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Sample records for solution-adaptive finite element

  1. A spatially adaptive grid-refinement approach for the finite element solution of the even-parity Boltzmann transport equation

    International Nuclear Information System (INIS)

    Mirza, Anwar M.; Iqbal, Shaukat; Rahman, Faizur

    2007-01-01

    A spatially adaptive grid-refinement approach has been investigated to solve the even-parity Boltzmann transport equation. A residual based a posteriori error estimation scheme has been utilized for checking the approximate solutions for various finite element grids. The local particle balance has been considered as an error assessment criterion. To implement the adaptive approach, a computer program ADAFENT (adaptive finite elements for neutron transport) has been developed to solve the second order even-parity Boltzmann transport equation using K + variational principle for slab geometry. The program has a core K + module which employs Lagrange polynomials as spatial basis functions for the finite element formulation and Legendre polynomials for the directional dependence of the solution. The core module is called in by the adaptive grid generator to determine local gradients and residuals to explore the possibility of grid refinements in appropriate regions of the problem. The a posteriori error estimation scheme has been implemented in the outer grid refining iteration module. Numerical experiments indicate that local errors are large in regions where the flux gradients are large. A comparison of the spatially adaptive grid-refinement approach with that of uniform meshing approach for various benchmark cases confirms its superiority in greatly enhancing the accuracy of the solution without increasing the number of unknown coefficients. A reduction in the local errors of the order of 10 2 has been achieved using the new approach in some cases

  2. A spatially adaptive grid-refinement approach for the finite element solution of the even-parity Boltzmann transport equation

    Energy Technology Data Exchange (ETDEWEB)

    Mirza, Anwar M. [Department of Computer Science, National University of Computer and Emerging Sciences, NUCES-FAST, A.K. Brohi Road, H-11, Islamabad (Pakistan)], E-mail: anwar.m.mirza@gmail.com; Iqbal, Shaukat [Faculty of Computer Science and Engineering, Ghulam Ishaq Khan (GIK) Institute of Engineering Science and Technology, Topi-23460, Swabi (Pakistan)], E-mail: shaukat@giki.edu.pk; Rahman, Faizur [Department of Physics, Allama Iqbal Open University, H-8 Islamabad (Pakistan)

    2007-07-15

    A spatially adaptive grid-refinement approach has been investigated to solve the even-parity Boltzmann transport equation. A residual based a posteriori error estimation scheme has been utilized for checking the approximate solutions for various finite element grids. The local particle balance has been considered as an error assessment criterion. To implement the adaptive approach, a computer program ADAFENT (adaptive finite elements for neutron transport) has been developed to solve the second order even-parity Boltzmann transport equation using K{sup +} variational principle for slab geometry. The program has a core K{sup +} module which employs Lagrange polynomials as spatial basis functions for the finite element formulation and Legendre polynomials for the directional dependence of the solution. The core module is called in by the adaptive grid generator to determine local gradients and residuals to explore the possibility of grid refinements in appropriate regions of the problem. The a posteriori error estimation scheme has been implemented in the outer grid refining iteration module. Numerical experiments indicate that local errors are large in regions where the flux gradients are large. A comparison of the spatially adaptive grid-refinement approach with that of uniform meshing approach for various benchmark cases confirms its superiority in greatly enhancing the accuracy of the solution without increasing the number of unknown coefficients. A reduction in the local errors of the order of 10{sup 2} has been achieved using the new approach in some cases.

  3. An h-adaptive finite element method for turbulent heat transfer

    Energy Technology Data Exchange (ETDEWEB)

    Carriington, David B [Los Alamos National Laboratory

    2009-01-01

    A two-equation turbulence closure model (k-{omega}) using an h-adaptive grid technique and finite element method (FEM) has been developed to simulate low Mach flow and heat transfer. These flows are applicable to many flows in engineering and environmental sciences. Of particular interest in the engineering modeling areas are: combustion, solidification, and heat exchanger design. Flows for indoor air quality modeling and atmospheric pollution transport are typical types of environmental flows modeled with this method. The numerical method is based on a hybrid finite element model using an equal-order projection process. The model includes thermal and species transport, localized mesh refinement (h-adaptive) and Petrov-Galerkin weighting for the stabilizing the advection. This work develops the continuum model of a two-equation turbulence closure method. The fractional step solution method is stated along with the h-adaptive grid method (Carrington and Pepper, 2002). Solutions are presented for 2d flow over a backward-facing step.

  4. An efficient finite element solution for gear dynamics

    International Nuclear Information System (INIS)

    Cooley, C G; Parker, R G; Vijayakar, S M

    2010-01-01

    A finite element formulation for the dynamic response of gear pairs is proposed. Following an established approach in lumped parameter gear dynamic models, the static solution is used as the excitation in a frequency domain solution of the finite element vibration model. The nonlinear finite element/contact mechanics formulation provides accurate calculation of the static solution and average mesh stiffness that are used in the dynamic simulation. The frequency domain finite element calculation of dynamic response compares well with numerically integrated (time domain) finite element dynamic results and previously published experimental results. Simulation time with the proposed formulation is two orders of magnitude lower than numerically integrated dynamic results. This formulation admits system level dynamic gearbox response, which may include multiple gear meshes, flexible shafts, rolling element bearings, housing structures, and other deformable components.

  5. Adaptive solution of the multigroup diffusion equation on irregular structured grids using a conforming finite element method formulation

    International Nuclear Information System (INIS)

    Ragusa, J. C.

    2004-01-01

    In this paper, a method for performing spatially adaptive computations in the framework of multigroup diffusion on 2-D and 3-D Cartesian grids is investigated. The numerical error, intrinsic to any computer simulation of physical phenomena, is monitored through an a posteriori error estimator. In a posteriori analysis, the computed solution itself is used to assess the accuracy. By efficiently estimating the spatial error, the entire computational process is controlled through successively adapted grids. Our analysis is based on a finite element solution of the diffusion equation. Bilinear test functions are used. The derived a posteriori error estimator is therefore based on the Hessian of the numerical solution. (authors)

  6. Adaptive finite-element ballooning analysis of bipolar ionized fields

    International Nuclear Information System (INIS)

    Al-Hamouz, Z.M.

    1995-01-01

    This paper presents an adaptive finite-element iterative method for the analysis of the ionized field around high-voltage bipolar direct-current (HVDC) transmission line conductors without resort to Deutsch's assumption. A new iterative finite-element ballooning technique is proposed to solve Poisson's equation wherein the commonly used artificial boundary around the transmission line conductors is simulated at infinity. Unlike all attempts reported in the literature for the solution of ionized field, the constancy of the conductors' surface field at the corona onset value is directly implemented in the finite-element formulation. In order to investigate the effectiveness of the proposed method, a laboratory model was built. It has been found that the calculated V-I characteristics and the ground-plane current density agreed well with those measured experimentally. The simplicity in computer programming in addition to the low number of iterations required to achieve convergence characterize this method of analysis

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

    KAUST Repository

    Chen, Huangxin; Salama, Amgad; Sun, Shuyu

    2016-01-01

    In this paper, we propose adaptive mixed finite element methods for simulating the single-phase Darcy flow in two-dimensional fractured porous media. The reduced model that we use for the simulation is a discrete fracture model coupling Darcy flows in the matrix and the fractures, and the fractures are modeled by one-dimensional entities. The Raviart-Thomas mixed finite element methods are utilized for the solution of the coupled Darcy flows in the matrix and the fractures. In order to improve the efficiency of the simulation, we use adaptive mixed finite element methods based on novel residual-based a posteriori error estimators. In addition, we develop an efficient upscaling algorithm to compute the effective permeability of the fractured porous media. Several interesting examples of Darcy flow in the fractured porous media are presented to demonstrate the robustness of the algorithm.

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

    KAUST Repository

    Chen, Huangxin

    2016-09-21

    In this paper, we propose adaptive mixed finite element methods for simulating the single-phase Darcy flow in two-dimensional fractured porous media. The reduced model that we use for the simulation is a discrete fracture model coupling Darcy flows in the matrix and the fractures, and the fractures are modeled by one-dimensional entities. The Raviart-Thomas mixed finite element methods are utilized for the solution of the coupled Darcy flows in the matrix and the fractures. In order to improve the efficiency of the simulation, we use adaptive mixed finite element methods based on novel residual-based a posteriori error estimators. In addition, we develop an efficient upscaling algorithm to compute the effective permeability of the fractured porous media. Several interesting examples of Darcy flow in the fractured porous media are presented to demonstrate the robustness of the algorithm.

  9. Overview of adaptive finite element analysis in computational geodynamics

    Science.gov (United States)

    May, D. A.; Schellart, W. P.; Moresi, L.

    2013-10-01

    The use of numerical models to develop insight and intuition into the dynamics of the Earth over geological time scales is a firmly established practice in the geodynamics community. As our depth of understanding grows, and hand-in-hand with improvements in analytical techniques and higher resolution remote sensing of the physical structure and state of the Earth, there is a continual need to develop more efficient, accurate and reliable numerical techniques. This is necessary to ensure that we can meet the challenge of generating robust conclusions, interpretations and predictions from improved observations. In adaptive numerical methods, the desire is generally to maximise the quality of the numerical solution for a given amount of computational effort. Neither of these terms has a unique, universal definition, but typically there is a trade off between the number of unknowns we can calculate to obtain a more accurate representation of the Earth, and the resources (time and computational memory) required to compute them. In the engineering community, this topic has been extensively examined using the adaptive finite element (AFE) method. Recently, the applicability of this technique to geodynamic processes has started to be explored. In this review we report on the current status and usage of spatially adaptive finite element analysis in the field of geodynamics. The objective of this review is to provide a brief introduction to the area of spatially adaptive finite analysis, including a summary of different techniques to define spatial adaptation and of different approaches to guide the adaptive process in order to control the discretisation error inherent within the numerical solution. An overview of the current state of the art in adaptive modelling in geodynamics is provided, together with a discussion pertaining to the issues related to using adaptive analysis techniques and perspectives for future research in this area. Additionally, we also provide a

  10. Adaptive finite element methods for differential equations

    CERN Document Server

    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 ...

  11. Verification of the coupled space-angle adaptivity algorithm for the finite element-spherical harmonics method via the method of manufactured solutions

    International Nuclear Information System (INIS)

    Park, H.; De Oliveira, C. R. E.

    2007-01-01

    This paper describes the verification of the recently developed space-angle self-adaptive algorithm for the finite element-spherical harmonics method via the Method of Manufactured Solutions. This method provides a simple, yet robust way for verifying the theoretical properties of the adaptive algorithm and interfaces very well with the underlying second-order, even-parity transport formulation. Simple analytic solutions in both spatial and angular variables are manufactured to assess the theoretical performance of the a posteriori error estimates. The numerical results confirm reliability of the developed space-angle error indicators. (authors)

  12. On the reliability of finite element solutions

    International Nuclear Information System (INIS)

    Prasad, K.S.R.K.

    1975-01-01

    The extent of reliability of the finite element method for analysis of nuclear reactor structures, and that of reactor vessels in particular and the need for the engineer to guard against the pitfalls that may arise out of both physical and mathematical models have been high-lighted. A systematic way of checking the model to obtain reasonably accurate solutions is presented. Quite often sophisticated elements are suggested for specific design and stress concentration problems. The desirability or otherwise of these elements, their scope and utility vis-a-vis the use of large stack of conventional elements are discussed from the view point of stress analysts. The methods of obtaining a check on the reliability of the finite element solutions either through modelling changes or an extrapolation technique are discussed. (author)

  13. Adaptive finite element techniques for the Maxwell equations using implicit a posteriori error estimates

    NARCIS (Netherlands)

    Harutyunyan, D.; Izsak, F.; van der Vegt, Jacobus J.W.; Bochev, Mikhail A.

    For the adaptive solution of the Maxwell equations on three-dimensional domains with N´ed´elec edge finite element methods, we consider an implicit a posteriori error estimation technique. On each element of the tessellation an equation for the error is formulated and solved with a properly chosen

  14. 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.

  15. Error-controlled adaptive finite elements in solid mechanics

    National Research Council Canada - National Science Library

    Stein, Erwin; Ramm, E

    2003-01-01

    ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Error-controlled Adaptive Finite-element-methods . . . . . . . . . . . . Missing Features and Properties of Today's General Purpose FE Programs for Structural...

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

    Science.gov (United States)

    Sheng, Lizeng

    The dissertation focuses on one of the major research needs in the area of adaptive/intelligent/smart structures, the development and application of finite element analysis and genetic algorithms for optimal design of large-scale adaptive structures. We first review some basic concepts in finite element method and genetic algorithms, along with the research on smart structures. Then we propose a solution methodology for solving a critical problem in the design of a next generation of large-scale adaptive structures---optimal placements of a large number of actuators to control thermal deformations. After briefly reviewing the three most frequently used general approaches to derive a finite element formulation, the dissertation presents techniques associated with general shell finite element analysis using flat triangular laminated composite elements. The element used here has three nodes and eighteen degrees of freedom and is obtained by combining a triangular membrane element and a triangular plate bending element. The element includes the coupling effect between membrane deformation and bending deformation. The membrane element is derived from the linear strain triangular element using Cook's transformation. The discrete Kirchhoff triangular (DKT) element is used as the plate bending element. For completeness, a complete derivation of the DKT is presented. Geometrically nonlinear finite element formulation is derived for the analysis of adaptive structures under the combined thermal and electrical loads. Next, we solve the optimization problems of placing a large number of piezoelectric actuators to control thermal distortions in a large mirror in the presence of four different thermal loads. We then extend this to a multi-objective optimization problem of determining only one set of piezoelectric actuator locations that can be used to control the deformation in the same mirror under the action of any one of the four thermal loads. A series of genetic algorithms

  17. Adaptive Smoothed Finite Elements (ASFEM) for history dependent material models

    International Nuclear Information System (INIS)

    Quak, W.; Boogaard, A. H. van den

    2011-01-01

    A successful simulation of a bulk forming process with finite elements can be difficult due to distortion of the finite elements. Nodal smoothed Finite Elements (NSFEM) are an interesting option for such a process since they show good distortion insensitivity and moreover have locking-free behavior and good computational efficiency. In this paper a method is proposed which takes advantage of the nodally smoothed field. This method, named adaptive smoothed finite elements (ASFEM), revises the mesh for every step of a simulation without mapping the history dependent material parameters. In this paper an updated-Lagrangian implementation is presented. Several examples are given to illustrate the method and to show its properties.

  18. Precise magnetostatic field using the finite element method

    International Nuclear Information System (INIS)

    Nascimento, Francisco Rogerio Teixeira do

    2013-01-01

    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)

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

    Science.gov (United States)

    Hu, Guanghui; Xie, Hehu; Xu, Fei

    2018-02-01

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

  20. Moving finite elements: A continuously adaptive method for computational fluid dynamics

    International Nuclear Information System (INIS)

    Glasser, A.H.; Miller, K.; Carlson, N.

    1991-01-01

    Moving Finite Elements (MFE), a recently developed method for computational fluid dynamics, promises major advances in the ability of computers to model the complex behavior of liquids, gases, and plasmas. Applications of computational fluid dynamics occur in a wide range of scientifically and technologically important fields. Examples include meteorology, oceanography, global climate modeling, magnetic and inertial fusion energy research, semiconductor fabrication, biophysics, automobile and aircraft design, industrial fluid processing, chemical engineering, and combustion research. The improvements made possible by the new method could thus have substantial economic impact. Moving Finite Elements is a moving node adaptive grid method which has a tendency to pack the grid finely in regions where it is most needed at each time and to leave it coarse elsewhere. It does so in a manner which is simple and automatic, and does not require a large amount of human ingenuity to apply it to each particular problem. At the same time, it often allows the time step to be large enough to advance a moving shock by many shock thicknesses in a single time step, moving the grid smoothly with the solution and minimizing the number of time steps required for the whole problem. For 2D problems (two spatial variables) the grid is composed of irregularly shaped and irregularly connected triangles which are very flexible in their ability to adapt to the evolving solution. While other adaptive grid methods have been developed which share some of these desirable properties, this is the only method which combines them all. In many cases, the method can save orders of magnitude of computing time, equivalent to several generations of advancing computer hardware

  1. Algorithms and data structures for massively parallel generic adaptive finite element codes

    KAUST Repository

    Bangerth, Wolfgang

    2011-12-01

    Today\\'s largest supercomputers have 100,000s of processor cores and offer the potential to solve partial differential equations discretized by billions of unknowns. However, the complexity of scaling to such large machines and problem sizes has so far prevented the emergence of generic software libraries that support such computations, although these would lower the threshold of entry and enable many more applications to benefit from large-scale computing. We are concerned with providing this functionality for mesh-adaptive finite element computations. We assume the existence of an "oracle" that implements the generation and modification of an adaptive mesh distributed across many processors, and that responds to queries about its structure. Based on querying the oracle, we develop scalable algorithms and data structures for generic finite element methods. Specifically, we consider the parallel distribution of mesh data, global enumeration of degrees of freedom, constraints, and postprocessing. Our algorithms remove the bottlenecks that typically limit large-scale adaptive finite element analyses. We demonstrate scalability of complete finite element workflows on up to 16,384 processors. An implementation of the proposed algorithms, based on the open source software p4est as mesh oracle, is provided under an open source license through the widely used deal.II finite element software library. © 2011 ACM 0098-3500/2011/12-ART10 $10.00.

  2. Studies on the numerical solution of three-dimensional stationary diffusion equations using the finite element method

    International Nuclear Information System (INIS)

    Franke, H.P.

    1976-05-01

    The finite element method is applied to the solution of the stationary 3D group diffusion equations. For this, a programme system with the name of FEM3D is established which also includes a module for semi-automatic mesh generation. Tetrahedral finite elements are used. The neutron fluxes are described by complete first- or second-order Lagrangian polynomials. General homogeneous boundary conditions are allowed. The studies show that realistic three-dimensional problems can be solved at less expense by iterative methods, in particular so when especially adapted matrix handling and storage schemes are used efficiently. (orig./RW) [de

  3. Parallel iterative procedures for approximate solutions of wave propagation by finite element and finite difference methods

    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.

  4. An object-oriented decomposition of the adaptive-hp finite element method

    Energy Technology Data Exchange (ETDEWEB)

    Wiley, J.C.

    1994-12-13

    Adaptive-hp methods are those which use a refinement control strategy driven by a local error estimate to locally modify the element size, h, and polynomial order, p. The result is an unstructured mesh in which each node may be associated with a different polynomial order and which generally require complex data structures to implement. Object-oriented design strategies and languages which support them, e.g., C++, help control the complexity of these methods. Here an overview of the major classes and class structure of an adaptive-hp finite element code is described. The essential finite element structure is described in terms of four areas of computation each with its own dynamic characteristics. Implications of converting the code for a distributed-memory parallel environment are also discussed.

  5. A finite element solution method for quadrics parallel computer

    International Nuclear Information System (INIS)

    Zucchini, A.

    1996-08-01

    A distributed preconditioned conjugate gradient method for finite element analysis has been developed and implemented on a parallel SIMD Quadrics computer. The main characteristic of the method is that it does not require any actual assembling of all element equations in a global system. The physical domain of the problem is partitioned in cells of n p finite elements and each cell element is assigned to a different node of an n p -processors machine. Element stiffness matrices are stored in the data memory of the assigned processing node and the solution process is completely executed in parallel at element level. Inter-element and therefore inter-processor communications are required once per iteration to perform local sums of vector quantities between neighbouring elements. A prototype implementation has been tested on an 8-nodes Quadrics machine in a simple 2D benchmark problem

  6. r-Adaptive mesh generation for shell finite element analysis

    International Nuclear Information System (INIS)

    Cho, Maenghyo; Jun, Seongki

    2004-01-01

    An r-adaptive method or moving grid technique relocates a grid so that it becomes concentrated in the desired region. This concentration improves the accuracy and efficiency of finite element solutions. We apply the r-adaptive method to computational mesh of shell surfaces, which is initially regular and uniform. The r-adaptive method, given by Liao and Anderson [Appl. Anal. 44 (1992) 285], aggregate the grid in the region with a relatively high weight function without any grid-tangling. The stress error estimator is calculated in the initial uniform mesh for a weight function. However, since the r-adaptive method is a method that moves the grid, shell surface geometry error such as curvature error and mesh distortion error will increase. Therefore, to represent the exact geometry of a shell surface and to prevent surface geometric errors, we use the Naghdi's shell theory and express the shell surface by a B-spline patch. In addition, using a nine-node element, which is relatively less sensitive to mesh distortion, we try to diminish mesh distortion error in the application of an r-adaptive method. In the numerical examples, it is shown that the values of the error estimator for a cylinder, hemisphere, and torus in the overall domain can be reduced effectively by using the mesh generated by the r-adaptive method. Also, the reductions of the estimated relative errors are demonstrated in the numerical examples. In particular, a new functional is proposed to construct an adjusted mesh configuration by considering a mesh distortion measure as well as the stress error function. The proposed weight function provides a reliable mesh adaptation method after a parameter value in the weight function is properly chosen

  7. Adaptive finite element method for shape optimization

    KAUST Repository

    Morin, Pedro; Nochetto, Ricardo H.; Pauletti, Miguel S.; Verani, Marco

    2012-01-01

    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.

  8. Adaptive finite element method for shape optimization

    KAUST Repository

    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.

  9. Eigenvalue solutions in finite element thermal transient problems

    International Nuclear Information System (INIS)

    Stoker, J.R.

    1975-01-01

    The eigenvalue economiser concept can be useful in solving large finite element transient heat flow problems in which the boundary heat transfer coefficients are constant. The usual economiser theory is equivalent to applying a unit thermal 'force' to each of a small sub-set of nodes on the finite element mesh, and then calculating sets of resulting steady state temperatures. Subsequently it is assumed that the required transient temperature distributions can be approximated by a linear combination of this comparatively small set of master temperatures. The accuracy of a reduced eigenvalue calculation depends upon a good choice of master nodes, which presupposes at least a little knowledge about what sort of shape is expected in the unknown temperature distributions. There are some instances, however, where a reasonably good idea exists of the required shapes, permitting a modification to the economiser process which leads to greater economy in the number of master temperatures. The suggested new approach is to use manually prescribed temperature distributions as the master distributions, rather than using temperatures resulting from unit thermal forces. Thus, with a little pre-knowledge one may write down a set of master distributions which, as a linear combination, can represent the required solution over the range of interest to a reasonable engineering accuracy, and using the minimum number of variables. The proposed modified eigenvalue economiser technique then uses the master distributions in an automatic way to arrive at the required solution. The technique is illustrated by some simple finite element examples

  10. Numerical solution of multi group-Two dimensional- Adjoint equation with finite element method

    International Nuclear Information System (INIS)

    Poursalehi, N.; Khalafi, H.; Shahriari, M.; Minoochehr

    2008-01-01

    Adjoint equation is used for perturbation theory in nuclear reactor design. For numerical solution of adjoint equation, usually two methods are applied. These are Finite Element and Finite Difference procedures. Usually Finite Element Procedure is chosen for solving of adjoint equation, because it is more use able in variety of geometries. In this article, Galerkin Finite Element method is discussed. This method is applied for numerical solving multi group, multi region and two dimensional (X, Y) adjoint equation. Typical reactor geometry is partitioned with triangular meshes and boundary condition for adjoint flux is considered zero. Finally, for a case of defined parameters, Finite Element Code was applied and results were compared with Citation Code

  11. An h-adaptive finite element solver for the calculations of the electronic structures

    International Nuclear Information System (INIS)

    Bao Gang; Hu Guanghui; Liu Di

    2012-01-01

    In this paper, a framework of using h-adaptive finite element method for the Kohn–Sham equation on the tetrahedron mesh is presented. The Kohn–Sham equation is discretized by the finite element method, and the h-adaptive technique is adopted to optimize the accuracy and the efficiency of the algorithm. The locally optimal block preconditioned conjugate gradient method is employed for solving the generalized eigenvalue problem, and an algebraic multigrid preconditioner is used to accelerate the solver. A variety of numerical experiments demonstrate the effectiveness of our algorithm for both the all-electron and the pseudo-potential calculations.

  12. Solution of problems with material nonlinearities with a coupled finite element/boundary element scheme using an iterative solver. Yucca Mountain Site Characterization Project

    International Nuclear Information System (INIS)

    Koteras, J.R.

    1996-01-01

    The prediction of stresses and displacements around tunnels buried deep within the earth is an important class of geomechanics problems. The material behavior immediately surrounding the tunnel is typically nonlinear. The surrounding mass, even if it is nonlinear, can usually be characterized by a simple linear elastic model. The finite element method is best suited for modeling nonlinear materials of limited volume, while the boundary element method is well suited for modeling large volumes of linear elastic material. A computational scheme that couples the finite element and boundary element methods would seem particularly useful for geomechanics problems. A variety of coupling schemes have been proposed, but they rely on direct solution methods. Direct solution techniques have large storage requirements that become cumbersome for large-scale three-dimensional problems. An alternative to direct solution methods is iterative solution techniques. A scheme has been developed for coupling the finite element and boundary element methods that uses an iterative solution method. This report shows that this coupling scheme is valid for problems where nonlinear material behavior occurs in the finite element region

  13. Adaptive Finite Element Method Assisted by Stochastic Simulation of Chemical Systems

    KAUST Repository

    Cotter, Simon L.; Vejchodský , Tomá š; Erban, Radek

    2013-01-01

    Stochastic models of chemical systems are often analyzed by solving the corresponding Fokker-Planck equation, which is a drift-diffusion partial differential equation for the probability distribution function. Efficient numerical solution of the Fokker-Planck equation requires adaptive mesh refinements. In this paper, we present a mesh refinement approach which makes use of a stochastic simulation of the underlying chemical system. By observing the stochastic trajectory for a relatively short amount of time, the areas of the state space with nonnegligible probability density are identified. By refining the finite element mesh in these areas, and coarsening elsewhere, a suitable mesh is constructed and used for the computation of the stationary probability density. Numerical examples demonstrate that the presented method is competitive with existing a posteriori methods. © 2013 Society for Industrial and Applied Mathematics.

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

    Science.gov (United States)

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

    2018-06-01

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

  15. Application of finite element method in the solution of transport equation

    International Nuclear Information System (INIS)

    Maiorino, J.R.; Vieira, W.J.

    1985-01-01

    It is presented the application of finite element method in the solution of second order transport equation (self-adjoint) for the even parity flux. The angular component is treated by expansion in Legendre polinomials uncoupled of the spatial component, which is approached by an expansion in base functions, interpolated in each spatial element. (M.C.K.) [pt

  16. Solution of the Lambda modes problem of a nuclear power reactor using an h–p finite element method

    International Nuclear Information System (INIS)

    Vidal-Ferrandiz, A.; Fayez, R.; Ginestar, D.; Verdú, G.

    2014-01-01

    Highlights: • An hp finite element method is proposed for the Lambda modes problem of a nuclear reactor. • Different strategies can be implemented for increasing the accuracy of the solutions. • 2D and 3D benchmarks have been studied obtaining accurate results. - Abstract: Lambda modes of a nuclear power reactor have interest in reactor physics since they have been used to develop modal methods and to study BWR reactor instabilities. An h–p-Adaptation finite element method has been implemented to compute the dominant modes the fundamental mode and the next subcritical modes of a nuclear reactor. The performance of this method has been studied in three benchmark problems, a homogeneous 2D reactor, the 2D BIBLIS reactor and the 3D IAEA reactor

  17. An adaptive finite element method for steady and transient problems

    International Nuclear Information System (INIS)

    Benner, R.E. Jr.; Davis, H.T.; Scriven, L.E.

    1987-01-01

    Distributing integral error uniformly over variable subdomains, or finite elements, is an attractive criterion by which to subdivide a domain for the Galerkin/finite element method when localized steep gradients and high curvatures are to be resolved. Examples are fluid interfaces, shock fronts and other internal layers, as well as fluid mechanical and other boundary layers, e.g. thin-film states at solid walls. The uniform distribution criterion is developed into an adaptive technique for one-dimensional problems. Nodal positions can be updated simultaneously with nodal values during Newton iteration, but it is usually better to adopt nearly optimal nodal positions during Newton iteration upon nodal values. Three illustrative problems are solved: steady convection with diffusion, gradient theory of fluid wetting on a solid surface and Buckley-Leverett theory of two phase Darcy flow in porous media

  18. Goal-Oriented Self-Adaptive hp Finite Element Simulation of 3D DC Borehole Resistivity Simulations

    KAUST Repository

    Calo, Victor M.

    2011-05-14

    In this paper we present a goal-oriented self-adaptive hp Finite Element Method (hp-FEM) with shared data structures and a parallel multi-frontal direct solver. The algorithm automatically generates (without any user interaction) a sequence of meshes delivering exponential convergence of a prescribed quantity of interest with respect to the number of degrees of freedom. The sequence of meshes is generated from a given initial mesh, by performing h (breaking elements into smaller elements), p (adjusting polynomial orders of approximation) or hp (both) refinements on the finite elements. The new parallel implementation utilizes a computational mesh shared between multiple processors. All computational algorithms, including automatic hp goal-oriented adaptivity and the solver work fully in parallel. We describe the parallel self-adaptive hp-FEM algorithm with shared computational domain, as well as its efficiency measurements. We apply the methodology described to the three-dimensional simulation of the borehole resistivity measurement of direct current through casing in the presence of invasion.

  19. Simulation of wireline sonic logging measurements acquired with Borehole-Eccentered tools using a high-order adaptive finite-element method

    KAUST Repository

    Pardo, David

    2011-07-01

    The paper introduces a high-order, adaptive finite-element method for simulation of sonic measurements acquired with borehole-eccentered logging instruments. The resulting frequency-domain based algorithm combines a Fourier series expansion in one spatial dimension with a two-dimensional high-order adaptive finite-element method (FEM), and incorporates a perfectly matched layer (PML) for truncation of the computational domain. The simulation method was verified for various model problems, including a comparison to a semi-analytical solution developed specifically for this purpose. Numerical results indicate that for a wireline sonic tool operating in a fast formation, the main propagation modes are insensitive to the distance from the center of the tool to the center of the borehole (eccentricity distance). However, new flexural modes arise with an increase in eccentricity distance. In soft formations, we identify a new dipole tool mode which arises as a result of tool eccentricity. © 2011 Elsevier Inc.

  20. Simulation of wireline sonic logging measurements acquired with Borehole-Eccentered tools using a high-order adaptive finite-element method

    KAUST Repository

    Pardo, David; Matuszyk, Paweł Jerzy; Muga, Ignacio; Torres-Verdí n, Carlos; Mora Cordova, Angel; Calo, Victor M.

    2011-01-01

    The paper introduces a high-order, adaptive finite-element method for simulation of sonic measurements acquired with borehole-eccentered logging instruments. The resulting frequency-domain based algorithm combines a Fourier series expansion in one spatial dimension with a two-dimensional high-order adaptive finite-element method (FEM), and incorporates a perfectly matched layer (PML) for truncation of the computational domain. The simulation method was verified for various model problems, including a comparison to a semi-analytical solution developed specifically for this purpose. Numerical results indicate that for a wireline sonic tool operating in a fast formation, the main propagation modes are insensitive to the distance from the center of the tool to the center of the borehole (eccentricity distance). However, new flexural modes arise with an increase in eccentricity distance. In soft formations, we identify a new dipole tool mode which arises as a result of tool eccentricity. © 2011 Elsevier Inc.

  1. A parallel direct solver for the self-adaptive hp Finite Element Method

    KAUST Repository

    Paszyński, Maciej R.; Pardo, David; Torres-Verdí n, Carlos; Demkowicz, Leszek F.; Calo, Victor M.

    2010-01-01

    measurement simulations problems. We measure the execution time and memory usage of the solver over a large regular mesh with 1.5 million degrees of freedom as well as on the highly non-regular mesh, generated by the self-adaptive h p-FEM, with finite elements

  2. Comparison of closed-form and finite-element solutions of thick laminated anisotropic rectangular plates

    Energy Technology Data Exchange (ETDEWEB)

    Reddy, J N; Chao, W C [Virginia Polytechnic Inst. and State Univ., Blacksburg (USA). Dept. of Engineering Science and Mechanics

    1981-04-01

    In this study the effects of reduced integration, mesh size, and element type (i.e. linear or quadratic) on the accuracy of a penalty-finite element based on the theory governing thick, laminated, anisotropic composite plates are investigated. In order to assess the accuracy of the present finite element, exact closed-form solutions are developed for cross-ply and antisymmetric angle-ply rectangular plates simply supported and subjected to sinusoidally distributed mechanical and/or thermal loadings, and free vibration.

  3. Discontinuous finite element solution of the radiation diffusion equation on arbitrary polygonal meshes and locally adapted quadrilateral grids

    International Nuclear Information System (INIS)

    Ragusa, Jean C.

    2015-01-01

    In this paper, we propose a piece-wise linear discontinuous (PWLD) finite element discretization of the diffusion equation for arbitrary polygonal meshes. It is based on the standard diffusion form and uses the symmetric interior penalty technique, which yields a symmetric positive definite linear system matrix. A preconditioned conjugate gradient algorithm is employed to solve the linear system. Piece-wise linear approximations also allow a straightforward implementation of local mesh adaptation by allowing unrefined cells to be interpreted as polygons with an increased number of vertices. Several test cases, taken from the literature on the discretization of the radiation diffusion equation, are presented: random, sinusoidal, Shestakov, and Z meshes are used. The last numerical example demonstrates the application of the PWLD discretization to adaptive mesh refinement

  4. Finite element simulation of moisture movement and solute transport in a large caisson

    International Nuclear Information System (INIS)

    Huyakorn, P.S.; Jones, B.G.; Parker, J.C.; Wadsworth, T.D.; White, H.O. Jr.

    1987-01-01

    The results of the solute transport experiments performed on compacted, crushed Bandelier Tuff in caisson B of the experimental cluster described by DePoorter (1981) are simulated. Both one- and three-dimensional simulations of solute transport have been performed using two selected finite element codes. Results of bromide and iodide tracer experiments conducted during near-steady flow conditions have been analyzed for pulse additions made on December 6, 1984, and followed over a period of up to 60 days. In addition, a pulse addition of nonconservative strontium tracer on September 28, 1984, during questionably steady flow conditions has been analyzed over a period of 240 days. One-dimensional finite element flow and transport simulations were carried out assuming the porous medium to be homogeneous and the injection source uniformly distributed. To evaluate effects of the nonuniform source distribution and also to investigate effects of inhomogeneous porous medium properties, three dimensional finite element analyses of transport were carried out. Implications of the three-dimensional effects for the design and analysis of future tracer studies are discussed

  5. Node-based finite element method for large-scale adaptive fluid analysis in parallel environments

    International Nuclear Information System (INIS)

    Toshimitsu, Fujisawa; Genki, Yagawa

    2003-01-01

    In this paper, a FEM-based (finite element method) mesh free method with a probabilistic node generation technique is presented. In the proposed method, all computational procedures, from the mesh generation to the solution of a system of equations, can be performed fluently in parallel in terms of nodes. Local finite element mesh is generated robustly around each node, even for harsh boundary shapes such as cracks. The algorithm and the data structure of finite element calculation are based on nodes, and parallel computing is realized by dividing a system of equations by the row of the global coefficient matrix. In addition, the node-based finite element method is accompanied by a probabilistic node generation technique, which generates good-natured points for nodes of finite element mesh. Furthermore, the probabilistic node generation technique can be performed in parallel environments. As a numerical example of the proposed method, we perform a compressible flow simulation containing strong shocks. Numerical simulations with frequent mesh refinement, which are required for such kind of analysis, can effectively be performed on parallel processors by using the proposed method. (authors)

  6. Node-based finite element method for large-scale adaptive fluid analysis in parallel environments

    Energy Technology Data Exchange (ETDEWEB)

    Toshimitsu, Fujisawa [Tokyo Univ., Collaborative Research Center of Frontier Simulation Software for Industrial Science, Institute of Industrial Science (Japan); Genki, Yagawa [Tokyo Univ., Department of Quantum Engineering and Systems Science (Japan)

    2003-07-01

    In this paper, a FEM-based (finite element method) mesh free method with a probabilistic node generation technique is presented. In the proposed method, all computational procedures, from the mesh generation to the solution of a system of equations, can be performed fluently in parallel in terms of nodes. Local finite element mesh is generated robustly around each node, even for harsh boundary shapes such as cracks. The algorithm and the data structure of finite element calculation are based on nodes, and parallel computing is realized by dividing a system of equations by the row of the global coefficient matrix. In addition, the node-based finite element method is accompanied by a probabilistic node generation technique, which generates good-natured points for nodes of finite element mesh. Furthermore, the probabilistic node generation technique can be performed in parallel environments. As a numerical example of the proposed method, we perform a compressible flow simulation containing strong shocks. Numerical simulations with frequent mesh refinement, which are required for such kind of analysis, can effectively be performed on parallel processors by using the proposed method. (authors)

  7. Elastic-Plastic J-Integral Solutions or Surface Cracks in Tension Using an Interpolation Methodology. Appendix C -- Finite Element Models Solution Database File, Appendix D -- Benchmark Finite Element Models Solution Database File

    Science.gov (United States)

    Allen, Phillip A.; Wells, Douglas N.

    2013-01-01

    No closed form solutions exist for the elastic-plastic J-integral for surface cracks due to the nonlinear, three-dimensional nature of the problem. Traditionally, each surface crack must be analyzed with a unique and time-consuming nonlinear finite element analysis. To overcome this shortcoming, the authors have developed and analyzed an array of 600 3D nonlinear finite element models for surface cracks in flat plates under tension loading. The solution space covers a wide range of crack shapes and depths (shape: 0.2 less than or equal to a/c less than or equal to 1, depth: 0.2 less than or equal to a/B less than or equal to 0.8) and material flow properties (elastic modulus-to-yield ratio: 100 less than or equal to E/ys less than or equal to 1,000, and hardening: 3 less than or equal to n less than or equal to 20). The authors have developed a methodology for interpolating between the goemetric and material property variables that allows the user to reliably evaluate the full elastic-plastic J-integral and force versus crack mouth opening displacement solution; thus, a solution can be obtained very rapidly by users without elastic-plastic fracture mechanics modeling experience. Complete solutions for the 600 models and 25 additional benchmark models are provided in tabular format.

  8. Finite element based composite solution for neutron transport problems

    International Nuclear Information System (INIS)

    Mirza, A.N.; Mirza, N.M.

    1995-01-01

    A finite element treatment for solving neutron transport problems is presented. The employs region-wise discontinuous finite elements for the spatial representation of the neutron angular flux, while spherical harmonics are used for directional dependence. Composite solutions has been obtained by using different orders of angular approximations in different parts of a system. The method has been successfully implemented for one dimensional slab and two dimensional rectangular geometry problems. An overall reduction in the number of nodal coefficients (more than 60% in some cases as compared to conventional schemes) has been achieved without loss of accuracy with better utilization of computational resources. The method also provides an efficient way of handling physically difficult situations such as treatment of voids in duct problems and sharply changing angular flux. It is observed that a great wealth of information about the spatial and directional dependence of the angular flux is obtained much more quickly as compared to Monte Carlo method, where most of the information in restricted to the locality of immediate interest. (author)

  9. Finite elements and approximation

    CERN Document Server

    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

  10. Finite element solution of quasistationary nonlinear magnetic field

    International Nuclear Information System (INIS)

    Zlamal, Milos

    1982-01-01

    The computation of quasistationary nonlinear two-dimensional magnetic field leads to the following problem. There is given a bounded domain OMEGA and an open nonempty set R included in OMEGA. We are looking for the magnetic vector potential u(x 1 , x 2 , t) which satisifies: 1) a certain nonlinear parabolic equation and an initial condition in R: 2) a nonlinear elliptic equation in S = OMEGA - R which is the stationary case of the above mentioned parabolic equation; 3) a boundary condition on delta OMEGA; 4) u as well as its conormal derivative are continuous accross the common boundary of R and S. This problem is formulated in two equivalent abstract ways. There is constructed an approximate solution completely discretized in space by a generalized Galerkin method (straight finite elements are a special case) and by backward A-stable differentiation methods in time. Existence and uniqueness of a weak solution is proved as well as a weak and strong convergence of the approximate solution to this solution. There are also derived error bounds for the solution of the two-dimensional nonlinear magnetic field equations under the assumption that the exact solution is sufficiently smooth

  11. 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.

  12. Structural modeling techniques by finite element method

    International Nuclear Information System (INIS)

    Kang, Yeong Jin; Kim, Geung Hwan; Ju, Gwan Jeong

    1991-01-01

    This book includes introduction table of contents chapter 1 finite element idealization introduction summary of the finite element method equilibrium and compatibility in the finite element solution degrees of freedom symmetry and anti symmetry modeling guidelines local analysis example references chapter 2 static analysis structural geometry finite element models analysis procedure modeling guidelines references chapter 3 dynamic analysis models for dynamic analysis dynamic analysis procedures modeling guidelines and modeling guidelines.

  13. TRIP: a finite element computer program for the solution of convection heat transfer problems

    International Nuclear Information System (INIS)

    Slagter, W.; Roodbergen, H.A.

    1976-01-01

    The theory and use of the finite element code TRIP are described. The code calculates temperature distributions in three-dimensional continua subjected to convection heat transfer. A variational principle for transport phenomena is applied to solve the convection heat transfer problem with temperature and heat flux boundary conditions. The finite element discretization technique is used to reduce the continuous spatial solution into a finite number of unknowns. The method is developed in detail to determine temperature distributions in coolant passages of fuel rod bundles which are idealized by hexahedral elements. The development of the TRIP code is discussed and the listing of the program is given in FORTRAN IV. An example is given to illustrate the validity and practicality of the method

  14. 3D adaptive finite element method for a phase field model for the moving contact line problems

    KAUST Repository

    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.

  15. Finite element methods a practical guide

    CERN Document Server

    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.

