite or infinite field.
Choice of input fields in stochastic finite elements
DEFF Research Database (Denmark)
Ditlevsen, Ove Dalager; Tarp-Johansen, Niels Jacob
1996-01-01
, the flexibility field, as the input to the stochastic finite element model. To answer this question the focus should be on the error of the output of the mechanical model rather than on the input field itself when discretizing the field through replacing it by a field defined in terms of a finite number of random...... variables. Several reported discretization methods define these random variables as integrals of the product of the field and some suitable weight functions. In particular, the weight functions can be Dirac delta functions whereby the random variables become the field values at a finite set of given points....... The replacement field is often defined as the linear regression of the original field on the considered vector of the weighted integrals of the field. For example, this holds for discretizations obtained by truncation of the Karhunen-Loeve expansion of the field, but only approximately so for truncations...
Choice of input fields in stochastic finite elements
DEFF Research Database (Denmark)
Ditlevsen, Ove Dalager; Tarp-Johansen, Niels Jacob
1999-01-01
, the flexibility field, as the input to the stochastic finite element model. To answer this question the focus should be on the error of the output of the mechanical model rather than on the input field itself when discretizing the held through replacing it by a field defined in terms of a finite number of random...... variables. Several reported discretization methods define these random variables as integrals of the product of the held and some suitable weight functions. In particular, the weight functions can be Dirac delta functions whereby the random variables become the field values at a finite set of given points....... The replacement field is often defined as the linear regression of the original field on the considered vector of the weighted integrals of the field. For example, this holds for discretizations obtained by truncation of the Karhunen-Loeve expansion of the field, but only approximately so for truncations...
Displacement fields denoising and strains extraction by finite element method
Institute of Scientific and Technical Information of China (English)
无
2011-01-01
Optical full-field measurement methods are now widely applied in various domains. In general,the displacement fields can be directly obtained from the measurement,however in mechanical analysis strain fields are preferred.To extract strain fields from noisy displacement fields is always a challenging topic.In this study,a finite element method for smoothing displacement fields and calculating strain fields is proposed.An experimental test case on a holed aluminum specimen under tension is applied to vali...
Symmetric Matrix Fields in the Finite Element Method
Directory of Open Access Journals (Sweden)
Gerard Awanou
2010-07-01
Full Text Available The theory of elasticity is used to predict the response of a material body subject to applied forces. In the linear theory, where the displacement is small, the stress tensor which measures the internal forces is the variable of primal importance. However the symmetry of the stress tensor which expresses the conservation of angular momentum had been a challenge for finite element computations. We review in this paper approaches based on mixed finite element methods.
Finite element modeling of electromagnetic fields and waves using NASTRAN
Moyer, E. Thomas, Jr.; Schroeder, Erwin
1989-01-01
The various formulations of Maxwell's equations are reviewed with emphasis on those formulations which most readily form analogies with Navier's equations. Analogies involving scalar and vector potentials and electric and magnetic field components are presented. Formulations allowing for media with dielectric and conducting properties are emphasized. It is demonstrated that many problems in electromagnetism can be solved using the NASTRAN finite element code. Several fundamental problems involving time harmonic solutions of Maxwell's equations with known analytic solutions are solved using NASTRAN to demonstrate convergence and mesh requirements. Mesh requirements are studied as a function of frequency, conductivity, and dielectric properties. Applications in both low frequency and high frequency are highlighted. The low frequency problems demonstrate the ability to solve problems involving media inhomogeneity and unbounded domains. The high frequency applications demonstrate the ability to handle problems with large boundary to wavelength ratios.
Two-Element Generation of Unitary Groups Over Finite Fields
2013-01-31
like to praise my Lord and Savior, Jesus Christ , for allowing me this opportunity to work on a Ph.D in mathematics, and for His sustaining grace...Ishibashi’s original result. The paper’s main theorem will show that all unitary groups over finite fields of odd characteristic are generated by only two
Bathe, Klaus-Jürgen
2015-01-01
Finite element procedures are now an important and frequently indispensable part of engineering analyses and scientific investigations. This book focuses on finite element procedures that are very useful and are widely employed. Formulations for the linear and nonlinear analyses of solids and structures, fluids, and multiphysics problems are presented, appropriate finite elements are discussed, and solution techniques for the governing finite element equations are given. The book presents general, reliable, and effective procedures that are fundamental and can be expected to be in use for a long time. The given procedures form also the foundations of recent developments in the field.
hp-finite-elements for simulating electromagnetic fields in optical devices with rough textures
Burger, S; Hammerschmidt, M; Herrmann, S; Pomplun, J; Schmidt, F; Wohlfeil, B; Zschiedrich, L
2015-01-01
The finite-element method is a preferred numerical method when electromagnetic fields at high accuracy are to be computed in nano-optics design. Here, we demonstrate a finite-element method using hp-adaptivity on tetrahedral meshes for computation of electromagnetic fields in a device with rough textures. The method allows for efficient computations on meshes with strong variations in element sizes. This enables to use precise geometry resolution of the rough textures. Convergence to highly accurate results is observed.
The finite element method for the global gravity field modelling
Kollár, Michal; Macák, Marek; Mikula, Karol; Minarechová, Zuzana
2014-05-01
We present a finite element approach for solving the fixed gravimetric boundary-value problem on a global level. To that goal, we have defined the computational domain bounded by the real topography and a chosen satellite level. The boundary-value problem consists of the Laplace equation for the disturbing potential and the Neumann boundary condition given by the gravity disturbances applied on the bottom boundary, and the Dirichlet boundary condition given by the disturbing potential applied on the upper boundary. Afterwards, the computational domain is meshed with several different meshes chosen to avoid the problem of simple spherical meshes that contain a singularity at poles. Our aim has been to show how the right mesh can improve results as well as significantly reduce the computational time. The practical implementation has been done in the FEM software ANSYS using 3D linear elements SOLID70 and for solving the linear system of equations, the preconditioned conjugate gradients method has been chosen. The obtained disturbing potential has been applied to calculate the geopotential value W0.
Development of Generic Field Classes for Finite Element and Finite Difference Problems
Directory of Open Access Journals (Sweden)
Diane A. Verner
1993-01-01
Full Text Available This article considers the development of a reusable object-oriented array library, as well as the use of this library in the construction of finite difference and finite element codes. The classes in this array library are also generic enough to be used to construct other classes specific to finite difference and finite element methods. We demonstrate the usefulness of this library by inserting it into two existing object-oriented scientific codes developed at Sandia National Laboratories. One of these codes is based on finite difference methods, whereas the other is based on finite element methods. Previously, these codes were separately maintained across a variety of sequential and parallel computing platforms. The use of object-oriented programming allows both codes to make use of common base classes. This offers a number of advantages related to optimization and portability. Optimization efforts, particularly important in large scientific codes, can be focused on a single library. Furthermore, by encapsulating machine dependencies within this library, the optimization of both codes on different architec-tures will only involve modification to a single library.
Hybrid finite-element/boundary-element method to calculate Oersted fields
Energy Technology Data Exchange (ETDEWEB)
Hertel, Riccardo, E-mail: hertel@ipcms.unistra.fr [Institut de Physique et Chimie des Matériaux de Strasbourg, Université de Strasbourg, CNRS UMR 7504, Strasbourg (France); Kákay, Attila [Peter Grünberg Institut (PGI-6), Forschungszentrum Jülich GmbH, D-52428 Jülich (Germany)
2014-11-15
The article presents a general-purpose hybrid finite-element/boundary-element method (FEM/BEM) to calculate magnetostatic fields generated by stationary electric currents. The efficiency of this code lies in its ability to simulate Oersted fields in complex geometries with non-uniform current density distributions. As a precursor to the calculation of the Oersted field, an FEM algorithm is employed to calculate the electric current density distribution. The accuracy of the code is confirmed by comparison with analytic results. Two examples show how this method provides important numerical data that can be directly plugged into micromagnetic simulations: The current density distribution in a thin magnetic strip with a notch, and the Oersted field in a three-dimensional contact geometry; similar to the type commonly used in spin-torque driven nano-oscillators. It is argued that a precise calculation of both, the Oersted field and the current density distribution, is essential for a reliable simulation of current-driven micromagnetic processes. - Highlights: • We present a numerical method to calculate Oersted fields for arbitrary geometries. • Description of a FEM algorithm to calculate current density distributions. • It is argued that these methods are valuable for micromagnetic STT-simulations. • Several examples are shown, highlighting the methods’ importance and accuracy.
Institute of Scientific and Technical Information of China (English)
Weibin Chen; Qiwen Zhan
2007-01-01
Plasmonic field enhancement in a fully coated dielectric near field scanning optical microscope (NSOM)probe under radial polarization illumination is analyzed using an axially symmetric three-dimensional (3D)finite element method (FEM) model. The enhancement factor strongly depends on the illumination spot size, taper angle of the probe, and the metal film thickness. The tolerance of the alignment angle is investigated. Probe designs with different metal coatings and their enhancement performance are studied as well. The nanometric spot size at the tip apex and high field enhancement of the apertureless NSOM probe have important potential application in semiconductor metrology.
Adaptive strategies using standard and mixed finite elements for wind field adjustment
Energy Technology Data Exchange (ETDEWEB)
Winter, G.; Montero, G.; Montenegro, R. [Univ. of Las Palmas de Gran Canaria, FL (United States)
1995-01-01
In order to find a map of wind velocities, this study tries to obtain an incompressible wind field that adjusts to an experimental one: also verifying the corresponding boundary conditions of physical interest. This problem has been solved by several authors using finite differences or standard finite element techniques. In this paper, this problem is solved by two different adaptive finite element methods. The first makes use of standard finite element techniques, using linear interpolation of a potential function. In the second, a direct computation of the velocity field is undertaken by means of a mixed finite element method. Several error indicators are proposed for both formulations together with an adaptive strategy. We have applied both methods to several typical test problems, as well as to realistic data corresponding to the Island of Fuerteventura, with satisfactory results from a numerical point of view. 13 refs., 16 figs., 1 tab.
Electric field calculations in brain stimulation based on finite elements
DEFF Research Database (Denmark)
Windhoff, Mirko; Opitz, Alexander; Thielscher, Axel
2013-01-01
, allowing for the creation of tetrahedral volume head meshes that can finally be used in the numerical calculations. The pipeline integrates and extends established (and mainly free) software for neuroimaging, computer graphics, and FEM calculations into one easy-to-use solution. We demonstrate...... elements. The latter is crucial to guarantee the numerical robustness of the FEM calculations. The pipeline will be released as open-source, allowing for the first time to perform realistic field calculations at an acceptable methodological complexity and moderate costs....
Kou, Jisheng
2017-06-09
In this paper, a new three-field weak formulation for Stokes problems is developed, and from this, a dual-mixed finite element method is proposed on a rectangular mesh. In the proposed mixed methods, the components of stress tensor are approximated by piecewise constant functions or Q1 functions, while the velocity and pressure are discretized by the lowest-order Raviart-Thomas element and the piecewise constant functions, respectively. Using quadrature rules, we demonstrate that this scheme can be reduced into a finite volume method on staggered grid, which is extensively used in computational fluid mechanics and engineering.
Finite Element - Artificial Transmitting Boundary Method for Acoustical Field on Tapered Waveguide
Institute of Scientific and Technical Information of China (English)
J.; S.; Yang; G; F.; Fan; J.; P.; Zhu; C.K.; Sun; Y.; H.; Zhu
2003-01-01
In earlier approach, the 2-D acoustical field profiles on the substrate region are often calculated with BPM. In this paper, we present a new approach based on the finite element -artificial transmitting boundary method and calculate acoustical field on the substrate region.
Scheerlinck, N.; Verboven, P.; Stigter, J.D.; Baerdenmaeker, de J.; Impe, van J.F.; Nicolai, B.A.
2000-01-01
A first-order perturbation algorithm for the computation of mean values and variances of transient temperature and moisture fields during coupled heat and mass transfer problems with random field parameters has been developed and implemented. The algorithm is based on the Galerkin finite-element dis
Energy Technology Data Exchange (ETDEWEB)
Lucarelli, Andrea [Laboratorium fuer Festkoerperphysik, ETH-Zuerich, CH-8093 Zuerich (Switzerland); Grilli, Francesco [Ecole Polytechnique Montreal, Montreal (Canada); Luepke, Gunter [Department of Applied Science, The College of William and Mary, Williamsburg, VA 23187-8795 (United States); Haugan, Timothy J; Barnes, Paul N [Air Force Research Laboratory, Wright-Patterson AFB, OH 45433-7919 (United States)
2009-10-15
We present a finite-element model for computing current and field distributions in multifilamentary superconducting thin films subjected to simultaneous effects of a transport ac current and a perpendicularly applied dc field. The model is implemented in the finite-element software package COMSOL Multiphysics and this solves Maxwell equations using a highly nonlinear resistivity to describe electrical superconducting characteristics. The time-dependent magnetic flux, current distributions, and ac losses are studied for different distances between filaments. We find that increasing the interfilamentary distance affects the transport and screening current distributions, reducing both the magnetic coupling and ac losses.
Ransom, Jonathan B.
2002-01-01
A multifunctional interface method with capabilities for variable-fidelity modeling and multiple method analysis is presented. The methodology provides an effective capability by which domains with diverse idealizations can be modeled independently to exploit the advantages of one approach over another. The multifunctional method is used to couple independently discretized subdomains, and it is used to couple the finite element and the finite difference methods. The method is based on a weighted residual variational method and is presented for two-dimensional scalar-field problems. A verification test problem and a benchmark application are presented, and the computational implications are discussed.
Finite Element Treatment of Vortex States in 3D Cubic Superconductors in a Tilted Magnetic Field
Peng, Lin; Cai, Chuanbing
2017-03-01
The time-dependent Ginzburg-Landau equations have been solved numerically by a finite element analysis for superconducting samples with a cubic shape in a tilted magnetic field. We obtain different vortex patterns as a function of the external magnetic field. With a magnetic field not parallel to the x- or y-axis, the vortices attempt to change their orientation accordingly. Our analysis of the corresponding changes in the magnetic response in different directions can provide information not only about vorticity but also about the three-dimensional vortex arrangement, even about the very subtle changes for the superconducting samples with a cubic shape in a tilted magnetic field.
Finite element analysis on the electromagnetic fields of active magnetic bearing
Energy Technology Data Exchange (ETDEWEB)
Ren, S; Liu, J [School of Mechanical Engineering, Shenyang Ligong University, Shenyang, 110168 (China); Bian, C [Institute of Information Science and Engineering, Northeastern University, Shenyang, 110004 (China)], E-mail: renshy@sina.com
2008-02-15
To increase the carrying capacity and reduce the weight and size of AMBs, it is necessary to use a ferromagnetic material with high magnetic flux density, which can make AMBs run in the nonlinear region. The simple linear model before is not gratifying, so some more precise analysis methods are demanded, the finite element method(shorted as FEM) is one of such methods. In this paper, the mathematic model and the simplified calculation of AMB rotor are introduced, and the finite elemental model and its boundary condition are produced. Then, the coupling phenomena of the magnetic fields and the effects of different parameters on the magnetic fields of AMB with a non-homocentric rotor are simulated using the FEM analysis software of ANSYS. The distributions of 2D magnetic lines of force and the flux density in rotor and stator are given. The conclusions are of instructed meaning for the design of AMBs.
ANALYSIS OF AUGMENTED THREE-FIELD MACRO-HYBRID MIXED FINITE ELEMENT SCHEMES
Institute of Scientific and Technical Information of China (English)
Gonzalo Alduncin
2009-01-01
On the basis of composition duality principles, augmented three-field macro-hybrid mixed variational problems and finite element schemes are analyzed. The compati-bility condition adopted here, for compositional dualization, is the coupling operator surjec-tivity, property that expresses in a general operator sense the Ladysenskaja-Babuska-Brezzi inf-sup condition. Variational macro-hybridization is performed under the assumption of decomposable primal and dual spaces relative to nonoverlapping domain decompositions. Then, through compositional dualization macro-hybrid mixed problems are obtained, with internal boundary dual traces as Lagrange multipliers. Also, "mass" preconditioned aug-mentation of three-field formulations are derived, stabilizing macro-hybrid mixed finite element schemes and rendering possible speed up of rates of convergence. Dual mixed incompressible Darcy flow problems illustrate the theory throughout the paper.
Mixed Finite Element Formulation for Magnetic Fluid Oil Flow in Electromagnetic Field
Directory of Open Access Journals (Sweden)
Tan Phey Hoon
2017-01-01
Full Text Available Pressure depletion and high viscosity of crude oil in oil reservoir are the main challenges in oil recovery process. A potential solution is to employ electromagnetic heating coupled with magnetic fluid injection. The present work delivers a fundamental study on the interaction between magnetic fluid flow with electromagnetic field. The two-dimensional, incompressible flow is solved numerically using mixed finite element method. The velocity fields, temperature and pressure are the variables of interest, to be obtained by solving mass, momentum and energy equations coupled with Maxwell’ equations. The fluid stress arises simultaneously with the external magnetic force which mobilises and increases the temperature of the oil flow. Verification is made against available data obtained from different numerical method reported in literature. The results justify feasibility of the mixed finite element formulation as an alternative for the modelling of the magnetic fluid flow.
Finite element simulation of three-dimensional temperature field in underwater welding
Institute of Scientific and Technical Information of China (English)
Liu Xiwen; Wang Guorong; Shi Yonghua; Zhong Jiguang
2007-01-01
Mathematical models of three-dimensional temperature fields in underwater welding with moving heat sources are built. Double ellipsoid Gauss model is proposed as heat sources models. Several factors which affect the temperature fields of underwater welding are analyzed. Water has little influence on thermal efficiency. Water convection coefficient varies with the temperature difference between the water and the workpiece, and water convection makes molten pool freeze quickly. With the increase of water depth, the dimensions of heat sources model should be reduced as arc shrinks. Finite element technology is used to solve mathematical models. ANSYS software is used as finite element tool, and ANSYS Parametric Design Language is used to develop subprograms for loading the moving heat sources and the various convection coefficients. Experiment results show that computational results by using double ellipsoid Gauss heat sources model accord well with the experimental results.
Finite Element Analysis of Temperature Field in Automotive Dry Friction Clutch
O.I. Abdullah; J. Schlattmann
2012-01-01
The friction clutch design is strongly dependent upon the frictional heat generated between contact surfaces during the slipping at beginning of engagement. Because of that the frictional heat generated firstly will reduce the performance of clutch system and then will lead to premature failure in some cases. Finite element method was used to investigate aneffect of thermal load type on the temperature field of the clutch system. Two-dimensional axisymmetric model was used to study the tempe...
Application of Wavelet Finite Element Method to Simulation of the Temperature Field of Copier Paper
Institute of Scientific and Technical Information of China (English)
无
2002-01-01
Simulation of the temperature field of copier paper in copier fusing is very important for improving the fusing property of reprography. The temperature field of copier paper varies with a high gradient when the copier paper is moving through the fusing rollers. By means of conventional shaft elements, the high gradient temperature variety causes the oscillation of the numerical solution. Based on the Daubechies scaling functions, a kind of wavelet-based element is constructed for the above problem. The temperature field of the copier paper moving through the fusing rollers is simulated using the two methods. Comparison of the results shows the advantages of the wavelet finite element method,which provides a new method for improving the copier properties.
B-Spline Finite Elements and their Efficiency in Solving Relativistic Mean Field Equations
Pöschl, W
1997-01-01
A finite element method using B-splines is presented and compared with a conventional finite element method of Lagrangian type. The efficiency of both methods has been investigated at the example of a coupled non-linear system of Dirac eigenvalue equations and inhomogeneous Klein-Gordon equations which describe a nuclear system in the framework of relativistic mean field theory. Although, FEM has been applied with great success in nuclear RMF recently, a well known problem is the appearance of spurious solutions in the spectra of the Dirac equation. The question, whether B-splines lead to a reduction of spurious solutions is analyzed. Numerical expenses, precision and behavior of convergence are compared for both methods in view of their use in large scale computation on FEM grids with more dimensions. A B-spline version of the object oriented C++ code for spherical nuclei has been used for this investigation.
Anisotropic Finite Element Modeling Based on a Harmonic Field for Patient-Specific Sclera
Directory of Open Access Journals (Sweden)
Xu Jia
2017-01-01
Full Text Available Purpose. This study examined the influence of anisotropic material for human sclera. Method. First, the individual geometry of patient-specific sclera was reproduced from a laser scan. Then, high quality finite element modeling of individual sclera was performed using a convenient automatic hexahedral mesh generator based on harmonic field and integrated with anisotropic material assignment function. Finally, comparison experiments were designed to investigate the effects of anisotropy on finite element modeling of sclera biomechanics. Results. The experimental results show that the presented approach can generate high quality anisotropic hexahedral mesh for patient-specific sclera. Conclusion. The anisotropy shows significant differences for stresses and strain distribution and careful consideration should be given to its use in biomechanical FE studies.
Anisotropic Finite Element Modeling Based on a Harmonic Field for Patient-Specific Sclera.
Jia, Xu; Liao, Shenghui; Duan, Xuanchu; Zheng, Wanqiu; Zou, Beiji
2017-01-01
Purpose. This study examined the influence of anisotropic material for human sclera. Method. First, the individual geometry of patient-specific sclera was reproduced from a laser scan. Then, high quality finite element modeling of individual sclera was performed using a convenient automatic hexahedral mesh generator based on harmonic field and integrated with anisotropic material assignment function. Finally, comparison experiments were designed to investigate the effects of anisotropy on finite element modeling of sclera biomechanics. Results. The experimental results show that the presented approach can generate high quality anisotropic hexahedral mesh for patient-specific sclera. Conclusion. The anisotropy shows significant differences for stresses and strain distribution and careful consideration should be given to its use in biomechanical FE studies.
Multi-field variational formulations and related finite elements for piezoelectric shells
Lammering, Rolf; Mesecke-Rischmann, Simone
2003-12-01
Smart structures technology characterized by structurally integrated sensors and actuators has recently expanded significantly especially as regards lightweight constructions in aeronautics and robotics, e.g. to allow vibration suppression and noise attenuation. In order to be capable of solving these complex issues the finite element method as a well established design tool has to be extended. This paper focuses on shallow sandwich composite shell structures with thin piezoelectric patches bonded to the surfaces. For the proper design of plate and shell structures with integrated piezoelectric materials, various variational formulations and corresponding finite elements are presented. The starting point is the well known two-field variational formulation where the linear piezoelectric effect is taken into account so that the displacements and the electric potential serve as independent variables. Here, the mostly assumed linear variation of the electric potential through the thickness is assumed. Next, it is shown that a quadratic variation of the electric potential through the thickness can be deduced directly from the charge conservation condition. This quadratic variation of the electric potential in the thickness direction is compared with the linear gradient of the first two-field variational formulation. Moreover, in order to allow the implementation of alternative formulations of the constitutive equations by switching of the independent variables and nonlinear material behaviour, a three-field variational formulation is presented in analogy to the Hu-Washizu principle. Adopting this variational principle a hybrid finite element is derived where the dielectric displacement is formulated as an additional degree of freedom. This independent variable can be condensed on the element level and does not enter the system of equations. For the first time all these different variational formulations are developed for a Reissner-Mindlin shallow shell element
Large eddy simulation for wind field analysis based on stabilized finite element method
Institute of Scientific and Technical Information of China (English)
Cheng HUANG; Yan BAO; Dai ZHOU; Jin-quan XU
2011-01-01
In this paper, a stabilized finite element technique, actualized by streamline upwind Petrov-Galerkin (SUPG) stabilized method and three-step finite element method (FEM), for large eddy simulation (LES) is developed to predict the wind flow with high Reynolds numbers. Weak form of LES motion equation is combined with the SUPG stabilized term for the spatial finite element discretization. An explicit three-step scheme is implemented for the temporal discretization. For the numerical example of 2D wind flow over a square rib at Re=4.2×105, the Smagorinsky's subgrid-scale (SSGS) model, the DSGS model, and the DSGS model with Cabot near-wall model are applied, and their results are analyzed and compared with experimental results. Furthermore, numerical examples of 3D wind flow around a surface-mounted cube with different Reynolds numbers are performed using DSGS model with Cabot near-wall model based on the present stabilized method to study the wind field and compared with experimental and numerical results. Finally, vortex structures for wind flow around a surface-mounted cube are studied by present numerical method. Stable and satisfactory results are obtained, which are consistent with most of the measurements even under coarse mesh.
A Mixed Multi-Field Finite Element Formulation for Thermopiezoelectric Composite Shells
Lee, Ho-Jun; Saravanos, Dimitris A.
1999-01-01
Analytical formulations are presented which account for the coupled mechanical, electrical, and thermal response of piezoelectric composite shell structures. A new mixed multi-field laminate theory is developed which combines "single layer" assumptions for the displacements along with layerwise fields for the electric potential and temperature. This laminate theory is formulated using curvilinear coordinates and is based on the principles of linear thermopiezoelectricity. The mechanics have the inherent capability to explicitly model both the active and sensory responses of piezoelectric composite shells in thermal environment. Finite element equations are derived and implemented for an eight-noded shell element. Numerical studies are conducted to investigate both the sensory and active responses of piezoelectric composite shell structures subjected to thermal loads. Results for a cantilevered plate with an attached piezoelectric layer are com- pared with corresponding results from a commercial finite element code and a previously developed program. Additional studies are conducted on a cylindrical shell with an attached piezoelectric layer to demonstrate capabilities to achieve thermal shape control on curved piezoelectric structures.
Institute of Scientific and Technical Information of China (English)
Xi F. XU
2015-01-01
The Green-function-based multiscale stochastic finite element method （MSFEM） has been formulated based on the stochastic variational principle. In this study a fast computing procedure based on the MSFEM is developed to solve random field geotechnical problems with a typical coefficient of variance less than 1. A unique fast computing advantage of the procedure enables computation performed only on those locations of interest, therefore saving a lot of computation. The numerical example on soil settlement shows that the procedure achieves significant computing efficiency compared with Monte Carlo method.
Energy Technology Data Exchange (ETDEWEB)
Nascimento, Francisco Rogerio Teixeira do
2013-07-01
The main objective of this work is to simulate electromagnetic fields using the Finite Element Method. Even in the easiest case of electrostatic and magnetostatic numerical simulation some problems appear when the nodal finite element is used. It is difficult to model vector fields with scalar functions mainly in non-homogeneous materials. With the aim to solve these problems two types of techniques are tried: the adaptive remeshing using nodal elements and the edge finite element that ensure the continuity of tangential components. Some numerical analysis of simple electromagnetic problems with homogeneous and non-homogeneous materials are performed using first, the adaptive remeshing based in various error indicators and second, the numerical solution of waveguides using edge finite element. (author)
Rao, M. N.; Tarun, S.; Schmidt, R.; Schröder, K.-U.
2016-05-01
In this article, we focus on static finite element (FE) simulation of piezoelectric laminated composite plates and shells, considering the nonlinear constitutive behavior of piezoelectric materials under large applied electric fields. Under the assumptions of small strains and large electric fields, the second-order nonlinear constitutive equations are used in the variational principle approach, to develop a nonlinear FE model. Numerical simulations are performed to study the effect of material nonlinearity for piezoelectric bimorph and laminated composite plates as well as cylindrical shells. In comparison to the experimental investigations existing in the literature, the results predicted by the present model agree very well. The importance of the present nonlinear model is highlighted especially in large applied electric fields, and it is shown that the difference between the results simulated by linear and nonlinear constitutive FE models cannot be omitted.
Institute of Scientific and Technical Information of China (English)
HU CaiBo; ZHOU YiJie; CAI YongEn
2009-01-01
In this paper, a new finite element model (FEM) In consideration of regional stress field and an earthquake triggering factor C are proposed for studying earthquake triggering and stress field evolution in an earthquake sequence. The factor C is defined as a ratio between the shear stress and the frictional strength on a slip surface, and it can be used to tell if earthquake is triggered or not. The new FEM and the factor C are used to study the aftershock triggering of the 1976 Tangshan earthquake sequence. The results indicate that the effects of the stress field and the heterogeneity of the Tangshan earthquake fault zone on the aftershock triggering are very important. The affershocks fallen in the earthquake triggering regions predicted by the new FEM are more than those fallen in the regions of △CFS≥0 predicted by seismic dislocation theory.
Institute of Scientific and Technical Information of China (English)
无
2009-01-01
In this paper, a new finite element model (FEM) in consideration of regional stress field and an earthquake triggering factor C are proposed for studying earthquake triggering and stress field evolution in an earthquake sequence. The factor C is defined as a ratio between the shear stress and the frictional strength on a slip surface, and it can be used to tell if earthquake is triggered or not. The new FEM and the factor C are used to study the aftershock triggering of the 1976 Tangshan earthquake sequence. The results indicate that the effects of the stress field and the heterogeneity of the Tangshan earthquake fault zone on the aftershock triggering are very important. The aftershocks fallen in the earthquake triggering regions predicted by the new FEM are more than those fallen in the regions of ΔCFS≥ 0 predicted by seismic dislocation theory.
Simulation on Temperature Field of Radiofrequency Lesions System Based on Finite Element Method
Xiao, D.; Qian, L.; Qian, Z.; Li, W.
2011-01-01
This paper mainly describes the way to get the volume model of damaged region according to the simulation on temperature field of radiofrequency ablation lesion system in curing Parkinson's disease based on finite element method. This volume model reflects, to some degree, the shape and size of the damaged tissue during the treatment with all tendencies in different time or core temperature. By using Pennes equation as heat conduction equation of radiofrequency ablation of biological tissue, the author obtains the temperature distribution field of biological tissue in the method of finite element for solving equations. In order to establish damage models at temperature points of 60°C, 65°C, 70°C, 75°C, 80°C, 85°C and 90 °C while the time points are 30s, 60s, 90s and 120s, Parkinson's disease model of nuclei is reduced to uniform, infinite model with RF pin at the origin. Theoretical simulations of these models are displayed, focusing on a variety of conditions about the effective lesion size on horizontal and vertical. The results show the binary complete quadratic non-linear joint temperature-time models of the maximum damage diameter and maximum height. The models can comprehensively reflect the degeneration of target tissue caused by radio frequency temperature and duration. This lay the foundation for accurately monitor of clinical RF treatment of Parkinson's disease in the future.
Finite elements and approximation
Zienkiewicz, O C
2006-01-01
A powerful tool for the approximate solution of differential equations, the finite element is extensively used in industry and research. This book offers students of engineering and physics a comprehensive view of the principles involved, with numerous illustrative examples and exercises.Starting with continuum boundary value problems and the need for numerical discretization, the text examines finite difference methods, weighted residual methods in the context of continuous trial functions, and piecewise defined trial functions and the finite element method. Additional topics include higher o
Advanced finite element technologies
Wriggers, Peter
2016-01-01
The book presents an overview of the state of research of advanced finite element technologies. Besides the mathematical analysis, the finite element development and their engineering applications are shown to the reader. The authors give a survey of the methods and technologies concerning efficiency, robustness and performance aspects. The book covers the topics of mathematical foundations for variational approaches and the mathematical understanding of the analytical requirements of modern finite element methods. Special attention is paid to finite deformations, adaptive strategies, incompressible, isotropic or anisotropic material behavior and the mathematical and numerical treatment of the well-known locking phenomenon. Beyond that new results for the introduced approaches are presented especially for challenging nonlinear problems.
Finite Element Analysis of 3-D Electromagnetic Field in Bloom Continuous Casting Mold
Institute of Scientific and Technical Information of China (English)
LIU Xu-dong; YANG Xiao-dong; ZHU Miao-yong; CHEN Yong; YANG Su-bo
2007-01-01
Three-dimensional finite element model of electromagnetic stirrer was built to predict magnetic field in a bloom continuous casting mold for steel during operation. The effects of current intensity, current frequency, and mold copper plate thickness on the magnetic field distribution in the mold were investigated. The results show that the magnetic induction intensity increases linearly with the increase in current intensity and decreases with the increase in current frequency. Increasing current intensity and frequency is available in increasing the electromagnetic force. The Joule heat decreases gradually from surface to center of bloom, and a maximum Joule heat can be found on corner of bloom. The prediction of magnetic induction intensity is in good agreement with the measured values.
Finite element mesh generation
Lo, Daniel SH
2014-01-01
Highlights the Progression of Meshing Technologies and Their ApplicationsFinite Element Mesh Generation provides a concise and comprehensive guide to the application of finite element mesh generation over 2D domains, curved surfaces, and 3D space. Organised according to the geometry and dimension of the problem domains, it develops from the basic meshing algorithms to the most advanced schemes to deal with problems with specific requirements such as boundary conformity, adaptive and anisotropic elements, shape qualities, and mesh optimization. It sets out the fundamentals of popular techniques
An inverse finite element method for determining residual and current stress fields in solids
Tartibi, M.; Steigmann, D. J.; Komvopoulos, K.
2016-11-01
The life expectancy of a solid component is traditionally predicted by assessing its expected stress cycle and comparing it to experimentally determined stress states at failure. The accuracy of this procedure is often compromised by unforeseen extremes in the loading cycle or material degradation. Residually stressed parts may either have longer or shorter lifespans than predicted. Thus, determination of the current state of stress (i.e., the residual stress in the absence of external loading) and material properties is particularly important. Typically, the material properties of a solid are determined by fitting experimental data obtained from the measured deformation response in the stress-free configuration. However, the characterization of the mechanical behavior of a residually stressed body requires, in principle, a method that is not restricted to specific constitutive models. Complementing a recently developed technique, known as the reversed updated Lagrangian finite element method (RULFEM), a new method called estimating the current state of stress (ECSS) is presented herein. ECSS is based on three-dimensional full-field displacement and force data of a body perturbed by small displacements and complements the first step of the incremental RULFEM method. The present method generates the current state of stress (or residual stress in the absence of external tractions) and the incremental elasticity tensor of each finite element used to discretize the deformable body. The validity of the ECSS method is demonstrated by two noise-free simulation cases.
An inverse finite element method for determining residual and current stress fields in solids
Tartibi, M.; Steigmann, D. J.; Komvopoulos, K.
2016-08-01
The life expectancy of a solid component is traditionally predicted by assessing its expected stress cycle and comparing it to experimentally determined stress states at failure. The accuracy of this procedure is often compromised by unforeseen extremes in the loading cycle or material degradation. Residually stressed parts may either have longer or shorter lifespans than predicted. Thus, determination of the current state of stress (i.e., the residual stress in the absence of external loading) and material properties is particularly important. Typically, the material properties of a solid are determined by fitting experimental data obtained from the measured deformation response in the stress-free configuration. However, the characterization of the mechanical behavior of a residually stressed body requires, in principle, a method that is not restricted to specific constitutive models. Complementing a recently developed technique, known as the reversed updated Lagrangian finite element method (RULFEM), a new method called estimating the current state of stress (ECSS) is presented herein. ECSS is based on three-dimensional full-field displacement and force data of a body perturbed by small displacements and complements the first step of the incremental RULFEM method. The present method generates the current state of stress (or residual stress in the absence of external tractions) and the incremental elasticity tensor of each finite element used to discretize the deformable body. The validity of the ECSS method is demonstrated by two noise-free simulation cases.
Capelli, Claudio; Biglino, Giovanni; Petrini, Lorenza; Migliavacca, Francesco; Cosentino, Daria; Bonhoeffer, Philipp; Taylor, Andrew M; Schievano, Silvia
2012-12-01
Finite element (FE) modelling can be a very resourceful tool in the field of cardiovascular devices. To ensure result reliability, FE models must be validated experimentally against physical data. Their clinical application (e.g., patients' suitability, morphological evaluation) also requires fast simulation process and access to results, while engineering applications need highly accurate results. This study shows how FE models with different mesh discretisations can suit clinical and engineering requirements for studying a novel device designed for percutaneous valve implantation. Following sensitivity analysis and experimental characterisation of the materials, the stent-graft was first studied in a simplified geometry (i.e., compliant cylinder) and validated against in vitro data, and then in a patient-specific implantation site (i.e., distensible right ventricular outflow tract). Different meshing strategies using solid, beam and shell elements were tested. Results showed excellent agreement between computational and experimental data in the simplified implantation site. Beam elements were found to be convenient for clinical applications, providing reliable results in less than one hour in a patient-specific anatomical model. Solid elements remain the FE choice for engineering applications, albeit more computationally expensive (>100 times). This work also showed how information on device mechanical behaviour differs when acquired in a simplified model as opposed to a patient-specific model.
Zhao, Bin
2015-02-01
Temperature-pressure coupled field analysis of liquefied petroleum gas (LPG) tank under jet fire can offer theoretical guidance for preventing the fire accidents of LPG tank, the application of super wavelet finite element on it is studied in depth. First, review of related researches on heat transfer analysis of LPG tank under fire and super wavelet are carried out. Second, basic theory of super wavelet transform is studied. Third, the temperature-pressure coupled model of gas phase and liquid LPG under jet fire is established based on the equation of state, the VOF model and the RNG k-ɛ model. Then the super wavelet finite element formulation is constructed using the super wavelet scale function as interpolating function. Finally, the simulation is carried out, and results show that the super wavelet finite element method has higher computing precision than wavelet finite element method.
Finite Element Analysis of Temperature Field in Automotive Dry Friction Clutch
Directory of Open Access Journals (Sweden)
O.I. Abdullah
2012-12-01
Full Text Available The friction clutch design is strongly dependent upon the frictional heat generated between contact surfaces during the slipping at beginning of engagement. Because of that the frictional heat generated firstly will reduce the performance of clutch system and then will lead to premature failure in some cases. Finite element method was used to investigate aneffect of thermal load type on the temperature field of the clutch system. Two-dimensional axisymmetric model was used to study the temperature distribution for the clutch system (pressure plate, clutch disc and flywheel during heating phase (slipping period and in the cooling phase (full engagement period. Depending on basic friction clutch design two types of thermal loads were applied; load type A (uniform pressure and load type B (uniform wear. Repeated engagements made at regular interval wereconsidered in this work. ANSYS13 has been used to perform the numerical calculation in this paper.
A finite element approach to self-consistent field theory calculations of multiblock polymers
Ackerman, David M; Fredrickson, Glenn H; Ganapathysubramanian, Baskar
2016-01-01
Self-consistent field theory (SCFT) has proven to be a powerful tool for modeling equilibrium microstructures of soft materials, particularly for multiblock polymers. A very successful approach to numerically solving the SCFT set of equations is based on using a spectral approach. While widely successful, this approach has limitations especially in the context of current technologically relevant applications. These limitations include non-trivial approaches for modeling complex geometries, difficulties in extending to non-periodic domains, as well as non-trivial extensions for spatial adaptivity. As a viable alternative to spectral schemes, we develop a finite element formulation of the SCFT paradigm for calculating equilibrium polymer morphologies. We discuss the formulation and address implementation challenges that ensure accuracy and efficiency. We explore higher order chain contour steppers that are efficiently implemented with Richardson Extrapolation. This approach is highly scalable and suitable for s...
Saravanos, Dimitris A.
1996-01-01
Mechanics for the analysis of laminated composite shells with piezoelectric actuators and sensors are presented. A new mixed-field laminate theory for piezoelectric shells is formulated in curvilinear coordinates which combines single-layer assumptions for the displacements and a layerwise representation for the electric potential. The resultant coupled governing equations for curvilinear piezoelectric laminates are described. Structural mechanics are subsequently developed and an 8-node finite-element is formulated for the static and dynamic analysis of adaptive composite structures of general laminations containing piezoelectric layers. Evaluations of the method and comparisons with reported results are presented for laminated piezoelectric-composite plates, a closed cylindrical shell with a continuous piezoceramic layer and a laminated composite semi-circular cantilever shell with discrete cylindrical piezoelectric actuators and/or sensors.
Scalable algorithms for three-field mixed finite element coupled poromechanics
Castelletto, Nicola; White, Joshua A.; Ferronato, Massimiliano
2016-12-01
We introduce a class of block preconditioners for accelerating the iterative solution of coupled poromechanics equations based on a three-field formulation. The use of a displacement/velocity/pressure mixed finite-element method combined with a first order backward difference formula for the approximation of time derivatives produces a sequence of linear systems with a 3 × 3 unsymmetric and indefinite block matrix. The preconditioners are obtained by approximating the two-level Schur complement with the aid of physically-based arguments that can be also generalized in a purely algebraic approach. A theoretical and experimental analysis is presented that provides evidence of the robustness, efficiency and scalability of the proposed algorithm. The performance is also assessed for a real-world challenging consolidation experiment of a shallow formation.
Institute of Scientific and Technical Information of China (English)
无
2007-01-01
Multilayer ceramic coatings were fabricated on steel substrate using a combined technique of hot dipping aluminum(HDA)and plasma electrolytic oxidation(PEO). A triangle of normalized layer thickness was created for describing thickness ratios of HDA/PEO coatings. Then, the effect of thickness ratio on stresses field of HDA/PEO coatings subjected to uniform normal contact load was investigated by finite element method. Results show that the surface tensile stress is mainly affected by the thickness ratio of Al layer when the total thickness of coating is unchanged. With the increase of Al layer thickness, the surface tensile stress rises quickly. When Al2O3 layer thickness increases, surface tensile stress is diminished. Meanwhile, the maximum shear stress moves rapidly towards internal part of HDA/PEO coatings. Shear stress at the Al2O3/Al interface is minimal when Al2O3 layer and Al layer have the same thickness.
Institute of Scientific and Technical Information of China (English)
Zhang-rong ZHAO; Yi-jie WU; Xin-jian GU; Lei ZHANG; Ji-feng YANG
2009-01-01
This study presents a new method to solve the difficult problem of precise machining a non-cylinder pinhole of a piston using embedded giant magnetostrictive material(GMM)in the component.We propose the finite element model of GMM smart component in electric,magnetic,and mechanical fields by step computation to optimize the design of GMM smart component.The proposed model is implemented by using COMSOL multi-physics V3.2a.The effects of the smart component on the deformation and the system resonance frequencies are studied.The results calculated by the model are in excellent agreement (relative errors are below 10%)with the experimental values.
2010-01-01
Finite element analysis is an engineering method for the numerical analysis of complex structures. This book provides a bird's eye view on this very broad matter through 27 original and innovative research studies exhibiting various investigation directions. Through its chapters the reader will have access to works related to Biomedical Engineering, Materials Engineering, Process Analysis and Civil Engineering. The text is addressed not only to researchers, but also to professional engineers, engineering lecturers and students seeking to gain a better understanding of where Finite Element Analysis stands today.
Institute of Scientific and Technical Information of China (English)
LUO Yun-ju; LIU Dong-yan; LIU Xin-rong
2006-01-01
The Nanwenquan (South Hot Spring) and Xiao quan (Small Hot Spring) in the Nanwenquan anticline are well-known attraction for their geothermal water, but currently, the two natural hot springs have hot flow naturally. In order to protect the geothermal water resource, the evolution of hydrodynamic field must be researched for the causation of the hydrodynamic field destroyed. The finite element numerical simulation was adopted and quantitative study on the geothermal water hydrodynamic field. The finite element model was set up to simulate the research sites, the simulated water level was compared with the actual water level, the feasibility of this model was proved when the simulated water level is approximate to actual one, and an applicable finite element model was obtained. The finite element model was used to simulate the evolution of the hydrodynamic field. This paper supplies a basis to exploit adequately and protect effectively the geothermal water resource, at the same time it is proved feasible in practice to apply finite element numerical simulation to quantitative study of the geothermal water.
Weiser, Martin
2016-01-01
All relevant implementation aspects of finite element methods are discussed in this book. The focus is on algorithms and data structures as well as on their concrete implementation. Theory is covered as far as it gives insight into the construction of algorithms. Throughout the exercises a complete FE-solver for scalar 2D problems will be implemented in Matlab/Octave.
Fatigue assessment of an existing steel bridge by finite element modelling and field measurements
Kwad, J.; Alencar, G.; Correia, J.; Jesus, A.; Calçada, R.; Kripakaran, P.
2017-05-01
The evaluation of fatigue life of structural details in metallic bridges is a major challenge for bridge engineers. A reliable and cost-effective approach is essential to ensure appropriate maintenance and management of these structures. Typically, local stresses predicted by a finite element model of the bridge are employed to assess the fatigue life of fatigue-prone details. This paper illustrates an approach for fatigue assessment based on measured data for a connection in an old bascule steel bridge located in Exeter (UK). A finite element model is first developed from the design information. The finite element model of the bridge is calibrated using measured responses from an ambient vibration test. The stress time histories are calculated through dynamic analysis of the updated finite element model. Stress cycles are computed through the rainflow counting algorithm, and the fatigue prone details are evaluated using the standard SN curves approach and the Miner’s rule. Results show that the proposed approach can estimate the fatigue damage of a fatigue prone detail in a structure using measured strain data.