  16. ABOUT SOLUTION OF MULTIPOINT BOUNDARY PROBLEMS OF TWO-DIMENSIONAL STRUCTURAL ANALYSIS WITH THE USE OF COMBINED APPLICATION OF FINITE ELEMENT METHOD AND DISCRETE-CONTINUAL FINITE ELEMENT METHOD PART 2: SPECIAL ASPECTS OF FINITE ELEMENT APPROXIMATION

    Directory of Open Access Journals (Sweden)

    Pavel A. Akimov

    2017-12-01

    Full Text Available As is well known, the formulation of a multipoint boundary problem involves three main components: a description of the domain occupied by the structure and the corresponding subdomains; description of the conditions inside the domain and inside the corresponding subdomains, the description of the conditions on the boundary of the domain, conditions on the boundaries between subdomains. This paper is a continuation of another work published earlier, in which the formulation and general principles of the approximation of the multipoint boundary problem of a static analysis of deep beam on the basis of the joint application of the finite element method and the discrete-continual finite element method were considered. It should be noted that the approximation within the fragments of a domain that have regular physical-geometric parameters along one of the directions is expedient to be carried out on the basis of the discrete-continual finite element method (DCFEM, and for the approximation of all other fragments it is necessary to use the standard finite element method (FEM. In the present publication, the formulas for the computing of displacements partial derivatives of displacements, strains and stresses within the finite element model (both within the finite element and the corresponding nodal values (with the use of averaging are presented. Boundary conditions between subdomains (respectively, discrete models and discrete-continual models and typical conditions such as “hinged support”, “free edge”, “perfect contact” (twelve basic (basic variants are available are under consideration as well. Governing formulas for computing of elements of the corresponding matrices of coefficients and vectors of the right-hand sides are given for each variant. All formulas are fully adapted for algorithmic implementation.

  17. Element-topology-independent preconditioners for parallel finite element computations

    Science.gov (United States)

    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.

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

    Energy Technology Data Exchange (ETDEWEB)

    Mohamed, M. Shadi, E-mail: m.s.mohamed@durham.ac.uk [School of Engineering and Computing Sciences, University of Durham, South Road, Durham DH1 3LE (United Kingdom); Seaid, Mohammed; Trevelyan, Jon [School of Engineering and Computing Sciences, University of Durham, South Road, Durham DH1 3LE (United Kingdom); Laghrouche, Omar [Institute for Infrastructure and Environment, Heriot-Watt University, Edinburgh EH14 4AS (United Kingdom)

    2013-10-15

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

  19. Electrical machine analysis using finite elements

    CERN Document Server

    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

  20. Finite element method for solving Kohn-Sham equations based on self-adaptive tetrahedral mesh

    International Nuclear Information System (INIS)

    Zhang Dier; Shen Lihua; Zhou Aihui; Gong Xingao

    2008-01-01

    A finite element (FE) method with self-adaptive mesh-refinement technique is developed for solving the density functional Kohn-Sham equations. The FE method adopts local piecewise polynomials basis functions, which produces sparsely structured matrices of Hamiltonian. The method is well suitable for parallel implementation without using Fourier transform. In addition, the self-adaptive mesh-refinement technique can control the computational accuracy and efficiency with optimal mesh density in different regions

  1. 3D CSEM inversion based on goal-oriented adaptive finite element method

    Science.gov (United States)

    Zhang, Y.; Key, K.

    2016-12-01

    We present a parallel 3D frequency domain controlled-source electromagnetic inversion code name MARE3DEM. Non-linear inversion of observed data is performed with the Occam variant of regularized Gauss-Newton optimization. The forward operator is based on the goal-oriented finite element method that efficiently calculates the responses and sensitivity kernels in parallel using a data decomposition scheme where independent modeling tasks contain different frequencies and subsets of the transmitters and receivers. To accommodate complex 3D conductivity variation with high flexibility and precision, we adopt the dual-grid approach where the forward mesh conforms to the inversion parameter grid and is adaptively refined until the forward solution converges to the desired accuracy. This dual-grid approach is memory efficient, since the inverse parameter grid remains independent from fine meshing generated around the transmitter and receivers by the adaptive finite element method. Besides, the unstructured inverse mesh efficiently handles multiple scale structures and allows for fine-scale model parameters within the region of interest. Our mesh generation engine keeps track of the refinement hierarchy so that the map of conductivity and sensitivity kernel between the forward and inverse mesh is retained. We employ the adjoint-reciprocity method to calculate the sensitivity kernels which establish a linear relationship between changes in the conductivity model and changes in the modeled responses. Our code uses a direcy solver for the linear systems, so the adjoint problem is efficiently computed by re-using the factorization from the primary problem. Further computational efficiency and scalability is obtained in the regularized Gauss-Newton portion of the inversion using parallel dense matrix-matrix multiplication and matrix factorization routines implemented with the ScaLAPACK library. We show the scalability, reliability and the potential of the algorithm to deal with

  2. Adaptive finite element analysis of incompressible viscous flow using posteriori error estimation and control of node density distribution

    International Nuclear Information System (INIS)

    Yashiki, Taturou; Yagawa, Genki; Okuda, Hiroshi

    1995-01-01

    The adaptive finite element method based on an 'a posteriori error estimation' is known to be a powerful technique for analyzing the engineering practical problems, since it excludes the instinctive aspect of the mesh subdivision and gives high accuracy with relatively low computational cost. In the adaptive procedure, both the error estimation and the mesh generation according to the error estimator are essential. In this paper, the adaptive procedure is realized by the automatic mesh generation based on the control of node density distribution, which is decided according to the error estimator. The global percentage error, CPU time, the degrees of freedom and the accuracy of the solution of the adaptive procedure are compared with those of the conventional method using regular meshes. Such numerical examples as the driven cavity flows of various Reynolds numbers and the flows around a cylinder have shown the very high performance of the proposed adaptive procedure. (author)

  3. Precise magnetostatic field using the finite element method; Calculo de campos magnetostaticos com precisao utilizando o metodo dos elementos finitos

    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)

  4. An adaptive finite element method for simulating surface tension with the gradient theory of fluid interfaces

    KAUST Repository

    Kou, Jisheng; Sun, Shuyu

    2014-01-01

    The gradient theory for the surface tension of simple fluids and mixtures is rigorously analyzed based on mathematical theory. The finite element approximation of surface tension is developed and analyzed, and moreover, an adaptive finite element method based on a physical-based estimator is proposed and it can be coupled efficiently with Newton's method as well. The numerical tests are carried out both to verify the proposed theory and to demonstrate the efficiency of the proposed method. © 2013 Elsevier B.V. All rights reserved.

  5. An adaptive finite element method for simulating surface tension with the gradient theory of fluid interfaces

    KAUST Repository

    Kou, Jisheng

    2014-01-01

    The gradient theory for the surface tension of simple fluids and mixtures is rigorously analyzed based on mathematical theory. The finite element approximation of surface tension is developed and analyzed, and moreover, an adaptive finite element method based on a physical-based estimator is proposed and it can be coupled efficiently with Newton\\'s method as well. The numerical tests are carried out both to verify the proposed theory and to demonstrate the efficiency of the proposed method. © 2013 Elsevier B.V. All rights reserved.

  6. Solution of finite element problems using hybrid parallelization with MPI and OpenMP Solution of finite element problems using hybrid parallelization with MPI and OpenMP

    Directory of Open Access Journals (Sweden)

    José Miguel Vargas-Félix

    2012-11-01

    Full Text Available The Finite Element Method (FEM is used to solve problems like solid deformation and heat diffusion in domains with complex geometries. This kind of geometries requires discretization with millions of elements; this is equivalent to solve systems of equations with sparse matrices and tens or hundreds of millions of variables. The aim is to use computer clusters to solve these systems. The solution method used is Schur substructuration. Using it is possible to divide a large system of equations into many small ones to solve them more efficiently. This method allows parallelization. MPI (Message Passing Interface is used to distribute the systems of equations to solve each one in a computer of a cluster. Each system of equations is solved using a solver implemented to use OpenMP as a local parallelization method.The Finite Element Method (FEM is used to solve problems like solid deformation and heat diffusion in domains with complex geometries. This kind of geometries requires discretization with millions of elements; this is equivalent to solve systems of equations with sparse matrices and tens or hundreds of millions of variables. The aim is to use computer clusters to solve these systems. The solution method used is Schur substructuration. Using it is possible to divide a large system of equations into many small ones to solve them more efficiently. This method allows parallelization. MPI (Message Passing Interface is used to distribute the systems of equations to solve each one in a computer of a cluster. Each system of equations is solved using a solver implemented to use OpenMP as a local parallelization method.

  7. Solution of the diffusion equations for several groups by the finite elements method

    International Nuclear Information System (INIS)

    Arredondo S, C.

    1975-01-01

    The code DELFIN has been implemented for the solution of the neutrons diffusion equations in two dimensions obtained by applying the approximation of several groups of energy. The code works with any number of groups and regions, and can be applied to thermal reactors as well as fast reactor. Providing it with the diffusion coefficients, the effective sections and the fission spectrum we obtain the results for the systems multiplying constant and the flows of each groups. The code was established using the method of finite elements, which is a form of resolution of the variational formulation of the equations applying the Ritz-Galerkin method with continuous polynomial functions by parts, in one case of the Lagrange type with rectangular geometry and up to the third grade. The obtained results and the comparison with the results in the literature, permit to reach the conclusion that it is convenient, to use the rectangular elements in all the cases where the geometry permits it, and demonstrate also that the finite elements method is better than the finite differences method. (author)

  8. Finite-element solutions of the AER-2 rod ejection benchmark by CRONOS

    International Nuclear Information System (INIS)

    Kolev, N.P.; Lenain, R.; Fedon-Magnaud, C.

    2001-01-01

    The finite-element option in CRONOS was used to analyse the AER-2 rod-ejection benchmark for WWER-440. The objective is to obtain spatially converged solutions by means of node subdivision and approximation refinement. This paper presents the first phase of analysis dealing with the initial and just-ejected states used for calculation of the initial reactivity. Fine-mesh and extrapolated to zero mesh size solutions were obtained and verified by comparison to MAG code solutions. These differences provide potential for large deviations in the transient results and deserve further attention in reactor safety analysis (Authors)

  9. Adaptive Finite Element Methods for Elliptic Problems with Discontinuous Coefficients

    KAUST Repository

    Bonito, Andrea; DeVore, Ronald A.; Nochetto, Ricardo H.

    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.

  10. A geometric toolbox for tetrahedral finite element partitions

    NARCIS (Netherlands)

    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.

  11. Application of Mass Lumped Higher Order Finite Elements

    International Nuclear Information System (INIS)

    J. Chen, H.R. Strauss, S.C. Jardin, W. Park, L.E. Sugiyama, G. Fu, J. Breslau

    2005-01-01

    There are many interesting phenomena in extended-MHD such as anisotropic transport, mhd, 2-fluid effects stellarator and hot particles. Any one of them challenges numerical analysts, and researchers are seeking for higher order methods, such as higher order finite difference, higher order finite elements and hp/spectral elements. It is true that these methods give more accurate solution than their linear counterparts. However, numerically they are prohibitively expensive. Here we give a successful solution of this conflict by applying mass lumped higher order finite elements. This type of elements not only keep second/third order accuracy but also scale closely to linear elements by doing mass lumping. This is especially true for second order lump elements. Full M3D and anisotropic transport models are studied

  12. The finite element method in engineering, 2nd edition

    International Nuclear Information System (INIS)

    Rao, S.S.

    1986-01-01

    This work provides a systematic introduction to the various aspects of the finite element method as applied to engineering problems. Contents include: introduction to finite element method; solution of finite element equations; solid and structural mechanics; static analysis; dynamic analysis; heat transfer; fluid mechanics and additional applications

  13. Parametric optimization and design validation based on finite element analysis of hybrid socket adapter for transfemoral prosthetic knee.

    Science.gov (United States)

    Kumar, Neelesh

    2014-10-01

    Finite element analysis has been universally employed for the stress and strain analysis in lower extremity prosthetics. The socket adapter was the principal subject of interest due to its importance in deciding the knee motion range. This article focused on the static and dynamic stress analysis of the designed hybrid adapter developed by the authors. A standard mechanical design validation approach using von Mises was followed. Four materials were considered for the analysis, namely, carbon fiber, oil-filled nylon, Al-6061, and mild steel. The paper analyses the static and dynamic stress on designed hybrid adapter which incorporates features of conventional male and female socket adapters. The finite element analysis was carried out for possible different angles of knee flexion simulating static and dynamic gait situation. Research was carried out on available design of socket adapter. Mechanical design of hybrid adapter was conceptualized and a CAD model was generated using Inventor modelling software. Static and dynamic stress analysis was carried out on different materials for optimization. The finite element analysis was carried out on the software Autodesk Inventor Professional Ver. 2011. The peak value of von Mises stress occurred in the neck region of the adapter and in the lower face region at rod eye-adapter junction in static and dynamic analyses, respectively. Oil-filled nylon was found to be the best material among the four with respect to strength, weight, and cost. Research investigations on newer materials for development of improved prosthesis will immensely benefit the amputees. The study analyze the static and dynamic stress on the knee joint adapter to provide better material used for hybrid design of adapter. © The International Society for Prosthetics and Orthotics 2013.

  14. Bimetal cup hydroforming of Al/St and Cu/St composites: Adaptive finite element analysis and experimental study

    Energy Technology Data Exchange (ETDEWEB)

    Hashemi, Abbas; Gollo, Mohammad Hoseinpour [Shahid Rajaee Teacher Training University, Tehran (Iran, Islamic Republic of); Seyedkashi, S. M. [University of Birjand, Birjand (Iran, Islamic Republic of)

    2016-05-15

    An adaptive Finite element analysis (FEA) was proposed in this paper for the industrial design of bimetal conical-cylindrical cup hydroforming. Forming circumstances for the perfect and imperfect parts were concluded through adaptive FEA using the ANSYS parametric design language. Effective parameters, including pressure loading path, layer placement order, and thickness ratio, were investigated for hydroforming of Al/St and Cu/St composite sheets. Experimental tests were implemented to validate adaptive finite element results. Rupture failure upon the pressure path occurred on the contact area between the blank and punch tip radius at low pressures and on the transition area of the conical-cylindrical portion at high pressures. The proposed method is applicable for any cylindrical, conical, or cylindrical/conical shapes with different materials and dimensions. Therefore, this method is beneficial as a practical design tool for engineers and researchers working in the process design of hydroformed shell products.

  15. Towards a unified solution of localization failure with mixed finite elements

    Science.gov (United States)

    Benedetti, Lorenzo; Cervera, Miguel; Chiumenti, Michele; Zeidler, Antonia; Fischer, Jan-Thomas

    2015-04-01

    Notwithstanding computational scientists made significant steps in the numerical simulation of failure in last three decades, the strain localization problem is still an open question. Especially in a geotechnical setting, when dealing with stability analysis of slopes, it is necessary to provide correct distribution of displacements, to evaluate the stresses in the ground and, therefore, to be able to identify the slip lines that brings to progressive collapse of the slope. Finite elements are an attractive method of solution thanks to profound mathematical foundations and the possibility of describing generic geometries. In order to account for the onset of localization band, the smeared crack approach [1] is introduced, that is the strain localization is assumed to occur in a band of finite width where the displacements are continuous and the strains are discontinuous but bounded. It is well known that this kind of approach poses some challenges. The standard irreducible formulation of FEM is known to be heavily affected by spurious mesh dependence when softening behavior occurs and, consequently, slip lines evolution is biased by the orientation of the mesh. Moreover, in the case of isochoric behavior, unbounded pressure oscillations arise and the consequent locking of the stresses pollutes the numerical solution. Both problems can be shown not to be related to the mathematical statement of the continuous problem but instead to its discrete (FEM) counterpart. Mixed finite element formulations represent a suitable alternative to mitigate these drawbacks. As it has been shown in previous works by Cervera [2], a mixed formulation in terms of displacements and pressure not only provides a propitious solution to the problem of incompressibility, but also it was found to possess the needed robustness in case of strain concentration. This presentation introduces a (stabilized) mixed finite element formulation with continuous linear strain and displacement

  16. Finite element computation of plasma equilibria

    International Nuclear Information System (INIS)

    Rivier, M.

    1977-01-01

    The applicability of the finite element method is investigated for the numerical solution of the nonlinear Grad-Shafranov equation with free boundary for the flux function of a plasma at equilibrium. This method is based on the case of variational principles and finite dimensional subspaces whose elements are piecewise polynomial functions obtained by a Lagrange type interpolation procedure over a triangulation of the domain. Two cases of plasma pressure (exponential and quadratic including a vacuum region) were examined. In both cases the nonuniqueness of the solutions was shown in exhibiting a deeper solution in the case of exponential pressure function, and a non-constant solution for a quadratic pressure function. In order to get this ''other'' solution, two linearization methods were tested with two different constraints. Different cross sections are investigated

  17. SOLUTION OF TRANSIENT HEAT CONDUCTION PROBLEM BY THE FINITE ELEMENT METHOD

    Directory of Open Access Journals (Sweden)

    Süleyman TAŞGETİREN

    1995-01-01

    Full Text Available Determination of temperature distribution is generally the first step in the design of machine elements subjected to ubnormal temperatures in their service life and for selection of materials. During this heat transfer analysis, the boundary and enviromental conditions must be modeled realistically and the geometry must be well represented. A variety of materials deviating from simple constant property isotropic material to composit materials having different properties according to direction of reinforcements are to be analysed. Then, the finite element method finds a large application area due to its use of same notation in heat transfer analysis and mechanical analysis of elements. In this study, the general formulation of two dimensional transient heat conduction is developed and a sample solution is given for arectangular bar subjected to convection baundary condition.

  18. Adaptive Multilevel Methods with Local Smoothing for $H^1$- and $H^{\\mathrm{curl}}$-Conforming High Order Finite Element Methods

    KAUST Repository

    Janssen, Bä rbel; Kanschat, Guido

    2011-01-01

    A multilevel method on adaptive meshes with hanging nodes is presented, and the additional matrices appearing in the implementation are derived. Smoothers of overlapping Schwarz type are discussed; smoothing is restricted to the interior of the subdomains refined to the current level; thus it has optimal computational complexity. When applied to conforming finite element discretizations of elliptic problems and Maxwell equations, the method's convergence rates are very close to those for the nonadaptive version. Furthermore, the smoothers remain efficient for high order finite elements. We discuss the implementation in a general finite element code using the example of the deal.II library. © 2011 Societ y for Industrial and Applied Mathematics.

  19. Solution of three-dimensional energy equation using finite element method

    International Nuclear Information System (INIS)

    Bhasin, V.; Singh, R.K.; Dutta, B.K.; Kushwaha, H.S.

    1993-01-01

    In the present work an attempt has been made to formulate an efficient 3-D finite element program for solving coupled momentum-energy equation with unsymmetric frontal solver and a suitable upwinding scheme. Based on the above solution technique of energy equation it can be concluded that upwinding scheme can lead to fairly accurate and smooth results even with coarse mesh. Otherwise the mesh size requirement will be extremely stringent for most of the practical problems. With upwinding the additional computer time required is marginally more. This effort has resulted in getting practical solution for large size real life problems in nuclear industry. The program was used for computation of temperature field in heavy water moderator of Madras Atomic Power Station (MAPS) reactor, in new mode of operation. (author). 9 refs., 7 figs

  20. Mesh-size errors in diffusion-theory calculations using finite-difference and finite-element methods

    International Nuclear Information System (INIS)

    Baker, A.R.

    1982-07-01

    A study has been performed of mesh-size errors in diffusion-theory calculations using finite-difference and finite-element methods. As the objective was to illuminate the issues, the study was performed for a 1D slab model of a reactor with one neutron-energy group for which analytical solutions were possible. A computer code SLAB was specially written to perform the finite-difference and finite-element calculations and also to obtain the analytical solutions. The standard finite-difference equations were obtained by starting with an expansion of the neutron current in powers of the mesh size, h, and keeping terms as far as h 2 . It was confirmed that these equations led to the well-known result that the criticality parameter varied with the square of the mesh size. An improved form of the finite-difference equations was obtained by continuing the expansion for the neutron current as far as the term in h 4 . In this case, the critical parameter varied as the fourth power of the mesh size. The finite-element solutions for 2 and 3 nodes per element revealed that the criticality parameter varied as the square and fourth power of the mesh size, respectively. Numerical results are presented for a bare reactive core of uniform composition with 2 zones of different uniform mesh and for a reactive core with an absorptive reflector. (author)

  1. 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.

  2. Finite element analysis of rotating beams physics based interpolation

    CERN Document Server

    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.

  3. Adaptive Multilevel Methods with Local Smoothing for $H^1$- and $H^{\\mathrm{curl}}$-Conforming High Order Finite Element Methods

    KAUST Repository

    Janssen, Bärbel

    2011-01-01

    A multilevel method on adaptive meshes with hanging nodes is presented, and the additional matrices appearing in the implementation are derived. Smoothers of overlapping Schwarz type are discussed; smoothing is restricted to the interior of the subdomains refined to the current level; thus it has optimal computational complexity. When applied to conforming finite element discretizations of elliptic problems and Maxwell equations, the method\\'s convergence rates are very close to those for the nonadaptive version. Furthermore, the smoothers remain efficient for high order finite elements. We discuss the implementation in a general finite element code using the example of the deal.II library. © 2011 Societ y for Industrial and Applied Mathematics.

  4. A posteriori estimator and adaptive mesh refinement for finite volume finite element method for monophasic flow and solute transport in porous media

    International Nuclear Information System (INIS)

    Amor, H.; Bourgeois, M.

    2012-01-01

    Document available in extended abstract form only. The disposal of high level, long lived waste in deep underground clay formations is investigated by several countries including France. In the safety assessment of such geological repositories, a thoughtful consideration must be given to the mechanisms and possible pathways of migration of radionuclides released from waste packages. However, when modelling the transfer of radionuclides throughout the disposal facilities and geological formations, the numerical simulations must take into consideration, in addition to long durations of concern, the variety in the properties as well as in geometrical scales of the different components of the overall disposal, including the host formation. This task presents significant computational challenges. Numerical methods used in the MELODIE software The MELODIE software is developed by IRSN, and constantly upgraded, with the aim to assess the long-term containment capabilities of underground and surface radioactive waste repositories. The MELODIE software models water flow and the phenomena involved in the transport of radionuclides in saturated and unsaturated porous media in 2 and 3 dimensions; chemical processes are represented by a retardation factor and a solubility limit, for sorption and solubility respectively, integrated in the computational equations. These equations are discretized using a so-called Finite Volume Finite Element method (FVFE), which is based on a Galerkin method to discretize time and variables, together with a Finite Volume method using the Godunov scheme for the convection term. The FVFE method is used to convert partial differential equations into a finite number of algebraic equations that match the number of nodes in the mesh used to model the considered domain. It is also used to stabilise the numerical scheme. In order to manage the variety in properties and geometrical scales of underground disposal components, an a posteriori error estimator

  5. A review of some a posteriori error estimates for adaptive finite element methods

    Czech Academy of Sciences Publication Activity Database

    Segeth, Karel

    2010-01-01

    Roč. 80, č. 8 (2010), s. 1589-1600 ISSN 0378-4754. [European Seminar on Coupled Problems. Jetřichovice, 08.06.2008-13.06.2008] R&D Projects: GA AV ČR(CZ) IAA100190803 Institutional research plan: CEZ:AV0Z10190503 Keywords : hp-adaptive finite element method * a posteriori error estimators * computational error estimates Subject RIV: BA - General Mathematics Impact factor: 0.812, year: 2010 http://www.sciencedirect.com/science/article/pii/S0378475408004230

  6. Australopithecus anamensis: a finite-element approach to studying the functional adaptations of extinct hominins.

    Science.gov (United States)

    Macho, Gabriele A; Shimizu, Daisuke; Jiang, Yong; Spears, Iain R

    2005-04-01

    Australopithecus anamensis is the stem species of all later hominins and exhibits the suite of characters traditionally associated with hominins, i.e., bipedal locomotion when on the ground, canine reduction, and thick-enameled teeth. The functional consequences of its thick enamel are, however, unclear. Without appropriate structural reinforcement, these thick-enameled teeth may be prone to failure. This article investigates the mechanical behavior of A. anamensis enamel and represents the first in a series that will attempt to determine the functional adaptations of hominin teeth. First, the microstructural arrangement of enamel prisms in A. anamensis teeth was reconstructed using recently developed software and was compared with that of extant hominoids. Second, a finite-element model of a block of enamel containing one cycle of prism deviation was reconstructed for Homo, Pan, Gorilla, and A. anamensis and the behavior of these tissues under compressive stress was determined. Despite similarities in enamel microstructure between A. anamensis and the African great apes, the structural arrangement of prismatic enamel in A. anamensis appears to be more effective in load dissipation under these compressive loads. The findings may imply that this hominin species was well adapted to puncture crushing and are in some respects contrary to expectations based on macromorphology of teeth. Taking together, information obtained from both finite-element analyses and dental macroanatomy leads us to suggest that A. anamensis was probably adapted for habitually consuming a hard-tough diet. However, additional tests are needed to understand the functional adaptations of A. anamensis teeth fully.

  7. Simulation of Stress Concentration Problems in Laminated Plates by Quasi-Trefftz Finite Element Models

    Directory of Open Access Journals (Sweden)

    Flávio Luiz de Silva Bussamra

    Full Text Available Abstract Hybrid quasi-Trefftz finite elements have been applied with success to the analysis of laminated plates. Two independent fields are approximated by linearly independent, hierarchical polynomials: the stress basis in the domain, adapted from Papkovitch-Neuber solution of Navier equations, and the displacement basis, defined on element surface. The stress field that satisfies the Trefftz constraint a priori for isotropic material is adapted for orthotropic materials, which leads to the term "quasi". In this work, the hexahedral hybrid quasi-Trefftz stress element is applied to the modeling of nonsymmetric laminates and laminated composite plates with geometric discontinuities. The hierarchical p-refinement is exploited.

  8. On Round-off Error for Adaptive Finite Element Methods

    KAUST Repository

    Alvarez-Aramberri, J.

    2012-06-02

    Round-off error analysis has been historically studied by analyzing the condition number of the associated matrix. By controlling the size of the condition number, it is possible to guarantee a prescribed round-off error tolerance. However, the opposite is not true, since it is possible to have a system of linear equations with an arbitrarily large condition number that still delivers a small round-off error. In this paper, we perform a round-off error analysis in context of 1D and 2D hp-adaptive Finite Element simulations for the case of Poisson equation. We conclude that boundary conditions play a fundamental role on the round-off error analysis, specially for the so-called ‘radical meshes’. Moreover, we illustrate the importance of the right-hand side when analyzing the round-off error, which is independent of the condition number of the matrix.

  9. On Round-off Error for Adaptive Finite Element Methods

    KAUST Repository

    Alvarez-Aramberri, J.; Pardo, David; Paszynski, Maciej; Collier, Nathan; Dalcin, Lisandro; Calo, Victor M.

    2012-01-01

    Round-off error analysis has been historically studied by analyzing the condition number of the associated matrix. By controlling the size of the condition number, it is possible to guarantee a prescribed round-off error tolerance. However, the opposite is not true, since it is possible to have a system of linear equations with an arbitrarily large condition number that still delivers a small round-off error. In this paper, we perform a round-off error analysis in context of 1D and 2D hp-adaptive Finite Element simulations for the case of Poisson equation. We conclude that boundary conditions play a fundamental role on the round-off error analysis, specially for the so-called ‘radical meshes’. Moreover, we illustrate the importance of the right-hand side when analyzing the round-off error, which is independent of the condition number of the matrix.

  10. Complex finite element sensitivity method for creep analysis

    International Nuclear Information System (INIS)

    Gomez-Farias, Armando; Montoya, Arturo; Millwater, Harry

    2015-01-01

    The complex finite element method (ZFEM) has been extended to perform sensitivity analysis for mechanical and structural systems undergoing creep deformation. ZFEM uses a complex finite element formulation to provide shape, material, and loading derivatives of the system response, providing an insight into the essential factors which control the behavior of the system as a function of time. A complex variable-based quadrilateral user element (UEL) subroutine implementing the power law creep constitutive formulation was incorporated within the Abaqus commercial finite element software. The results of the complex finite element computations were verified by comparing them to the reference solution for the steady-state creep problem of a thick-walled cylinder in the power law creep range. A practical application of the ZFEM implementation to creep deformation analysis is the calculation of the skeletal point of a notched bar test from a single ZFEM run. In contrast, the standard finite element procedure requires multiple runs. The value of the skeletal point is that it identifies the location where the stress state is accurate, regardless of the certainty of the creep material properties. - Highlights: • A novel finite element sensitivity method (ZFEM) for creep was introduced. • ZFEM has the capability to calculate accurate partial derivatives. • ZFEM can be used for identification of the skeletal point of creep structures. • ZFEM can be easily implemented in a commercial software, e.g. Abaqus. • ZFEM results were shown to be in excellent agreement with analytical solutions

  11. On the application of finite element method in the solution of steady state diffusion equation

    International Nuclear Information System (INIS)

    Ono, S.

    1982-01-01

    The solution of the steady state neutron diffusion equation is obtained by using the finite element method. Specifically the variational approach is used for one dimensional problems and the weighted residual method (Galerkin) for one and two dimensional problems. The spatial domain is divided into retangular elements and the neutron flux is approximated by linear (one dimensional case), and bilinear (two-dimensional case) functions. Numerical results are obtained with a FORTRAN IV computer program and compared with those obtained by the finite difference CITATION code. The results show that linear or bilinear functions, do not satisfactorily describe the differential parameters in highly heterogeneous reactor cases, but provide good results for integral parameters such as multiplication factor. (Author) [pt

  12. Development of polygon elements based on the scaled boundary finite element method

    International Nuclear Information System (INIS)

    Chiong, Irene; Song Chongmin

    2010-01-01

    We aim to extend the scaled boundary finite element method to construct conforming polygon elements. The development of the polygonal finite element is highly anticipated in computational mechanics as greater flexibility and accuracy can be achieved using these elements. The scaled boundary polygonal finite element will enable new developments in mesh generation, better accuracy from a higher order approximation and better transition elements in finite element meshes. Polygon elements of arbitrary number of edges and order have been developed successfully. The edges of an element are discretised with line elements. The displacement solution of the scaled boundary finite element method is used in the development of shape functions. They are shown to be smooth and continuous within the element, and satisfy compatibility and completeness requirements. Furthermore, eigenvalue decomposition has been used to depict element modes and outcomes indicate the ability of the scaled boundary polygonal element to express rigid body and constant strain modes. Numerical tests are presented; the patch test is passed and constant strain modes verified. Accuracy and convergence of the method are also presented and the performance of the scaled boundary polygonal finite element is verified on Cook's swept panel problem. Results show that the scaled boundary polygonal finite element method outperforms a traditional mesh and accuracy and convergence are achieved from fewer nodes. The proposed method is also shown to be truly flexible, and applies to arbitrary n-gons formed of irregular and non-convex polygons.

  13. A variational numerical method based on finite elements for the nonlinear solution characteristics of the periodically forced Chen system

    Science.gov (United States)

    Khan, Sabeel M.; Sunny, D. A.; Aqeel, M.

    2017-09-01

    Nonlinear dynamical systems and their solutions are very sensitive to initial conditions and therefore need to be approximated carefully. In this article, we present and analyze nonlinear solution characteristics of the periodically forced Chen system with the application of a variational method based on the concept of finite time-elements. Our approach is based on the discretization of physical time space into finite elements where each time-element is mapped to a natural time space. The solution of the system is then determined in natural time space using a set of suitable basis functions. The numerical algorithm is presented and implemented to compute and analyze nonlinear behavior at different time-step sizes. The obtained results show an excellent agreement with the classical RK-4 and RK-5 methods. The accuracy and convergence of the method is shown by comparing numerically computed results with the exact solution for a test problem. The presented method has shown a great potential in dealing with the solutions of nonlinear dynamical systems and thus can be utilized in delineating different features and characteristics of their solutions.

  14. Thermal stresses in rectangular plates: variational and finite element solutions

    International Nuclear Information System (INIS)

    Laura, P.A.A.; Gutierrez, R.H.; Sanchez Sarmiento, G.; Basombrio, F.G.

    1978-01-01

    This paper deals with the development of an approximate method for the analysis of thermal stresses in rectangular plates (plane stress problem) and an evaluation of the relative accuracy of the finite element method. The stress function is expanded in terms of polynomial coordinate functions which identically satisfy the boundary conditions, and a variational approach is used to determine the expansion coefficients. The results are in good agreement with a finite element approach. (Auth.)

  15. SANTOS - a two-dimensional finite element program for the quasistatic, large deformation, inelastic response of solids

    Energy Technology Data Exchange (ETDEWEB)

    Stone, C.M.

    1997-07-01

    SANTOS is a finite element program designed to compute the quasistatic, large deformation, inelastic response of two-dimensional planar or axisymmetric solids. The code is derived from the transient dynamic code PRONTO 2D. The solution strategy used to compute the equilibrium states is based on a self-adaptive dynamic relaxation solution scheme, which is based on explicit central difference pseudo-time integration and artificial mass proportional damping. The element used in SANTOS is a uniform strain 4-node quadrilateral element with an hourglass control scheme to control the spurious deformation modes. Finite strain constitutive models for many common engineering materials are included. A robust master-slave contact algorithm for modeling sliding contact is implemented. An interface for coupling to an external code is also provided. 43 refs., 22 figs.

  16. Seakeeping with the semi-Lagrangian particle finite element method

    Science.gov (United States)

    Nadukandi, Prashanth; Servan-Camas, Borja; Becker, Pablo Agustín; Garcia-Espinosa, Julio

    2017-07-01

    The application of the semi-Lagrangian particle finite element method (SL-PFEM) for the seakeeping simulation of the wave adaptive modular vehicle under spray generating conditions is presented. The time integration of the Lagrangian advection is done using the explicit integration of the velocity and acceleration along the streamlines (X-IVAS). Despite the suitability of the SL-PFEM for the considered seakeeping application, small time steps were needed in the X-IVAS scheme to control the solution accuracy. A preliminary proposal to overcome this limitation of the X-IVAS scheme for seakeeping simulations is presented.

  17. Numerical experiment on finite element method for matching data

    International Nuclear Information System (INIS)

    Tokuda, Shinji; Kumakura, Toshimasa; Yoshimura, Koichi.

    1993-03-01

    Numerical experiments are presented on the finite element method by Pletzer-Dewar for matching data of an ordinary differential equation with regular singular points by using model equation. Matching data play an important role in nonideal MHD stability analysis of a magnetically confined plasma. In the Pletzer-Dewar method, the Frobenius series for the 'big solution', the fundamental solution which is not square-integrable at the regular singular point, is prescribed. The experiments include studies of the convergence rate of the matching data obtained by the finite element method and of the effect on the results of computation by truncating the Frobenius series at finite terms. It is shown from the present study that the finite element method is an effective method for obtaining the matching data with high accuracy. (author)

  18. Finite element time domain modeling of controlled-Source electromagnetic data with a hybrid boundary condition

    DEFF Research Database (Denmark)

    Cai, Hongzhu; Hu, Xiangyun; Xiong, Bin

    2017-01-01

    method which is unconditionally stable. We solve the diffusion equation for the electric field with a total field formulation. The finite element system of equation is solved using the direct method. The solutions of electric field, at different time, can be obtained using the effective time stepping...... method with trivial computation cost once the matrix is factorized. We try to keep the same time step size for a fixed number of steps using an adaptive time step doubling (ATSD) method. The finite element modeling domain is also truncated using a semi-adaptive method. We proposed a new boundary...... condition based on approximating the total field on the modeling boundary using the primary field corresponding to a layered background model. We validate our algorithm using several synthetic model studies....

  19. A numerical comparison between the multiple-scales and finite-element solution for sound propagation in lined flow ducts

    NARCIS (Netherlands)

    Rienstra, S.W.; Eversman, W.

    2001-01-01

    An explicit, analytical, multiple-scales solution for modal sound transmission through slowly varying ducts with mean flow and acoustic lining is tested against a numerical finite-element solution solving the same potential flow equations. The test geometry taken is representative of a high-bypass

  20. Solution of the neutron diffusion equation at two groups of energy by method of triangular finite elements

    International Nuclear Information System (INIS)

    Correia Filho, A.

    1981-04-01

    The Neutron Diffusion Equation at two groups of energy is solved with the use of the Finite - Element Method with first order triangular elements. The program EFTDN (Triangular Finite Elements on Neutron Diffusion) was developed using the language FORTRAN IV. The discrete formulation of the Diffusion Equation is obtained with the application of the Galerkin's Method. In order to solve the eigenvalue - problem, the Method of the Power is applied and, with the purpose of the convergence of the results, Chebshev's polynomial expressions are applied. On the solution of the systems of equations Gauss' Method is applied, divided in two different parts: triangularization of the matrix of coeficients and retrosubstitution taking in account the sparsity of the system. Several test - problems are solved, among then two P.W.R. type reactors, the ZION-1 with 1300 MWe and the 2D-IAEA - Benchmark. Comparision of results with standard solutions show the validity of application of the EFM and precision of the results. (Author) [pt

  1. Advances in 3D electromagnetic finite element modeling

    International Nuclear Information System (INIS)

    Nelson, E.M.

    1997-01-01

    Numerous advances in electromagnetic finite element analysis (FEA) have been made in recent years. The maturity of frequency domain and eigenmode calculations, and the growth of time domain applications is briefly reviewed. A high accuracy 3D electromagnetic finite element field solver employing quadratic hexahedral elements and quadratic mixed-order one-form basis functions will also be described. The solver is based on an object-oriented C++ class library. Test cases demonstrate that frequency errors less than 10 ppm can be achieved using modest workstations, and that the solutions have no contamination from spurious modes. The role of differential geometry and geometrical physics in finite element analysis is also discussed

  2. Numerical solution of recirculating flow by a simple finite element recursion relation

    Energy Technology Data Exchange (ETDEWEB)

    Pepper, D W; Cooper, R E

    1980-01-01

    A time-split finite element recursion relation, based on linear basis functions, is used to solve the two-dimensional equations of motion. Recirculating flow in a rectangular cavity and free convective flow in an enclosed container are analyzed. The relation has the advantage of finite element accuracy and finite difference speed and simplicity. Incorporating dissipation parameters in the functionals decreases numerical dispersion and improves phase lag.

  3. Direct numerical simulations of particle-laden density currents with adaptive, discontinuous finite elements

    Directory of Open Access Journals (Sweden)

    S. D. Parkinson

    2014-09-01

    Full Text Available High-resolution direct numerical simulations (DNSs are an important tool for the detailed analysis of turbidity current dynamics. Models that resolve the vertical structure and turbulence of the flow are typically based upon the Navier–Stokes equations. Two-dimensional simulations are known to produce unrealistic cohesive vortices that are not representative of the real three-dimensional physics. The effect of this phenomena is particularly apparent in the later stages of flow propagation. The ideal solution to this problem is to run the simulation in three dimensions but this is computationally expensive. This paper presents a novel finite-element (FE DNS turbidity current model that has been built within Fluidity, an open source, general purpose, computational fluid dynamics code. The model is validated through re-creation of a lock release density current at a Grashof number of 5 × 106 in two and three dimensions. Validation of the model considers the flow energy budget, sedimentation rate, head speed, wall normal velocity profiles and the final deposit. Conservation of energy in particular is found to be a good metric for measuring model performance in capturing the range of dynamics on a range of meshes. FE models scale well over many thousands of processors and do not impose restrictions on domain shape, but they are computationally expensive. The use of adaptive mesh optimisation is shown to reduce the required element count by approximately two orders of magnitude in comparison with fixed, uniform mesh simulations. This leads to a substantial reduction in computational cost. The computational savings and flexibility afforded by adaptivity along with the flexibility of FE methods make this model well suited to simulating turbidity currents in complex domains.

  4. Computing the dynamics of biomembranes by combining conservative level set and adaptive finite element methods

    OpenAIRE

    Laadhari , Aymen; Saramito , Pierre; Misbah , Chaouqi

    2014-01-01

    International audience; The numerical simulation of the deformation of vesicle membranes under simple shear external fluid flow is considered in this paper. A new saddle-point approach is proposed for the imposition of the fluid incompressibility and the membrane inextensibility constraints, through Lagrange multipliers defined in the fluid and on the membrane respectively. Using a level set formulation, the problem is approximated by mixed finite elements combined with an automatic adaptive ...

  5. A study on the nonlinear finite element analysis of reinforced concrete structures: shell finite element formulation

    Energy Technology Data Exchange (ETDEWEB)

    Lee, Sang Jin; Seo, Jeong Moon

    2000-08-01

    The main goal of this research is to establish a methodology of finite element analysis of containment building predicting not only global behaviour but also local failure mode. In this report, we summerize some existing numerical analysis techniques to be improved for containment building. In other words, a complete description of the standard degenerated shell finite element formulation is provided for nonlinear stress analysis of nuclear containment structure. A shell finite element is derived using the degenerated solid concept which does not rely on a specific shell theory. Reissner-Mindlin assumptions are adopted to consider the transverse shear deformation effect. In order to minimize the sensitivity of the constitutive equation to structural types, microscopic material model is adopted. The four solution algorithms based on the standard Newton-Raphson method are discussed. Finally, two numerical examples are carried out to test the performance of the adopted shell medel.

  6. A study on the nonlinear finite element analysis of reinforced concrete structures: shell finite element formulation

    International Nuclear Information System (INIS)

    Lee, Sang Jin; Seo, Jeong Moon

    2000-08-01

    The main goal of this research is to establish a methodology of finite element analysis of containment building predicting not only global behaviour but also local failure mode. In this report, we summerize some existing numerical analysis techniques to be improved for containment building. In other words, a complete description of the standard degenerated shell finite element formulation is provided for nonlinear stress analysis of nuclear containment structure. A shell finite element is derived using the degenerated solid concept which does not rely on a specific shell theory. Reissner-Mindlin assumptions are adopted to consider the transverse shear deformation effect. In order to minimize the sensitivity of the constitutive equation to structural types, microscopic material model is adopted. The four solution algorithms based on the standard Newton-Raphson method are discussed. Finally, two numerical examples are carried out to test the performance of the adopted shell medel

  7. Finite element solution of two dimensional time dependent heat equation

    International Nuclear Information System (INIS)

    Maaz

    1999-01-01

    A Microsoft Windows based computer code, named FHEAT, has been developed for solving two dimensional heat problems in Cartesian and Cylindrical geometries. The programming language is Microsoft Visual Basic 3.0. The code makes use of Finite element formulation for spatial domain and Finite difference formulation for time domain. Presently the code is capable of solving two dimensional steady state and transient problems in xy- and rz-geometries. The code is capable excepting both triangular and rectangular elements. Validation and benchmarking was done against hand calculations and published results. (author)

  8. Numerical solution of critical state in superconductivity by finite element software

    Energy Technology Data Exchange (ETDEWEB)

    Hong, Z; Campbell, A M; Coombs, T A [Cambridge University Engineering Department, Trumpington Street, Cambridge CB2 1PZ (United Kingdom)

    2006-12-15

    A numerical method is proposed to analyse the electromagnetic behaviour of systems including high-temperature superconductors (HTSCs) in time-varying external fields and superconducting cables carrying AC transport current. The E-J constitutive law together with an H-formulation is used to calculate the current distribution and electromagnetic fields in HTSCs, and the magnetization of HTSCs; then the forces in the interaction between the electromagnet and the superconductor and the AC loss of the superconducting cable can be obtained. This numerical method is based on solving the partial differential equations time dependently and is adapted to the commercial finite element software Comsol Multiphysics 3.2. The advantage of this method is to make the modelling of the superconductivity simple, flexible and extendable.

  9. High accuracy 3D electromagnetic finite element analysis

    International Nuclear Information System (INIS)

    Nelson, Eric M.

    1997-01-01

    A high accuracy 3D electromagnetic finite element field solver employing quadratic hexahedral elements and quadratic mixed-order one-form basis functions will be described. The solver is based on an object-oriented C++ class library. Test cases demonstrate that frequency errors less than 10 ppm can be achieved using modest workstations, and that the solutions have no contamination from spurious modes. The role of differential geometry and geometrical physics in finite element analysis will also be discussed

  10. High accuracy 3D electromagnetic finite element analysis

    International Nuclear Information System (INIS)

    Nelson, E.M.

    1996-01-01

    A high accuracy 3D electromagnetic finite element field solver employing quadratic hexahedral elements and quadratic mixed-order one-form basis functions will be described. The solver is based on an object-oriented C++ class library. Test cases demonstrate that frequency errors less than 10 ppm can be achieved using modest workstations, and that the solutions have no contamination from spurious modes. The role of differential geometry and geometrical physics in finite element analysis will also be discussed

  11. Finite element electromagnetic field computation on the Sequent Symmetry 81 parallel computer

    International Nuclear Information System (INIS)

    Ratnajeevan, S.; Hoole, H.

    1990-01-01

    Finite element field analysis algorithms lend themselves to parallelization and this fact is exploited in this paper to implement a finite element analysis program for electromagnetic field computation on the Sequent Symmetry 81 parallel computer with three processors. In terms of waiting time, the maximum gains are to be made in matrix solution and therefore this paper concentrates on the gains in parallelizing the solution part of finite element analysis. An outline of how parallelization could be exploited in most finite element operations is given in this paper although the actual implemention of parallelism on the Sequent Symmetry 81 parallel computer was in sparsity computation, matrix assembly and the matrix solution areas. In all cases, the algorithms were modified suit the parallel programming application rather than allowing the compiler to parallelize on existing algorithms

  12. Modeling of heterogeneous elastic materials by the multiscale hp-adaptive finite element method

    Science.gov (United States)

    Klimczak, Marek; Cecot, Witold

    2018-01-01

    We present an enhancement of the multiscale finite element method (MsFEM) by combining it with the hp-adaptive FEM. Such a discretization-based homogenization technique is a versatile tool for modeling heterogeneous materials with fast oscillating elasticity coefficients. No assumption on periodicity of the domain is required. In order to avoid direct, so-called overkill mesh computations, a coarse mesh with effective stiffness matrices is used and special shape functions are constructed to account for the local heterogeneities at the micro resolution. The automatic adaptivity (hp-type at the macro resolution and h-type at the micro resolution) increases efficiency of computation. In this paper details of the modified MsFEM are presented and a numerical test performed on a Fichera corner domain is presented in order to validate the proposed approach.

  13. Use of heterogeneous finite elements generated by collision probability solutions to calculate a pool reactor core

    International Nuclear Information System (INIS)

    Calabrese, C.R.; Grant, C.R.

    1990-01-01

    This work presents comparisons between measured fluxes obtained by activation of Manganese foils in the light water, enriched uranium research pool reactor RA-2 MTR (Materials Testing Reactors) fuel element) and fluxes calculated by the finite element method FEM using DELFIN code, and describes the heterogeneus finite elements by a set of solutions of the transport equations for several different configurations obtained using the collision probability code HUEMUL. The agreement between calculated and measured fluxes is good, and the advantage of using FEM is showed because to obtain the flux distribution with same detail using an usual diffusion calculation it would be necessary 12000 mesh points against the 2000 points that FEM uses, hence the processing time is reduced in a factor ten. An interesting alternative to use in MTR fuel management is presented. (Author) [es

  14. Finite-element method modeling of hyper-frequency structures

    International Nuclear Information System (INIS)

    Zhang, Min

    1990-01-01

    The modelization of microwave propagation problems, including Eigen-value problem and scattering problem, is accomplished by the finite element method with vector functional and scalar functional. For Eigen-value problem, propagation modes in waveguides and resonant modes in cavities can be calculated in a arbitrarily-shaped structure with inhomogeneous material. Several microwave structures are resolved in order to verify the program. One drawback associated with the vector functional is the appearance of spurious or non-physical solutions. A penalty function method has been introduced to reduce spurious' solutions. The adaptive charge method is originally proposed in this thesis to resolve waveguide scattering problem. This method, similar to VSWR measuring technique, is more efficient to obtain the reflection coefficient than the matrix method. Two waveguide discontinuity structures are calculated by the two methods and their results are compared. The adaptive charge method is also applied to a microwave plasma excitor. It allows us to understand the role of different physical parameters of excitor in the coupling of microwave energy to plasma mode and the mode without plasma. (author) [fr

  15. Finite-element time-domain modeling of electromagnetic data in general dispersive medium using adaptive Padé series

    Science.gov (United States)

    Cai, Hongzhu; Hu, Xiangyun; Xiong, Bin; Zhdanov, Michael S.

    2017-12-01

    The induced polarization (IP) method has been widely used in geophysical exploration to identify the chargeable targets such as mineral deposits. The inversion of the IP data requires modeling the IP response of 3D dispersive conductive structures. We have developed an edge-based finite-element time-domain (FETD) modeling method to simulate the electromagnetic (EM) fields in 3D dispersive medium. We solve the vector Helmholtz equation for total electric field using the edge-based finite-element method with an unstructured tetrahedral mesh. We adopt the backward propagation Euler method, which is unconditionally stable, with semi-adaptive time stepping for the time domain discretization. We use the direct solver based on a sparse LU decomposition to solve the system of equations. We consider the Cole-Cole model in order to take into account the frequency-dependent conductivity dispersion. The Cole-Cole conductivity model in frequency domain is expanded using a truncated Padé series with adaptive selection of the center frequency of the series for early and late time. This approach can significantly increase the accuracy of FETD modeling.

  16. Preliminary Formulation of Finite Element Solution for the 1-D, 1-G Time Dependent Neutron Diffusion Equation without Consideration about Delay Neutron

    Energy Technology Data Exchange (ETDEWEB)

    Ryu, Eun Hyun; Song, Yong Mann; Park, Joo Hwan [Korea Atomic Energy Research Institute, Daejeon (Korea, Republic of)

    2013-05-15

    If time-dependent equation is solved with the FEM, the limitation of the input geometry will disappear. It has often been pointed out that the numerical methods implemented in the RFSP code are not state-of-the-art. Although an acceleration method such as the Coarse Mesh Finite Difference (CMFD) for Finite Difference Method (FDM) does not exist for the FEM, one should keep in mind that the number of time steps for the transient simulation is not large. The rigorous formulation in this study will richen the theoretical basis of the FEM and lead to an extension of the dynamics code to deal with a more complicated problem. In this study, the formulation for the 1-D, 1-G Time Dependent Neutron Diffusion Equation (TDNDE) without consideration of the delay neutron will first be done. A problem including one multiplying medium will be solved. Also several conclusions from a comparison between the numerical and analytic solutions, a comparison between solutions with various element orders, and a comparison between solutions with different time differencing will be made to be certain about the formulation and FEM solution. By investigating various cases with different values of albedo, theta, and the order of elements, it can be concluded that the finite element solution is agree well with the analytic solution. The higher the element order used, the higher the accuracy improvements are obtained.

  17. A parallel direct solver for the self-adaptive hp Finite Element Method

    KAUST Repository

    Paszyński, Maciej R.

    2010-03-01

    In this paper we present a new parallel multi-frontal direct solver, dedicated for the hp Finite Element Method (hp-FEM). The self-adaptive hp-FEM generates in a fully automatic mode, a sequence of hp-meshes delivering exponential convergence of the error with respect to the number of degrees of freedom (d.o.f.) as well as the CPU time, by performing a sequence of hp refinements starting from an arbitrary initial mesh. The solver constructs an initial elimination tree for an arbitrary initial mesh, and expands the elimination tree each time the mesh is refined. This allows us to keep track of the order of elimination for the solver. The solver also minimizes the memory usage, by de-allocating partial LU factorizations computed during the elimination stage of the solver, and recomputes them for the backward substitution stage, by utilizing only about 10% of the computational time necessary for the original computations. The solver has been tested on 3D Direct Current (DC) borehole resistivity measurement simulations problems. We measure the execution time and memory usage of the solver over a large regular mesh with 1.5 million degrees of freedom as well as on the highly non-regular mesh, generated by the self-adaptive h p-FEM, with finite elements of various sizes and polynomial orders of approximation varying from p = 1 to p = 9. From the presented experiments it follows that the parallel solver scales well up to the maximum number of utilized processors. The limit for the solver scalability is the maximum sequential part of the algorithm: the computations of the partial LU factorizations over the longest path, coming from the root of the elimination tree down to the deepest leaf. © 2009 Elsevier Inc. All rights reserved.

  18. Preliminary analysis of construction of the test drift in boom clay at Mol using plasticity solutions and finite elements

    International Nuclear Information System (INIS)

    Mair, R.J.; Taylor, R.N.; Higgins, K.G.; Potts, D.M.

    1989-01-01

    Analyses have been undertaken on an advancing tunnel heading at great depth in a clay formation corresponding to the test drift construction at Mol. Belgium. Simplifying assumptions enable plasticity solutions to be used to model the behaviour of a tunnel heading in a linear elastic-perfectly plastic soil. Finite element analysis with the same soil model has been undertaken of the test drift construction, assuming axisymmetric conditions. The results are compared with the plasticity solutions and with the measurements of lining stresses, soil movements and pore pressures by SCK/CEN. Good agreement is obtained between the plasticity solutions and finite element analysis. The measured immediate build-up of stress on the linings is well-predicted and reasonable agreement is obtained between predicted and measured soil movements. The measured pore-pressure changes are poorly predicted by the analyses

  19. An approximative solution for limit load of piping branch junctions with circumferential crack and finite element validation

    International Nuclear Information System (INIS)

    Xuan Fuzhen; Liu Changjun; Li Peining

    2005-01-01

    This paper is concerned with the prediction of limit load of the piping branch junctions with circumferential crack under internal pressure. Recently, we have developed a new approach for predicting the limit load of two-cylinder intersection structures with diameter ratio larger than 0.5, which has been successfully applied to defect free cases under various loading conditions. In the present work, we consider the extension of the approach to cover cracked piping branch junctions. On the basis of stress analysis in the vicinity of intersection line, a closed form of limit load solution for piping branch junctions with circumferential crack was developed. Then, 36 finite element (FE) models of piping branch junction with various dimensions of structure and crack were analyzed by using nonlinear finite element software. The limit loads from FE analysis and the proposed solution are compared with each other. Overall good agreement between the estimated solutions and the FE results provides confidence in the use of the proposed formulae for defect assessment of piping branch junctions in practice

  20. Matrix equation decomposition and parallel solution of systems resulting from unstructured finite element problems in electromagnetics

    Energy Technology Data Exchange (ETDEWEB)

    Cwik, T. [California Institute of Technology, Pasadena, CA (United States); Katz, D.S. [Cray Research, El Segundo, CA (United States)

    1996-12-31

    Finite element modeling has proven useful for accurately simulating scattered or radiated electromagnetic fields from complex three-dimensional objects whose geometry varies on the scale of a fraction of an electrical wavelength. An unstructured finite element model of realistic objects leads to a large, sparse, system of equations that needs to be solved efficiently with regard to machine memory and execution time. Both factorization and iterative solvers can be used to produce solutions to these systems of equations. Factorization leads to high memory requirements that limit the electrical problem size of three-dimensional objects that can be modeled. An iterative solver can be used to efficiently solve the system without excessive memory use and in a minimal amount of time if the convergence rate is controlled.

  1. Simple one-dimensional finite element algorithm with multi-dimensional capabilities

    International Nuclear Information System (INIS)

    Pepper, D.W.; Baker, A.J.

    1978-01-01

    The application of the finite element procedure for the solution of partial differential equations is gaining widespread acceptance. The ability of the finite element procedure to solve problems which are arbitrarily shaped as well as the alleviation of boundary condition problems is well known. By using local interpolation functionals over each subdomain, or element, a set of linearized algebraic equations are obtained which can be solved using any direct, iterative, or inverse numerical technique. Subsequent use of an explicit or implicit integration procedure permits closure of the solution over the global domain

  2. High accuracy 3D electromagnetic finite element analysis

    International Nuclear Information System (INIS)

    Nelson, E.M.

    1997-01-01

    A high accuracy 3D electromagnetic finite element field solver employing quadratic hexahedral elements and quadratic mixed-order one-form basis functions will be described. The solver is based on an object-oriented C++ class library. Test cases demonstrate that frequency errors less than 10 ppm can be achieved using modest workstations, and that the solutions have no contamination from spurious modes. The role of differential geometry and geometrical physics in finite element analysis will also be discussed. copyright 1997 American Institute of Physics

  3. Implementation of advanced finite element technology in structural analysis computer codes

    International Nuclear Information System (INIS)

    Kohli, T.D.; Wiley, J.W.; Koss, P.W.

    1975-01-01

    Advances in finite element technology over the last several years have been rapid and have largely outstripped the ability of general purpose programs in the public domain to assimilate them. As a result, it has become the burden of the structural analyst to incorporate these advances himself. This paper discusses the implementation and extension of specific technological advances in Bechtel structural analysis programs. In general these advances belong in two categories: (1) the finite elements themselves and (2) equation solution algorithms. Improvements in the finite elements involve increased accuracy of the elements and extension of their applicability to various specialized modelling situations. Improvements in solution algorithms have been almost exclusively aimed at expanding problem solving capacity. (Auth.)

  4. Fast solution of neutron diffusion problem by reduced basis finite element method

    International Nuclear Information System (INIS)

    Chunyu, Zhang; Gong, Chen

    2018-01-01

    Highlights: •An extremely efficient method is proposed to solve the neutron diffusion equation with varying the cross sections. •Three orders of speedup is achieved for IAEA benchmark problems. •The method may open a new possibility of efficient high-fidelity modeling of large scale problems in nuclear engineering. -- Abstract: For the important applications which need carry out many times of neutron diffusion calculations such as the fuel depletion analysis and the neutronics-thermohydraulics coupling analysis, fast and accurate solutions of the neutron diffusion equation are demanding but necessary. In the present work, the certified reduced basis finite element method is proposed and implemented to solve the generalized eigenvalue problems of neutron diffusion with variable cross sections. The order reduced model is built upon high-fidelity finite element approximations during the offline stage. During the online stage, both the k eff and the spatical distribution of neutron flux can be obtained very efficiently for any given set of cross sections. Numerical tests show that a speedup of around 1100 is achieved for the IAEA two-dimensional PWR benchmark problem and a speedup of around 3400 is achieved for the three-dimensional counterpart with the fission cross-sections, the absorption cross-sections and the scattering cross-sections treated as parameters.

  5. The finite element response matrix method

    International Nuclear Information System (INIS)

    Nakata, H.; Martin, W.R.

    1983-02-01

    A new technique is developed with an alternative formulation of the response matrix method implemented with the finite element scheme. Two types of response matrices are generated from the Galerkin solution to the weak form of the diffusion equation subject to an arbitrary current and source. The piecewise polynomials are defined in two levels, the first for the local (assembly) calculations and the second for the global (core) response matrix calculations. This finite element response matrix technique was tested in two 2-dimensional test problems, 2D-IAEA benchmark problem and Biblis benchmark problem, with satisfatory results. The computational time, whereas the current code is not extensively optimized, is of the same order of the well estabilished coarse mesh codes. Furthermore, the application of the finite element technique in an alternative formulation of response matrix method permits the method to easily incorporate additional capabilities such as treatment of spatially dependent cross-sections, arbitrary geometrical configurations, and high heterogeneous assemblies. (Author) [pt

  6. Finite element analysis of inelastic structural behavior

    International Nuclear Information System (INIS)

    Argyris, J.H.; Szimmat, J.; Willam, K.J.

    1977-01-01

    The paper describes recent achievements in the finite element analysis of inelastic material behavior. The main purpose is to examine the interaction of three disciplines; (i) the finite element formulation of large deformation problems in the light of a systematic linearization, (ii) the constitutive modelling of inelastic processes in the rate-dependent and rate-independent response regime and (iii) the numerical solution of nonlinear rate problems via incremental iteration techniques. In the first part, alternative finite element models are developed for the idealization of large deformation problems. A systematic approach is presented to linearize the field equations locally by an incremental procedure. The finite element formulation is then examined for the description of inelastic material processes. In the second part, nonlinear and inelastic material phenomena are classified and illustrated with representative examples of concrete and metal components. In particular, rate-dependent and rate-independent material behavior is examined and representative constitutive models are assessed for their mathematical characterization. Hypoelastic, elastoplastic and endochronic models are compared for the description rate-independent material phenomena. In the third part, the numerial solution of inelastic structural behavior is discussed. In this context, several incremental techniques are developed and compared for tracing the evolution of the inelastic process. The numerical procedures are examined with regard to stability and accuracy to assess the overall efficiency. The 'optimal' incremental technique is then contrasted with the computer storage requirements to retain the data for the 'memory-characteristics' of the constitutive model

  7. About solution of multipoint boundary problem of static analysis of deep beam with the use of combined application of finite element method and discrete-continual finite element method. part 1: formulation of the problem and general principles of approximation

    Directory of Open Access Journals (Sweden)

    Lyakhovich Leonid

    2017-01-01

    Full Text Available This paper is devoted to formulation and general principles of approximation of multipoint boundary problem of static analysis of deep beam with the use of combined application of finite element method (FEM discrete-continual finite element method (DCFEM. The field of application of DCFEM comprises structures with regular physical and geometrical parameters in some dimension (“basic” dimension. DCFEM presupposes finite element approximation for non-basic dimension while in the basic dimension problem remains continual. DCFEM is based on analytical solutions of resulting multipoint boundary problems for systems of ordinary differential equations with piecewise-constant coefficients.

  8. Basic Finite Element Method

    International Nuclear Information System (INIS)

    Lee, Byeong Hae

    1992-02-01

    This book gives descriptions of basic finite element method, which includes basic finite element method and data, black box, writing of data, definition of VECTOR, definition of matrix, matrix and multiplication of matrix, addition of matrix, and unit matrix, conception of hardness matrix like spring power and displacement, governed equation of an elastic body, finite element method, Fortran method and programming such as composition of computer, order of programming and data card and Fortran card, finite element program and application of nonelastic problem.

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

    Science.gov (United States)

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

    2010-09-20

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

  10. Comparison of 3-D finite elements for incompressible fluid flow

    International Nuclear Information System (INIS)

    Robichaud, M.; Tanguy, P.A.

    1985-01-01

    In recent years, the finite element method applied to the solution of incompressible fluid flow has been in constant evolution. In the present state-of-the-art, 2-D problems are solved routinely and reliable results are obtained at a reasonable cost. In 3-D the finite element method is still undergoing active research and many methods have been proposed to solve the Navier-Stokes equations at 'low cost'. These methods have in common the choice of the element which has a trilinear velocity and a discontinuous constant pressure (Q1-PO). The prohibitive cost of 3-D finite element method in fluid flow is the reason for this choice: the Q1-PO is the simplest and the cheapest 3-D element. However, as mentioned in (5) and (6), it generates 'spurious' pressure modes phenomenon called checkerboarding. On regular mesh these spurious modes can be filtered but on distorted mesh the pressure solution is meaningless. (author)

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

    Science.gov (United States)

    Bartels, Robert E.

    2005-01-01

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

  12. An Experimental and Finite Element Protocol to Investigate the Transport of Neutral and Charged Solutes across Articular Cartilage.

    Science.gov (United States)

    Arbabi, Vahid; Pouran, Behdad; Zadpoor, Amir A; Weinans, Harrie

    2017-04-23

    Osteoarthritis (OA) is a debilitating disease that is associated with degeneration of articular cartilage and subchondral bone. Degeneration of articular cartilage impairs its load-bearing function substantially as it experiences tremendous chemical degradation, i.e. proteoglycan loss and collagen fibril disruption. One promising way to investigate chemical damage mechanisms during OA is to expose the cartilage specimens to an external solute and monitor the diffusion of the molecules. The degree of cartilage damage (i.e. concentration and configuration of essential macromolecules) is associated with collisional energy loss of external solutes while moving across articular cartilage creates different diffusion characteristics compared to healthy cartilage. In this study, we introduce a protocol, which consists of several steps and is based on previously developed experimental micro-Computed Tomography (micro-CT) and finite element modeling. The transport of charged and uncharged iodinated molecules is first recorded using micro-CT, which is followed by applying biphasic-solute and multiphasic finite element models to obtain diffusion coefficients and fixed charge densities across cartilage zones.

  13. Advances in dynamic relaxation techniques for nonlinear finite element analysis

    International Nuclear Information System (INIS)

    Sauve, R.G.; Metzger, D.R.

    1995-01-01

    Traditionally, the finite element technique has been applied to static and steady-state problems using implicit methods. When nonlinearities exist, equilibrium iterations must be performed using Newton-Raphson or quasi-Newton techniques at each load level. In the presence of complex geometry, nonlinear material behavior, and large relative sliding of material interfaces, solutions using implicit methods often become intractable. A dynamic relaxation algorithm is developed for inclusion in finite element codes. The explicit nature of the method avoids large computer memory requirements and makes possible the solution of large-scale problems. The method described approaches the steady-state solution with no overshoot, a problem which has plagued researchers in the past. The method is included in a general nonlinear finite element code. A description of the method along with a number of new applications involving geometric and material nonlinearities are presented. They include: (1) nonlinear geometric cantilever plate; (2) moment-loaded nonlinear beam; and (3) creep of nuclear fuel channel assemblies

  14. New mixed finite-element methods

    International Nuclear Information System (INIS)

    Franca, L.P.

    1987-01-01

    New finite-element methods are proposed for mixed variational formulations. The methods are constructed by adding to the classical Galerkin method various least-squares like terms. The additional terms involve integrals over element interiors, and include mesh-parameter dependent coefficients. The methods are designed to enhance stability. Consistency is achieved in the sense that exact solutions identically satisfy the variational equations.Applied to several problems, simple finite-element interpolations are rendered convergent, including convenient equal-order interpolations generally unstable within the Galerkin approach. The methods are subdivided into two classes according to the manner in which stability is attained: (1) circumventing Babuska-Brezzi condition methods; (2) satisfying Babuska-Brezzi condition methods. Convergence is established for each class of methods. Applications of the first class of methods to Stokes flow and compressible linear elasticity are presented. The second class of methods is applied to the Poisson, Timoshenko beam and incompressible elasticity problems. Numerical results demonstrate the good stability and accuracy of the methods, and confirm the error estimates

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

    Science.gov (United States)

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

    2014-01-01

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

  16. Finite Volume Element (FVE) discretization and multilevel solution of the axisymmetric heat equation

    Science.gov (United States)

    Litaker, Eric T.

    1994-12-01

    The axisymmetric heat equation, resulting from a point-source of heat applied to a metal block, is solved numerically; both iterative and multilevel solutions are computed in order to compare the two processes. The continuum problem is discretized in two stages: finite differences are used to discretize the time derivatives, resulting is a fully implicit backward time-stepping scheme, and the Finite Volume Element (FVE) method is used to discretize the spatial derivatives. The application of the FVE method to a problem in cylindrical coordinates is new, and results in stencils which are analyzed extensively. Several iteration schemes are considered, including both Jacobi and Gauss-Seidel; a thorough analysis of these schemes is done, using both the spectral radii of the iteration matrices and local mode analysis. Using this discretization, a Gauss-Seidel relaxation scheme is used to solve the heat equation iteratively. A multilevel solution process is then constructed, including the development of intergrid transfer and coarse grid operators. Local mode analysis is performed on the components of the amplification matrix, resulting in the two-level convergence factors for various combinations of the operators. A multilevel solution process is implemented by using multigrid V-cycles; the iterative and multilevel results are compared and discussed in detail. The computational savings resulting from the multilevel process are then discussed.

  17. A finite element conjugate gradient FFT method for scattering

    Science.gov (United States)

    Collins, Jeffery D.; Ross, Dan; Jin, J.-M.; Chatterjee, A.; Volakis, John L.

    1991-01-01

    Validated results are presented for the new 3D body of revolution finite element boundary integral code. A Fourier series expansion of the vector electric and mangnetic fields is employed to reduce the dimensionality of the system, and the exact boundary condition is employed to terminate the finite element mesh. The mesh termination boundary is chosen such that is leads to convolutional boundary operatores of low O(n) memory demand. Improvements of this code are discussed along with the proposed formulation for a full 3D implementation of the finite element boundary integral method in conjunction with a conjugate gradiant fast Fourier transformation (CGFFT) solution.

  18. Moving mesh finite element method for finite time extinction of distributed parameter systems with positive exponential feedback

    International Nuclear Information System (INIS)

    Garnadi, A.D.

    1997-01-01

    In the distributed parameter systems with exponential feedback, non-global existence of solution is not always exist. For some positive initial values, there exist finite time T such that the solution goes to infinity, i.e. finite time extinction or blow-up. Here is present a numerical solution using Moving Mesh Finite Element to solve the distributed parameter systems with exponential feedback close to blow-up time. The numerical behavior of the mesh close to the time of extinction is the prime interest in this study

  19. Fluid-structure finite-element vibrational analysis

    Science.gov (United States)

    Feng, G. C.; Kiefling, L.

    1974-01-01

    A fluid finite element has been developed for a quasi-compressible fluid. Both kinetic and potential energy are expressed as functions of nodal displacements. Thus, the formulation is similar to that used for structural elements, with the only differences being that the fluid can possess gravitational potential, and the constitutive equations for fluid contain no shear coefficients. Using this approach, structural and fluid elements can be used interchangeably in existing efficient sparse-matrix structural computer programs such as SPAR. The theoretical development of the element formulations and the relationships of the local and global coordinates are shown. Solutions of fluid slosh, liquid compressibility, and coupled fluid-shell oscillation problems which were completed using a temporary digital computer program are shown. The frequency correlation of the solutions with classical theory is excellent.

  20. A Posteriori Error Estimation for Finite Element Methods and Iterative Linear Solvers

    Energy Technology Data Exchange (ETDEWEB)

    Melboe, Hallgeir

    2001-10-01

    This thesis addresses a posteriori error estimation for finite element methods and iterative linear solvers. Adaptive finite element methods have gained a lot of popularity over the last decades due to their ability to produce accurate results with limited computer power. In these methods a posteriori error estimates play an essential role. Not only do they give information about how large the total error is, they also indicate which parts of the computational domain should be given a more sophisticated treatment in order to reduce the error. A posteriori error estimates are traditionally aimed at estimating the global error, but more recently so called goal oriented error estimators have been shown a lot of interest. The name reflects the fact that they estimate the error in user-defined local quantities. In this thesis the main focus is on global error estimators for highly stretched grids and goal oriented error estimators for flow problems on regular grids. Numerical methods for partial differential equations, such as finite element methods and other similar techniques, typically result in a linear system of equations that needs to be solved. Usually such systems are solved using some iterative procedure which due to a finite number of iterations introduces an additional error. Most such algorithms apply the residual in the stopping criterion, whereas the control of the actual error may be rather poor. A secondary focus in this thesis is on estimating the errors that are introduced during this last part of the solution procedure. The thesis contains new theoretical results regarding the behaviour of some well known, and a few new, a posteriori error estimators for finite element methods on anisotropic grids. Further, a goal oriented strategy for the computation of forces in flow problems is devised and investigated. Finally, an approach for estimating the actual errors associated with the iterative solution of linear systems of equations is suggested. (author)

  1. Exponentially-convergent Monte Carlo via finite-element trial spaces

    International Nuclear Information System (INIS)

    Morel, Jim E.; Tooley, Jared P.; Blamer, Brandon J.

    2011-01-01

    Exponentially-Convergent Monte Carlo (ECMC) methods, also known as adaptive Monte Carlo and residual Monte Carlo methods, were the subject of intense research over a decade ago, but they never became practical for solving the realistic problems. We believe that the failure of previous efforts may be related to the choice of trial spaces that were global and thus highly oscillatory. As an alternative, we consider finite-element trial spaces, which have the ability to treat fully realistic problems. As a first step towards more general methods, we apply piecewise-linear trial spaces to the spatially-continuous two-stream transport equation. Using this approach, we achieve exponential convergence and computationally demonstrate several fundamental properties of finite-element based ECMC methods. Finally, our results indicate that the finite-element approach clearly deserves further investigation. (author)

  2. Quality-assurance study of the special-purpose finite-element program SPECTROM: II. Plasticity problems

    International Nuclear Information System (INIS)

    Callahan, G.D.; Fossum, A.F.

    1982-11-01

    General plasticity theory and solution techniques as are currently employed in RE/SPEC's finite element plasticity code SPECTROM-II are presented. Various yield functions are discussed and their differences are illustrated using example problems. Comparison of the results of SPECTROM-II with analytical solutions, numerical solutions, and the general purpose finite element program MARC-CDC show excellent agreement

  3. Generalized finite elements

    International Nuclear Information System (INIS)

    Wachspress, E.

    2009-01-01

    Triangles and rectangles are the ubiquitous elements in finite element studies. Only these elements admit polynomial basis functions. Rational functions provide a basis for elements having any number of straight and curved sides. Numerical complexities initially associated with rational bases precluded extensive use. Recent analysis has reduced these difficulties and programs have been written to illustrate effectiveness. Although incorporation in major finite element software requires considerable effort, there are advantages in some applications which warrant implementation. An outline of the basic theory and of recent innovations is presented here. (authors)

  4. Maxwell's equations in axisymmetrical geometry: coupling H(curl) finite element in volume and H(div) finite element in surface. The numerical code FuMel

    International Nuclear Information System (INIS)

    Cambon, S.; Lacoste, P.

    2011-01-01

    We propose a finite element method to solve the axisymmetric scattering problem posed on a regular bounded domain. Here we shall show how to reduce the initial 3D problem into a truncated sum of 2D independent problems posed into a meridian plane of the object. Each of these problem results in the coupling of a partial differential equation into the interior domain and an integral equation on the surface simulating the free space. Then variational volume and boundary integral formulations of Maxwell's equation on regular surfaces are derived. We introduce some general finite element adapted to cylindrical coordinates and constructed from nodal and mixed finite element both for the interior (volume) and for the integral equation (surface). (authors)

  5. 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.

  6. Domain Decomposition Solvers for Frequency-Domain Finite Element Equations

    KAUST Repository

    Copeland, Dylan

    2010-10-05

    The paper is devoted to fast iterative solvers for frequency-domain finite element equations approximating linear and nonlinear parabolic initial boundary value problems with time-harmonic excitations. Switching from the time domain to the frequency domain allows us to replace the expensive time-integration procedure by the solution of a simple linear elliptic system for the amplitudes belonging to the sine- and to the cosine-excitation or a large nonlinear elliptic system for the Fourier coefficients in the linear and nonlinear case, respectively. The fast solution of the corresponding linear and nonlinear system of finite element equations is crucial for the competitiveness of this method. © 2011 Springer-Verlag Berlin Heidelberg.

  7. Domain Decomposition Solvers for Frequency-Domain Finite Element Equations

    KAUST Repository

    Copeland, Dylan; Kolmbauer, Michael; Langer, Ulrich

    2010-01-01

    The paper is devoted to fast iterative solvers for frequency-domain finite element equations approximating linear and nonlinear parabolic initial boundary value problems with time-harmonic excitations. Switching from the time domain to the frequency domain allows us to replace the expensive time-integration procedure by the solution of a simple linear elliptic system for the amplitudes belonging to the sine- and to the cosine-excitation or a large nonlinear elliptic system for the Fourier coefficients in the linear and nonlinear case, respectively. The fast solution of the corresponding linear and nonlinear system of finite element equations is crucial for the competitiveness of this method. © 2011 Springer-Verlag Berlin Heidelberg.

  8. Finite element approximation to the even-parity transport equation

    International Nuclear Information System (INIS)

    Lewis, E.E.

    1981-01-01

    This paper studies the finite element method, a procedure for reducing partial differential equations to sets of algebraic equations suitable for solution on a digital computer. The differential equation is cast into the form of a variational principle, the resulting domain then subdivided into finite elements. The dependent variable is then approximated by a simple polynomial, and these are linked across inter-element boundaries by continuity conditions. The finite element method is tailored to a variety of transport problems. Angular approximations are formulated, and the extent of ray effect mitigation is examined. Complex trial functions are introduced to enable the inclusion of buckling approximations. The ubiquitous curved interfaces of cell calculations, and coarse mesh methods are also treated. A concluding section discusses limitations of the work to date and suggests possible future directions

  9. Linear finite element method for one-dimensional diffusion problems

    Energy Technology Data Exchange (ETDEWEB)

    Brandao, Michele A.; Dominguez, Dany S.; Iglesias, Susana M., E-mail: micheleabrandao@gmail.com, E-mail: dany@labbi.uesc.br, E-mail: smiglesias@uesc.br [Universidade Estadual de Santa Cruz (LCC/DCET/UESC), Ilheus, BA (Brazil). Departamento de Ciencias Exatas e Tecnologicas. Laboratorio de Computacao Cientifica

    2011-07-01

    We describe in this paper the fundamentals of Linear Finite Element Method (LFEM) applied to one-speed diffusion problems in slab geometry. We present the mathematical formulation to solve eigenvalue and fixed source problems. First, we discretized a calculus domain using a finite set of elements. At this point, we obtain the spatial balance equations for zero order and first order spatial moments inside each element. Then, we introduce the linear auxiliary equations to approximate neutron flux and current inside the element and architect a numerical scheme to obtain the solution. We offer numerical results for fixed source typical model problems to illustrate the method's accuracy for coarse-mesh calculations in homogeneous and heterogeneous domains. Also, we compare the accuracy and computational performance of LFEM formulation with conventional Finite Difference Method (FDM). (author)

  10. Finite elements methods in mechanics

    CERN Document Server

    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...

  11. Development of a three-dimensional neutron transport code DFEM based on the double finite element method

    International Nuclear Information System (INIS)

    Fujimura, Toichiro

    1996-01-01

    A three-dimensional neutron transport code DFEM has been developed by the double finite element method to analyze reactor cores with complex geometry as large fast reactors. Solution algorithm is based on the double finite element method in which the space and angle finite elements are employed. A reactor core system can be divided into some triangular and/or quadrangular prism elements, and the spatial distribution of neutron flux in each element is approximated with linear basis functions. As for the angular variables, various basis functions are applied, and their characteristics were clarified by comparison. In order to enhance the accuracy, a general method is derived to remedy the truncation errors at reflective boundaries, which are inherent in the conventional FEM. An adaptive acceleration method and the source extrapolation method were applied to accelerate the convergence of the iterations. The code structure is outlined and explanations are given on how to prepare input data. A sample input list is shown for reference. The eigenvalue and flux distribution for real scale fast reactors and the NEA benchmark problems were presented and discussed in comparison with the results of other transport codes. (author)

  12. Finite element solution of nonlinear eddy current problems with periodic excitation and its industrial applications.

    Science.gov (United States)

    Bíró, Oszkár; Koczka, Gergely; Preis, Kurt

    2014-05-01

    An efficient finite element method to take account of the nonlinearity of the magnetic materials when analyzing three-dimensional eddy current problems is presented in this paper. The problem is formulated in terms of vector and scalar potentials approximated by edge and node based finite element basis functions. The application of Galerkin techniques leads to a large, nonlinear system of ordinary differential equations in the time domain. The excitations are assumed to be time-periodic and the steady-state periodic solution is of interest only. This is represented either in the frequency domain as a finite Fourier series or in the time domain as a set of discrete time values within one period for each finite element degree of freedom. The former approach is the (continuous) harmonic balance method and, in the latter one, discrete Fourier transformation will be shown to lead to a discrete harmonic balance method. Due to the nonlinearity, all harmonics, both continuous and discrete, are coupled to each other. The harmonics would be decoupled if the problem were linear, therefore, a special nonlinear iteration technique, the fixed-point method is used to linearize the equations by selecting a time-independent permeability distribution, the so-called fixed-point permeability in each nonlinear iteration step. This leads to uncoupled harmonics within these steps. As industrial applications, analyses of large power transformers are presented. The first example is the computation of the electromagnetic field of a single-phase transformer in the time domain with the results compared to those obtained by traditional time-stepping techniques. In the second application, an advanced model of the same transformer is analyzed in the frequency domain by the harmonic balance method with the effect of the presence of higher harmonics on the losses investigated. Finally a third example tackles the case of direct current (DC) bias in the coils of a single-phase transformer.

  13. A parallel adaptive finite difference algorithm for petroleum reservoir simulation

    Energy Technology Data Exchange (ETDEWEB)

    Hoang, Hai Minh

    2005-07-01

    Adaptive finite differential for problems arising in simulation of flow in porous medium applications are considered. Such methods have been proven useful for overcoming limitations of computational resources and improving the resolution of the numerical solutions to a wide range of problems. By local refinement of the computational mesh where it is needed to improve the accuracy of solutions, yields better solution resolution representing more efficient use of computational resources than is possible with traditional fixed-grid approaches. In this thesis, we propose a parallel adaptive cell-centered finite difference (PAFD) method for black-oil reservoir simulation models. This is an extension of the adaptive mesh refinement (AMR) methodology first developed by Berger and Oliger (1984) for the hyperbolic problem. Our algorithm is fully adaptive in time and space through the use of subcycling, in which finer grids are advanced at smaller time steps than the coarser ones. When coarse and fine grids reach the same advanced time level, they are synchronized to ensure that the global solution is conservative and satisfy the divergence constraint across all levels of refinement. The material in this thesis is subdivided in to three overall parts. First we explain the methodology and intricacies of AFD scheme. Then we extend a finite differential cell-centered approximation discretization to a multilevel hierarchy of refined grids, and finally we are employing the algorithm on parallel computer. The results in this work show that the approach presented is robust, and stable, thus demonstrating the increased solution accuracy due to local refinement and reduced computing resource consumption. (Author)

  14. Object-oriented philosophy in designing adaptive finite-element package for 3D elliptic deferential equations

    Science.gov (United States)

    Zhengyong, R.; Jingtian, T.; Changsheng, L.; Xiao, X.

    2007-12-01

    Although adaptive finite-element (AFE) analysis is becoming more and more focused in scientific and engineering fields, its efficient implementations are remain to be a discussed problem as its more complex procedures. In this paper, we propose a clear C++ framework implementation to show the powerful properties of Object-oriented philosophy (OOP) in designing such complex adaptive procedure. In terms of the modal functions of OOP language, the whole adaptive system is divided into several separate parts such as the mesh generation or refinement, a-posterior error estimator, adaptive strategy and the final post processing. After proper designs are locally performed on these separate modals, a connected framework of adaptive procedure is formed finally. Based on the general elliptic deferential equation, little efforts should be added in the adaptive framework to do practical simulations. To show the preferable properties of OOP adaptive designing, two numerical examples are tested. The first one is the 3D direct current resistivity problem in which the powerful framework is efficiently shown as only little divisions are added. And then, in the second induced polarization£¨IP£©exploration case, new adaptive procedure is easily added which adequately shows the strong extendibility and re-usage of OOP language. Finally we believe based on the modal framework adaptive implementation by OOP methodology, more advanced adaptive analysis system will be available in future.

  15. Solution of Fokker–Planck equation by finite element and finite ...

    Indian Academy of Sciences (India)

    The response of a structural system to white noise excitation (delta-correlated) constitutes a Markov vector process whose transitional probability density function (TPDF) is governed by both the forward Fokker–Planck and backward Kolmogorov equations. Numerical solution of these equations by finite element and finite ...

  16. Application of hexagonal element scheme in finite element method to three-dimensional diffusion problem of fast reactors

    International Nuclear Information System (INIS)

    Ishiguro, Misako; Higuchi, Kenji

    1983-01-01

    The finite element method is applied in Galerkin-type approximation to three-dimensional neutron diffusion equations of fast reactors. A hexagonal element scheme is adopted for treating the hexagonal lattice which is typical for fast reactors. The validity of the scheme is verified by applying the scheme as well as alternative schemes to the neutron diffusion calculation of a gas-cooled fast reactor of actual scale. The computed results are compared with corresponding values obtained using the currently applied triangular-element and also with conventional finite difference schemes. The hexagonal finite element scheme is found to yield a reasonable solution to the problem taken up here, with some merit in terms of saving in computing time, but the resulting multiplication factor differs by 1% and the flux by 9% compared with the triangular mesh finite difference scheme. The finite element method, even in triangular element scheme, would appear to incur error in inadmissible amount and which could not be easily eliminated by refining the nodes. (author)

  17. Randomized Oversampling for Generalized Multiscale Finite Element Methods

    KAUST Repository

    Calo, Victor M.