Boucher, C. R.; Li, Zehao; Ahheng, C. I.; Albrecht, J. D.; Ram-Mohan, L. R.
2016-04-01
Maxwell's vector field equations and their numerical solution represent significant challenges for physical domains with complex geometries. There are several limitations in the presently prevalent approaches to the calculation of field distributions in physical domains, in particular, with the vector finite elements. In order to quantify and resolve issues, we consider the modeling of the field equations for the prototypical examples of waveguides. We employ the finite element method with a new set of Hermite interpolation polynomials derived recently by us using group theoretic considerations. We show that (i) the approach presented here yields better accuracy by several orders of magnitude, with a smoother representation of fields than the vector finite elements for waveguide calculations. (ii) This method does not generate any spurious solutions that plague Lagrange finite elements, even though the C1 -continuous Hermite polynomials are also scalar in nature. (iii) We present solutions for propagating modes in inhomogeneous waveguides satisfying dispersion relations that can be derived directly, and investigate their behavior as the ratio of dielectric constants is varied both theoretically and numerically. Additional comparisons and advantages of the proposed method are detailed in this article. The Hermite interpolation polynomials are shown to provide a robust, accurate, and efficient means of solving Maxwell's equations in a variety of media, potentially offering a computationally inexpensive means of designing devices for optoelectronics and plasmonics of increasing complexity.
Hano, Mitsuo; Hotta, Masashi
A new multigrid method based on high-order vector finite elements is proposed in this paper. Low level discretizations in this method are obtained by using low-order vector finite elements for the same mesh. Gauss-Seidel method is used as a smoother, and a linear equation of lowest level is solved by ICCG method. But it is often found that multigrid solutions do not converge into ICCG solutions. An elimination algolithm of constant term using a null space of the coefficient matrix is also described. In three dimensional magnetostatic field analysis, convergence time and number of iteration of this multigrid method are discussed with the convectional ICCG method.
Institute of Scientific and Technical Information of China (English)
Monan Wang∗; Lei Sun
2015-01-01
A 3D femoral model was built to obtain the three⁃dimensional temperature distribution of femur and its surrounding tissues and provide references for clinical applications. According to the relationship between gray⁃value and material properties, the model was assigned with various materials to make sure that it is more similar to the real femur in geometry and physical properties. 3D temperature distribution is obtained by using finite element analysis software ANSYS 11�0 on the basis of heat conduction theory, Laplace equation, Pennes bio⁃heat transfer equation, thermo physical parameters of bone tissues, the boundary condition, and initial conditions. Taken the asymmetry of the 3D distribution of temperature into account, it is necessary to adopt the heating method with multiple heat sources. This method can ensure that the temperature fields match well with the tumor tissues and kill the tumor cells efficiently under the condition of protecting the normal tissues from damage. The analysis results supply important guidance for determining the needle position and the needle number and controlling the intensity of heating.
Application of finite-element sensitivities to power cable thermal field analysis
Energy Technology Data Exchange (ETDEWEB)
Al-Saud, M.S.; El-Kady, M.A.; Findlay, R.D. [McMaster Univ., Hamilton, ON (Canada). Dept. of Electrical and Computer Engineering
2006-07-01
A new approach for calculating the thermal field and ampacity of electrical cables was presented. The proposed perturbed finite-element analysis technique provides sensitivity information of the cable ampacity with respect to fluctuations in the cable thermal circuit parameters. As such, it can assess the effects on the permissible cable loading caused by these fluctuations without repeating the entire thermal analysis when parameters of the thermal circuit of power cables change according to geographical and seasonal variations. The technique can be applied to the design phase and the operational aspects of power cables buried in complex media of soil, heat sources and sinks or other variable boundary conditions. The sensitivity information is useful in determining the important and non-important parameter variations in terms of their relative effect on the cable temperature and ampacity. This paper described the analytical and computational aspects of the sensitivity methodology and demonstrated the usefulness of the developed methodology in 6 directly buried cable systems under different loading, soil and atmospheric conditions. The sensitivity results showed that the variations of the thermal conductivity of the soil affects the cable temperatures more than variations of other parameters. 8 refs., 5 tabs., 5 figs.
Directory of Open Access Journals (Sweden)
Nikolić Radovan H.
2014-01-01
Full Text Available This paper is the result of research and operation modeling of the new systems for cooling of cutting tools based on thermoelectric module. A copper inlay with thermoelectric module on the back side was added to a standard turning tool for metal processing. For modeling and simulating the operation of thermoelectric module, finite element method was used as a method for successful solving the problems of inhomogeneous transient temperature field on the cutting tip of lathe knives. Developed mathematical model is implemented in the software package PAK-T through which numerical results are obtained. Experimental research was done in different conditions of thermoelectric module operation. Cooling of the hot module side was done by a heat exchanger based on fluid using automatic temperature regulator. After the calculation is done, numerical results are in good agreement with experimental. It can be concluded that developed mathematical model can be used successfully for modeling of cooling of cutting tools. [Projekat Ministarstva nauke Republike Srbije, br. TR32036
A finite element approach to self-consistent field theory calculations of multiblock polymers
Ackerman, David M.; Delaney, Kris; Fredrickson, Glenn H.; Ganapathysubramanian, Baskar
2017-02-01
Self-consistent field theory (SCFT) has proven to be a powerful tool for modeling equilibrium microstructures of soft materials, particularly for multiblock polymers. A very successful approach to numerically solving the SCFT set of equations is based on using a spectral approach. While widely successful, this approach has limitations especially in the context of current technologically relevant applications. These limitations include non-trivial approaches for modeling complex geometries, difficulties in extending to non-periodic domains, as well as non-trivial extensions for spatial adaptivity. As a viable alternative to spectral schemes, we develop a finite element formulation of the SCFT paradigm for calculating equilibrium polymer morphologies. We discuss the formulation and address implementation challenges that ensure accuracy and efficiency. We explore higher order chain contour steppers that are efficiently implemented with Richardson Extrapolation. This approach is highly scalable and suitable for systems with arbitrary shapes. We show spatial and temporal convergence and illustrate scaling on up to 2048 cores. Finally, we illustrate confinement effects for selected complex geometries. This has implications for materials design for nanoscale applications where dimensions are such that equilibrium morphologies dramatically differ from the bulk phases.
Cai, Hongzhu; Hu, Xiangyun; Li, Jianhui; Endo, Masashi; Xiong, Bin
2017-02-01
We solve the 3D controlled-source electromagnetic (CSEM) problem using the edge-based finite element method. The modeling domain is discretized using unstructured tetrahedral mesh. We adopt the total field formulation for the quasi-static variant of Maxwell's equation and the computation cost to calculate the primary field can be saved. We adopt a new boundary condition which approximate the total field on the boundary by the primary field corresponding to the layered earth approximation of the complicated conductivity model. The primary field on the modeling boundary is calculated using fast Hankel transform. By using this new type of boundary condition, the computation cost can be reduced significantly and the modeling accuracy can be improved. We consider that the conductivity can be anisotropic. We solve the finite element system of equations using a parallelized multifrontal solver which works efficiently for multiple source and large scale electromagnetic modeling.
Institute of Scientific and Technical Information of China (English)
LI Yuguo; LUO Ming; PEI Jianxin
2013-01-01
In this paper,we extend the scope of numerical simulations of marine controlled-source electromagnetic (CSEM) fields in a particular case of anisotropy (dipping anisotropy) to the general case of anisotropy by using an adaptive finite element approach.In comparison to a dipping anisotropy case,the first order spatial derivatives of the strike-parallel components arise in the partial differential equations for generally anisotropic media,which cause a non-symmetric linear system of equations for finite element modeling.The adaptive finite element method is employed to obtain numerical solutions on a sequence of refined unstructured triangular meshes,which allows for arbitrary model geometries including bathymetry and dipping layers.Numerical results of a 2D anisotropic model show both anisotropy strike and dipping angles have great influence on the marine CSEM responses.
Institute of Scientific and Technical Information of China (English)
Zhang Xiaozhi; Hu Jinjun; Xie Lili; Wang Haiyun
2006-01-01
This paper briefly reviews the characteristics and major processes of the explicit finite element method in modeling the near-fault ground motion field. The emphasis is on the finite element-related problems in the finite fault source modeling. A modified kinematic source model is presented, in which vibration with some high frequency components is introduced into the traditional slip time function to ensure that the source and ground motion include sufficient high frequency components. The model presented is verified through a simple modeling example. It is shown that the predicted near-fault ground motion field exhibits similar characteristics to those observed in strong motion records, such as the hanging wall effect, vertical effect, fling step effect and velocity pulse effect, etc.
Wang, Wei; Qiao, Qingli; Gao, Weiping; Wu, Jun
2014-12-01
We studied the influence of electrode array parameters on temperature distribution to the retina during the use of retinal prosthesis in order to avoid thermal damage to retina caused by long-term electrical stimulation. Based on real epiretinal prosthesis, a three-dimensional model of electrical stimulation for retina with 4 X 4 microelectrode array had been established using the finite element software (COMSOL Multiphysics). The steady-state temperature field of electrical stimulation of the retina was calculated, and the effects of the electrode parameters such as the distance between the electrode contacts, the materials and area of the electrode contact on temperature field were considered. The maximum increase in the retina steady temperature was about 0. 004 degrees C with practical stimulation current. When the distance between the electrode contacts was changed from 130 microm to 520 microm, the temperature was reduced by about 0.006 microC. When the contact radius was doubled from 130 microm to 260 microm, the temperature decrease was about 0.005 degrees C. It was shown that there were little temperature changes in the retina with a 4 x 4 epiretinal microelectrode array, reflecting the safety of electrical stimulation. It was also shown that the maximum temperature in the retina decreased with increasing the distance between the electrode contacts, as well as increasing the area of electrode contact. However, the change of the maximum temperature was very small when the distance became larger than the diameter of electrode contact. There was no significant difference in the effects of temperature increase among the different electrode materials. Rational selection of the distance between the electrode contacts and their area in electrode design can reduce the temperature rise induced by electrical stimulation.
Finite Element Numerical Simulation and PIV Measurement of Flow Field inside Metering-in Spool Valve
Institute of Scientific and Technical Information of China (English)
GAO Dianrong; QIAO Haijun; LU Xianghui
2009-01-01
The finite element method (FEM) and particle image velocimetry (PIV) technique are utilized to get the flow field along the inlet passage, the chamber, the metering port and the outlet passage of spool valve at three different valve openings. For FEM numerical simulation, the stream function ψ -vorticity ω forms of continuity and Navier-Stokes equations are employed and FEM is applied to discrete the equations. Homemade simulation codes are executed to compute the values of stream function and vorticity at each node in the flow domain, then according to the correlation between stream function and velocity components, the velocity vectors of the whole field are calculated. For PIV experiment, pulse Nd: YAG laser is exploited to generate laser beam, cylindrical and spherical lenses are combined each other to produce 1.0 mm thickness laser sheet to illuminate the object plane, Polystyrene spherical particle with diameter of 30-50 μm is seeded in the fluid as a tracing particles, Kodak ES1.0 CCD camera is employed to capture the images of interested, the images are processed with fast Fourier transform (FFT) cross-correlation algorithm and the processing results is displayed. Both results of numerical simulation and PIV experimental show that there are three main areas in the spool valve where vortex is formed.Numerical results also indicate that the valve opening have some effects on the flow structure of the valve. The investigation is helpful for qualitatively analyzing the energy loss, noise generating, steady state flow forces and even designing the geometry structure and flow passage.
DEFF Research Database (Denmark)
Mikkelsen, Lars Pilgaard
2015-01-01
strength and fatigue performance is essential. Nevertheless, testing composites includes some challenges regarding stiffness determination using conventional strain gauges and achieving correct material failure unaffected by the gripping region during fatigue testing. Challenges, which in the present study......, has been addressed using the finite element method. During this, a verification of experimental observations, a deeper understanding on the test coupon loading and thereby improved test methods has been achieved....
3D Finite Element Modeling of the 2009 L'Aquila Earthquake Deformation Field
Volpe, M.; Casarotti, E.; Piersanti, A.
2009-12-01
The L'Aquila earthquake (Mw 6.3) occurred on April 6th at 01:32 UTC in the Central Appennines at a depth of about 9 km and was felt all over Central Italy. The main shock was preceded by a long seismic sequence started several months before and was followed by thousands of aftershocks, some of them with Mw>4. We built up a high resolution three-dimensional model, incorporating surface topography, which was discretized using 20-nodes brick elements. The element horizontal size is biased from 500 m to 2 km using the paving meshing algorithm in combination with an appropriate adaptive sizing function. A realistic rheology was introduced from a vp/vpvs travel time tomographic model. We computed the co-seismic deformation induced by the earthquake by means of a recently developed finite elements simulation tool, FEMSA (Finite Element Modeling for Seismic Applications). We used different seismic source models obtained from fault inversion of GPS measurements, joint inversion of strong motion and GPS data and from inversion of DInSAR displacements. The synthetic deformation patterns were compared with the experimental results in order to evaluate which source model better reconciles the data and quantify the trade off introduced by 1D simulations.
Institute of Scientific and Technical Information of China (English)
Qiang Du; Liyong Zhu
2006-01-01
In this paper, we study numerical approximations of a recently proposed phase field model for the vesicle membrane deformation governed by the variation of the elastic bending energy. To overcome the challenges of high order nonlinear differential systems and the nonlinear constraints associated with the problem, we present the phase field bending elasticity model in a nested saddle point formulation. A mixed finite element method is then employed to compute the equilibrium configuration of a vesicle membrane with prescribed volume and surface area. Coupling the approximation results for a related linearized problem and the general theory of Brezzi-Rappaz-Raviart, optimal order error estimates for the finite element approximations of the phase field model are obtained. Numerical results areprovided to substantiate the derived estimates.
Simulation of near-fault bedrock strong ground-motion field by explicit finite element method
Institute of Scientific and Technical Information of China (English)
ZHANG Xiao-zhi; HU Jin-jun; XIE Li-li; WANG Hai-yun
2006-01-01
Based on presumed active fault and corresponding model, this paper predicted the near-fault ground motion filed of a scenario earthquake (Mw=6 3/4 ) in an active fault by the explicit finite element method in combination with the source time function with improved transmitting artificial boundary and with high-frequency vibration contained.The results indicate that the improved artificial boundary is stable in numerical computation and the predicted strong ground motion has a consistent characteristic with the observed motion.
Electrical machine analysis using finite elements
Bianchi, Nicola
2005-01-01
OUTLINE OF ELECTROMAGNETIC FIELDSVector AnalysisElectromagnetic FieldsFundamental Equations SummaryReferencesBASIC PRINCIPLES OF FINITE ELEMENT METHODSIntroductionField Problems with Boundary ConditionsClassical Method for the Field Problem SolutionThe Classical Residual Method (Galerkin's Method)The Classical Variational Method (Rayleigh-Ritz's Method)The Finite Element MethodReferencesAPPLICATIONS OF THE FINITE ELEMENT METHOD TO TWO-DIMENSIONAL FIELDSIntroductionLinear Interpolation of the Function fApplication of the Variational MethodSimple Descriptions of Electromagnetic FieldsAppendix: I
Automation of finite element methods
Korelc, Jože
2016-01-01
New finite elements are needed as well in research as in industry environments for the development of virtual prediction techniques. The design and implementation of novel finite elements for specific purposes is a tedious and time consuming task, especially for nonlinear formulations. The automation of this process can help to speed up this process considerably since the generation of the final computer code can be accelerated by order of several magnitudes. This book provides the reader with the required knowledge needed to employ modern automatic tools like AceGen within solid mechanics in a successful way. It covers the range from the theoretical background, algorithmic treatments to many different applications. The book is written for advanced students in the engineering field and for researchers in educational and industrial environments.
Rout, Matruprasad; Pal, Surjya Kanta; Singh, Shiv Brat
2017-02-01
Studies on the effect of strain path during rolling has been carried out for a long time, but the same has not been done using Finite Element Analysis (FEA). Change in strain path affects the state variables in the rolled plate like stress, strain, temperature etc. In the current work, Finite Element Analysis for cross rolling of AISI 304 austenitic stainless steel has been carried out by rotating the plate by 90° in between the passes. To analyze stress and strain fields in the material for cross rolling, a full 3D model of work-roll and plate has been developed using rigid-viscoplastic finite element method. The stress and strain fields, considering von-Mises yield criteria, are calculated by using updated Lagrangian method. In addition to these, the model also calculates the normal pressure and strain rate distribution in the plate during cross rolling. The nature of the variations of stress and strain fields in the plate, predicted by the model, is in good agreement with the previously published works for unidirectional rolling.
Institute of Scientific and Technical Information of China (English)
曹代勇; 张杰林; 关英斌; 钱光谟; 吴国强; 韩远方; 赵志明
1995-01-01
The structural deformation of Lu' an mining area is characterized by a remarkable feature of zoning along E-W direction, in the east.limb of Qinshui basin, Shanxi Province, China. The regional tectonic stress fields and basement tectonics are two fundamental factors to control the cover tectonic framework. This paper uses the finite-element method with a elastic-plastic plan problem model to simulate the three periods of stress fields resulting from field geological study. Based on these works, the formation and evolution of tectonic framework of Lu' an mining area have been discussed.
Field Test of a Hybrid Finite-Difference and Analytic Element Regional Model.
Abrams, D B; Haitjema, H M; Feinstein, D T; Hunt, R J
2016-01-01
Regional finite-difference models often have cell sizes that are too large to sufficiently model well-stream interactions. Here, a steady-state hybrid model is applied whereby the upper layer or layers of a coarse MODFLOW model are replaced by the analytic element model GFLOW, which represents surface waters and wells as line and point sinks. The two models are coupled by transferring cell-by-cell leakage obtained from the original MODFLOW model to the bottom of the GFLOW model. A real-world test of the hybrid model approach is applied on a subdomain of an existing model of the Lake Michigan Basin. The original (coarse) MODFLOW model consists of six layers, the top four of which are aggregated into GFLOW as a single layer, while the bottom two layers remain part of MODFLOW in the hybrid model. The hybrid model and a refined "benchmark" MODFLOW model simulate similar baseflows. The hybrid and benchmark models also simulate similar baseflow reductions due to nearby pumping when the well is located within the layers represented by GFLOW. However, the benchmark model requires refinement of the model grid in the local area of interest, while the hybrid approach uses a gridless top layer and is thus unaffected by grid discretization errors. The hybrid approach is well suited to facilitate cost-effective retrofitting of existing coarse grid MODFLOW models commonly used for regional studies because it leverages the strengths of both finite-difference and analytic element methods for predictions in mildly heterogeneous systems that can be simulated with steady-state conditions.
GPU-based interactive cut-surface extraction from high-order finite element fields.
Nelson, Blake; Haimes, Robert; Kirby, Robert M
2011-12-01
We present a GPU-based ray-tracing system for the accurate and interactive visualization of cut-surfaces through 3D simulations of physical processes created from spectral/hp high-order finite element methods. When used by the numerical analyst to debug the solver, the ability for the imagery to precisely reflect the data is critical. In practice, the investigator interactively selects from a palette of visualization tools to construct a scene that can answer a query of the data. This is effective as long as the implicit contract of image quality between the individual and the visualization system is upheld. OpenGL rendering of scientific visualizations has worked remarkably well for exploratory visualization for most solver results. This is due to the consistency between the use of first-order representations in the simulation and the linear assumptions inherent in OpenGL (planar fragments and color-space interpolation). Unfortunately, the contract is broken when the solver discretization is of higher-order. There have been attempts to mitigate this through the use of spatial adaptation and/or texture mapping. These methods do a better job of approximating what the imagery should be but are not exact and tend to be view-dependent. This paper introduces new rendering mechanisms that specifically deal with the kinds of native data generated by high-order finite element solvers. The exploratory visualization tools are reassessed and cast in this system with the focus on image accuracy. This is accomplished in a GPU setting to ensure interactivity.
Solution of Finite Element Equations
DEFF Research Database (Denmark)
Krenk, Steen
An important step in solving any problem by the finite element method is the solution of the global equations. Numerical solution of linear equations is a subject covered in most courses in numerical analysis. However, the equations encountered in most finite element applications have some special...
Advanced finite element method in structural engineering
Long, Yu-Qiu; Long, Zhi-Fei
2009-01-01
This book systematically introduces the research work on the Finite Element Method completed over the past 25 years. Original theoretical achievements and their applications in the fields of structural engineering and computational mechanics are discussed.
Massively Parallel Finite Element Programming
Heister, Timo
2010-01-01
Today\\'s large finite element simulations require parallel algorithms to scale on clusters with thousands or tens of thousands of processor cores. We present data structures and algorithms to take advantage of the power of high performance computers in generic finite element codes. Existing generic finite element libraries often restrict the parallelization to parallel linear algebra routines. This is a limiting factor when solving on more than a few hundreds of cores. We describe routines for distributed storage of all major components coupled with efficient, scalable algorithms. We give an overview of our effort to enable the modern and generic finite element library deal.II to take advantage of the power of large clusters. In particular, we describe the construction of a distributed mesh and develop algorithms to fully parallelize the finite element calculation. Numerical results demonstrate good scalability. © 2010 Springer-Verlag.
Energy Technology Data Exchange (ETDEWEB)
Jamshidian, M., E-mail: jamshidian@cc.iut.ac.ir [Department of Mechanical Engineering, Isfahan University of Technology, Isfahan 84156-83111 (Iran, Islamic Republic of); Institute of Structural Mechanics, Bauhaus-University Weimar, Marienstrasse 15, 99423 Weimar (Germany); Thamburaja, P., E-mail: prakash.thamburaja@gmail.com [Department of Mechanical & Materials Engineering, Universiti Kebangsaan Malaysia (UKM), Bangi 43600 (Malaysia); Rabczuk, T., E-mail: timon.rabczuk@tdt.edu.vn [Division of Computational Mechanics, Ton Duc Thang University, Ho Chi Minh City (Viet Nam); Faculty of Civil Engineering, Ton Duc Thang University, Ho Chi Minh City (Viet Nam)
2016-12-15
A previously-developed finite-deformation- and crystal-elasticity-based constitutive theory for stressed grain growth in cubic polycrystalline bodies has been augmented to include a description of excess surface energy and grain-growth stagnation mechanisms through the use of surface effect state variables in a thermodynamically-consistent manner. The constitutive theory was also implemented into a multiscale coupled finite-element and phase-field computational framework. With the material parameters in the constitutive theory suitably calibrated, our three-dimensional numerical simulations show that the constitutive model is able to accurately predict the experimentally-determined evolution of crystallographic texture and grain size statistics in polycrystalline copper thin films deposited on polyimide substrate and annealed at high-homologous temperatures. In particular, our numerical analyses show that the broad texture transition observed in the annealing experiments of polycrystalline thin films is caused by grain growth stagnation mechanisms. - Graphical abstract: - Highlights: • Developing a theory for stressed grain growth in polycrystalline thin films. • Implementation into a multiscale coupled finite-element and phase-field framework. • Quantitative reproduction of the experimental grain growth data by simulations. • Revealing the cause of texture transition to be due to the stagnation mechanisms.
Mullen, Gary L
2013-01-01
Poised to become the leading reference in the field, the Handbook of Finite Fields is exclusively devoted to the theory and applications of finite fields. More than 80 international contributors compile state-of-the-art research in this definitive handbook. Edited by two renowned researchers, the book uses a uniform style and format throughout and each chapter is self contained and peer reviewed. The first part of the book traces the history of finite fields through the eighteenth and nineteenth centuries. The second part presents theoretical properties of finite fields, covering polynomials,
The finite element method in electromagnetics
Jin, Jianming
2014-01-01
A new edition of the leading textbook on the finite element method, incorporating major advancements and further applications in the field of electromagnetics The finite element method (FEM) is a powerful simulation technique used to solve boundary-value problems in a variety of engineering circumstances. It has been widely used for analysis of electromagnetic fields in antennas, radar scattering, RF and microwave engineering, high-speed/high-frequency circuits, wireless communication, electromagnetic compatibility, photonics, remote sensing, biomedical engineering, and space exploration. The
Directory of Open Access Journals (Sweden)
Constantin Gabriel Dobrean
2016-10-01
Full Text Available The study shows the numerical simulation of the magnetic field for a permanent magnet synchronous generator prototype. Through the study, the OPERA software environment, a program based on the numerical computation using the finite element method and used for the virtual simulation of the synchronous generator prototype, is shown. This 5 kVA power, permanent magnet and low speed prototype is meant for uses in hydraulic driven applications, namely wind applications, and was performed within a cooperations between the Faculty of Automation and Computers and the Faculty of Electrical and Power Engineering within the “Politehnica” University of Timișoara.
Finite element and finite difference methods in electromagnetic scattering
Morgan, MA
2013-01-01
This second volume in the Progress in Electromagnetic Research series examines recent advances in computational electromagnetics, with emphasis on scattering, as brought about by new formulations and algorithms which use finite element or finite difference techniques. Containing contributions by some of the world's leading experts, the papers thoroughly review and analyze this rapidly evolving area of computational electromagnetics. Covering topics ranging from the new finite-element based formulation for representing time-harmonic vector fields in 3-D inhomogeneous media using two coupled sca
quadratic spline finite element method
Directory of Open Access Journals (Sweden)
A. R. Bahadir
2002-01-01
Full Text Available The problem of heat transfer in a Positive Temperature Coefficient (PTC thermistor, which may form one element of an electric circuit, is solved numerically by a finite element method. The approach used is based on Galerkin finite element using quadratic splines as shape functions. The resulting system of ordinary differential equations is solved by the finite difference method. Comparison is made with numerical and analytical solutions and the accuracy of the computed solutions indicates that the method is well suited for the solution of the PTC thermistor problem.
Finite element computational fluid mechanics
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.
Programming the finite element method
Smith, I M; Margetts, L
2013-01-01
Many students, engineers, scientists and researchers have benefited from the practical, programming-oriented style of the previous editions of Programming the Finite Element Method, learning how to develop computer programs to solve specific engineering problems using the finite element method. This new fifth edition offers timely revisions that include programs and subroutine libraries fully updated to Fortran 2003, which are freely available online, and provides updated material on advances in parallel computing, thermal stress analysis, plasticity return algorithms, convection boundary c
Schröder, Jörg; Viebahn, Nils; Wriggers, Peter; Auricchio, Ferdinando; Steeger, Karl
2017-05-01
In this work we investigate different mixed finite element formulations for the detection of critical loads for the possible occurrence of bifurcation and limit points. In detail, three- and two-field formulations for incompressible and quasi-incompressible materials are analyzed. In order to apply various penalty functions for the volume dilatation in displacement/pressure mixed elements we propose a new consistent scheme capturing the non linearities of the penalty constraints. It is shown that for all mixed formulations, which can be reduced to a generalized displacement scheme, a straight forward stability analysis is possible. However, problems based on the classical saddle-point structure require a different analyses based on the change of the signature of the underlying matrix system. The basis of these investigations is the work from Auricchio et al. (Comput Methods Appl Mech Eng 194:1075-1092, 2005, Comput Mech 52:1153-1167, 2013).
DEFF Research Database (Denmark)
Damkilde, Lars; Pedersen, Ronnie
2012-01-01
This paper describes a new triangular plane element which can be considered as a linear strain triangular element (LST) extended with incompatible displacement modes. The extended element will have a full cubic interpolation of strains and stresses. The extended LST-element is connected with other...... elements similar to the LST-element i.e. through three corner nodes and three mid-side nodes. The incompatible modes are associated with two displacement gradients at each mid-side node and displacements in the central node. The element passes the patch test and converges to the exact solution. The element...... has been tested on a standard linear test such as Cook’s panel, and is shown as expected to be somewhat more flexible than the LST-element and the compatible quadratic strain element (QST). The extended element has also been applied to material non-linear geotechnical problems. Geotechnical problems...
Second order tensor finite element
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.
Institute of Scientific and Technical Information of China (English)
Hao Kuan-Sheng; Huang Song-Ling; Zhao Wei; Wang Shen
2011-01-01
This paper presents an analytical method for electromagnetic acoustic transducers (EMATs) under voltage excitation and considers the non-uniform distribution of the biased magnetic field. A complete model of EMATs including the non-uniform biased magnetic field, a pulsed eddy current field and the acoustic field is built up. The pulsed voltage excitation is transformed to the frequency domain by fast Fourier transformation (FFT). In terms of the time harmonic field equations of the EMAT system, the impedances of the coils under different frequencies are calculated according to the circuit-field coupling method and Poynting's theorem. Then the currents under different frequencies are calculated according to Ohm's law and the pulsed current excitation is obtained by inverse fast Fourier transformation (IFFT).Lastly, the sequentially coupled finite element method (FEM) is used to calculate the Lorentz force in the EMATs under the current excitation. An actual EMAT with a two-layer two-bundle printed circuit board (PCB) coil, a rectangular permanent magnet and an aluminium specimen is analysed. The coil impedances and the pulsed current are calculated and compared with the experimental results. Their agreement verified the validity of the proposed method. Furthermore, the influences of lift-off distances and the non-uniform static nagnetic field on the Lorentz force under pulsed voltage excitation are studied.
Finite element methods for engineers
Fenner, Roger T
2013-01-01
This book is intended as a textbook providing a deliberately simple introduction to finite element methods in a way that should be readily understandable to engineers, both students and practising professionals. Only the very simplest elements are considered, mainly two dimensional three-noded “constant strain triangles”, with simple linear variation of the relevant variables. Chapters of the book deal with structural problems (beams), classification of a broad range of engineering into harmonic and biharmonic types, finite element analysis of harmonic problems, and finite element analysis of biharmonic problems (plane stress and plane strain). Full Fortran programs are listed and explained in detail, and a range of practical problems solved in the text. Despite being somewhat unfashionable for general programming purposes, the Fortran language remains very widely used in engineering. The programs listed, which were originally developed for use on mainframe computers, have been thoroughly updated for use ...
Energy Technology Data Exchange (ETDEWEB)
Aristovich, K Y; Khan, S H [School of Engineering and Mathematical Sciences, City University London, Northampton Square, London EC1V 0HB (United Kingdom); Borovkov, A I, E-mail: kirill.aristovich.1@city.ac.uk [St Petersburg State Polytechnic University, Polytechnicheskaya Street 29, St Petersburg, 195251 (Russian Federation)
2011-08-17
This paper presents an investigation of optimal parameters for finite element (FE) solution of the forward problem in magnetic field tomography (MFT) brain imaging based on magnetoencephalography (MEG). It highlights detailed analyses of the main parameters involved and evaluates their optimal values for various cases of FE model solutions (e.g., steady-state, transient, etc.). In each case, a detail study of some of the main parameters and their effects on FE solution and its accuracy are carefully tested and evaluated. These parameters include: total number and size of 3D FE elements used, number and size of elements used in surface discretisation (of both white and grey matters of the brain), number and size of elements used for approximation of current sources, number of anisotropic properties used in steady-state and transient solutions, and the time steps used in transient analyses. The optimal values of these parameters in relation to solution accuracy and mesh convergence criteria have been found and presented.
Aristovich, K. Y.; Khan, S. H.; Borovkov, A. I.
2011-08-01
This paper presents an investigation of optimal parameters for finite element (FE) solution of the forward problem in magnetic field tomography (MFT) brain imaging based on magnetoencephalography (MEG). It highlights detailed analyses of the main parameters involved and evaluates their optimal values for various cases of FE model solutions (e.g., steady-state, transient, etc.). In each case, a detail study of some of the main parameters and their effects on FE solution and its accuracy are carefully tested and evaluated. These parameters include: total number and size of 3D FE elements used, number and size of elements used in surface discretisation (of both white and grey matters of the brain), number and size of elements used for approximation of current sources, number of anisotropic properties used in steady-state and transient solutions, and the time steps used in transient analyses. The optimal values of these parameters in relation to solution accuracy and mesh convergence criteria have been found and presented.
Lee, Won Hee; Deng, Zhi-De; Kim, Tae-Seong; Laine, Andrew F.; Lisanby, Sarah H.; Peterchev, Angel V.
2012-01-01
We present the first computational study investigating the electric field (E-field) strength generated by various electroconvulsive therapy (ECT) electrode configurations in specific brain regions of interest (ROIs) that have putative roles in the therapeutic action and/or adverse side effects of ECT. This study also characterizes the impact of the white matter (WM) conductivity anisotropy on the E-field distribution. A finite element head model incorporating tissue heterogeneity and WM anisotropic conductivity was constructed based on structural magnetic resonance imaging (MRI) and diffusion tensor MRI data. We computed the spatial E-field distributions generated by three standard ECT electrode placements including bilateral (BL), bifrontal (BF), and right unilateral (RUL) and an investigational electrode configuration for focal electrically administered seizure therapy (FEAST). The key results are that (1) the median E-field strength over the whole brain is 3.9, 1.5, 2.3, and 2.6 V/cm for the BL, BF, RUL, and FEAST electrode configurations, respectively, which coupled with the broad spread of the BL E-field suggests a biophysical basis for observations of superior efficacy of BL ECT compared to BF and RUL ECT; (2) in the hippocampi, BL ECT produces a median E-field of 4.8 V/cm that is 1.5–2.8 times stronger than that for the other electrode configurations, consistent with the more pronounced amnestic effects of BL ECT; and (3) neglecting the WM conductivity anisotropy results in E-field strength error up to 18% overall and up to 39% in specific ROIs, motivating the inclusion of the WM conductivity anisotropy in accurate head models. This computational study demonstrates how the realistic finite element head model incorporating tissue conductivity anisotropy provides quantitative insight into the biophysics of ECT, which may shed light on the differential clinical outcomes seen with various forms of ECT, and may guide the development of novel stimulation
Institute of Scientific and Technical Information of China (English)
J. Li; W. Liu; Y.Q. Lai; Q.Y. Li; Y.X. Liu
2006-01-01
Two full 3D steady mathematical models are developed by finite element method (FEM) to calculate coupled physics fields: the electro-magnetic model is built and solved first and so is the fluid motion model with the acquired electromagnetic force as source body forces in Navier-Stokes equations. Effects caused by the ferromagnetic shell, busbar system around, and open boundary problem as well as inside induced current were considered in terms of the magnetic field. Furthermore, a new modeling method is found to set up solid models and then mesh them entirely with so-called structuralized grids, namely hex-mesh. Examples of 75kA prebaked cell with two kinds of busbar arrangements are presented. Results agree with those disclosed in the literature and confirm that the coupled simulation is valid. It is also concluded that the usage of these models facilitates the consistent analysis of the electric field to magnetic field and then flow motion to the greater extent, local distributions of current density and magnetic flux density are very much dependent on the cell structure, the steel shell is a shield to reduce the magnetic field and flow pattern is two dimensional in the main body of the metal pad.
Averett, Rodney D; Scogin, Tyler; Walker, Mitchell L R
2016-01-01
Blood clots occur in the human body when they are required to prevent bleeding. In pathological states such as diabetes and sickle cell disease, blood clots can also form undesirably due to hypercoagulable plasma conditions. With the continued effort in developing fibrin therapies for potential life-saving solutions, more mechanical modeling is needed to understand the properties of fibrin structures with inclusions. In this study, a fibrin matrix embedded with magnetic micro particles was subjected to a magnetic field to determine the plastic deformation of the clot. Using finite element analysis, we estimate the magnetic force from an electromagnet at a sample space located approximately 3 cm away from the coil center. This electromagnetic force along with gravity is applied on a fibrin sub model to calculate the stresses and displacements. Initial analyses show the forces are not sufficient to create fibrinolysis and hence we extended the study using parametric sweep analysis and redesign the coil paramete...
Energy Technology Data Exchange (ETDEWEB)
Aristovich, K Y; Khan, S H, E-mail: kirill.aristovich.1@city.ac.u [School of Engineering and Mathematical Sciences, City University London, Northampton Square, London EC1V 0HB (United Kingdom)
2010-07-01
Complex multi-scale Finite Element (FE) analyses always involve high number of elements and therefore require very long time of computations. This is caused by the fact, that considered effects on smaller scales have greater influences on the whole model and larger scales. Thus, mesh density should be as high as required by the smallest scale factor. New submodelling routine has been developed to sufficiently decrease the time of computation without loss of accuracy for the whole solution. The presented approach allows manipulation of different mesh sizes on different scales and, therefore total optimization of mesh density on each scale and transfer results automatically between the meshes corresponding to respective scales of the whole model. Unlike classical submodelling routine, the new technique operates with not only transfer of boundary conditions but also with volume results and transfer of forces (current density load in case of electromagnetism), which allows the solution of full Maxwell's equations in FE space. The approach was successfully implemented for electromagnetic solution in the forward problem of Magnetic Field Tomography (MFT) based on Magnetoencephalography (MEG), where the scale of one neuron was considered as the smallest and the scale of whole-brain model as the largest. The time of computation was reduced about 100 times, with the initial requirements of direct computations without submodelling routine of 10 million elements.
Finite elements of nonlinear continua
Oden, J T
2000-01-01
Geared toward undergraduate and graduate students, this text extends applications of the finite element method from linear problems in elastic structures to a broad class of practical, nonlinear problems in continuum mechanics. It treats both theory and applications from a general and unifying point of view.The text reviews the thermomechanical principles of continuous media and the properties of the finite element method, and then brings them together to produce discrete physical models of nonlinear continua. The mathematical properties of these models are analyzed, along with the numerical s
FINITE ELEMENT ANALYSIS OF STRUCTURES
Directory of Open Access Journals (Sweden)
PECINGINA OLIMPIA-MIOARA
2015-05-01
Full Text Available The application of finite element method is analytical when solutions can not be applied for deeper study analyzes static, dynamic or other types of requirements in different points of the structures .In practice it is necessary to know the behavior of the structure or certain parts components of the machine under the influence of certain factors static and dynamic . The application of finite element in the optimization of components leads to economic growth , to increase reliability and durability organs studied, thus the machine itself.
Reinoso, J.; Paggi, M.; Linder, C.
2017-02-01
Fracture of technological thin-walled components can notably limit the performance of their corresponding engineering systems. With the aim of achieving reliable fracture predictions of thin structures, this work presents a new phase field model of brittle fracture for large deformation analysis of shells relying on a mixed enhanced assumed strain (EAS) formulation. The kinematic description of the shell body is constructed according to the solid shell concept. This enables the use of fully three-dimensional constitutive models for the material. The proposed phase field formulation integrates the use of the (EAS) method to alleviate locking pathologies, especially Poisson thickness and volumetric locking. This technique is further combined with the assumed natural strain method to efficiently derive a locking-free solid shell element. On the computational side, a fully coupled monolithic framework is consistently formulated. Specific details regarding the corresponding finite element formulation and the main aspects associated with its implementation in the general purpose packages FEAP and ABAQUS are addressed. Finally, the applicability of the current strategy is demonstrated through several numerical examples involving different loading conditions, and including linear and nonlinear hyperelastic constitutive models.
Reinoso, J.; Paggi, M.; Linder, C.
2017-06-01
Fracture of technological thin-walled components can notably limit the performance of their corresponding engineering systems. With the aim of achieving reliable fracture predictions of thin structures, this work presents a new phase field model of brittle fracture for large deformation analysis of shells relying on a mixed enhanced assumed strain (EAS) formulation. The kinematic description of the shell body is constructed according to the solid shell concept. This enables the use of fully three-dimensional constitutive models for the material. The proposed phase field formulation integrates the use of the (EAS) method to alleviate locking pathologies, especially Poisson thickness and volumetric locking. This technique is further combined with the assumed natural strain method to efficiently derive a locking-free solid shell element. On the computational side, a fully coupled monolithic framework is consistently formulated. Specific details regarding the corresponding finite element formulation and the main aspects associated with its implementation in the general purpose packages FEAP and ABAQUS are addressed. Finally, the applicability of the current strategy is demonstrated through several numerical examples involving different loading conditions, and including linear and nonlinear hyperelastic constitutive models.
Finite-element analysis of magnetic field driven transport at inlaid platinum microdisk electrodes.
Mehta, Dipesh; White, Henry S
2003-02-17
We describe a computer-assisted analysis of three-dimensional magnetohydrodynamic (MHD) fluid flow resulting from the passage of electrochemically generated charge through a uniform magnetic field. Magnetic field driven molecular transport in electrochemical systems offers a number of emerging opportunities in research and technology. For instance, electrochemical microfluidic transport and molecule trapping using magnetic fields and field gradients have been demonstrated in recent reports from this laboratory. A key limitation of these investigations is the difficulty in analyzing magnetic field driven flow and transport, due to the complexity of the governing equations of fluid mechanics, electrochemical molecular transport, and magnetic forces. In general, quantitative expressions describing the distribution and fluxes of electroactive species under the influence of a magnetic field cannot be obtained by a direct analytical solution.
Latest Trends in Finite Element Analysis
Directory of Open Access Journals (Sweden)
L. S. Madhav
1996-01-01
Full Text Available This paper highlights the advances in computer graphics and the computational power of the processors which have promoted a method of analysis, applicable to almost all the fields of engineering. The advantages of the computers have been judiciously used in the design of algorithms, based on the principles of finite difference, finite element, boundary element, etc., intended for the analysis of engineering components. The concept of finite element method which has been generalised with the availability of commercial software, is also reviewed with a special emphasis on the future trends. The modelling and visualisation techniques have also been discussed with an inner perspective on future of visual display of multidimensional complex information. The application of these techniques in some fields is also indicated.
Tomio, Ryosuke; Akiyama, Takenori; Horikoshi, Tomo; Ohira, Takayuki; Yoshida, Kazunari
2015-12-30
Transcranial MEP (tMEP) monitoring is more readily performed than cortical MEP (cMEP), however, tMEP is considered as less accurate than cMEP. The craniotomy procedure and changes in CSF levels must affect current spread. These changes can impair the accuracy. The aim of this study was to investigate the influence of skull deformation and cerebrospinal fluid (CSF) decrease on tMEP monitoring during frontotemporal craniotomy. We used the finite element method to visualize the electric field in the brain, which was generated by transcranial electric stimulation, using realistic 3-dimensional head models developed from T1-weighted images. Surfaces of 5 layers of the head were separated as accurately as possible. We created 3 brain types and 5 craniotomy models. The electric field in the brain radiates out from the cortex just below the electrodes. When the CSF layer is thick, a decrease in CSF volume and depression of CSF surface level during the craniotomy has a major impact on the electric field. When the CSF layer is thin and the distance between the skull and brain is short, the craniotomy has a larger effect on the electric field than the CSF decrease. So far no report in the literature the electric field during intraoperative tMEP using a 3-dimensional realistic head model. Our main finding was that the intensity of the electric field in the brain is most affected by changes in the thickness and volume of the CSF layer. Copyright © 2015 Elsevier B.V. All rights reserved.
The Relation of Finite Element and Finite Difference Methods
Vinokur, M.
1976-01-01
Finite element and finite difference methods are examined in order to bring out their relationship. It is shown that both methods use two types of discrete representations of continuous functions. They differ in that finite difference methods emphasize the discretization of independent variable, while finite element methods emphasize the discretization of dependent variable (referred to as functional approximations). An important point is that finite element methods use global piecewise functional approximations, while finite difference methods normally use local functional approximations. A general conclusion is that finite element methods are best designed to handle complex boundaries, while finite difference methods are superior for complex equations. It is also shown that finite volume difference methods possess many of the advantages attributed to finite element methods.
García, E.; Oliver, A.; Diaz, O.; Diez, Y.; Gubern-Mérida, A.; Martí, R.; Martí, J.
2017-03-01
Patient-specific finite element (FE) models of the breast have received increasing attention due to the potential capability of fusing images from different modalities. During the Magnetic Resonance Imaging (MRI) to X-ray mammography registration procedure, the FE model is compressed mimicking the mammographic acquisition. Subsequently, suspicious lesions in the MRI volume can be projected into the 2D mammographic space. However, most registration algorithms do not provide the reverse information, avoiding to obtain the 3D geometrical information from the lesions localized in the mammograms. In this work we introduce a fast method to localize the 3D position of the lesion within the MRI, using both cranio-caudal (CC) and medio-lateral oblique (MLO) mammographic projections, indexing the tetrahedral elements of the biomechanical model by means of an uniform grid. For each marked lesion in the Full-Field Digital Mammogram (FFDM), the X-ray path from source to the marker is calculated. Barycentric coordinates are computed in the tetrahedrons traversed by the ray. The list of elements and coordinates allows to localize two curves within the MRI and the closest point between both curves is taken as the 3D position of the lesion. The registration errors obtained in the mammographic space are 9.89 +/- 3.72 mm in CC- and 8.04 +/- 4.68 mm in MLO-projection and the error in the 3D MRI space is equal to 10.29 +/- 3.99 mm. Regarding the uniform grid, it is computed spending between 0.1 and 0.7 seconds. The average time spent to compute the 3D location of a lesion is about 8 ms.