    2016-03-23

    In this paper, we develop efficient multiscale methods for flows in heterogeneous media. We use the generalized multiscale finite element (GMsFEM) framework. GMsFEM approximates the solution space locally using a few multiscale basis functions. This approximation selects an appropriate snapshot space and a local spectral decomposition, e.g., the use of oversampled regions, in order to achieve an efficient model reduction. However, the successful construction of snapshot spaces may be costly if too many local problems need to be solved in order to obtain these spaces. We use a moderate quantity of local solutions (or snapshot vectors) with random boundary conditions on oversampled regions with zero forcing to deliver an efficient methodology. Motivated by the randomized algorithm presented in [P. G. Martinsson, V. Rokhlin, and M. Tygert, A Randomized Algorithm for the approximation of Matrices, YALEU/DCS/TR-1361, Yale University, 2006], we consider a snapshot space which consists of harmonic extensions of random boundary conditions defined in a domain larger than the target region. Furthermore, we perform an eigenvalue decomposition in this small space. We study the application of randomized sampling for GMsFEM in conjunction with adaptivity, where local multiscale spaces are adaptively enriched. Convergence analysis is provided. We present representative numerical results to validate the method proposed.

  18. On the Robustness and Prospects of Adaptive BDDC Methods for Finite Element Discretizations of Elliptic PDEs with High-Contrast Coefficients

    KAUST Repository

    Zampini, Stefano

    2016-06-02

    Balancing Domain Decomposition by Constraints (BDDC) methods have proven to be powerful preconditioners for large and sparse linear systems arising from the finite element discretization of elliptic PDEs. Condition number bounds can be theoretically established that are independent of the number of subdomains of the decomposition. The core of the methods resides in the design of a larger and partially discontinuous finite element space that allows for fast application of the preconditioner, where Cholesky factorizations of the subdomain finite element problems are additively combined with a coarse, global solver. Multilevel and highly-scalable algorithms can be obtained by replacing the coarse Cholesky solver with a coarse BDDC preconditioner. BDDC methods have the remarkable ability to control the condition number, since the coarse space of the preconditioner can be adaptively enriched at the cost of solving local eigenproblems. The proper identification of these eigenproblems extends the robustness of the methods to any heterogeneity in the distribution of the coefficients of the PDEs, not only when the coefficients jumps align with the subdomain boundaries or when the high contrast regions are confined to lie in the interior of the subdomains. The specific adaptive technique considered in this paper does not depend upon any interaction of discretization and partition; it relies purely on algebraic operations. Coarse space adaptation in BDDC methods has attractive algorithmic properties, since the technique enhances the concurrency and the arithmetic intensity of the preconditioning step of the sparse implicit solver with the aim of controlling the number of iterations of the Krylov method in a black-box fashion, thus reducing the number of global synchronization steps and matrix vector multiplications needed by the iterative solver; data movement and memory bound kernels in the solve phase can be thus limited at the expense of extra local ops during the setup of

  19. Hybrid Direct and Iterative Solver with Library of Multi-criteria Optimal Orderings for h Adaptive Finite Element Method Computations

    KAUST Repository

    AbouEisha, Hassan M.

    2016-06-02

    In this paper we present a multi-criteria optimization of element partition trees and resulting orderings for multi-frontal solver algorithms executed for two dimensional h adaptive finite element method. In particular, the problem of optimal ordering of elimination of rows in the sparse matrices resulting from adaptive finite element method computations is reduced to the problem of finding of optimal element partition trees. Given a two dimensional h refined mesh, we find all optimal element partition trees by using the dynamic programming approach. An element partition tree defines a prescribed order of elimination of degrees of freedom over the mesh. We utilize three different metrics to estimate the quality of the element partition tree. As the first criterion we consider the number of floating point operations(FLOPs) performed by the multi-frontal solver. As the second criterion we consider the number of memory transfers (MEMOPS) performed by the multi-frontal solver algorithm. As the third criterion we consider memory usage (NONZEROS) of the multi-frontal direct solver. We show the optimization results for FLOPs vs MEMOPS as well as for the execution time estimated as FLOPs+100MEMOPS vs NONZEROS. We obtain Pareto fronts with multiple optimal trees, for each mesh, and for each refinement level. We generate a library of optimal elimination trees for small grids with local singularities. We also propose an algorithm that for a given large mesh with identified local sub-grids, each one with local singularity. We compute Schur complements over the sub-grids using the optimal trees from the library, and we submit the sequence of Schur complements into the iterative solver ILUPCG.

  20. An Eulerian-Lagrangian finite-element method for modeling crack growth in creeping materials

    International Nuclear Information System (INIS)

    Lee Hae Sung.

    1991-01-01

    This study is concerned with the development of finite-element-solution methods for analysis of quasi-static, ductile crack growth in history-dependent materials. The mixed Eulerian-Langrangian description (ELD) kinematic model is shown to have several desirable properties for modeling inelastic crack growth. Accordingly, a variational statement based on the ELD for history-dependent materials is developed, and a new moving-grid finite-element method based on the variational statement is presented. The moving-grid finite-element method based on the variational statement is presented. The moving-grid finite-element method is applied to the analysis of transient, quasi-static, mode-III crack growth in creeping materials. A generalized Petrov-Galerkin method (GPG) is developed that simultaneously stabilizes the statement to admit L 2 basis functions for the nonlinear strain field. Quasi-static, model-III crack growth in creeping materials under small-scale-yielding (SSY) conditions is considered. The GPG/ELD moving-grid finite-element formulation is used to model a transient crack-growth problem. The GPG/ELD results compare favorably with previously-published numerical results and the asymptotic solutions

  1. A non conforming finite element method for computing eigenmodes of resonant cavities

    International Nuclear Information System (INIS)

    Touze, F.; Le Meur, G.

    1990-06-01

    We present here a non conforming finite element in R 3 . This finite element, built on tetrahedrons, is particularly suited for computing eigenmodes. The main advantage of this element is that it preserves some structural properties of the space in which the solutions of the Maxwell's equations are to be found. Numerical results are presented for both two-dimensional and three-dimensional cases

  2. Solutions manual to accompany finite mathematics models and applications

    CERN Document Server

    Morris, Carla C

    2015-01-01

    A solutions manual to accompany Finite Mathematics: Models and Applications In order to emphasize the main concepts of each chapter, Finite Mathematics: Models and Applications features plentiful pedagogical elements throughout such as special exercises, end notes, hints, select solutions, biographies of key mathematicians, boxed key principles, a glossary of important terms and topics, and an overview of use of technology. The book encourages the modeling of linear programs and their solutions and uses common computer software programs such as LINDO. In addition to extensive chapters on pr

  3. Methods for high-resolution anisotropic finite element modeling of the human head: automatic MR white matter anisotropy-adaptive mesh generation.

    Science.gov (United States)

    Lee, Won Hee; Kim, Tae-Seong

    2012-01-01

    This study proposes an advanced finite element (FE) head modeling technique through which high-resolution FE meshes adaptive to the degree of tissue anisotropy can be generated. Our adaptive meshing scheme (called wMesh) uses MRI structural information and fractional anisotropy maps derived from diffusion tensors in the FE mesh generation process, optimally reflecting electrical properties of the human brain. We examined the characteristics of the wMeshes through various qualitative and quantitative comparisons to the conventional FE regular-sized meshes that are non-adaptive to the degree of white matter anisotropy. We investigated numerical differences in the FE forward solutions that include the electrical potential and current density generated by current sources in the brain. The quantitative difference was calculated by two statistical measures of relative difference measure (RDM) and magnification factor (MAG). The results show that the wMeshes are adaptive to the anisotropic density of the WM anisotropy, and they better reflect the density and directionality of tissue conductivity anisotropy. Our comparison results between various anisotropic regular mesh and wMesh models show that there are substantial differences in the EEG forward solutions in the brain (up to RDM=0.48 and MAG=0.63 in the electrical potential, and RDM=0.65 and MAG=0.52 in the current density). Our analysis results indicate that the wMeshes produce different forward solutions that are different from the conventional regular meshes. We present some results that the wMesh head modeling approach enhances the sensitivity and accuracy of the FE solutions at the interfaces or in the regions where the anisotropic conductivities change sharply or their directional changes are complex. The fully automatic wMesh generation technique should be useful for modeling an individual-specific and high-resolution anisotropic FE head model incorporating realistic anisotropic conductivity distributions

  4. Domain decomposition based iterative methods for nonlinear elliptic finite element problems

    Energy Technology Data Exchange (ETDEWEB)

    Cai, X.C. [Univ. of Colorado, Boulder, CO (United States)

    1994-12-31

    The class of overlapping Schwarz algorithms has been extensively studied for linear elliptic finite element problems. In this presentation, the author considers the solution of systems of nonlinear algebraic equations arising from the finite element discretization of some nonlinear elliptic equations. Several overlapping Schwarz algorithms, including the additive and multiplicative versions, with inexact Newton acceleration will be discussed. The author shows that the convergence rate of the Newton`s method is independent of the mesh size used in the finite element discretization, and also independent of the number of subdomains into which the original domain in decomposed. Numerical examples will be presented.

  5. A new Eulerian-Lagrangian finite element simulator for solute transport in discrete fracture-matrix systems

    Energy Technology Data Exchange (ETDEWEB)

    Birkholzer, J.; Karasaki, K. [Lawrence Berkeley National Lab., CA (United States). Earth Sciences Div.

    1996-07-01

    Fracture network simulators have extensively been used in the past for obtaining a better understanding of flow and transport processes in fractured rock. However, most of these models do not account for fluid or solute exchange between the fractures and the porous matrix, although diffusion into the matrix pores can have a major impact on the spreading of contaminants. In the present paper a new finite element code TRIPOLY is introduced which combines a powerful fracture network simulator with an efficient method to account for the diffusive interaction between the fractures and the adjacent matrix blocks. The fracture network simulator used in TRIPOLY features a mixed Lagrangian-Eulerian solution scheme for the transport in fractures, combined with an adaptive gridding technique to account for sharp concentration fronts. The fracture-matrix interaction is calculated with an efficient method which has been successfully used in the past for dual-porosity models. Discrete fractures and matrix blocks are treated as two different systems, and the interaction is modeled by introducing sink/source terms in both systems. It is assumed that diffusive transport in the matrix can be approximated as a one-dimensional process, perpendicular to the adjacent fracture surfaces. A direct solution scheme is employed to solve the coupled fracture and matrix equations. The newly developed combination of the fracture network simulator and the fracture-matrix interaction module allows for detailed studies of spreading processes in fractured porous rock. The authors present a sample application which demonstrate the codes ability of handling large-scale fracture-matrix systems comprising individual fractures and matrix blocks of arbitrary size and shape.

  6. Modelling Convergence of Finite Element Analysis of Cantilever Beam

    African Journals Online (AJOL)

    Convergence studies are carried out by investigating the convergence of numerical results as the number of elements is increased. If convergence is not obtained, the engineer using the finite element method has absolutely no indication whether the results are indicative of a meaningful approximation to the correct solution ...

  7. Application of the finite element method to the neutron transport equation

    International Nuclear Information System (INIS)

    Martin, W.R.

    1976-01-01

    This paper examines the theoretical and practical application of the finite element method to the neutron transport equation. It is shown that in principle the system of equations obtained by application of the finite element method can be solved with certain physical restrictions concerning the criticality of the medium. The convergence of this approximate solution to the exact solution with mesh refinement is examined, and a non-optical estimate of the convergence rate is obtained analytically. It is noted that the numerical results indicate a faster convergence rate and several approaches to obtain this result analytically are outlined. The practical application of the finite element method involved the development of a computer code capable of solving the neutron transport equation in 1-D plane geometry. Vacuum, reflecting, or specified incoming boundary conditions may be analyzed, and all are treated as natural boundary conditions. The time-dependent transport equation is also examined and it is shown that the application of the finite element method in conjunction with the Crank-Nicholson time discretization method results in a system of algebraic equations which is readily solved. Numerical results are given for several critical slab eigenvalue problems, including anisotropic scattering, and the results compare extremely well with benchmark results. It is seen that the finite element code is more efficient than a standard discrete ordinates code for certain problems. A problem with severe heterogeneities is considered and it is shown that the use of discontinuous spatial and angular elements results in a marked improvement in the results. Finally, time-dependent problems are examined and it is seen that the phenomenon of angular mode separation makes the numerical treatment of the transport equation in slab geometry a considerable challenge, with the result that the angular mesh has a dominant effect on obtaining acceptable solutions

  8. Massively Parallel Finite Element Programming

    KAUST Repository

    Heister, Timo; Kronbichler, Martin; Bangerth, Wolfgang

    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.

  9. Massively Parallel Finite Element Programming

    KAUST Repository

    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.

  10. Bubble-Enriched Least-Squares Finite Element Method for Transient Advective Transport

    Directory of Open Access Journals (Sweden)

    Rajeev Kumar

    2008-01-01

    Full Text Available The least-squares finite element method (LSFEM has received increasing attention in recent years due to advantages over the Galerkin finite element method (GFEM. The method leads to a minimization problem in the L2-norm and thus results in a symmetric and positive definite matrix, even for first-order differential equations. In addition, the method contains an implicit streamline upwinding mechanism that prevents the appearance of oscillations that are characteristic of the Galerkin method. Thus, the least-squares approach does not require explicit stabilization and the associated stabilization parameters required by the Galerkin method. A new approach, the bubble enriched least-squares finite element method (BELSFEM, is presented and compared with the classical LSFEM. The BELSFEM requires a space-time element formulation and employs bubble functions in space and time to increase the accuracy of the finite element solution without degrading computational performance. We apply the BELSFEM and classical least-squares finite element methods to benchmark problems for 1D and 2D linear transport. The accuracy and performance are compared.

  11. 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

  12. Finite element computational fluid mechanics

    International Nuclear Information System (INIS)

    Baker, A.J.

    1983-01-01

    This book analyzes finite element theory as applied to computational fluid mechanics. It includes a chapter on using the heat conduction equation to expose the essence of finite element theory, including higher-order accuracy and convergence in a common knowledge framework. Another chapter generalizes the algorithm to extend application to the nonlinearity of the Navier-Stokes equations. Other chapters are concerned with the analysis of a specific fluids mechanics problem class, including theory and applications. Some of the topics covered include finite element theory for linear mechanics; potential flow; weighted residuals/galerkin finite element theory; inviscid and convection dominated flows; boundary layers; parabolic three-dimensional flows; and viscous and rotational flows

  13. Solution of free-boundary problems using finite-element/Newton methods and locally refined grids - Application to analysis of solidification microstructure

    Science.gov (United States)

    Tsiveriotis, K.; Brown, R. A.

    1993-01-01

    A new method is presented for the solution of free-boundary problems using Lagrangian finite element approximations defined on locally refined grids. The formulation allows for direct transition from coarse to fine grids without introducing non-conforming basis functions. The calculation of elemental stiffness matrices and residual vectors are unaffected by changes in the refinement level, which are accounted for in the loading of elemental data to the global stiffness matrix and residual vector. This technique for local mesh refinement is combined with recently developed mapping methods and Newton's method to form an efficient algorithm for the solution of free-boundary problems, as demonstrated here by sample calculations of cellular interfacial microstructure during directional solidification of a binary alloy.

  14. A parallel finite element method for the analysis of crystalline solids

    DEFF Research Database (Denmark)

    Sørensen, N.J.; Andersen, B.S.

    1996-01-01

    A parallel finite element method suitable for the analysis of 3D quasi-static crystal plasticity problems has been developed. The method is based on substructuring of the original mesh into a number of substructures which are treated as isolated finite element models related via the interface...... conditions. The resulting interface equations are solved using a direct solution method. The method shows a good speedup when increasing the number of processors from 1 to 8 and the effective solution of 3D crystal plasticity problems whose size is much too large for a single work station becomes possible....

  15. A novel hybrid stress-function finite element method immune to severe mesh distortion

    International Nuclear Information System (INIS)

    Cen Song; Zhou Mingjue; Fu Xiangrong

    2010-01-01

    This paper introduces a hybrid stress-function finite element method proposed recently for developing 2D finite element models immune to element shapes. Deferent from the first version of the hybrid-stress element constructed by Pian, the stress function φ of 2D elastic or fracture problem is regarded as the functional variable of the complementary energy functional. Then, the basic analytical solutions of φ are taken as the trial functions for finite element models, and meanwhile, the corresponding unknown stress-function constants are introduced. By using the principle of minimum complementary energy, these unknown stress-function constants can be expressed in terms of the displacements along element edges. Finally, the complementary energy functional can be rewritten in terms of element nodal displacement vector, and thus, the element stiffness matrix of such hybrid-function element can be obtained. As examples, two (8- and 12-node) quadrilateral plane elements and an arbitrary polygonal crack element are constructed by employing different basic analytical solutions of different stress functions. Numerical results show that, the 8- and 12-node plane models can produce the exact solutions for pure bending and linear bending problems, respectively, even the element shape degenerates into triangle and concave quadrangle; and the crack element can also predict accurate results with very low computational cost in analysis of stress-singularity problems.

  16. Two-dimensional finite element solution for the simultaneous transport of water and solutes through a nonhomogeneous aquifer under transient saturated unsaturated flow conditions

    International Nuclear Information System (INIS)

    Gureghian, A.B.

    1979-01-01

    A mathematical model of ground water transport through an aquifer is presented. The solute of interest is a metal tracer or radioactive material which may undergo decay through a sorbing unconfined aquifer. The subject is developed under the following headings: flow equation, solute equation, boundary conditions, finite element formulation, element formulation, solution scheme (flow equation, solute equation), results and discussions, water movement in a ditch drained aquifer under transient state, water and solute movement in a homogeneous and unsaturated soil, transport of 226 Ra in nonhomogeneous aquifer, tailings pond lined, and tailings pond unlined. It is concluded that this mathematical model may have a wide variety of applications. The uranium milling industry may find it useful to evaluate the hydrogeological suitability of their disposal sites. It may prove suited for the design of clay disposal ponds destined to hold hazardous liquids. It may also provide a means of estimating the long-term impact of radionuclides or other pollutants on the quality of ground water. 31 references, 9 figures, 3 tables

  17. Finite element analysis of the neutron transport equation in spherical geometry

    International Nuclear Information System (INIS)

    Kim, Yong Ill; Kim, Jong Kyung; Suk, Soo Dong

    1992-01-01

    The Galerkin formulation of the finite element method is applied to the integral law of the first-order form of the one-group neutron transport equation in one-dimensional spherical geometry. Piecewise linear or quadratic Lagrange polynomials are utilized in the integral law for the angular flux to establish a set of linear algebraic equations. Numerical analyses are performed for the scalar flux distribution in a heterogeneous sphere as well as for the criticality problem in a uniform sphere. For the criticality problems in the uniform sphere, the results of the finite element method, with the use of continuous finite elements in space and angle, are compared with the exact solutions. In the heterogeneous problem, the scalar flux distribution obtained by using discontinuous angular and spatical finite elements is in good agreement with that from the ANISN code calculation. (Author)

  18. Finite element analysis of three dimensional crack growth by the use of a boundary element sub model

    DEFF Research Database (Denmark)

    Lucht, Tore

    2009-01-01

    A new automated method to model non-planar three dimensional crack growth is proposed which combines the advantages of both the boundary element method and the finite element method. The proposed method links the two methods by a submodelling strategy in which the solution of a global finite...... element model containing an approximation of the crack is interpolated to a much smaller boundary element model containing a fine discretization of the real crack. The method is validated through several numerical comparisons and by comparison to crack growth measured in a test specimen for an engineering...

  19. Extended finite element method and its application in heterogeneous materials with inclusions

    International Nuclear Information System (INIS)

    Du Chengbin; Jiang Shouyan; Ying Zongquan

    2010-01-01

    To simplify the technology of finite element mesh generation for particle reinforced material, enrichment techniques is used to account for the material interfaces in the framework of extended finite element method (XFEM). The geometry of material distribution is described by level set function, which allows one to model the internal boundaries of the microstructure without the adaptation of the mesh. The enrichment function is used to improve the shape function of classical finite element method (FEM) for the nodes supporting the elements cut by the interface. The key issue of XFEM including constructing displacement pattern, establishment of the governing equation and scheme of numerical integration is also presented. It is not necessarily matching the internal features of the inclusions using XFEM, so the generation of finite element mesh can be performed easily. Finally, a plate with multi-circular inclusions under uniaxial tension is simulated by XFEM and FEM, respectively. The results show that XFEM is highly effective and efficient.

  20. Finite element model to study calcium distribution in oocytes ...

    African Journals Online (AJOL)

    Parvaiz Ahmad Naik

    2015-03-20

    Mar 20, 2015 ... Department of Mathematics, Maulana Azad National Institute of Technology, Bhopal 462051 ... finite element method has been employed to obtain the solution. ..... Nelson MT, Cheng H, Rubart M. Relaxation of arterial smooth.

  1. Coupled porohyperelastic mass transport (PHEXPT) finite element models for soft tissues using ABAQUS.

    Science.gov (United States)

    Vande Geest, Jonathan P; Simon, B R; Rigby, Paul H; Newberg, Tyler P

    2011-04-01

    Finite element models (FEMs) including characteristic large deformations in highly nonlinear materials (hyperelasticity and coupled diffusive/convective transport of neutral mobile species) will allow quantitative study of in vivo tissues. Such FEMs will provide basic understanding of normal and pathological tissue responses and lead to optimization of local drug delivery strategies. We present a coupled porohyperelastic mass transport (PHEXPT) finite element approach developed using a commercially available ABAQUS finite element software. The PHEXPT transient simulations are based on sequential solution of the porohyperelastic (PHE) and mass transport (XPT) problems where an Eulerian PHE FEM is coupled to a Lagrangian XPT FEM using a custom-written FORTRAN program. The PHEXPT theoretical background is derived in the context of porous media transport theory and extended to ABAQUS finite element formulations. The essential assumptions needed in order to use ABAQUS are clearly identified in the derivation. Representative benchmark finite element simulations are provided along with analytical solutions (when appropriate). These simulations demonstrate the differences in transient and steady state responses including finite deformations, total stress, fluid pressure, relative fluid, and mobile species flux. A detailed description of important model considerations (e.g., material property functions and jump discontinuities at material interfaces) is also presented in the context of finite deformations. The ABAQUS-based PHEXPT approach enables the use of the available ABAQUS capabilities (interactive FEM mesh generation, finite element libraries, nonlinear material laws, pre- and postprocessing, etc.). PHEXPT FEMs can be used to simulate the transport of a relatively large neutral species (negligible osmotic fluid flux) in highly deformable hydrated soft tissues and tissue-engineered materials.

  2. The finite element method scheme for a solution of an evolution variational inequality with a nonlocal space operator

    Science.gov (United States)

    Glazyrina, O. V.; Pavlova, M. F.

    2016-11-01

    We consider the parabolic inequality with monotone with respect to a gradient space operator, which is depended on integral with respect to space variables solution characteristic. We construct a two-layer differential scheme for this problem with use of penalty method, semidiscretization with respect to time variable method and the finite element method (FEM) with respect to space variables. We proved a convergence of constructed mothod.

  3. A finite element method for neutron transport

    International Nuclear Information System (INIS)

    Ackroyd, R.T.

    1978-01-01

    A variational treatment of the finite element method for neutron transport is given based on a version of the even-parity Boltzmann equation which does not assume that the differential scattering cross-section has a spherical harmonic expansion. The theory of minimum and maximum principles is based on the Cauchy-Schwartz equality and the properties of a leakage operator G and a removal operator C. For systems with extraneous sources, two maximum and one minimum principles are given in boundary free form, to ease finite element computations. The global error of an approximate variational solution is given, the relationship of one the maximum principles to the method of least squares is shown, and the way in which approximate solutions converge locally to the exact solution is established. A method for constructing local error bounds is given, based on the connection between the variational method and the method of the hypercircle. The source iteration technique and a maximum principle for a system with extraneous sources suggests a functional for a variational principle for a self-sustaining system. The principle gives, as a consequence of the properties of G and C, an upper bound to the lowest eigenvalue. A related functional can be used to determine both upper and lower bounds for the lowest eigenvalue from an inspection of any approximate solution for the lowest eigenfunction. The basis for the finite element is presented in a general form so that two modes of exploitation can be undertaken readily. The model can be in phase space, with positional and directional co-ordinates defining points of the model, or it can be restricted to the positional co-ordinates and an expansion in orthogonal functions used for the directional co-ordinates. Suitable sets of functions are spherical harmonics and Walsh functions. The latter set is appropriate if a discrete direction representation of the angular flux is required. (author)

  4. Compatible-strain mixed finite element methods for incompressible nonlinear elasticity

    Science.gov (United States)

    Faghih Shojaei, Mostafa; Yavari, Arash

    2018-05-01

    We introduce a new family of mixed finite elements for incompressible nonlinear elasticity - compatible-strain mixed finite element methods (CSFEMs). Based on a Hu-Washizu-type functional, we write a four-field mixed formulation with the displacement, the displacement gradient, the first Piola-Kirchhoff stress, and a pressure-like field as the four independent unknowns. Using the Hilbert complexes of nonlinear elasticity, which describe the kinematics and the kinetics of motion, we identify the solution spaces of the independent unknown fields. In particular, we define the displacement in H1, the displacement gradient in H (curl), the stress in H (div), and the pressure field in L2. The test spaces of the mixed formulations are chosen to be the same as the corresponding solution spaces. Next, in a conforming setting, we approximate the solution and the test spaces with some piecewise polynomial subspaces of them. Among these approximation spaces are the tensorial analogues of the Nédélec and Raviart-Thomas finite element spaces of vector fields. This approach results in compatible-strain mixed finite element methods that satisfy both the Hadamard compatibility condition and the continuity of traction at the discrete level independently of the refinement level of the mesh. By considering several numerical examples, we demonstrate that CSFEMs have a good performance for bending problems and for bodies with complex geometries. CSFEMs are capable of capturing very large strains and accurately approximating stress and pressure fields. Using CSFEMs, we do not observe any numerical artifacts, e.g., checkerboarding of pressure, hourglass instability, or locking in our numerical examples. Moreover, CSFEMs provide an efficient framework for modeling heterogeneous solids.

  5. Navier-Stokes equations by the finite element method

    International Nuclear Information System (INIS)

    Portella, P.E.

    1984-01-01

    A computer program to solve the Navier-Stokes equations by using the Finite Element Method is implemented. The solutions variables investigated are stream-function/vorticity in the steady case and velocity/pressure in the steady state and transient cases. For steady state flow the equations are solved simultaneously by the Newton-Raphson method. For the time dependent formulation, a fractional step method is employed to discretize in time and artificial viscosity is used to preclude spurious oscilations in the solution. The element used is the three node triangle. Some numerical examples are presented and comparisons are made with applications already existent. (Author) [pt

  6. The CUBLAS and CULA based GPU acceleration of adaptive finite element framework for bioluminescence tomography.

    Science.gov (United States)

    Zhang, Bo; Yang, Xiang; Yang, Fei; Yang, Xin; Qin, Chenghu; Han, Dong; Ma, Xibo; Liu, Kai; Tian, Jie

    2010-09-13

    In molecular imaging (MI), especially the optical molecular imaging, bioluminescence tomography (BLT) emerges as an effective imaging modality for small animal imaging. The finite element methods (FEMs), especially the adaptive finite element (AFE) framework, play an important role in BLT. The processing speed of the FEMs and the AFE framework still needs to be improved, although the multi-thread CPU technology and the multi CPU technology have already been applied. In this paper, we for the first time introduce a new kind of acceleration technology to accelerate the AFE framework for BLT, using the graphics processing unit (GPU). Besides the processing speed, the GPU technology can get a balance between the cost and performance. The CUBLAS and CULA are two main important and powerful libraries for programming on NVIDIA GPUs. With the help of CUBLAS and CULA, it is easy to code on NVIDIA GPU and there is no need to worry about the details about the hardware environment of a specific GPU. The numerical experiments are designed to show the necessity, effect and application of the proposed CUBLAS and CULA based GPU acceleration. From the results of the experiments, we can reach the conclusion that the proposed CUBLAS and CULA based GPU acceleration method can improve the processing speed of the AFE framework very much while getting a balance between cost and performance.

  7. Finite Element Analysis of Folded Airbag in Frontal Impact of Adapted Vehicles for Disabled Drivers

    Science.gov (United States)

    Masiá, J.; Eixerés, B.; Dols, J. F.; Esquerdo, T. V.

    2009-11-01

    The car control adaptations are used in vehicles in order to facilitate the driving to persons with physical handicaps. This does not have to suppose a decrease of the passive safety that is required to the vehicles. In order to analyze this relation there will be characterized the different control adaptations that are in use together with the different devices of passive safety that can be mounted in the vehicles in diverse cases of impact in order to generate models of simulation. The methodology used to generate this simulation consists of the first phase in which there develops the three-dimensional model of the driving place. For it, there has been used a commercial software of three-dimensional design. Once realized this one divides, the model is imported to the finite elements software in which meshing is generated. Finally, dynamic simulation software is used to assign the most important characteristics like material properties, contact interfaces, gas expansion models, airbag fold types, etc.

  8. A first course in finite elements

    CERN Document Server

    Fish, Jacob

    2007-01-01

    Developed from the authors, combined total of 50 years undergraduate and graduate teaching experience, this book presents the finite element method formulated as a general-purpose numerical procedure for solving engineering problems governed by partial differential equations.  Focusing on the formulation and application of the finite element method through the integration of finite element theory, code development, and software application, the book is both introductory and self-contained, as well as being a hands-on experience for any student. This authoritative text on Finite Elements:Adopts

  9. Finite elements volumes methods: applications to the Navier-Stokes equations and convergence results

    International Nuclear Information System (INIS)

    Emonot, P.

    1992-01-01

    In the first chapter are described the equations modeling incompressible fluid flow and a quick presentation of finite volumes method. The second chapter is an introduction to the finite elements volumes method. The box model is described and a method adapted to Navier-Stokes problems is proposed. The third chapter shows a fault analysis of the finite elements volumes method for the Laplacian problem and some examples in one, two, three dimensional calculations. The fourth chapter is an extension of the error analysis of the method for the Navier-Stokes problem

  10. Finite element simulations of two rock mechanics tests

    International Nuclear Information System (INIS)

    Dahlke, H.J.; Lott, S.A.

    1986-04-01

    Rock mechanics tests are performed to determine in situ stress conditions and material properties of an underground rock mass. To design stable underground facilities for the permanent storage of high-level nuclear waste, determination of these properties and conditions is a necessary first step. However, before a test and its associated equipment can be designed, the engineer needs to know the range of expected values to be measured by the instruments. Sensitivity studies by means of finite element simulations are employed in this preliminary design phase to evaluate the pertinent parameters and their effects on the proposed measurements. The simulations, of two typical rock mechanics tests, the plate bearing test and the flat-jack test, by means of the finite element analysis, are described. The plate bearing test is used to determine the rock mass deformation modulus. The flat-jack test is used to determine the in situ stress conditions of the host rock. For the plate bearing test, two finite element models are used to simulate the classic problem of a load on an elastic half space and the actual problem of a plate bearing test in an underground tunnel of circular cross section. For the flat-jack simulation, a single finite element model is used to simulate both horizontal and vertical slots. Results will be compared to closed-form solutions available in the literature

  11. A simple finite element method for boundary value problems with a Riemann–Liouville derivative

    KAUST Repository

    Jin, Bangti; Lazarov, Raytcho; Lu, Xiliang; Zhou, Zhi

    2016-01-01

    © 2015 Elsevier B.V. All rights reserved. We consider a boundary value problem involving a Riemann-Liouville fractional derivative of order α∈(3/2,2) on the unit interval (0,1). The standard Galerkin finite element approximation converges slowly due to the presence of singularity term xα-1 in the solution representation. In this work, we develop a simple technique, by transforming it into a second-order two-point boundary value problem with nonlocal low order terms, whose solution can reconstruct directly the solution to the original problem. The stability of the variational formulation, and the optimal regularity pickup of the solution are analyzed. A novel Galerkin finite element method with piecewise linear or quadratic finite elements is developed, and L2(D) error estimates are provided. The approach is then applied to the corresponding fractional Sturm-Liouville problem, and error estimates of the eigenvalue approximations are given. Extensive numerical results fully confirm our theoretical study.

  12. A simple finite element method for boundary value problems with a Riemann–Liouville derivative

    KAUST Repository

    Jin, Bangti

    2016-02-01

    © 2015 Elsevier B.V. All rights reserved. We consider a boundary value problem involving a Riemann-Liouville fractional derivative of order α∈(3/2,2) on the unit interval (0,1). The standard Galerkin finite element approximation converges slowly due to the presence of singularity term xα-1 in the solution representation. In this work, we develop a simple technique, by transforming it into a second-order two-point boundary value problem with nonlocal low order terms, whose solution can reconstruct directly the solution to the original problem. The stability of the variational formulation, and the optimal regularity pickup of the solution are analyzed. A novel Galerkin finite element method with piecewise linear or quadratic finite elements is developed, and L2(D) error estimates are provided. The approach is then applied to the corresponding fractional Sturm-Liouville problem, and error estimates of the eigenvalue approximations are given. Extensive numerical results fully confirm our theoretical study.

  13. Evaluation of the finite element software ABAQUS for biomechanical modelling of biphasic tissues.

    Science.gov (United States)

    Wu, J Z; Herzog, W; Epstein, M

    1998-02-01

    The biphasic cartilage model proposed by Mow et al. (1980) has proven successful to capture the essential mechanical features of articular cartilage. In order to analyse the joint contact mechanics in real, anatomical joints, the cartilage model needs to be implemented into a suitable finite element code to approximate the irregular surface geometries of such joints. However, systematic and extensive evaluation of the capacity of commercial software for modelling the contact mechanics with biphasic cartilage layers has not been made. This research was aimed at evaluating the commercial finite element software ABAQUS for analysing biphasic soft tissues. The solutions obtained using ABAQUS were compared with those obtained using other finite element models and analytical solutions for three numerical tests: an unconfined indentation test, a test with the contact of a spherical cartilage surface with a rigid plate, and an axi-symmetric joint contact test. It was concluded that the biphasic cartilage model can be implemented into the commercial finite element software ABAQUS to analyse practical joint contact problems with biphasic articular cartilage layers.

  14. A study on the improvement of shape optimization associated with the modification of a finite element

    International Nuclear Information System (INIS)

    Sung, Jin Il; Yoo, Jeong Hoon

    2002-01-01

    In this paper, we investigate the effect and the importance of the accuracy of finite element analysis in the shape optimization based on the finite element method and improve the existing finite element which has inaccuracy in some cases. And then, the shape optimization is performed by using the improved finite element. One of the main stream to improve finite element is the prevention of locking phenomenon. In case of bending dominant problems, finite element solutions cannot be reliable because of shear locking phenomenon. In the process of shape optimization, the mesh distortion is large due to the change of the structure outline. So, we have to raise the accuracy of finite element analysis for the large mesh distortion. We cannot guarantee the accurate result unless the finite element itself is accurate or the finite elements are remeshed. So, we approach to more accurate shape optimization to diminish these inaccuracies by improving the existing finite element. The shape optimization using the modified finite element is applied to a two and three dimensional simple beam. Results show that the modified finite element has improved the optimization results

  15. Finite element analysis of the Girkmann problem using the modern hp-version and the classical h-version

    KAUST Repository

    Niemi, Antti; Babuška, Ivo M.; Pitkä ranta, Juhani; Demkowicz, Leszek F.

    2011-01-01

    elasticity theory and (2) by using a dimensionally reduced shell-ring model. In the first approach the problem is solved with a fully automatic hp-adaptive finite element solver whereas the classical h-version of the finite element method is used

  16. Discontinuous finite element and characteristics methods for neutrons transport equation solution in heterogeneous grids

    International Nuclear Information System (INIS)

    Masiello, E.

    2006-01-01

    The principal goal of this manuscript is devoted to the investigation of a new type of heterogeneous mesh adapted to the shape of the fuel pins (fuel-clad-moderator). The new heterogeneous mesh guarantees the spatial modelling of the pin-cell with a minimum of regions. Two methods are investigated for the spatial discretization of the transport equation: the discontinuous finite element method and the method of characteristics for structured cells. These methods together with the new representation of the pin-cell result in an appreciable reduction of calculation points. They allow an exact modelling of the fuel pin-cell without spatial homogenization. A new synthetic acceleration technique based on an angular multigrid is also presented for the speed up of the inner iterations. These methods are good candidates for transport calculations for a nuclear reactor core. A second objective of this work is the application of method of characteristics for non-structured geometries to the study of double heterogeneity problem. The letters is characterized by fuel material with a stochastic dispersion of heterogeneous grains, and until now was solved with a model based on collision probabilities. We propose a new statistical model based on renewal-Markovian theory, which makes possible to take into account the stochastic nature of the problem and to avoid the approximations of the collision probability model. The numerical solution of this model is guaranteed by the method of characteristics. (author)

  17. Modelling optimization involving different types of elements in finite element analysis

    International Nuclear Information System (INIS)

    Wai, C M; Rivai, Ahmad; Bapokutty, Omar

    2013-01-01

    Finite elements are used to express the mechanical behaviour of a structure in finite element analysis. Therefore, the selection of the elements determines the quality of the analysis. The aim of this paper is to compare and contrast 1D element, 2D element, and 3D element used in finite element analysis. A simple case study was carried out on a standard W460x74 I-beam. The I-beam was modelled and analyzed statically with 1D elements, 2D elements and 3D elements. The results for the three separate finite element models were compared in terms of stresses, deformation and displacement of the I-beam. All three finite element models yield satisfactory results with acceptable errors. The advantages and limitations of these elements are discussed. 1D elements offer simplicity although lacking in their ability to model complicated geometry. 2D elements and 3D elements provide more detail yet sophisticated results which require more time and computer memory in the modelling process. It is also found that the choice of element in finite element analysis is influence by a few factors such as the geometry of the structure, desired analysis results, and the capability of the computer

  18. Adaptive Algebraic Multigrid for Finite Element Elliptic Equations with Random Coefficients

    Energy Technology Data Exchange (ETDEWEB)

    Kalchev, D

    2012-04-02

    This thesis presents a two-grid algorithm based on Smoothed Aggregation Spectral Element Agglomeration Algebraic Multigrid (SA-{rho}AMGe) combined with adaptation. The aim is to build an efficient solver for the linear systems arising from discretization of second-order elliptic partial differential equations (PDEs) with stochastic coefficients. Examples include PDEs that model subsurface flow with random permeability field. During a Markov Chain Monte Carlo (MCMC) simulation process, that draws PDE coefficient samples from a certain distribution, the PDE coefficients change, hence the resulting linear systems to be solved change. At every such step the system (discretized PDE) needs to be solved and the computed solution used to evaluate some functional(s) of interest that then determine if the coefficient sample is acceptable or not. The MCMC process is hence computationally intensive and requires the solvers used to be efficient and fast. This fact that at every step of MCMC the resulting linear system changes, makes an already existing solver built for the old problem perhaps not as efficient for the problem corresponding to the new sampled coefficient. This motivates the main goal of our study, namely, to adapt an already existing solver to handle the problem (with changed coefficient) with the objective to achieve this goal to be faster and more efficient than building a completely new solver from scratch. Our approach utilizes the local element matrices (for the problem with changed coefficients) to build local problems associated with constructed by the method agglomerated elements (a set of subdomains that cover the given computational domain). We solve a generalized eigenproblem for each set in a subspace spanned by the previous local coarse space (used for the old solver) and a vector, component of the error, that the old solver cannot handle. A portion of the spectrum of these local eigen-problems (corresponding to eigenvalues close to zero) form the

  19. Finite element method solution of simplified P3 equation for flexible geometry handling

    International Nuclear Information System (INIS)

    Ryu, Eun Hyun; Joo, Han Gyu

    2011-01-01

    In order to obtain efficiently core flux solutions which would be much closer to the transport solution than the diffusion solution is, not being limited by the geometry of the core, the simplified P 3 (SP 3 ) equation is solved with the finite element method (FEM). A generic mesh generator, GMSH, is used to generate linear and quadratic mesh data. The linear system resulting from the SP 3 FEM discretization is solved by Krylov subspace methods (KSM). A symmetric form of the SP 3 equation is derived to apply the conjugate gradient method rather than the KSMs for nonsymmetric linear systems. An optional iso-parametric quadratic mapping scheme, which is to selectively model nonlinear shapes with a quadratic mapping to prevent significant mismatch in local domain volume, is also implemented for efficient application of arbitrary geometry handling. The gain in the accuracy attainable by the SP 3 solution over the diffusion solution is assessed by solving numerous benchmark problems having various core geometries including the IAEA PWR problems involving rectangular fuels and the Takeda fast reactor problems involving hexagonal fuels. The reference transport solution is produced by the McCARD Monte Carlo code and the multiplication factor and power distribution errors are assessed. In addition, the effect of quadratic mapping is examined for circular cell problems. It is shown that significant accuracy gain is possible with the SP 3 solution for the fast reactor problems whereas only marginal improvement is noted for thermal reactor problems. The quadratic mapping is also quite effective handling geometries with curvature. (author)

  20. New formulations on the finite element method for boundary value problems with internal/external boundary layers

    International Nuclear Information System (INIS)

    Pereira, Luis Carlos Martins

    1998-06-01

    New Petrov-Galerkin formulations on the finite element methods for convection-diffusion problems with boundary layers are presented. Such formulations are based on a consistent new theory on discontinuous finite element methods. Existence and uniqueness of solutions for these problems in the new finite element spaces are demonstrated. Some numerical experiments shows how the new formulation operate and also their efficacy. (author)

  1. Adaptive contact elements for three-dimensional fluid-structure interfaces

    International Nuclear Information System (INIS)

    Kulak, R.F.

    1985-01-01

    A finite element method is developed for treating the mechanics of contact between two deformable bodies which occurs, for example, at fluid-structure interfaces. The method uses a family of adaptive contact elements, which are based upon the penalty method, to handle all of the possible contact configurations that can occur between the discretized contacting bodies. The contact element's nodal connectivity is allowed to change during the computations in order to accommodate finite sliding. The infusion of these elements in the interface results in satisfying the force equilibrium condition during contact. The methodology has been implemented into the NEPTUNE code. Results are presented for an illustrative problem

  2. Adaptive contact elements for three-dimensional fluid-structure interfaces

    Energy Technology Data Exchange (ETDEWEB)

    Kulak, R.F.

    1985-01-01

    A finite element method is developed for treating the mechanics of contact between two deformable bodies which occurs, for example, at fluid-structure interfaces. The method uses a family of adaptive contact elements, which are based upon the penalty method, to handle all of the possible contact configurations that can occur between the discretized contacting bodies. The contact element's nodal connectivity is allowed to change during the computations in order to accommodate finite sliding. The infusion of these elements in the interface results in satisfying the force equilibrium condition during contact. The methodology has been implemented into the NEPTUNE code. Results are presented for an illustrative problem.