3D Finite Element Analysis of TBM Water Diversion Tunnel Segment Coupled with Seepage Field
Institute of Scientific and Technical Information of China (English)
钟登华; 胡能明; 程正飞; 吕鹏; 佟大威
2016-01-01
In most studies of tunnel boring machine(TBM)tunnelling, the groundwater pressure was not consid-ered, or was simplified and exerted on the boundary of lining structure. Meanwhile, the leakage, which mainly oc-curs in the segment joints, was often ignored in the relevant studies of TBM tunnelling. Additionally, the geological models in these studies were simplified to different extents, and mostly were simplified as homogenous bodies. Considering the deficiencies above, a 3D refined model of the surrounding rock of a tunnel is firstly established using NURBS-TIN-BReP hybrid data structure in this paper. Then the seepage field of the surrounding rock con-sidering the leakage in the segment joints is simulated. Finally, the stability of TBM water diversion tunnel is stud-ied coupled with the seepage simulation, to analyze the stress-strain conditions, the axial force and the bending moment of tunnel segment considering the leakage in the segment joints. The results illustrate that the maximum radial displacement, the minimum principal stress, the maximum principal stress and the axial force of segment lining considering the seepage effect are all larger than those disregarding the seepage effect.
DOLFIN: Automated Finite Element Computing
Logg, Anders; 10.1145/1731022.1731030
2011-01-01
We describe here a library aimed at automating the solution of partial differential equations using the finite element method. By employing novel techniques for automated code generation, the library combines a high level of expressiveness with efficient computation. Finite element variational forms may be expressed in near mathematical notation, from which low-level code is automatically generated, compiled and seamlessly integrated with efficient implementations of computational meshes and high-performance linear algebra. Easy-to-use object-oriented interfaces to the library are provided in the form of a C++ library and a Python module. This paper discusses the mathematical abstractions and methods used in the design of the library and its implementation. A number of examples are presented to demonstrate the use of the library in application code.
Finite elements methods in mechanics
Eslami, M Reza
2014-01-01
This book covers all basic areas of mechanical engineering, such as fluid mechanics, heat conduction, beams, and elasticity with detailed derivations for the mass, stiffness, and force matrices. It is especially designed to give physical feeling to the reader for finite element approximation by the introduction of finite elements to the elevation of elastic membrane. A detailed treatment of computer methods with numerical examples are provided. In the fluid mechanics chapter, the conventional and vorticity transport formulations for viscous incompressible fluid flow with discussion on the method of solution are presented. The variational and Galerkin formulations of the heat conduction, beams, and elasticity problems are also discussed in detail. Three computer codes are provided to solve the elastic membrane problem. One of them solves the Poisson’s equation. The second computer program handles the two dimensional elasticity problems, and the third one presents the three dimensional transient heat conducti...
Selective Smoothed Finite Element Method
Institute of Scientific and Technical Information of China (English)
无
2007-01-01
The paper examines three selective schemes for the smoothed finite element method (SFEM) which was formulated by incorporating a cell-wise strain smoothing operation into the standard compatible finite element method (FEM). These selective SFEM schemes were formulated based on three selective integration FEM schemes with similar properties found between the number of smoothing cells in the SFEM and the number of Gaussian integration points in the FEM. Both scheme 1 and scheme 2 are free of nearly incompressible locking, but scheme 2 is more general and gives better results than scheme 1. In addition, scheme 2 can be applied to anisotropic and nonlinear situations, while scheme 1 can only be applied to isotropic and linear situations. Scheme 3 is free of shear locking. This scheme can be applied to plate and shell problems. Results of the numerical study show that the selective SFEM schemes give more accurate results than the FEM schemes.
Sun, Jian
2011-08-06
In this paper, an extraordinary magnetoresistance (EMR) device made of an InSb/Au hybrid structure was investigated. Those devices have a large potential in becoming a new generation of highly sensitive and cheap magnetic micro sensors. A crucial factor for the performance is the interface between the InSb and Au, which suffers from a certain contact resistivity. The Finite Element Method (FEM) was employed to simulate the current redistribution in the device, under an applied magnetic field. Specifically, the influence of the contact resistivity between the InSb bulk and Au shunt was studied. In a device with optimized geometry and without contact resistivity between the layers of InSb and Au, the EMR effect and the sensitivity show values of 1.89 × 104% and 0.02%/(10-4 T), respectively, at 1 Tesla. For values of contact resistivity up to 10-8cm2 the EMR effect is almost constant, while for higher values the EMR effect decreases exponentially. However, the sensitivity of the device does not decrease until 5 × 10-6 cm2 of contact resistivity. Only beyond this value the sensitivity, which in most cases is associated with the performance of the device, will deteriorate. © Springer Science+Business Media, LLC 2011.
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
Infinite Possibilities for the Finite Element.
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)
3D adaptive finite element method for a phase field model for the moving contact line problems
Shi, Yi
2013-08-01
In this paper, we propose an adaptive finite element method for simulating the moving contact line problems in three dimensions. The model that we used is the coupled Cahn-Hilliard Navier-Stokes equations with the generalized Navier boundary condition(GNBC) proposed in [18]. In our algorithm, to improve the efficiency of the simulation, we use the residual type adaptive finite element algorithm. It is well known that the phase variable decays much faster away from the interface than the velocity variables. There- fore we use an adaptive strategy that will take into account of such difference. Numerical experiments show that our algorithm is both efficient and reliable. © 2013 American Institute of Mathematical Sciences.
Peridynamic Multiscale Finite Element Methods
Energy Technology Data Exchange (ETDEWEB)
Costa, Timothy [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States); Bond, Stephen D. [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States); Littlewood, David John [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States); Moore, Stan Gerald [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)
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
Stenvall, A.; Siahrang, M.; Grilli, F.; Sirois, F.
2013-04-01
It is well known that twisting current-carrying conductors helps to reduce their coupling losses. However, the impact of twisting on self-field hysteresis losses has not been as extensively investigated as that on the reduction of coupling losses. This is mostly because the reduction of coupling losses has been an important issue to tackle in the past, and it is not possible to consider twisting within the classical two-dimensional (2D) approaches for the computation of self-field hysteresis losses. Recently, numerical codes considering the effect of twisting in continuous symmetries have appeared. For general three-dimensional (3D) simulations, one issue is that no robust, widely accepted and easy to obtain model for expressing the relationship between the current density and the electric field is available. On the other hand, we can consider that in these helicoidal structures currents flow only along the helicoidal trajectories. This approach allows one to use the scalar power-law for superconductor resistivity and makes the eddy current approach to a solution of a hysteresis loss problem feasible. In this paper we use the finite element method to solve the eddy current model in helicoidal structures in 2D domains utilizing the helicoidal symmetry. The developed tool uses the full 3D geometry but allows discretization which takes advantage of the helicoidal symmetry to reduce the computational domain to a 2D one. We utilize in this tool the non-linear power law for modelling the resistivity in the superconducting regions and study how the self-field losses are influenced by the twisting of a 10-filament wire. Additionally, in the case of high aspect ratio tapes, we compare the results computed with the new tool and a one-dimensional program based on the integral equation method and developed for simulating single layer power cables made of ReBCO coated conductors. Finally, we discuss modelling issues and present open questions related to helicoidal structures
The finite element method its basis and fundamentals
Zienkiewicz, Olek C; Zhu, JZ
2013-01-01
The Finite Element Method: Its Basis and Fundamentals offers a complete introduction to the basis of the finite element method, covering fundamental theory and worked examples in the detail required for readers to apply the knowledge to their own engineering problems and understand more advanced applications. This edition sees a significant rearrangement of the book's content to enable clearer development of the finite element method, with major new chapters and sections added to cover: Weak forms Variational forms Multi-dimensional field prob
FINITE-ELEMENT MODELING OF SALT TECTONICS
Directory of Open Access Journals (Sweden)
Natalia Bakhova
2012-09-01
Full Text Available The two-dimensional thermal model of graben structure in the presence of salt tectonics on the basis of a finite elements method is constructed. The analysis of the thermal field is based on the solution of stationary equation of heat conductivity with variable boundary conditions. The high precision of temperatures distribution and heat flows is received. The decision accuracy is no more than 0,6 %.
Finite element model of needle electrode sensitivity
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.
Finite Element Analysis of Reverberation Chambers
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 differential forms on cubical meshes
Arnold, Douglas N
2012-01-01
We develop a family of finite element spaces of differential forms defined on cubical meshes in any number of dimensions. The family contains elements of all polynomial degrees and all form degrees. In two dimensions, these include the serendipity finite elements and the rectangular BDM elements. In three dimensions they include a recent generalization of the serendipity spaces, and new H(curl) and H(div) finite element spaces. Spaces in the family can be combined to give finite element subcomplexes of the de Rham complex which satisfy the basic hypotheses of the finite element exterior calculus, and hence can be used for stable discretization of a variety of problems. The construction and properties of the spaces are established in a uniform manner using finite element exterior calculus.
Finite Element Program Generator and Its Application in Engineering
Institute of Scientific and Technical Information of China (English)
WANShui; HUHong; CHENJian-pin
2004-01-01
A completely new finite element software, Finite ElementProgram Generator (FEPG), is introduced and its designing thought and organizing structure is presented.FEPG uses the method of components and the technique of artificial intelligence to generate finite element program automatically by a computer according to the general principles of mathematic and internal rules of finite element method,as is similar to the deduction of mathematics.FEPG breaks through the limitation of present finite element software,which only applies to special discipline,while FEPG is suitable for all kinds of differential equations solved by finite element method.Now FEPG has been applied to superconductor research,electromagnetic field study,petroleum exploration,transportation,structure engineering,water conservancy,ship mechanics, solid-liquid coupling problems and liquid dynamics,etc.in China.
Elements with Square Roots in Finite Groups
Institute of Scientific and Technical Information of China (English)
M.S. Lucido; M.R. Pournaki
2005-01-01
In this paper, we study the probability that a randomly chosen element in a finite group has a square root, in particular the simple groups of Lie type of rank 1, the sporadic finite simple groups and the alternating groups.
Conforming finite elements with embedded strong discontinuities
Dias-da-Costa, D.; Alfaiate, J.; Sluys, L.J.; Areias, P.; Fernandes, C.; Julio, E.
2012-01-01
The possibility of embedding strong discontinuities into finite elements allowed the simulation of different problems, namely, brickwork masonry fracture, dynamic fracture, failure in finite strain problems and simulation of reinforcement concrete members. However, despite the significant contributi
Finite element modeling of permanent magnet devices
Brauer, J. R.; Larkin, L. A.; Overbye, V. D.
1984-03-01
New techniques are presented for finite element modeling of permanent magnets in magnetic devices such as motors and generators. These techniques extend a previous sheet-current permanent magnet model that applies only for straight line B-H loops and rectangular-shaped magnets. Here Maxwell's equations are used to derive the model of a permanent magnet having a general curved B-H loop and any geometric shape. The model enables a nonlinear magnetic finite element program to use Newton-Raphson iteration to solve for saturable magnetic fields in a wide variety of devices containing permanent magnets and steels. The techniques are applied to a brushless dc motor with irregular-shaped permanent magnets. The calculated motor torque agrees well with measured torque.
Finite Element Simulation of Metal Quenching
Institute of Scientific and Technical Information of China (English)
方刚; 曾攀
2004-01-01
The evolution of the phase transformation and the resulting internal stresses and strains in metallic parts during quenching were modeled numerically. The numerical simulation of the metal quenching process was based on the metallo-thermo-mechanical theory using the finite element method to couple the temperature, phase transformation, and stress-strain fields. The numerical models are presented for the heat treatment and kinetics of the phase transformation. The finite element models and the phase transition kinetics accurately predict the distribution of the microstructure volume fractions, the temperature, the distortion, and the stress-strain relation during quenching. The two examples used to validate the models are the quenching of a small gear and of a large turbine rotor. The simulation results for the martensite phase volume fraction, the stresses, and the distortion in the gear agree well with the experimental data. The models can be used to optimize the quenching conditions to ensure product quality.
Introduction to nonlinear finite element analysis
Kim, Nam-Ho
2015-01-01
This book introduces the key concepts of nonlinear finite element analysis procedures. The book explains the fundamental theories of the field and provides instructions on how to apply the concepts to solving practical engineering problems. Instead of covering many nonlinear problems, the book focuses on three representative problems: nonlinear elasticity, elastoplasticity, and contact problems. The book is written independent of any particular software, but tutorials and examples using four commercial programs are included as appendices: ANSYS, NASTRAN, ABAQUS, and MATLAB. In particular, the MATLAB program includes all source codes so that students can develop their own material models, or different algorithms. This book also: · Presents clear explanations of nonlinear finite element analysis for elasticity, elastoplasticity, and contact problems · Includes many informative examples of nonlinear analyses so that students can clearly understand the nonlinear theory · ...
Domain decomposition methods for mortar finite elements
Energy Technology Data Exchange (ETDEWEB)
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.
Unified Framework for Finite Element Assembly
Alnæs, Martin Sandve; Mardal, Kent-Andre; Skavhaug, Ola; Langtangen, Hans Petter; 10.1504/IJCSE.2009.029160
2012-01-01
At the heart of any finite element simulation is the assembly of matrices and vectors from discrete variational forms. We propose a general interface between problem-specific and general-purpose components of finite element programs. This interface is called Unified Form-assembly Code (UFC). A wide range of finite element problems is covered, including mixed finite elements and discontinuous Galerkin methods. We discuss how the UFC interface enables implementations of variational form evaluation to be independent of mesh and linear algebra components. UFC does not depend on any external libraries, and is released into the public domain.
Vibration Analysis of Beams by Spline Finite Element
Institute of Scientific and Technical Information of China (English)
YANG Hao; SUN Li
2011-01-01
In this paper,the spline finite element method is developed to investigate free vibration problems of beams.The cubic B-spline functions are used to construct the displacement field.The assembly of elements and the introduction of boundary conditions follow the standard finite element procedure.The results under various boundary conditions are compared with those obtained by the exact method and the finite difference method.It shows that the results are in excellent agreement with the analytical results and much more accurate than the results obtained by the finite difference method,especially for higher order modes.
Superconvergence for rectangular serendipity finite elements
Institute of Scientific and Technical Information of China (English)
CHEN; Chuanmiao(陈传淼)
2003-01-01
Based on an orthogonal expansion and orthogonality correction in an element, superconvergenceat symmetric points for any degree rectangular serendipity finite element approximation to second order ellipticproblem is proved, and its behaviour up to the boundary is also discussed.
Stochastic finite elements: Where is the physics?
Directory of Open Access Journals (Sweden)
Ostoja-Starzewski Martin
2011-01-01
Full Text Available The micromechanics based on the Hill-Mandel condition indicates that the majority of stochastic finite element methods hinge on random field (RF models of material properties (such as Hooke’s law having no physical content, or even at odds with physics. At the same time, that condition allows one to set up the RFs of stiffness and compliance tensors in function of the mesoscale and actual random microstructure of the given material. The mesoscale is defined through a Statistical Volume Element (SVE, i.e. a material domain below the Representative Volume Element (RVE level. The paper outlines a procedure for stochastic scale-dependent homogenization leading to a determination of mesoscale one-point and two-point statistics and, thus, a construction of analytical RF models.
Finite elements and finite differences for transonic flow calculations
Hafez, M. M.; Murman, E. M.; Wellford, L. C.
1978-01-01
The paper reviews the chief finite difference and finite element techniques used for numerical solution of nonlinear mixed elliptic-hyperbolic equations governing transonic flow. The forms of the governing equations for unsteady two-dimensional transonic flow considered are the Euler equation, the full potential equation in both conservative and nonconservative form, the transonic small-disturbance equation in both conservative and nonconservative form, and the hodograph equations for the small-disturbance case and the full-potential case. Finite difference methods considered include time-dependent methods, relaxation methods, semidirect methods, and hybrid methods. Finite element methods include finite element Lax-Wendroff schemes, implicit Galerkin method, mixed variational principles, dual iterative procedures, optimal control methods and least squares.
Continuous finite element methods for Hamiltonian systems
Institute of Scientific and Technical Information of China (English)
无
2007-01-01
By applying the continuous finite element methods of ordinary differential equations, the linear element methods are proved having second-order pseudo-symplectic scheme and the quadratic element methods are proved having third-order pseudosymplectic scheme respectively for general Hamiltonian systems, and they both keep energy conservative. The finite element methods are proved to be symplectic as well as energy conservative for linear Hamiltonian systems. The numerical results are in agreement with theory.
Element-topology-independent preconditioners for parallel finite element computations
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.
Element-topology-independent preconditioners for parallel finite element computations
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.
Why do probabilistic finite element analysis ?
Thacker, B H
2008-01-01
The intention of this book is to provide an introduction to performing probabilistic finite element analysis. As a short guideline, the objective is to inform the reader of the use, benefits and issues associated with performing probabilistic finite element analysis without excessive theory or mathematical detail.
Finite-Element Software for Conceptual Design
DEFF Research Database (Denmark)
Lindemann, J.; Sandberg, G.; Damkilde, Lars
2010-01-01
and research. Forcepad is an effort to provide a conceptual design and teaching tool in a finite-element software package. Forcepad is a two-dimensional finite-element application based on the same conceptual model as image editing applications such as Adobe Photoshop or Microsoft Paint. Instead of using...
Non-linear finite element modeling
DEFF Research Database (Denmark)
Mikkelsen, Lars Pilgaard
The note is written for courses in "Non-linear finite element method". The note has been used by the author teaching non-linear finite element modeling at Civil Engineering at Aalborg University, Computational Mechanics at Aalborg University Esbjerg, Structural Engineering at the University...... on the governing equations and methods of implementing....
Scalable, Finite Element Analysis of Electromagnetic Scattering and Radiation
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.
Yoshikawa, Masanobu; Kosaka, Kenichi; Seki, Hirohumi; Kimoto, Tsunenobu
2016-07-01
We measured the depolarized and polarized Raman spectra of a 4H-SiC metal-oxide-semiconductor field-effect transistor (MOSFET) and found that compressive stress of approximately 20 MPa occurs under the source and gate electrodes and tensile stress of approximately 10 MPa occurs between the source and gate electrodes. The experimental result was in close agreement with the result obtained by calculation using the finite element method (FEM). A combination of Raman spectroscopy and FEM provides much data on the stresses in 4H-SiC MOSFET.
Tao, Ran
2015-05-01
Laminated composites are materials with complex architecture made of continuous fibers embedded within a polymeric resin. The properties of the raw materials can vary from one point to another due to different local processing conditions or complex geometrical features for example. A first step towards the identification of these spatially varying material parameters is to image with precision the displacement fields in this complex microstructure when subjected to mechanical loading. This thesis is aimed to accurately measure the displacement and strain fields at the fiber-matrix scale in a cross-ply composite. First, the theories of both local subset-based digital image correlation (DIC) and global finite-element based DIC are outlined. Second, in-situ secondary electron tensile images obtained by scanning electron microscopy (SEM) are post-processed by both DIC techniques. Finally, it is shown that when global DIC is applied with a conformal mesh, it can capture more accurately sharp local variations in the strain fields as it takes into account the underlying microstructure. In comparison to subset-based local DIC, finite-element based global DIC is better suited for capturing gradients across the fiber-matrix interfaces.
Sarkis, C.; Silva, L.; Gandin, Ch-A.; Plapp, M.
2016-03-01
Dendritic growth is computed with automatic adaptation of an anisotropic and unstructured finite element mesh. The energy conservation equation is formulated for solid and liquid phases considering an interface balance that includes the Gibbs-Thomson effect. An equation for a diffuse interface is also developed by considering a phase field function with constant negative value in the liquid and constant positive value in the solid. Unknowns are the phase field function and a dimensionless temperature, as proposed by [1]. Linear finite element interpolation is used for both variables, and discretization stabilization techniques ensure convergence towards a correct non-oscillating solution. In order to perform quantitative computations of dendritic growth on a large domain, two additional numerical ingredients are necessary: automatic anisotropic unstructured adaptive meshing [2,[3] and parallel implementations [4], both made available with the numerical platform used (CimLib) based on C++ developments. Mesh adaptation is found to greatly reduce the number of degrees of freedom. Results of phase field simulations for dendritic solidification of a pure material in two and three dimensions are shown and compared with reference work [1]. Discussion on algorithm details and the CPU time will be outlined.
Finite element analysis of optical waveguides
Mabaya, N.; Lagasse, P. E.; Vandenbulcke, P.
1981-06-01
Several finite element programs for the computation of the guided modes of optical waveguides are presented. The advantages and limitations of a very general program for the analysis of anisotropic guides are presented. A possible solution to the problem of the spurious numerical modes, encountered when calculating higher order modes, is proposed. For isotropic waveguides, it is shown that both EH- and HE-type modes can be very accurately approximated by two different scalar finite element programs. Finally, a boundary perturbation method is outlined that makes it possible to calculate the attenuation coefficient of leaky modes in single material guides, starting from a finite element calculation.
Will Finite Elements Replace Structural Mechanics?
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.
Superconvergence of tricubic block finite elements
Institute of Scientific and Technical Information of China (English)
2009-01-01
In this paper, we first introduce interpolation operator of projection type in three dimen- sions, from which we derive weak estimates for tricubic block finite elements. Then using the estimate for the W 2, 1-seminorm of the discrete derivative Green’s function and the weak estimates, we show that the tricubic block finite element solution uh and the tricubic interpolant of projection type Πh3u have superclose gradient in the pointwise sense of the L∞-norm. Finally, this supercloseness is applied to superconvergence analysis, and the global superconvergence of the finite element approximation is derived.
Finite element computation of 2-D magnetic field of solenoid with current%通电螺线管2维磁场有限元计算
Institute of Scientific and Technical Information of China (English)
彭斓; 杨中海; 胡权; 黄桃; 李斌
2011-01-01
Finite element computation of 2-D magnetic field of solenoid with current has been implemented. It adopted first or second order interpolation based finite element method to solve the 2-D magnetic field of the solenoid. The single solenoid model and the periodic structure model were analyzed and simulated. The results were compared with the results of Ansoft Maxwell 2D. It is shown that, compared with the first order interpolation based finite element method, the second order interpolation one has a faster convergence rate and a better accuracy on the axis of symmetry.%通过对通电螺线管磁系统理论分析,实现了通电螺线管2维磁场计算.该算法是采用一次、二次插值函数计算螺线管模型磁场的有限元算法,用于求解螺线管内外任意位置处的磁感应强度分布.实现了螺线管及周期结构的计算,并将结果与Ansoft Maxwell 2-D的计算结果进行了对比.结果表明:较一次插值函数有限元算法相比,二次插值函数算法在对称轴上轴向磁感应强度的分布更准确,体现了该算法的优越性,具有显著的工程应用价值.
Finite element methods a practical guide
Whiteley, Jonathan
2017-01-01
This book presents practical applications of the finite element method to general differential equations. The underlying strategy of deriving the finite element solution is introduced using linear ordinary differential equations, thus allowing the basic concepts of the finite element solution to be introduced without being obscured by the additional mathematical detail required when applying this technique to partial differential equations. The author generalizes the presented approach to partial differential equations which include nonlinearities. The book also includes variations of the finite element method such as different classes of meshes and basic functions. Practical application of the theory is emphasised, with development of all concepts leading ultimately to a description of their computational implementation illustrated using Matlab functions. The target audience primarily comprises applied researchers and practitioners in engineering, but the book may also be beneficial for graduate students.
Moving Finite Elements in 2-D.
1984-08-06
34 . - ; .-’- . - . -- .- -. . - -.. -- ; -. - - - - - ." . ,- . -••. - - ; . IOSR : TR. SAI-84/1299 (0 N MOVING FINITE ELEMENTS IN 2-I Final Report AFOSR Contract: F4962U-81-C-UO73 Program Manager
Finite element modeling of corneal strip extensometry
CSIR Research Space (South Africa)
Botha, N
2012-12-01
Full Text Available numerically modelled in several studies, this study focusses on accurately modelling the strip extensiometry test. Two methods were considered to simulate the experimental conditions namely, a single phase and a two phase method. A finite element model...
A survey of mixed finite element methods
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.
Gleadall, Andrew; Pan, Jingzhe; Ding, Lifeng; Kruft, Marc-Anton; Curcó, David
2015-11-01
Molecular dynamics (MD) simulations are widely used to analyse materials at the atomic scale. However, MD has high computational demands, which may inhibit its use for simulations of structures involving large numbers of atoms such as amorphous polymer structures. An atomic-scale finite element method (AFEM) is presented in this study with significantly lower computational demands than MD. Due to the reduced computational demands, AFEM is suitable for the analysis of Young's modulus of amorphous polymer structures. This is of particular interest when studying the degradation of bioresorbable polymers, which is the topic of an accompanying paper. AFEM is derived from the inter-atomic potential energy functions of an MD force field. The nonlinear MD functions were adapted to enable static linear analysis. Finite element formulations were derived to represent interatomic potential energy functions between two, three and four atoms. Validation of the AFEM was conducted through its application to atomic structures for crystalline and amorphous poly(lactide).
Infinite to finite: An overview of finite element analysis
Directory of Open Access Journals (Sweden)
Srirekha A
2010-01-01
Full Text Available The method of finite elements was developed at perfectly right times; growing computer capacities, growing human skills and industry demands for ever faster and cost effective product development providing unlimited possibilities for the researching community. This paper reviews the basic concept, current status, advances, advantages, limitations and applications of finite element method (FEM in restorative dentistry and endodontics. Finite element method is able to reveal the otherwise inaccessible stress distribution within the tooth-restoration complex and it has proven to be a useful tool in the thinking process for the understanding of tooth biomechanics and the biomimetic approach in restorative dentistry. Further improvement of the non-linear FEM solutions should be encouraged to widen the range of applications in dental and oral health science.
Finite element modeling of the human pelvis
Energy Technology Data Exchange (ETDEWEB)
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.
Surgery simulation using fast finite elements
DEFF Research Database (Denmark)
Bro-Nielsen, Morten
1996-01-01
This paper describes our recent work on real-time surgery simulation using fast finite element models of linear elasticity. In addition, we discuss various improvements in terms of speed and realism......This paper describes our recent work on real-time surgery simulation using fast finite element models of linear elasticity. In addition, we discuss various improvements in terms of speed and realism...
A NOTE ON FINITE ELEMENT WAVELETS
Institute of Scientific and Technical Information of China (English)
谌秋辉; 陈翰麟
2001-01-01
The refinability and approximation order of finite element multi-scale vector are discussed in [1]. But the coefficients in the conditions of approximation order of finite element multi-scale vector are incorrect there. The main purpose of this note is to make a correction of the error in the main result of [1]. These coefficients are very important for the properties of wavelets, such as vanishing moments and regularity.
Hiramatsu, Y.; Otabe, E. S.; Kiuchi, M.
The trapped magnetic field properties of superconducting MgB2 bulk magnets with various shapes such as a triangular, a quadrangular, a hexangular bulk were calculated by the Finite Elements Method (FEM). The effect for the combination of several numbers of bulks was also investigated for several kinds of shapes to obtain large area of bulk surface in spite of one large bulk. In this calculation, the simple magnetization process replaced by the field-cool magnetization was used to obtain the equivalent distribution of the magnetic field, and the thermal equation in FEM was omitted. The trapped magnetic field for the triangular bulk by FEM was compared with the experimental result. It was found that the calculated results agreed well with the experimental result. The maximum trapped magnetic field was obtained in the cylindrical shape among several kinds of shapes. The trapped magnetic field was increased by the combination of multi-bulks. It was confirmed that the trapped magnetic field of the multi-bulks was larger than that of the single bulk. The trapped magnetic field increases with increasing the number of the bulks.
Finite element analysis of flexible, rotating blades
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.
Energy Technology Data Exchange (ETDEWEB)
Klein, B. [Kassel Univ. (Germany). Leichbau, CAD und Entwicklungsmethodik
2007-07-01
Virtual product development at the workstation has become reality, creating a link between 3D-CAD, MKS, FEM, STRUOPT and Rapid Prototyping. Engineers must have good knowledge of computer-assisted techniques. The key element of CAE is the finite element method (FEM) which is a universal analytical tool providing deep insight into the elastic, dynamic, cinematic/kinetic, thermal, and fluid-mechanical characteristics of components and systems. On the basis of these simulations, reliable predictions are possible that will shorten innovation and trial periods and result in very short amortisation periods of FEM investments. This is shown by the textbook in a very clear and illustrative manner. Case studies are presented to enable the reader to deepen her knowledge by herself. (orig.)
Finite-Element Modelling of Biotransistors
Directory of Open Access Journals (Sweden)
Selvaganapathy PR
2010-01-01
Full Text Available Abstract Current research efforts in biosensor design attempt to integrate biochemical assays with semiconductor substrates and microfluidic assemblies to realize fully integrated lab-on-chip devices. The DNA biotransistor (BioFET is an example of such a device. The process of chemical modification of the FET and attachment of linker and probe molecules is a statistical process that can result in variations in the sensed signal between different BioFET cells in an array. In order to quantify these and other variations and assess their importance in the design, complete physical simulation of the device is necessary. Here, we perform a mean-field finite-element modelling of a short channel, two-dimensional BioFET device. We compare the results of this model with one-dimensional calculation results to show important differences, illustrating the importance of the molecular structure, placement and conformation of DNA in determining the output signal.
An implicit discontinuous Galerkin finite element model for water waves
van der Vegt, Jacobus J.W.; Ambati, V.R.; Bokhove, Onno
2005-01-01
We discuss a new higher order accurate discontinuous Galerkin finite element method for non-linear free surface gravity waves. The algorithm is based on an arbitrary Lagrangian Eulerian description of the flow field using deforming elements and a moving mesh, which makes it possible to represent
Directory of Open Access Journals (Sweden)
Amor Chowdhury
2016-09-01
Full Text Available The presented paper describes accurate distance measurement for a field-sensed magnetic suspension system. The proximity measurement is based on a Hall effect sensor. The proximity sensor is installed directly on the lower surface of the electro-magnet, which means that it is very sensitive to external magnetic influences and disturbances. External disturbances interfere with the information signal and reduce the usability and reliability of the proximity measurements and, consequently, the whole application operation. A sensor fusion algorithm is deployed for the aforementioned reasons. The sensor fusion algorithm is based on the Unscented Kalman Filter, where a nonlinear dynamic model was derived with the Finite Element Modelling approach. The advantage of such modelling is a more accurate dynamic model parameter estimation, especially in the case when the real structure, materials and dimensions of the real-time application are known. The novelty of the paper is the design of a compact electro-magnetic actuator with a built-in low cost proximity sensor for accurate proximity measurement of the magnetic object. The paper successively presents a modelling procedure with the finite element method, design and parameter settings of a sensor fusion algorithm with Unscented Kalman Filter and, finally, the implementation procedure and results of real-time operation.
Chowdhury, Amor; Sarjaš, Andrej
2016-09-15
The presented paper describes accurate distance measurement for a field-sensed magnetic suspension system. The proximity measurement is based on a Hall effect sensor. The proximity sensor is installed directly on the lower surface of the electro-magnet, which means that it is very sensitive to external magnetic influences and disturbances. External disturbances interfere with the information signal and reduce the usability and reliability of the proximity measurements and, consequently, the whole application operation. A sensor fusion algorithm is deployed for the aforementioned reasons. The sensor fusion algorithm is based on the Unscented Kalman Filter, where a nonlinear dynamic model was derived with the Finite Element Modelling approach. The advantage of such modelling is a more accurate dynamic model parameter estimation, especially in the case when the real structure, materials and dimensions of the real-time application are known. The novelty of the paper is the design of a compact electro-magnetic actuator with a built-in low cost proximity sensor for accurate proximity measurement of the magnetic object. The paper successively presents a modelling procedure with the finite element method, design and parameter settings of a sensor fusion algorithm with Unscented Kalman Filter and, finally, the implementation procedure and results of real-time operation.
Finite element analysis of magnetization reversal in granular thin films
Spargo, A W
2002-01-01
This thesis develops a Galerkin finite element model of magnetisation dynamics in granular thin films. The governing equations of motion are the Gilbert equations with an effective magnetic field taking contributions from exchange interactions, magnetocrystalline anisotropy, applied magnetic field as well as the magnetostatic field given by Maxwells equations. The magnetostatic field is formulated as a scalar potential described by Poissons equation which is solved using a second order finite element method. The Gilbert equations are discretized in time using an implicit midpoint method which naturally conserves the magnitude of the magnetisation vector. An infinite thin film is approximated using periodic boundary conditions with material microstructure represented using the Voronoi tessellation. The effects of thermal fluctuations are modelled by the stochastic Langevin-Gilbert equations, again solved by a Galerkin finite element method. The implicit midpoint time-stepping scheme ensures that solutions conv...
Quadrature representation of finite element variational forms
DEFF Research Database (Denmark)
Ølgaard, Kristian Breum; Wells, Garth N.
2012-01-01
This chapter addresses the conventional run-time quadrature approach for the numerical integration of local element tensors associated with finite element variational forms, and in particular automated optimizations that can be performed to reduce the number of floating point operations...
Finite Element Computational Dynamics of Rotating Systems
Directory of Open Access Journals (Sweden)
Jaroslav Mackerle
1999-01-01
Full Text Available This bibliography lists references to papers, conference proceedings and theses/dissertations dealing with finite element analysis of rotor dynamics problems that were published in 1994–1998. It contains 319 citations. Also included, as separate subsections, are finite element analyses of rotor elements – discs, shafts, spindles, and blades. Topics dealing with fracture mechanics, contact and stability problems of rotating machinery are also considered in specific sections. The last part of the bibliography presents papers dealing with specific industrial applications.
Error computation for adaptive finite element analysis
Khan, A A; Memon, I R; Ming, X Y
2002-01-01
The paper gives a simple numerical procedure for computations of errors generated by the discretisation process of finite element method. The procedure given is based on the ZZ error estimator which is believed to be reasonable accurate and thus can be readily implemented in any existing finite element codes. The devised procedure not only estimates the global energy norm error but also evaluates the local errors in individual elements. In the example, the given procedure is combined with an adaptive refinement procedure, which provides guidance for optimal mesh designing and allows the user to obtain a desired accuracy with a limited number of interaction. (author)
Experimental Finite Element Approach for Stress Analysis
Directory of Open Access Journals (Sweden)
Ahmet Erklig
2014-01-01
Full Text Available This study aims to determining the strain gauge location points in the problems of stress concentration, and it includes both experimental and numerical results. Strain gauges were proposed to be positioned to corresponding locations on beam and blocks to related node of elements of finite element models. Linear and nonlinear cases were studied. Cantilever beam problem was selected as the linear case to approve the approach and conforming contact problem was selected as the nonlinear case. An identical mesh structure was prepared for the finite element and the experimental models. The finite element analysis was carried out with ANSYS. It was shown that the results of the experimental and the numerical studies were in good agreement.
Intra Plate Stresses Using Finite Element Modelling
Directory of Open Access Journals (Sweden)
Jayalakshmi S.
2016-10-01
Full Text Available One of the most challenging problems in the estimation of seismic hazard is the ability to quantify seismic activity. Empirical models based on the available earthquake catalogue are often used to obtain activity of source regions. The major limitation with this approach is the lack of sufficient data near a specified source. The non-availability of data poses difficulties in obtaining distribution of earthquakes with large return periods. Such events recur over geological time scales during which tectonic processes, including mantle convection, formation of faults and new plate boundaries, are likely to take place. The availability of geometries of plate boundaries, plate driving forces, lithospheric stress field and GPS measurements has provided numerous insights on the mechanics of tectonic plates. In this article, a 2D finite element model of Indo-Australian plate is developed with the focus of representing seismic activity in India. The effect of large scale geological features including sedimentary basins, fold belts and cratons on the stress field in India is explored in this study. In order to address long term behaviour, the orientation of stress field and tectonic faults of the present Indo-Australian plate are compared with a reconstructed stress field from the early Miocene (20 Ma.
Exact finite elements for conduction and convection
Thornton, E. A.; Dechaumphai, P.; Tamma, K. K.
1981-01-01
An appproach for developing exact one dimensional conduction-convection finite elements is presented. Exact interpolation functions are derived based on solutions to the governing differential equations by employing a nodeless parameter. Exact interpolation functions are presented for combined heat transfer in several solids of different shapes, and for combined heat transfer in a flow passage. Numerical results demonstrate that exact one dimensional elements offer advantages over elements based on approximate interpolation functions. Previously announced in STAR as N81-31507
Finite element analysis for acoustic characteristics of a magnetostrictive transducer
Kim, Jaehwan; Jung, Eunmi
2005-12-01
This paper presents a finite element analysis for a magnetostrictive transducer by taking into account the nonlinear behavior of the magnetostrictive material and fluid interaction. A finite element formulation is derived for the coupling of magnetostrictive and elastic materials based upon a separated magnetic and displacement field calculation and a curve fitting technique of material properties. The fluid and structure coupled problem is taken into account based upon pressure and velocity potential fields formulation. Infinite wave envelope elements are introduced at an artificial boundary to deal with the infinite fluid domain. A finite element code for the analysis of a magnetostrictive transducer is developed. A magnetostrictive tonpilz transducer is taken as an example and verification for the developed program is made by comparing with a commercial code. The acoustic characteristics of the magnetostrictive tonpilz transducer are calculated in terms of radiation pattern and transmitted current response.
DEFF Research Database (Denmark)
Cai, Hongzhu; Hu, Xiangyun; Li, Jianhui
2017-01-01
to calculate the primary field can be saved. We adopt a new boundary condition which approximate the total field on the boundary by the primary field corresponding to the layered earth approximation of the complicated conductivity model. The primary field on the modeling boundary is calculated using fast...
Probabilistic finite elements for transient analysis in nonlinear continua
Liu, W. K.; Belytschko, T.; Mani, A.
1985-01-01
The probabilistic finite element method (PFEM), which is a combination of finite element methods and second-moment analysis, is formulated for linear and nonlinear continua with inhomogeneous random fields. Analogous to the discretization of the displacement field in finite element methods, the random field is also discretized. The formulation is simplified by transforming the correlated variables to a set of uncorrelated variables through an eigenvalue orthogonalization. Furthermore, it is shown that a reduced set of the uncorrelated variables is sufficient for the second-moment analysis. Based on the linear formulation of the PFEM, the method is then extended to transient analysis in nonlinear continua. The accuracy and efficiency of the method is demonstrated by application to a one-dimensional, elastic/plastic wave propagation problem. The moments calculated compare favorably with those obtained by Monte Carlo simulation. Also, the procedure is amenable to implementation in deterministic FEM based computer programs.
An iterative algorithm for finite element analysis
Laouafa, F.; Royis, P.
2004-03-01
In this paper, we state in a new form the algebraic problem arising from the one-field displacement finite element method (FEM). The displacement approach, in this discrete form, can be considered as the dual approach (force or equilibrium) with subsidiary constraints. This approach dissociates the nonlinear operator to the linear ones and their sizes are linear functions of integration rule which is of interest in the case of reduced integration. This new form of the problem leads to an inexpensive improvement of FEM computations, which acts at local, elementary and global levels. We demonstrate the numerical performances of this approach which is independent of the mesh structure. Using the GMRES algorithm we build, for nonsymmetric problems, a new algorithm based upon the discretized field of strain. The new algorithms proposed are more closer to the mechanical problem than the classical ones because all fields appear during the resolution process. The sizes of the different operators arising in these new forms are linear functions of integration rule, which is of great interest in the case of reduced integration.
Finite Element Methods and Their Applications
Chen, Zhangxin
2005-01-01
This book serves as a text for one- or two-semester courses for upper-level undergraduates and beginning graduate students and as a professional reference for people who want to solve partial differential equations (PDEs) using finite element methods. The author has attempted to introduce every concept in the simplest possible setting and maintain a level of treatment that is as rigorous as possible without being unnecessarily abstract. Quite a lot of attention is given to discontinuous finite elements, characteristic finite elements, and to the applications in fluid and solid mechanics including applications to porous media flow, and applications to semiconductor modeling. An extensive set of exercises and references in each chapter are provided.
Preconditioned CG-solvers and finite element grids
Energy Technology Data Exchange (ETDEWEB)
Bauer, R.; Selberherr, S. [Technical Univ. of Vienna (Austria)
1994-12-31
To extract parasitic capacitances in wiring structures of integrated circuits the authors developed the two- and three-dimensional finite element program SCAP (Smart Capacitance Analysis Program). The program computes the task of the electrostatic field from a solution of Poisson`s equation via finite elements and calculates the energies from which the capacitance matrix is extracted. The unknown potential vector, which has for three-dimensional applications 5000-50000 unknowns, is computed by a ICCG solver. Currently three- and six-node triangular, four- and ten-node tetrahedronal elements are supported.
Finite elements for analysis and design
Akin, J E; Davenport, J H
1994-01-01
The finite element method (FEM) is an analysis tool for problem-solving used throughout applied mathematics, engineering, and scientific computing. Finite Elements for Analysis and Design provides a thoroughlyrevised and up-to-date account of this important tool and its numerous applications, with added emphasis on basic theory. Numerous worked examples are included to illustrate the material.Key Features* Akin clearly explains the FEM, a numerical analysis tool for problem-solving throughout applied mathematics, engineering and scientific computing* Basic theory has bee
Stochastic Finite Elements in Reliability-Based Structural Optimization
DEFF Research Database (Denmark)
Sørensen, John Dalsgaard; Engelund, S.
1995-01-01
Application of stochastic finite elements in structural optimization is considered. It is shown how stochastic fields modelling e.g. the modulus of elasticity can be discretized in stochastic variables and how a sensitivity analysis of the reliability of a structural system with respect to optimi......Application of stochastic finite elements in structural optimization is considered. It is shown how stochastic fields modelling e.g. the modulus of elasticity can be discretized in stochastic variables and how a sensitivity analysis of the reliability of a structural system with respect...
Stochastic Finite Elements in Reliability-Based Structural Optimization
DEFF Research Database (Denmark)
Sørensen, John Dalsgaard; Engelund, S.
Application of stochastic finite elements in structural optimization is considered. It is shown how stochastic fields modelling e.g. the modulus of elasticity can be discretized in stochastic variables and how a sensitivity analysis of the reliability of a structural system with respect to optimi......Application of stochastic finite elements in structural optimization is considered. It is shown how stochastic fields modelling e.g. the modulus of elasticity can be discretized in stochastic variables and how a sensitivity analysis of the reliability of a structural system with respect...
NEW ALGORITHM OF COUPLING ELEMENT-FREE GALERKIN WITH FINITE ELEMENT METHOD
Institute of Scientific and Technical Information of China (English)
ZHAO Guang-ming; SONG Shun-cheng
2005-01-01
Through the construction of a new ramp function, the element-free Galerkin method and finite element coupling method were applied to the whole field, and was made fit for the structure of element nodes within the interface regions, both satisfying the essential boundary conditions and deploying meshless nodes and finite elements in a convenient and flexible way, which can meet the requirements of computation for complicated field. The comparison between the results of the present study and the corresponding analytical solutions shows this method is feasible and effective.
Numerical computation of transonic flows by finite-element and finite-difference methods
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.
Baqersad, Javad
Health monitoring of rotating structures such as wind turbines and helicopter rotors is generally performed using conventional sensors that provide a limited set of data at discrete locations near or on the hub. These sensors usually provide no data on the blades or interior locations where failures may occur. Within this work, an unique expansion algorithm was extended and combined with finite element (FE) modeling and an optical measurement technique to identify the dynamic strain in rotating structures. The merit of the approach is shown by using the approach to predict the dynamic strain on a small non-rotating and rotating wind turbine. A three-bladed wind turbine having 2.3-meter long blades was placed in a semi-built-in boundary condition using a hub, a machining chuck, and a steel block. A finite element model of the three wind turbine blades assembled to the hub was created and used to extract resonant frequencies and mode shapes. The FE model was validated and updated using experimental modal tests. For the non-rotating optical test, the turbine was excited using a sinusoidal excitation, a pluck test, arbitrary impacts on three blades, and random force excitations with a mechanical shaker. The response of the structure to the excitations was measured using three-dimensional point tracking. A pair of high-speed cameras was used to measure the displacement of optical targets on the structure when the blades were vibrating. The measured displacements at discrete locations were expanded and applied to the finite element model of the structure to extract the full-field dynamic strain. The results of the work show an excellent correlation between the strain predicted using the proposed approach and the strain measured with strain-gages for all of the three loading conditions. Similar to the non-rotating case, optical measurements were also preformed on a rotating wind turbine. The point tracking technique measured both rigid body displacement and flexible
Finite Element Residual Stress Analysis of Planetary Gear Tooth
Directory of Open Access Journals (Sweden)
Jungang Wang
2013-01-01
Full Text Available A method to simulate residual stress field of planetary gear is proposed. In this method, the finite element model of planetary gear is established and divided to tooth zone and profile zone, whose different temperature field is set. The gear's residual stress simulation is realized by the thermal compression stress generated by the temperature difference. Based on the simulation, the finite element model of planetary gear train is established, the dynamic meshing process is simulated, and influence of residual stress on equivalent stress of addendum, pitch circle, and dedendum of internal and external meshing planetary gear tooth profile is analyzed, according to non-linear contact theory, thermodynamic theory, and finite element theory. The results show that the equivalent stresses of planetary gear at both meshing and nonmeshing surface are significantly and differently reduced by residual stress. The study benefits fatigue cracking analysis and dynamic optimization design of planetary gear train.
Orthodontic treatment: Introducing finite element analysis
Driel, W.D. van; Leeuwen, E.J. van
1998-01-01
The aim of orthodontic treatment is the displacement of teeth by means ofspecial appliances, like braces and brackets. Through these appliances the orthodontist can apply a set of forces to the teeth which wilt result in its displacement through the jawbone. Finite Element analysis of this process e
Interval Finite Element Analysis of Wing Flutter
Institute of Scientific and Technical Information of China (English)
Wang Xiaojun; Qiu Zhiping
2008-01-01
The influences of uncertainties in structural parameters on the flutter speed of wing are studied. On the basis of the deterministic flutter analysis model of wing, the uncertainties in structural parameters are considered and described by interval numbers. By virtue of first-order Taylor series expansion, the lower and upper bound curves of the transient decay rate coefficient versus wind velocity are given. So the interval estimation of the flutter critical wind speed of wing can be obtained, which is more reasonable than the point esti- mation obtained by the deterministic flutter analysis and provides the basis for the further non-probabilistic interval reliability analysis of wing flutter. The flow chart for interval finite element model of flutter analysis of wing is given. The proposed interval finite element model and the stochastic finite element model for wing flutter analysis are compared by the examples of a three degrees of freedorn airfoil and fuselage and a 15° swepthack wing, and the results have shown the effectiveness and feasibility of the presented model. The prominent advantage of the proposed interval finite element model is that only the bounds of uncertain parameters axe required, and the probabilistic distribution densities or other statistical characteristics are not needed.
Fast finite elements for surgery simulation
DEFF Research Database (Denmark)
Bro-Nielsen, Morten
1997-01-01
This paper discusses volumetric deformable models for modeling human body parts and organs in surgery simulation systems. These models are built using finite element models for linear elastic materials. To achieve real-time response condensation has been applied to the system stiffness matrix, an...
Opitz, Alexander; Legon, Wynn; Rowlands, Abby; Bickel, Warren K; Paulus, Walter; Tyler, William J
2013-11-01
Recent evidence indicates subject-specific gyral folding patterns and white matter anisotropy uniquely shape electric fields generated by TMS. Current methods for predicting the brain regions influenced by TMS involve projecting the TMS coil position or center of gravity onto realistic head models derived from structural and functional imaging data. Similarly, spherical models have been used to estimate electric field distributions generated by TMS pulses delivered from a particular coil location and position. In the present paper we inspect differences between electric field computations estimated using the finite element method (FEM) and projection-based approaches described above. We then more specifically examined an approach for estimating cortical excitation volumes based on individualistic FEM simulations of electric fields. We evaluated this approach by performing neurophysiological recordings during MR-navigated motormapping experiments. We recorded motor evoked potentials (MEPs) in response to single pulse TMS using two different coil orientations (45° and 90° to midline) at 25 different locations (5×5 grid, 1cm spacing) centered on the hotspot of the right first dorsal interosseous (FDI) muscle in left motor cortex. We observed that motor excitability maps varied within and between subjects as a function of TMS coil position and orientation. For each coil position and orientation tested, simulations of the TMS-induced electric field were computed using individualistic FEM models and compared to MEP amplitudes obtained during our motormapping experiments. We found FEM simulations of electric field strength, which take into account subject-specific gyral geometry and tissue conductivity anisotropy, significantly correlated with physiologically observed MEP amplitudes (rmax=0.91, p=1.8×10(-5) rmean=0.81, p=0.01). These observations validate the implementation of individualistic FEM models to account for variations in gyral folding patterns and tissue
Deng, Zhi-De; Lisanby, Sarah H.; Peterchev, Angel V.
2011-02-01
We present the first computational study comparing the electric field induced by various electroconvulsive therapy (ECT) and magnetic seizure therapy (MST) paradigms. Four ECT electrode configurations (bilateral, bifrontal, right unilateral, and focal electrically administered seizure therapy) and three MST coil configurations (circular, cap, and double cone) were modeled. The model incorporated a modality-specific neural activation threshold. ECT (0.3 ms pulse width) and MST induced the maximum electric field of 2.1-2.5 V cm-1 and 1.1-2.2 V cm-1 in the brain, corresponding to 6.2-7.2 times and 1.2-2.3 times the neural activation threshold, respectively. The MST electric field is more confined to the superficial cortex compared to ECT. The brain volume stimulated was much larger with ECT (up to 100%) than with MST (up to 8.2%). MST with the double-cone coil was the most focal, and bilateral ECT was the least focal. Our results suggest a possible biophysical explanation of the reduced side effects of MST compared to ECT. Our results also indicate that the conventional ECT pulse amplitude (800-900 mA) is much higher than necessary for seizure induction. Reducing the ECT pulse amplitude should be explored as a potential means of diminishing side effects.
On Hybrid and mixed finite element methods
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.
Finite Dynamic Elements and Modal Analysis
Directory of Open Access Journals (Sweden)
N.J. Fergusson
1993-01-01
Full Text Available A general modal analysis scheme is derived for forced response that makes use of high accuracy modes computed by the dynamic element method. The new procedure differs from the usual modal analysis in that the modes are obtained from a power series expansion for the dynamic stiffness matrix that includes an extra dynamic correction term in addition to the static stiffness matrix and the consistent mass matrix based on static displacement. A cantilevered beam example is used to demonstrate the relative accuracies of the dynamic element and the traditional finite element methods.
Finite element analysis of tibial fractures
DEFF Research Database (Denmark)
Wong, Christian Nai En; Mikkelsen, Mikkel Peter W; Hansen, Leif Berner
2010-01-01
INTRODUCTION: Fractures of the tibial shaft are relatively common injuries. There are indications that tibial shaft fractures share characteristics in terms of site, type and local fracture mechanisms. In this study, we aimed to set up a mathematical, computer-based model using finite element...... analysis of the bones of the lower leg to examine if such a model is adequate for prediction of fracture locations and patterns. In future studies, we aim to use these biomechanical results to examine fracture prevention, among others, and to simulate different types of osteosynthesis and the process...... Project. The data consisted of 21,219 3D elements with a cortical shell and a trabecular core. Three types of load of torsion, a direct lateral load and axial compression were applied. RESULTS: The finite element linear static analysis resulted in relevant fracture localizations and indicated relevant...
Alhamadi, Mohd A. Wahed
1992-01-01
A three dimensional finite element (3D-FE) method for the computation of global distributions of 30 magnetic fields in electric machines containing permanent magnets is presented. The formulation of this 3D-FE method is based on a coupled magnetic vector potential - magnetic scalar potential (CMVP-MSP) approach. In this CMVP-MSP method, the modeling and formulations of permanent magnet volumes, suited to first and second order MVP 3D-FE environments as well as first order MSP 3D-FE environment, are developed in this dissertation. The development of the necessary 3D-FE grids and algorithms for the application of the CMVP -MSP method to an example brushless dc motor, whose field is three dimensional due to the skewed permanent magnet mounts on its rotor, is also given here. It should be mentioned that the entire volume of the case-study machine from one end to another is considered in the global magnetic field computations. A complete set of results of application of the CMVP-MSP method to the computation of the global 3D field distributions and associated motor parameters under no-load and load conditions are presented in this dissertation. In addition, a complete simulation of the dynamic performance of the motor drive system using the parameters obtained from the 3D-FE field solutions are presented for no-load and various other load conditions. All the above mentioned results are experimentally verified by corresponding oscillograms obtained in the laboratory. These results are also compared with results obtained from motor parameters based on various 2D-FE approaches, showing that for certain types of skewed permanent magnet mounts, 3D-FE based parameters can make significant qualitative and quantitative improvements in motor-drive simulation results.
Directory of Open Access Journals (Sweden)
Yifei Yan
2016-01-01
Full Text Available A novel optimised back analysis method is proposed in this paper. The in situ stress field of an underground gas storage (UGS reservoir in a Turkey salt cavern is analysed by the basic theory of elastic mechanics. A finite element method is implemented to optimise and approximate the objective function by systematically adjusting boundary loads. Optimising calculation is performed based on a novel method to reduce the error between measurement and calculation as much as possible. Compared with common back analysis methods such as regression method, the method proposed can further improve the calculation precision. By constructing a large circular geometric model, the effect of stress concentration is eliminated and a minimum difference between computed and measured stress can be guaranteed in the rectangular objective region. The efficiency of the proposed method is investigated and confirmed by its capability on restoring in situ stress field, which agrees well with experimental results. The characteristics of stress distribution of chosen UGS wells are obtained based on the back analysis results and by applying the corresponding fracture criterion, the shaft walls are proven safe.
Surface processing methods for point sets using finite elements
Clarenz, Ulrich; Rumpf, Martin; Telea, Alexandru
2004-01-01
We present a framework for processing point-based surfaces via partial differential equations (PDEs). Our framework efficiently and effectively brings well-known PDE-based processing techniques to the field of point-based surfaces. At the core of our method is a finite element discretization of PDEs
Kriging-Based Finite Element Method: Element-By-Element Kriging Interpolation
Directory of Open Access Journals (Sweden)
W. Kanok-Nukulchai
2009-01-01
Full Text Available An enhancement of the finite element method with Kriging shape functions (K-FEM was recently proposed. In this method, the field variables of a boundary value problem are approximated using ‘element-by-element’ piecewise Kriging interpolation (el-KI. For each element, the interpolation function is constructed from a set of nodes within a prescribed domain of influence comprising the element and its several layers of neighbouring elements. This paper presents a numerical study on the accuracy and convergence of the el-KI in function fitting problems. Several examples of functions in two-dimensional space are employed in this study. The results show that very accurate function fittings and excellent convergence can be attained by the el-KI.
THE NONCONFORMING FINITE ELEMENT METHOD FOR SIGNORINI PROBLEM
Institute of Scientific and Technical Information of China (English)
Dongying Hua; Lieheng Wang
2007-01-01
We present the Crouzeix-Raviart linear nonconforming finite element approximation of the variational inequality resulting from Signorini problem. We show if the displacement field is of H2 regularity, then the convergence rate can be improved from (O)(h3/4) to quasi-optimal (O)(h|log h|1/4) with respect to the energy norm as that of the continuous linear finite element approximation. If stronger but reasonable regularity is available,the convergence rate can be improved to the optimal (O)(h) as expected by the linear approximation.
Experimentally validated finite element model of electrocaloric multilayer ceramic structures
Energy Technology Data Exchange (ETDEWEB)
Smith, N. A. S., E-mail: nadia.smith@npl.co.uk, E-mail: maciej.rokosz@npl.co.uk, E-mail: tatiana.correia@npl.co.uk; Correia, T. M., E-mail: nadia.smith@npl.co.uk, E-mail: maciej.rokosz@npl.co.uk, E-mail: tatiana.correia@npl.co.uk [National Physical Laboratory, Hampton Road, TW11 0LW Middlesex (United Kingdom); Rokosz, M. K., E-mail: nadia.smith@npl.co.uk, E-mail: maciej.rokosz@npl.co.uk, E-mail: tatiana.correia@npl.co.uk [National Physical Laboratory, Hampton Road, TW11 0LW Middlesex (United Kingdom); Department of Materials, Imperial College London, London SW7 2AZ (United Kingdom)
2014-07-28
A novel finite element model to simulate the electrocaloric response of a multilayer ceramic capacitor (MLCC) under real environment and operational conditions has been developed. The two-dimensional transient conductive heat transfer model presented includes the electrocaloric effect as a source term, as well as accounting for radiative and convective effects. The model has been validated with experimental data obtained from the direct imaging of MLCC transient temperature variation under application of an electric field. The good agreement between simulated and experimental data, suggests that the novel experimental direct measurement methodology and the finite element model could be used to support the design of optimised electrocaloric units and operating conditions.
Two-dimensional finite-element temperature variance analysis
Heuser, J. S.
1972-01-01
The finite element method is extended to thermal analysis by forming a variance analysis of temperature results so that the sensitivity of predicted temperatures to uncertainties in input variables is determined. The temperature fields within a finite number of elements are described in terms of the temperatures of vertices and the variational principle is used to minimize the integral equation describing thermal potential energy. A computer calculation yields the desired solution matrix of predicted temperatures and provides information about initial thermal parameters and their associated errors. Sample calculations show that all predicted temperatures are most effected by temperature values along fixed boundaries; more accurate specifications of these temperatures reduce errors in thermal calculations.
Energy Technology Data Exchange (ETDEWEB)
Ngnegueu, T.; Mailhot, M.; Munar, A. [Jeumont Schneider Transformateurs, Lyon (France); Sacotte, M. [France-Transfo. Voie romaine, Mezieres-Les-Metz (France)
1995-05-01
In this paper, the authors present a finite element model for the calculation of zero phase sequence reactance for three phase three leg core type power transformers. An axisymmetrical approximation is assumed. A simplified model is used to assess the tank`s hottest spot temperature.
Shi, X.; Utada, H.; Jiaying, W.
2009-12-01
The vector finite-element method combined with divergence corrections based on the magnetic field H, referred to as VFEH++ method, is developed to simulate the magnetotelluric (MT) responses of 3-D conductivity models. The advantages of the new VFEH++ method are the use of edge-elements to eliminate the vector parasites and the divergence corrections to explicitly guarantee the divergence-free conditions in the whole modeling domain. 3-D MT topographic responses are modeling using the new VFEH++ method, and are compared with those calculated by other numerical methods. The results show that MT responses can be modeled highly accurate using the VFEH+ +method. The VFEH++ algorithm is also employed for the 3-D MT data inversion incorporating topography. The 3-D MT inverse problem is formulated as a minimization problem of the regularized misfit function. In order to avoid the huge memory requirement and very long time for computing the Jacobian sensitivity matrix for Gauss-Newton method, we employ the conjugate gradient (CG) approach to solve the inversion equation. In each iteration of CG algorithm, the cost computation is the product of the Jacobian sensitivity matrix with a model vector x or its transpose with a data vector y, which can be transformed into two pseudo-forwarding modeling. This avoids the full explicitly Jacobian matrix calculation and storage which leads to considerable savings in the memory required by the inversion program in PC computer. The performance of CG algorithm will be illustrated by several typical 3-D models with horizontal earth surface and topographic surfaces. The results show that the VFEH++ and CG algorithms can be effectively employed to 3-D MT field data inversion.
INTERVAL ARITHMETIC AND STATIC INTERVAL FINITE ELEMENT METHOD
Institute of Scientific and Technical Information of China (English)
郭书祥; 吕震宙
2001-01-01
When the uncertainties of structures may be bounded in intervals, through some suitable discretization, interval finite element method can be constructed by combining the interval analysis with the traditional finite element method(FEM). The two parameters,median and deviation, were used to represent the uncertainties of interval variables. Based on the arithmetic rules of intervals, some properties and arithmetic rules of interval variables were demonstrated. Combining the procedure of interval analysis with FEM, a static linear interval finite element method was presented to solve the non-random uncertain structures. The solving of the characteristic parameters of n-freedom uncertain displacement field of the static governing equation was transformed into 2 n-order linear equations. It is shown by a numerical example that the proposed method is practical and effective.
Quantum Computing over Finite Fields
James, Roshan P; Sabry, Amr
2011-01-01
In recent work, Benjamin Schumacher and Michael~D. Westmoreland investigate a version of quantum mechanics which they call "modal quantum theory" but which we prefer to call "discrete quantum theory". This theory is obtained by instantiating the mathematical framework of Hilbert spaces with a finite field instead of the field of complex numbers. This instantiation collapses much the structure of actual quantum mechanics but retains several of its distinguishing characteristics including the notions of superposition, interference, and entanglement. Furthermore, discrete quantum theory excludes local hidden variable models, has a no-cloning theorem, and can express natural counterparts of quantum information protocols such as superdense coding and teleportation. Our first result is to distill a model of discrete quantum computing from this quantum theory. The model is expressed using a monadic metalanguage built on top of a universal reversible language for finite computations, and hence is directly implementab...
SURFACE FINITE ELEMENTS FOR PARABOLIC EQUATIONS
Institute of Scientific and Technical Information of China (English)
G. Dziuk; C.M. Elliott
2007-01-01
In this article we define a surface finite element method (SFEM) for the numerical solution of parabolic partial differential equations on hypersurfaces Γ in (R)n+1. The key idea is based on the approximation of Γ by a polyhedral surface Γh consisting of a union of simplices (triangles for n = 2, intervals for n = 1) with vertices on Γ. A finite element space of functions is then defined by taking the continuous functions on Γh which are linear affine on each simplex of the polygonal surface. We use surface gradients to define weak forms of elliptic operators and naturally generate weak formulations of elliptic and parabolic equations on Γ. Our finite element method is applied to weak forms of the equations. The computation of the mass and element stiffness matrices are simple and straightforward.We give an example of error bounds in the case of semi-discretization in space for a fourth order linear problem. Numerical experiments are described for several linear and nonlinear partial differential equations. In particular the power of the method is demonstrated by employing it to solve highly nonlinear second and fourth order problems such as surface Allen-Cahn and Cahn-Hilliard equations and surface level set equations for geodesic mean curvature flow.
Finite element modelling of solidification phenomena
Indian Academy of Sciences (India)
K N Seetharamu; R Paragasam; Ghulam A Quadir; Z A Zainal; B Sathya Prasad; T Sundararajan
2001-02-01
The process of solidification process is complex in nature and the simulation of such process is required in industry before it is actually undertaken. Finite element method is used to simulate the heat transfer process accompanying the solidification process. The metal and the mould along with the air gap formation is accounted in the heat transfer simulation. Distortion of the casting is caused due to non-uniform shrinkage associated with the process. Residual stresses are induced in the final castings. Simulation of the shrinkage and the thermal stresses are also carried out using finite element methods. The material behaviour is considered as visco-plastic. The simulations are compared with available experimental data and the comparison is found to be good. Special considerations regarding the simulation of solidification process are also brought out.
Finite element simulations with ANSYS workbench 16
Lee , Huei-Huang
2015-01-01
Finite Element Simulations with ANSYS Workbench 16 is a comprehensive and easy to understand workbook. It utilizes step-by-step instructions to help guide readers to learn finite element simulations. Twenty seven real world case studies are used throughout the book. Many of these cases are industrial or research projects the reader builds from scratch. All the files readers may need if they have trouble are available for download on the publishers website. Companion videos that demonstrate exactly how to preform each tutorial are available to readers by redeeming the access code that comes in the book. Relevant background knowledge is reviewed whenever necessary. To be efficient, the review is conceptual rather than mathematical. Key concepts are inserted whenever appropriate and summarized at the end of each chapter. Additional exercises or extension research problems are provided as homework at the end of each chapter. A learning approach emphasizing hands-on experiences spreads through this entire book. A...
Finite element modelling of SAW correlator
Tikka, Ajay C.; Al-Sarawi, Said F.; Abbott, Derek
2007-12-01
Numerical simulations of SAW correlators so far are limited to delta function and equivalent circuit models. These models are not accurate as they do not replicate the actual behaviour of the device. Manufacturing a correlator to specifically realise a different configuration is both expensive and time consuming. With the continuous improvement in computing capacity, switching to finite element modelling would be more appropriate. In this paper a novel way of modelling a SAW correlator using finite element analysis is presented. This modelling approach allows the consideration of different code implementation and device structures. This is demonstrated through simulation results for a 5×2-bit Barker sequence encoded SAW correlator. These results show the effect of both bulk and leaky modes on the device performance at various operating frequencies. Moreover, the ways in which the gain of the correlator can be optimised though variation of design parameters will also be outlined.
FINITE ELEMENT ANALYSIS FOR PERIFLEX COUPLINGS
Directory of Open Access Journals (Sweden)
URDEA Mihaela
2015-06-01
Full Text Available The Periflex shaft couplings with rubber sleeve have a hig elasticity and link two shafts in diesel-engine and electric drives. They are simple from the point of view of construction, easily mounted and dismounted. The main goal of this paper is to present a finite element analysis for the Periflex coupling using the Generative Structural Analysis from CATIA software package. This paper presents important information about how to prepare an assembly for creating a static analysis case and also the important steps for developing a finite element analysis. It is very important that the analysis model should have the same behavior as the real, also the loading model. The results are images corresponding to Von Mises Stresses and Translational Displacement magnitude.
FINITE ELEMENT METHODS FOR SOBOLEV EQUATIONS
Institute of Scientific and Technical Information of China (English)
Tang Liu; Yan-ping Lin; Ming Rao; J. R. Cannon
2002-01-01
A new high-order time-stepping finite element method based upon the high-order numerical integration formula is formulated for Sobolev equations, whose computations consist of an iteration procedure coupled with a system of two elliptic equations. The optimal and superconvergence error estimates for this new method axe derived both in space and in time. Also, a class of new error estimates of convergence and superconvergence for the time-continuous finite element method is demonstrated in which there are no time derivatives of the exact solution involved, such that these estimates can be bounded by the norms of the known data. Moreover, some useful a-posteriori error estimators are given on the basis of the superconvergence estimates.
Finite element analysis of human joints
Energy Technology Data Exchange (ETDEWEB)
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 analysis of tibial fractures
DEFF Research Database (Denmark)
Wong, Christian Nai En; Mikkelsen, Mikkel Peter W; Hansen, Leif Berner
2010-01-01
INTRODUCTION: Fractures of the tibial shaft are relatively common injuries. There are indications that tibial shaft fractures share characteristics in terms of site, type and local fracture mechanisms. In this study, we aimed to set up a mathematical, computer-based model using finite element...... analysis of the bones of the lower leg to examine if such a model is adequate for prediction of fracture locations and patterns. In future studies, we aim to use these biomechanical results to examine fracture prevention, among others, and to simulate different types of osteosynthesis and the process...... of bony healing. The biomechanical results are the basis for fracture healing, biomechanical fall analysis and stability analysis of osteosynthesis. MATERIAL AND METHODS: A finite element model of the bony part of the lower leg was generated on the basis of computed tomography data from the Visible Human...
Multiphase Transformer Modelling using Finite Element Method
Directory of Open Access Journals (Sweden)
Nor Azizah Mohd Yusoff
2015-03-01
Full Text Available In the year of 1970 saw the starting invention of the five-phase motor as the milestone in advanced electric motor. Through the years, there are many researchers, which passionately worked towards developing for multiphase drive system. They developed a static transformation system to obtain a multiphase supply from the available three-phase supply. This idea gives an influence for further development in electric machines as an example; an efficient solution for bulk power transfer. This paper highlighted the detail descriptions that lead to five-phase supply with fixed voltage and frequency by using Finite-Element Method (FEM. Identifying of specification on a real transformer had been done before applied into software modeling. Therefore, Finite-Element Method provides clearly understandable in terms of visualize the geometry modeling, connection scheme and output waveform.
The finite element modeling of spiral ropes
Institute of Scientific and Technical Information of China (English)
Juan Wu
2014-01-01
Accurate understanding the behavior of spiral rope is complicated due to their complex geometry and complex contact conditions between the wires. This study proposed the finite element models of spiral ropes subjected to tensile loads. The parametric equations developed in this paper were implemented for geometric modeling of ropes. The 3D geometric models with different twisting manner, equal diameters of wires were generated in details by using Pro/ENGINEER software. The results of the present finite element analysis were on an acceptable level of accuracy as compared with those of theoretical and experimental data. Further development is ongoing to analysis the equivalent stresses induced by twisting manner of cables. The twisting manner of wires was important to spiral ropes in the three wire layers and the outer twisting manner of wires should be contrary to that of the second layer, no matter what is the first twisting manner of wires.
Finite element contact analysis of fractal surfaces
Energy Technology Data Exchange (ETDEWEB)
Sahoo, Prasanta; Ghosh, Niloy [Department of Mechanical Engineering, Jadavpur University, Kolkata 700032 (India)
2007-07-21
The present study considers finite element analysis of non-adhesive, frictionless elastic/elastic-plastic contact between a rigid flat plane and a self-affine fractal rough surface using the commercial finite element package ANSYS. Three-dimensional rough surfaces are generated using a modified two-variable Weierstrass-Mandelbrot function with given fractal parameters. Parametric studies are done to consider the general relations between contact properties and key material and surface parameters. The present analysis is validated with available experimental results in the literature. Non-dimensional contact area and displacement are obtained as functions of non-dimensional load for varying fractal surface parameters in the case of elastic contact and for varying rates of strain hardening in the case of elastic-plastic contact of fractal surfaces.
Adaptive Mixed Finite Element Methods for Parabolic Optimal Control Problems
Zuliang Lu
2011-01-01
We will investigate the adaptive mixed finite element methods for parabolic optimal control problems. The state and the costate are approximated by the lowest-order Raviart-Thomas mixed finite element spaces, and the control is approximated by piecewise constant elements. We derive a posteriori error estimates of the mixed finite element solutions for optimal control problems. Such a posteriori error estimates can be used to construct more efficient and reliable adaptive mixed finite element ...
Finite element simulation of heat transfer
Bergheau, Jean-Michel
2010-01-01
This book introduces the finite element method applied to the resolution of industrial heat transfer problems. Starting from steady conduction, the method is gradually extended to transient regimes, to traditional non-linearities, and to convective phenomena. Coupled problems involving heat transfer are then presented. Three types of couplings are discussed: coupling through boundary conditions (such as radiative heat transfer in cavities), addition of state variables (such as metallurgical phase change), and coupling through partial differential equations (such as electrical phenomena).? A re
Finite Element Simulation for Interfacial Evolutions
Institute of Scientific and Technical Information of China (English)
JianmingHUANG; WeiYANG
1998-01-01
A three-dimensional finite element scheme based upon a weak statement of the classical theory is explored to simulate migration of interfaces in materials under linear evaporation and condensation kinetics,The present scheme is exemplified by two cases:facet formation of single crystals;and the evolution of a tri-crystal film on a substrate where the effect of multiple kinetics is demonstrated.
Quick finite elements for electromagnetic waves
Pelosi, Giuseppe; Selleri, Stefano
2009-01-01
This practical book and accompanying software enables you to quickly and easily work out challenging microwave engineering and high-frequency electromagnetic problems using the finite element method (FEM) Using clear, concise text and dozens of real-world application examples, the book provides a detailed description of FEM implementation, while the software provides the code and tools needed to solve the three major types of EM problems: guided propagation, scattering, and radiation.
EXODUS II: A finite element data model
Energy Technology Data Exchange (ETDEWEB)
Schoof, L.A.; Yarberry, V.R.
1994-09-01
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 (API).
Finite element methods for incompressible flow problems
John, Volker
2016-01-01
This book explores finite element methods for incompressible flow problems: Stokes equations, stationary Navier-Stokes equations, and time-dependent Navier-Stokes equations. It focuses on numerical analysis, but also discusses the practical use of these methods and includes numerical illustrations. It also provides a comprehensive overview of analytical results for turbulence models. The proofs are presented step by step, allowing readers to more easily understand the analytical techniques.
Nonlinear Finite Element Analysis of Ocean Cables
Institute of Scientific and Technical Information of China (English)
Nam-Il KIM; Sang-Soo JEON; Moon-Young KIM
2004-01-01
This study has focused on developing numerical procedures for the dynamic nonlinear analysis of cable structures subjected to wave forces and ground motions in the ocean. A geometrically nonlinear finite element procedure using the isoparametric curved cable element based on the Lagrangian formulation is briefly summarized. A simple and accurate method to determine the initial equilibrium state of cable systems associated with self-weights, buoyancy and the motion of end points is presented using the load incremental method combined with penalty method. Also the Newmark method is used for dynamic nonlinear analysis of ocean cables. Numerical examples are presented to validate the present numerical method.
Finite Element Method in Machining Processes
Markopoulos, Angelos P
2013-01-01
Finite Element Method in Machining Processes provides a concise study on the way the Finite Element Method (FEM) is used in the case of manufacturing processes, primarily in machining. The basics of this kind of modeling are detailed to create a reference that will provide guidelines for those who start to study this method now, but also for scientists already involved in FEM and want to expand their research. A discussion on FEM, formulations and techniques currently in use is followed up by machining case studies. Orthogonal cutting, oblique cutting, 3D simulations for turning and milling, grinding, and state-of-the-art topics such as high speed machining and micromachining are explained with relevant examples. This is all supported by a literature review and a reference list for further study. As FEM is a key method for researchers in the manufacturing and especially in the machining sector, Finite Element Method in Machining Processes is a key reference for students studying manufacturing processes but al...
Directory of Open Access Journals (Sweden)
Jailson A. Da Nóbrega
2016-01-01
Full Text Available Metallic materials undergo many metallurgical changes when subjected to welding thermal cycles, and these changes have a considerable influence on the thermo-mechanical properties of welded structures. One method for evaluating the welding thermal cycle variables, while still in the project phase, would be simulation using computational methods. This paper presents an evaluation of the temperature field and residual stresses in a multipass weld of API 5L X80 steel, which is extensively used in oil and gas industry, using the Finite Element Method (FEM. In the simulation, the following complex phenomena were considered: the variation in physical and mechanical properties of the material as a function of the temperature, welding speed and convection and radiation mechanisms. Additionally, in order to characterize a multipass weld using the Gas Tungsten Arc Welding process for the root pass and the Shielded Metal Arc Welding process for the filling passes, the analytical heat source proposed by Goldak and Chakravarti was used. In addition, we were able to analyze the influence of the mesh refinement in the simulation results. The findings indicated a significant variation of about 50% in the peak temperature values. Furthermore, changes were observed in terms of the level and profile of the welded joint residual stresses when more than one welding pass was considered.
Directory of Open Access Journals (Sweden)
Yu-chuan Yang
2016-01-01
Full Text Available The slope stability problem is an important issue for the safety of human beings and structures. The stability analysis of the three-dimensional (3D slope is essential to prevent landslides, but the most important and difficult problem is how to determine the 3D critical slip surface with the minimum factor of safety in earth slopes. Basing on the slope stress field with the finite element method, a stability analysis method is proposed to determine the critical slip surface and the corresponding safety factor of 3D soil slopes. Spherical and ellipsoidal slip surfaces are considered through the analysis. The moment equilibrium is used to compute the safety factor combined with the Mohr-Coulomb criteria and the limit equilibrium principle. Some assumptions are introduced to reduce the search range of center points and the radius of spheres or ellipsoids. The proposed method is validated by a classical 3D benchmark soil slope. Simulated results indicate that the safety factor of the benchmark slope is 2.14 using the spherical slip surface and 2.19 using the ellipsoidal slip surface, which is close to the results of previous methods. The simulated results indicate that the proposed method can be used for the stability analysis of a 3D soil slope.
Ruiz-Baier, Ricardo; Lunati, Ivan
2016-10-01
We present a novel discretization scheme tailored to a class of multiphase models that regard the physical system as consisting of multiple interacting continua. In the framework of mixture theory, we consider a general mathematical model that entails solving a system of mass and momentum equations for both the mixture and one of the phases. The model results in a strongly coupled and nonlinear system of partial differential equations that are written in terms of phase and mixture (barycentric) velocities, phase pressure, and saturation. We construct an accurate, robust and reliable hybrid method that combines a mixed finite element discretization of the momentum equations with a primal discontinuous finite volume-element discretization of the mass (or transport) equations. The scheme is devised for unstructured meshes and relies on mixed Brezzi-Douglas-Marini approximations of phase and total velocities, on piecewise constant elements for the approximation of phase or total pressures, as well as on a primal formulation that employs discontinuous finite volume elements defined on a dual diamond mesh to approximate scalar fields of interest (such as volume fraction, total density, saturation, etc.). As the discretization scheme is derived for a general formulation of multicontinuum physical systems, it can be readily applied to a large class of simplified multiphase models; on the other, the approach can be seen as a generalization of these models that are commonly encountered in the literature and employed when the latter are not sufficiently accurate. An extensive set of numerical test cases involving two- and three-dimensional porous media are presented to demonstrate the accuracy of the method (displaying an optimal convergence rate), the physics-preserving properties of the mixed-primal scheme, as well as the robustness of the method (which is successfully used to simulate diverse physical phenomena such as density fingering, Terzaghi's consolidation
Hybrid Fundamental Solution Based Finite Element Method: Theory and Applications
Changyong Cao; Qing-Hua Qin
2015-01-01
An overview on the development of hybrid fundamental solution based finite element method (HFS-FEM) and its application in engineering problems is presented in this paper. The framework and formulations of HFS-FEM for potential problem, plane elasticity, three-dimensional elasticity, thermoelasticity, anisotropic elasticity, and plane piezoelectricity are presented. In this method, two independent assumed fields (intraelement filed and auxiliary frame field) are employed. The formulations for...
Stochastic finite element applications in rigid pavement performance
Attoh-Okine, Nii O.
1999-05-01
Rigid pavement structures have uncertainties and variability in their structural layers and components. These variations and uncertainties are seldomly included in performance assessment and evaluation in pavement systems. This paper proposes to use Stochastic Finite Element Method (SFEM) in rigid pavement faulting and load transfer efficiency. The SFEM uses random parameters, as stochastic process namely random fields. These random fields are characterized, quantitatively by spatial functions of statistical moment like the mean, variance and covariance.
A finite element parametric modeling technique of aircraft wing structures
Institute of Scientific and Technical Information of China (English)
Tang Jiapeng; Xi Ping; Zhang Baoyuan; Hu Bifu
2013-01-01
A finite element parametric modeling method of aircraft wing structures is proposed in this paper because of time-consuming characteristics of finite element analysis pre-processing. The main research is positioned during the preliminary design phase of aircraft structures. A knowledge-driven system of fast finite element modeling is built. Based on this method, employing a template parametric technique, knowledge including design methods, rules, and expert experience in the process of modeling is encapsulated and a finite element model is established automatically, which greatly improves the speed, accuracy, and standardization degree of modeling. Skeleton model, geometric mesh model, and finite element model including finite element mesh and property data are established on parametric description and automatic update. The outcomes of research show that the method settles a series of problems of parameter association and model update in the pro-cess of finite element modeling which establishes a key technical basis for finite element parametric analysis and optimization design.
Finite Element Based Design and Optimization for Piezoelectric Accelerometers
DEFF Research Database (Denmark)
Liu, Bin; Kriegbaum, B.; Yao, Q.
1998-01-01
A systematic Finite Element design and optimisation procedure is implemented for the development of piezoelectric accelerometers. Most of the specifications of accelerometers can be obtained using the Finite Element simulations. The deviations between the simulated and calibrated sensitivities...
Application of finite-element-methods in food processing
DEFF Research Database (Denmark)
Risum, Jørgen
2004-01-01
Presentation of the possible use of finite-element-methods in food processing. Examples from diffusion studies are given.......Presentation of the possible use of finite-element-methods in food processing. Examples from diffusion studies are given....
Finite element modeling for materials engineers using Matlab
Oluwole, Oluleke
2014-01-01
Finite Element Modeling for Materials Engineers Using MATLAB® combines the finite element method with MATLAB to offer materials engineers a fast and code-free way of modeling for many materials processes.
Finite Element Post-processing Data Field Visualization Research%有限元后处理数据场可视化研究
Institute of Scientific and Technical Information of China (English)
晁岱兵; 陈显呈; 邓伟; 彭清
2012-01-01
采用Python语言基于OpenGL的可视化开发,通过算法和程序的编制,对有限元分析结果数据进行重构显示.利用图形函数实现了八节点六面体三维数据场的网格模型建立,并进行面消隐；利用glColorPointer函数对网格模型各个节点上的标量场进行颜色映射,重构出效果良好的应力应变云图.比较了线性插值和余弦插值两种不同方法形成颜色渲染效果差异,同时对二次和三次不同颜色分量数学模型对渲染效果的影响进行对比研究.%Python is applied to visual development based on OpenGL interface. The result data of finite element analysis is reconstruc tured through algorithm and program. The data field of grid model with eight node hexahedron is built and the surfaces are hided by graphic function. The scalar field on nodes of the grid model is mapped with different colors by glColorPointer function; the stress-strain diagram is reconstructured well. The different render effect of linear interpolation is compared with one of consine interpolation, and the color rendering of second mathematical model is compared with one of third mathematical model and they are researched on.
González-Estrada, Octavio A; Bordas, Stéphane P A; Duflot, Marc; Kerfriden, Pierre; Giner, Eugenio
2011-01-01
Purpose: This paper aims at assessing the effect of (1) the statical admissibility of the recovered solution; (2) the ability of the recovered solution to represent the singular solution; on the accuracy, local and global effectivity of recovery-based error estimators for enriched finite element methods (e.g. the extended finite element method, XFEM). Design/methodology/approach: We study the performance of two recovery techniques. The first is a recently developed superconvergent patch recovery procedure with equilibration and enrichment (SPR-CX). The second is known as the extended moving least squares recovery (XMLS), which enriches the recovered solutions but does not enforce equilibrium constraints. Both are extended recovery techniques as the polynomial basis used in the recovery process is enriched with singular terms for a better description of the singular nature of the solution. Findings: Numerical results comparing the convergence and the effectivity index of both techniques with those obtained wit...
A finite element model of ferroelectric/ferroelastic polycrystals
Energy Technology Data Exchange (ETDEWEB)
HWANG,STEPHEN C.; MCMEEKING,ROBERT M.
2000-02-17
A finite element model of polarization switching in a polycrystalline ferroelectric/ferroelastic ceramic is developed. It is assumed that a crystallite switches if the reduction in potential energy of the polycrystal exceeds a critical energy barrier per unit volume of switching material. Each crystallite is represented by a finite element with the possible dipole directions assigned randomly subject to crystallographic constraints. The model accounts for both electric field induced (i.e. ferroelectric) switching and stress induced (i.e. ferroelastic) switching with piezoelectric interactions. Experimentally measured elastic, dielectric, and piezoelectric constants are used consistently, but different effective critical energy barriers are selected phenomenologically. Electric displacement versus electric field, strain versus electric field, stress versus strain, and stress versus electric displacement loops of a ceramic lead lanthanum zirconate titanate (PLZT) are modeled well below the Curie temperature.
Cheng, J.; Johnson, B.; Everett, M.
2003-12-01
Preliminary field work shows slug interference tests using an array of multilevel active and monitoring wells have potential of permitting enhanced aquifer characterization. Analysis of these test data, however, ultimately will rely on numerical geophysical inverse models. In order to gain insight as well as to provide synthetic data sets, we use a 3-D finite element analysis (code:FEHM-LANL) to explore the effect of idealized, low permeability, stratigraphical and structural (faults) heterogeneities on the transient head field associated with a slug test in a packer-isolated interval of an open borehole. The borehole and packers are modeled explicitly; wellbore storage is selected to match values of field tests. The homogeneous model exhibits excellent agreement with that of the semi-analytical model of Liu and Butler (1995). Models are axisymmetric with a centrally located slugged interval within a homogenous, isotropic, confined aquifer with embedded, horizontal or vertical zones of lower permeability that represent low permeability strata or faults, respectively. Either one or two horizontal layers are located opposite the borehole packers, which is a common situation at the field site; layer thickness (0.15-0.75 m), permeability contrast (up to 4 orders of magnitude contrast) and lateral continuity of layers are varied between models. The effect of a "hole" in a layer also is assessed. Fault models explore effects of thickness (0.05-0.75 m) and permeability contrast as well as additional effects associated with the offset of low permeability strata. Results of models are represented most clearly by contour maps of time of arrival and normalized amplitude of peak head perturbation, but transient head histories at selected locations provide additional insight. Synthesis of the models is on-going but a few points can be made at present. Spatial patterns are distinctive and allow easy discrimination between stratigraphic and structural impedance features. Time
Finite rotation shells basic equations and finite elements for Reissner kinematics
Wisniewski, K
2010-01-01
This book covers theoretical and computational aspects of non-linear shells. Several advanced topics of shell equations and finite elements - not included in standard textbooks on finite elements - are addressed, and the book includes an extensive bibliography.
Finite element modeling methods for photonics
Rahman, B M Azizur
2013-01-01
The term photonics can be used loosely to refer to a vast array of components, devices, and technologies that in some way involve manipulation of light. One of the most powerful numerical approaches available to engineers developing photonic components and devices is the Finite Element Method (FEM), which can be used to model and simulate such components/devices and analyze how they will behave in response to various outside influences. This resource provides a comprehensive description of the formulation and applications of FEM in photonics applications ranging from telecommunications, astron
Finite element simulation of asphalt fatigue testing
DEFF Research Database (Denmark)
Ullidtz, Per; Kieler, Thomas Lau; Kargo, Anders
1997-01-01
damage mechanics.The paper describes how continuum damage mechanics may be used with a finite element program to explain the progressive deterioration of asphalt mixes under laboratory fatigue testing. Both constant stress and constant strain testing are simulated, and compared to the actual results from...... three point and four point fatigue test on different mixes. It is shown that the same damage law, based on energy density, may be used to explain the gradual deterioration under constant stress as well as under constant strain testing.Some of the advantages of using this method for interpreting fatigue...
The serendipity family of finite elements
Arnold, Douglas N
2011-01-01
We give a new, simple, dimension-independent definition of the serendipity finite element family. The shape functions are the span of all monomials which are linear in at least s-r of the variables where s is the degree of the monomial or, equivalently, whose superlinear degree (total degree with respect to variables entering at least quadratically) is at most r. The degrees of freedom are given by moments of degree at most r-2d on each face of dimension d. We establish unisolvence and a geometric decomposition of the space.
Generalized multiscale finite element methods: Oversampling strategies
Efendiev, Yalchin R.
2014-01-01
In this paper, we propose oversampling strategies in the generalized multiscale finite element method (GMsFEM) framework. The GMsFEM, which has been recently introduced in Efendiev et al. (2013b) [Generalized Multiscale Finite Element Methods, J. Comput. Phys., vol. 251, pp. 116-135, 2013], allows solving multiscale parameter-dependent problems at a reduced computational cost by constructing a reduced-order representation of the solution on a coarse grid. The main idea of the method consists of (1) the construction of snapshot space, (2) the construction of the offline space, and (3) construction of the online space (the latter for parameter-dependent problems). In Efendiev et al. (2013b) [Generalized Multiscale Finite Element Methods, J. Comput. Phys., vol. 251, pp. 116-135, 2013], it was shown that the GMsFEM provides a flexible tool to solve multiscale problems with a complex input space by generating appropriate snapshot, offline, and online spaces. In this paper, we develop oversampling techniques to be used in this context (see Hou and Wu (1997) where oversampling is introduced for multiscale finite element methods). It is known (see Hou and Wu (1997)) that the oversampling can improve the accuracy of multiscale methods. In particular, the oversampling technique uses larger regions (larger than the target coarse block) in constructing local basis functions. Our motivation stems from the analysis presented in this paper, which shows that when using oversampling techniques in the construction of the snapshot space and offline space, GMsFEM will converge independent of small scales and high contrast under certain assumptions. We consider the use of a multiple eigenvalue problems to improve the convergence and discuss their relation to single spectral problems that use oversampled regions. The oversampling procedures proposed in this paper differ from those in Hou and Wu (1997). In particular, the oversampling domains are partially used in constructing local
Finite element modelingof spherical induction actuator
Galary, Grzegorz
2005-01-01
The thesis deals with finite element method simulations of the two-degree of freedom spherical induction actuator performed using the 2D and 3D models. In some cases non-linear magnetization curves, rotor movement and existence of higher harmonics are taken into account. The evolution of the model leading to its simplification is presented. Several rotor structures are tested, namely the one-layer, two-layers and two-layers-with-teeth rotor. The study of some rotor parameters, i.e. t...