  3. Generalization of mixed multiscale finite element methods with applications

    Energy Technology Data Exchange (ETDEWEB)

    Lee, C S [Texas A & M Univ., College Station, TX (United States)

    2016-08-01

    Many science and engineering problems exhibit scale disparity and high contrast. The small scale features cannot be omitted in the physical models because they can affect the macroscopic behavior of the problems. However, resolving all the scales in these problems can be prohibitively expensive. As a consequence, some types of model reduction techniques are required to design efficient solution algorithms. For practical purpose, we are interested in mixed finite element problems as they produce solutions with certain conservative properties. Existing multiscale methods for such problems include the mixed multiscale finite element methods. We show that for complicated problems, the mixed multiscale finite element methods may not be able to produce reliable approximations. This motivates the need of enrichment for coarse spaces. Two enrichment approaches are proposed, one is based on generalized multiscale finte element metthods (GMsFEM), while the other is based on spectral element-based algebraic multigrid (rAMGe). The former one, which is called mixed GMsFEM, is developed for both Darcy’s flow and linear elasticity. Application of the algorithm in two-phase flow simulations are demonstrated. For linear elasticity, the algorithm is subtly modified due to the symmetry requirement of the stress tensor. The latter enrichment approach is based on rAMGe. The algorithm differs from GMsFEM in that both of the velocity and pressure spaces are coarsened. Due the multigrid nature of the algorithm, recursive application is available, which results in an efficient multilevel construction of the coarse spaces. Stability, convergence analysis, and exhaustive numerical experiments are carried out to validate the proposed enrichment approaches. iii

  4. Linear and Nonlinear Finite Elements.

    Science.gov (United States)

    1983-12-01

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

  5. A weak Galerkin least-squares finite element method for div-curl systems

    Science.gov (United States)

    Li, Jichun; Ye, Xiu; Zhang, Shangyou

    2018-06-01

    In this paper, we introduce a weak Galerkin least-squares method for solving div-curl problem. This finite element method leads to a symmetric positive definite system and has the flexibility to work with general meshes such as hybrid mesh, polytopal mesh and mesh with hanging nodes. Error estimates of the finite element solution are derived. The numerical examples demonstrate the robustness and flexibility of the proposed method.

  6. Domain decomposition solvers for nonlinear multiharmonic finite element equations

    KAUST Repository

    Copeland, D. M.

    2010-01-01

    In many practical applications, for instance, in computational electromagnetics, the excitation is time-harmonic. Switching from the time domain to the frequency domain allows us to replace the expensive time-integration procedure by the solution of a simple elliptic equation for the amplitude. This is true for linear problems, but not for nonlinear problems. However, due to the periodicity of the solution, we can expand the solution in a Fourier series. Truncating this Fourier series and approximating the Fourier coefficients by finite elements, we arrive at a large-scale coupled nonlinear system for determining the finite element approximation to the Fourier coefficients. The construction of fast solvers for such systems is very crucial for the efficiency of this multiharmonic approach. In this paper we look at nonlinear, time-harmonic potential problems as simple model problems. We construct and analyze almost optimal solvers for the Jacobi systems arising from the Newton linearization of the large-scale coupled nonlinear system that one has to solve instead of performing the expensive time-integration procedure. © 2010 de Gruyter.

  7. Heat Conduction Analysis Using Semi Analytical Finite Element Method

    International Nuclear Information System (INIS)

    Wargadipura, A. H. S.

    1997-01-01

    Heat conduction problems are very often found in science and engineering fields. It is of accrual importance to determine quantitative descriptions of this important physical phenomena. This paper discusses the development and application of a numerical formulation and computation that can be used to analyze heat conduction problems. The mathematical equation which governs the physical behaviour of heat conduction is in the form of second order partial differential equations. The numerical resolution used in this paper is performed using the finite element method and Fourier series, which is known as semi-analytical finite element methods. The numerical solution results in simultaneous algebraic equations which is solved using the Gauss elimination methodology. The computer implementation is carried out using FORTRAN language. In the final part of the paper, a heat conduction problem in a rectangular plate domain with isothermal boundary conditions in its edge is solved to show the application of the computer program developed and also a comparison with analytical solution is discussed to assess the accuracy of the numerical solution obtained

  8. Finite element method for solving neutron transport problems

    International Nuclear Information System (INIS)

    Ferguson, J.M.; Greenbaum, A.

    1984-01-01

    A finite element method is introduced for solving the neutron transport equations. Our method falls into the category of Petrov-Galerkin solution, since the trial space differs from the test space. The close relationship between this method and the discrete ordinate method is discussed, and the methods are compared for simple test problems

  9. Finite element method for computational fluid dynamics with any type of elements; Finite Element Methode zur numerischen Stroemungsberechnung mit beliebigen Elementen

    Energy Technology Data Exchange (ETDEWEB)

    Steibler, P.

    2000-07-01

    The unsteady, turbulent flow is to be calculated in a complex geometry. For this purpose a stabilized finite element formulation in which the same functions for velocity and pressure are used is developed. Thus the process remains independent of the type of elements. This simplifies the application. Above all, it is easier to deal with the boundary conditions. The independency from the elements is also achieved by the extended uzawa-algorithm which uses quadratic functions for velocity and an element-constant pressure. This method is also programmed. In order to produce the unstructured grids, an algorithm is implemented which produces meshes consisting of triangular and tetrahedral elements with flow-dependent adaptation. With standard geometries both calculation methods are compared with results. Finally the flow in a draft tube of a Kaplan turbine is calculated and compared with results from model tests. (orig.) [German] Die instationaere, turbulente Stroemung in einer komplexen Geometrie soll berechnet werden. Dazu wird eine Stabilisierte Finite Element Formulierung entwickelt, bei der die gleichen Ansatzfunktionen fuer Geschwindigkeiten und Druck verwendet werden. Das Verfahren wird damit unabhaengig von der Form der Elemente. Dies vereinfacht die Anwendung. Vor allem wird der Umgang mit den Randbedingungen erleichert. Die Elementunabhaengigkeit erreicht man auch mit dem erweiterten Uzawa-Algorithmus, welcher quadratische Ansatzfunktionen fuer die Geschwindigkeiten und elementweisen konstanten Druck verwendet. Dieses Verfahren wird ebenso implementiert. Zur Erstellung der unstrukturierten Gitter wird ein Algorithmus erzeugt, der Netze aus Dreiecks- und Tetraederelementen erstellt, welche stroemungsabhaengige Groessen besitzen koennen. Anhand einiger Standardgeometrien werden die beiden Berechnungsmethoden mit Ergebnissen aus der Literatur verglichen. Als praxisrelevantes Beispiel wird abschliessend die Stroemung in einem Saugrohr einer Kaplanturbine berechnet

  10. 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...

  11. A solution for the integration of finite element analysis in a ship design environment

    International Nuclear Information System (INIS)

    Finifter, D.; Wyniecki, P.; Castel, J. de

    1982-01-01

    The DEMAIN system for the pre- and post-processing of finite element analyses of ship structures is presented. It is shown that this new modelling concept, although being self-contained and specialized, has features which relate it to computer-aided design applications of a more general nature. Thus, compared to other finite element pre/post-processors, it allows a more natural occurrence of the structural analysis task in the design flow and can be considered a major step towards an integrated design and analysis system. (orig.)

  12. A solution of the dispersion-convection equation of radial tracer transportation by the finite element variational method

    International Nuclear Information System (INIS)

    Hubert, J.

    1979-01-01

    The variational finite element method (of the Rayleigh-Ritz type) has been applied to solve the standard diffusion-convection equation of radial flow in a dispersive medium. It was shown that the imposing of the boundary condition ΔC/Δx = 0 (=null concentration gradient) introduced great errors in computation results. To remedy it this condition was imposed at the free end of the artifical domain. Its other end joined to the downstream boundary of the investigated domain. The results of calculations compared with the known analytical solutions of the parallel flow show their good accuracy. The method was used to discuss the applicability of the approximate analytical solutions of the radial flow. (author)

  13. Finite element transport methods for criticality calculations - current status and potential applications

    International Nuclear Information System (INIS)

    Oliveira, C.R.E. de; Goddard, A.

    1991-01-01

    In this paper we review the current status of the finite element method applied to the solution of the neutron transport equation and we discuss its potential role in the field of criticality safety. We show that the method's ability in handling complex, irregular geometry in two- and three-dimensions coupled with its accurate solutions potentially renders it an attractive alternative to the longer-established Monte Carlo method. Details of the most favoured form of the method - that which combines finite elements in space and spherical harmonics in angle - are presented. This form of the method, which has been extensively investigated over the last decade by research groups at the University of London, has been numerically implemented in the finite element code EVENT. The code has among its main features the capability of solving fixed source eigenvalue and time-dependent complex geometry problems in two- and three-dimensions. Other features of the code include anisotropic up- and down-scatter, direct and/or adjoint solutions and access to standard data libraries. Numerical examples, ranging from simple criticality benchmark studies to the analysis of idealised three-dimensional reactor cores, are presented to demonstrate the potential of the method. (author)

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

    Science.gov (United States)

    Romero, Ignacio; Segurado, Javier; LLorca, Javier

    2008-04-01

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

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

    International Nuclear Information System (INIS)

    Romero, Ignacio; Segurado, Javier; LLorca, Javier

    2008-01-01

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

  16. A combined finite volume-nonconforming finite element scheme for compressible two phase flow in porous media

    KAUST Repository

    Saad, Bilal Mohammed; Saad, Mazen Naufal B M

    2014-01-01

    We propose and analyze a combined finite volume-nonconforming finite element scheme on general meshes to simulate the two compressible phase flow in porous media. The diffusion term, which can be anisotropic and heterogeneous, is discretized by piecewise linear nonconforming triangular finite elements. The other terms are discretized by means of a cell-centered finite volume scheme on a dual mesh, where the dual volumes are constructed around the sides of the original mesh. The relative permeability of each phase is decentred according the sign of the velocity at the dual interface. This technique also ensures the validity of the discrete maximum principle for the saturation under a non restrictive shape regularity of the space mesh and the positiveness of all transmissibilities. Next, a priori estimates on the pressures and a function of the saturation that denote capillary terms are established. These stabilities results lead to some compactness arguments based on the use of the Kolmogorov compactness theorem, and allow us to derive the convergence of a subsequence of the sequence of approximate solutions to a weak solution of the continuous equations, provided the mesh size tends to zero. The proof is given for the complete system when the density of the each phase depends on its own pressure. © 2014 Springer-Verlag Berlin Heidelberg.

  17. A combined finite volume-nonconforming finite element scheme for compressible two phase flow in porous media

    KAUST Repository

    Saad, Bilal Mohammed

    2014-06-28

    We propose and analyze a combined finite volume-nonconforming finite element scheme on general meshes to simulate the two compressible phase flow in porous media. The diffusion term, which can be anisotropic and heterogeneous, is discretized by piecewise linear nonconforming triangular finite elements. The other terms are discretized by means of a cell-centered finite volume scheme on a dual mesh, where the dual volumes are constructed around the sides of the original mesh. The relative permeability of each phase is decentred according the sign of the velocity at the dual interface. This technique also ensures the validity of the discrete maximum principle for the saturation under a non restrictive shape regularity of the space mesh and the positiveness of all transmissibilities. Next, a priori estimates on the pressures and a function of the saturation that denote capillary terms are established. These stabilities results lead to some compactness arguments based on the use of the Kolmogorov compactness theorem, and allow us to derive the convergence of a subsequence of the sequence of approximate solutions to a weak solution of the continuous equations, provided the mesh size tends to zero. The proof is given for the complete system when the density of the each phase depends on its own pressure. © 2014 Springer-Verlag Berlin Heidelberg.

  18. A Analysis of the Low Frequency Sound Field in Non-Rectangular Enclosures Using the Finite Element Method.

    Science.gov (United States)

    Geddes, Earl Russell

    The details of the low frequency sound field for a rectangular room can be studied by the use of an established analytic technique--separation of variables. The solution is straightforward and the results are well-known. A non -rectangular room has boundary conditions which are not separable and therefore other solution techniques must be used. This study shows that the finite element method can be adapted for use in the study of sound fields in arbitrary shaped enclosures. The finite element acoustics problem is formulated and the modification of a standard program, which is necessary for solving acoustic field problems, is examined. The solution of the semi-non-rectangular room problem (one where the floor and ceiling remain parallel) is carried out by a combined finite element/separation of variables approach. The solution results are used to construct the Green's function for the low frequency sound field in five rooms (or data cases): (1) a rectangular (Louden) room; (2) The smallest wall of the Louden room canted 20 degrees from normal; (3) The largest wall of the Louden room canted 20 degrees from normal; (4) both the largest and the smallest walls are canted 20 degrees; and (5) a five-sided room variation of Case 4. Case 1, the rectangular room was calculated using both the finite element method and the separation of variables technique. The results for the two methods are compared in order to access the accuracy of the finite element method models. The modal damping coefficient are calculated and the results examined. The statistics of the source and receiver average normalized RMS P('2) responses in the 80 Hz, 100 Hz, and 125 Hz one-third octave bands are developed. The receiver averaged pressure response is developed to determine the effect of the source locations on the response. Twelve source locations are examined and the results tabulated for comparison. The effect of a finite sized source is looked at briefly. Finally, the standard deviation of the

  19. Strain-based finite elements for the analysis of cylinders with holes and normally intersecting cylinders

    International Nuclear Information System (INIS)

    Sabir, A.B.

    1983-01-01

    A finite element solution to the problems of stress distribution for cylindrical shells with circular and elliptical holes and also for normally intersecting thin elastic cylindrical shells is given. Quadrilateral and triangular curved finite elements are used in the analysis. The elements are of a new class, based on simple independent generalised strain functions insofar as this is allowed by the compatibility equations. The elements also satisfy exactly the requirements of strain-free-rigid body displacements and uses only the external 'geometrical' nodal degrees of freedom to avoid the difficulties associated with unnecessary internal degrees of freedom. We first develop strain based quadrilateral and triangular elements and apply them to the solution of the problem of stress concentrations in the neighbourhood of small and large circular and elliptical holes when the cylinders are subjected to a uniform axial tension. These results are compared with analytical solutions based on shallow shell approximations and show that the use of these strain based elements obviates the need for using an inordinately large number of elements. Normally intersecting cylinders are common configurations in structural components for nuclear reactor systems and design information for such configurations are generally lacking. The opportunity is taken in the present paper to provide a finite element solution to this problem. A method of substructing will be introduced to enable a solution to the large number of non banded set of simultaneous equations encountered. (orig./HP)

  20. Finite element formulation for dynamics of planar flexible multi-beam system

    International Nuclear Information System (INIS)

    Liu Zhuyong; Hong Jiazhen; Liu Jinyang

    2009-01-01

    In some previous geometric nonlinear finite element formulations, due to the use of axial displacement, the contribution of all the elements lying between the reference node of zero axial displacement and the element to the foreshortening effect should be taken into account. In this paper, a finite element formulation is proposed based on geometric nonlinear elastic theory and finite element technique. The coupling deformation terms of an arbitrary point only relate to the nodal coordinates of the element at which the point is located. Based on Hamilton principle, dynamic equations of elastic beams undergoing large overall motions are derived. To investigate the effect of coupling deformation terms on system dynamic characters and reduce the dynamic equations, a complete dynamic model and three reduced models of hub-beam are prospected. When the Cartesian deformation coordinates are adopted, the results indicate that the terms related to the coupling deformation in the inertia forces of dynamic equations have small effect on system dynamic behavior and may be neglected, whereas the terms related to coupling deformation in the elastic forces are important for system dynamic behavior and should be considered in dynamic equation. Numerical examples of the rotating beam and flexible beam system are carried out to demonstrate the accuracy and validity of this dynamic model. Furthermore, it is shown that a small number of finite elements are needed to obtain a stable solution using the present coupling finite element formulation

  1. A Floating Node Method for the Modelling of Discontinuities Within a Finite Element

    Science.gov (United States)

    Pinho, Silvestre T.; Chen, B. Y.; DeCarvalho, Nelson V.; Baiz, P. M.; Tay, T. E.

    2013-01-01

    This paper focuses on the accurate numerical representation of complex networks of evolving discontinuities in solids, with particular emphasis on cracks. The limitation of the standard finite element method (FEM) in approximating discontinuous solutions has motivated the development of re-meshing, smeared crack models, the eXtended Finite Element Method (XFEM) and the Phantom Node Method (PNM). We propose a new method which has some similarities to the PNM, but crucially: (i) does not introduce an error on the crack geometry when mapping to natural coordinates; (ii) does not require numerical integration over only part of a domain; (iii) can incorporate weak discontinuities and cohesive cracks more readily; (iv) is ideally suited for the representation of multiple and complex networks of (weak, strong and cohesive) discontinuities; (v) leads to the same solution as a finite element mesh where the discontinuity is represented explicitly; and (vi) is conceptually simpler than the PNM.

  2. Probabilistic finite elements

    Science.gov (United States)

    Belytschko, Ted; Wing, Kam Liu

    1987-01-01

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

  3. Finite element and finite difference methods in electromagnetic scattering

    CERN Document Server

    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

  4. The finite element solution of two-dimensional transverse magnetic scattering problems on the connection machine

    International Nuclear Information System (INIS)

    Hutchinson, S.; Costillo, S.; Dalton, K.; Hensel, E.

    1990-01-01

    A study is conducted of the finite element solution of the partial differential equations governing two-dimensional electromagnetic field scattering problems on a SIMD computer. A nodal assembly technique is introduced which maps a single node to a single processor. The physical domain is first discretized in parallel to yield the node locations of an O-grid mesh. Next, the system of equations is assembled and then solved in parallel using a conjugate gradient algorithm for complex-valued, non-symmetric, non-positive definite systems. Using this technique and Thinking Machines Corporation's Connection Machine-2 (CM-2), problems with more than 250k nodes are solved. Results of electromagnetic scattering, governed by the 2-d scalar Hemoholtz wave equations are presented in this paper. Solutions are demonstrated for a wide range of objects. A summary of performance data is given for the set of test problems

  5. Discontinuous Galerkin finite element methods for hyperbolic differential equations

    NARCIS (Netherlands)

    van der Vegt, Jacobus J.W.; van der Ven, H.; Boelens, O.J.; Boelens, O.J.; Toro, E.F.

    2002-01-01

    In this paper a suryey is given of the important steps in the development of discontinuous Galerkin finite element methods for hyperbolic partial differential equations. Special attention is paid to the application of the discontinuous Galerkin method to the solution of the Euler equations of gas

  6. Comparisons of Particle Tracking Techniques and Galerkin Finite Element Methods in Flow Simulations on Watershed Scales

    Science.gov (United States)

    Shih, D.; Yeh, G.

    2009-12-01

    This paper applies two numerical approximations, the particle tracking technique and Galerkin finite element method, to solve the diffusive wave equation in both one-dimensional and two-dimensional flow simulations. The finite element method is one of most commonly approaches in numerical problems. It can obtain accurate solutions, but calculation times may be rather extensive. The particle tracking technique, using either single-velocity or average-velocity tracks to efficiently perform advective transport, could use larger time-step sizes than the finite element method to significantly save computational time. Comparisons of the alternative approximations are examined in this poster. We adapt the model WASH123D to examine the work. WASH123D is an integrated multimedia, multi-processes, physics-based computational model suitable for various spatial-temporal scales, was first developed by Yeh et al., at 1998. The model has evolved in design capability and flexibility, and has been used for model calibrations and validations over the course of many years. In order to deliver a locally hydrological model in Taiwan, the Taiwan Typhoon and Flood Research Institute (TTFRI) is working with Prof. Yeh to develop next version of WASH123D. So, the work of our preliminary cooperationx is also sketched in this poster.

  7. Adaptive solution of some steady-state fluid-structure interaction problems

    International Nuclear Information System (INIS)

    Etienne, S.; Pelletier, D.

    2003-01-01

    This paper presents a general integrated and coupled formulation for modeling the steady-state interaction of a viscous incompressible flow with an elastic structure undergoing large displacements (geometric non-linearities). This constitutes an initial step towards developing a sensitivity analysis formulation for this class of problems. The formulation uses velocity and pressures as unknowns in a flow domain and displacements in the structural components. An interface formulation is presented that leads to clear and simple finite element implementation of the equilibrium conditions at the fluid-solid interface. Issues of error estimation and mesh adaptation are discussed. The adaptive formulation is verified on a problem with a closed form solution. It is then applied to a sample case for which the structure undergoes large displacements induced by the flow. (author)

  8. Stresses in faulted tunnel models by photoelasticity and adaptive finite element

    International Nuclear Information System (INIS)

    Ladkany, S.G.; Huang, Y.

    1995-01-01

    Research efforts in this area continue to investigate the development of a proper technique to analyze the stresses in the Ghost Dance fault and the effect of the fault on the stability of drifts in the proposed repository. Results from two parallel techniques are being compared to each other - Photoelastic models and Finite Element (FE) models. The Photoelastic plexiglass model (88.89 mm thick ampersand 256.1 mm long and wide) has two adjacent spare openings (57.95 mm long and wide) and a central round opening (57.95 mm diameter) placed at a clear distance approximately equal to its diameter from the square openings. The vertical loading on top of the model is 2269 N (500 lb.). Saw cuts (0.5388 mm wide), representing a fault, are being propagated from the tunnels outward with stress measurements taken at predefined locations, as the saw cuts increase in length. The FE model duplicates exactly the Photoelastic models. The adaptive mesh generation method is used to refine the FE grid at every step of the analysis. This nonlinear interactive computational techniques uses various uses various percent tolerance errors in the convergence of stress values as a measure in ending the iterative process

  9. Thermohydraulic analysis in pipelines using the finite element method

    International Nuclear Information System (INIS)

    Costa, L.E.; Idelsohn, S.R.

    1984-01-01

    The Finite Element Method (FEM) is employed for the numerical solution of fluid flow problems with combined heat transfer mechanisms. Boussinesq approximations are used for the solution of the governing equations. The application of the FEM leads to a set of simultaneous nonlinear equations. The development of the method, for the solution of bidimensional and axisymmetric problems, is presented. Examples of fluid flow in pipes, including natural and forced convection, are solved with the proposed method and discussed in the paper. (Author) [pt

  10. Transport and dispersion of pollutants in surface impoundments: a finite element model

    International Nuclear Information System (INIS)

    Yeh, G.T.

    1980-07-01

    A surface impoundment model in finite element (SIMFE) is presented to enable the simulation of flow circulations and pollutant transport and dispersion in natural or artificial lakes, reservoirs or ponds with any number of islands. This surface impoundment model consists of two sub-models: hydrodynamic and pollutant transport models. Both submodels are simulated by the finite element method. While the hydrodynamic model is solved by the standard Galerkin finite element scheme, the pollutant transport model can be solved by any of the twelve optional finite element schemes built in the program. Theoretical approximations and the numerical algorithm of SIMFE are described. Detail instruction of the application are given and listing of FORTRAN IV source program are provided. Two sample problems are given. One is for an idealized system with a known solution to show the accuracy and partial validation of the models. The other is applied to Prairie Island for a set of hypothetical input data, typifying a class of problems to which SIMFE may be applied

  11. Transport and dispersion of pollutants in surface impoundments: a finite element model

    Energy Technology Data Exchange (ETDEWEB)

    Yeh, G.T.

    1980-07-01

    A surface impoundment model in finite element (SIMFE) is presented to enable the simulation of flow circulations and pollutant transport and dispersion in natural or artificial lakes, reservoirs or ponds with any number of islands. This surface impoundment model consists of two sub-models: hydrodynamic and pollutant transport models. Both submodels are simulated by the finite element method. While the hydrodynamic model is solved by the standard Galerkin finite element scheme, the pollutant transport model can be solved by any of the twelve optional finite element schemes built in the program. Theoretical approximations and the numerical algorithm of SIMFE are described. Detail instruction of the application are given and listing of FORTRAN IV source program are provided. Two sample problems are given. One is for an idealized system with a known solution to show the accuracy and partial validation of the models. The other is applied to Prairie Island for a set of hypothetical input data, typifying a class of problems to which SIMFE may be applied.

  12. Three-dimensional modeling with finite element codes

    Energy Technology Data Exchange (ETDEWEB)

    Druce, R.L.

    1986-01-17

    This paper describes work done to model magnetostatic field problems in three dimensions. Finite element codes, available at LLNL, and pre- and post-processors were used in the solution of the mathematical model, the output from which agreed well with the experimentally obtained data. The geometry used in this work was a cylinder with ports in the periphery and no current sources in the space modeled. 6 refs., 8 figs.

  13. Stress Analysis of a TRISO Coated Particle Fuel by Using ABAQUS Finite Element Visco-Elastoplastic Solutions

    International Nuclear Information System (INIS)

    Cho, Moon Sung; Kim, Y. M.; Lee, Y. W.

    2006-01-01

    The fundamental design for a gas-cooled reactor relies on an understanding of the behavior of a coated particle fuel. KAERI, which has been carrying out the Korean VHTR (Very High Temperature modular gas cooled Reactor) Project since 2004, is developing a fuel performance analysis code for a VHTR named COPA (COated Particle fuel Analysis). A validation of COPA was attempted by comparing its benchmark results with the visco-elastic solutions obtained from the ABAQUS code calculations for the IAEA-CRP-6 TRISO coated particle benchmark problems involving a creep, swelling, and pressure. However, the ABAQUS finite element model used for the above-mentioned analysis did not consider the material nonlinearity of the SiC coating layer that showed stress levels higher than the assumed yield point of the material. In this study, a consideration of the material nonlinearity is included in the ABAQUS model to obtain the visco-elastoplastic solutions and the results are compared with the visco-elastic solutions obtained from the previous ABAQUS model

  14. Study on the influence of finite element formulation and equation of motion solution scheme on FEM analysis results based on the asymmetrically loaded plate problem

    Directory of Open Access Journals (Sweden)

    Marcin Krzeszowiec

    2015-03-01

    Full Text Available Computer simulations of physical phenomena are at the moment common both in science and industry. The possibility of finding approximate solutions for complicated systems of differential equations, mathematically describing issues in the fields of mechanics, physics or chemistry, allows for shorten design and research time, often significantly reducing the need for expensive experimental studies or costly production of prototypes. However, the mentioned prevalence of these methods, particularly the Finite Element Method, resulted in analysis outcomes to be often in advance regarded as accurate ones. The purpose of the article is to showcase, on a simple stress analysis problem, how parameters such as the density of the finite element mesh, finite element formulation or integration scheme significantly influence on the simulation results and how easy it is to end up with the results that do not hold any physical sense, despite the fact that all the basic assumptions of correct analysis (suitable boundary conditions, total system energy stored etc. have been met. The results of this study can serve as a warning against premature conclusion drawing from calculations carried out by means of FEM simulation.[b]Keywords[/b]: computational mechanics, finite element method, shell elements, numerical integration

  15. Solution of 3D inverse scattering problems by combined inverse equivalent current and finite element methods

    International Nuclear Information System (INIS)

    Kılıç, Emre; Eibert, Thomas F.

    2015-01-01

    An approach combining boundary integral and finite element methods is introduced for the solution of three-dimensional inverse electromagnetic medium scattering problems. Based on the equivalence principle, unknown equivalent electric and magnetic surface current densities on a closed surface are utilized to decompose the inverse medium problem into two parts: a linear radiation problem and a nonlinear cavity problem. The first problem is formulated by a boundary integral equation, the computational burden of which is reduced by employing the multilevel fast multipole method (MLFMM). Reconstructed Cauchy data on the surface allows the utilization of the Lorentz reciprocity and the Poynting's theorems. Exploiting these theorems, the noise level and an initial guess are estimated for the cavity problem. Moreover, it is possible to determine whether the material is lossy or not. In the second problem, the estimated surface currents form inhomogeneous boundary conditions of the cavity problem. The cavity problem is formulated by the finite element technique and solved iteratively by the Gauss–Newton method to reconstruct the properties of the object. Regularization for both the first and the second problems is achieved by a Krylov subspace method. The proposed method is tested against both synthetic and experimental data and promising reconstruction results are obtained

  16. Solution of 3D inverse scattering problems by combined inverse equivalent current and finite element methods

    Energy Technology Data Exchange (ETDEWEB)

    Kılıç, Emre, E-mail: emre.kilic@tum.de; Eibert, Thomas F.

    2015-05-01

    An approach combining boundary integral and finite element methods is introduced for the solution of three-dimensional inverse electromagnetic medium scattering problems. Based on the equivalence principle, unknown equivalent electric and magnetic surface current densities on a closed surface are utilized to decompose the inverse medium problem into two parts: a linear radiation problem and a nonlinear cavity problem. The first problem is formulated by a boundary integral equation, the computational burden of which is reduced by employing the multilevel fast multipole method (MLFMM). Reconstructed Cauchy data on the surface allows the utilization of the Lorentz reciprocity and the Poynting's theorems. Exploiting these theorems, the noise level and an initial guess are estimated for the cavity problem. Moreover, it is possible to determine whether the material is lossy or not. In the second problem, the estimated surface currents form inhomogeneous boundary conditions of the cavity problem. The cavity problem is formulated by the finite element technique and solved iteratively by the Gauss–Newton method to reconstruct the properties of the object. Regularization for both the first and the second problems is achieved by a Krylov subspace method. The proposed method is tested against both synthetic and experimental data and promising reconstruction results are obtained.

  17. A least squares principle unifying finite element, finite difference and nodal methods for diffusion theory

    International Nuclear Information System (INIS)

    Ackroyd, R.T.

    1987-01-01

    A least squares principle is described which uses a penalty function treatment of boundary and interface conditions. Appropriate choices of the trial functions and vectors employed in a dual representation of an approximate solution established complementary principles for the diffusion equation. A geometrical interpretation of the principles provides weighted residual methods for diffusion theory, thus establishing a unification of least squares, variational and weighted residual methods. The complementary principles are used with either a trial function for the flux or a trial vector for the current to establish for regular meshes a connection between finite element, finite difference and nodal methods, which can be exact if the mesh pitches are chosen appropriately. Whereas the coefficients in the usual nodal equations have to be determined iteratively, those derived via the complementary principles are given explicitly in terms of the data. For the further development of the connection between finite element, finite difference and nodal methods, some hybrid variational methods are described which employ both a trial function and a trial vector. (author)

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

    Science.gov (United States)

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

    2015-05-01

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

  19. Finite element modelling

    International Nuclear Information System (INIS)

    Tonks, M.R.; Williamson, R.; Masson, R.

    2015-01-01

    The Finite Element Method (FEM) is a numerical technique for finding approximate solutions to boundary value problems. While FEM is commonly used to solve solid mechanics equations, it can be applied to a large range of BVPs from many different fields. FEM has been used for reactor fuels modelling for many years. It is most often used for fuel performance modelling at the pellet and pin scale, however, it has also been used to investigate properties of the fuel material, such as thermal conductivity and fission gas release. Recently, the United Stated Department Nuclear Energy Advanced Modelling and Simulation Program has begun using FEM as the basis of the MOOSE-BISON-MARMOT Project that is developing a multi-dimensional, multi-physics fuel performance capability that is massively parallel and will use multi-scale material models to provide a truly predictive modelling capability. (authors)

  20. A finite element perspective on nonlinear FFT-based micromechanical simulations

    NARCIS (Netherlands)

    Zeman, J.; de Geus, T.W.J.; Vondrejc, J.; Peerlings, R.H.J.; Geers, M.G.D.

    2017-01-01

    Fourier solvers have become efficient tools to establish structure-property relations in heterogeneous materials. Introduced as an alternative to the Finite Element (FE) method, they are based on fixed-point solutions of the Lippmann-Schwinger type integral equation. Their computational efficiency

  1. Comparison between results of solution of Burgers' equation and Laplace's equation by Galerkin and least-square finite element methods

    Science.gov (United States)

    Adib, Arash; Poorveis, Davood; Mehraban, Farid

    2018-03-01

    In this research, two equations are considered as examples of hyperbolic and elliptic equations. In addition, two finite element methods are applied for solving of these equations. The purpose of this research is the selection of suitable method for solving each of two equations. Burgers' equation is a hyperbolic equation. This equation is a pure advection (without diffusion) equation. This equation is one-dimensional and unsteady. A sudden shock wave is introduced to the model. This wave moves without deformation. In addition, Laplace's equation is an elliptical equation. This equation is steady and two-dimensional. The solution of Laplace's equation in an earth dam is considered. By solution of Laplace's equation, head pressure and the value of seepage in the directions X and Y are calculated in different points of earth dam. At the end, water table is shown in the earth dam. For Burgers' equation, least-square method can show movement of wave with oscillation but Galerkin method can not show it correctly (the best method for solving of the Burgers' equation is discrete space by least-square finite element method and discrete time by forward difference.). For Laplace's equation, Galerkin and least square methods can show water table correctly in earth dam.

  2. Finite element simulation of piezoelectric transformers.

    Science.gov (United States)

    Tsuchiya, T; Kagawa, Y; Wakatsuki, N; Okamura, H

    2001-07-01

    Piezoelectric transformers are nothing but ultrasonic resonators with two pairs of electrodes provided on the surface of a piezoelectric substrate in which electrical energy is carried in the mechanical form. The input and output electrodes are arranged to provide the impedance transformation, which results in the voltage transformation. As they are operated at a resonance, the electrical equivalent circuit approach has traditionally been developed in a rather empirical way and has been used for analysis and design. The present paper deals with the analysis of the piezoelectric transformers based on the three-dimensional finite element modelling. The PIEZO3D code that we have developed is modified to include the external loading conditions. The finite element approach is now available for a wide variety of the electrical boundary conditions. The equivalent circuit of lumped parameters can also be derived from the finite element method (FEM) solution if required. The simulation of the present transformers is made for the low intensity operation and compared with the experimental results. Demonstration is made for basic Rosen-type transformers in which the longitudinal mode of a plate plays an important role; in which the equivalent circuit of lumped constants has been used. However, there are many modes of vibration associated with the plate, the effect of which cannot always be ignored. In the experiment, the double resonances are sometimes observed in the vicinity of the operating frequency. The simulation demonstrates that this is due to the coupling of the longitudinal mode with the flexural mode. Thus, the simulation provides an invaluable guideline to the transformer design.

  3. Use of the iterative solution method for coupled finite element and boundary element modeling

    International Nuclear Information System (INIS)

    Koteras, J.R.

    1993-07-01

    Tunnels buried deep within the earth constitute an important class geomechanics problems. Two numerical techniques used for the analysis of geomechanics problems, the finite element method and the boundary element method, have complementary characteristics for applications to problems of this type. The usefulness of combining these two methods for use as a geomechanics analysis tool has been recognized for some time, and a number of coupling techniques have been proposed. However, not all of them lend themselves to efficient computational implementations for large-scale problems. This report examines a coupling technique that can form the basis for an efficient analysis tool for large scale geomechanics problems through the use of an iterative equation solver

  4. Analysis of global multiscale finite element methods for wave equations with continuum spatial scales

    KAUST Repository

    Jiang, Lijian; Efendiev, Yalchin; Ginting, Victor

    2010-01-01

    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.

  5. Analysis of global multiscale finite element methods for wave equations with continuum spatial scales

    KAUST Repository

    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.

  6. Numerical modeling of contaminant transport in fractured porous media using mixed finite-element and finitevolume methods

    KAUST Repository

    Dong, Chen; Sun, Shuyu; Taylor, Glenn A.

    2011-01-01

    A mathematical model for contaminant species passing through fractured porous media is presented. In the numerical model, we combine two locally conservative methods; i.e., the mixed finite-element (MFE) method and the finite-volume method. Adaptive

  7. Finite element type of stress analysis for parts based on S235 JR steel welding

    Directory of Open Access Journals (Sweden)

    C. Babis

    2014-04-01

    Full Text Available The determination of static and/or variable stress, in case of complex shaped welded structures is hard to achieve. One solution, though, is the use of finite element method, implemented by means of various specialized software. Nowadays, this method has become very popular due to its high precision of data obtained through both research and finite element analysis. Hence, the present paper deals with the modelling of the pull-out behaviour of concave and convex welded joints through finite element method.

  8. FEHM, Finite Element Heat and Mass Transfer Code

    International Nuclear Information System (INIS)

    Zyvoloski, G.A.

    2002-01-01

    1 - Description of program or function: FEHM is a numerical simulation code for subsurface transport processes. It models 3-D, time-dependent, multiphase, multicomponent, non-isothermal, reactive flow through porous and fractured media. It can accurately represent complex 3-D geologic media and structures and their effects on subsurface flow and transport. Its capabilities include flow of gas, water, and heat; flow of air, water, and heat; multiple chemically reactive and sorbing tracers; finite element/finite volume formulation; coupled stress module; saturated and unsaturated media; and double porosity and double porosity/double permeability capabilities. 2 - Methods: FEHM uses a preconditioned conjugate gradient solution of coupled linear equations and a fully implicit, fully coupled Newton Raphson solution of nonlinear equations. It has the capability of simulating transport using either a advection/diffusion solution or a particle tracking method. 3 - Restriction on the complexity of the problem: Disk space and machine memory are the only limitations

  9. Application of finite element numerical technique to nuclear reactor geometries

    Energy Technology Data Exchange (ETDEWEB)

    Rouai, N M [Nuclear engineering department faculty of engineering Al-fateh universty, Tripoli (Libyan Arab Jamahiriya)

    1995-10-01

    Determination of the temperature distribution in nuclear elements is of utmost importance to ensure that the temperature stays within safe limits during reactor operation. This paper discusses the use of Finite element numerical technique (FE) for the solution of the two dimensional heat conduction equation in geometries related to nuclear reactor cores. The FE solution stats with variational calculus which considers transforming the heat conduction equation into an integral equation I(O) and seeks a function that minimizes this integral and hence gives the solution to the heat conduction equation. In this paper FE theory as applied to heat conduction is briefly outlined and a 2-D program is used to apply the theory to simple shapes and to two gas cooled reactor fuel elements. Good results are obtained for both cases with reasonable number of elements. 7 figs.

  10. Application of finite element numerical technique to nuclear reactor geometries

    International Nuclear Information System (INIS)

    Rouai, N. M.

    1995-01-01

    Determination of the temperature distribution in nuclear elements is of utmost importance to ensure that the temperature stays within safe limits during reactor operation. This paper discusses the use of Finite element numerical technique (FE) for the solution of the two dimensional heat conduction equation in geometries related to nuclear reactor cores. The FE solution stats with variational calculus which considers transforming the heat conduction equation into an integral equation I(O) and seeks a function that minimizes this integral and hence gives the solution to the heat conduction equation. In this paper FE theory as applied to heat conduction is briefly outlined and a 2-D program is used to apply the theory to simple shapes and to two gas cooled reactor fuel elements. Good results are obtained for both cases with reasonable number of elements. 7 figs

  11. A Finite Element Versus Analytical Approach to the Solution of the Current Diffusion Equation in Tokamaks

    Czech Academy of Sciences Publication Activity Database

    Šesnic, S.; Dorić, V.; Poljak, D.; Šušnjara, A.; Artaud, J.F.

    2018-01-01

    Roč. 46, č. 4 (2018), s. 1027-1034 ISSN 0093-3813 R&D Projects: GA MŠk(CZ) 8D15001 Institutional support: RVO:61389021 Keywords : Finite element analysis * Tokamaks * current diffusion equation (CDE) * finite-element method (FEM) Subject RIV: BL - Plasma and Gas Discharge Physics OBOR OECD: Fluids and plasma physics (including surface physics) Impact factor: 1.052, year: 2016

  12. A new dedicated finite element for push-over analysis of reinforced concrete shear wall systems

    Directory of Open Access Journals (Sweden)

    Delal Doğru ORMANCI

    2016-06-01

    Full Text Available In this study, a finite element which has been analyzed based on anisotropic behavior of reinforced shear walls is developed. Element stiffness matrices were varied based on whether the element is in the tension or the compression zone of the cross-section. Nonlinear behavior of reinforced shear wall model is investigated under horizontal loads. This behavior is defined with a similar approach to plastic hinge assumption in frame structures that the finite element behaves lineer elastic between joints and plastic deformations are concentrated on joints as vertical plastic displacements. According to this acceptance, plastic behavior of reinforced shear wall occurs when the vertical strain reaches elastic strain limit. In the definition of finite element, displacement functions are chosen considering that the partition of shear walls just at floor levels, are enough for solution. Results of this study are compared with the solution obtained from a different computer programme and experimental results.

  13. A collocation finite element method with prior matrix condensation

    International Nuclear Information System (INIS)

    Sutcliffe, W.J.

    1977-01-01

    For thin shells with general loading, sixteen degrees of freedom have been used for a previous finite element solution procedure using a Collocation method instead of the usual variational based procedures. Although the number of elements required was relatively small, nevertheless the final matrix for the simultaneous solution of all unknowns could become large for a complex compound structure. The purpose of the present paper is to demonstrate a method of reducing the final matrix size, so allowing solution for large structures with comparatively small computer storage requirements while retaining the accuracy given by high order displacement functions. Collocation points, a number are equilibrium conditions which must be satisfied independently of the overall compatibility of forces and deflections for a complete structure. (Auth.)

  14. Five-point Element Scheme of Finite Analytic Method for Unsteady Groundwater Flow

    Institute of Scientific and Technical Information of China (English)

    Xiang Bo; Mi Xiao; Ji Changming; Luo Qingsong

    2007-01-01

    In order to improve the finite analytic method's adaptability for irregular unit, by using coordinates rotation technique this paper establishes a five-point element scheme of finite analytic method. It not only solves unsteady groundwater flow equation but also gives the boundary condition. This method can be used to calculate the three typical questions of groundwater. By compared with predecessor's computed result, the result of this method is more satisfactory.

  15. Hybrid finite difference/finite element solution method development for non-linear superconducting magnet and electrical circuit breakdown transient analysis

    International Nuclear Information System (INIS)

    Kraus, H.G.; Jones, J.L.

    1986-01-01

    The problem of non-linear superconducting magnet and electrical protection circuit system transients is formulated. To enable studying the effects of coil normalization transients, coil distortion (due to imbalanced magnetic forces), internal coil arcs and shorts, and other normal and off-normal circuit element responses, the following capabilities are included: temporal, voltage and current-dependent voltage sources, current sources, resistors, capacitors and inductors. The concept of self-mutual inductance, and the form of the associated inductance matrix, is discussed for internally shorted coils. This is a Kirchhoff's voltage loop law and Kirchhoff's current node law formulation. The non-linear integrodifferential equation set is solved via a unique hybrid finite difference/integral finite element technique. (author)

  16. A coupled boundary element-finite difference solution of the elliptic modified mild slope equation

    DEFF Research Database (Denmark)

    Naserizadeh, R.; Bingham, Harry B.; Noorzad, A.

    2011-01-01

    The modified mild slope equation of [5] is solved using a combination of the boundary element method (BEM) and the finite difference method (FDM). The exterior domain of constant depth and infinite horizontal extent is solved by a BEM using linear or quadratic elements. The interior domain...

  17. FINITE ELEMENT MODEL FOR PREDICTING RESIDUAL ...

    African Journals Online (AJOL)

    FINITE ELEMENT MODEL FOR PREDICTING RESIDUAL STRESSES IN ... the transverse residual stress in the x-direction (σx) had a maximum value of 375MPa ... the finite element method are in fair agreement with the experimental results.

  18. Soft tissue deformation using a Hierarchical Finite Element Model.

    Science.gov (United States)

    Faraci, Alessandro; Bello, Fernando; Darzi, Ara

    2004-01-01

    Simulating soft tissue deformation in real-time has become increasingly important in order to provide a realistic virtual environment for training surgical skills. Several methods have been proposed with the aim of rendering in real-time the mechanical and physiological behaviour of human organs, one of the most popular being Finite Element Method (FEM). In this paper we present a new approach to the solution of the FEM problem introducing the concept of parent and child mesh within the development of a hierarchical FEM. The online selection of the child mesh is presented with the purpose to adapt the mesh hierarchy in real-time. This permits further refinement of the child mesh increasing the detail of the deformation without slowing down the simulation and giving the possibility of integrating force feedback. The results presented demonstrate the application of our proposed framework using a desktop virtual reality (VR) system that incorporates stereo vision with integrated haptics co-location via a desktop Phantom force feedback device.

  19. Sensitivity analysis of the Galerkin finite element method neutron diffusion solver to the shape of the elements

    Energy Technology Data Exchange (ETDEWEB)

    Hosseini, Seyed Abolfaz [Dept. of Energy Engineering, Sharif University of Technology, Tehran (Iran, Islamic Republic of)

    2017-02-15

    The purpose of the present study is the presentation of the appropriate element and shape function in the solution of the neutron diffusion equation in two-dimensional (2D) geometries. To this end, the multigroup neutron diffusion equation is solved using the Galerkin finite element method in both rectangular and hexagonal reactor cores. The spatial discretization of the equation is performed using unstructured triangular and quadrilateral finite elements. Calculations are performed using both linear and quadratic approximations of shape function in the Galerkin finite element method, based on which results are compared. Using the power iteration method, the neutron flux distributions with the corresponding eigenvalue are obtained. The results are then validated against the valid results for IAEA-2D and BIBLIS-2D benchmark problems. To investigate the dependency of the results to the type and number of the elements, and shape function order, a sensitivity analysis of the calculations to the mentioned parameters is performed. It is shown that the triangular elements and second order of the shape function in each element give the best results in comparison to the other states.

  20. Finite-element-analysis of fields radiated from ICRF antenna

    International Nuclear Information System (INIS)

    Yamanaka, Kaoru; Sugihara, Ryo.

    1984-04-01

    In several simple geometries, electromagnetic fields radiated from a loop antenna, on which a current oscillately flows across the static magnetic field B-vector 0 , are calculated by the finite element method (FEM) as well as by analytic methods in a cross section of a plasma cylinder. A finite wave number along B-vector 0 is assumed. Good agreement between FEM and the analytic solutions is obtained, which indicates the accuracy of FEM solutions. The method is applied to calculations of fields from a half-turn antenna and reasonable results are obtained. It is found that a straightforward application of FEM to problems in an anisotropic medium may bring about erroneous results and that an appropriate coordinate transformation is needed for FEM to become applicable. (author)

  1. Finite-Element 2D and 3D PIC Modeling of RF Devices with Applications to Multipacting

    CERN Document Server

    De Ford, John F; Petillo, John

    2005-01-01

    Multipacting currently limits the performance of many high power radio-frequency (RF) devices, particularly couplers and windows. Models have helped researchers understand and mitigate this problem in 2D structures, but useful multipacting models for complicated 3D structures are still a challenge. A combination of three recent technologies that have been developed in the Analyst and MICHELLE codes begin to address this challenge: high-order adaptive finite-element RF field calculations, advanced particle tracking on unstructured grids, and comprehensive secondary emission models. Analyst employs high-order adaptive finite-element methods to accurately compute driven RF fields and eigenmodes in complex geometries, particularly near edges, corners, and curved surfaces. To perform a multipacting analysis, we use the mesh and fields from Analyst in a modified version of the self-consistent, finite-element gun code MICHELLE. MICHELLE has both a fast, accurate, and reliable particle tracker for unstructured grids ...

  2. An efficient structural finite element for inextensible flexible risers

    Science.gov (United States)

    Papathanasiou, T. K.; Markolefas, S.; Khazaeinejad, P.; Bahai, H.

    2017-12-01

    A core part of all numerical models used for flexible riser analysis is the structural component representing the main body of the riser as a slender beam. Loads acting on this structural element are self-weight, buoyant and hydrodynamic forces, internal pressure and others. A structural finite element for an inextensible riser with a point-wise enforcement of the inextensibility constrain is presented. In particular, the inextensibility constraint is applied only at the nodes of the meshed arc length parameter. Among the virtues of the proposed approach is the flexibility in the application of boundary conditions and the easy incorporation of dissipative forces. Several attributes of the proposed finite element scheme are analysed and computation times for the solution of some simplified examples are discussed. Future developments aim at the appropriate implementation of material and geometric parameters for the beam model, i.e. flexural and torsional rigidity.

  3. Finite element analysis of piezoelectric materials

    International Nuclear Information System (INIS)

    Lowrie, F.; Stewart, M.; Cain, M.; Gee, M.

    1999-01-01

    This guide is intended to help people wanting to do finite element analysis of piezoelectric materials by answering some of the questions that are peculiar to piezoelectric materials. The document is not intended as a complete beginners guide for finite element analysis in general as this is better dealt with by the individual software producers. The guide is based around the commercial package ANSYS as this is a popular package amongst piezoelectric material users, however much of the information will still be useful to users of other finite element codes. (author)

  4. Parallel eigenanalysis of finite element models in a completely connected architecture

    Science.gov (United States)

    Akl, F. A.; Morel, M. R.

    1989-01-01

    A parallel algorithm is presented for the solution of the generalized eigenproblem in linear elastic finite element analysis, (K)(phi) = (M)(phi)(omega), where (K) and (M) are of order N, and (omega) is order of q. The concurrent solution of the eigenproblem is based on the multifrontal/modified subspace method and is achieved in a completely connected parallel architecture in which each processor is allowed to communicate with all other processors. The algorithm was successfully implemented on a tightly coupled multiple-instruction multiple-data parallel processing machine, Cray X-MP. A finite element model is divided into m domains each of which is assumed to process n elements. Each domain is then assigned to a processor or to a logical processor (task) if the number of domains exceeds the number of physical processors. The macrotasking library routines are used in mapping each domain to a user task. Computational speed-up and efficiency are used to determine the effectiveness of the algorithm. The effect of the number of domains, the number of degrees-of-freedom located along the global fronts and the dimension of the subspace on the performance of the algorithm are investigated. A parallel finite element dynamic analysis program, p-feda, is documented and the performance of its subroutines in parallel environment is analyzed.

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

    Science.gov (United States)

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

    2017-12-01

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

  6. Finite rotation shells basic equations and finite elements for Reissner kinematics

    CERN Document Server

    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.

  7. A collocation--Galerkin finite element model of cardiac action potential propagation.

    Science.gov (United States)

    Rogers, J M; McCulloch, A D

    1994-08-01

    A new computational method was developed for modeling the effects of the geometric complexity, nonuniform muscle fiber orientation, and material inhomogeneity of the ventricular wall on cardiac impulse propagation. The method was used to solve a modification to the FitzHugh-Nagumo system of equations. The geometry, local muscle fiber orientation, and material parameters of the domain were defined using linear Lagrange or cubic Hermite finite element interpolation. Spatial variations of time-dependent excitation and recovery variables were approximated using cubic Hermite finite element interpolation, and the governing finite element equations were assembled using the collocation method. To overcome the deficiencies of conventional collocation methods on irregular domains, Galerkin equations for the no-flux boundary conditions were used instead of collocation equations for the boundary degrees-of-freedom. The resulting system was evolved using an adaptive Runge-Kutta method. Converged two-dimensional simulations of normal propagation showed that this method requires less CPU time than a traditional finite difference discretization. The model also reproduced several other physiologic phenomena known to be important in arrhythmogenesis including: Wenckebach periodicity, slowed propagation and unidirectional block due to wavefront curvature, reentry around a fixed obstacle, and spiral wave reentry. In a new result, we observed wavespeed variations and block due to nonuniform muscle fiber orientation. The findings suggest that the finite element method is suitable for studying normal and pathological cardiac activation and has significant advantages over existing techniques.

  8. Moving mesh finite element method for finite time extinction of distributed parameter systems with positive exponential feedback; Lokakarya Komputasi dalam Sains dan Teknologi Nuklir VI

    Energy Technology Data Exchange (ETDEWEB)

    Garnadi, A D [Department of Matematics, Bogor Institute of Agriculture, Bogor (Indonesia)

    1997-07-01

    In the distributed parameter systems with exponential feedback, non-global existence of solution is not always exist. For some positive initial values, there exist finite time T such that the solution goes to infinity, i.e. finite time extinction or blow-up. Here is present a numerical solution using Moving Mesh Finite Element to solve the distributed parameter systems with exponential feedback close to blow-up time. The numerical behavior of the mesh close to the time of extinction is the prime interest in this study.

  9. HYFRAC3D, 3-D Hydraulic Rock Fracture Propagation by Finite Element Method

    International Nuclear Information System (INIS)

    Advani, S.H.; Lee, J.K.; Lee, T.S.

    2001-01-01

    1 - Description of program or function: HYFRAC3D is a finite element program for simulation of three-dimensional fracture geometries with a two-dimensional planar solution. The model predicts the height, width and wing length over time for a hydraulic fracture propagating in a multi-layered system of rock with variable fluid flow and rock mechanics properties. 2 - Method of solution: The program uses the finite element Method of solution. A backward difference scheme is used by taking the weight functions on the time axis. This implicit time matching scheme requires iteration since the fracture configuration at time t+dt is not known. 3 - Restrictions on the complexity of the problem: Graphics output is not available and program is limited to fracture propagation in a single plane without proppant transport

  10. OPTIM, Minimization of Band-Width of Finite Elements Problems

    International Nuclear Information System (INIS)

    Huart, M.

    1977-01-01

    1 - Nature of the physical problem solved: To minimize the band-width of finite element problems. 2 - Method of solution: A surface is constructed from the x-y-coordinates of each node using its node number as z-value. This surface consists of triangles. Nodes are renumbered in such a way as to minimize the surface area. 3 - Restrictions on the complexity of the problem: This program is applicable to 2-D problems. It is dimensioned for a maximum of 1000 elements

  11. The Fourier-finite-element approximation of the lame equations in axisymmetric domains with edges

    International Nuclear Information System (INIS)

    Nkemzil, Boniface

    2003-10-01

    This paper is concerned with a priori error estimates and convergence analysis of the Fourier-finite-element solutions of the Neumann problem for the Lame equations in axisymmetric domains Ω-circumflex is contained in R 3 with reentrant edges. The Fourier-FEM combines the approximating Fourier method with respect to the rotational angle using trigonometric polynomials of degree N (N →∞), with the finite-element method on the plane meridian domain of Ω-circumflex with mesh size h (h → 0) for approximating the Fourier coefficients. The asymptotic behavior of the solution near reentrant edges is described by singular functions in non-tensor product form and treated numerically by means of finite element method on locally graded meshes. For the right-hand side f-circumflex is an element of (L 2 (Ω-circumflex)) 3 , it is proved that the rate of convergence of the combined approximations in the norms of (W 2 1 (Ω-circumflex)) 3 is of the order O(h 2-l +N -(2-l) ) (l=0,1). (author)

  12. Investigations on Actuator Dynamics through Theoretical and Finite Element Approach

    Directory of Open Access Journals (Sweden)

    Somashekhar S. Hiremath

    2010-01-01

    Full Text Available This paper gives a new approach for modeling the fluid-structure interaction of servovalve component-actuator. The analyzed valve is a precision flow control valve-jet pipe electrohydraulic servovalve. The positioning of an actuator depends upon the flow rate from control ports, in turn depends on the spool position. Theoretical investigation is made for No-load condition and Load condition for an actuator. These are used in finite element modeling of an actuator. The fluid-structure-interaction (FSI is established between the piston and the fluid cavities at the piston end. The fluid cavities were modeled with special purpose hydrostatic fluid elements while the piston is modeled with brick elements. The finite element method is used to simulate the variation of cavity pressure, cavity volume, mass flow rate, and the actuator velocity. The finite element analysis is extended to study the system's linearized response to harmonic excitation using direct solution steady-state dynamics. It was observed from the analysis that the natural frequency of the actuator depends upon the position of the piston in the cylinder. This is a close match with theoretical and simulation results. The effect of bulk modulus is also presented in the paper.

  13. Generalized multiscale finite element methods (GMsFEM)

    KAUST Repository

    Efendiev, Yalchin R.; Galvis, Juan; Hou, Thomasyizhao

    2013-01-01

    In this paper, we propose a general approach called Generalized Multiscale Finite Element Method (GMsFEM) for performing multiscale simulations for problems without scale separation over a complex input space. As in multiscale finite element methods (MsFEMs), the main idea of the proposed approach is to construct a small dimensional local solution space that can be used to generate an efficient and accurate approximation to the multiscale solution with a potentially high dimensional input parameter space. In the proposed approach, we present a general procedure to construct the offline space that is used for a systematic enrichment of the coarse solution space in the online stage. The enrichment in the online stage is performed based on a spectral decomposition of the offline space. In the online stage, for any input parameter, a multiscale space is constructed to solve the global problem on a coarse grid. The online space is constructed via a spectral decomposition of the offline space and by choosing the eigenvectors corresponding to the largest eigenvalues. The computational saving is due to the fact that the construction of the online multiscale space for any input parameter is fast and this space can be re-used for solving the forward problem with any forcing and boundary condition. Compared with the other approaches where global snapshots are used, the local approach that we present in this paper allows us to eliminate unnecessary degrees of freedom on a coarse-grid level. We present various examples in the paper and some numerical results to demonstrate the effectiveness of our method. © 2013 Elsevier Inc.

  14. Generalized multiscale finite element methods (GMsFEM)

    KAUST Repository

    Efendiev, Yalchin R.

    2013-10-01

    In this paper, we propose a general approach called Generalized Multiscale Finite Element Method (GMsFEM) for performing multiscale simulations for problems without scale separation over a complex input space. As in multiscale finite element methods (MsFEMs), the main idea of the proposed approach is to construct a small dimensional local solution space that can be used to generate an efficient and accurate approximation to the multiscale solution with a potentially high dimensional input parameter space. In the proposed approach, we present a general procedure to construct the offline space that is used for a systematic enrichment of the coarse solution space in the online stage. The enrichment in the online stage is performed based on a spectral decomposition of the offline space. In the online stage, for any input parameter, a multiscale space is constructed to solve the global problem on a coarse grid. The online space is constructed via a spectral decomposition of the offline space and by choosing the eigenvectors corresponding to the largest eigenvalues. The computational saving is due to the fact that the construction of the online multiscale space for any input parameter is fast and this space can be re-used for solving the forward problem with any forcing and boundary condition. Compared with the other approaches where global snapshots are used, the local approach that we present in this paper allows us to eliminate unnecessary degrees of freedom on a coarse-grid level. We present various examples in the paper and some numerical results to demonstrate the effectiveness of our method. © 2013 Elsevier Inc.

  15. 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.

  16. Multigrid Finite Element Method in Calculation of 3D Homogeneous and Composite Solids

    Directory of Open Access Journals (Sweden)

    A.D. Matveev

    2016-12-01

    Full Text Available In the present paper, a method of multigrid finite elements to calculate elastic three-dimensional homogeneous and composite solids under static loading has been suggested. The method has been developed based on the finite element method algorithms using homogeneous and composite three-dimensional multigrid finite elements (MFE. The procedures for construction of MFE of both rectangular parallelepiped and complex shapes have been shown. The advantages of MFE are that they take into account, following the rules of the microapproach, heterogeneous and microhomogeneous structures of the bodies, describe the three-dimensional stress-strain state (without any simplifying hypotheses in homogeneous and composite solids, as well as generate small dimensional discrete models and numerical solutions with a high accuracy.

  17. Hybrid-finite-element analysis of some nonlinear and 3-dimensional problems of engineering fracture mechanics

    Science.gov (United States)

    Atluri, S. N.; Nakagaki, M.; Kathiresan, K.

    1980-01-01

    In this paper, efficient numerical methods for the analysis of crack-closure effects on fatigue-crack-growth-rates, in plane stress situations, and for the solution of stress-intensity factors for arbitrary shaped surface flaws in pressure vessels, are presented. For the former problem, an elastic-plastic finite element procedure valid for the case of finite deformation gradients is developed and crack growth is simulated by the translation of near-crack-tip elements with embedded plastic singularities. For the latter problem, an embedded-elastic-singularity hybrid finite element method, which leads to a direct evaluation of K-factors, is employed.

  18. Aranha: a 2D mesh generator for triangular finite elements

    International Nuclear Information System (INIS)

    Fancello, E.A.; Salgado, A.C.; Feijoo, R.A.

    1990-01-01

    A method for generating unstructured meshes for linear and quadratic triangular finite elements is described in this paper. Some topics on the C language data structure used in the development of the program Aranha are also presented. The applicability for adaptive remeshing is shown and finally several examples are included to illustrate the performance of the method in irregular connected planar domains. (author)

  19. Why do probabilistic finite element analysis ?

    CERN Document Server

    Thacker, Ben 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.

  20. Application of finite element techniques in predicting the acoustic properties of turbofan inlets

    Science.gov (United States)

    Majjigi, R. K.; Sigman, R. K.; Zinn, B. T.

    1978-01-01

    An analytical technique was developed for predicting the acoustic performance of turbofan inlets carrying a subsonic axisymmetric steady flow. The finite element method combined with the method of weighted residuals is used in predicting the acoustic properties of variable area, annular ducts with or without acoustic treatments along their walls. An approximate solution for the steady inviscid flow field is obtained using an integral method for calculating the incompressible potential flow field in the inlet with a correction to account for compressibility effects. The accuracy of the finite element technique was assessed by comparison with available analytical solutions for the problems of plane and spinning wave propagation through a hard walled annular cylinder with a constant mean flow.

  1. A finite element perspective on non-linear FFT-based micromechanical simulations

    NARCIS (Netherlands)

    Zeman, J.; de Geus, T.W.J.; Vondřejc, J.; Peerlings, R.H.J.; Geers, M.G.D.

    2016-01-01

    Fourier solvers have become efficient tools to establish structure-property relations in heterogeneous materials. Introduced as an alternative to the Finite Element (FE) method, they are based on fixed-point solutions of the Lippmann-Schwinger type integral equation. Their computational efficiency

  2. SAFE-3D, Stress Analysis of 3-D Composite Structure by Finite Elements Method

    International Nuclear Information System (INIS)

    Cornell, D.C.; Jadhav, K.; Crowell, J.S.

    1969-01-01

    1 - Description of problem or function: SAFE-3D is a finite-element program for the three-dimensional elastic analysis of heterogeneous composite structures. The program uses the following types of finite elements - (1) tetrahedral elements to represent the continuum, (2) triangular plane stress membrane elements to represent inner liner or outer case, and (3) uniaxial tension-compression elements to represent internal reinforcement. The structure can be of arbitrary geometry and have any distribution of material properties, temperatures, surface loadings, and boundary conditions. 2 - Method of solution: The finite-element variational method is used. Equilibrium equations are solved by the alternating component iterative method. 3 - Restrictions on the complexity of the problem - Maxima of: 5000 nodes; 16000 elements. The program cannot be applied to incompressible solids and is not recommended for Poisson's ratio in the range of nu between 0.495 and 0.5

  3. Finite element analysis theory and application with ANSYS

    CERN Document Server

    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...

  4. Finite element application to global reactor analysis

    International Nuclear Information System (INIS)

    Schmidt, F.A.R.

    1981-01-01

    The Finite Element Method is described as a Coarse Mesh Method with general basis and trial functions. Various consequences concerning programming and application of Finite Element Methods in reactor physics are drawn. One of the conclusions is that the Finite Element Method is a valuable tool in solving global reactor analysis problems. However, problems which can be described by rectangular boxes still can be solved with special coarse mesh programs more efficiently. (orig.) [de

  5. 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...

  6. Books and monographs on finite element technology

    Science.gov (United States)

    Noor, A. K.

    1985-01-01

    The present paper proviees a listing of all of the English books and some of the foreign books on finite element technology, taking into account also a list of the conference proceedings devoted solely to finite elements. The references are divided into categories. Attention is given to fundamentals, mathematical foundations, structural and solid mechanics applications, fluid mechanics applications, other applied science and engineering applications, computer implementation and software systems, computational and modeling aspects, special topics, boundary element methods, proceedings of symmposia and conferences on finite element technology, bibliographies, handbooks, and historical accounts.

  7. Generalized multiscale finite element methods: Oversampling strategies

    KAUST Repository

    Efendiev, Yalchin R.; Galvis, Juan; Li, Guanglian; Presho, Michael

    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

  8. Solution of two energy-group neutron diffusion equation by triangular elements

    International Nuclear Information System (INIS)

    Correia Filho, A.

    1981-01-01

    The application of the triangular finite elements of first order in the solution of two energy-group neutron diffusion equation in steady-state conditions is aimed at. The EFTDN (triangular finite elements in neutrons diffusion) computer code in FORTRAN IV language is developed. The discrete formulation of the diffusion equation is obtained applying the Galerkin method. The power method is used to solve the eigenvalues' problem and the convergence is accelerated through the use of Chebshev polynomials. For the equation systems solution the Gauss method is applied. The results of the analysis of two test-problems are presented. (Author) [pt

  9. The Dynamic Response of an Euler-Bernoulli Beam on an Elastic Foundation by Finite Element Analysis using the Exact Stiffness Matrix

    International Nuclear Information System (INIS)

    Kim, Jeong Soo; Kim, Moon Kyum

    2012-01-01

    In this study, finite element analysis of beam on elastic foundation, which received great attention of researchers due to its wide applications in engineering, is performed for estimating dynamic responses of shallow foundation using exact stiffness matrix. First, element stiffness matrix based on the closed solution of beam on elastic foundation is derived. Then, we performed static finite element analysis included exact stiffness matrix numerically, comparing results from the analysis with some exact analysis solutions well known for verification. Finally, dynamic finite element analysis is performed for a shallow foundation structure under rectangular pulse loading using trapezoidal method. The dynamic analysis results exist in the reasonable range comparing solution of single degree of freedom problem under a similar condition. The results show that finite element analysis using exact stiffness matrix is evaluated as a good tool of estimating the dynamic response of structures on elastic foundation.

  10. Effect of randomness on multi-frequency aeroelastic responses resolved by Unsteady Adaptive Stochastic Finite Elements

    International Nuclear Information System (INIS)

    Witteveen, Jeroen A.S.; Bijl, Hester

    2009-01-01

    The Unsteady Adaptive Stochastic Finite Elements (UASFE) method resolves the effect of randomness in numerical simulations of single-mode aeroelastic responses with a constant accuracy in time for a constant number of samples. In this paper, the UASFE framework is extended to multi-frequency responses and continuous structures by employing a wavelet decomposition pre-processing step to decompose the sampled multi-frequency signals into single-frequency components. The effect of the randomness on the multi-frequency response is then obtained by summing the results of the UASFE interpolation at constant phase for the different frequency components. Results for multi-frequency responses and continuous structures show a three orders of magnitude reduction of computational costs compared to crude Monte Carlo simulations in a harmonically forced oscillator, a flutter panel problem, and the three-dimensional transonic AGARD 445.6 wing aeroelastic benchmark subject to random fields and random parameters with various probability distributions.

  11. Global limit load solutions for thick-walled cylinders with circumferential cracks under combined internal pressure, axial force and bending moment − Part II: Finite element validation

    International Nuclear Information System (INIS)

    Li, Yuebing; Lei, Yuebao; Gao, Zengliang

    2014-01-01

    Global limit load solutions for thick-walled cylinders with circumferential internal/external surface and through-wall defects under combined positive/negative axial force, positive/negative global bending moment and internal pressure have been developed in Part I of this paper. In this Part II, elastic-perfectly plastic 3-D finite element (FE) analyses are performed for selected cases, covering a wide range of geometries and load combinations, to validate the developed limit load solutions. The results show that these limit load solutions can predict the FE data very well for the cases with shallow or deep and short cracks and are conservative. For the cases with very long and deep cracks, the predictions are reasonably accurate and more conservative. -- Highlights: • Elastic-perfectly plastic 3D finite element limiting analyses of cylinders. • Thin/thick-walled cylinders with circumferential surface defects. • Combined loading for pressure, end-force and global bending moment. • Totally 1458 cases analysed and tabulated normalised results provided. • Results used to validate the developed limit load solutions in Part I of this paper

  12. Probabilistic finite elements for fracture mechanics

    Science.gov (United States)

    Besterfield, Glen

    1988-01-01

    The probabilistic finite element method (PFEM) is developed for probabilistic fracture mechanics (PFM). A finite element which has the near crack-tip singular strain embedded in the element is used. Probabilistic distributions, such as expectation, covariance and correlation stress intensity factors, are calculated for random load, random material and random crack length. The method is computationally quite efficient and can be expected to determine the probability of fracture or reliability.

  13. A Posteriori Finite Element Bounds for Sensitivity Derivatives of Partial-Differential-Equation Outputs. Revised

    Science.gov (United States)

    Lewis, Robert Michael; Patera, Anthony T.; Peraire, Jaume

    1998-01-01

    We present a Neumann-subproblem a posteriori finite element procedure for the efficient and accurate calculation of rigorous, 'constant-free' upper and lower bounds for sensitivity derivatives of functionals of the solutions of partial differential equations. The design motivation for sensitivity derivative error control is discussed; the a posteriori finite element procedure is described; the asymptotic bounding properties and computational complexity of the method are summarized; and illustrative numerical results are presented.

  14. Application of 1 D Finite Element Method in Combination with Laminar Solution Method for Pipe Network Analysis

    Science.gov (United States)

    Dudar, O. I.; Dudar, E. S.

    2017-11-01

    The features of application of the 1D dimensional finite element method (FEM) in combination with the laminar solutions method (LSM) for the calculation of underground ventilating networks are considered. In this case the processes of heat and mass transfer change the properties of a fluid (binary vapour-air mix). Under the action of gravitational forces it leads to such phenomena as natural draft, local circulation, etc. The FEM relations considering the action of gravity, the mass conservation law, the dependence of vapour-air mix properties on the thermodynamic parameters are derived so that it allows one to model the mentioned phenomena. The analogy of the elastic and plastic rod deformation processes to the processes of laminar and turbulent flow in a pipe is described. Owing to this analogy, the guaranteed convergence of the elastic solutions method for the materials of plastic type means the guaranteed convergence of the LSM for any regime of a turbulent flow in a rough pipe. By means of numerical experiments the convergence rate of the FEM - LSM is investigated. This convergence rate appeared much higher than the convergence rate of the Cross - Andriyashev method. Data of other authors on the convergence rate comparison for the finite element method, the Newton method and the method of gradient are provided. These data allow one to conclude that the FEM in combination with the LSM is one of the most effective methods of calculation of hydraulic and ventilating networks. The FEM - LSM has been used for creation of the research application programme package “MineClimate” allowing to calculate the microclimate parameters in the underground ventilating networks.

  15. An enriched finite element model with q-refinement for radiative boundary layers in glass cooling

    Energy Technology Data Exchange (ETDEWEB)

    Mohamed, M. Shadi [Institute for Infrastructure and Environment, Heriot-Watt University, Edinburgh EH14 4AS (United Kingdom); Seaid, Mohammed; Trevelyan, Jon [School of Engineering and Computing Sciences, University of Durham, South Road, Durham DH1 3LE (United Kingdom); Laghrouche, Omar [Institute for Infrastructure and Environment, Heriot-Watt University, Edinburgh EH14 4AS (United Kingdom)

    2014-02-01

    Radiative cooling in glass manufacturing is simulated using the partition of unity finite element method. The governing equations consist of a semi-linear transient heat equation for the temperature field and a stationary simplified P{sub 1} approximation for the radiation in non-grey semitransparent media. To integrate the coupled equations in time we consider a linearly implicit scheme in the finite element framework. A class of hyperbolic enrichment functions is proposed to resolve boundary layers near the enclosure walls. Using an industrial electromagnetic spectrum, the proposed method shows an immense reduction in the number of degrees of freedom required to achieve a certain accuracy compared to the conventional h-version finite element method. Furthermore the method shows a stable behaviour in treating the boundary layers which is shown by studying the solution close to the domain boundaries. The time integration choice is essential to implement a q-refinement procedure introduced in the current study. The enrichment is refined with respect to the steepness of the solution gradient near the domain boundary in the first few time steps and is shown to lead to a further significant reduction on top of what is already achieved with the enrichment. The performance of the proposed method is analysed for glass annealing in two enclosures where the simplified P{sub 1} approximation solution with the partition of unity method, the conventional finite element method and the finite difference method are compared to each other and to the full radiative heat transfer as well as the canonical Rosseland model.

  16. An assessment of finite element synthesis model using 3D FEM

    International Nuclear Information System (INIS)

    Jagannathan, V.; Rastogi, B.P

    1983-01-01

    For the solution of multigroup diffusion theory equations a code system called FEMSYN has been developed. The code FEMSYN incorporates a finite difference (FD) module, a finite element (FE) module and one module based on single channel flux synthesis (SCFS) method, which uses trial functions generated by either FD or FE method. The 3D problems can be tackled by all the three modules. The 3D FE solutions are cheaper in comparison with fine mesh FD computations and are quite accurate. The accuracy is improved by proper choice of rectangular and triangular right prismatic elements and polynomial order in case of 3D FE analyses. Synthesis method using FE trial functions provides the fastest means of solution for 3D problems. In this paper, the FE synthesis method has been compared with 3D FE technique for the case of IAEA PWR benchmark problem. It is concluded from the above comparison that FE synthesis method can give at negligible computational efforts, accurate eigenvalue estimates and satisfactory prediction of reactor core power profiles

  17. Distributed Finite Element Analysis Using a Transputer Network

    Science.gov (United States)

    Watson, James; Favenesi, James; Danial, Albert; Tombrello, Joseph; Yang, Dabby; Reynolds, Brian; Turrentine, Ronald; Shephard, Mark; Baehmann, Peggy

    1989-01-01

    The principal objective of this research effort was to demonstrate the extraordinarily cost effective acceleration of finite element structural analysis problems using a transputer-based parallel processing network. This objective was accomplished in the form of a commercially viable parallel processing workstation. The workstation is a desktop size, low-maintenance computing unit capable of supercomputer performance yet costs two orders of magnitude less. To achieve the principal research objective, a transputer based structural analysis workstation termed XPFEM was implemented with linear static structural analysis capabilities resembling commercially available NASTRAN. Finite element model files, generated using the on-line preprocessing module or external preprocessing packages, are downloaded to a network of 32 transputers for accelerated solution. The system currently executes at about one third Cray X-MP24 speed but additional acceleration appears likely. For the NASA selected demonstration problem of a Space Shuttle main engine turbine blade model with about 1500 nodes and 4500 independent degrees of freedom, the Cray X-MP24 required 23.9 seconds to obtain a solution while the transputer network, operated from an IBM PC-AT compatible host computer, required 71.7 seconds. Consequently, the $80,000 transputer network demonstrated a cost-performance ratio about 60 times better than the $15,000,000 Cray X-MP24 system.

  18. Experimental verifications of a structural damage identification technique using reduced order finite-element model

    Science.gov (United States)

    Li, Rui; Zhou, Li; Yang, Jann N.

    2010-04-01

    An objective of the structural health monitoring system is to identify the state of the structure and to detect the damage when it occurs. Analysis techniques for the damage identification of structures, based on vibration data measured from sensors, have received considerable attention. Recently, a new damage tracking technique, referred to as the adaptive quadratic sum-square error (AQSSE) technique, has been proposed, and simulation studies demonstrated that the AQSSE technique is quite effective in identifying structural damages. In this paper, the adaptive quadratic sumsquare error (AQSSE) along with the reduced-order finite-element method is proposed to identify the damages of complex structures. Experimental tests were conducted to verify the capability of the proposed damage detection approach. A series of experimental tests were performed using a scaled cantilever beam subject to the white noise and sinusoidal excitations. The capability of the proposed reduced-order finite-element based adaptive quadratic sum-square error (AQSSE) method in detecting the structural damage is demonstrated by the experimental results.

  19. A unidirectional approach for d-dimensional finite element methods for higher order on sparse grids

    Energy Technology Data Exchange (ETDEWEB)

    Bungartz, H.J. [Technische Universitaet Muenchen (Germany)

    1996-12-31

    In the last years, sparse grids have turned out to be a very interesting approach for the efficient iterative numerical solution of elliptic boundary value problems. In comparison to standard (full grid) discretization schemes, the number of grid points can be reduced significantly from O(N{sup d}) to O(N(log{sub 2}(N)){sup d-1}) in the d-dimensional case, whereas the accuracy of the approximation to the finite element solution is only slightly deteriorated: For piecewise d-linear basis functions, e. g., an accuracy of the order O(N{sup - 2}(log{sub 2}(N)){sup d-1}) with respect to the L{sub 2}-norm and of the order O(N{sup -1}) with respect to the energy norm has been shown. Furthermore, regular sparse grids can be extended in a very simple and natural manner to adaptive ones, which makes the hierarchical sparse grid concept applicable to problems that require adaptive grid refinement, too. An approach is presented for the Laplacian on a uinit domain in this paper.

  20. Introduction to finite and spectral element methods using Matlab

    CERN Document Server

    Pozrikidis, Constantine

    2014-01-01

    The Finite Element Method in One Dimension. Further Applications in One Dimension. High-Order and Spectral Elements in One Dimension. The Finite Element Method in Two Dimensions. Quadratic and Spectral Elements in Two Dimensions. Applications in Mechanics. Viscous Flow. Finite and Spectral Element Methods in Three Dimensions. Appendices. References. Index.

  1. Finite Element Methods and Their Applications

    CERN Document Server

    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.

  2. Finite Element Analysis of Dam-Reservoir Interaction Using High-Order Doubly Asymptotic Open Boundary

    Directory of Open Access Journals (Sweden)

    Yichao Gao

    2011-01-01

    Full Text Available The dam-reservoir system is divided into the near field modeled by the finite element method, and the far field modeled by the excellent high-order doubly asymptotic open boundary (DAOB. Direct and partitioned coupled methods are developed for the analysis of dam-reservoir system. In the direct coupled method, a symmetric monolithic governing equation is formulated by incorporating the DAOB with the finite element equation and solved using the standard time-integration methods. In contrast, the near-field finite element equation and the far-field DAOB condition are separately solved in the partitioned coupled methodm, and coupling is achieved by applying the interaction force on the truncated boundary. To improve its numerical stability and accuracy, an iteration strategy is employed to obtain the solution of each step. Both coupled methods are implemented on the open-source finite element code OpenSees. Numerical examples are employed to demonstrate the performance of these two proposed methods.

  3. Mechanical strength calculation of the disk type windings with elastic couplings by the finite element method

    International Nuclear Information System (INIS)

    Sivkova, G.N.; Spirchenko, Yu.V.; Chvartatskij, P.V.

    1981-01-01

    Stressed-deformed state of toroidal field coils of the disc type with elastic couplings of the tokamaks has been investigated with provision for the effect of the central core pliability by means of the two-dimensional version of the finite element method. Numerical solution of the finite element method is performed by means of the ES 1040 computer according to the computer code permitting taking account of boundary conditions of elastic support. The calculation has been performed using as the example the project of T-20 facility coil of the disc type. Consideration of pliability of the central core of the facility inductor is accomplished by the introduction of additional rigidities to the complete matrix of rigidity. Scheme of the structure distretization includes 141 units, 211 elements. The accuracy of solution depends on the reduction accuracy of the volume load to unit forces and on the number of finite elements. Analysis of the solution convergence is performed by the comparison of solutions obtained for three different schemes of the disk discretization without regard for the inductor pliability. The comparative analysis of the results shows that transfer epures for all the three discretization versions practically coincide and stresses differ not more than by 10%. On the whole the above investigation has demonstrated good convergence of the problem solution [ru

  4. The finite element response Matrix method

    International Nuclear Information System (INIS)

    Nakata, H.; Martin, W.R.

    1983-01-01

    A new method for global reactor core calculations is described. This method is based on a unique formulation of the response matrix method, implemented with a higher order finite element method. The unique aspects of this approach are twofold. First, there are two levels to the overall calculational scheme: the local or assembly level and the global or core level. Second, the response matrix scheme, which is formulated at both levels, consists of two separate response matrices rather than one response matrix as is generally the case. These separate response matrices are seen to be quite beneficial for the criticality eigenvalue calculation, because they are independent of k /SUB eff/. The response matrices are generated from a Galerkin finite element solution to the weak form of the diffusion equation, subject to an arbitrary incoming current and an arbitrary distributed source. Calculational results are reported for two test problems, the two-dimensional International Atomic Energy Agency benchmark problem and a two-dimensional pressurized water reactor test problem (Biblis reactor), and they compare well with standard coarse mesh methods with respect to accuracy and efficiency. Moreover, the accuracy (and capability) is comparable to fine mesh for a fraction of the computational cost. Extension of the method to treat heterogeneous assemblies and spatial depletion effects is discussed

  5. Steam generator tube rupture simulation using extended finite element method

    Energy Technology Data Exchange (ETDEWEB)

    Mohanty, Subhasish, E-mail: smohanty@anl.gov; Majumdar, Saurin; Natesan, Ken

    2016-08-15

    Highlights: • Extended finite element method used for modeling the steam generator tube rupture. • Crack propagation is modeled in an arbitrary solution dependent path. • The FE model is used for estimating the rupture pressure of steam generator tubes. • Crack coalescence modeling is also demonstrated. • The method can be used for crack modeling of tubes under severe accident condition. - Abstract: A steam generator (SG) is an important component of any pressurized water reactor. Steam generator tubes represent a primary pressure boundary whose integrity is vital to the safe operation of the reactor. SG tubes may rupture due to propagation of a crack created by mechanisms such as stress corrosion cracking, fatigue, etc. It is thus important to estimate the rupture pressures of cracked tubes for structural integrity evaluation of SGs. The objective of the present paper is to demonstrate the use of extended finite element method capability of commercially available ABAQUS software, to model SG tubes with preexisting flaws and to estimate their rupture pressures. For the purpose, elastic–plastic finite element models were developed for different SG tubes made from Alloy 600 material. The simulation results were compared with experimental results available from the steam generator tube integrity program (SGTIP) sponsored by the United States Nuclear Regulatory Commission (NRC) and conducted at Argonne National Laboratory (ANL). A reasonable correlation was found between extended finite element model results and experimental results.

  6. Steam generator tube rupture simulation using extended finite element method

    International Nuclear Information System (INIS)

    Mohanty, Subhasish; Majumdar, Saurin; Natesan, Ken

    2016-01-01

    Highlights: • Extended finite element method used for modeling the steam generator tube rupture. • Crack propagation is modeled in an arbitrary solution dependent path. • The FE model is used for estimating the rupture pressure of steam generator tubes. • Crack coalescence modeling is also demonstrated. • The method can be used for crack modeling of tubes under severe accident condition. - Abstract: A steam generator (SG) is an important component of any pressurized water reactor. Steam generator tubes represent a primary pressure boundary whose integrity is vital to the safe operation of the reactor. SG tubes may rupture due to propagation of a crack created by mechanisms such as stress corrosion cracking, fatigue, etc. It is thus important to estimate the rupture pressures of cracked tubes for structural integrity evaluation of SGs. The objective of the present paper is to demonstrate the use of extended finite element method capability of commercially available ABAQUS software, to model SG tubes with preexisting flaws and to estimate their rupture pressures. For the purpose, elastic–plastic finite element models were developed for different SG tubes made from Alloy 600 material. The simulation results were compared with experimental results available from the steam generator tube integrity program (SGTIP) sponsored by the United States Nuclear Regulatory Commission (NRC) and conducted at Argonne National Laboratory (ANL). A reasonable correlation was found between extended finite element model results and experimental results.

  7. The Mixed Finite Element Multigrid Method for Stokes Equations

    Science.gov (United States)

    Muzhinji, K.; Shateyi, S.; Motsa, S. S.

    2015-01-01

    The stable finite element discretization of the Stokes problem produces a symmetric indefinite system of linear algebraic equations. A variety of iterative solvers have been proposed for such systems in an attempt to construct efficient, fast, and robust solution techniques. This paper investigates one of such iterative solvers, the geometric multigrid solver, to find the approximate solution of the indefinite systems. The main ingredient of the multigrid method is the choice of an appropriate smoothing strategy. This study considers the application of different smoothers and compares their effects in the overall performance of the multigrid solver. We study the multigrid method with the following smoothers: distributed Gauss Seidel, inexact Uzawa, preconditioned MINRES, and Braess-Sarazin type smoothers. A comparative study of the smoothers shows that the Braess-Sarazin smoothers enhance good performance of the multigrid method. We study the problem in a two-dimensional domain using stable Hood-Taylor Q 2-Q 1 pair of finite rectangular elements. We also give the main theoretical convergence results. We present the numerical results to demonstrate the efficiency and robustness of the multigrid method and confirm the theoretical results. PMID:25945361

  8. Programming the finite element method

    CERN Document Server

    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

  9. Modal representation of geometrically nonlinear behavior by the finite element method

    International Nuclear Information System (INIS)

    Nagy, D.A.