A finite element model of ultrasonic extrusion
Energy Technology Data Exchange (ETDEWEB)
Lucas, M [Department of Mechanical Engineering, University of Glasgow, G12 8QQ (United Kingdom); Daud, Y, E-mail: m.lucas@mech.gla.ac.u [College of Science and Technology, UTM City Campus, Kuala Lumpur (Malaysia)
2009-08-01
Since the 1950's researchers have carried out investigations into the effects of applying ultrasonic excitation to metals undergoing elastic and plastic deformation. Experiments have been conducted where ultrasonic excitation is superimposed in complex metalworking operations such as wire drawing and extrusion, to identify the benefits of ultrasonic vibrations. This study presents a finite element analysis of ultrasonic excitation applied to the extrusion of a cylindrical aluminium bar. The effects of friction on the extrusion load are reported for the two excitation configurations of radially and axially applied ultrasonic vibrations and the results are compared with experimental data reported in the literature.
A finite element model of ultrasonic extrusion
Lucas, M.; Daud, Y.
2009-08-01
Since the 1950's researchers have carried out investigations into the effects of applying ultrasonic excitation to metals undergoing elastic and plastic deformation. Experiments have been conducted where ultrasonic excitation is superimposed in complex metalworking operations such as wire drawing and extrusion, to identify the benefits of ultrasonic vibrations. This study presents a finite element analysis of ultrasonic excitation applied to the extrusion of a cylindrical aluminium bar. The effects of friction on the extrusion load are reported for the two excitation configurations of radially and axially applied ultrasonic vibrations and the results are compared with experimental data reported in the literature.
Iterative methods for mixed finite element equations
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.
Mixed finite elements for global tide models
Cotter, Colin J
2014-01-01
We study mixed finite element methods for the linearized rotating shallow water equations with linear drag and forcing terms. By means of a strong energy estimate for an equivalent second-order formulation for the linearized momentum, we prove long-time stability of the system without energy accumulation -- the geotryptic state. A priori error estimates for the linearized momentum and free surface elevation are given in $L^2$ as well as for the time derivative and divergence of the linearized momentum. Numerical results confirm the theoretical results regarding both energy damping and convergence rates.
Implicit extrapolation methods for multilevel finite element computations
Energy Technology Data Exchange (ETDEWEB)
Jung, M.; Ruede, U. [Technische Universitaet Chemnitz-Zwickau (Germany)
1994-12-31
The finite element package FEMGP has been developed to solve elliptic and parabolic problems arising in the computation of magnetic and thermomechanical fields. FEMGP implements various methods for the construction of hierarchical finite element meshes, a variety of efficient multilevel solvers, including multigrid and preconditioned conjugate gradient iterations, as well as pre- and post-processing software. Within FEMGP, multigrid {tau}-extrapolation can be employed to improve the finite element solution iteratively to higher order. This algorithm is based on an implicit extrapolation, so that the algorithm differs from a regular multigrid algorithm only by a slightly modified computation of the residuals on the finest mesh. Another advantage of this technique is, that in contrast to explicit extrapolation methods, it does not rely on the existence of global error expansions, and therefore neither requires uniform meshes nor global regularity assumptions. In the paper the authors will analyse the {tau}-extrapolation algorithm and present experimental results in the context of the FEMGP package. Furthermore, the {tau}-extrapolation results will be compared to higher order finite element solutions.
A nonlinear truss finite element with varying stiffness
Directory of Open Access Journals (Sweden)
Ďuriš R.
2007-11-01
Full Text Available This contribution deals with a new truss element with varying stiffness intended to geometric and physically nonlinear analysis of composite structures. We present a two-node straight composite truss finite element derived by new nonincremental full geometric nonlinear approach. Stiffness matrix of this composite truss contains transfer constants, which accurately describe the polynomial longitudinal variation of cross-section area and material properties. These variations could be caused by nonhomogenous temperature field or by varying components volume fractions of the composite or/and functionally graded materials (FGM´s. Numerical examples were solved to verify the established relations. The accuracy of the new proposed finite truss element are compared and discused.
A direct implementation for influence lines in finite element software
DEFF Research Database (Denmark)
Jepsen, Michael S.; Damkilde, Lars
2014-01-01
The use of influence lines is a recognized method for determining the critical design load conditions and this paper shows a direct method for applying influence lines in any structural finite element software. The main idea is to equate displacement or angular discontinuities with nodal forces...... to consistent nodal forces, which makes it very suitable for implementation in finite element schemes and applicable for all element types, such as shell, plates, beams etc. This paper derives the consistent nodal forces for angular, lateral and axial displacement discontinuities for a Bernoulli-Euler beam......, and subsequently obtain the influence function only applying a single load case without changing the geometry or boundary conditions of the model. The new approach for determining Influence lines is based on the Müller-Breslau principle, but the discontinuous displacement fields are in the new approach equated...
Finite Element Simulation of the Optical Modes of Semiconductor Lasers
Pomplun, J; Schmidt, F; Schliwa, A; Bimberg, D; Pietrzak, A; Wenzel, H; Erbert, G; 10.1002/pssb.200945451
2010-01-01
In the present article we investigate optical near fields in semiconductor lasers. We perform finite element simulations for two different laser types, namely a super large optical waveguide (SLOW) laser, which is an edge emitter, and a vertical cavity surface emitting laser (VCSEL). We give the mathematical formulation of the different eigenvalue problems that arise for our examples and explain their numerical solution with the finite element method. Thereby, we also comment on the usage of transparent boundary conditions, which have to be applied to respect the exterior environment, e.g., the very large substrate and surrounding air. For the SLOW laser we compare the computed near fields to experimental data for different design parameters of the device. For the VCSEL example a comparison to simplified 1D mode calculations is carried out.
A finite element model for residual stress in repair welds
Energy Technology Data Exchange (ETDEWEB)
Feng, Z. [Edison Welding Inst., Columbus, OH (United States); Wang, X.L.; Spooner, S.; Goodwin, G.M.; Maziasz, P.J.; Hubbard, C.R.; Zacharia, T. [Oak Ridge National Lab., TN (United States)
1996-03-28
This paper describes a three-dimensional finite element model for calculation of the residual stress distribution caused by repair welding. Special user subroutines were developed to simulate the continuous deposition of filler metal during welding. The model was then tested by simulating the residual stress/strain field of a FeAl weld overlay clad on a 2{1/4}Cr-1 Mo steel plate, for which neutron diffraction measurement data of the residual strain field were available. It is shown that the calculated residual stress distribution was consistent with that determined with neutron diffraction. High tensile residual stresses in both the longitudinal and transverse directions were observed around the weld toe at the end of the weld. The strong spatial dependency of the residual stresses in the region around the weld demonstrates that the common two-dimensional cross-section finite element models should not be used for repair welding analysis.
A variational H(div) finite element discretisation for perfect incompressible fluids
Natale, Andrea; Cotter, Colin J.
2016-01-01
We propose a finite element discretisation approach for the incompressible Euler equations which mimics their geometric structure and their variational derivation. In particular, we derive a finite element method that arises from a nonholonomic variational principle and an appropriately defined Lagrangian, where finite element H(div) vector fields are identified with advection operators; this is the first successful extension of the structure-preserving discretisation of Pavlov et al. (2009) ...
Finite element analysis of multilayer coextrusion.
Energy Technology Data Exchange (ETDEWEB)
Hopkins, Matthew Morgan; Schunk, Peter Randall; Baer, Thomas A. (Proctor & Gamble Company, West Chester, OH); Mrozek, Randy A. (Army Research Laboratory, Adelphi, MD); Lenhart, Joseph Ludlow (Army Research Laboratory, Adelphi, MD); Rao, Rekha Ranjana; Collins, Robert (Oak Ridge National Laboratory); 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.
Finite element analysis of bolted flange connections
Hwang, D. Y.; Stallings, J. M.
1994-06-01
A 2-D axisymmetric finite element model and a 3-D solid finite element model of a high pressure bolted flange joint were generated to investigate the stress behaviors. This investigation includes comparisons for axisymmetric loading of both the 2-D and 3-D models, the effects of non-axisymmetric bolt pretensions in the 3-D models, and the differences between 2-D and 3-D models subjected to non-axisymmetric loading. Comparisons indicated differences in von Mises stress up to 12% at various points due to the non-axisymmetric bolt pretensions. Applied bending moments were converted to equivalent axial forces for use in the 2-D model. It was found that the largest von Mises stresses in 3-D model did not occur on the side of the connection where the bending stresses and applied axial stresses were additive. Hence, in the 2-D model where the equivalent axial force (for bending moment) and applied axial forces were added, the 2-D model under estimated the maximum von Mises stress obtained from the 3-D model by 30%.
Impeller deflection and modal finite element analysis.
Energy Technology Data Exchange (ETDEWEB)
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.
A multigrid solution method for mixed hybrid finite elements
Energy Technology Data Exchange (ETDEWEB)
Schmid, W. [Universitaet Augsburg (Germany)
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.
Finite Element Modeling of Metasurfaces with Generalized Sheet Transition Conditions
Sandeep, Srikumar; Caloz, Christophe
2016-01-01
A modeling of metasurfaces in the finite element method (FEM) based on generalized sheet transition conditions (GSTCs) is presented. The discontinuities in electromagnetic fields across a metasurface as represented by the GSTC are modeled by assigning nodes to both sides of the metasurface. The FEM-GSTC formulation in both 1D and 2D domains is derived and implemented. The method is extended to handle more general bianistroptic metasurfaces. The formulations are validated by several illustrative examples.
Quality Assessment and Control of Finite Element Solutions.
1986-05-01
34Computation of Stress Field Parameters in Areas of Steep Stress Gradients," Communciations in Applied Numerical Methods , Vol. 2, 1986, pp. 133-137. 56. Szabo...Methods for Second Derivatives in Finite Element Approximation of Linear Elasticity Problems," Communications in Applied % Numerical Methods , Vol. 1, 1985...Procedures," Communications in Applied Numerical Methods , Vol. 1, 1985, pp. 3-9. 176. Fletcher, C. A. J., Computational Galerkin Methods, Springer
Stochastic Finite Element Analysis of Plate and Shell Construction
Institute of Scientific and Technical Information of China (English)
无
2000-01-01
The response of random plate and shell construction is analyzed with the stochastic finite element method (SFEM). Random material properties and geometric dimensions of construction are involved in this paper. A simplified isoparametric local average model is used to describe the random field. Numerical results of the examples indicate that the approach presented herein is an economical and efficient solution for such an analysis compared with Monte Carlo simulation (MCS).
Accurate finite element modeling of acoustic waves
Idesman, A.; Pham, D.
2014-07-01
In the paper we suggest an accurate finite element approach for the modeling of acoustic waves under a suddenly applied load. We consider the standard linear elements and the linear elements with reduced dispersion for the space discretization as well as the explicit central-difference method for time integration. The analytical study of the numerical dispersion shows that the most accurate results can be obtained with the time increments close to the stability limit. However, even in this case and the use of the linear elements with reduced dispersion, mesh refinement leads to divergent numerical results for acoustic waves under a suddenly applied load. This is explained by large spurious high-frequency oscillations. For the quantification and the suppression of spurious oscillations, we have modified and applied a two-stage time-integration technique that includes the stage of basic computations and the filtering stage. This technique allows accurate convergent results at mesh refinement as well as significantly reduces the numerical anisotropy of solutions. We should mention that the approach suggested is very general and can be equally applied to any loading as well as for any space-discretization technique and any explicit or implicit time-integration method.
MIG堆焊温度场有限元求解及验证%Finite element solution of temperature field of MIG bead weld and its verification
Institute of Scientific and Technical Information of China (English)
黄健康; 韩日宏; 薛诚; 石玗; 樊丁
2011-01-01
A temperature field model of MIG bead weld was set up and it was used for temperature computations by using the double ellipsoid heat sources. Taking account of the impact of temperature on the material properties and heat dissipation from its surface and using the adaptive grid technology, a numeric analysis of model was performed and the transient temperature field of the welding process as well as the thermal cycle curve for the characteristic points on the back of workpiece were got. Experiment of MIG bead weld was conducted and thermal cycle curves of the corresponding points were got by using thermoelectric couple and its results were compared to those of simulation computation. The results showed that calculated and experimental results were basically the same, and the model of MIG bead weld was accurate and the finite element solution was feasible.%建立MIG堆焊过程的温度场模型,通过移动双椭球热源模型进行计算,考虑温度对材料性能参数以及工件表面散热条件的影响,并运用自适应网格技术,对模型进行数值分析,得到MIG堆焊过程的瞬态温度场和工件背面特征点的热循环曲线.并进行MIG平板堆焊的实际焊接试验,利用热电偶采集对应特征点的试验数据并与模拟结果进行对比比较.结果表明:计算得到的特征点焊接热循环曲线与试验结果基本一致,所建立的MIG堆焊温度场模型是准确的,温度场有限元求解是可行的.
Diagonal multi-soliton matrix elements in finite volume
Pálmai, T
2012-01-01
We consider diagonal matrix elements of local operators between multi-soliton 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 Tak\\'acs 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 a Contactless Power Transformer with Metamaterial
Directory of Open Access Journals (Sweden)
Lan Jian Yu
2013-07-01
Full Text Available Wireless power transfer technologies enable power transfer to loads through air. The contactless power transformer is a key element of it. In this work, a new transformer with metamaterial is proposed, through which the power transfer distance increases. The electromagnetic properties about metamaterial are discussed at first. Then, the finite element analyses of this transformer are presented as well. The magnetic field distributions and the computational results show that this type of transformer can enlarge the power transfer range of a wireless power transfer system.
On conforming mixed finite element methods for incompressible viscous flow problems
Gunzburger, M. D; Nicolaides, R. A.; Peterson, J. S.
1982-01-01
The application of conforming mixed finite element methods to obtain approximate solutions of linearized Navier-Stokes equations is examined. Attention is given to the convergence rates of various finite element approximations of the pressure and the velocity field. The optimality of the convergence rates are addressed in terms of comparisons of the approximation convergence to a smooth solution in relation to the best approximation available for the finite element space used. Consideration is also devoted to techniques for efficient use of a Gaussian elimination algorithm to obtain a solution to a system of linear algebraic equations derived by finite element discretizations of linear partial differential equations.
Composite Extension Finite Fields for Low Overhead Network Coding
DEFF Research Database (Denmark)
Heide, Janus; Roetter, Daniel Enrique Lucani
2015-01-01
packet. This work advocates the use of multiple composite extension finite fields to address these challenges. The key of our approach is to design a series of finite fields where increasingly larger fields are based on a previous smaller field. For example, the design of a field with 256 elements F2222...... is based on polynomial arithmetic over a field with 16 elements F222, in turn based on a field with 4 elements F22. We propose a technique to modify standard Random Linear Network Coding (RLNC) to utilize a set of these fields instead of a single field and analyze the performance. The results show...... that total overhead is reduced due to reduced size of the coding vector, while maintaining low linear dependency between coded packets. The overhead can in some cases be reduced to less than one-fifth compared to standard RLNC and importantly the ability to recode is preserved....
Distinguishing division algebras by finite splitting fields
Krashen, Daniel
2010-01-01
This paper is concerned with the problem of determining the number of division algebras which share the same collection of finite splitting fields. As a corollary we are able to determine when two central division algebras may be distinguished by their finite splitting fields over certain fields.
Test Simulation using Finite Element Method
Energy Technology Data Exchange (ETDEWEB)
Ali, M B; Abdullah, S; Nuawi, M Z; Ariffin, A K, E-mail: abgbas@yahoo.com [Department of Mechanical and Materials Engineering, Faculty of Engineering and Built Environment Universiti Kebangsaan Malaysia 43600 Bangi, Selangor (Malaysia)
2011-02-15
The dynamic responses of the standard Charpy impact machine are experimentally studied using the relevant data acquisition system, for the purpose of obtaining the impact response. For this reason, the numerical analysis by means of the finite element method has been used for experiment findings. Modelling of the charpy test was performed in order to obtain strain in the striker during the test. Two types of standard charpy specimens fabricated from different materials, i.e. aluminium 6061 and low carbon steel 1050, were used for the impact simulation testing. The related parameters on between different materials, energy absorbed, strain signal, power spectrum density (PSD) and the relationship between those parameters was finally correlated and discussed.
Friction welding; Magnesium; Finite element; Shear test.
Directory of Open Access Journals (Sweden)
Leonardo Contri Campanelli
2013-06-01
Full Text Available Friction spot welding (FSpW is one of the most recently developed solid state joining technologies. In this work, based on former publications, a computer aided draft and engineering resource is used to model a FSpW joint on AZ31 magnesium alloy sheets and subsequently submit the assembly to a typical shear test loading, using a linear elastic model, in order to conceive mechanical tests results. Finite element analysis shows that the plastic flow is concentrated on the welded zone periphery where yield strength is reached. It is supposed that “through the weld” and “circumferential pull-out” variants should be the main failure behaviors, although mechanical testing may provide other types of fracture due to metallurgical features.
Finite element methods in resistivity logging
Lovell, J. R.
1993-09-01
Resistivity measurements are used in geophysical logging to help determine hydrocarbon reserves. The derivation of formation parameters from resistivity measurements is a complicated nonlinear procedure often requiring additional geological information. This requires an excellent understanding of tool physics, both to design new tools and interpret the measurements of existing tools. The Laterolog measurements in particular are difficult to interpret because the response is very nonlinear as a function of electrical conductivity, unlike Induction measurements. Forward modeling of the Laterolog is almost invariably done with finite element codes which require the inversion of large sparse matrices. Modern techniques can be used to accelerate this inversion. Moreover, an understanding of the tool physics can help refine these numerical techniques.
Optimizing the Evaluation of Finite Element Matrices
Kirby, Robert C; Logg, Anders; Scott, L Ridgway; 10.1137/040607824
2012-01-01
Assembling stiffness matrices represents a significant cost in many finite element computations. We address the question of optimizing the evaluation of these matrices. By finding redundant computations, we are able to significantly reduce the cost of building local stiffness matrices for the Laplace operator and for the trilinear form for Navier-Stokes. For the Laplace operator in two space dimensions, we have developed a heuristic graph algorithm that searches for such redundancies and generates code for computing the local stiffness matrices. Up to cubics, we are able to build the stiffness matrix on any triangle in less than one multiply-add pair per entry. Up to sixth degree, we can do it in less than about two. Preliminary low-degree results for Poisson and Navier-Stokes operators in three dimensions are also promising.
Nonlinear Finite Element Analysis of Sloshing
Directory of Open Access Journals (Sweden)
Siva Srinivas Kolukula
2013-01-01
Full Text Available The disturbance on the free surface of the liquid when the liquid-filled tanks are excited is called sloshing. This paper examines the nonlinear sloshing response of the liquid free surface in partially filled two-dimensional rectangular tanks using finite element method. The liquid is assumed to be inviscid, irrotational, and incompressible; fully nonlinear potential wave theory is considered and mixed Eulerian-Lagrangian scheme is adopted. The velocities are obtained from potential using least square method for accurate evaluation. The fourth-order Runge-Kutta method is employed to advance the solution in time. A regridding technique based on cubic spline is employed to avoid numerical instabilities. Regular harmonic excitations and random excitations are used as the external disturbance to the container. The results obtained are compared with published results to validate the numerical method developed.
Adaptive finite element methods for differential equations
Bangerth, Wolfgang
2003-01-01
These Lecture Notes discuss concepts of `self-adaptivity' in the numerical solution of differential equations, with emphasis on Galerkin finite element methods. The key issues are a posteriori error estimation and it automatic mesh adaptation. Besides the traditional approach of energy-norm error control, a new duality-based technique, the Dual Weighted Residual method for goal-oriented error estimation, is discussed in detail. This method aims at economical computation of arbitrary quantities of physical interest by properly adapting the computational mesh. This is typically required in the design cycles of technical applications. For example, the drag coefficient of a body immersed in a viscous flow is computed, then it is minimized by varying certain control parameters, and finally the stability of the resulting flow is investigated by solving an eigenvalue problem. `Goal-oriented' adaptivity is designed to achieve these tasks with minimal cost. At the end of each chapter some exercises are posed in order ...
Adaptive finite element method for shape optimization
Morin, Pedro
2012-01-16
We examine shape optimization problems in the context of inexact sequential quadratic programming. Inexactness is a consequence of using adaptive finite element methods (AFEM) to approximate the state and adjoint equations (via the dual weighted residual method), update the boundary, and compute the geometric functional. We present a novel algorithm that equidistributes the errors due to shape optimization and discretization, thereby leading to coarse resolution in the early stages and fine resolution upon convergence, and thus optimizing the computational effort. We discuss the ability of the algorithm to detect whether or not geometric singularities such as corners are genuine to the problem or simply due to lack of resolution - a new paradigm in adaptivity. © EDP Sciences, SMAI, 2012.
Finite element exterior calculus: from Hodge theory to numerical stability
Arnold, Douglas N; Winther, Ragnar
2009-01-01
This article reports on the confluence of two streams of research, one emanating from the fields of numerical analysis and scientific computation, the other from topology and geometry. In it we consider the numerical discretization of partial differential equations that are related to differential complexes so that de Rham cohomology and Hodge theory are key tools for the continuous problem. After a brief introduction to finite element methods, the discretization methods we consider, we develop an abstract Hilbert space framework for analyzing stability and convergence. In this framework, the differential complex is represented by a complex of Hilbert spaces and stability is obtained by transferring Hodge theoretic structures from the continuous level to the discrete. We show stable discretization discretization is achieved if the finite element spaces satisfy two hypotheses: they form a subcomplex and there exists a bounded cochain projection from the full complex to the subcomplex. Next, we consider the mos...
Finite element model of magnetoconvection of a ferrofluid
Snyder, Suzanne M.; Cader, Tahir; Finlayson, Bruce A.
2003-06-01
Combined natural and magnetic convective heat transfer through a ferrofluid in a cubic enclosure is simulated numerically. The momentum equation includes a magnetic term that arises when a magnetic fluid is in the presence of a magnetic field gradient and a temperature gradient. In order to validate the theory, the wall temperature isotherms and Nusselt numbers are compared to experimental work of Sawada et al. (Int. J. Appl. Electromagn. Mater. 4 (1994) 329). Results are obtained using standard computational fluid dynamics codes, with modifications to account for the Langevin factor when needed. The CFD code FIDAP uses the finite element method, sometimes with a user-defined subroutine. The CFD code FEMLAB uses the finite element method with a user-supplied body force.
A mixed finite element method for the unilateral contact problem in elasticity
Institute of Scientific and Technical Information of China (English)
无
2006-01-01
In this paper, we provide a new mixed finite element approximation of the variational inequality resulting from the unilateral contact problem in elasticity. We use the continuous piecewise P2-P1 finite element to approximate the displacement field and the normal stress component on the contact region. Optimal convergence rates are obtained under the reasonable regularity hypotheses. Numerical example verifies our results.
Finite element simulation of wheel impact test
Directory of Open Access Journals (Sweden)
S.H. Yang
2008-06-01
Full Text Available Purpose: In order to achieve better performance and quality, the wheel design and manufacturing use a number of wheel tests (rotating bending test, radial fatigue test, and impact test to insure that the wheel meets the safety requirements. The test is very time consuming and expensive. Computer simulation of these tests can significantly reduce the time and cost required to perform a wheel design. In this study, nonlinear dynamic finite element is used to simulate the SAE wheel impact test.Design/methodology/approach: The test fixture used for the impact test consists of a striker with specified weight. The test is intended to simulate actual vehicle impact conditions. The tire-wheel assembly is mounted at 13° angle to the vertical plane with the edge of the weight in line with outer radius of the rim. The striker is dropped from a specified height above the highest point of the tire-wheel assembly and contacts the outboard flange of the wheel.Because of the irregular geometry of the wheel, the finite element model of an aluminium wheel is constructed by tetrahedral element. A mesh convergence study is carried out to ensure the convergence of the mesh model. The striker is assumed to be rigid elements. Initially, the striker contacts the highest area of the wheel, and the initial velocity of the striker is calculated from the impact height. The simulated strains at two locations on the disc are verified by experimental measurements by strain gages. The damage parameter of a wheel during the impact test is a strain energy density from the calculated result.Findings: The prediction of a wheel failure at impact is based on the condition that fracture will occur if the maximum strain energy density of the wheel during the impact test exceeds the total plastic work of the wheel material from tensile test. The simulated results in this work show that the total plastic work can be effectively employed as a fracture criterion to predict a wheel
Interpolation theory of anisotropic finite elements and applications
Institute of Scientific and Technical Information of China (English)
CHEN ShaoChun; XIAO LiuChao
2008-01-01
Interpolation theory is the foundation of finite element methods. In this paper, after reviewing some existed interpolation theorems of anisotropic finite element methods, we present a new way to analyse the interpolation error of anisotropic elements based on Newton's formula of polynomial interpolation as well as its applications.
Convergence of adaptive finite element methods for eigenvalue problems
Garau, Eduardo M.; Morin, Pedro; Zuppa, Carlos
2008-01-01
In this article we prove convergence of adaptive finite element methods for second order elliptic eigenvalue problems. We consider Lagrange finite elements of any degree and prove convergence for simple as well as multiple eigenvalues under a minimal refinement of marked elements, for all reasonable marking strategies, and starting from any initial triangulation.
Interpolation theory of anisotropic finite elements and applications
Institute of Scientific and Technical Information of China (English)
2008-01-01
Interpolation theory is the foundation of finite element methods.In this paper,after reviewing some existed interpolation theorems of anisotropic finite element methods,we present a new way to analyse the interpolation error of anisotropic elements based on Newton’s formula of polynomial interpolation as well as its applications.
Galerkin finite-element simulation of a geothermal reservoir
Mercer, J.W.; Pinder, G.F.
1973-01-01
The equations describing fluid flow and energy transport in a porous medium can be used to formulate a mathematical model capable of simulating the transient response of a hot-water geothermal reservoir. The resulting equations can be solved accurately and efficiently using a numerical scheme which combines the finite element approach with the Galerkin method of approximation. Application of this numerical model to the Wairakei geothermal field demonstrates that hot-water geothermal fields can be simulated using numerical techniques currently available and under development. ?? 1973.
Finite element analysis theory and application with ANSYS
Moaveni, Saeed
2015-01-01
For courses in Finite Element Analysis, offered in departments of Mechanical or Civil and Environmental Engineering. While many good textbooks cover the theory of finite element modeling, Finite Element Analysis: Theory and Application with ANSYS is the only text available that incorporates ANSYS as an integral part of its content. Moaveni presents the theory of finite element analysis, explores its application as a design/modeling tool, and explains in detail how to use ANSYS intelligently and effectively. Teaching and Learning Experience This program will provide a better teaching and learning experience-for you and your students. It will help: *Present the Theory of Finite Element Analysis: The presentation of theoretical aspects of finite element analysis is carefully designed not to overwhelm students. *Explain How to Use ANSYS Effectively: ANSYS is incorporated as an integral part of the content throughout the book. *Explore How to Use FEA as a Design/Modeling Tool: Open-ended design problems help stude...
Impact of new computing systems on finite element computations
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.
Radial flow of slightly compressible fluids: A finite element-finite ...
African Journals Online (AJOL)
Journal of the Nigerian Association of Mathematical Physics ... Open Access DOWNLOAD FULL TEXT Subscription or Fee Access. Radial flow of slightly compressible fluids: A finite element-finite differences approach. JA Akpobi, ED Akpobi ...
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.
Hybrid Fundamental Solution Based Finite Element Method: Theory and Applications
Directory of Open Access Journals (Sweden)
Changyong Cao
2015-01-01
Full Text Available An overview on the development of hybrid fundamental solution based finite element method (HFS-FEM and its application in engineering problems is presented in this paper. The framework and formulations of HFS-FEM for potential problem, plane elasticity, three-dimensional elasticity, thermoelasticity, anisotropic elasticity, and plane piezoelectricity are presented. In this method, two independent assumed fields (intraelement filed and auxiliary frame field are employed. The formulations for all cases are derived from the modified variational functionals and the fundamental solutions to a given problem. Generation of elemental stiffness equations from the modified variational principle is also described. Typical numerical examples are given to demonstrate the validity and performance of the HFS-FEM. Finally, a brief summary of the approach is provided and future trends in this field are identified.
Introduction to finite element analysis using MATLAB and Abaqus
Khennane, Amar
2013-01-01
There are some books that target the theory of the finite element, while others focus on the programming side of things. Introduction to Finite Element Analysis Using MATLAB(R) and Abaqus accomplishes both. This book teaches the first principles of the finite element method. It presents the theory of the finite element method while maintaining a balance between its mathematical formulation, programming implementation, and application using commercial software. The computer implementation is carried out using MATLAB, while the practical applications are carried out in both MATLAB and Abaqus. MA
Ablative Thermal Response Analysis Using the Finite Element Method
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.
An improved optimal elemental method for updating finite element models
Institute of Scientific and Technical Information of China (English)
Duan Zhongdong(段忠东); Spencer B.F.; Yan Guirong(闫桂荣); Ou Jinping(欧进萍)
2004-01-01
The optimal matrix method and optimal elemental method used to update finite element models may not provide accurate results. This situation occurs when the test modal model is incomplete, as is often the case in practice. An improved optimal elemental method is presented that defines a new objective function, and as a byproduct, circumvents the need for mass normalized modal shapes, which are also not readily available in practice. To solve the group of nonlinear equations created by the improved optimal method, the Lagrange multiplier method and Matlab function fmincon are employed. To deal with actual complex structures,the float-encoding genetic algorithm (FGA) is introduced to enhance the capability of the improved method. Two examples, a 7-degree of freedom (DOF) mass-spring system and a 53-DOF planar frame, respectively, are updated using the improved method.Thc example results demonstrate the advantages of the improved method over existing optimal methods, and show that the genetic algorithm is an effective way to update the models used for actual complex structures.
Tadepalli, Srinivas C; Erdemir, Ahmet; Cavanagh, Peter R
2011-08-11
Finite element analysis has been widely used in the field of foot and footwear biomechanics to determine plantar pressures as well as stresses and strains within soft tissue and footwear materials. When dealing with anatomical structures such as the foot, hexahedral mesh generation accounts for most of the model development time due to geometric complexities imposed by branching and embedded structures. Tetrahedral meshing, which can be more easily automated, has been the approach of choice to date in foot and footwear biomechanics. Here we use the nonlinear finite element program Abaqus (Simulia, Providence, RI) to examine the advantages and disadvantages of tetrahedral and hexahedral elements under compression and shear loading, material incompressibility, and frictional contact conditions, which are commonly seen in foot and footwear biomechanics. This study demonstrated that for a range of simulation conditions, hybrid hexahedral elements (Abaqus C3D8H) consistently performed well while hybrid linear tetrahedral elements (Abaqus C3D4H) performed poorly. On the other hand, enhanced quadratic tetrahedral elements with improved stress visualization (Abaqus C3D10I) performed as well as the hybrid hexahedral elements in terms of contact pressure and contact shear stress predictions. Although the enhanced quadratic tetrahedral element simulations were computationally expensive compared to hexahedral element simulations in both barefoot and footwear conditions, the enhanced quadratic tetrahedral element formulation seems to be very promising for foot and footwear applications as a result of decreased labor and expedited model development, all related to facilitated mesh generation.
Energy Technology Data Exchange (ETDEWEB)
Kim, S. [Purdue Univ., West Lafayette, IN (United States)
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.
MORTAR FINITE VOLUME METHOD WITH ADINI ELEMENT FOR BIHARMONIC PROBLEM
Institute of Scientific and Technical Information of China (English)
Chun-jia Bi; Li-kang Li
2004-01-01
In this paper, we construct and analyse a mortar finite volume method for the dis-cretization for the biharmonic problem in R2. This method is based on the mortar-type Adini nonconforming finite element spaces. The optimal order H2-seminorm error estimate between the exact solution and the mortar Adini finite volume solution of the biharmonic equation is established.
Finite Element Analysis (FEA) in Design and Production.
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)
A Finite Element Analysis of Optimal Variable Thickness Sheets
DEFF Research Database (Denmark)
Petersson, Joakim S
1996-01-01
A quasimixed Finite Element (FE) method for maximum stiffness of variablethickness sheets is analysed. The displacement is approximated with ninenode Lagrange quadrilateral elements and the thickness is approximated aselementwise constant. One is guaranteed that the FE displacement solutionswill...
Finite element simulation of asphalt fatigue testing
DEFF Research Database (Denmark)
Ullidtz, Per; Kieler, Thomas Lau; Kargo, Anders
1997-01-01
The traditional interpretation of fatigue tests on asphalt mixes has been in terms of a logarithmic linear relationship between the constant stress or strain amplitude and the number of load repetitions to cause failure, often defined as a decrease in modulus to half the initial value. To accomod......The traditional interpretation of fatigue tests on asphalt mixes has been in terms of a logarithmic linear relationship between the constant stress or strain amplitude and the number of load repetitions to cause failure, often defined as a decrease in modulus to half the initial value....... To accomodate non-constant stress or strain, a mode factor may be introduced or the dissipated energy may be used instead of stress or strain.Cracking of asphalt (or other materials) may be described as a process consisting of three phases. In phase one diffuse microcracking is formed in the material...... damage mechanics.The paper describes how continuum damage mechanics may be used with a finite element program to explain the progressive deterioration of asphalt mixes under laboratory fatigue testing. Both constant stress and constant strain testing are simulated, and compared to the actual results from...
Finite Element Simulation for Springback Prediction Compensation
Directory of Open Access Journals (Sweden)
Agus Dwi Anggono
2011-01-01
Full Text Available An accurate modelling of the sheet metal deformations including the springback prediction is one of the key factors in the efficient utilisation of Finite Element Method (FEM process simulation in industrial application. Assuming that springback can be predicted accurately, there still remains the problem of how to use such results to appear at a suitable die design to produce a target part shape. It is this second step of springback compensation that is addressed in the current work. This paper presents an evaluation of a standard benchmark model defined as Benchmark II of Numisheet 2008, S-channel model with various drawbeads and blank holder force (BHF. The tool geometry modified based on springback calculation for a part to compensate springback. The result shows that the combination of the smooth bead with BHF of 650 kN resulted in the minimum springback and the tool compensation was successfully to accommodate the springback errors.
Studying a dental pathology by finite elements
Directory of Open Access Journals (Sweden)
Fernando Mejía Umaña
2010-04-01
Full Text Available Abfractives lesions or abfractions are non-cavity lesions of dental structures in which a biomechanical factor has been identified as being the most probable cause for it occurring. Even throught such lesion can be presented in any tooth, it occurs more frequently in people aged over 35. This article presents some results obtained by the Universidad Nacional de Colombia's multidisciplinary research group for studying "dental material's structure and propierties". The introduction describes such lesion's characteristics and possible causes. The results of various modelling exercises using finite elements (in two and three dimensions are presented regarding a first premolar tooth subjected to normal mastication load and also to abnormal loads produced by occlusion problems. The most important findings (accompanied by clinical observations were that: areas of high concentration of forces were identified where lesions were frequently presented, associated with loads whose line of action did not pass through the central part of the section of tooth at cervical level; a direct relationship between facets of wear being orientated with the direction of forces produced by a high concentration of force; and the presence of high compression forces in the cervical region.
Finite element modeling of retinal prosthesis mechanics
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.
Finite Element Analysis of Deformed Legs of Offshore Platform Structures
Institute of Scientific and Technical Information of China (English)
柳春图; 秦太验; 段梦兰
2002-01-01
The element stiffness matrix of the equivalent beam or pipe element of the deformed leg of the platform is derived bythe finite element method. The stresses and displacements of some damaged components are calculated, and the numeri-cal solutions agree well with those obtained by the fine mesh finite element method. Finally, as an application of thismethod, the stresses of some platform structures are calculated and analyzed.
Hydrothermal analysis in engineering using control volume finite element method
Sheikholeslami, Mohsen
2015-01-01
Control volume finite element methods (CVFEM) bridge the gap between finite difference and finite element methods, using the advantages of both methods for simulation of multi-physics problems in complex geometries. In Hydrothermal Analysis in Engineering Using Control Volume Finite Element Method, CVFEM is covered in detail and applied to key areas of thermal engineering. Examples, exercises, and extensive references are used to show the use of the technique to model key engineering problems such as heat transfer in nanofluids (to enhance performance and compactness of energy systems),
Magnetic Elements at Finite Temperature and Large Deviation Theory
Kohn, R. V.; Reznikoff, M. G.; vanden-Eijnden, E.
2005-08-01
We investigate thermally activated phenomena in micromagnetics using large deviation theory and concepts from stochastic resonance. We give a natural mathematical definition of finite-temperature astroids, finite-temperature hysteresis loops, etc. Generically, these objects emerge when the (generalized) Arrhenius timescale governing the thermally activated barrier crossing event of magnetic switching matches the timescale at which the magnetic element is pulsed or ramped by an external field; in the special and physically relevant case of multiple-pulse experiments, on the other hand, short-time switching can lead to non-Arrhenius behavior. We show how large deviation theory can be used to explain some properties of the astroids, like their shrinking and sharpening as the number of applied pulses is increased. We also investigate the influence of the dynamics, in particular the relative importance of the gyromagnetic and the damping terms. Finally, we discuss some issues and open questions regarding spatially nonuniform magnetization.
Finite Element Model of Cardiac Electrical Conduction.
Yin, John Zhihao
1994-01-01
In this thesis, we develop mathematical models to study electrical conduction of the heart. One important pattern of wave propagation of electrical excitation in the heart is reentry which is believed to be the underlying mechanism of some dangerous cardiac arhythmias such as ventricular tachycardia and ventricular fibrillation. We present in this thesis a new ionic channel model of the ventricular cardiac cell membrane to study the microscopic electrical properties of myocardium. We base our model on recent single channel experiment data and a simple physical diffusion model of the calcium channel. Our ionic channel model of myocardium has simpler differential equations and fewer parameters than previous models. Further more, our ionic channel model achieves better results in simulating the strength-interval curve when we connect the membrane patch model to form a one dimensional cardiac muscle strand. We go on to study a finite element model which uses multiple states and non-nearest neighbor interactions to include curvature and dispersion effects. We create a generalized lattice randomization to overcome the artifacts generated by the interaction between the local dynamics and the regularities of the square lattice. We show that the homogeneous model does not display spontaneous wavefront breakup in a reentrant wave propagation once the lattice artifacts have been smoothed out by lattice randomization with a randomization scale larger than the characteristic length of the interaction. We further develop a finite 3-D 3-state heart model which employs a probability interaction rule. This model is applied to the simulation of Body Surface Laplacian Mapping (BSLM) using a cylindrical volume conductor as the torso model. We show that BSLM has a higher spatial resolution than conventional mapping methods in revealing the underlying electrical activities of the heart. The results of these studies demonstrate that mathematical modeling and computer simulation are very
Galerkin finite element scheme for magnetostrictive structures and composites
Kannan, Kidambi Srinivasan
The ever increasing-role of magnetostrictives in actuation and sensing applications is an indication of their importance in the emerging field of smart structures technology. As newer, and more complex, applications are developed, there is a growing need for a reliable computational tool that can effectively address the magneto-mechanical interactions and other nonlinearities in these materials and in structures incorporating them. This thesis presents a continuum level quasi-static, three-dimensional finite element computational scheme for modeling the nonlinear behavior of bulk magnetostrictive materials and particulate magnetostrictive composites. Models for magnetostriction must deal with two sources of nonlinearities-nonlinear body forces/moments in equilibrium equations governing magneto-mechanical interactions in deformable and magnetized bodies; and nonlinear coupled magneto-mechanical constitutive models for the material of interest. In the present work, classical differential formulations for nonlinear magneto-mechanical interactions are recast in integral form using the weighted-residual method. A discretized finite element form is obtained by applying the Galerkin technique. The finite element formulation is based upon three dimensional eight-noded (isoparametric) brick element interpolation functions and magnetostatic infinite elements at the boundary. Two alternative possibilities are explored for establishing the nonlinear incremental constitutive model-characterization in terms of magnetic field or in terms of magnetization. The former methodology is the one most commonly used in the literature. In this work, a detailed comparative study of both methodologies is carried out. The computational scheme is validated, qualitatively and quantitatively, against experimental measurements published in the literature on structures incorporating the magnetostrictive material Terfenol-D. The influence of nonlinear body forces and body moments of magnetic origin
Extended Finite Element Method for Fracture Analysis of Structures
Mohammadi, Soheil
2008-01-01
This important textbook provides an introduction to the concepts of the newly developed extended finite element method (XFEM) for fracture analysis of structures, as well as for other related engineering applications.One of the main advantages of the method is that it avoids any need for remeshing or geometric crack modelling in numerical simulation, while generating discontinuous fields along a crack and around its tip. The second major advantage of the method is that by a small increase in number of degrees of freedom, far more accurate solutions can be obtained. The method has recently been
Finite element stress analysis of the CMS magnet coil
Desirelli, Alberto; Farinon, S; Levesy, B; Ps, C; Rey, J M; Sgobba, Stefano
2000-01-01
The Compact Muon Solenoid (CMS) is one of the experiments which are being designed in the framework of the Large Hadron Collider (LHC) project at CERN. The design field of the CMS magnet is 4 T, the magnetic length is 12.38 m and the aperture is 6.36 m. This is achieved with a 4 layer-5 module superconducting Al-stabilized coil energised at a nominal current of 20 kA. The finite element analysis (FEA) carried out is axisymmetric elasto-plastic. FEA has also been carried out on the suspension system and on the conductor. (8 refs).
The Research of Welding Residual Stress Based Finite Element Method
Directory of Open Access Journals (Sweden)
Qinghua Bai
2013-06-01
Full Text Available Welding residual stress was caused by local heating during the welding process, tensile residual stress reduce fatigue strength and corrosion resistance, Compressive residual stress decreases stability limit. So it will produce brittle fracture, reduce working life and strength of workpiece; Based on the simulation of welding process with finite element method, calculate the welding temperature field and residual stress, and then measure residual stress in experiments, So as to get the best welding technology and welding parameters, to reduce welding residual stress effective, it has very important significance.
Finite element analysis for general elastic multi-structures
Institute of Scientific and Technical Information of China (English)
无
2006-01-01
A finite element method is introduced to solve the general elastic multi-structure problem, in which the displacements on bodies, the longitudinal displacements on plates and the longitudinal displacements on beams are discretized using conforming linear elements, the rotational angles on beams are discretized using conforming elements of second order, the transverse displacements on plates and beams are discretized by the Morley elements and the Hermite elements of third order, respectively. The generalized Korn's inequality is established on related nonconforming element spaces, which implies the unique solvability of the finite element method. Finally, the optimal error estimate in the energy norm is derived for the method.
Finite element form of FDV for widely varying flowfields
Richardson, G. A.; Cassibry, J. T.; Chung, T. J.; Wu, S. T.
2010-01-01
We present the Flowfield Dependent Variation (FDV) method for physical applications that have widely varying spatial and temporal scales. Our motivation is to develop a versatile numerical method that is accurate and stable in simulations with complex geometries and with wide variations in space and time scales. The use of a finite element formulation adds capabilities such as flexible grid geometries and exact enforcement of Neumann boundary conditions. While finite element schemes are used extensively by researchers solving computational fluid dynamics in many engineering fields, their use in space physics, astrophysical fluids and laboratory magnetohydrodynamic simulations with shocks has been predominantly overlooked. The FDV method is unique in that numerical diffusion is derived from physical parameters rather than traditional artificial viscosity methods. Numerical instabilities account for most of the difficulties when capturing shocks in these regimes. The first part of this paper concentrates on the presentation of our numerical method formulation for Newtonian and relativistic hydrodynamics. In the second part we present several standard simulation examples that test the method's limitations and verify the FDV method. We show that our finite element formulation is stable and accurate for a range of both Mach numbers and Lorentz factors in one-dimensional test problems. We also present the converging/diverging nozzle which contains both incompressible and compressible flow in the flowfield over a range of subsonic and supersonic regions. We demonstrate the stability of our method and the accuracy by comparison with the results of other methods including the finite difference Total Variation Diminishing method. We explore the use of FDV for both non-relativistic and relativistic fluids (hydrodynamics) with strong shocks in order to establish the effectiveness in future applications of this method in astrophysical and laboratory plasma environments.