    1977-01-01

    A method is presented for representing mild geometrically nonlinear static behavior of thin-type structures, within the finite element method, in terms of linear elastic and linear (bifurcation) buckling analysis results for structural loading or geometry situations which violate the idealized restrictive (perfect) interpretation of linear behavior up to bifurcation. Formulation of the finite element displacement method for material linearity but retaining the full, nonlinear strain-displacement relations (geometric nonlinearity) leads to highly nonlinear equations relating the unknown nodal generalized displacements r to the applied loading R. Restriction to small strains alone does not linearize these equations for thin-type structural configurations; only explicitly requiring that all products of displacement gadients be much smaller than the gadients themselves reduces the equations to the familiar linear form Ksub(e)r=R, where Ksub(e) is the elastic stiffness. Assuming then that the solutions r of the linear equations also satisfies the full nonlinear equations (i.e., that the above explicit requirement is satisfied), a second solution to the full equations can be sought for a one-parameter loading path lambdaR, leading to the well-known linear (bifurcation) buckling eigenvalue problem Ksub(e)X=-Ksub(g)XΛ where Ksub(g) is the geometric stiffness, X the matrix whose columns are the eigenvectors (so-called buckling mode shapes) and Λ is a diagonal matrix of eigenvalues lambda(i) (so-called load scale factors). From the viewpoint of the practising structural analyst using finite element software, the method presented here gives broader and deeper significance to an existing linear (bifurcation) buckling analysis capability, in that the additional computations are minimal beyond those already required for a linear static and buckling analysis, and should be easily performable within any well-designed general purpose finite element system

  10. Simplified Qualitative Discrete Numerical Model to Determine Cracking Pattern in Brittle Materials by Means of Finite Element Method

    Directory of Open Access Journals (Sweden)

    J. Ochoa-Avendaño

    2017-01-01

    Full Text Available This paper presents the formulation, implementation, and validation of a simplified qualitative model to determine the crack path of solids considering static loads, infinitesimal strain, and plane stress condition. This model is based on finite element method with a special meshing technique, where nonlinear link elements are included between the faces of the linear triangular elements. The stiffness loss of some link elements represents the crack opening. Three experimental tests of bending beams are simulated, where the cracking pattern calculated with the proposed numerical model is similar to experimental result. The advantages of the proposed model compared to discrete crack approaches with interface elements can be the implementation simplicity, the numerical stability, and the very low computational cost. The simulation with greater values of the initial stiffness of the link elements does not affect the discontinuity path and the stability of the numerical solution. The exploded mesh procedure presented in this model avoids a complex nonlinear analysis and regenerative or adaptive meshes.

  11. Mixed Element Formulation for the Finite Element-Boundary Integral Method

    National Research Council Canada - National Science Library

    Meese, J; Kempel, L. C; Schneider, S. W

    2006-01-01

    A mixed element approach using right hexahedral elements and right prism elements for the finite element-boundary integral method is presented and discussed for the study of planar cavity-backed antennas...

  12. Finite element analysis of irradiation-induced dilation of the fuel subassembly duct in LMFBR

    International Nuclear Information System (INIS)

    Gao Fuhai; Fu Hao; Li Nan; Yang Kongli; Wang Mingzhen

    2013-01-01

    Background: The calculation of irradiation-induced dilation of the fuel subassembly duct in LMFBR is important for fast reactor core design.. Purpose: To investigate how to calculate the dilation by using finite element method (FEM). Methods: First, irradiation-induced creep and swelling material models are introduced. Then, a theoretical solution based on a simplified bending plate model is briefly given. Finally, a stress update scheme for the adopted material models is presented and furthermore embedded into ABAQUS user interface UMAT to conduct finite element analysis. Both solutions are compared and discussed. Results: FEM successfully predicts the duct dilation and its solution agrees well with theoretical one in small deformation. Conclusions: The proposed stress update scheme is effective, The accuracy of the theory solution declines when dilation becomes larger. The maximum stress occurs at the duct corner point, and the location has stress relaxation effect. (authors)

  13. Discontinuous finite element treatment of duct problems in transport calculations

    International Nuclear Information System (INIS)

    Mirza, A. M.; Qamar, S.

    1998-01-01

    A discontinuous finite element approach is presented to solve the even-parity Boltzmann transport equation for duct problems. Presence of ducts in a system results in the streaming of particles and hence requires the employment of higher order angular approximations to model the angular flux. Conventional schemes based on the use of continuous trial functions require the same order of angular approximations to be used everywhere in the system, resulting in wastage of computational resources. Numerical investigations for the test problems presented in this paper indicate that the discontinuous finite elements eliminate the above problems and leads to computationally efficient and economical methods. They are also found to be more suitable for treating the sharp changes in the angular flux at duct-observer interfaces. The new approach provides a single-pass alternate to extrapolation and interactive schemes which need multiple passes of the solution strategy to acquire convergence. The method has been tested with the help of two case studies, namely straight and dog-leg duct problems. All results have been verified against those obtained from Monte Carlo simulations and K/sup +/ continuous finite element method. (author)

  14. Optimal convergence recovery for the Fourier-finite-element approximation of Maxwell's equations in non-smooth axisymmetric domains

    International Nuclear Information System (INIS)

    Nkemzi, B.

    2005-10-01

    Three-dimensional time-harmonic Maxwell's problems in axisymmetric domains Ω-circumflex with edges and conical points on the boundary are treated by means of the Fourier-finite-element method. The Fourier-fem combines the approximating Fourier series expansion of the solution with respect to the rotational angle using trigonometric polynomials of degree N (N → ∞), with the finite element approximation of the Fourier coefficients on the plane meridian domain Ω a is a subset of R + 2 of Ω-circumflex with mesh size h (h → 0). The singular behaviors of the Fourier coefficients near angular points of the domain Ω a are fully described by suitable singular functions and treated numerically by means of the singular function method with the finite element method on graded meshes. It is proved that the rate of convergence of the mixed approximations in H 1 (Ω-circumflex) 3 is of the order O (h+N -1 ) as known for the classical Fourier-finite-element approximation of problems with regular solutions. (author)

  15. Elastic shells of revolution under nonstationary thermal loading using ring finite elements

    International Nuclear Information System (INIS)

    Yao Zhenhan

    1986-01-01

    The report deals with the analysis of elastic shells of revolution under nonstationary thermal loading using ring finite elements. First, a ring element for moderately thick shells is derived which should also be employed for thin shells when either higher Fourier components of the displacements, or deflection patterns with very steep gradients occur. Then, a ring element for the analysis of heat conduction in shells of revolution is derived, and algorithms for the numerical solution of linear stationary, nonlinear stationary, as well as linear nonstationary problems are presented. Finally, a ring element for the coupled thermoelastic analysis of shells of revolution is developed, and an algorithm for the solution of weakly coupled problems is given. (orig.) [de

  16. Iterative and multigrid methods in the finite element solution of incompressible and turbulent fluid flow

    Science.gov (United States)

    Lavery, N.; Taylor, C.

    1999-07-01

    Multigrid and iterative methods are used to reduce the solution time of the matrix equations which arise from the finite element (FE) discretisation of the time-independent equations of motion of the incompressible fluid in turbulent motion. Incompressible flow is solved by using the method of reduce interpolation for the pressure to satisfy the Brezzi-Babuska condition. The k-l model is used to complete the turbulence closure problem. The non-symmetric iterative matrix methods examined are the methods of least squares conjugate gradient (LSCG), biconjugate gradient (BCG), conjugate gradient squared (CGS), and the biconjugate gradient squared stabilised (BCGSTAB). The multigrid algorithm applied is based on the FAS algorithm of Brandt, and uses two and three levels of grids with a V-cycling schedule. These methods are all compared to the non-symmetric frontal solver. Copyright

  17. 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...

  18. Using Finite Element Method

    Directory of Open Access Journals (Sweden)

    M.H.R. Ghoreishy

    2008-02-01

    Full Text Available This research work is devoted to the footprint analysis of a steel-belted radial tyre (185/65R14 under vertical static load using finite element method. Two models have been developed in which in the first model the tread patterns were replaced by simple ribs while the second model was consisted of details of the tread blocks. Linear elastic and hyper elastic (Arruda-Boyce material models were selected to describe the mechanical behavior of the reinforcing and rubbery parts, respectively. The above two finite element models of the tyre were analyzed under inflation pressure and vertical static loads. The second model (with detailed tread patterns was analyzed with and without friction effect between tread and contact surfaces. In every stage of the analysis, the results were compared with the experimental data to confirm the accuracy and applicability of the model. Results showed that neglecting the tread pattern design not only reduces the computational cost and effort but also the differences between computed deformations do not show significant changes. However, more complicated variables such as shape and area of the footprint zone and contact pressure are affected considerably by the finite element model selected for the tread blocks. In addition, inclusion of friction even in static state changes these variables significantly.

  19. Error estimates for the Fourier-finite-element approximation of the Lame system in nonsmooth axisymmetric domains

    International Nuclear Information System (INIS)

    Nkemzi, Boniface

    2003-10-01

    This paper is concerned with the effective implementation of the Fourier-finite-element method, which combines the approximating Fourier and the finite-element methods, for treating the Derichlet problem for the Lam.6 equations in axisymmetric domains Ω-circumflex is contained in R 3 with conical vertices and reentrant edges. The partial Fourier decomposition reduces the three-dimensional boundary value problem to an infinite sequence of decoupled two-dimensional boundary value problems on the plane meridian domain Ω α is contained in R + 2 of Ω-circumflex with solutions u, n (n = 0,1,2,...) being the Fourier coefficients of the solution u of the 3D problem. The asymptotic behavior of the Fourier coefficients near the angular points of Ω α , is described by appropriate singular vector-functions and treated numerically by linear finite elements on locally graded meshes. For the right-hand side function f-circumflex is an element of (L 2 (Ω-circumflex)) 3 it is proved that with appropriate mesh grading the rate of convergence of the combined approximations in (W 2 1 (Ω-circumflex)) 3 is of the order O(h + N -1 ), where h and N are the parameters of the finite-element and Fourier approximations, respectively, with h → 0 and N → ∞. (author)

  20. Generalized multiscale finite element methods. nonlinear elliptic equations

    KAUST Repository

    Efendiev, Yalchin R.; Galvis, Juan; Li, Guanglian; Presho, Michael

    2013-01-01

    In this paper we use the Generalized Multiscale Finite Element Method (GMsFEM) framework, introduced in [26], in order to solve nonlinear elliptic equations with high-contrast coefficients. The proposed solution method involves linearizing the equation so that coarse-grid quantities of previous solution iterates can be regarded as auxiliary parameters within the problem formulation. With this convention, we systematically construct respective coarse solution spaces that lend themselves to either continuous Galerkin (CG) or discontinuous Galerkin (DG) global formulations. Here, we use Symmetric Interior Penalty Discontinuous Galerkin approach. Both methods yield a predictable error decline that depends on the respective coarse space dimension, and we illustrate the effectiveness of the CG and DG formulations by offering a variety of numerical examples. © 2014 Global-Science Press.

  1. Non-linear finite element analyses applicable for the design of large reinforced concrete structures

    NARCIS (Netherlands)

    Engen, M; Hendriks, M.A.N.; Øverli, Jan Arve; Åldstedt, Erik

    2017-01-01

    In order to make non-linear finite element analyses applicable during assessments of the ultimate load capacity or the structural reliability of large reinforced concrete structures, there is need for an efficient solution strategy with a low modelling uncertainty. A solution strategy comprises

  2. A piecewise linear finite element discretization of the diffusion equation for arbitrary polyhedral grids

    Energy Technology Data Exchange (ETDEWEB)

    Bailey, Teresa S. [Texas A and M University, Department of Nuclear Engineering, College Station, TX 77843-3133 (United States)], E-mail: baileyte@tamu.edu; Adams, Marvin L. [Texas A and M University, Department of Nuclear Engineering, College Station, TX 77843-3133 (United States)], E-mail: mladams@tamu.edu; Yang, Brian [Lawrence Livermore National Laboratory, Livermore, CA 94551 (United States); Zika, Michael R. [Lawrence Livermore National Laboratory, Livermore, CA 94551 (United States)], E-mail: zika@llnl.gov

    2008-04-01

    We develop a piecewise linear (PWL) Galerkin finite element spatial discretization for the multi-dimensional radiation diffusion equation. It uses recently introduced piecewise linear weight and basis functions in the finite element approximation and it can be applied on arbitrary polygonal (2D) or polyhedral (3D) grids. We first demonstrate some analytical properties of the PWL method and perform a simple mode analysis to compare the PWL method with Palmer's vertex-centered finite-volume method and with a bilinear continuous finite element method. We then show that this new PWL method gives solutions comparable to those from Palmer's. However, since the PWL method produces a symmetric positive-definite coefficient matrix, it should be substantially more computationally efficient than Palmer's method, which produces an asymmetric matrix. We conclude that the Galerkin PWL method is an attractive option for solving diffusion equations on unstructured grids.

  3. A piecewise linear finite element discretization of the diffusion equation for arbitrary polyhedral grids

    International Nuclear Information System (INIS)

    Bailey, Teresa S.; Adams, Marvin L.; Yang, Brian; Zika, Michael R.

    2008-01-01

    We develop a piecewise linear (PWL) Galerkin finite element spatial discretization for the multi-dimensional radiation diffusion equation. It uses recently introduced piecewise linear weight and basis functions in the finite element approximation and it can be applied on arbitrary polygonal (2D) or polyhedral (3D) grids. We first demonstrate some analytical properties of the PWL method and perform a simple mode analysis to compare the PWL method with Palmer's vertex-centered finite-volume method and with a bilinear continuous finite element method. We then show that this new PWL method gives solutions comparable to those from Palmer's. However, since the PWL method produces a symmetric positive-definite coefficient matrix, it should be substantially more computationally efficient than Palmer's method, which produces an asymmetric matrix. We conclude that the Galerkin PWL method is an attractive option for solving diffusion equations on unstructured grids

  4. A piecewise linear finite element discretization of the diffusion equation for arbitrary polyhedral grids

    Energy Technology Data Exchange (ETDEWEB)

    Bailey, T S; Adams, M L [Texas A M Univ., Dept. of Nuclear Engineering, College Station, TX (United States); Yang, B; Zika, M R [Lawrence Livermore National Lab., Livermore, CA (United States)

    2005-07-01

    We develop a piecewise linear (PWL) Galerkin finite element spatial discretization for the multi-dimensional radiation diffusion equation. It uses piecewise linear weight and basis functions in the finite element approximation, and it can be applied on arbitrary polygonal (2-dimensional) or polyhedral (3-dimensional) grids. We show that this new PWL method gives solutions comparable to those from Palmer's finite-volume method. However, since the PWL method produces a symmetric positive definite coefficient matrix, it should be substantially more computationally efficient than Palmer's method, which produces an asymmetric matrix. We conclude that the Galerkin PWL method is an attractive option for solving diffusion equations on unstructured grids. (authors)

  5. ANSYS mechanical APDL for finite element analysis

    CERN Document Server

    Thompson, Mary Kathryn

    2017-01-01

    ANSYS Mechanical APDL for Finite Element Analysis provides a hands-on introduction to engineering analysis using one of the most powerful commercial general purposes finite element programs on the market. Students will find a practical and integrated approach that combines finite element theory with best practices for developing, verifying, validating and interpreting the results of finite element models, while engineering professionals will appreciate the deep insight presented on the program's structure and behavior. Additional topics covered include an introduction to commands, input files, batch processing, and other advanced features in ANSYS. The book is written in a lecture/lab style, and each topic is supported by examples, exercises and suggestions for additional readings in the program documentation. Exercises gradually increase in difficulty and complexity, helping readers quickly gain confidence to independently use the program. This provides a solid foundation on which to build, preparing readers...

  6. Numerical analysis of creep brittle rupture by the finite element method

    International Nuclear Information System (INIS)

    Goncalves, O.J.A.; Owen, D.R.J.

    1983-01-01

    In this work an implicit algorithm is proposed for the numerical analysis of creep brittle rupture problems by the finite element method. This kind of structural failure, typical in components operating at high temperatures for long periods of time, is modelled using either a three dimensional generalization of the Kachanov-Rabotnov equations due to Leckie and Hayhurst or the Monkman-Grant fracture criterion together with the Linear Life Fraction Rule. The finite element equations are derived by the displacement method and isoparametric elements are used for the spatial discretization. Geometric nonlinear effects (large displacements) are accounted for by an updated Lagrangian formulation. Attention is also focussed on the solution of the highly stiff differential equations that govern damage growth. Finally the numerical results of a three-dimensional analysis of a pressurized thin cylinder containing oxidised pits in its external wall are discussed. (orig.)

  7. CHILES, Singularity Strength of Linear Elastic Bodies by Finite Elements Method

    International Nuclear Information System (INIS)

    Benzley, S.E.; Beisinger, Z.E.

    1981-01-01

    1 - Description of problem or function: CHILES is a finite element computer program that calculates the strength of singularities in linear elastic bodies. Plane stress, plane strain, and axisymmetric conditions are treated. Crack tip singularity problems are solved by this version of the code, but any type of integrable singularity may be properly modeled by modifying selected subroutines in the program. 2 - Method of solution: A generalized, quadrilateral finite element that includes a singular point at a corner node is incorporated in the code. The displacement formulation is used and inter-element compatibility is maintained so that monotone convergence is preserved. 3 - Restrictions on the complexity of the problem: CHILES allows three singular points to be modeled in the body being analyzed and each singular point may have coupled Mode I and II deformations. 1000 nodal points may be used

  8. Finite elements of nonlinear continua

    CERN Document Server

    Oden, John Tinsley

    1972-01-01

    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

  9. Radiative transfer with finite elements. Pt. 1. Basic method and tests

    Energy Technology Data Exchange (ETDEWEB)

    Richling, S. [Heidelberg Univ. (Germany). Inst. fuer Theoretische Astrophysik; Meinkoehn, E. [Heidelberg Univ. (Germany). Inst. fuer Theoretische Astrophysik]|[Heidelberg Univ. (Germany). Inst. fuer Angewandte Mathematik; Kryzhevoi, N. [Heidelberg Univ. (Germany). Inst. fuer Theoretische Astrophysik]|[Heidelberg Univ. (DE). Interdisziplinaeres Zentrum fuer Wissenschaftliches Rechnen (IWR); Kanschat, G. [Heidelberg Univ. (Germany). Inst. fuer Angewandte Mathematik]|[Heidelberg Univ. (DE). Interdisziplinaeres Zentrum fuer Wissenschaftliches Rechnen (IWR)

    2001-10-01

    A finite element method for solving the monochromatic radiation transfer equation including scattering in three dimensions is presented. The algorithm employs unstructured grids which are adaptively refined. Adaptivity as well as ordinate parallelization reduce memory requirements and execution time and make it possible to calculate the radiation field across several length scales for objects with strong opacity gradients. An a posteriori error estimate for one particular quantity is obtained by solving the dual problem. The application to a sample of test problems reveals the properties of the implementation. (orig.)

  10. COMPARISONS OF THE FINITE-ELEMENT-WITH-DISCONTIGUOUS-SUPPORT METHOD TO CONTINUOUS-ENERGY MONTE CARLO FOR PIN-CELL PROBLEMS

    Energy Technology Data Exchange (ETDEWEB)

    A. T. Till; M. Hanuš; J. Lou; J. E. Morel; M. L. Adams

    2016-05-01

    The standard multigroup (MG) method for energy discretization of the transport equation can be sensitive to approximations in the weighting spectrum chosen for cross-section averaging. As a result, MG often inaccurately treats important phenomena such as self-shielding variations across a material. From a finite-element viewpoint, MG uses a single fixed basis function (the pre-selected spectrum) within each group, with no mechanism to adapt to local solution behavior. In this work, we introduce the Finite-Element-with-Discontiguous-Support (FEDS) method, whose only approximation with respect to energy is that the angular flux is a linear combination of unknowns multiplied by basis functions. A basis function is non-zero only in the discontiguous set of energy intervals associated with its energy element. Discontiguous energy elements are generalizations of bands and are determined by minimizing a norm of the difference between snapshot spectra and their averages over the energy elements. We begin by presenting the theory of the FEDS method. We then compare to continuous-energy Monte Carlo for one-dimensional slab and two-dimensional pin-cell problem. We find FEDS to be accurate and efficient at producing quantities of interest such as reaction rates and eigenvalues. Results show that FEDS converges at a rate that is approximately first-order in the number of energy elements and that FEDS is less sensitive to weighting spectrum than standard MG.

  11. Finite-element 3D simulation tools for high-current relativistic electron beams

    Science.gov (United States)

    Humphries, Stanley; Ekdahl, Carl

    2002-08-01

    The DARHT second-axis injector is a challenge for computer simulations. Electrons are subject to strong beam-generated forces. The fields are fully three-dimensional and accurate calculations at surfaces are critical. We describe methods applied in OmniTrak, a 3D finite-element code suite that can address DARHT and the full range of charged-particle devices. The system handles mesh generation, electrostatics, magnetostatics and self-consistent particle orbits. The MetaMesh program generates meshes of conformal hexahedrons to fit any user geometry. The code has the unique ability to create structured conformal meshes with cubic logic. Organized meshes offer advantages in speed and memory utilization in the orbit and field solutions. OmniTrak is a versatile charged-particle code that handles 3D electric and magnetic field solutions on independent meshes. The program can update both 3D field solutions from the calculated beam space-charge and current-density. We shall describe numerical methods for orbit tracking on a hexahedron mesh. Topics include: 1) identification of elements along the particle trajectory, 2) fast searches and adaptive field calculations, 3) interpolation methods to terminate orbits on material surfaces, 4) automatic particle generation on multiple emission surfaces to model space-charge-limited emission and field emission, 5) flexible Child law algorithms, 6) implementation of the dual potential model for 3D magnetostatics, and 7) assignment of charge and current from model particle orbits for self-consistent fields.

  12. A finite-element for the analysis of shell intersections

    International Nuclear Information System (INIS)

    Koves, W.J.; Nair, S.

    1994-01-01

    The analysis of discontinuity stresses at shell intersections is a problem of great importance in several major industries. Some of the major areas of interest are pressure-containing equipment, such as reactors and piping, in the nuclear and fossil power industry; pressure vessels and heat exchangers in the petrochemical industry; bracing in offshore oil platforms; and aerospace structures. A specialized shell-intersection finite element, which is compatible with adjoining shell elements, has been developed that has the capability of physically representing the complex three-dimensional geometry and stress state at shell intersections. The element geometry is a contoured shape that matches a wide variety of practical nozzle configurations used in ASME Code pressure vessel construction, and allows computational rigor. A closed-form theory of elasticity solution was used to compute the stress state and strain energy in the element. The concept of an energy-equivalent nodal displacement and force vector set was then developed to allow complete compatibility with adjoining shell elements and retain the analytical rigor within the element. This methodology provides a powerful and robust computation scheme that maintains the computational efficiency of shell element solutions. The shell-intersection element was then applied to the cylinder-sphere and cylinder-cylinder intersection problems

  13. Finite element formulation for fluid-structure interaction in three-dimensional space

    International Nuclear Information System (INIS)

    Kulak, R.F.

    1979-01-01

    A development is presented for a three-dimension hexahedral hydrodynamic finite-element. Using trilinear shape functions and assuming a constant pressure field in each element, simple relations were obtained for internal nodal forces. Because the formulation was based upon a rate approach it was applicable to problems involving large displacements. This element was incorporated into an existing plate-shell finite element code. Diagonal mass matrices were used and the resulting discrete equations of motion were solved using explicit temporal integrator. Results for several problems were presented which compare numerical predictions to closed form analytical solutions. In addition, the fluid-structure interaction problem of a fluid-filled, cylindrical vessel containing internal cylinders was studied. The internal cylinders were cantilever supported from the top cover of the vessel and were periodically located circumferentially at a fixed radius. A pressurized cylindrical cavity located at the bottom of the vessel at its centerline provided the loading

  14. Space and Time Adaptive Two-Mesh hp-Finite Element Method for Transient Microwave Heating Problems

    Czech Academy of Sciences Publication Activity Database

    Dubcová, Lenka; Šolín, Pavel; Červený, Jakub; Kůs, Pavel

    1-2, č. 30 (2010), s. 23-40 ISSN 0272-6343 R&D Projects: GA ČR(CZ) GA102/07/0496; GA AV ČR IAA100760702 Institutional research plan: CEZ:AV0Z20570509 Keywords : hp-finite element method * microwave heating * edge elements Subject RIV: JA - Electronics ; Optoelectronics, Electrical Engineering Impact factor: 0.844, year: 2010

  15. Assessment of finite element and smoothed particles hydrodynamics methods for modeling serrated chip formation in hardened steel

    Directory of Open Access Journals (Sweden)

    Usama Umer

    2016-05-01

    Full Text Available This study aims to perform comparative analyses in modeling serrated chip morphologies using traditional finite element and smoothed particles hydrodynamics methods. Although finite element models are being employed in predicting machining performance variables for the last two decades, many drawbacks and limitations exist with the current finite element models. The problems like excessive mesh distortions, high numerical cost of adaptive meshing techniques, and need of geometric chip separation criteria hinder its practical implementation in metal cutting industries. In this study, a mesh free method, namely, smoothed particles hydrodynamics, is implemented for modeling serrated chip morphology while machining AISI H13 hardened tool steel. The smoothed particles hydrodynamics models are compared with the traditional finite element models, and it has been found that the smoothed particles hydrodynamics models have good capabilities in handling large distortions and do not need any geometric or mesh-based chip separation criterion.

  16. Finite element analysis of the Girkmann problem using the modern hp-version and the classical h-version

    KAUST Repository

    Niemi, Antti

    2011-06-03

    We perform finite element analysis of the so called Girkmann problem in structural mechanics. The problem involves an axially symmetric spherical shell stiffened with a foot ring and is approached (1) by using the axisymmetric formulation of linear elasticity theory and (2) by using a dimensionally reduced shell-ring model. In the first approach the problem is solved with a fully automatic hp-adaptive finite element solver whereas the classical h-version of the finite element method is used in the second approach. We study the convergence behaviour of the different numerical models and show that accurate stress resultants can be obtained with both models by using effective post-processing formulas. © Springer-Verlag London Limited 2011.

  17. Fiber-reinforced materials: finite elements for the treatment of the inextensibility constraint

    Science.gov (United States)

    Auricchio, Ferdinando; Scalet, Giulia; Wriggers, Peter

    2017-12-01

    The present paper proposes a numerical framework for the analysis of problems involving fiber-reinforced anisotropic materials. Specifically, isotropic linear elastic solids, reinforced by a single family of inextensible fibers, are considered. The kinematic constraint equation of inextensibility in the fiber direction leads to the presence of an undetermined fiber stress in the constitutive equations. To avoid locking-phenomena in the numerical solution due to the presence of the constraint, mixed finite elements based on the Lagrange multiplier, perturbed Lagrangian, and penalty method are proposed. Several boundary-value problems under plane strain conditions are solved and numerical results are compared to analytical solutions, whenever the derivation is possible. The performed simulations allow to assess the performance of the proposed finite elements and to discuss several features of the developed formulations concerning the effective approximation for the displacement and fiber stress fields, mesh convergence, and sensitivity to penalty parameters.

  18. Two-dimensional finite element neutron diffusion analysis using hierarchic shape functions

    International Nuclear Information System (INIS)

    Carpenter, D.C.

    1997-01-01

    Recent advances have been made in the use of p-type finite element method (FEM) for structural and fluid dynamics problems that hold promise for reactor physics problems. These advances include using hierarchic shape functions, element-by-element iterative solvers and more powerful mapping techniques. Use of the hierarchic shape functions allows greater flexibility and efficiency in implementing energy-dependent flux expansions and incorporating localized refinement of the solution space. The irregular matrices generated by the p-type FEM can be solved efficiently using element-by-element conjugate gradient iterative solvers. These solvers do not require storage of either the global or local stiffness matrices and can be highly vectorized. Mapping techniques based on blending function interpolation allow exact representation of curved boundaries using coarse element grids. These features were implemented in a developmental two-dimensional neutron diffusion program based on the use of hierarchic shape functions (FEM2DH). Several aspects in the effective use of p-type analysis were explored. Two choices of elemental preconditioning were examined--the proper selection of the polynomial shape functions and the proper number of functions to use. Of the five shape function polynomials tested, the integral Legendre functions were the most effective. The serendipity set of functions is preferable over the full tensor product set. Two global preconditioners were also examined--simple diagonal and incomplete Cholesky. The full effectiveness of the finite element methodology was demonstrated on a two-region, two-group cylindrical problem but solved in the x-y coordinate space, using a non-structured element grid. The exact, analytic eigenvalue solution was achieved with FEM2DH using various combinations of element grids and flux expansions

  19. A finite-element model in vorticity and current function for the numerical solution of the Navier-Stokes equations

    International Nuclear Information System (INIS)

    Cunha Furtado, F. da; Galeao, A.C.N.R.

    1984-01-01

    A numerical procedure for the integration of the incompressible Navier-Stokes equations, when expressed in terms of a stream function equation and a vorticity transport equation, is presented. This procedure comprises: the variational formulation of the equations, the construction of the approximation spaces by the finite element method and the discretization via the Galerkin method. For the stationary problems, the system of non-linear algebraic equations resulting from the discretization is solved by the Newton-Raphson algorithm. Finally, for the transient problems, the solution of the non-linear ordinary differential equations resulting from the spatial discretization is accomplished through a Crank-Nicolson scheme. (Author) [pt

  20. A self-adaptive finite element approach for simulation of mixed-mode delamination using cohesive zone models

    NARCIS (Netherlands)

    Samimi, M.; Dommelen, van J.A.W.; Geers, M.G.D.

    2011-01-01

    Oscillations observed in the load–displacement response of brittle interfaces modeled by cohesive zone elements in a quasi-static finite element framework are artifacts of the discretization. The typical limit points in this oscillatory path can be traced by application of path-following techniques,

  1. Finite element analysis of beam-to-column joints in steel frames under cyclic loading

    Directory of Open Access Journals (Sweden)

    Elsayed Mashaly

    2011-03-01

    Full Text Available The aim of this paper is to present a simple and accurate three-dimensional (3D finite element model (FE capable of predicting the actual behavior of beam-to-column joints in steel frames subjected to lateral loads. The software package ANSYS is used to model the joint. The bolted extended-end-plate connection was chosen as an important type of beam–column joints. The extended-end-plate connection is chosen for its complexity in the analysis and behavior due to the number of connection components and their inheritable non-linear behavior. Two experimental tests in the literature were chosen to verify the finite element model. The results of both the experimental and the proposed finite element were compared. One of these tests was monotonically loaded, whereas the second was cyclically loaded. The finite element model is improved to enhance the defects of the finite element model used. These defects are; the long time need for the analysis and the inability of the contact element type to follow the behavior of moment–rotation curve under cyclic loading. As a contact element, the surface-to-surface element is used instead of node-to-node element to enhance the model. The FE results show good correlation with the experimental one. An attempt to improve a new technique for modeling bolts is conducted. The results show that this technique is supposed to avoid the defects above, give much less elements number and less solution time than the other modeling techniques.

  2. Variational Multiscale Finite Element Method for Flows in Highly Porous Media

    KAUST Repository

    Iliev, O.; Lazarov, R.; Willems, J.

    2011-01-01

    We present a two-scale finite element method (FEM) for solving Brinkman's and Darcy's equations. These systems of equations model fluid flows in highly porous and porous media, respectively. The method uses a recently proposed discontinuous Galerkin FEM for Stokes' equations by Wang and Ye and the concept of subgrid approximation developed by Arbogast for Darcy's equations. In order to reduce the "resonance error" and to ensure convergence to the global fine solution, the algorithm is put in the framework of alternating Schwarz iterations using subdomains around the coarse-grid boundaries. The discussed algorithms are implemented using the Deal.II finite element library and are tested on a number of model problems. © 2011 Society for Industrial and Applied Mathematics.

  3. Architecture and program structures for a special purpose finite element computer

    Energy Technology Data Exchange (ETDEWEB)

    Norrie, D.H.; Norrie, C.W.

    1983-01-01

    The development of very large scale integration (VLSI) has made special-purpose computers economically possible. With such a machine, the loss of flexibility compared with a general-purpose computer can be offset by the increased speed which can be obtained by tailoring the architecture to the particular problem or class of problem. The first kind of special-purpose machine has its architecture modelled on the physical structure of the problem and the second kind has its design tailored to the computational algorithm used. The parallel finite element machine (PARFEM) being designed at the University of Calgary for the solution of finite element problems is of the second kind. Its conceptual design is described and progress to date outlined. 14 references.

  4. Variational Multiscale Finite Element Method for Flows in Highly Porous Media

    KAUST Repository

    Iliev, O.

    2011-10-01

    We present a two-scale finite element method (FEM) for solving Brinkman\\'s and Darcy\\'s equations. These systems of equations model fluid flows in highly porous and porous media, respectively. The method uses a recently proposed discontinuous Galerkin FEM for Stokes\\' equations by Wang and Ye and the concept of subgrid approximation developed by Arbogast for Darcy\\'s equations. In order to reduce the "resonance error" and to ensure convergence to the global fine solution, the algorithm is put in the framework of alternating Schwarz iterations using subdomains around the coarse-grid boundaries. The discussed algorithms are implemented using the Deal.II finite element library and are tested on a number of model problems. © 2011 Society for Industrial and Applied Mathematics.

  5. Spectral/hp least-squares finite element formulation for the Navier-Stokes equations

    International Nuclear Information System (INIS)

    Pontaza, J.P.; Reddy, J.N.

    2003-01-01

    We consider the application of least-squares finite element models combined with spectral/hp methods for the numerical solution of viscous flow problems. The paper presents the formulation, validation, and application of a spectral/hp algorithm to the numerical solution of the Navier-Stokes equations governing two- and three-dimensional stationary incompressible and low-speed compressible flows. The Navier-Stokes equations are expressed as an equivalent set of first-order equations by introducing vorticity or velocity gradients as additional independent variables and the least-squares method is used to develop the finite element model. High-order element expansions are used to construct the discrete model. The discrete model thus obtained is linearized by Newton's method, resulting in a linear system of equations with a symmetric positive definite coefficient matrix that is solved in a fully coupled manner by a preconditioned conjugate gradient method. Spectral convergence of the L 2 least-squares functional and L 2 error norms is verified using smooth solutions to the two-dimensional stationary Poisson and incompressible Navier-Stokes equations. Numerical results for flow over a backward-facing step, steady flow past a circular cylinder, three-dimensional lid-driven cavity flow, and compressible buoyant flow inside a square enclosure are presented to demonstrate the predictive capability and robustness of the proposed formulation

  6. A comparison of numerical methods used for finite element modelling of soft tissue deformation

    KAUST Repository

    Pathmanathan, P; Gavaghan, D; Whiteley, J

    2009-01-01

    Soft tissue deformation is often modelled using incompressible non-linear elasticity, with solutions computed using the finite element method. There are a range of options available when using the finite element method, in particular the polynomial degree of the basis functions used for interpolating position and pressure, and the type of element making up the mesh. The effect of these choices on the accuracy of the computed solution is investigated, using a selection of model problems motivated by typical deformations seen in soft tissue modelling. Model problems are set up with discontinuous material properties (as is the case for the breast), steeply changing gradients in the body force (as found in contracting cardiac tissue), and discontinuous first derivatives in the solution at the boundary, caused by a discontinuous applied force (as in the breast during mammography). It was found that the choice of pressure basis functions is vital in the presence of a material interface, higher-order schemes do not perform as well as may be expected when there are sharp gradients, and in general it is important to take the expected regularity of the solution into account when choosing a numerical scheme. © IMechE 2009.

  7. A comparison of numerical methods used for finite element modelling of soft tissue deformation

    KAUST Repository

    Pathmanathan, P

    2009-05-01

    Soft tissue deformation is often modelled using incompressible non-linear elasticity, with solutions computed using the finite element method. There are a range of options available when using the finite element method, in particular the polynomial degree of the basis functions used for interpolating position and pressure, and the type of element making up the mesh. The effect of these choices on the accuracy of the computed solution is investigated, using a selection of model problems motivated by typical deformations seen in soft tissue modelling. Model problems are set up with discontinuous material properties (as is the case for the breast), steeply changing gradients in the body force (as found in contracting cardiac tissue), and discontinuous first derivatives in the solution at the boundary, caused by a discontinuous applied force (as in the breast during mammography). It was found that the choice of pressure basis functions is vital in the presence of a material interface, higher-order schemes do not perform as well as may be expected when there are sharp gradients, and in general it is important to take the expected regularity of the solution into account when choosing a numerical scheme. © IMechE 2009.

  8. Laminar forced convective/conductive heat transfer by finite element method

    International Nuclear Information System (INIS)

    Kushwaha, H.S.; Kakodkar, A.

    1982-01-01

    The present study is directed at developing a finite element computer program for solution of decoupled convective/conductive heat transfer problems. Penalty function formulation has been used to solve momentum equations and subsequently transient energy equation is solved using modified Crank-Nicolson method. The optimal upwinding scheme has been employed in energy equation to remove oscillations at high Peclet number. (author)

  9. An adaptative finite element method for turbulent flow simulations

    International Nuclear Information System (INIS)

    Arnoux-Guisse, F.; Bonnin, O.; Leal de Sousa, L.; Nicolas, G.

    1995-05-01

    After outlining the space and time discretization methods used in the N3S thermal hydraulic code developed at EDF/NHL, we describe the possibilities of the peripheral version, the Adaptative Mesh, which comprises two separate parts: the error indicator computation and the development of a module subdividing elements usable by the solid dynamics code ASTER and the electromagnetism code TRIFOU also developed by R and DD. The error indicators implemented in N3S are described. They consist of a projection indicator quantifying the space error in laminar or turbulent flow calculations and a Navier-Stokes residue indicator calculated on each element. The method for subdivision of triangles into four sub-triangles and tetrahedra into eight sub-tetrahedra is then presented with its advantages and drawbacks. It is illustrated by examples showing the efficiency of the module. The last concerns the 2 D case of flow behind a backward-facing step. (authors). 9 refs., 5 figs., 1 tab

  10. Finite Element Analysis of Pipe T-Joint

    OpenAIRE

    P.M.Gedkar; Dr. D.V. Bhope

    2012-01-01

    This paper reports stress analysis of two pressurized cylindrical intersection using finite element method. The different combinations of dimensions of run pipe and the branch pipe are used to investigate thestresses in pipe at the intersection. In this study the stress analysis is accomplished by finite element package ANSYS.

  11. Monte Carlo particle simulation and finite-element techniques for tandem mirror transport

    International Nuclear Information System (INIS)

    Rognlien, T.D.; Cohen, B.I.; Matsuda, Y.; Stewart, J.J. Jr.

    1987-01-01

    A description is given of numerical methods used in the study of axial transport in tandem mirrors owing to Coulomb collisions and rf diffusion. The methods are Monte Carlo particle simulations and direct solution to the Fokker-Planck equations by finite-element expansion. (author)

  12. Monte Carlo particle simulation and finite-element techniques for tandem mirror transport

    International Nuclear Information System (INIS)

    Rognlien, T.D.; Cohen, B.I.; Matsuda, Y.; Stewart, J.J. Jr.

    1985-12-01

    A description is given of numerical methods used in the study of axial transport in tandem mirrors owing to Coulomb collisions and rf diffusion. The methods are Monte Carlo particle simulations and direct solution to the Fokker-Planck equations by finite-element expansion. 11 refs

  13. Modelling cohesive laws in finite element simulations via an adapted contact procedure in ABAQUS

    DEFF Research Database (Denmark)

    Feih, S.

    2004-01-01

    is not straightforward, and most existing publications consider theoretical and therefore simpler softening shapes. Two possible methods of bridging law approximation areexplained and compared in this report. The bridging laws were implemented in a numerical user subroutine in the finite element code ABAQUS. The main...

  14. Introduction to finite element analysis using MATLAB and Abaqus

    CERN Document Server

    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

  15. Goal-Oriented Self-Adaptive hp Finite Element Simulation of 3D DC Borehole Resistivity Simulations

    KAUST Repository

    Calo, Victor M.; Pardo, David; Paszyński, Maciej R.

    2011-01-01

    (adjusting polynomial orders of approximation) or hp (both) refinements on the finite elements. The new parallel implementation utilizes a computational mesh shared between multiple processors. All computational algorithms, including automatic hp goal

  16. COYOTE: a finite element computer program for nonlinear heat conduction problems

    International Nuclear Information System (INIS)

    Gartling, D.K.

    1978-06-01

    COYOTE is a finite element computer program designed for the solution of two-dimensional, nonlinear heat conduction problems. The theoretical and mathematical basis used to develop the code is described. Program capabilities and complete user instructions are presented. Several example problems are described in detail to demonstrate the use of the program

  17. Nonlinear finite element modeling of corrugated board

    Science.gov (United States)

    A. C. Gilchrist; J. C. Suhling; T. J. Urbanik

    1999-01-01

    In this research, an investigation on the mechanical behavior of corrugated board has been performed using finite element analysis. Numerical finite element models for corrugated board geometries have been created and executed. Both geometric (large deformation) and material nonlinearities were included in the models. The analyses were performed using the commercial...

  18. Coupling nonlinear Stokes and Darcy flow using mortar finite elements

    KAUST Repository

    Ervin, Vincent J.

    2011-11-01

    We study a system composed of a nonlinear Stokes flow in one subdomain coupled with a nonlinear porous medium flow in another subdomain. Special attention is paid to the mathematical consequence of the shear-dependent fluid viscosity for the Stokes flow and the velocity-dependent effective viscosity for the Darcy flow. Motivated by the physical setting, we consider the case where only flow rates are specified on the inflow and outflow boundaries in both subdomains. We recast the coupled Stokes-Darcy system as a reduced matching problem on the interface using a mortar space approach. We prove a number of properties of the nonlinear interface operator associated with the reduced problem, which directly yield the existence, uniqueness and regularity of a variational solution to the system. We further propose and analyze a numerical algorithm based on mortar finite elements for the interface problem and conforming finite elements for the subdomain problems. Optimal a priori error estimates are established for the interface and subdomain problems, and a number of compatibility conditions for the finite element spaces used are discussed. Numerical simulations are presented to illustrate the algorithm and to compare two treatments of the defective boundary conditions. © 2010 Published by Elsevier B.V. on behalf of IMACS.