THE PRACTICAL ANALYSIS OF FINITE ELEMENTS METHOD ERRORS
Directory of Open Access Journals (Sweden)
Natalia Bakhova
2011-03-01
Full Text Available Abstract. The most important in the practical plan questions of reliable estimations of finite elementsmethod errors are considered. Definition rules of necessary calculations accuracy are developed. Methodsand ways of the calculations allowing receiving at economical expenditures of computing work the best finalresults are offered.Keywords: error, given the accuracy, finite element method, lagrangian and hermitian elements.
Finite Element Modelling of Seismic Liquefaction in Soils
Galavi, V.; Petalas, A.; Brinkgreve, R.B.J.
2013-01-01
Numerical aspects of seismic liquefaction in soils as implemented in the finite element code, PLAXIS, is described in this paper. After description of finite element equations of dynamic problems, three practical dynamic boundary conditions, namely viscous boundary tractions, tied degrees of freedom
Parallel direct solver for finite element modeling of manufacturing processes
DEFF Research Database (Denmark)
Nielsen, Chris Valentin; Martins, P.A.F.
2017-01-01
The central processing unit (CPU) time is of paramount importance in finite element modeling of manufacturing processes. Because the most significant part of the CPU time is consumed in solving the main system of equations resulting from finite element assemblies, different approaches have been...
Finite element models applied in active structural acoustic control
Oude Nijhuis, Marco H.H.; Boer, de André; Rao, Vittal S.
2002-01-01
This paper discusses the modeling of systems for active structural acoustic control. The finite element method is applied to model structures including the dynamics of piezoelectric sensors and actuators. A model reduction technique is presented to make the finite element model suitable for controll
Viscoelastic finite-element analysis of human skull - dura mater ...
African Journals Online (AJOL)
SERVER
2008-03-18
Mar 18, 2008 ... In the work, the dynamic characteristics of the human skull-dura mater ... Ansys' finite element processor, a simplified three-dimensional finite element ... brain, cerebrospinal fluid (CSF), and the brain's blood ... ICP is often not preventable. .... The creep of linear viscoelastic solid can be simulated by the.
A geometric toolbox for tetrahedral finite element partitions
Brandts, J.; Korotov, S.; Křížek, M.; Axelsson, O.; Karátson, J.
2011-01-01
In this work we present a survey of some geometric results on tetrahedral partitions and their refinements in a unified manner. They can be used for mesh generation and adaptivity in practical calculations by the finite element method (FEM), and also in theoretical finite element (FE) analysis. Spec
ALTERNATING DIRECTION FINITE ELEMENT METHOD FOR SOME REACTION DIFFUSION MODELS
Institute of Scientific and Technical Information of China (English)
江成顺; 刘蕴贤; 沈永明
2004-01-01
This paper is concerned with some nonlinear reaction - diffusion models. To solve this kind of models, the modified Laplace finite element scheme and the alternating direction finite element scheme are established for the system of patrical differential equations. Besides, the finite difference method is utilized for the ordinary differential equation in the models. Moreover, by the theory and technique of prior estimates for the differential equations, the convergence analyses and the optimal L2- norm error estimates are demonstrated.
OBJECT-ORIENTED FINITE ELEMENT ANALYSIS AND PROGRAMMING IN VC + +
Institute of Scientific and Technical Information of China (English)
马永其; 冯伟
2002-01-01
The design of finite element analysis program using object-oriented programming(OOP) techniques is presented. The objects, classes and the subclasses used in theprogramming are explained. The system of classes library of finite element analysis programand Windows-type Graphical User Interfaces by VC + + and its MFC are developed. Thereliability, reusability and extensibility of program are enhanced. It is a reference todevelop the large-scale, versatile and powerful systems of object-oriented finite elementsoftware.
Finite Element Method for Analysis of Material Properties
DEFF Research Database (Denmark)
Rauhe, Jens Christian
description of the material microstructure the finite element models must contain a large number of elements and this problem is solved by using the preconditioned conjugated gradient solver with an Element-By-Element preconditioner. Finite element analysis provides the volume averaged stresses and strains...... and the finite element method. The material microstructure of the heterogeneous material is non-destructively determined using X-ray microtomography. A software program has been generated which uses the X-ray tomographic data as an input for the mesh generation of the material microstructure. To obtain a proper...... which are used for the determination of the effective properties of the heterogeneous material. Generally, the properties determined using the finite element method coupled with X-ray microtomography are in good agreement with both experimentally determined properties and properties determined using...
Finite-dimensional division algebras over fields
Jacobson, Nathan
2009-01-01
Finite-Dimensional Division Algebras over fields determine, by the Wedderburn Theorem, the semi-simple finite-dimensional algebras over a field. They lead to the definition of the Brauer group and to certain geometric objects, the Brauer-Severi varieties. The book concentrates on those algebras that have an involution. Algebras with involution appear in many contexts; they arose first in the study of the so-called 'multiplication algebras of Riemann matrices'. The largest part of the book is the fifth chapter, dealing with involutorial simple algebras of finite dimension over a field. Of parti
Finite element simulation of thick sheet thermoforming
Mercier, Daniel
This PhD was organized as collaboration between Lehigh University and the Ecole des Mines d'Albi on the subject: "Numerical simulation of thick sheet thermoforming". The research applications cover a wide range of products from thermoforming, e.g., packaging, automobile parts, appliance parts, large-scale panels and covers. Due to the special nature of this PhD, and the requirements of each hosting institutes, the research was split accordingly into two parts: At Lehigh University, under the supervision of Prof. Herman F. Nied, a full three-dimensional finite element program was developed in order to simulate the mechanical deformation during the process of thermoforming. The material behavior is considered hyperelastic with the property of incompressibility. The deformed structure may exhibit symmetries and may use a large choice of boundary conditions. A contact procedure for molds and/or displacements caused by a plug was implemented to complete the similarity with the thermoforming process. The research focused on simulating the observed nonlinear behaviors and their instabilities. The author emphasized the impact of large deformation on the numerical results and demonstrated the need for a remeshing capability. At the Ecole des Mines d'Albi, under the supervision of Prof. Fabrice Schmidt, an equi-biaxial rheometer was developed and built in order to determine the material properties during the process of thermoforming. Thermoplastic materials consist of long macromolecular chains that when stretched, during the process of sheet extrusion, exhibit a transversal isotropic behavior. The rheometer technique is the inflation of a circular membrane made of extruded thermoplastics. The resulting strain is identified by video analysis during the membrane inflation. This dissertation focused on technical issues related to heating with the goal of overcoming the difficulty of producing a homogeneous temperature distribution.
Finite element analysis of posterior cervical fixation.
Duan, Y; Wang, H H; Jin, A M; Zhang, L; Min, S X; Liu, C L; Qiu, S J; Shu, X Q
2015-02-01
Despite largely, used in the past, biomechanical test, to investigate the fixation techniques of subaxial cervical spine, information is lacking about the internal structural response to external loading. It is not yet clear which technique represents the best choice and whether stabilization devices can be efficient and beneficial for three-column injuries (TCI). The different posterior cervical fixation techniques (pedicle screw PS, lateral mass screw LS, and transarticular screw TS) have respective indications. A detailed, geometrically accurate, nonlinear C3-C7 finite element model (FEM) had been successfully developed and validated. Then three FEMs were reconstructed from different fixation techniques after C4-C6 TCI. A compressive preload of 74N combined with a pure moment of 1.8 Nm in flexion, extension, left-right lateral bending, and left-right axial rotation was applied to the FEMs. The ROM results showed that there were obvious significant differences when comparing the different fixation techniques. PS and TS techniques can provide better immediate stabilization, compared to LS technique. The stress results showed that the variability of von Mises stress in the TS fixation device was minimum and LS fixation device was maximum. Furthermore, the screws inserted by TS technique had high stress concentration at the middle part of the screws. Screw inserted by PS and LS techniques had higher stress concentration at the actual cap-rod-screw interface. The research considers that spinal surgeon should first consider using the TS technique to treat cervical TCI. If PS technique is used, we should eventually prolong the need for external bracing in order to reduce the higher risk of fracture on fixation devices. If LS technique is used, we should add anterior cervical operation for acquire a better immediate stabilization. Copyright © 2014 Elsevier Masson SAS. All rights reserved.
Thermal Analysis of Thin Plates Using the Finite Element Method
Er, G. K.; Iu, V. P.; Liu, X. L.
2010-05-01
The isotropic thermal plate is analyzed with finite element method. The solution procedure is presented. The elementary stiffness matrix and loading vector are derived rigorously with variation principle and the principle of minimum potential energy. Numerical results are obtained based on the derived equations and tested with available exact solutions. The problems in the finite element analysis are figured out. It is found that the finite element solutions can not converge as the number of elements increases around the corners of the plate. The derived equations presented in this paper are fundamental for our further study on more complicated thermal plate analysis.
Finite Element Analysis of Fluid-Conveying Timoshenko Pipes
Directory of Open Access Journals (Sweden)
Chih-Liang Chu
1995-01-01
Full Text Available A general finite element formulation using cubic Hermitian interpolation for dynamic analysis of pipes conveying fluid is presented. Both the effects of shearing deformations and rotary inertia are considered. The development retains the use of the classical four degrees-of-freedom for a two-node element. The effect of moving fluid is treated as external distributed forces on the support pipe and the fluid finite element matrices are derived from the virtual work done due to the fluid inertia forces. Finite element matrices for both the support pipe and moving fluid are derived and given explicitly. A numerical example is given to demonstrate the validity of the model.
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Shimizu, Takeshi [Toshiba Corp., Kawasaki, Kanagawa (Japan). Nuclear Engineering Lab.
1996-05-01
A two-dimensional steady-state distributed parameter code SPOTBOW has been developed for predicting the fine structure of cladding temperature in an liquid metal fast breeder reactor (LMFBR) fuel assembly where the deformation of fuel pins is induced by irradiation swelling, creep and thermal distortion under high burn-up operating condition. When the deformed fuel pin approaches adjacent pins and wrapper tube and comes in contact with those, the peak temperature, known as the hot spot temperature, can appear somewhere on the outer surface of the cladding. The temperature rise across the film is an important consideration in the cladding temperature analysis. Fully developed turbulent momentum and heat transfer equations based on the empirical turbulent model are solved by using the Galerkin finite element method which is suitable for the problem of the complicated boundary shape, such as the wire-wrapped fuel pin bundle. A new iteration procedure has been developed for solving the above equations by using the rise in coolant temperature, which is obtained with subchannel analysis codes, as a boundary condition. Calculated results are presented for local temperature distribution in normal and bowing pin bundle geometry, as compared with experiments. (author).
Miller, Eric J.; Manalo, Russel; Tessler, Alexander
2016-01-01
A study was undertaken to investigate the measurement of wing deformation and internal loads using measured strain data. Future aerospace vehicle research depends on the ability to accurately measure the deformation and internal loads during ground testing and in flight. The approach uses the inverse Finite Element Method (iFEM). The iFEM is a robust, computationally efficient method that is well suited for real-time measurement of real-time structural deformation and loads. The method has been validated in previous work, but has yet to be applied to a large-scale test article. This work is in preparation for an upcoming loads test of a half-span test wing in the Flight Loads Laboratory at the National Aeronautics and Space Administration Armstrong Flight Research Center (Edwards, California). The method has been implemented into an efficient MATLAB® (The MathWorks, Inc., Natick, Massachusetts) code for testing different sensor configurations. This report discusses formulation and implementation along with the preliminary results from a representative aerospace structure. The end goal is to investigate the modeling and sensor placement approach so that the best practices can be applied to future aerospace projects.
PHG: A Toolbox for Developing Parallel Adaptive Finite Element Programs
Institute of Scientific and Technical Information of China (English)
ZHANG Linbo
2011-01-01
@@ Significance of the finite element method The finite element method (Feng, 1965) is mainly used for numerical solution of partial differential equations.It consists of partitioning the computational domain into a mesh composed of disjoint smaller sub-domains called elements which cover the whole domain, and approximating the solution in each element using simple functions (usually polynomials) so that the original problem can be turned into a suitable one to be solved on modern computers.The finite element method has a very wide range of applications as one of the most important methods in scientific and engineering computing.In the finite element method, two key factors which can affect the computational efficiency and precision of the computed solution are quality and distribution of the mesh elements.The adaptive finite element method, first proposed by I.Babuska and W.Rheinboldt in 1978 (Babuska et al., 1978), automatically adjusts and optimizes the distribution of mesh elements according to estimation on the distribution of the error of the computed solution, in order to improve the precision of the computed solution.Recent researches show that for many problems with locally singular solutions, by using mathematically rigorous a posteriori error estimates and suitable adaptive strategy, the adaptive finite element method can produce quasi-optimal meshes and dramatically improve the overall computational efficiency.
A Finite Circular Arch Element Based on Trigonometric Shape Functions
Directory of Open Access Journals (Sweden)
H. Saffari
2007-01-01
Full Text Available The curved-beam finite element formulation by trigonometric function for curvature is presented. Instead of displacement function, trigonometric function is introduced for curvature to avoid the shear and membrane locking phenomena. Element formulation is carried out in polar coordinates. The element with three nodal parameters is chosen on curvature. Then, curvature field in the element is interpolated as the conventional trigonometric functions. Shape functions are obtained as usual by matrix operations. To consider the boundary conditions, a transformation matrix between nodal curvature and nodal displacement vectors is introduced. The equilibrium equation is written by minimizing the total potential energy in terms of the displacement components. In such equilibrium equation, the locking phenomenon is eliminated. The interesting point in this method is that for most problems, it is sufficient to use only one element to obtain the solution. Four examples are presented in order to verify the element formulation and to show the accuracy and efficiency of the method. The results are compared with those of other concepts.
Transient finite element analysis of ultrasonic welding of PEEK
Institute of Scientific and Technical Information of China (English)
Wang Xiaolin; Li Ruiqi; Yan Jiuchun; Yang Shiqin
2006-01-01
Finite element method was adopted to investigate the temperature profile during ultrasonic welding of PEEK (polyetheretherketone ). The comparison of temperature fields was made among the triangular, semicircular and rectangular energy directors. The results show that the highest temperature appears on the sample surfaces in the welding interface. For triangular and semicircular energy directors, the gradient of their temperature fields become larger with welding amplitude increasing, and the temperature decreases along the normal line of surface. The melting point can be rapidly reached before large scale plastic deformation occurs as welding amplitude exceeds 25 μm for triangular energy and 35 μm for semicircular energy director. But for the rectangular energy director, its temperature field is dispersed even under 35 μm welding amplitude.
Zero modes in finite range magnetic fields
Adam, C; Nash, C
2000-01-01
We find a class of Fermion zero modes of Abelian Dirac operators in three dimensional Euclidean space where the gauge potentials and the related magnetic fields are nonzero only in a finite space region.
Kaltenbacher, Manfred
2015-01-01
Like the previous editions also the third edition of this book combines the detailed physical modeling of mechatronic systems and their precise numerical simulation using the Finite Element (FE) method. Thereby, the basic chapter concerning the Finite Element (FE) method is enhanced, provides now also a description of higher order finite elements (both for nodal and edge finite elements) and a detailed discussion of non-conforming mesh techniques. The author enhances and improves many discussions on principles and methods. In particular, more emphasis is put on the description of single fields by adding the flow field. Corresponding to these field, the book is augmented with the new chapter about coupled flow-structural mechanical systems. Thereby, the discussion of computational aeroacoustics is extended towards perturbation approaches, which allows a decomposition of flow and acoustic quantities within the flow region. Last but not least, applications are updated and restructured so that the book meets mode...
Finite Element Analysis of Connecting Rod of IC Engine
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Samal Prasanta Kumar
2015-01-01
Full Text Available A connecting rod of IC engine is subjected to complex dynamic loading conditions. Therefore it is a critical machine element which attracts researchers’ attention. This paper aims at development of simple 3D model, finite element analyses and the optimization by intuition of the connecting rod for robust design. In this study the detailed load analysis under in-service loading conditions was performed for a typical connecting rod. The CAD model was prepared taking the detailed dimensions from a standard machine drawing text book. Based on the gas pressure variation in the cylinder of an IC engine, the piston forces were calculated for critical positions. MATLAB codes were written for this calculation. Altair Hypermesh and Hyperview were used for pre-processing and post-processing of the model respectively. The finite element analyses were performed using Altair Radioss. The results obtained were compared to a case study for the field failure of the connecting rod. By comparing the induced stress result with the yield strength of the material, the component was redesigned. This was done to save some mass keeping in mind that the induced stress value should be well below the yield strength of the material. The optimized connecting rod is 11.3% lighter than the original design.
Finite element method for thermal analysis of concentrating solar receivers
Shtrakov, Stanko; Stoilov, Anton
2006-01-01
Application of finite element method and heat conductivity transfer model for calculation of temperature distribution in receiver for dish-Stirling concentrating solar system is described. The method yields discretized equations that are entirely local to the elements and provides complete geometric flexibility. A computer program solving the finite element method problem is created and great number of numerical experiments is carried out. Illustrative numerical results are given for an array...
PRECONDITIONING HIGHER ORDER FINITE ELEMENT SYSTEMS BY ALGEBRAIC MULTIGRID METHOD OF LINEAR ELEMENTS
Institute of Scientific and Technical Information of China (English)
Yun-qing Huang; Shi Shu; Xi-jun Yu
2006-01-01
We present and analyze a robust preconditioned conjugate gradient method for the higher order Lagrangian finite element systems of a class of elliptic problems. An auxiliary linear element stiffness matrix is chosen to be the preconditioner for higher order finite elements. Then an algebraic multigrid method of linear finite element is applied for solving the preconditioner. The optimal condition number which is independent of the mesh size is obtained. Numerical experiments confirm the efficiency of the algorithm.
Mixed Generalized Multiscale Finite Element Methods and Applications
Chung, Eric T.
2015-03-03
In this paper, we present a mixed generalized multiscale finite element method (GMsFEM) for solving flow in heterogeneous media. Our approach constructs multiscale basis functions following a GMsFEM framework and couples these basis functions using a mixed finite element method, which allows us to obtain a mass conservative velocity field. To construct multiscale basis functions for each coarse edge, we design a snapshot space that consists of fine-scale velocity fields supported in a union of two coarse regions that share the common interface. The snapshot vectors have zero Neumann boundary conditions on the outer boundaries, and we prescribe their values on the common interface. We describe several spectral decompositions in the snapshot space motivated by the analysis. In the paper, we also study oversampling approaches that enhance the accuracy of mixed GMsFEM. A main idea of oversampling techniques is to introduce a small dimensional snapshot space. We present numerical results for two-phase flow and transport, without updating basis functions in time. Our numerical results show that one can achieve good accuracy with a few basis functions per coarse edge if one selects appropriate offline spaces. © 2015 Society for Industrial and Applied Mathematics.
Probabilistic finite elements for fatigue and fracture analysis
Belytschko, Ted; Liu, Wing Kam
1993-01-01
An overview of the probabilistic finite element method (PFEM) developed by the authors and their colleagues in recent years is presented. The primary focus is placed on the development of PFEM for both structural mechanics problems and fracture mechanics problems. The perturbation techniques are used as major tools for the analytical derivation. The following topics are covered: (1) representation and discretization of random fields; (2) development of PFEM for the general linear transient problem and nonlinear elasticity using Hu-Washizu variational principle; (3) computational aspects; (4) discussions of the application of PFEM to the reliability analysis of both brittle fracture and fatigue; and (5) a stochastic computational tool based on stochastic boundary element (SBEM). Results are obtained for the reliability index and corresponding probability of failure for: (1) fatigue crack growth; (2) defect geometry; (3) fatigue parameters; and (4) applied loads. These results show that initial defect is a critical parameter.
Automation Tools for Finite Element Analysis of Adhesively Bonded Joints
Tahmasebi, Farhad; Brodeur, Stephen J. (Technical Monitor)
2002-01-01
This article presents two new automation creation tools that obtain stresses and strains (Shear and peel) in adhesively bonded joints. For a given adhesively bonded joint Finite Element model, in which the adhesive is characterised using springs, these automation tools read the corresponding input and output files, use the spring forces and deformations to obtain the adhesive stresses and strains, sort the stresses and strains in descending order, and generate plot files for 3D visualisation of the stress and strain fields. Grids (nodes) and elements can be numbered in any order that is convenient for the user. Using the automation tools, trade-off studies, which are needed for design of adhesively bonded joints, can be performed very quickly.
Probabilistic finite elements for fatigue and fracture analysis. Final report
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Belytschko, T.; Liu, W.K.
1993-04-01
An overview of the probabilistic finite element method (PFEM) developed by the authors and their colleagues in recent years is presented. The primary focus is placed on the development of PFEM for both structural mechanics problems and fracture mechanics problems. The perturbation techniques are used as major tools for the analytical derivation. The following topics are covered: (1) representation and discretization of random fields; (2) development of PFEM for the general linear transient problem and nonlinear elasticity using Hu-Washizu variational principle; (3) computational aspects; (4) discussions of the application of PFEM to the reliability analysis of both brittle fracture and fatigue; and (5) a stochastic computational tool based on stochastic boundary element (SBEM). Results are obtained for the reliability index and corresponding probability of failure for: (1) fatigue crack growth; (2) defect geometry; (3) fatigue parameters; and (4) applied loads. These results show that initial defect is a critical parameter.
A conjecture on a class of elements of finite order in K2Fp
Institute of Scientific and Technical Information of China (English)
无
2001-01-01
For a local field F the finite subgroups of K2F are expressed by a class of special elements of finite order, which makes a famous theorem built by Moore, Carroll, Tate and Merkurjev more explicit and also disproves a conjecture posed by Browkin.
Finite Element Simulation of Blanking Process
Directory of Open Access Journals (Sweden)
Afzal Ahmed
2012-10-01
daya penembusan sebanyak 42%. Daya tebukan yang diukur melalui eksperimen dan simulasi kekal pada kira-kira 90kN melepasi penembusan punch sebanyak 62%. Apabila ketebalan keputusan kunci ditambah, ketinggian retak dikurangkan dan ini meningkatkan kualiti pengosongan.KEYWORDS: simulation; finite element simulation; blanking; computer aided manufacturing
Energy Technology Data Exchange (ETDEWEB)
Koch, Stephan
2009-03-30
This thesis is concerned with the numerical simulation of electromagnetic fields in the quasi-static approximation which is applicable in many practical cases. Main emphasis is put on higher-order finite element methods. Quasi-static applications can be found, e.g., in accelerator physics in terms of the design of magnets required for beam guidance, in power engineering as well as in high-voltage engineering. Especially during the first design and optimization phase of respective devices, numerical models offer a cheap alternative to the often costly assembly of prototypes. However, large differences in the magnitude of the material parameters and the geometric dimensions as well as in the time-scales of the electromagnetic phenomena involved lead to an unacceptably long simulation time or to an inadequately large memory requirement. Under certain circumstances, the simulation itself and, in turn, the desired design improvement becomes even impossible. In the context of this thesis, two strategies aiming at the extension of the range of application for numerical simulations based on the finite element method are pursued. The first strategy consists in parallelizing existing methods such that the computation can be distributed over several computers or cores of a processor. As a consequence, it becomes feasible to simulate a larger range of devices featuring more degrees of freedom in the numerical model than before. This is illustrated for the calculation of the electromagnetic fields, in particular of the eddy-current losses, inside a superconducting dipole magnet developed at the GSI Helmholtzzentrum fuer Schwerionenforschung as a part of the FAIR project. As the second strategy to improve the efficiency of numerical simulations, a hybrid discretization scheme exploiting certain geometrical symmetries is established. Using this method, a significant reduction of the numerical effort in terms of required degrees of freedom for a given accuracy is achieved. The
Effective Stiffness: Generalizing Effective Resistance Sampling to Finite Element Matrices
Avron, Haim
2011-01-01
We define the notion of effective stiffness and show that it can used to build sparsifiers, algorithms that sparsify linear systems arising from finite-element discretizations of PDEs. In particular, we show that sampling $O(n\\log n)$ elements according to probabilities derived from effective stiffnesses yields an high quality preconditioner that can be used to solve the linear system in a small number of iterations. Effective stiffness generalizes the notion of effective resistance, a key ingredient of recent progress in developing nearly linear symmetric diagonally dominant (SDD) linear solvers. Solving finite elements problems is of considerably more interest than the solution of SDD linear systems, since the finite element method is frequently used to numerically solve PDEs arising in scientific and engineering applications. Unlike SDD systems, which are relatively easy to precondition, there has been limited success in designing fast solvers for finite element systems, and previous algorithms usually tar...
Essentials of finite element modeling and adaptive refinement
Dow, John O
2012-01-01
Finite Element Analysis is a very popular, computer-based tool that uses a complex system of points called nodes to make a grid called a ""mesh. "" The mesh contains the material and structural properties that define how the structure will react to certain loading conditions, allowing virtual testing and analysis of stresses or changes applied to the material or component design. This groundbreaking text extends the usefulness of finite element analysis by helping both beginners and advanced users alike. It simplifies, improves, and extends both the finite element method while at the same t
A mixed finite element for the analysis of laminated plates
Putcha, N. S.; Reddy, J. N.
1983-01-01
A new mixed shear-flexible finite element based on the Hellinger-Reissner's variational principle is developed. The element is constructed using a mixed formulation of the shear deformation theory of laminated composite plates, and consists of three displacements, two shear rotations, and three moments as the independent degrees of freedom. The numerical convergence and accuracy characteristics of the element are investigated for bending of laminated anisotropic composite plates. The element is relatively simple to construct and has better accuracy and convergence features when compared to other conventional finite elements.
Chen, Jiefu; Zeng, Shubin; Dong, Qiuzhao; Huang, Yueqin
2017-02-01
An axisymmetric semianalytical finite element method is proposed and employed for rapid simulations of electromagnetic telemetry in layered underground formation. In this method, the layered media is decomposed into several subdomains and the interfaces between subdomains are discretized by conventional finite elements. Then a Riccati equation based high precision integration scheme is applied to exploit the homogeneity along the vertical direction in each layer. This semianalytical finite element scheme is very efficient in modeling electromagnetic telemetry in layered formation. Numerical examples as well as a field case with water based mud as drilling fluid are given to demonstrate the validity and effectiveness of this method.
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Kim, Ju Hee [Korea Military Academy, Seoul (Korea, Republic of); Kim, Yun Jae [Korea University, Seoul (Korea, Republic of); Kim, Joung Soo [KAERI, Daejeon (Korea, Republic of)
2013-07-15
By using finite element analysis, we proposed an applicable finite element method of laser shock peening (LSP) and discussed various parameters, such as solution time, stability limit, dynamic yield stress, peak pressure, pressure pulse duration, laser spot size, and multiple LSP. The effects of parameters related to the finite element simulation of the LSP process on the residual stresses of 35CD4 30HRC steel alloy are discussed. Parametric sensitivity analyses were performed to establish the optimum processing variables of the LSP process. In addition, we evaluated the effects of initial residual stress, such as welding-induced residual stress field.
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Dobrev, Veselin A. [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States); Kolev, Tzanio V. [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States); Rieben, Robert N. [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)
2012-09-20
The numerical approximation of the Euler equations of gas dynamics in a movingLagrangian frame is at the heart of many multiphysics simulation algorithms. Here, we present a general framework for high-order Lagrangian discretization of these compressible shock hydrodynamics equations using curvilinear finite elements. This method is an extension of the approach outlined in [Dobrev et al., Internat. J. Numer. Methods Fluids, 65 (2010), pp. 1295--1310] and can be formulated for any finite dimensional approximation of the kinematic and thermodynamic fields, including generic finite elements on two- and three-dimensional meshes with triangular, quadrilateral, tetrahedral, or hexahedral zones. We discretize the kinematic variables of position and velocity using a continuous high-order basis function expansion of arbitrary polynomial degree which is obtained via a corresponding high-order parametric mapping from a standard reference element. This enables the use of curvilinear zone geometry, higher-order approximations for fields within a zone, and a pointwise definition of mass conservation which we refer to as strong mass conservation. Moreover, we discretize the internal energy using a piecewise discontinuous high-order basis function expansion which is also of arbitrary polynomial degree. This facilitates multimaterial hydrodynamics by treating material properties, such as equations of state and constitutive models, as piecewise discontinuous functions which vary within a zone. To satisfy the Rankine--Hugoniot jump conditions at a shock boundary and generate the appropriate entropy, we introduce a general tensor artificial viscosity which takes advantage of the high-order kinematic and thermodynamic information available in each zone. Finally, we apply a generic high-order time discretization process to the semidiscrete equations to develop the fully discrete numerical algorithm. Our method can be viewed as the high-order generalization of the so-called staggered
Institute of Scientific and Technical Information of China (English)
无
2006-01-01
In this paper, we study the semi-discrete mortar upwind finite volume element method with the Crouzeix-Raviart element for the parabolic convection diffusion problems.It is proved that the semi-discrete mortar upwind finite volume element approximations derived are convergent in the H1- and L2-norms.
Visualizing Higher Order Finite Elements: FY05 Yearly Report.
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Thompson, David; Pebay, Philippe Pierre
2005-11-01
This report contains an algorithm for decomposing higher-order finite elementsinto regions appropriate for isosurfacing and proves the conditions under which thealgorithm will terminate. Finite elements are used to create piecewise polynomialapproximants to the solution of partial differential equations for which no analyticalsolution exists. These polynomials represent fields such as pressure, stress, and mo-mentim. In the past, these polynomials have been linear in each parametric coordinate.Each polynomial coefficient must be uniquely determined by a simulation, and thesecoefficients are called degrees of freedom. When there are not enough degrees of free-dom, 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 increas-ing the order of the polynomial approximation (instead of increasing the number offinite elements, each of which has its own set of coefficients) can allow some typesof simulations to produce a valid approximation with many fewer degrees of freedomthan increasing the number of finite elements alone. However, once the simulation hasdetermined the values of all the coefficients in a higher-order approximant, tools donot exist for visual inspection of the solution.This report focuses on a technique for the visual inspection of higher-order finiteelement simulation results based on decomposing each finite element into simplicialregions where existing visualization algorithms such as isosurfacing will work. Therequirements of the isosurfacing algorithm are enumerated and related to the placeswhere the partial derivatives of the polynomial become zero. The original isosurfacingalgorithm is then applied to each of these regions in turn.3 AcknowledgementThe authors would like to thank David Day and Louis Romero for their insight into poly-nomial system solvers and the LDRD Senior Council for the opportunity to pursue thisresearch. The authors were
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Ponta, Fernando; Ferreira, Fabiana
2001-07-01
This paper applies the finite element method for the calculation of line magnetic field transversal profile using own routine calculation. Using a real case, simulations were performed under various conditions gathering distortion elements, obtaining the field profile. By analysing these results conclusions are drawing related to the changes produced by the distortions on the magnetic field configuration and evaluations of the surrounding elements influence are evaluated.
Finite Element Method for Analysis of Material Properties
DEFF Research Database (Denmark)
Rauhe, Jens Christian
The use of cellular and composite materials have in recent years become more and more common in all kinds of structural components and accurate knowledge of the effective properties is therefore essential. In this wok the effective properties are determined using the real material microstructure...... and the finite element method. The material microstructure of the heterogeneous material is non-destructively determined using X-ray microtomography. A software program has been generated which uses the X-ray tomographic data as an input for the mesh generation of the material microstructure. To obtain a proper...... description of the material microstructure the finite element models must contain a large number of elements and this problem is solved by using the preconditioned conjugated gradient solver with an Element-By-Element preconditioner. Finite element analysis provides the volume averaged stresses and strains...
Adaptive Finite Element Methods for Elliptic Problems with Discontinuous Coefficients
Bonito, Andrea
2013-01-01
Elliptic PDEs with discontinuous diffusion coefficients occur in application domains such as diffusions through porous media, electromagnetic field propagation on heterogeneous media, and diffusion processes on rough surfaces. The standard approach to numerically treating such problems using finite element methods is to assume that the discontinuities lie on the boundaries of the cells in the initial triangulation. However, this does not match applications where discontinuities occur on curves, surfaces, or manifolds, and could even be unknown beforehand. One of the obstacles to treating such discontinuity problems is that the usual perturbation theory for elliptic PDEs assumes bounds for the distortion of the coefficients in the L∞ norm and this in turn requires that the discontinuities are matched exactly when the coefficients are approximated. We present a new approach based on distortion of the coefficients in an Lq norm with q < ∞ which therefore does not require the exact matching of the discontinuities. We then use this new distortion theory to formulate new adaptive finite element methods (AFEMs) for such discontinuity problems. We show that such AFEMs are optimal in the sense of distortion versus number of computations, and report insightful numerical results supporting our analysis. © 2013 Societ y for Industrial and Applied Mathematics.
Finite Element Calculation of Discrete Stratified Fluid Vibrations
Directory of Open Access Journals (Sweden)
Ko Ko Win
2016-01-01
Full Text Available Many publications, which consider a problem of small vibrations of an incompressible ideal fluid, completely filling the stationary cylindrical tank, have the long lists of references in the field concerned. This paper uses the finite element method to consider vibrations of three incompressible fluids, defines natural frequencies of vibrations, and builds the vibration forms of the interface surface of fluids for the double-tone vibrations. It shows how the vibration frequency depends on the ratios of vibrating fluid density and thicknesses of fluid layers and compares the numerical calculation results with the analytically obtained exact values.The paper describes a variational formulation of the problem concerning the natural vibrations of immiscible fluids and using the finite element method provides a numerical implementation to define the fixed values of the functional that meets the variational problem. The reliability of the numerical results obtained is proved by their approximation to the result of calculating frequencies derived from the solutions of the problem of natural vibrations of fluid in a cylindrical vessel with a different fluid depth. To perform all numerical calculations was used the Matlab software.
Institute of Scientific and Technical Information of China (English)
Bahattin Kanber; O.Yavuz Bozkurt
2006-01-01
In this work,the finite element analysis of the elasto-plastic plate bending problems is carried out using transition rectangular plate elements.The shape functions of the transition plate elements are derived based on a practical rule.The transition plate elements are all quadrilateral and can be used to obtain efficient finite element models using minimum number of elements.The mesh convergence rates of the models including the transition elements are compared with the regular element models.To verify the developed elements,simple tests are demonstrated and various elasto-plastic problems are solved.Their results are compared with ANSYS results.
Determining matrix elements and resonance widths from finite volume: the dangerous mu-terms
Takacs, G
2011-01-01
The standard numerical approach to determining matrix elements of local operators and width of resonances uses the finite volume dependence of energy levels and matrix elements. Finite size corrections that decay exponentially in the volume are usually neglected or taken into account using perturbation expansion in effective field theory. Using two-dimensional sine-Gordon field theory as "toy model" it is shown that some exponential finite size effects could be much larger than previously thought, potentially spoiling the determination of matrix elements in frameworks such as lattice QCD. The particular class of finite size corrections considered here are mu-terms arising from bound state poles in the scattering amplitudes. In sine-Gordon model, these can be explicitly evaluated and shown to explain the observed discrepancies to high precision. It is argued that the effects observed are not special to the two-dimensional setting, but rather depend on general field theoretic features that are common with model...
Finite Element Crash Simulations and Impact-Induced Injuries
Directory of Open Access Journals (Sweden)
Jaroslav Mackerle
1999-01-01
Full Text Available This bibliography lists references to papers, conference proceedings and theses/dissertations dealing with finite element simulations of crashes, impact-induced injuries and their protection that were published in 1980–1998. 390 citations are listed.
Generalized multiscale finite element method. Symmetric interior penalty coupling
Efendiev, Yalchin R.
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. © 2013 Elsevier Inc.
Finite Element Models for Electron Beam Freeform Fabrication Process Project
National Aeronautics and Space Administration — This Small Business Innovation Research Phase II proposal offers to develop a comprehensive computer simulation methodology based on the finite element method for...
Finite Element Models for Electron Beam Freeform Fabrication Process Project
National Aeronautics and Space Administration — This Small Business Innovation Research proposal offers to develop the most accurate, comprehensive and efficient finite element models to date for simulation of the...
Vehicle Interior Noise Prediction Using Energy Finite Element Analysis Project
National Aeronautics and Space Administration — It is proposed to develop and implement a computational technique based on Energy Finite Element Analysis (EFEA) for interior noise prediction of advanced aerospace...
Structural analysis with the finite element method linear statics
Oñate, Eugenio
2013-01-01
STRUCTURAL ANALYSIS WITH THE FINITE ELEMENT METHOD Linear Statics Volume 1 : The Basis and Solids Eugenio Oñate The two volumes of this book cover most of the theoretical and computational aspects of the linear static analysis of structures with the Finite Element Method (FEM). The content of the book is based on the lecture notes of a basic course on Structural Analysis with the FEM taught by the author at the Technical University of Catalonia (UPC) in Barcelona, Spain for the last 30 years. Volume1 presents the basis of the FEM for structural analysis and a detailed description of the finite element formulation for axially loaded bars, plane elasticity problems, axisymmetric solids and general three dimensional solids. Each chapter describes the background theory for each structural model considered, details of the finite element formulation and guidelines for the application to structural engineering problems. The book includes a chapter on miscellaneous topics such as treatment of inclined supports, elas...
Finite Element Crash Simulations and Impact-Induced Injuries
Mackerle, Jaroslav
1999-01-01
This bibliography lists references to papers, conference proceedings and theses/dissertations dealing with finite element simulations of crashes, impact-induced injuries and their protection that were published in 1980–1998. 390 citations are listed.
Finite element analysis of rotating beams physics based interpolation
Ganguli, Ranjan
2017-01-01
This book addresses the solution of rotating beam free-vibration problems using the finite element method. It provides an introduction to the governing equation of a rotating beam, before outlining the solution procedures using Rayleigh-Ritz, Galerkin and finite element methods. The possibility of improving the convergence of finite element methods through a judicious selection of interpolation functions, which are closer to the problem physics, is also addressed. The book offers a valuable guide for students and researchers working on rotating beam problems – important engineering structures used in helicopter rotors, wind turbines, gas turbines, steam turbines and propellers – and their applications. It can also be used as a textbook for specialized graduate and professional courses on advanced applications of finite element analysis.
Finite element model updating using bayesian framework and modal properties
CSIR Research Space (South Africa)
Marwala, T
2005-01-01
Full Text Available Finite element (FE) models are widely used to predict the dynamic characteristics of aerospace structures. These models often give results that differ from measured results and therefore need to be updated to match measured results. Some...
Accurate Parallel Algorithm for Adini Nonconforming Finite Element
Institute of Scientific and Technical Information of China (English)
罗平; 周爱辉
2003-01-01
Multi-parameter asymptotic expansions are interesting since they justify the use of multi-parameter extrapolation which can be implemented in parallel and are well studied in many papers for the conforming finite element methods. For the nonconforming finite element methods, however, the work of the multi-parameter asymptotic expansions and extrapolation have seldom been found in the literature. This paper considers the solution of the biharmonic equation using Adini nonconforming finite elements and reports new results for the multi-parameter asymptotic expansions and extrapolation. The Adini nonconforming finite element solution of the biharmonic equation is shown to have a multi-parameter asymptotic error expansion and extrapolation. This expansion and a multi-parameter extrapolation technique were used to develop an accurate approximation parallel algorithm for the biharmonic equation. Finally, numerical results have verified the extrapolation theory.
COHESIVE ZONE FINITE ELEMENT-BASED MODELING OF HYDRAULIC FRACTURES
Institute of Scientific and Technical Information of China (English)
Zuorong Chen; A.P. Bunger; Xi Zhang; Robert G. Jeffrey
2009-01-01
Hydraulic fracturing is a powerful technology used to stimulate fluid production from reservoirs. The fully 3-D numerical simulation of the hydraulic fracturing process is of great importance to the efficient application of this technology, but is also a great challenge because of the strong nonlinear coupling between the viscous flow of fluid and fracture propagation. By taking advantage of a cohesive zone method to simulate the fracture process, a finite element model based on the existing pore pressure cohesive finite elements has been established to investigate the propagation of a penny-shaped hydraulic fracture in an infinite elastic medium. The effect of cohesive material parameters and fluid viscosity on the hydraulic fracture behaviour has been investigated. Excellent agreement between the finite element results and analytical solutions for the limiting case where the fracture process is dominated by rock fracture toughness demonstrates the ability of the cohesive zone finite element model in simulating the hydraulic fracture growth for this case.
SPECTRAL FINITE ELEMENT METHOD FOR A UNSTEADY TRANSPORT EQUATION
Institute of Scientific and Technical Information of China (English)
MeiLiquan
1999-01-01
In this paper,a new numerical method,the coupling method of spherical harmonic function spectral and finite elements,for a unsteady transport equation is dlscussed,and the error analysis of this scheme is proved.
On mixed finite element techniques for elliptic problems
Directory of Open Access Journals (Sweden)
M. Aslam Noor
1983-01-01
mildly nonlinear elliptic problems by means of finite element methods of mixed type. The technique is based on an extended variational principle, in which the constraint of interelement continuity has been removed at the expense of introducing a Lagrange multiplier.
Comparison of different precondtioners for nonsymmtric finite volume element methods
Energy Technology Data Exchange (ETDEWEB)
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 Meshes Auto-Generation for the Welted Bifurcation
Institute of Scientific and Technical Information of China (English)
YUANMei; LIYa-ping
2004-01-01
In this paper, firstly, a mathematical model for a specific kind of welted bifurcation is established, the parametric equation for the intersecting curve is resulted in. Secondly, a method for partitioning finite element meshes of the welted bifurcation is put forward, its main idea is that developing the main pipe surface and the branch pipe surface respectively, dividing meshes on each developing plane and obtaining meshes points, then transforming their plane coordinates into space coordinates. Finally, an applied program for finite element meshes auto-generation is simply introduced, which adopt ObjectARX technique and its running result can be shown in AutoCAD. The meshes generated in AutoCAD can be exported conveniently to most of finite element analysis soft wares, and the finite element computing result can satisfy the engineering precision requirement.
A Note on Powers in Finite Fields
DEFF Research Database (Denmark)
Aabrandt, Andreas; Hansen, Vagn Lundsgaard
2016-01-01
for squares in odd prime fields, giving it a formulation which is apt for generalization to arbitrary finite fields and powers. Our proof uses algebra rather than classical number theory, which makes it convenient when presenting basic methods of applied algebra in the classroom....
Engineering and Design: Geotechnical Analysis by the Finite Element Method
2007-11-02
used it to determine stresses and movements in embank- ments, and Reyes and Deer described its application to analysis of underground openings in rock...3-D steady-state seepage analysis of permeability of the cutoff walls was varied from 10 to Cerrillos Dam near Ponce , Puerto Rico, for the U.S.-6 10...36 Hughes, T. J. R. (1987). The Finite Element Reyes , S. F., and Deene, D. K. (1966). “Elastic Method, Linear Static and Dynamic Finite Element
On the error bounds of nonconforming finite elements
Institute of Scientific and Technical Information of China (English)
无
2010-01-01
We prove that the error estimates of a large class of nonconforming finite elements are dominated by their approximation errors, which means that the well-known Cea’s lemma is still valid for these nonconforming finite element methods. Furthermore, we derive the error estimates in both energy and L2 norms under the regularity assumption u ∈ H1+s(Ω) with any s > 0. The extensions to other related problems are possible.
Anisotropic rectangular nonconforming finite element analysis for Sobolev equations
Institute of Scientific and Technical Information of China (English)
SHI Dong-yang; WANG Hai-hong; GUO Cheng
2008-01-01
An anisotropic rectangular nonconforming finite element method for solving the Sobolev equations is discussed under semi-discrete and full discrete schemes.The corresponding optimal convergence error estimates and superclose property are derived,which are the same as the traditional conforming finite elements.Furthermore,the global superconvergence is obtained using a post-processing technique.The numerical results show the validity of the theoretical analysis.
A FINITE ELEMENT MODEL FOR SEISMICITY INDUCED BY FAULT INTERACTION
Institute of Scientific and Technical Information of China (English)
Chen Huaran; Li Yiqun; He Qiaoyun; Zhang Jieqing; Ma Hongsheng; Li Li
2003-01-01
On ths basis of interaction between faults, a finite element model for Southwest China is constructed, and the stress adjustment due to the strong earthquake occurrence in this region was studied. The preliminary results show that many strong earthquakes occurred in the area of increased stress in the model. Though the results are preliminary, the quasi-3D finite element model is meaningful for strong earthquake prediction.
A FINITE ELEMENT MODEL FOR SEISMICITY INDUCED BY FAULT INTERACTION
Institute of Scientific and Technical Information of China (English)
ChenHuaran; LiYiqun; HeQiaoyun; ZhangJieqing; MaHongsheng; LiLi
2003-01-01
On ths basis of interaction between faults, a finite element model for Southwest China is constructed, and the stress adjustment due to the strong earthquake occurrence in this region was studied. The preliminary results show that many strong earthquakes occurred in the are a of increased stress in the model. Though the results are preliminary, the quasi-3D finite element model is meaningful for strong earthquake prediction.
THE DERIVATIVE PATCH INTERPOLATING RECOVERY TECHNIQUE FOR FINITE ELEMENT APPROXIMATIONS
Institute of Scientific and Technical Information of China (English)
TieZhang; Yan-pingLin; R.J.Tait
2004-01-01
A derivative patch interpolating recovery technique is analyzed for the finite element approximation to the second order elliptic boundary value problems in two dimensional case.It is shown that the convergence rate of the recovered gradient admits superc onvergence on the recovered subdomain, and is two order higher than the optimal global convergence rate (ultracovergence) at an internal node point when even order finite element spaces and local uniform meshes are used.
Integration of geometric modeling and advanced finite element preprocessing
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.
Finite element analysis to model complex mitral valve repair.
Labrosse, Michel; Mesana, Thierry; Baxter, Ian; Chan, Vincent
2016-01-01
Although finite element analysis has been used to model simple mitral repair, it has not been used to model complex repair. A virtual mitral valve model was successful in simulating normal and abnormal valve function. Models were then developed to simulate an edge-to-edge repair and repair employing quadrangular resection. Stress contour plots demonstrated increased stresses along the mitral annulus, corresponding to the annuloplasty. The role of finite element analysis in guiding clinical practice remains undetermined.
Determination of a synchronous generator characteristics via Finite Element Analysis
Directory of Open Access Journals (Sweden)
Kolondzovski Zlatko
2005-01-01
Full Text Available In the paper a determination of characteristics of a small salient pole synchronous generator (SG is presented. Machine characteristics are determined via Finite Element Analysis (FEA and for that purpose is used the software package FEMM Version 3.3. After performing their calculation and analysis, one can conclude that most of the characteristics presented in this paper can be obtained only by using the Finite Element Method (FEM.
A finite element primer for beginners the basics
Zohdi, Tarek I
2014-01-01
The purpose of this primer is to provide the basics of the Finite Element Method, primarily illustrated through a classical model problem, linearized elasticity. The topics covered are:(1) Weighted residual methods and Galerkin approximations,(2) A model problem for one-dimensional?linear elastostatics,(3) Weak formulations in one dimension,(4) Minimum principles in one dimension,(5) Error estimation in one dimension,(5) Construction of Finite Element basis functions in one dimension,(6) Gaussian Quadrature,(7) Iterative solvers and element by element data structures,(8) A model problem for th
Finite Element Model Updating Using Response Surface Method
Marwala, Tshilidzi
2007-01-01
This paper proposes the response surface method for finite element model updating. The response surface method is implemented by approximating the finite element model surface response equation by a multi-layer perceptron. The updated parameters of the finite element model were calculated using genetic algorithm by optimizing the surface response equation. The proposed method was compared to the existing methods that use simulated annealing or genetic algorithm together with a full finite element model for finite element model updating. The proposed method was tested on an unsymmetri-cal H-shaped structure. It was observed that the proposed method gave the updated natural frequen-cies and mode shapes that were of the same order of accuracy as those given by simulated annealing and genetic algorithm. Furthermore, it was observed that the response surface method achieved these results at a computational speed that was more than 2.5 times as fast as the genetic algorithm and a full finite element model and 24 ti...
Enhanced patch test of finite element methods
Institute of Scientific and Technical Information of China (English)
CHEN; Wanji
2006-01-01
Theoretically, the constant stress patch test is not rigorous. Also, either the patch test of non-zero constant shear for Mindlin plate problem or non-zero strain gradient curvature of the microstructures cannot be performed. To improve the theory of the patch test, in this paper, based on the variational principle with relaxed continuity requirement of nonconforming element for homogeneous differential equations, the author proposed the individual element condition for passing the patch test and the convergence condition of the element: besides passing the patch test, the element function should include the rigid body modes and constant strain modes and satisfy the weak continuity condition, and no extra zero energy modes occur. Moreover, the author further established a variational principle with relaxed continuity requirement of nonconforming element for inhomogeneous differential equations, the enhanced patch test condition and the individual element condition. To assure the convergence of the element that should pass the enhanced patch test, the element function should include the rigid body modes and non-zero strain modes which satisfied the equilibrium equations, and no spurious zero energy modes occur and should satisfy new weak continuity condition. The theory of the enhanced patch test proposed in this paper can be applied to both homogeneous and inhomogeneous differential equations. Based on this theory, the patch test of the non-zero constant shear stress for Mindlin plate and the C0-1 patch test of the non-zero constant curvature for the couple stress/strain gradient theory were established.
CSIR Research Space (South Africa)
Loveday, PW
2007-03-01
Full Text Available conventional finite element methods available in commercial software, these models tend to be very large. An alternative method is to use specially formulated waveguide finite elements (sometimes called Semi-Analytical Finite Elements). Models using...
Advances in the study of hybrid finite elements
Institute of Scientific and Technical Information of China (English)
无
2000-01-01
Some new concepts and research progress in hybrid finite elements advanced in recent years are in troduced. On the basis of incompatible energy consistency analysis, the optimal condition of hybrid elements is derived and the formulation for fulfilling this condition is given. A post-processing penalty equilibrium optimization technique of hybrid element is presented to create high quality hybrid model. For incompressible problems, a method of deviatoric hybrid element is proposed and unification of computation between compressible and incompressible media is achieved.
THE SPACE-TIME FINITE ELEMENT METHOD FOR PARABOLIC PROBLEMS
Institute of Scientific and Technical Information of China (English)
李宏; 刘儒勋
2001-01-01
Adaptive space-time finite element method, continuous in space but discontinuous in time for semi-linear parabolic problems is discussed. The approach is based on a combination of finite element and finite difference techniques. The existence and uniqueness of the weak solution are proved without any assumptions on choice of the spacetime meshes. Basic error estimates in L∞ (L2) norm, that is maximum-norm in time, L2norm in space are obtained. The numerical results are given in the last part and the analysis between theoretic and experimental results are obtained.
Institute of Scientific and Technical Information of China (English)
刘俊; 林皋; 李建波
2011-01-01
为精确研究超高压输电线路在复杂工况下的工频电场,采用比例边界有限元方法,在建立相应的电场计算模型基础上,利用变分原理并通过比例边界坐标变换,推导出工频电场的比例边界有限元方程、电位求解公式及电场求解公式,分析了超高压输电线路在穿越较复杂地形时的工频电场,探讨了超高压输电线路下存在介质块对工频电场的影响,并将算例计算结果与其他数值方法进行了比较.结果表明,比例边界有限元方法精度高、计算工作量小.%A scaled boundary finite element method (SBFEM) is developed for precise study of power frequency electric field generated by the EHV transmission lines under complex conditions. The electric field model is established, and variational principle technique and coordinate transformation between scaled and Cartesian coordinate is used to derive the scaled boundary finite element equations. The formulation of calculation of electric potential and field is also obtained.The method is also to solve the power-frequency electric field of EHV transmission lines under condition of complex landscape and media block. Numerical experiment is carried out and compared with other numerical methods. The results show that the proposed method yields excellent results, quick convergence and less amount of computation time.
A Comparison of Continuous Mass-lumped Finite Elements and Finite Differences for 3D
Zhebel, E.; Minisini, S.; Kononov, A.; Mulder, W.A.
2012-01-01
The finite-difference method is widely used for time-domain modelling of the wave equation because of its ease of implementation of high-order spatial discretization schemes, parallelization and computational efficiency. However, finite elements on tetrahedral meshes are more accurate in complex geo
Asymptotic Behavior of the Finite Difference and the Finite Element Methods for Parabolic Equations
Institute of Scientific and Technical Information of China (English)
LIU Yang; FENG Hui
2005-01-01
The asymptotic convergence of the solution of the parabolic equation is proved. By the eigenvalues estimation, we obtain that the approximate solutions by the finite difference method and the finite element method are asymptotically convergent. Both methods are considered in continuous time.
A Comparison of Continuous Mass-lumped Finite Elements and Finite Differences for 3D
Zhebel, E.; Minisini, S.; Kononov, A.; Mulder, W.A.
2012-01-01
The finite-difference method is widely used for time-domain modelling of the wave equation because of its ease of implementation of high-order spatial discretization schemes, parallelization and computational efficiency. However, finite elements on tetrahedral meshes are more accurate in complex
Institute of Scientific and Technical Information of China (English)
陈蔚
2003-01-01
The transient behavior of a semiconductor device consists of a Poisson equation for the electric potential and of two nonlinear parabolic equations for the electron density and hole density.The electric potential equation is discretized by a mixed finite element method.The electron and hole density equations are treated by implicit-explicit multistep finite element methods.The schemes are very efficient.The optimal order error estimates both in time and space are derived.
Error Estimates for Finite-Element Navier-Stokes Solvers without Standard Inf-Sup Conditions
Institute of Scientific and Technical Information of China (English)
JianGuo LIU; Jie LIU; Robert L.PEGO
2009-01-01
The authors establish error estimates for recently developed finite-element methods for incompressible viscous flow in domains with no-slip boundary conditions. The methods arise by discretization of a well-posed extended Navier-Stokes dynamics for which pressure is determined from current velocity and force fields. The methods use C1 elements for velocity and C0 elements for pressure. A stability estimate is proved for a related finite-element projection method close to classical time-splitting methods of Orszag, Israeli, DeVille and Karniadakis.
B Free Finite Element Approach for Saturated Porous Media: Consolidation
Directory of Open Access Journals (Sweden)
M. M. Stickle
2016-01-01
Full Text Available The B free finite element approach is applied to the governing equations describing the consolidation process in saturated poroelastic medium with intrinsically incompressible solid and fluid phases. Under this approach, where Voigt notation is avoided, the finite element equilibrium equations and the linearization of the coupled governing equations are fully derived using tensor algebra. In order to assess the B free approach for the consolidation equations, direct comparison with analytical solution of the response of a homogeneous and isotropic water-saturated poroelastic finite column under harmonic load is presented. The results illustrate the capability of this finite element approach of reproducing accurately the response of quasistatic phenomena in a saturated porous medium.
The features of finite-element modeling of a structural element of flexible woven composites
Directory of Open Access Journals (Sweden)
Dmitry A. Kozhanov
2016-03-01
Full Text Available The features of finite-element modeling of both an element itself and its behavior under uniaxial tension have been demonstrated with a structural element of flexible woven composites. The main components of the material, such as reinforcing fabric and material's matrix were examined in modeling. The reinforcing fabric is a plain weave. These yarns were taken as an elastic material. The matrix of the material was considered to be a soft polymer with the possible occurrence of irreversible elastic-plastic deformations. Moreover, the possible occurrence of damages in the structure of the material under high loads was taken into account in modeling. The fields of stresses and strains were built; the zones of the material's internal damages under uniaxial tension were demonstrated. The risk zones of weave were revealed.
A multilevel finite element method for Fredholm integral eigenvalue problems
Xie, Hehu; Zhou, Tao
2015-12-01
In this work, we proposed a multigrid finite element (MFE) method for solving the Fredholm integral eigenvalue problems. The main motivation for such studies is to compute the Karhunen-Loève expansions of random fields, which play an important role in the applications of uncertainty quantification. In our MFE framework, solving the eigenvalue problem is converted to doing a series of integral iterations and eigenvalue solving in the coarsest mesh. Then, any existing efficient integration scheme can be used for the associated integration process. The error estimates are provided, and the computational complexity is analyzed. It is noticed that the total computational work of our method is comparable with a single integration step in the finest mesh. Several numerical experiments are presented to validate the efficiency of the proposed numerical method.
A Lagrange multiplier based divide and conquer finite element algorithm
Farhat, C.
1991-01-01
A novel domain decomposition method based on a hybrid variational principle is presented. Prior to any computation, a given finite element mesh is torn into a set of totally disconnected submeshes. First, an incomplete solution is computed in each subdomain. Next, the compatibility of the displacement field at the interface nodes is enforced via discrete, polynomial and/or piecewise polynomial Lagrange multipliers. In the static case, each floating subdomain induces a local singularity that is resolved very efficiently. The interface problem associated with this domain decomposition method is, in general, indefinite and of variable size. A dedicated conjugate projected gradient algorithm is developed for solving the latter problem when it is not feasible to explicitly assemble the interface operator. When implemented on local memory multiprocessors, the proposed methodology requires less interprocessor communication than the classical method of substructuring. It is also suitable for parallel/vector computers with shared memory and compares favorably with factorization based parallel direct methods.
Viscous incompressible flow simulation using penalty finite element method
Directory of Open Access Journals (Sweden)
Sharma R.L.
2012-04-01
Full Text Available Numerical analysis of Navier–Stokes equations in velocity– pressure variables with traction boundary conditions for isothermal incompressible flow is presented. Specific to this study is formulation of boundary conditions on synthetic boundary characterized by traction due to friction and surface tension. The traction and open boundary conditions have been investigated in detail. Navier-Stokes equations are discretized in time using Crank-Nicolson scheme and in space using Galerkin finite element method. Pressure being unknown and is decoupled from the computations. It is determined as post processing of the velocity field. The justification to simulate this class of flow problems is presented through benchmark tests - classical lid-driven cavity flowwidely used by numerous authors due to its simple geometry and complicated flow behavior and squeezed flow between two parallel plates amenable to analytical solution. Results are presented for very low to high Reynolds numbers and compared with the benchmark results.
Institute of Scientific and Technical Information of China (English)
无
2000-01-01
The present study aims at developing a new method-Random M icrostructure Finite Element Method (RMFEM)for the effective properties of composite materials . In this method, a random microstructure model is used to simulate the microstructure of the real composite materials. The physical fields in such a randm microstructure model under specified boundary and initial conditions are analyzed by finite element method. The effective properties of composite materials can be obtained from the analysis results. As verification, some effective properties of composite materials, such as elastic module,thermal expansion coefficient, thermal conductivity and elastoplastic properties, are investigated by random microstructure finite element method. The numerical results are given together with the experimental data. It i- revealed that the random microstructure finite element method is a very valid method for the determination of the effective properties of composite materials.
Finite Element Vibration Analysis of Beams, Plates and Shells
Directory of Open Access Journals (Sweden)
Jaroslav Mackerle
1999-01-01
Full Text Available This bibliography lists references to papers, conference proceedings and theses/dissertations dealing with finite element vibration analysis of beams, plates and shells that were published in 1994–1998. It contains 361 citations. Also included, as separated subsections, are vibration analysis of composite materials and vibration analysis of structural elements with cracks/contacts.
A COMBINED HYBRID FINITE ELEMENT METHOD FOR PLATE BENDING PROBLEMS
Institute of Scientific and Technical Information of China (English)
Tian-xiao Zhou; Xiao-ping Xie
2003-01-01
In this paper, a combined hybrid method is applied to finite element discretization ofplate bending problems. It is shown that the resultant schemes are stabilized, i.e., theconvergence of the schemes is independent of inf-sup conditions and any other patch test.Based on this, two new series of plate elements are proposed.
Efficient Finite Element Methods for Transient Analysis of Shells.
1985-04-01
Triangular Shell Element with Improved Membrane Interpolation," Communications in Applied Numerical Methods , in press 1985. Results of this work were...in Applied Numerical Methods , to appear. G.R. Cowper, G.M. Lindberg and M.D. Olson (1970), "A Shallow Shell Finite Element of Triangular Shape," Int. J
Finite element modeling of blast lung injury in sheep.
Gibbons, Melissa M; Dang, Xinglai; Adkins, Mark; Powell, Brian; Chan, Philemon
2015-04-01
A detailed 3D finite element model (FEM) of the sheep thorax was developed to predict heterogeneous and volumetric lung injury due to blast. A shared node mesh of the sheep thorax was constructed from a computed tomography (CT) scan of a sheep cadaver, and while most material properties were taken from literature, an elastic-plastic material model was used for the ribs based on three-point bending experiments performed on sheep rib specimens. Anesthetized sheep were blasted in an enclosure, and blast overpressure data were collected using the blast test device (BTD), while surface lung injury was quantified during necropsy. Matching blasts were simulated using the sheep thorax FEM. Surface lung injury in the FEM was matched to pathology reports by setting a threshold value of the scalar output termed the strain product (maximum value of the dot product of strain and strain-rate vectors over all simulation time) in the surface elements. Volumetric lung injury was quantified by applying the threshold value to all elements in the model lungs, and a correlation was found between predicted volumetric injury and measured postblast lung weights. All predictions are made for the left and right lungs separately. This work represents a significant step toward the prediction of localized and heterogeneous blast lung injury, as well as volumetric injury, which was not recorded during field testing for sheep.
Research of Stamp Forming Simulation Based on Finite Element Method
Institute of Scientific and Technical Information of China (English)
SU Xaio-ping; XU Lian
2008-01-01
We point out that the finite element method offers a greta functional improvement for analyzing the stamp forming process of an automobile panel. Using the finite element theory and the simulation method of sheet stamping forming, the element model of sheet forming is built based on software HyperMesh,and the simulation of the product's sheet forming process is analyzed based on software Dynaform. A series of simulation results are obtained. It is clear that the simulation results from the theoretical basis for the product's die design and are useful for selecting process parameters.
Finite element analysis of two disk rotor system
Dixit, Harsh Kumar
2016-05-01
A finite element model of simple horizontal rotor system is developed for evaluating its dynamic behaviour. The model is based on Timoshenko beam element and accounts for the effect of gyroscopic couple and other rotational forces. Present rotor system consists of single shaft which is supported by bearings at both ends and two disks are mounted at different locations. The natural frequencies, mode shapes and orbits of rotating system for a specific range of rotation speed are obtained by developing a MATLAB code for solving the finite element equations of rotary system. Consequently, Campbell diagram is plotted for finding a relationship between natural whirl frequencies and rotation of the rotor.
Adaptive grid finite element model of the tokamak scrapeoff layer
Energy Technology Data Exchange (ETDEWEB)
Kuprat, A.P.; Glasser, A.H. [Los Alamos National Lab., NM (United States)
1995-07-01
The authors discuss unstructured grids for application to transport in the tokamak edge SOL. They have developed a new metric with which to judge element elongation and resolution requirements. Using this method, the authors apply a standard moving finite element technique to advance the SOL equations while inserting/deleting dynamically nodes that violate an elongation criterion. In a tokamak plasma, this method achieves a more uniform accuracy, and results in highly stretched triangular finite elements, except near separatrix X-point where transport is more isotropic.
Model Reduction in Dynamic Finite Element Analysis of Lightweight Structures
DEFF Research Database (Denmark)
Flodén, Ola; Persson, Kent; Sjöström, Anders
2012-01-01
The application of wood as a construction material when building multi-storey buildings has many advantages, e.g., light weight, sustainability and low energy consumption during the construction and lifecycle of the building. However, compared to heavy structures, it is a greater challenge to build...... lightweight structures without noise and disturbing vibrations between storeys and rooms. The dynamic response of floor and wall structures may be investigated using finite element models with three-dimensional solid elements [1]. In order to analyse the global response of complete buildings, finite element...
Footbridge between finite volumes and finite elements with applications to CFD
Pascal, Frédéric; Ghidaglia, Jean-Michel
2001-12-01
The aim of this paper is to introduce a new algorithm for the discretization of second-order elliptic operators in the context of finite volume schemes on unstructured meshes. We are strongly motivated by partial differential equations (PDEs) arising in computational fluid dynamics (CFD), like the compressible Navier-Stokes equations. Our technique consists of matching up a finite volume discretization based on a given mesh with a finite element representation on the same mesh. An inverse operator is also built, which has the desirable property that in the absence of diffusion, one recovers exactly the finite volume solution. Numerical results are also provided. Copyright
ELASTO-PLASTIC FINITE ELEMENT ANALYSIS OF HOOK'S JOINT
Directory of Open Access Journals (Sweden)
Adnan ATICI
1996-03-01
Full Text Available In this study, stress analysis has been done in Hooke's joint by the finite element method. In finite element meshing, isoparametric quadrilateral elements with four nodes has been chosen and Lagrange polynomial has been used as the interpolation function. The special computer program has been written for the automatic mesh generation. In addition the other program has been developed to solve the finite element problems. Elastoplastic stress analysis is done to calculate the residual stresses in hooke's joint. Elasto-plastic stress values are calculated under loading from 400 daN to 1000 daN with increment of 100 daN. In this analysis "The initial stress method" is used.
Finite element analysis of piezoelectric underwater transducers for acoustic characteristics
Energy Technology Data Exchange (ETDEWEB)
Kim, Jae Hwan [Inha University, Incheon (Korea, Republic of); Kim, Heung Soo [Catholic University, Daegu (Korea, Republic of)
2009-02-15
This paper presents a simulation technique for analyzing acoustic characteristics of piezoelectric underwater transducers. A finite element method is adopted for modeling piezoelectric coupled problems including material damping and fluid-structure interaction problems by taking system matrices in complex form. For the finite element modeling of unbounded acoustic fluid, infinite wave envelope element (IWEE) is adopted to take into account the infinite domain. An in-house finite element program is developed and technical issues for implementing the program are explained. Using the simulation program, acoustic characteristics of tonpilz transducer are analyzed in terms of modal analysis, radiated pressure distribution, pressure spectrum, transmitting-voltage response and impedance analysis along with experimental comparison. The developed simulation technique can be used for designing ultrasonic transducers in the areas of nondestructive evaluation, underwater acoustics and bioengineering
Effective Finite Elements for Shell Analysis.
1984-02-20
conjunction with a shallow shell theory . It 2 should be noteJ that contrary to the results of earlier investigators [12,19], use of a shallow shell theory in...the inadequacy of the shallow shell theory for the relatively deep element emerging from such a coarse mesh. A considerable improvement is obtained
Endovascular nonthermal irreversible electroporation: a finite element analysis.
Maor, Elad; Rubinsky, Boris
2010-03-01
Tissue ablation finds an increasing use in modern medicine. Nonthermal irreversible electroporation (NTIRE) is a biophysical phenomenon and an emerging novel tissue ablation modality, in which electric fields are applied in a pulsed mode to produce nanoscale defects to the cell membrane phospholipid bilayer, in such a way that Joule heating is minimized and thermal damage to other molecules in the treated volume is reduced while the cells die. Here we present a two-dimensional transient finite element model to simulate the electric field and thermal damage to the arterial wall due to an endovascular NTIRE novel device. The electric field was used to calculate the Joule heating effect, and a transient solution of the temperature is presented using the Pennes bioheat equation. This is followed by a kinetic model of the thermal damage based on the Arrhenius formulation and calculation of the Henriques and Moritz thermal damage integral. The analysis shows that the endovascular application of 90, 100 mus pulses with a potential difference of 600 V can induce electric fields of 1000 V/cm and above across the entire arterial wall, which are sufficient for irreversible electroporation. The temperature in the arterial wall reached a maximum of 66.7 degrees C with a pulse frequency of 4 Hz. Thermal damage integral showed that this protocol will thermally damage less than 2% of the molecules around the electrodes. In conclusion, endovascular NTIRE is possible. Our study sets the theoretical basis for further preclinical and clinical trials with endovascular NTIRE.
FINITE ELEMENT METHODS FOR THE NAVIER-STOKES EQUATIONS BY H(div) ELEMENTS
Institute of Scientific and Technical Information of China (English)
Junping Wang; Xiaoshen Wang; Xiu Ye
2008-01-01
We derived and analyzed a new numerical scheme for the Navier-Stokes equations by using H(div) conforming finite elements. A great deal of effort was given to an establishment of some Sobolev-type inequalities for piecewise smooth functions. In particular, the newly derived Sobolev inequalities were employed to provide a mathematical theory for the H(div) finite element scheme. For example, it was proved that the new finite element scheme has solutions which admit a certain boundedness in terms of the input data. A solution uniqueness was also possible when the input data satisfies a certain smallness condition. Optimal-order error estimates for the corresponding finite element solutions were established in various Sobolev norms. The finite element solutions from the new scheme feature a full satisfaction of the continuity equation which is highly demanded in scientific computing.
Variational formulation of high performance finite elements: Parametrized variational principles
Felippa, Carlos A.; Militello, Carmello
1991-01-01
High performance elements are simple finite elements constructed to deliver engineering accuracy with coarse arbitrary grids. This is part of a series on the variational basis of high-performance elements, with emphasis on those constructed with the free formulation (FF) and assumed natural strain (ANS) methods. Parametrized variational principles that provide a foundation for the FF and ANS methods, as well as for a combination of both are presented.
New triangular and quadrilateral plate-bending finite elements
Narayanaswami, R.
1974-01-01
A nonconforming plate-bending finite element of triangular shape and associated quadrilateral elements are developed. The transverse displacement is approximated within the element by a quintic polynomial. The formulation takes into account the effects of transverse shear deformation. Results of the static and dynamic analysis of a square plate, with edges simply supported or clamped, are compared with exact solutions. Good accuracy is obtained in all calculations.
On Using Particle Finite Element for Hydrodynamics Problems Solving
Directory of Open Access Journals (Sweden)
E. V. Davidova
2015-01-01
Full Text Available The aim of the present research is to develop software for the Particle Finite Element Method (PFEM and its verification on the model problem of viscous incompressible flow simulation in a square cavity. The Lagrangian description of the medium motion is used: the nodes of the finite element mesh move together with the fluid that allows to consider them as particles of the medium. Mesh cells deform when in time-stepping procedure, so it is necessary to reconstruct the mesh to provide stability of the finite element numerical procedure.Meshing algorithm allows us to obtain the mesh, which satisfies the Delaunay criteria: it is called \\the possible triangles method". This algorithm is based on the well-known Fortune method of Voronoi diagram constructing for a certain set of points in the plane. The graphical representation of the possible triangles method is shown. It is suitable to use generalization of Delaunay triangulation in order to construct meshes with polygonal cells in case of multiple nodes close to be lying on the same circle.The viscous incompressible fluid flow is described by the Navier | Stokes equations and the mass conservation equation with certain initial and boundary conditions. A fractional steps method, which allows us to avoid non-physical oscillations of the pressure, provides the timestepping procedure. Using the finite element discretization and the Bubnov | Galerkin method allows us to carry out spatial discretization.For form functions calculation of finite element mesh with polygonal cells, \
Finite Element Analysis of Circular Plate using SolidWorks
Energy Technology Data Exchange (ETDEWEB)
Kang, Yeo Jin; Jhung, Myung Jo [Korea Institute of Nuclear Safety, Daejeon (Korea, Republic of)
2011-10-15
Circular plates are used extensively in mechanical engineering for nuclear reactor internal components. The examples in the reactor vessel internals are upper guide structure support plate, fuel alignment plate, lower support plate etc. To verify the structural integrity of these plates, the finite element analyses are performed, which require the development of the finite element model. Sometimes it is very costly and time consuming to make the model especially for the beginners who start their engineering job for the structural analysis, necessitating a simple method to develop the finite element model for the pursuing structural analysis. Therefore in this study, the input decks are generated for the finite element analysis of a circular plate as shown in Fig. 1, which can be used for the structural analysis such as modal analysis, response spectrum analysis, stress analysis, etc using the commercial program Solid Works. The example problems are solved and the results are included for analysts to perform easily the finite element analysis of the mechanical plate components due to various loadings. The various results presented in this study would be helpful not only for the benchmark calculations and results comparisons but also as a part of the knowledge management for the future generation of young designers, scientists and computer analysts
Hamilton, H. B.; Strangas, E.
1980-01-01
The time dependent solution of the magnetic field is introduced as a method for accounting for the variation, in time, of the machine parameters in predicting and analyzing the performance of the electrical machines. The method of time dependent finite element was used in combination with an also time dependent construction of a grid for the air gap region. The Maxwell stress tensor was used to calculate the airgap torque from the magnetic vector potential distribution. Incremental inductances were defined and calculated as functions of time, depending on eddy currents and saturation. The currents in all the machine circuits were calculated in the time domain based on these inductances, which were continuously updated. The method was applied to a chopper controlled DC series motor used for electric vehicle drive, and to a salient pole sychronous motor with damper bars. Simulation results were compared to experimentally obtained ones.
Directory of Open Access Journals (Sweden)
O. González Quintero
2008-09-01
Full Text Available En este estudio es usado el Método de Elementos Finitos (MEF para modelar el contacto bajo carga de los flancos deldiente tratados con un proceso de endurecimiento combinado. Este proceso de endurecimiento permite crear tensiones decompresión en las capas superficiales para favorecer la obtención de una mejor resistencia a la fatiga de los elementos demáquinas. En el trabajo se analiza el tránsito de la deformación de elástica a elastoplástica, el desarrollo y distribución de latensión residual según aumenta la deformación plástica, el complejo campo de tensiones que prevalecen alrededor delcontacto de un par de dientes de engranaje durante su funcionamiento y la valoración del límite de fluencia local.Palabras claves: Engranajes, endurecimiento subestructural, deformación plástica, envejecimiento, Métodode Elementos Finitos.___________________________________________________________________________Abstract:Finite Element Method (FEM is used in this study to model the contact in the gear tooth flanks. In the selection of thecombined hardening described in this report was considerate a procedure of hardening directed to generate compression stressin the surface layers for improve the fatigue resistance of machine elements. In this paper are analyzed the following results: thetransition from the elastic to elastoplastic deformation, the development of the residual stress distribution with increasingplastic deformation, determination of the complex stress field around the contact of a typical gear teeth during his functioningas well as the determination of local yield strength.Key words: Gears, subestructural hardening, plastic deformation, aging, Finite Element Method.6ta Conferencia
Neutrix Calculus and Finite Quantum Field Theory
Ng, Y J
2004-01-01
In general, quantum field theories require regularizations and infinite renormalizations due to ultraviolet divergences in their loop calculations. Furthermore, perturbation series in theories like QED are not convergent series, but are asymptotic series in their interaction couplings. We propose to apply neutrix calculus, developed by van der Corput and Hadamard in connection with asymptotic series, to tackle divergent integrals, yielding finite renormalizations for the parameters in quantum field theories. We observe that quantum gravity theories are rendered more manageable, and that both renormalizable field theories and effective field theories can be accommodated in the framework of neutrix calculus.
The Ginzburg-Landau Equation Solved by the Finite Element Method
DEFF Research Database (Denmark)
Alstrøm, Tommy Sonne; Sørensen, Mads Peter; Pedersen, Niels Falsig
2006-01-01
vortices when the magnetic field exceeds a threshold value. These superconductors are called type II supercon-ductors. In this article we solve numerically the time dependent Ginzburg-Landau equation coupled to a magnetic field for type II superconductors of complex geometry, where the finite element...
Modelling the electromagnetic performance of moving rail gun launchers using finite elements
Rodger, D.; Leonard, P. J.
1993-01-01
A finite element technique for modelling 3D transient eddy currents in 'smooth rotor' conductors moving at constant velocity is described. A method for joining discontinuous A fields at the interface between conductors in sliding electrical contact has been implemented in the MEGA software package for 2 and 3D electromagnetic field analysis.
Finite element analysis of hysteresis effects in piezoelectric transducers
Simkovics, Reinhard; Landes, Hermann; Kaltenbacher, Manfred; Hoffelner, Johann; Lerch, Reinhard
2000-06-01
The design of ultrasonic transducers for high power applications, e.g. in medical therapy or production engineering, asks for effective computer aided design tools to analyze the occurring nonlinear effects. In this paper the finite-element-boundary-element package CAPA is presented that allows to model different types of electromechanical sensors and actuators. These transducers are based on various physical coupling effects, such as piezoelectricity or magneto- mechanical interactions. Their computer modeling requires the numerical solution of a multifield problem, such as coupled electric-mechanical fields or magnetic-mechanical fields as well as coupled mechanical-acoustic fields. With the reported software environment we are able to compute the dynamic behavior of electromechanical sensors and actuators by taking into account geometric nonlinearities, nonlinear wave propagation and ferroelectric as well as magnetic material nonlinearities. After a short introduction to the basic theory of the numerical calculation schemes, two practical examples will demonstrate the applicability of the numerical simulation tool. As a first example an ultrasonic thickness mode transducer consisting of a piezoceramic material used for high power ultrasound production is examined. Due to ferroelectric hysteresis, higher order harmonics can be detected in the actuators input current. Also in case of electrical and mechanical prestressing a resonance frequency shift occurs, caused by ferroelectric hysteresis and nonlinear dependencies of the material coefficients on electric field and mechanical stresses. As a second example, a power ultrasound transducer used in HIFU-therapy (high intensity focused ultrasound) is presented. Due to the compressibility and losses in the propagating fluid a nonlinear shock wave generation can be observed. For both examples a good agreement between numerical simulation and experimental data has been achieved.
Jiang, Lijian
2010-08-01
In this paper, we discuss a numerical multiscale approach for solving wave equations with heterogeneous coefficients. Our interest comes from geophysics applications and we assume that there is no scale separation with respect to spatial variables. To obtain the solution of these multiscale problems on a coarse grid, we compute global fields such that the solution smoothly depends on these fields. We present a Galerkin multiscale finite element method using the global information and provide a convergence analysis when applied to solve the wave equations. We investigate the relation between the smoothness of the global fields and convergence rates of the global Galerkin multiscale finite element method for the wave equations. Numerical examples demonstrate that the use of global information renders better accuracy for wave equations with heterogeneous coefficients than the local multiscale finite element method. © 2010 IMACS.
Institute of Scientific and Technical Information of China (English)
GUZELBEY Ibrahim H.; KANBER Bahattin; AKPOLAT Abdullah
2004-01-01
In this study, the stress based finite element method is coupled with the boundary element method in two different ways. In the first one, the ordinary distribution matrix is used for coupling. In the second one, the stress traction equilibrium is used at the interface line of both regions as a new coupling process. This new coupling procedure is presented without a distribution matrix. Several case studies are solved for the validation of the developed coupling procedure. The results of case studies are compared with the distribution matrix coupling, displacement based finite element method, assumed stress finite element method, boundary element method, ANSYS and analytical results whenever possible. It is shown that the coupling of the stress traction equilibrium with assumed stress finite elements gives as accurate results as those by the distribution matrix coupling.
Finite element model updating of natural fibre reinforced composite structure in structural dynamics
Directory of Open Access Journals (Sweden)
Sani M.S.M.
2016-01-01
Full Text Available Model updating is a process of making adjustment of certain parameters of finite element model in order to reduce discrepancy between analytical predictions of finite element (FE and experimental results. Finite element model updating is considered as an important field of study as practical application of finite element method often shows discrepancy to the test result. The aim of this research is to perform model updating procedure on a composite structure as well as trying improving the presumed geometrical and material properties of tested composite structure in finite element prediction. The composite structure concerned in this study is a plate of reinforced kenaf fiber with epoxy. Modal properties (natural frequency, mode shapes, and damping ratio of the kenaf fiber structure will be determined using both experimental modal analysis (EMA and finite element analysis (FEA. In EMA, modal testing will be carried out using impact hammer test while normal mode analysis using FEA will be carried out using MSC. Nastran/Patran software. Correlation of the data will be carried out before optimizing the data from FEA. Several parameters will be considered and selected for the model updating procedure.
A Finite Element Method for Cracked Components of Structures
Institute of Scientific and Technical Information of China (English)
刘立名; 段梦兰; 秦太验; 刘玉标; 柳春图; 余建星
2003-01-01
In this paper, a method is developed for determining the effective stiffness of the cracked component. The stiffness matrix of the cracked component is integrated into the global stiffness matrix of the finite element model of the global platform for the FE calculation of the structure in any environmental conditions. The stiffness matrix equation of the cracked component is derived by use of the finite variation principle and fracture mechanics. The equivalent parameters defining the element that simulates the cracked component are mathematically presented, and can be easily used for the FE calculation of large scale cracked structures together with any finite element program. The theories developed are validated by both lab tests and numerical calculations, and applied to the evaluation of crack effect on the strength of a fixed platform and a self-elevating drilling rig.
An Object Oriented, Finite Element Framework for Linear Wave Equations
Energy Technology Data Exchange (ETDEWEB)
Koning, J M
2004-08-12
This dissertation documents an object oriented framework which can be used to solve any linear wave equation. The linear wave equations are expressed in the differential forms language. This differential forms expression allows a strict discrete interpretation of the system. The framework is implemented using the Galerkin Finite Element Method to define the discrete differential forms and operators. Finite element basis functions including standard scalar Nodal and vector Nedelec basis functions are used to implement the discrete differential forms resulting in a mixed finite element system. Discretizations of scalar and vector wave equations in the time and frequency domains will be demonstrated in both differential forms and vector calculi. This framework conserves energy, maintains physical continuity, is valid on unstructured grids, conditionally stable and second order accurate. Examples including linear electrodynamics, acoustics, elasticity and magnetohydrodynamics are demonstrated.
Engineering computation of structures the finite element method
Neto, Maria Augusta; Roseiro, Luis; Cirne, José; Leal, Rogério
2015-01-01
This book presents theories and the main useful techniques of the Finite Element Method (FEM), with an introduction to FEM and many case studies of its use in engineering practice. It supports engineers and students to solve primarily linear problems in mechanical engineering, with a main focus on static and dynamic structural problems. Readers of this text are encouraged to discover the proper relationship between theory and practice, within the finite element method: Practice without theory is blind, but theory without practice is sterile. Beginning with elasticity basic concepts and the classical theories of stressed materials, the work goes on to apply the relationship between forces, displacements, stresses and strains on the process of modeling, simulating and designing engineered technical systems. Chapters discuss the finite element equations for static, eigenvalue analysis, as well as transient analyses. Students and practitioners using commercial FEM software will find this book very helpful. It us...
An Object Oriented, Finite Element Framework for Linear Wave Equations
Energy Technology Data Exchange (ETDEWEB)
Koning, Joseph M. [Univ. of California, Berkeley, CA (United States)
2004-03-01
This dissertation documents an object oriented framework which can be used to solve any linear wave equation. The linear wave equations are expressed in the differential forms language. This differential forms expression allows a strict discrete interpretation of the system. The framework is implemented using the Galerkin Finite Element Method to define the discrete differential forms and operators. Finite element basis functions including standard scalar Nodal and vector Nedelec basis functions are used to implement the discrete differential forms resulting in a mixed finite element system. Discretizations of scalar and vector wave equations in the time and frequency domains will be demonstrated in both differential forms and vector calculi. This framework conserves energy, maintains physical continuity, is valid on unstructured grids, conditionally stable and second order accurate. Examples including linear electrodynamics, acoustics, elasticity and magnetohydrodynamics are demonstrated.
Finite element modeling for volume phantom in Electrical Impedance Tomography
Directory of Open Access Journals (Sweden)
I. O. Rybina
2011-10-01
Full Text Available Using surface phantom, "shadows" of currents, which flow below and under surface tomographic lays, include on this lay, that is cause of adding errors in reconstruction image. For processing modeling in studied object volume isotropic finite elements should be used. Cube is chosen for finite element modeling in this work. Cube is modeled as sum of six rectangular (in the base pyramids, each pyramid consists of four triangular pyramids (with rectangular triangle in the base and hypotenuse, which is equal to cube rib to provide its uniformity and electrical definition. In the case of modeling on frequencies higher than 100 kHz biological tissue resistivities are complex. In this case weight coefficient k will be complex in received cube electrical model (inverse conductivity matrix of the cube finite element.
The Finite Element Numerical Modelling of 3D Magnetotelluric
Directory of Open Access Journals (Sweden)
Ligang Cao
2014-01-01
Full Text Available The ideal numerical simulation of 3D magnetotelluric was restricted by the methodology complexity and the time-consuming calculation. Boundary values, the variation of weighted residual equation, and the hexahedral mesh generation method of finite element are three major causes. A finite element method for 3D magnetotelluric numerical modeling is presented in this paper as a solution for the problem mentioned above. In this algorithm, a hexahedral element coefficient matrix for magnetoelluric finite method is developed, which solves large-scale equations using preconditioned conjugate gradient of the first-type boundary conditions. This algorithm is verified using the homogeneous model, and the positive landform model, as well as the low resistance anomaly model.
EXPLICIT ERROR ESTIMATES FOR MIXED AND NONCONFORMING FINITE ELEMENTS
Institute of Scientific and Technical Information of China (English)
Shipeng Mao; Zhong-Ci Shi
2009-01-01
In this paper, we study the explicit expressions of the constants in the error estimates of the lowest order mixed and nonconforming finite element methods. We start with an ex-plicit relation between the error constant of the lowest order Raviart-Thomas interpolation error and the geometric characters of the triangle. This gives an explicit error constant of the lowest order mixed finite element method. Furthermore, similar results can be ex-tended to the nonconforming P1 scheme based on its close connection with the lowest order Raviart-Thomas method. Meanwhile, such explicit a priori error estimates can be used as computable error bounds, which are also consistent with the maximal angle condition for the optimal error estimates of mixed and nonconforming finite element methods.Mathematics subject classification: 65N12, 65N15, 65N30, 65N50.
Finite element simulation of barge impact into a rigid wall
Directory of Open Access Journals (Sweden)
H.W. Leheta
2014-03-01
Many approaches have been developed in order to obtain these impact loads. In general, collision mechanics for floating units is classified into, external mechanics and internal mechanics. In external mechanics, analytical approaches are used to determine the absorbed energy acting on the vessel from the collision, while in internal mechanics analytical approaches are used to determine the ability of the ship’s structure to withstand the absorbed energy. Due to the difficulty and the highly expected cost to perform model testing and impact data for validation, finite element simulation provides an alternative tool for physical validation. In this study, a simulation of barge impact to a rigid wall is presented using the explicit nonlinear finite element code LS-DYNA3D. A conventional fine mesh finite element barge model is created. Impact results are obtained at two different speeds in order to show the consequence of barge and wall damage.
Institute of Scientific and Technical Information of China (English)
孙正华; 方平; 毛东建; 张彪
2012-01-01
Inspection items and method of steel tower were discussed in this paper. Firstly, some items such as degree of gravity vertical, thickness of anti-corrosion coating, dimension of components , connection quality of welding and bolt were inspected and dynamic characteristic of the radar tower was tested in the field through environmental excitation. Secondly, the finite element model of the radar tower was developed and analyzed through the ANSYS software based on the data from field tests and the design documents. It is shown that the results of dynamical characteristic calculated by the finite element model are accordance with those measured from the field test. Therefore, it can be concluded that the finite element model is valid and can be taken as the foundation for the following dynamic response study. Finally, the static and dynamic responses of the radar tower were calculated by the finite element model. It is shown that the ratio of resistance and the action of the radar steel tower components is more than 1.0 and it can be concluded that the bearing capacity of the radar steel tower under the current condition can satisfy with the normal use requirement.%本文探讨了铁塔钢结构工程的检测项目与检测方法,首先,通过对某铁塔工程的倾斜率、尺寸、涂层厚度、连接质量等各项参数的现场检测,并结合环境激励的方法对铁塔工程进行动力特性测试.然后,根据现场实测数据及设计图纸资料,利用ANSYS有限元软件建立铁塔结构的有限元模型并进行分析.分析结果表明:铁塔工程的有限元模型动力特性计算结果和现场实测结果相比较接近,说明所建立的有限元模型可以满足工程需要,并可以为进一步分析提供基础.最后,对该有限元模型在设计荷载作用下进行静动力响应分析,计算结果表明:铁塔结构各构件的抗力和作用效应之比均大于1.0,说明该铁塔工程在目前状况下其承载能力可以满足正常使用要求.
An acoustic finite element including viscothermal effects
Nijhof, M.J.J.; Wijnant, Y.H.; Boer, de A.
2007-01-01
In acoustics it is generally assumed that viscous- en thermal boundary layer effects play a minor role in the propagation of sound waves. Hence, these effects are neglected in the basic set of equations describing the sound field. However, for geometries that include small confinements of air or thi
Finite Elements on Point Based Surfaces
Clarenz, U.; Rumpf, M.; Telea, A.
2004-01-01
We present a framework for processing point-based surfaces via partial differential equations (PDEs). Our framework efficiently and effectively brings well-known PDE-based processing techniques to the field of point-based surfaces. Our method is based on the construction of local tangent planes and
Finite Element Analysis of Magnetoelastic Plate Problems.
1981-08-01
are gradually changing this situation. High energy devices such as fusion reactors, superconductive energy storage devices, MHD generators, and...energy technoloay. Desion of fusion reactors, superconductive enerqy storage devices, MHD generators, etc., all involve considerations of strong magnetic...Sonmnerfeld, A., Electrodynamcs. Lectures on Theoretical Physics, Vol. IIi, Academic Press, 1. 50. Williams, L. P., The Origins of Field Theory, Random
Solomou, Alexandros G.; Machairas, Theodoros T.; Karakalas, Anargyros A.; Saravanos, Dimitris A.
2017-06-01
A thermo-mechanically coupled finite element (FE) for the simulation of multi-layered shape memory alloy (SMA) beams admitting large displacements and rotations (LDRs) is developed to capture the geometrically nonlinear effects which are present in many SMA applications. A generalized multi-field beam theory implementing a SMA constitutive model based on small strain theory, thermo-mechanically coupled governing equations and multi-field kinematic hypotheses combining first order shear deformation assumptions with a sixth order polynomial temperature field through the thickness of the beam section are extended to admit LDRs. The co-rotational formulation is adopted, where the motion of the beam is decomposed to rigid body motion and relative small deformation in the local frame. A new generalized multi-layered SMA FE is formulated. The nonlinear transient spatial discretized equations of motion of the SMA structure are synthesized and solved using the Newton-Raphson method combined with an implicit time integration scheme. Correlations of models incorporating the present beam FE with respective results of models incorporating plane stress SMA FEs, demonstrate excellent agreement of the predicted LDRs response, temperature and phase transformation fields, as well as, significant gains in computational time.
FINITE ELEMENT ANALYSIS OF AXIAL FEED BAR ROLLING
Institute of Scientific and Technical Information of China (English)
C.G. Xu; G.H. Liu; G.S. Ren; Z. Shen; C.P. Ma; W. W. Ren
2007-01-01
A flexible technique of hot working of bars by axial feed rolling was introduced. The processdeformation, strain field, stress field, and temperature field of the parts are analyzed by finite elementmethod (FEM)-simulation software DEFORM-3D. The material flow rule and tool load have beeninvestigated.
Fast Stiffness Matrix Calculation for Nonlinear Finite Element Method
Directory of Open Access Journals (Sweden)
Emir Gülümser
2014-01-01
Full Text Available We propose a fast stiffness matrix calculation technique for nonlinear finite element method (FEM. Nonlinear stiffness matrices are constructed using Green-Lagrange strains, which are derived from infinitesimal strains by adding the nonlinear terms discarded from small deformations. We implemented a linear and a nonlinear finite element method with the same material properties to examine the differences between them. We verified our nonlinear formulation with different applications and achieved considerable speedups in solving the system of equations using our nonlinear FEM compared to a state-of-the-art nonlinear FEM.
Splitting extrapolation based on domain decomposition for finite element approximations
Institute of Scientific and Technical Information of China (English)
吕涛; 冯勇
1997-01-01
Splitting extrapolation based on domain decomposition for finite element approximations is a new technique for solving large scale scientific and engineering problems in parallel. By means of domain decomposition, a large scale multidimensional problem is turned to many discrete problems involving several grid parameters The multi-variate asymptotic expansions of finite element errors on independent grid parameters are proved for linear and nonlin ear second order elliptic equations as well as eigenvalue problems. Therefore after solving smaller problems with similar sizes in parallel, a global fine grid approximation with higher accuracy is computed by the splitting extrapolation method.
Compatible finite element spaces for geophysical fluid dynamics
Natale, Andrea
2016-01-01
Compatible finite elements provide a framework for preserving important structures in equations of geophysical fluid dynamics, and are becoming important in their use for building atmosphere and ocean models. We survey the application of compatible finite element spaces to geophysical fluid dynamics, including the application to the nonlinear rotating shallow water equations, and the three-dimensional compressible Euler equations. We summarise analytic results about dispersion relations and conservation properties, and present new results on approximation properties in three dimensions on the sphere, and on hydrostatic balance properties.
Least-squares finite-element lattice Boltzmann method.
Li, Yusong; LeBoeuf, Eugene J; Basu, P K
2004-06-01
A new numerical model of the lattice Boltzmann method utilizing least-squares finite element in space and Crank-Nicolson method in time is presented. The new method is able to solve problem domains that contain complex or irregular geometric boundaries by using finite-element method's geometric flexibility and numerical stability, while employing efficient and accurate least-squares optimization. For the pure advection equation on a uniform mesh, the proposed method provides for fourth-order accuracy in space and second-order accuracy in time, with unconditional stability in the time domain. Accurate numerical results are presented through two-dimensional incompressible Poiseuille flow and Couette flow.
NURBS-enhanced finite element method for Euler equations
Sevilla Cárdenas, Rubén; Fernandez Mendez, Sonia; Huerta, Antonio , coaut.
2008-01-01
This is the pre-peer reviewed version of the following article: Sevilla, R.; Fernandez, S.; Huerta, A. NURBS-enhanced finite element method for Euler equations. "International journal for numerical methods in fluids", Juliol 2008, vol. 57, núm. 9, p. 1051-1069., which has been published in final form at http://www3.interscience.wiley.com/journal/117905455/abstract In this work, the NURBS-enhanced finite element method (NEFEM) is combined with a discontinuous Galerkin (DG) formulation for t...
Substructure System Identification for Finite Element Model Updating
Craig, Roy R., Jr.; Blades, Eric L.
1997-01-01
This report summarizes research conducted under a NASA grant on the topic 'Substructure System Identification for Finite Element Model Updating.' The research concerns ongoing development of the Substructure System Identification Algorithm (SSID Algorithm), a system identification algorithm that can be used to obtain mathematical models of substructures, like Space Shuttle payloads. In the present study, particular attention was given to the following topics: making the algorithm robust to noisy test data, extending the algorithm to accept experimental FRF data that covers a broad frequency bandwidth, and developing a test analytical model (TAM) for use in relating test data to reduced-order finite element models.
FINITE ELEMENT IMPLEMENTATION OF DELAMINATION IN COMPOSITE PLATES
Directory of Open Access Journals (Sweden)
Milan Žmindák
2012-12-01
Full Text Available Modelling of composite structures by finite element (FE codes to effectively model certain critical failure modes such as delamination is limited. Previous efforts to model delamination and debonding failure modes using FE codes have typically relied on ad hoc failure criteria and quasi-static fracture data. Improvements to these modelling procedures can be made by using an approach based on fracture mechanics. A study of modelling delamination using the finite element code ANSYS was conducted. This investigation demonstrates the modelling of composites through improved delamination modelling. Further developments to this approach may be improved.
Matlab and C programming for Trefftz finite element methods
Qin, Qing-Hua
2008-01-01
Although the Trefftz finite element method (FEM) has become a powerful computational tool in the analysis of plane elasticity, thin and thick plate bending, Poisson's equation, heat conduction, and piezoelectric materials, there are few books that offer a comprehensive computer programming treatment of the subject. Collecting results scattered in the literature, MATLAB® and C Programming for Trefftz Finite Element Methods provides the detailed MATLAB® and C programming processes in applications of the Trefftz FEM to potential and elastic problems. The book begins with an introduction to th
SPLITTING MODULUS FINITE ELEMENT METHOD FOR ORTHOGONAL ANISOTROPIC PLATE BENGING
Institute of Scientific and Technical Information of China (English)
党发宁; 荣廷玉; 孙训方
2001-01-01
Splitting modulus variational principle in linear theory of solid mechanics was introduced, the principle for thin plate was derived, and splitting modulus finite element method of thin plate was established too. The distinctive feature of the splitting model is that its functional contains one or more arbitrary additional parameters, called splitting factors,so stiffness of the model can be adjusted by properly selecting the splitting factors. Examples show that splitting modulus method has high precision and the ability to conquer some illconditioned problems in usual finite elements. The cause why the new method could transform the ill-conditioned problems into well-conditioned problem, is analyzed finally.
Preconditioning for Mixed Finite Element Formulations of Elliptic Problems
Wildey, Tim
2013-01-01
In this paper, we discuss a preconditioning technique for mixed finite element discretizations of elliptic equations. The technique is based on a block-diagonal approximation of the mass matrix which maintains the sparsity and positive definiteness of the corresponding Schur complement. This preconditioner arises from the multipoint flux mixed finite element method and is robust with respect to mesh size and is better conditioned for full permeability tensors than a preconditioner based on a diagonal approximation of the mass matrix. © Springer-Verlag Berlin Heidelberg 2013.
Robust Hybrid Finite Element Methods for Antennas and Microwave Circuits
Gong, J.; Volakis, John L.
1996-01-01
One of the primary goals in this dissertation is concerned with the development of robust hybrid finite element-boundary integral (FE-BI) techniques for modeling and design of conformal antennas of arbitrary shape. Both the finite element and integral equation methods will be first overviewed in this chapter with an emphasis on recently developed hybrid FE-BI methodologies for antennas, microwave and millimeter wave applications. The structure of the dissertation is then outlined. We conclude the chapter with discussions of certain fundamental concepts and methods in electromagnetics, which are important to this study.
FINITE ELEMENT MODELING OF THIN CIRCULAR SANDWICH PLATES DEFLECTION
Directory of Open Access Journals (Sweden)
K. S. Kurachka
2014-01-01
Full Text Available A mathematical model of a thin circular sandwich plate being under the vertical load is proposed. The model employs the finite element method and takes advantage of an axisymmetric finite element that leads to the small dimension of the resulting stiffness matrix and sufficient accuracy for practical calculations. The analytical expressions for computing local stiffness matrices are found, which can significantly speed up the process of forming the global stiffness matrix and increase the accuracy of calculations. A software is under development and verification. The discrepancy between the results of the mathematical model and those of analytical formulas for homogeneous thin circularsandwich plates does not exceed 7%.
The Finite Element Method An Introduction with Partial Differential Equations
Davies, A J
2011-01-01
The finite element method is a technique for solving problems in applied science and engineering. The essence of this book is the application of the finite element method to the solution of boundary and initial-value problems posed in terms of partial differential equations. The method is developed for the solution of Poisson's equation, in a weighted-residual context, and then proceeds to time-dependent and nonlinear problems. The relationship with the variational approach is alsoexplained. This book is written at an introductory level, developing all the necessary concepts where required. Co
Local and Parallel Finite Element Algorithms for Eigenvalue Problems
Institute of Scientific and Technical Information of China (English)
Jinchao Xu; Aihui Zhou
2002-01-01
Some new local and parallel finite element algorithms are proposed and analyzed in this paper for eigenvalue problems. With these algorithms, the solution of an eigenvalue problem on a fine grid is reduced to the solution of an eigenvalue problem on a relatively coarse grid together with solutions of some linear algebraic systems on fine grid by using some local and parallel procedure. A theoretical tool for analyzing these algorithms is some local error estimate that is also obtained in this paper for finite element approximations of eigenvectors on general shape-regular grids.
Diffusive mesh relaxation in ALE finite element numerical simulations
Energy Technology Data Exchange (ETDEWEB)
Dube, E.I.
1996-06-01
The theory for a diffusive mesh relaxation algorithm is developed for use in three-dimensional Arbitary Lagrange/Eulerian (ALE) finite element simulation techniques. This mesh relaxer is derived by a variational principle for an unstructured 3D grid using finite elements, and incorporates hourglass controls in the numerical implementation. The diffusive coefficients are based on the geometric properties of the existing mesh, and are chosen so as to allow for a smooth grid that retains the general shape of the original mesh. The diffusive mesh relaxation algorithm is then applied to an ALE code system, and results from several test cases are discussed.
Discontinuous Galerkin finite element methods for gradient plasticity.
Energy Technology Data Exchange (ETDEWEB)
Garikipati, Krishna. (University of Michigan, Ann Arbor, MI); Ostien, Jakob T.
2010-10-01
In this report we apply discontinuous Galerkin finite element methods to the equations of an incompatibility based formulation of gradient plasticity. The presentation is motivated with a brief overview of the description of dislocations within a crystal lattice. A tensor representing a measure of the incompatibility with the lattice is used in the formulation of a gradient plasticity model. This model is cast in a variational formulation, and discontinuous Galerkin machinery is employed to implement the formulation into a finite element code. Finally numerical examples of the model are shown.
ADAPTIVE FINITE ELEMENT METHOD FOR ANALYSIS OF POLLUTANT DISPERSION IN SHALLOW WATER
Institute of Scientific and Technical Information of China (English)
Somboon Otarawanna; Pramote Dechaumphai
2005-01-01
A finite element method for analysis of pollutant dispersion in shallow water is presented. The analysis is divided into two parts: ( 1 ) computation of the velocity flow field and water surface elevation, and (2) computation of the pollutant concentration field from the dispersion model. The method was combined with an adaptive meshing technique to increase the solution accuracy ,as well as to reduce the computational time and computer memory. The finite element formulation and the computer programs were validated by several examples that have known solutions. In addition, the capability of the combined method was demonstrated by analyzing pollutant dispersion in Chao Phraya River near the gulf of Thailand.
A variational method for finite element stress recovery: Applications in one-dimension
Riggs, H. Ronald
1992-09-01
It is well-known that stresses (and strains) calculated by a displacement-based finite element analysis are generally not as accurate as the displacements. In addition, the calculated stress field is typically discontinuous at element interfaces. Because the stresses are typically of more interest than the displacements, several procedures have been proposed to obtain a smooth stress field, given the finite element stresses, and to improve the accuracy. Hinton and Irons introduced global least squares smoothing of discrete data defined on a plane using a finite element formulation. Tessler and co-workers recently developed a conceptually similar formulation for smoothing of two-dimensional data based on a discrete least square approximation with a penalty constraint. The penalty constraint results in a stress field which is C(exp 1)-continuous, a result not previously obtained. The approach requires additional, 'smoothing' finite element analysis and for their two-dimensional application, they used a conforming C(exp 0)-continuous triangular finite element based on a conforming plate element. This paper presents the results of a detailed investigation into the application of Tessler's smoothing procedure to the smoothing of finite element stresses from one-dimensional problems. Although the one-dimensional formulation has some practical applicability, such as in truss, beam, axisymmetric mechanics, and one-dimensional heat conduction, the primary motivation for developing the one-dimensional smoothing case is to explore the characteristics of the general smoothing strategy. In particular, it is used to describe the behavior of the method and to explore the suitability of criteria proposed for the smoothing analysis. Prior to presenting numerical results, the variational formulation of the smoothing strategy is presented and a criterion for the smoothing analysis is described.
SUPERCONVERGENCE ANALYSIS FOR CUBIC TRIANGULAR ELEMENT OF THE FINITE ELEMENT
Institute of Scientific and Technical Information of China (English)
Qi-ding Zhu
2000-01-01
In this paper, we construct a projection interpolation for cubic triangular ele- ment by using othogonal expansion triangular method. We show two fundamental formulas of estimation on a special partion and obtain a superconvergence result of 1 -e order higher for the placement function and its tangential derivative on the third order Lobatto points and Gauss points on each edge of triangular element.
Behaviour of Lagrangian triangular mixed fluid finite elements
Indian Academy of Sciences (India)
S Gopalakrishnan; G Devi
2000-02-01
The behaviour of mixed fluid finite elements, formulated based on the Lagrangian frame of reference, is investigated to understand the effects of locking due to incompressibility and irrotational constraints. For this purpose, both linear and quadratic mixed triangular fluid elements are formulated. It is found that there exists a close relationship between the penalty finite element approach that uses reduced/selective numerical integration to alleviate locking, and the mixed finite element approach. That is, performing reduced/selective integration in the penalty approach amounts to reducing the order of pressure interpolation in the mixed finite element approach for obtaining similar results. A number of numerical experiments are performed to determine the optimum degree of interpolation of both the mean pressure and the rotational pressure in order that the twin constraints are satisfied exactly. For this purpose, the benchmark solution of the rigid rectangular tank is used. It is found that, irrespective of the degree of mean and the rotational pressure interpolation, the linear triangle mesh, with or without central bubble function (incompatible mode), locks when both the constraints are enforced simultaneously. However, for quadratic triangle, linear interpolation of the mean pressure and constant rotational pressure ensures exact satisfaction of the constraints and the mesh does not lock. Based on the results obtained from the numerical experiments, a number of important conclusions are arrived at.
Parallel finite element modeling of earthquake ground response and liquefaction
Institute of Scientific and Technical Information of China (English)
Jinchi Lu(陆金池); Jun Peng(彭军); Ahmed Elgamal; Zhaohui Yang(杨朝晖); Kincho H. Law
2004-01-01
Parallel computing is a promising approach to alleviate the computational demand in conducting large-scale finite element analyses. This paper presents a numerical modeling approach for earthquake ground response and liquefaction using the parallel nonlinear finite element program, ParCYCLIC, designed for distributed-memory message-passing parallel computer systems. In ParCYCLIC, finite elements are employed within an incremental plasticity, coupled solid-fluid formulation. A constitutive model calibrated by physical tests represents the salient characteristics of sand liquefaction and associated accumulation of shear deformations. Key elements of the computational strategy employed in ParCYCLIC include the development of a parallel sparse direct solver, the deployment of an automatic domain decomposer, and the use of the Multilevel Nested Dissection algorithm for ordering of the finite element nodes. Simulation results of centrifuge test models using ParCYCLIC are presented. Performance results from grid models and geotechnical simulations show that ParCYCLIC is efficiently scalable to a large number of processors.
A multiscale mortar multipoint flux mixed finite element method
Wheeler, Mary Fanett
2012-02-03
In this paper, we develop a multiscale mortar multipoint flux mixed finite element method for second order elliptic problems. The equations in the coarse elements (or subdomains) are discretized on a fine grid scale by a multipoint flux mixed finite element method that reduces to cell-centered finite differences on irregular grids. The subdomain grids do not have to match across the interfaces. Continuity of flux between coarse elements is imposed via a mortar finite element space on a coarse grid scale. With an appropriate choice of polynomial degree of the mortar space, we derive optimal order convergence on the fine scale for both the multiscale pressure and velocity, as well as the coarse scale mortar pressure. Some superconvergence results are also derived. The algebraic system is reduced via a non-overlapping domain decomposition to a coarse scale mortar interface problem that is solved using a multiscale flux basis. Numerical experiments are presented to confirm the theory and illustrate the efficiency and flexibility of the method. © EDP Sciences, SMAI, 2012.
Finite element approach for transient analysis of multibody systems
Wu, Shih-Chin; Chang, Che-Wei; Housner, Jerrold M.
1992-01-01
A three-dimensional, finite element based formulation for the transient dynamics of constrained multibody systems with trusslike configurations is presented. A convected coordinate system is used to define the rigid-body motion of individual elements in the system. Deformation of each element is defined relative to its convected coordinate system. The formulation is oriented toward joint-dominated structures. Through a series of sequential transformations, the joint degree of freedom is built into the equations of motion of the element to reduce geometric constraints. Based on the derivation, a general-purpose code has been developed. Two examples are presented to illustrate the application of the code.
A new formulation of hybrid/mixed finite element
Pian, T. H. H.; Kang, D.; Chen, D.-P.
1983-01-01
A new formulation of finite element method is accomplished by the Hellinger-Reissner principle for which the stress equilibrium conditions are not introduced initially but are brought-in through the use of additional internal displacement parameters. The method can lead to the same result as the assumed stress hybrid model. However, it is more general and more flexible. The use of natural coordinates for stress assumptions leads to elements which are less sensitive to the choice of reference coordinates. Numerical solutions by 3-D solid element indicate that more efficient elements can be constructed by assumed stresses which only partially satisfy the equilibrium conditions.
Towers of Function Fields over Non-prime Finite Fields
DEFF Research Database (Denmark)
Bassa, Alp; Beelen, Peter; Garcia, Arnaldo
2015-01-01
Over all non-prime finite fields, we construct some recursive towers of function fields with many rational places. Thus we obtain a substantial improvement on all known lower bounds for Ihara’s quantity A(ℓ), for ℓ = pn with p prime and n > 3 odd. We relate the explicit equations to Drinfeld modu...
Towers of Function Fields over Non-prime Finite Fields
DEFF Research Database (Denmark)
Bassa, Alp; Beelen, Peter; Garcia, Arnaldo;
2015-01-01
Over all non-prime finite fields, we construct some recursive towers of function fields with many rational places. Thus we obtain a substantial improvement on all known lower bounds for Ihara’s quantity A(ℓ), for ℓ = pn with p prime and n > 3 odd. We relate the explicit equations to Drinfeld...
On Linear Operator Channels over Finite Fields
Yang, Shenghao; Ho, Siu-Wai; Meng, Jin; Yang, En-Hui; Yeung, Raymond W.
2010-01-01
Motivated by linear network coding, communication channels perform linear operation over finite fields, namely linear operator channels (LOCs), are studied in this paper. For such a channel, its output vector is a linear transform of its input vector, and the transformation matrix is randomly and independently generated. The transformation matrix is assumed to remain constant for every T input vectors and to be unknown to both the transmitter and the receiver. There are NO constraints on the ...
Deng, Yongbo; Korvink, Jan G.
2016-05-01
This paper develops a topology optimization procedure for three-dimensional electromagnetic waves with an edge element-based finite-element method. In contrast to the two-dimensional case, three-dimensional electromagnetic waves must include an additional divergence-free condition for the field variables. The edge element-based finite-element method is used to both discretize the wave equations and enforce the divergence-free condition. For wave propagation described in terms of the magnetic field in the widely used class of non-magnetic materials, the divergence-free condition is imposed on the magnetic field. This naturally leads to a nodal topology optimization method. When wave propagation is described using the electric field, the divergence-free condition must be imposed on the electric displacement. In this case, the material in the design domain is assumed to be piecewise homogeneous to impose the divergence-free condition on the electric field. This results in an element-wise topology optimization algorithm. The topology optimization problems are regularized using a Helmholtz filter and a threshold projection method and are analysed using a continuous adjoint method. In order to ensure the applicability of the filter in the element-wise topology optimization version, a regularization method is presented to project the nodal into an element-wise physical density variable.
Deng, Yongbo; Korvink, Jan G
2016-05-01
This paper develops a topology optimization procedure for three-dimensional electromagnetic waves with an edge element-based finite-element method. In contrast to the two-dimensional case, three-dimensional electromagnetic waves must include an additional divergence-free condition for the field variables. The edge element-based finite-element method is used to both discretize the wave equations and enforce the divergence-free condition. For wave propagation described in terms of the magnetic field in the widely used class of non-magnetic materials, the divergence-free condition is imposed on the magnetic field. This naturally leads to a nodal topology optimization method. When wave propagation is described using the electric field, the divergence-free condition must be imposed on the electric displacement. In this case, the material in the design domain is assumed to be piecewise homogeneous to impose the divergence-free condition on the electric field. This results in an element-wise topology optimization algorithm. The topology optimization problems are regularized using a Helmholtz filter and a threshold projection method and are analysed using a continuous adjoint method. In order to ensure the applicability of the filter in the element-wise topology optimization version, a regularization method is presented to project the nodal into an element-wise physical density variable.
Korvink, Jan G.
2016-01-01
This paper develops a topology optimization procedure for three-dimensional electromagnetic waves with an edge element-based finite-element method. In contrast to the two-dimensional case, three-dimensional electromagnetic waves must include an additional divergence-free condition for the field variables. The edge element-based finite-element method is used to both discretize the wave equations and enforce the divergence-free condition. For wave propagation described in terms of the magnetic field in the widely used class of non-magnetic materials, the divergence-free condition is imposed on the magnetic field. This naturally leads to a nodal topology optimization method. When wave propagation is described using the electric field, the divergence-free condition must be imposed on the electric displacement. In this case, the material in the design domain is assumed to be piecewise homogeneous to impose the divergence-free condition on the electric field. This results in an element-wise topology optimization algorithm. The topology optimization problems are regularized using a Helmholtz filter and a threshold projection method and are analysed using a continuous adjoint method. In order to ensure the applicability of the filter in the element-wise topology optimization version, a regularization method is presented to project the nodal into an element-wise physical density variable. PMID:27279766
Finite Element Modeling of scattered electromagnetic waves for stroke analysis.
Priyadarshini, N; Rajkumar, E R
2013-01-01
Stroke has become one of the leading causes of mortality worldwide and about 800 in every 100,000 people suffer from stroke each year. The occurrence of stroke is ranked third among the causes of acute death and first among the causes for neurological dysfunction. Currently, Neurological examinations followed by medical imaging with CT, MRI or Angiography are used to provide better identification of the location and the type of the stroke, however they are neither fast, cost-effective nor portable. Microwave technology has emerged to complement these modalities to diagnose stroke as it is sensitive to the differences between the distinct dielectric properties of the brain tissues and blood. This paper investigates the possibility of diagnosing the type of stroke using Finite Element Analysis (FEA). The object of interest is a simulated head phantom with stroke, created with its specifying material characteristics like electrical conductivity and relative permittivity. The phantom is then placed in an electromagnetic field generated by a dipole antenna radiating at 1 GHz. The FEM forward model solver computes the scattered electromagnetic field by finding the solution for the Maxwell's wave equation in the head volume. Subsequently the inverse scattering problem is solved using the Contrast Source Inversion (CSI) method to reconstruct the dielectric profile of the head phantom.
Multiphase control volume finite element simulations of fractured reservoirs
Fu, Yao
With rapid evolution of hardware and software techniques in energy sector, reservoir simulation has become a powerful tool for field development planning and reservoir management. Many of the widely used commercial simulators were originally designed for structured grids and implemented with finite difference method (FDM). In recent years, technical advances in griding, fluid modeling, linear solver, reservoir and geological modeling, etc. have created new opportunities. At the same time, new reservoir simulation technology is required for solving large-scale heterogeneous problems. A three-dimensional, three-phase black-oil reservoir simulator has been developed using the control volume finite element (CVFE) formulation. Flux-based upstream weighting is employed to ensure flux continuity. The CVFE method is embedded in a fully-implicit formulation. State-of-the-art parallel, linear solvers are used. The implementation takes the advantages of object-oriented programming capabilities of C++ to provide maximum reuse and extensibility for future students. The results from the simulator have excellent agreement with those from commercial simulators. The convergence properties of the new simulator are verified using the method of manufactured solutions. The pressure and saturation solutions are verified to be first-order convergent as expected. The efficiency of the simulators and their capability to handle real large-scale field models are improved by implementing the models in parallel. Another aspect of the work dealt with multiphase flow of fractured reservoirs was performed. The discrete-fracture model is implemented in the simulator. Fractures and faults are represented by lines and planes in two- and three-dimensional spaces, respectively. The difficult task of generating an unstructured mesh for complex domains with fractures and faults is accomplished in this study. Applications of this model for two-phase and three-phase simulations in a variety of fractured
Finite Element Analysis of the Crack Propagation for Solid Materials
Directory of Open Access Journals (Sweden)
Miloud Souiyah
2009-01-01
Full Text Available Problem statement: The use of fracture mechanics techniques in the assessment of performance and reliability of structure is on increase and the prediction of crack propagation in structure play important part. The finite element method is widely used for the evaluation of SIF for various types of crack configurations. Source code program of two-dimensional finite element model had been developed, to demonstrate the capability and its limitations, in predicting the crack propagation trajectory and the SIF values under linear elastic fracture analysis. Approach: Two different geometries were used on this finite element model in order, to analyze the reliability of this program on the crack propagation in linear and nonlinear elastic fracture mechanics. These geometries were namely; a rectangular plate with crack emanating from square-hole and Double Edge Notched Plate (DENT. Where, both geometries are in tensile loading and under mode I conditions. In addition, the source code program of this model was written by FORTRAN language. Therefore, a Displacement Extrapolation Technique (DET was employed particularly, to predict the crack propagations directions and to, calculate the Stress Intensity Factors (SIFs. Furthermore, the mesh for the finite elements was the unstructured type; generated using the advancing front method. And, the global h-type adaptive mesh was adopted based on the norm stress error estimator. While, the quarter-point singular elements were uniformly generated around the crack tip in the form of a rosette. Moreover, make a comparison between this current study with other relevant and published research study. Results: The application of the source code program of 2-D finite element model showed a significant result on linear elastic fracture mechanics. Based on the findings of the two different geometries from the current study, the result showed a good agreement. And, it seems like very close compare to the other published
A Stochastic Wavelet Finite Element Method for 1D and 2D Structures Analysis
Directory of Open Access Journals (Sweden)
Xingwu Zhang
2014-01-01
Full Text Available A stochastic finite element method based on B-spline wavelet on the interval (BSWI-SFEM is presented for static analysis of 1D and 2D structures in this paper. Instead of conventional polynomial interpolation, the scaling functions of BSWI are employed to construct the displacement field. By means of virtual work principle and BSWI, the wavelet finite elements of beam, plate, and plane rigid frame are obtained. Combining the Monte Carlo method and the constructed BSWI elements together, the BSWI-SFEM is formulated. The constructed BSWI-SFEM can deal with the problems of structural response uncertainty caused by the variability of the material properties, static load amplitudes, and so on. Taking the widely used Timoshenko beam, the Mindlin plate, and the plane rigid frame as examples, numerical results have demonstrated that the proposed method can give a higher accuracy and a better constringency than the conventional stochastic finite element methods.
A two-scale finite element formulation for the dynamic analysis of heterogeneous materials
Energy Technology Data Exchange (ETDEWEB)
Ionita, Axinte [Los Alamos National Laboratory
2008-01-01
In the analysis of heterogeneous materials using a two-scale Finite Element Method (FEM) the usual assumption is that the Representative Volume Element (RVE) of the micro-scale is much smaller than the finite element discretization of the macro-scale. However there are situations in which the RVE becomes comparable with, or even bigger than the finite element. These situations are considered in this article from the perspective of a two-scale FEM dynamic analysis. Using the principle of virtual power, new equations for the fluctuating fields are developed in terms of velocities rather than displacements. To allow more flexibility in the analysis, a scaling deformation tensor is introduced together with a procedure for its determination. Numerical examples using the new approach are presented.
Karlovitz, L. A.; Atluri, S. N.; Xue, W.-M.
1985-01-01
The extensions of Reissner's two-field (stress and displacement) principle to the cases wherein the displacement field is discontinuous and/or the stress field results in unreciprocated tractions, at a finite number of surfaces ('interelement boundaries') in a domain (as, for instance, when the domain is discretized into finite elements), is considered. The conditions for the existence, uniqueness, and stability of mixed-hybrid finite element solutions based on such discontinuous fields, are summarized. The reduction of these global conditions to local ('element') level, and the attendant conditions on the ranks of element matrices, are discussed. Two examples of stable, invariant, least-order elements - a four-node square planar element and an eight-node cubic element - are discussed in detail.
Calibration of a finite element composite delamination model by experiments
DEFF Research Database (Denmark)
Gaiotti, M.; Rizzo, C.M.; Branner, Kim;
2013-01-01
distinct sub-laminates. The work focuses on experimental validation of a finite element model built using the 9-noded MITC9 shell elements, which prevent locking effects and aiming to capture the highly non linear buckling features involved in the problem. The geometry has been numerically defined...... modes related to the production methods is presented in this paper. A microscopic analysis of the fracture surfaces was carried out in order to better understand the failure mechanisms. © 2013 Taylor & Francis Group....
Finite Element Modeling of the Buckling Response of Sandwich Panels
Rose, Cheryl A.; Moore, David F.; Knight, Norman F., Jr.; Rankin, Charles C.
2002-01-01
A comparative study of different modeling approaches for predicting sandwich panel buckling response is described. The study considers sandwich panels with anisotropic face sheets and a very thick core. Results from conventional analytical solutions for sandwich panel overall buckling and face-sheet-wrinkling type modes are compared with solutions obtained using different finite element modeling approaches. Finite element solutions are obtained using layered shell element models, with and without transverse shear flexibility, layered shell/solid element models, with shell elements for the face sheets and solid elements for the core, and sandwich models using a recently developed specialty sandwich element. Convergence characteristics of the shell/solid and sandwich element modeling approaches with respect to in-plane and through-the-thickness discretization, are demonstrated. Results of the study indicate that the specialty sandwich element provides an accurate and effective modeling approach for predicting both overall and localized sandwich panel buckling response. Furthermore, results indicate that anisotropy of the face sheets, along with the ratio of principle elastic moduli, affect the buckling response and these effects may not be represented accurately by analytical solutions. Modeling recommendations are also provided.
FEWA: a Finite Element model of Water flow through Aquifers
Energy Technology Data Exchange (ETDEWEB)
Yeh, G.T.; Huff, D.D.
1983-11-01
This report documents the implementation and demonstration of a Finite Element model of Water flow through Aquifers (FEWA). The particular features of FEWA are its versatility and flexibility to deal with as many real-world problems as possible. Point as well as distributed sources/sinks are included to represent recharges/pumpings and rainfall infiltrations. All sources/sinks can be transient or steady state. Prescribed hydraulic head on the Dirichlet boundaries and fluxes on Neumann or Cauchy boundaries can be time-dependent or constant. Source/sink strength over each element and node, hydraulic head at each Dirichlet boundary node, and flux at each boundary segment can vary independently of each other. Either completely confined or completely unconfined aquifers, or partially confined and partially unconfined aquifers can be dealt with effectively. Discretization of a compound region with very irregular curved boundaries is made easy by including both quadrilateral and triangular elements in the formulation. Large-field problems can be solved efficiently by including a pointwise iterative solution strategy as an optional alternative to the direct elimination solution method for the matrix equation approximating the partial differential equation of groundwater flow. FEWA also includes transient flow through confining leaky aquifers lying above and/or below the aquifer of interest. The model is verified against three simple cases to which analytical solutions are available. It is then demonstrated by two examples of how the model can be applied to heterogeneous and anisotropic aquifers with transient boundary conditions, time-dependent sources/sinks, and confining aquitards for a confined aquifer of variable thickness and for a free surface problem in an unconfined aquifer, respectively. 20 references, 25 figures, 8 tables.
ON FINITE ELEMENT METHODS FOR INHOMOGENEOUS DIELECTRIC WAVEGUIDES
Institute of Scientific and Technical Information of China (English)
Zhiming Chen; Jian-hua Yuan
2004-01-01
We investigate the problem of computing electromagnetic guided waves in a closed,inhomogeneous, pillared three-dimensional waveguide at a given frequency. The problem is formulated as a generalized eigenvalue problem. By modifying the sesquilinear form associated with the eigenvalue problem, we provide a new convergence analysis for the finite element approximations. Numerical results are reported to illustrate the performance of the method.
A Finite Element Solution for Barrel Dynamic Stress
Institute of Scientific and Technical Information of China (English)
ZENG Zhi-yin; NING Bian-fang; WANG Zai-sen
2007-01-01
With the APDL language of ANSYS finite element analysis software, the solution program for barrel dynamic stress is developed. The paper describes the pivotal problems of dynamic strength design and provides a foundation for realizing the engineering and programming of barrel dynamic strength design.
Finite Element Vibration and Dynamic Response Analysis of Engineering Structures
Directory of Open Access Journals (Sweden)
Jaroslav Mackerle
2000-01-01
Full Text Available This bibliography lists references to papers, conference proceedings, and theses/dissertations dealing with finite element vibration and dynamic response analysis of engineering structures that were published from 1994 to 1998. It contains 539 citations. The following types of structures are included: basic structural systems; ground structures; ocean and coastal structures; mobile structures; and containment structures.
Hyperelastic Modelling and Finite Element Analysing of Rubber Bushing
Directory of Open Access Journals (Sweden)
Merve Yavuz ERKEK
2015-03-01
Full Text Available The objective of this paper is to obtain stiffness curves of rubber bushings which are used in automotive industry with hyperelastic finite element model. Hyperelastic material models were obtained with different material tests. Stress and strain values and static stiffness curves were determined. It is shown that, static stiffness curves are nonlinear. The level of stiffness affects the vehicle dynamics behaviour.
Piezoelectric Accelerometers Modification Based on the Finite Element Method
DEFF Research Database (Denmark)
Liu, Bin; Kriegbaum, B.
2000-01-01
The paper describes the modification of piezoelectric accelerometers using a Finite Element (FE) method. Brüel & Kjær Accelerometer Type 8325 is chosen as an example to illustrate the advanced accelerometer development procedure. The deviation between the measurement and FE simulation results...
Finite-Element Analysis of Forced Convection and Conduction
Wieting, A. R.
1982-01-01
TAP2 thermal-analysis program was developed as part of research on finite element methodology for thermal analysis of convectively cooled structures, such as scramjet engines and hypersonic aircraft. Program simplifies computations when both structural and thermal analyses are required and is suited for thermal analysis of nuclear reactors and solar-panel heating systems.
A FINITE VOLUME ELEMENT METHOD FOR THERMAL CONVECTION PROBLEMS
Institute of Scientific and Technical Information of China (English)
芮洪兴
2004-01-01
Consider the finite volume element method for the thermal convection problem with the infinite Prandtl number. The author uses a conforming piecewise linear function on a fine triangulation for velocity and temperature, and a piecewise constant function on a coarse triangulation for pressure. For general triangulation the optimal order H1 norm error estimates are given.
DISCONTINUOUS FINITE ELEMENT METHOD FOR CONVECTION-DIFFUSION EQUATIONS
Institute of Scientific and Technical Information of China (English)
Abdellatif Agouzal
2000-01-01
A discontinuous finite element method for convection-diffusion equations is proposed and analyzed. This scheme is designed to produce an approximate solution which is completely discontinuous. Optimal order of convergence is obtained for model problem. This is the same convergence rate known for the classical methods.
MULTIGRID FOR THE MORTAR FINITE ELEMENT FOR PARABOLIC PROBLEM
Institute of Scientific and Technical Information of China (English)
Xue-jun Xu; Jin-ru Chen
2003-01-01
In this paper, a mortar finite element method for parabolic problem is presented. Multigrid method is used for solving the resulting discrete system. It is shown that the multigrid method is optimal, I.e, the convergence rate is independent of the mesh size L and the time step parameter т.
Boundary control of parabolic systems - Finite-element approximation
Lasiecka, I.
1980-01-01
The finite element approximation of a Dirichlet type boundary control problem for parabolic systems is considered. An approach based on the direct approximation of an input-output semigroup formula is applied. Error estimates are derived for optimal state and optimal control, and it is noted that these estimates are actually optimal with respect to the approximation theoretic properties.
An Eulerean finite element model for penetration in layered soil
Berg, van den Peter; Borst, de Rene; Huetink, Han
1996-01-01
An Eulerean large-strain finite element formulation is presented to simulate static soil penetration. The method is an extension of the Updated Lagrangean description to an Eulerean formulation taking into account convection of deformation-history-dependent properties as well as material properties.
Closed Loop Finite Element Modeling of Piezoelectric Smart Structures
Directory of Open Access Journals (Sweden)
Guang Meng
2006-01-01
Full Text Available The objective of this paper is to develop a general design and analysis scheme for actively controlled piezoelectric smart structures. The scheme involves dynamic modeling of a smart structure, designing control laws and closed-loop simulation in a finite element environment. Based on the structure responses determined by finite element method, a modern system identification technique known as Observer/Kalman filter Identification (OKID technique is used to determine the system Markov parameters. The Eigensystem Realization Algorithm (ERA is then employed to develop an explicit state space model of the equivalent linear system for control law design. The Linear Quadratic Gaussian (LQG control law design technique is employed to design a control law. By using ANSYS parametric design language (APDL, the control law is incorporated into the ANSYS finite element model to perform closed loop simulations. Therefore, the control law performance can be evaluated in the context of a finite element environment. Finally, numerical examples have demonstrated the validity and efficiency of the proposed design scheme. Without any further modifications, the design scheme can be readily applied to other complex smart structures.
On the Approaching Domain Obtained by Finite Element Method
Institute of Scientific and Technical Information of China (English)
邹青松; 李永海
2002-01-01
The use of finite element method leads to replacing the initial domain by an approaching domain,Under some appropriate assumptions,we prove that there exists a W1,+∞-diffeomorphism from the original domain to the approaching domain.
Finite element modelling of fibre-reinforced brittle materials
Kullaa, J.
1997-01-01
The tensile constitutive behaviour of fibre-reinforced brittle materials can be extended to two or three dimensions by using the finite element method with crack models. The three approaches in this study include the smeared and discrete crack concepts and a multi-surface plasticity model. The tensi
Finite element analysis of bone loss around failing implants
Wolff, J.; Narra, N.; Antalainen, A.K.; Valášek, J.; Kaiser, J.; Sandór, G.K.; Marcián, P.
2014-01-01
Dental implants induce diverse forces on their surrounding bone. However, when excessive unphysiological forces are applied, resorption of the neighbouring bone may occur. The aim of this study was to assess possible causes of bone loss around failing dental implants using finite element analysis. A
An Orthogonal Residual Procedure for Nonlinear Finite Element Equations
DEFF Research Database (Denmark)
Krenk, S.
A general and robust solution procedure for nonlinear finite element equations with limit points is developed. At each equilibrium iteration the magnitude of the load is adjusted such that the residual force is orthogonal to the current displacement increment from the last equilibrium state...
A Finite Element Approach to Modeling Abrasive Wear Modes
Woldman, M.; Heide, van der E.; Tinga, T.; Masen, M.A.
2016-01-01
Machine components operating in sandy environments will wear because of the abrasive interaction with sand particles. In this work, a method is derived to predict the amount of wear caused by such abrasive action, in order to improve the maintenance concept of the components. A finite element model
Finite element estimation of acoustical response functions in HID lamps
Energy Technology Data Exchange (ETDEWEB)
Baumann, Bernd; Wolff, Marcus [Department of Mechanical Engineering and Production, School of Engineering and Computer Science, Hamburg University of Applied Sciences, Berliner Tor 21, 20099 Hamburg (Germany); Hirsch, John; Antonis, Piet [Philips Lighting BV, Lightlabs, Mathildelaan 1, 5600 JM Eindhoven (Netherlands); Bhosle, Sounil [Universite de Toulouse (United States); Barrientos, Ricardo Valdivia, E-mail: bernd.baumann@haw-hamburg.d [National Nuclear Research Institute, Highway Mexico-Toluca s/n, La Marquesa, Ocoyoacac, CP 52750 (Mexico)
2009-11-21
High intensity discharge lamps can experience flickering and even destruction when operated at high frequency alternating current. The cause of these problems has been identified as acoustic resonances inside the lamp's arc tube. Here, a finite element approach for the calculation of the acoustic response function is described. The developed model does not include the plasma dynamics.
Space-time discontinuous Galerkin finite element methods
Vegt, van der J.J.W.; Deconinck, H.; Ricchiuto, M.
2006-01-01
In these notes an introduction is given to space-time discontinuous Galerkin (DG) finite element methods for hyperbolic and parabolic conservation laws on time dependent domains. the space-time DG discretization is explained in detail, including the definition of the numerical fluxes and stabilizati
THE SUPERCONVERGENCE ANALYSIS OF AN ANISOTROPIC FINITE ELEMENT
Institute of Scientific and Technical Information of China (English)
SHI Dongyang; ZHU Huiqing
2005-01-01
This paper deals with the high accuracy analysis of bilinear finite element on the class of anisotropic rectangular meshes. The inverse inequalities on anisotropic meshes are established. The superclose and the superconvergence are obtained for the second order elliptic problem. A numerical test is given, which coincides with our theoretical analysis.
Finite element analysis of boron diffusion in wooden Poles
DEFF Research Database (Denmark)
Krabbenhøft, Kristian; Hoffmeyer, Preben; Bechgaard, Carl;
2004-01-01
The problem of describing the migration of dissolved boron in wood is treated with special reference to the commonly used remedial treatment of wooden poles. The governing equations are derived and discussed together with some of the material parameters required. The equations are solved by the f...... by the finite element method and, finally, results showing the effect of different treatment strategies are presented....
Hands on applied finite element analysis application with ANSYS
Arslan, Mehmet Ali
2015-01-01
Hands on Applied Finite Element Analysis Application with Ansys is truly an extraordinary book that offers practical ways of tackling FEA problems in machine design and analysis. In this book, 35 good selection of example problems have been presented, offering students the opportunity to apply their knowledge to real engineering FEA problem solutions by guiding them with real life hands on experience.