  19. Self-Assessment of Finite Element Solutions Applied to Transient Phenomena in Solid Continuum Mechanics

    Czech Academy of Sciences Publication Activity Database

    Okrouhlík, Miloslav; Pták, Svatopluk; Valdek, U.

    2009-01-01

    Roč. 16, č. 2 (2009), s. 103-121 ISSN 1802-1484 R&D Projects: GA AV ČR 1ET400760509 Institutional research plan: CEZ:AV0Z20760514 Keywords : stress wave propagation * finite element method * validity of models Subject RIV: BI - Acoustics

  20. Development of efficient finite elements for structural integrity analysis of solid rocket motor propellant grains

    International Nuclear Information System (INIS)

    Marimuthu, R.; Nageswara Rao, B.

    2013-01-01

    Solid propellant rocket motors (SRM) are regularly used in the satellite launch vehicles which consist of mainly three different structural materials viz., solid propellant, liner, and casing materials. It is essential to assess the structural integrity of solid propellant grains under the specified gravity, thermal and pressure loading conditions. For this purpose finite elements developed following the Herrmann formulation are: twenty node brick element (BH20), eight node quadrilateral plane strain element (PH8) and, eight node axi-symmetric solid of revolution element (AH8). The time-dependent nature of the solid propellant grains is taken into account utilizing the direct inverse method of Schepary to specify the effective Young's modulus and Poisson's ratio. The developed elements are tested considering various problems prior to implementation in the in-house software package (viz., Finite Element Analysis of STructures, FEAST). Several SRM configurations are analyzed to assess the structural integrity under different loading conditions. Finite element analysis results are found to be in good agreement with those obtained earlier from MARC software. -- Highlights: • Developed efficient Herrmann elements. • Accuracy of finite elements demonstrated solving several known solution problems. • Time dependent structural response obtained using the direct inverse method of Schepary. • Performed structural analysis of grains under gravity, thermal and pressure loads

  1. Bibliography for finite elements. [2200 references

    Energy Technology Data Exchange (ETDEWEB)

    Whiteman, J R [comp.

    1975-01-01

    This bibliography cites almost all of the significant papers on advances in the mathematical theory of finite elements. Reported are applications in aeronautical, civil, mechanical, nautical and nuclear engineering. Such topics as classical analysis, functional analysis, approximation theory, fluids, and diffusion are covered. Over 2200 references to publications up to the end of 1974 are included. Publications are listed alphabetically by author and also by keywords. In addition, finite element packages are listed.

  2. A piecewise linear finite element discretization of the diffusion equation for arbitrary polyhedral grids

    Energy Technology Data Exchange (ETDEWEB)

    Bailey, T.S.; Adams, M.L. [Texas A M Univ., Dept. of Nuclear Engineering, College Station, TX (United States); Yang, B.; Zika, M.R. [Lawrence Livermore National Lab., Livermore, CA (United States)

    2005-07-01

    We develop a piecewise linear (PWL) Galerkin finite element spatial discretization for the multi-dimensional radiation diffusion equation. It uses piecewise linear weight and basis functions in the finite element approximation, and it can be applied on arbitrary polygonal (2-dimensional) or polyhedral (3-dimensional) grids. We show that this new PWL method gives solutions comparable to those from Palmer's finite-volume method. However, since the PWL method produces a symmetric positive definite coefficient matrix, it should be substantially more computationally efficient than Palmer's method, which produces an asymmetric matrix. We conclude that the Galerkin PWL method is an attractive option for solving diffusion equations on unstructured grids. (authors)

  3. Adaptive Finite Element-Discrete Element Analysis for Microseismic Modelling of Hydraulic Fracture Propagation of Perforation in Horizontal Well considering Pre-Existing Fractures

    Directory of Open Access Journals (Sweden)

    Yongliang Wang

    2018-01-01

    Full Text Available Hydrofracturing technology of perforated horizontal well has been widely used to stimulate the tight hydrocarbon reservoirs for gas production. To predict the hydraulic fracture propagation, the microseismicity can be used to infer hydraulic fractures state; by the effective numerical methods, microseismic events can be addressed from changes of the computed stresses. In numerical models, due to the challenges in accurately representing the complex structure of naturally fractured reservoir, the interaction between hydraulic and pre-existing fractures has not yet been considered and handled satisfactorily. To overcome these challenges, the adaptive finite element-discrete element method is used to refine mesh, effectively identify the fractures propagation, and investigate microseismic modelling. Numerical models are composed of hydraulic fractures, pre-existing fractures, and microscale pores, and the seepage analysis based on the Darcy’s law is used to determine fluid flow; then moment tensors in microseismicity are computed based on the computed stresses. Unfractured and naturally fractured models are compared to assess the influences of pre-existing fractures on hydrofracturing. The damaged and contact slip events were detected by the magnitudes, B-values, Hudson source type plots, and focal spheres.

  4. Determination of Nonlinear Stiffness Coefficients for Finite Element Models with Application to the Random Vibration Problem

    Science.gov (United States)

    Muravyov, Alexander A.

    1999-01-01

    In this paper, a method for obtaining nonlinear stiffness coefficients in modal coordinates for geometrically nonlinear finite-element models is developed. The method requires application of a finite-element program with a geometrically non- linear static capability. The MSC/NASTRAN code is employed for this purpose. The equations of motion of a MDOF system are formulated in modal coordinates. A set of linear eigenvectors is used to approximate the solution of the nonlinear problem. The random vibration problem of the MDOF nonlinear system is then considered. The solutions obtained by application of two different versions of a stochastic linearization technique are compared with linear and exact (analytical) solutions in terms of root-mean-square (RMS) displacements and strains for a beam structure.

  5. Solving the transport equation with quadratic finite elements: Theory and applications

    International Nuclear Information System (INIS)

    Ferguson, J.M.

    1997-01-01

    At the 4th Joint Conference on Computational Mathematics, the author presented a paper introducing a new quadratic finite element scheme (QFEM) for solving the transport equation. In the ensuing year the author has obtained considerable experience in the application of this method, including solution of eigenvalue problems, transmission problems, and solution of the adjoint form of the equation as well as the usual forward solution. He will present detailed results, and will also discuss other refinements of his transport codes, particularly for 3-dimensional problems on rectilinear and non-rectilinear grids

  6. Superconvergence of mixed finite element approximations to 3-D Maxwell's equations in metamaterials

    KAUST Repository

    Huang, Yunqing

    2011-09-01

    Numerical simulation of metamaterials has attracted more and more attention since 2000, after the first metamaterial with negative refraction index was successfully constructed. In this paper we construct a fully-discrete leap-frog type finite element scheme to solve the three-dimensional time-dependent Maxwell\\'s equations when metamaterials are involved. First, we obtain some superclose results between the interpolations of the analytical solutions and finite element solutions obtained using arbitrary orders of Raviart-Thomas-Nédélec mixed spaces on regular cubic meshes. Then we prove the superconvergence result in the discrete l2 norm achieved for the lowest-order Raviart-Thomas-Nédélec space. To our best knowledge, such superconvergence results have never been obtained elsewhere. Finally, we implement the leap-frog scheme and present numerical results justifying our theoretical analysis. © 2011 Elsevier Inc.

  7. Superconvergence of mixed finite element approximations to 3-D Maxwell's equations in metamaterials

    KAUST Repository

    Huang, Yunqing; Li, Jichun; Yang, Wei; Sun, Shuyu

    2011-01-01

    Numerical simulation of metamaterials has attracted more and more attention since 2000, after the first metamaterial with negative refraction index was successfully constructed. In this paper we construct a fully-discrete leap-frog type finite element scheme to solve the three-dimensional time-dependent Maxwell's equations when metamaterials are involved. First, we obtain some superclose results between the interpolations of the analytical solutions and finite element solutions obtained using arbitrary orders of Raviart-Thomas-Nédélec mixed spaces on regular cubic meshes. Then we prove the superconvergence result in the discrete l2 norm achieved for the lowest-order Raviart-Thomas-Nédélec space. To our best knowledge, such superconvergence results have never been obtained elsewhere. Finally, we implement the leap-frog scheme and present numerical results justifying our theoretical analysis. © 2011 Elsevier Inc.

  8. A parallel adaptive finite element simplified spherical harmonics approximation solver for frequency domain fluorescence molecular imaging

    International Nuclear Information System (INIS)

    Lu Yujie; Zhu Banghe; Rasmussen, John C; Sevick-Muraca, Eva M; Shen Haiou; Wang Ge

    2010-01-01

    Fluorescence molecular imaging/tomography may play an important future role in preclinical research and clinical diagnostics. Time- and frequency-domain fluorescence imaging can acquire more measurement information than the continuous wave (CW) counterpart, improving the image quality of fluorescence molecular tomography. Although diffusion approximation (DA) theory has been extensively applied in optical molecular imaging, high-order photon migration models need to be further investigated to match quantitation provided by nuclear imaging. In this paper, a frequency-domain parallel adaptive finite element solver is developed with simplified spherical harmonics (SP N ) approximations. To fully evaluate the performance of the SP N approximations, a fast time-resolved tetrahedron-based Monte Carlo fluorescence simulator suitable for complex heterogeneous geometries is developed using a convolution strategy to realize the simulation of the fluorescence excitation and emission. The validation results show that high-order SP N can effectively correct the modeling errors of the diffusion equation, especially when the tissues have high absorption characteristics or when high modulation frequency measurements are used. Furthermore, the parallel adaptive mesh evolution strategy improves the modeling precision and the simulation speed significantly on a realistic digital mouse phantom. This solver is a promising platform for fluorescence molecular tomography using high-order approximations to the radiative transfer equation.

  9. A suitable low-order, eight-node tetrahedral finite element for solids

    Energy Technology Data Exchange (ETDEWEB)

    Key, S.W.; Heinstein, M.S.; Stone, C.M.; Mello, F.J.; Blanford, M.L.; Budge, K.G.

    1998-03-01

    To use the all-tetrahedral mesh generation existing today, the authors have explored the creation of a computationally efficient eight-node tetrahedral finite element (a four-node tetrahedral finite element enriched with four mid-face nodal points). The derivation of the element`s gradient operator, studies in obtaining a suitable mass lumping, and the element`s performance in applications are presented. In particular they examine the eight-node tetrahedral finite element`s behavior in longitudinal plane wave propagation, in transverse cylindrical wave propagation, and in simulating Taylor bar impacts. The element samples only constant strain states and, therefore, has 12 hour-glass modes. In this regard it bears similarities to the eight-node, mean-quadrature hexahedral finite element. Comparisons with the results obtained from the mean-quadrature eight-node hexahedral finite element and the four-node tetrahedral finite element are included. Given automatic all-tetrahedral meshing, the eight-node, constant-strain tetrahedral finite element is a suitable replacement for the eight-node hexahedral finite element in those cases where mesh generation requires an inordinate amount of user intervention and direction to obtain acceptable mesh properties.

  10. The finite element method its basis and fundamentals

    CERN Document Server

    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

  11. Lagrangian and Eulerian finite element techniques for transient fluid-structure interaction problems

    International Nuclear Information System (INIS)

    Donea, J.; Fasoli-Stella, P.; Giuliani, S.

    1977-01-01

    The basic finite element equations for transient compressible fluid flow are presented in a form that allows the elements to be moved with the fluid in normal Lagrangian fashion, to be held fixed in a Eulerian manner, or to be moved in some arbitrarily specified way. The co-existence of Lagrangian and Eulerian regions within the finite element mesh will permit to handle greater distortions in the fluid motion than would be allowed by a purely Lagrangian method, with more resolution than is afforded by a purely Eulerian method. To achieve a mixed formulation, the conservation statements of mass, momentum and energy are expressed in integral form over a reference volume whose surface may be moving with an arbitrarily prescribed velocity. Direct use can be made of the integral forms of the mass and energy equations to adjust the element density and specific internal energy. The Galerkin process is employed to formulate a variational statement associated with the momentum equation. The difficulties associated with the presence of convective terms in the conservation equations are handled by expressing transports of mass, momentum and energy terms of intermediate velocities derived at each cycle from the previous cycle velocities and accelerations. The hydrodynamic elements presented are triangles, quadrilaterals with constant pressure and density. The finite element equations associated with these elements are described in the necessary detail. Numerical results are presented based on purely Lagrangian, purely Eulerian and mixed formulations. Simple problems with analytic solution are solved first to show the validity and accuracy of the proposed mixed finite element formulation. Then, practical problems are illustrated in the field of fast reactor safety analysis

  12. A suitable low-order, eight-node tetrahedral finite element for solids

    International Nuclear Information System (INIS)

    Key, S.W.; Heinstein, M.S.; Stone, C.M.; Mello, F.J.; Blanford, M.L.; Budge, K.G.

    1998-03-01

    To use the all-tetrahedral mesh generation existing today, the authors have explored the creation of a computationally efficient eight-node tetrahedral finite element (a four-node tetrahedral finite element enriched with four mid-face nodal points). The derivation of the element's gradient operator, studies in obtaining a suitable mass lumping, and the element's performance in applications are presented. In particular they examine the eight-node tetrahedral finite element's behavior in longitudinal plane wave propagation, in transverse cylindrical wave propagation, and in simulating Taylor bar impacts. The element samples only constant strain states and, therefore, has 12 hour-glass modes. In this regard it bears similarities to the eight-node, mean-quadrature hexahedral finite element. Comparisons with the results obtained from the mean-quadrature eight-node hexahedral finite element and the four-node tetrahedral finite element are included. Given automatic all-tetrahedral meshing, the eight-node, constant-strain tetrahedral finite element is a suitable replacement for the eight-node hexahedral finite element in those cases where mesh generation requires an inordinate amount of user intervention and direction to obtain acceptable mesh properties

  13. Elastic-plastic and creep analyses by assumed stress finite elements

    International Nuclear Information System (INIS)

    Pian, T.H.H.; Spilker, R.L.; Lee, S.W.

    1975-01-01

    A formulation is presented of incremental finite element solutions for both initial stress and initial strain problems based on modified complementary energy principle with relaxed inter-element continuity requirement. The corresponding finite element model is the assumed stress hybrid model which has stress parameters in the interior of each element and displacements at the individual nodes as unknowns. The formulation includes an important consideration that the states of stress and strain and the beginning of each increment may not satisfy the equilibrium and compatibility equations. These imbalance and mismatch conditions all lead to correction terms for the equivalent nodal forces of the matrix equations. The initial stress method is applied to elastic-plastic analysis of structures. In this case the stress parameters for the individual elements can be eliminated resulting to a system of equations with only nodal displacements as unknowns. Two different complementary energy principles can be formulated, in one of which the equilibrium of the final state of stress is maintained while in the other the equilibrium of the stress increments is maintained. Each of these two different formulations can be combined with different iterative schemes to be used at each incremental steps of the elastic-plastic analysis. It is also indicated clearly that for the initial stress method the state of stress at the beginning of each increments is in general, not in equilibrium and an imbalance correction is needed. Results of a comprehensive evaluation of various solution procedures by the initial stress method using the assumed stress hybrid elements are presented. The example used is the static response of a thick wall cylinder of elastic-perfectly plastic material under internal pressure. Solid of revolution elements with rectangular cross sections are used

  14. Mixed finite element-based fully conservative methods for simulating wormhole propagation

    KAUST Repository

    Kou, Jisheng; Sun, Shuyu; Wu, Yuanqing

    2015-01-01

    Wormhole propagation during reactive dissolution of carbonates plays a very important role in the product enhancement of oil and gas reservoir. Because of high velocity and nonuniform porosity, the Darcy–Forchheimer model is applicable for this problem instead of conventional Darcy framework. We develop a mixed finite element scheme for numerical simulation of this problem, in which mixed finite element methods are used not only for the Darcy–Forchheimer flow equations but also for the solute transport equation by introducing an auxiliary flux variable to guarantee full mass conservation. In theoretical analysis aspects, based on the cut-off operator of solute concentration, we construct an analytical function to control and handle the change of porosity with time; we treat the auxiliary flux variable as a function of velocity and establish its properties; we employ the coupled analysis approach to deal with the fully coupling relation of multivariables. From this, the stability analysis and a priori error estimates for velocity, pressure, concentration and porosity are established in different norms. Numerical results are also given to verify theoretical analysis and effectiveness of the proposed scheme.

  15. Mixed finite element-based fully conservative methods for simulating wormhole propagation

    KAUST Repository

    Kou, Jisheng

    2015-10-11

    Wormhole propagation during reactive dissolution of carbonates plays a very important role in the product enhancement of oil and gas reservoir. Because of high velocity and nonuniform porosity, the Darcy–Forchheimer model is applicable for this problem instead of conventional Darcy framework. We develop a mixed finite element scheme for numerical simulation of this problem, in which mixed finite element methods are used not only for the Darcy–Forchheimer flow equations but also for the solute transport equation by introducing an auxiliary flux variable to guarantee full mass conservation. In theoretical analysis aspects, based on the cut-off operator of solute concentration, we construct an analytical function to control and handle the change of porosity with time; we treat the auxiliary flux variable as a function of velocity and establish its properties; we employ the coupled analysis approach to deal with the fully coupling relation of multivariables. From this, the stability analysis and a priori error estimates for velocity, pressure, concentration and porosity are established in different norms. Numerical results are also given to verify theoretical analysis and effectiveness of the proposed scheme.

  16. An adaptively refined XFEM with virtual node polygonal elements for dynamic crack problems

    Science.gov (United States)

    Teng, Z. H.; Sun, F.; Wu, S. C.; Zhang, Z. B.; Chen, T.; Liao, D. M.

    2018-02-01

    By introducing the shape functions of virtual node polygonal (VP) elements into the standard extended finite element method (XFEM), a conforming elemental mesh can be created for the cracking process. Moreover, an adaptively refined meshing with the quadtree structure only at a growing crack tip is proposed without inserting hanging nodes into the transition region. A novel dynamic crack growth method termed as VP-XFEM is thus formulated in the framework of fracture mechanics. To verify the newly proposed VP-XFEM, both quasi-static and dynamic cracked problems are investigated in terms of computational accuracy, convergence, and efficiency. The research results show that the present VP-XFEM can achieve good agreement in stress intensity factor and crack growth path with the exact solutions or experiments. Furthermore, better accuracy, convergence, and efficiency of different models can be acquired, in contrast to standard XFEM and mesh-free methods. Therefore, VP-XFEM provides a suitable alternative to XFEM for engineering applications.

  17. An Investigation of Two Finite Element Modeling Solutions for Biomechanical Simulation Using a Case Study of a Mandibular Bone.

    Science.gov (United States)

    Liu, Yun-Feng; Fan, Ying-Ying; Dong, Hui-Yue; Zhang, Jian-Xing

    2017-12-01

    The method used in biomechanical modeling for finite element method (FEM) analysis needs to deliver accurate results. There are currently two solutions used in FEM modeling for biomedical model of human bone from computerized tomography (CT) images: one is based on a triangular mesh and the other is based on the parametric surface model and is more popular in practice. The outline and modeling procedures for the two solutions are compared and analyzed. Using a mandibular bone as an example, several key modeling steps are then discussed in detail, and the FEM calculation was conducted. Numerical calculation results based on the models derived from the two methods, including stress, strain, and displacement, are compared and evaluated in relation to accuracy and validity. Moreover, a comprehensive comparison of the two solutions is listed. The parametric surface based method is more helpful when using powerful design tools in computer-aided design (CAD) software, but the triangular mesh based method is more robust and efficient.

  18. Finite element formulation for a digital image correlation method

    International Nuclear Information System (INIS)

    Sun Yaofeng; Pang, John H. L.; Wong, Chee Khuen; Su Fei

    2005-01-01

    A finite element formulation for a digital image correlation method is presented that will determine directly the complete, two-dimensional displacement field during the image correlation process on digital images. The entire interested image area is discretized into finite elements that are involved in the common image correlation process by use of our algorithms. This image correlation method with finite element formulation has an advantage over subset-based image correlation methods because it satisfies the requirements of displacement continuity and derivative continuity among elements on images. Numerical studies and a real experiment are used to verify the proposed formulation. Results have shown that the image correlation with the finite element formulation is computationally efficient, accurate, and robust

  19. Distributed Adaptive Finite-Time Approach for Formation-Containment Control of Networked Nonlinear Systems Under Directed Topology.

    Science.gov (United States)

    Wang, Yujuan; Song, Yongduan; Ren, Wei

    2017-07-06

    This paper presents a distributed adaptive finite-time control solution to the formation-containment problem for multiple networked systems with uncertain nonlinear dynamics and directed communication constraints. By integrating the special topology feature of the new constructed symmetrical matrix, the technical difficulty in finite-time formation-containment control arising from the asymmetrical Laplacian matrix under single-way directed communication is circumvented. Based upon fractional power feedback of the local error, an adaptive distributed control scheme is established to drive the leaders into the prespecified formation configuration in finite time. Meanwhile, a distributed adaptive control scheme, independent of the unavailable inputs of the leaders, is designed to keep the followers within a bounded distance from the moving leaders and then to make the followers enter the convex hull shaped by the formation of the leaders in finite time. The effectiveness of the proposed control scheme is confirmed by the simulation.

  20. 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....

  1. Discontinuous Galerkin finite element method for solving population density functions of cortical pyramidal and thalamic neuronal populations.

    Science.gov (United States)

    Huang, Chih-Hsu; Lin, Chou-Ching K; Ju, Ming-Shaung

    2015-02-01

    Compared with the Monte Carlo method, the population density method is efficient for modeling collective dynamics of neuronal populations in human brain. In this method, a population density function describes the probabilistic distribution of states of all neurons in the population and it is governed by a hyperbolic partial differential equation. In the past, the problem was mainly solved by using the finite difference method. In a previous study, a continuous Galerkin finite element method was found better than the finite difference method for solving the hyperbolic partial differential equation; however, the population density function often has discontinuity and both methods suffer from a numerical stability problem. The goal of this study is to improve the numerical stability of the solution using discontinuous Galerkin finite element method. To test the performance of the new approach, interaction of a population of cortical pyramidal neurons and a population of thalamic neurons was simulated. The numerical results showed good agreement between results of discontinuous Galerkin finite element and Monte Carlo methods. The convergence and accuracy of the solutions are excellent. The numerical stability problem could be resolved using the discontinuous Galerkin finite element method which has total-variation-diminishing property. The efficient approach will be employed to simulate the electroencephalogram or dynamics of thalamocortical network which involves three populations, namely, thalamic reticular neurons, thalamocortical neurons and cortical pyramidal neurons. Copyright © 2014 Elsevier Ltd. All rights reserved.

  2. On symmetric pyramidal finite elements

    Czech Academy of Sciences Publication Activity Database

    Liu, L.; Davies, K. B.; Yuan, K.; Křížek, Michal

    2004-01-01

    Roč. 11, 1-2 (2004), s. 213-227 ISSN 1492-8760 R&D Projects: GA AV ČR IAA1019201 Institutional research plan: CEZ:AV0Z1019905 Keywords : mesh generation * finite element method * composite elements Subject RIV: BA - General Mathematics Impact factor: 0.108, year: 2004

  3. Finite-element analysis of dynamic fracture

    Science.gov (United States)

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

    1976-01-01

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

  4. The finite element method in electromagnetics

    CERN Document Server

    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

  5. Finite elements for analysis and design

    CERN Document Server

    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

  6. Parallelized Three-Dimensional Resistivity Inversion Using Finite Elements And Adjoint State Methods

    Science.gov (United States)

    Schaa, Ralf; Gross, Lutz; Du Plessis, Jaco

    2015-04-01

    The resistivity method is one of the oldest geophysical exploration methods, which employs one pair of electrodes to inject current into the ground and one or more pairs of electrodes to measure the electrical potential difference. The potential difference is a non-linear function of the subsurface resistivity distribution described by an elliptic partial differential equation (PDE) of the Poisson type. Inversion of measured potentials solves for the subsurface resistivity represented by PDE coefficients. With increasing advances in multichannel resistivity acquisition systems (systems with more than 60 channels and full waveform recording are now emerging), inversion software require efficient storage and solver algorithms. We developed the finite element solver Escript, which provides a user-friendly programming environment in Python to solve large-scale PDE-based problems (see https://launchpad.net/escript-finley). Using finite elements, highly irregular shaped geology and topography can readily be taken into account. For the 3D resistivity problem, we have implemented the secondary potential approach, where the PDE is decomposed into a primary potential caused by the source current and the secondary potential caused by changes in subsurface resistivity. The primary potential is calculated analytically, and the boundary value problem for the secondary potential is solved using nodal finite elements. This approach removes the singularity caused by the source currents and provides more accurate 3D resistivity models. To solve the inversion problem we apply a 'first optimize then discretize' approach using the quasi-Newton scheme in form of the limited-memory Broyden-Fletcher-Goldfarb-Shanno (L-BFGS) method (see Gross & Kemp 2013). The evaluation of the cost function requires the solution of the secondary potential PDE for each source current and the solution of the corresponding adjoint-state PDE for the cost function gradients with respect to the subsurface

  7. Finite Element Method in Machining Processes

    CERN Document Server

    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...

  8. Solving nonlinear nonstationary problem of heat-conductivity by finite element method

    Directory of Open Access Journals (Sweden)

    Антон Янович Карвацький

    2016-11-01

    Full Text Available Methodology and effective solving algorithm of non-linear dynamic problems of thermal and electric conductivity with significant temperature dependence of thermal and physical properties are given on the basis of finite element method (FEM and Newton linearization method. Discrete equations system FEM was obtained with the use of Galerkin method, where the main function is the finite element form function. The methodology based on successive solving problems of thermal and electrical conductivity has been examined in the work in order to minimize the requirements for calculating resources (RAM. in particular. Having used Mathcad software original programming code was developed to solve the given problem. After investigation of the received results, comparative analyses of accurate solution data and results of numerical solutions, obtained with the use of Matlab programming products, was held. The geometry of one fourth part of the finite sized cylinder was used to test the given numerical model. The discretization of the calculation part was fulfilled using the open programming software for automated Gmsh nets with tetrahedral units, while ParaView, which is an open programming code as well, was used to visualize the calculation results. It was found out that the maximum value violation of potential and temperature determination doesn`t exceed 0,2-0,83% in the given work according to the problem conditions

  9. Elastic-plastic analysis using an efficient formulation of the finite element method

    International Nuclear Information System (INIS)

    Aamodt, B.; Mo, O.

    1975-01-01

    Based on the flow theory of plasticity, the von Mises or the Tresca yield criterion and the isotropic hardening law, an incremental stiffness relationship can be established for a finite element model of the elasto-plastic structure. However, instead of including all degrees of freedom and all finite elements of the total model in a nonlinear solution process, a separation of elastic and plastic parts of the structure can be carried out. Such a separation can be obtained by identifying elastic parts of the structure as 'elastic' superelements and elasto-plastic parts of the structure as 'elasto-plastic' superelements. Also, it may be of advantage to use several levels of superelements in modelling the elastic parts of the structure. For the 'elasto-plastic' superelements the specific plastic computations such as updating of the incremental stiffness matrix and subsequent reduction (i.e. static condensation of all degrees of freedom being local to the superelements) have to be carried out repeatedly during the nonlinear solution process. The solution of the nonlinear equations is performed utilizing a combination of load incrementation and equilibrium interations. The present method of analysis is demonstrated for two larger examples of elasto-plastic analysis. (Auth.)

  10. Finite-element model of ultrasonic NDE [nondestructive evaluation

    International Nuclear Information System (INIS)

    Lord, W.

    1989-07-01

    An understanding of the way in which ultrasound interacts with defects in materials is essential to the development of improved nondestructive testing procedures for the inspection of critical power plant components. Traditionally, the modeling of such phenomena has been approached from an analytical standpoint in which appropriate assumptions are made concerning material properties, geometrical constraints and defect boundaries in order to arrive at closed form solutions. Such assumptions, by their very nature, tend to inhibit the development of complete input/output NDT system models suitable for predicting realistic piezoelectric transducer signals from the interaction of pulsed, finite-aperture ultrasound with arbitrarily shaped defects in the kinds of materials of interest to the utilities. The major thrust of EPRI Project RP 2687-2 is to determine the feasibility of applying finite element analysis techniques to overcome these problems. 85 refs., 64 figs., 3 tabs

  11. Inside finite elements

    CERN Document Server

    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.

  12. Thermal analysis of cracked bodies using finite element techniques

    International Nuclear Information System (INIS)

    Hellen, T.K.; Price, R.H.; Harrison, R.P.

    1975-01-01

    The paper develops the potential energy equation in terms of finite element theory including thermal loads. Following this, the energy release rate and consequently the stress intensity factors are derived. Considerations of the classical near crack tip equations are made and deficiencies with the popular substitution methods are highlighted. A method of removing these deficiencies is described. Various energy methods are reconsidered in terms of the role of the thermal energy contribution to the potential energy. These methods include work of crack closure, energy compliance and virtual crack extensions with no other change in nodal geometry, and therefore only requires the recalculation of the stiffness matrices of the crack tip elements. An example of a quadratic temperature gradient parallel to the crack plane in an edge cracked plate is described. Comparisons of the various finite element methods are made and generally show good agreement. A second application compares the virtual crack extension method with an approximate analytical solution in determining stress intensity factors for a thick hollow cylinder with an axial crack for various depths through the wall thickness and for different times. Initially the cylinder is at a uniform high temperature and is then subjected to a sustained cooling shock. Analytical solutions are available for temperature and stress distributions in the uncracked pipe. The stress intensity for a shallow crack in the early stages of the transient has been determined using a superposition procedure. Comparison of the analytical and computed results shows good agreement between the methods

  13. A direct solver with reutilization of LU factorizations for h-adaptive finite element grids with point singularities

    KAUST Repository

    Paszyński, Maciej R.

    2013-04-01

    This paper describes a direct solver algorithm for a sequence of finite element meshes that are h-refined towards one or several point singularities. For such a sequence of grids, the solver delivers linear computational cost O(N) in terms of CPU time and memory with respect to the number of unknowns N. The linear computational cost is achieved by utilizing the recursive structure provided by the sequence of h-adaptive grids with a special construction of the elimination tree that allows for reutilization of previously computed partial LU (or Cholesky) factorizations over the entire unrefined part of the computational mesh. The reutilization technique reduces the computational cost of the entire sequence of h-refined grids from O(N2) down to O(N). Theoretical estimates are illustrated with numerical results on two- and three-dimensional model problems exhibiting one or several point singularities. © 2013 Elsevier Ltd. All rights reserved.

  14. A direct solver with reutilization of LU factorizations for h-adaptive finite element grids with point singularities

    KAUST Repository

    Paszyński, Maciej R.; Calo, Victor M.; Pardo, David

    2013-01-01

    This paper describes a direct solver algorithm for a sequence of finite element meshes that are h-refined towards one or several point singularities. For such a sequence of grids, the solver delivers linear computational cost O(N) in terms of CPU time and memory with respect to the number of unknowns N. The linear computational cost is achieved by utilizing the recursive structure provided by the sequence of h-adaptive grids with a special construction of the elimination tree that allows for reutilization of previously computed partial LU (or Cholesky) factorizations over the entire unrefined part of the computational mesh. The reutilization technique reduces the computational cost of the entire sequence of h-refined grids from O(N2) down to O(N). Theoretical estimates are illustrated with numerical results on two- and three-dimensional model problems exhibiting one or several point singularities. © 2013 Elsevier Ltd. All rights reserved.

  15. Finite Element Modelling of Seismic Liquefaction in Soils

    NARCIS (Netherlands)

    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

  16. Finite element modeling of ultrasonic inspection of weldments

    International Nuclear Information System (INIS)

    Dewey, B.R.; Adler, L.; Oliver, B.F.; Pickard, C.A.

    1983-01-01

    High performance weldments for critical service applications require 100% inspection. Balanced against the adaptability of the ultrasonic method for automated inspection are the difficulties encountered with nonhomogeneous and anisotropic materials. This research utilizes crystals and bicrystals of nickel to model austenitic weld metal, where the anisotropy produces scattering and mode conversion, making detection and measurement of actual defects difficult. Well characterized samples of Ni are produced in a levitation zone melting facility. Crystals in excess of 25 mm diameter and length are large enough to permit ultrasonic measurements of attenuation, wave speed, and spectral content. At the same time, the experiments are duplicated as finite element models for comparison purposes

  17. Convergence of a residual based artificial viscosity finite element method

    KAUST Repository

    Nazarov, Murtazo

    2013-02-01

    We present a residual based artificial viscosity finite element method to solve conservation laws. The Galerkin approximation is stabilized by only residual based artificial viscosity, without any least-squares, SUPG, or streamline diffusion terms. We prove convergence of the method, applied to a scalar conservation law in two space dimensions, toward an unique entropy solution for implicit time stepping schemes. © 2012 Elsevier B.V. All rights reserved.

  18. Finite element simulations of interactions between multiple hydraulic fractures in a poroelastic rock

    DEFF Research Database (Denmark)

    Salimzadeh, Saeed; Usui, Tomoya; Paluszny, Adriana

    2017-01-01

    A fully coupled three-dimensional finite-element model for hydraulic fractures in permeable rocks is presented, and used to investigate the ranges of applicability of the classical analytical solutions that are known to be valid in limiting cases. This model simultaneously accounts for fluid flow...

  19. Calculation of two-dimensional thermal transients by the finite element method

    International Nuclear Information System (INIS)

    Fontoura Rodrigues, J.L.A. da; Barcellos, C.S. de

    1981-01-01

    The linear heat conduction through anisotropic and/or heterogeneous matter, in either two-dimensional fields with any kind of geometry or three-dimensional fields with axial symmetry is analysed. It only accepts time-independent boundary conditions and it is possible to have internal heat generation. The solution is obtained by modal analysis employing the finite element method under Galerkin formulation. (Author) [pt

  20. Coupled convective and conductive heat transfer by up-wind finite element method

    International Nuclear Information System (INIS)

    Kushwaha, H.S.

    1981-01-01

    Some of concepts relating to finite element formulation of the Navier-Stoke's equations using mixed formulation and Penality formulation have been discussed. The two different approaches for solution of nonlinear differential equations for two different types of formulation have been described. Incremental Newton Raphson method can also be applied to mixed formulation. (author)

  1. A Finite Element Method for Simulation of Compressible Cavitating Flows

    Science.gov (United States)

    Shams, Ehsan; Yang, Fan; Zhang, Yu; Sahni, Onkar; Shephard, Mark; Oberai, Assad

    2016-11-01

    This work focuses on a novel approach for finite element simulations of multi-phase flows which involve evolving interface with phase change. Modeling problems, such as cavitation, requires addressing multiple challenges, including compressibility of the vapor phase, interface physics caused by mass, momentum and energy fluxes. We have developed a mathematically consistent and robust computational approach to address these problems. We use stabilized finite element methods on unstructured meshes to solve for the compressible Navier-Stokes equations. Arbitrary Lagrangian-Eulerian formulation is used to handle the interface motions. Our method uses a mesh adaptation strategy to preserve the quality of the volumetric mesh, while the interface mesh moves along with the interface. The interface jump conditions are accurately represented using a discontinuous Galerkin method on the conservation laws. Condensation and evaporation rates at the interface are thermodynamically modeled to determine the interface velocity. We will present initial results on bubble cavitation the behavior of an attached cavitation zone in a separated boundary layer. We acknowledge the support from Army Research Office (ARO) under ARO Grant W911NF-14-1-0301.

  2. A stabilized finite element formulation for the solution of the Navier-Stokes equations in axisymmetric geometry

    International Nuclear Information System (INIS)

    Souza, Altivo Monteiro de

    2008-12-01

    The world energy consumption has been increasing strongly in recent years. Nuclear energy has been regarded as a suitable option to supply this growing energy demand in industrial scale. In view of the need of improving the understanding and capacity of analysis of nuclear power plants, modern simulation techniques for flow and heat transfer problems are gaining greater importance. A large number of problems found in nuclear reactor engineering can be dealt assuming axial symmetry. Thus, in this work a stabilized finite element formulation for the solution of the Navier-Stokes and energy equations for axisymmetric problems have been developed and tested. The formulation has been implemented in the NS S OLVER M PI 2 D A program developed at the Parallel Computation Laboratory of the Instituto de Engenharia Nuclear (LCP/IEN) and is now available either for safety analysis or design of nuclear systems. (author)

  3. A finite element model for protein transport in vivo

    Directory of Open Access Journals (Sweden)

    Montas Hubert J

    2007-06-01

    Full Text Available Abstract Background Biological mass transport processes determine the behavior and function of cells, regulate interactions between synthetic agents and recipient targets, and are key elements in the design and use of biosensors. Accurately predicting the outcomes of such processes is crucial to both enhancing our understanding of how these systems function, enabling the design of effective strategies to control their function, and verifying that engineered solutions perform according to plan. Methods A Galerkin-based finite element model was developed and implemented to solve a system of two coupled partial differential equations governing biomolecule transport and reaction in live cells. The simulator was coupled, in the framework of an inverse modeling strategy, with an optimization algorithm and an experimental time series, obtained by the Fluorescence Recovery after Photobleaching (FRAP technique, to estimate biomolecule mass transport and reaction rate parameters. In the inverse algorithm, an adaptive method was implemented to calculate sensitivity matrix. A multi-criteria termination rule was developed to stop the inverse code at the solution. The applicability of the model was illustrated by simulating the mobility and binding of GFP-tagged glucocorticoid receptor in the nucleoplasm of mouse adenocarcinoma. Results The numerical simulator shows excellent agreement with the analytic solutions and experimental FRAP data. Detailed residual analysis indicates that residuals have zero mean and constant variance and are normally distributed and uncorrelated. Therefore, the necessary and sufficient criteria for least square parameter optimization, which was used in this study, were met. Conclusion The developed strategy is an efficient approach to extract as much physiochemical information from the FRAP protocol as possible. Well-posedness analysis of the inverse problem, however, indicates that the FRAP protocol provides insufficient

  4. OPTIMIZATION OF I-SECTION PROFILE DESIGN BY THE FINITE ELEMENT METHOD

    Directory of Open Access Journals (Sweden)

    Patryk Różyło

    2016-03-01

    Full Text Available This paper discusses the problem of design optimization for an I-section profile. The optimization process was performed using the Abaqus program. The numerical analysis of a strictly static problem was based on the finite element method. The scope of the analysis involved both determination of stresses and displacements in the profile and structure topology optimization. The main focus of the numerical analysis was put on reducing profile volume while maintaining the same load and similar stresses prior to and after optimization. The solution of the optimization problem is just an example of the potential of using this method in combination with the finite element method in the Abaqus environment. Nowadays numerical analysis is the most effective cost-reducing alternative to experimental tests and it enables structure examination by means of a computer.

  5. Mixed finite element simulations in two-dimensional groundwater flow problems

    International Nuclear Information System (INIS)

    Kimura, Hideo

    1989-01-01

    A computer code of groundwater flow in two-dimensional porous media based on the mixed finite element method was developed for accurate approximations of Darcy velocities in safety evaluation of radioactive waste disposal. The mixed finite element procedure solves for both the Darcy velocities and pressure heads simultaneously in the Darcy equation and continuity equation. Numerical results of a single well pumping at a constant rate in a uniform flow field showed that the mixed finite element method gives more accurate Darcy velocities nearly 50 % on average error than standard finite element method. (author)

  6. Impact of new computing systems on finite element computations

    International Nuclear Information System (INIS)

    Noor, A.K.; Fulton, R.E.; Storaasi, O.O.

    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

  7. Finite size effects of a pion matrix element

    International Nuclear Information System (INIS)

    Guagnelli, M.; Jansen, K.; Palombi, F.; Petronzio, R.; Shindler, A.; Wetzorke, I.

    2004-01-01

    We investigate finite size effects of the pion matrix element of the non-singlet, twist-2 operator corresponding to the average momentum of non-singlet quark densities. Using the quenched approximation, they come out to be surprisingly large when compared to the finite size effects of the pion mass. As a consequence, simulations of corresponding nucleon matrix elements could be affected by finite size effects even stronger which could lead to serious systematic uncertainties in their evaluation

  8. Variational approach to probabilistic finite elements

    Science.gov (United States)

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

    1991-08-01

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

  9. Verification of Orthogrid Finite Element Modeling Techniques

    Science.gov (United States)

    Steeve, B. E.

    1996-01-01

    The stress analysis of orthogrid structures, specifically with I-beam sections, is regularly performed using finite elements. Various modeling techniques are often used to simplify the modeling process but still adequately capture the actual hardware behavior. The accuracy of such 'Oshort cutso' is sometimes in question. This report compares three modeling techniques to actual test results from a loaded orthogrid panel. The finite element models include a beam, shell, and mixed beam and shell element model. Results show that the shell element model performs the best, but that the simpler beam and beam and shell element models provide reasonable to conservative results for a stress analysis. When deflection and stiffness is critical, it is important to capture the effect of the orthogrid nodes in the model.

  10. Review of Tomographic Imaging using Finite Element Method

    Directory of Open Access Journals (Sweden)

    Mohd Fua’ad RAHMAT

    2011-12-01

    Full Text Available Many types of techniques for process tomography were proposed and developed during the past 20 years. This paper review the techniques and the current state of knowledge and experience on the subject, aimed at highlighting the problems associated with the non finite element methods, such as the ill posed, ill conditioned which relates to the accuracy and sensitivity of measurements. In this paper, considerations for choice of sensors and its applications were outlined and descriptions of non finite element tomography systems were presented. The finite element method tomography system as obtained from recent works, suitable for process control and measurement were also presented.

  11. Magnetic materials and 3D finite element modeling

    CERN Document Server

    Bastos, Joao Pedro A

    2014-01-01

    Magnetic Materials and 3D Finite Element Modeling explores material characterization and finite element modeling (FEM) applications. This book relates to electromagnetic analysis based on Maxwell’s equations and application of the finite element (FE) method to low frequency devices. A great source for senior undergraduate and graduate students in electromagnetics, it also supports industry professionals working in magnetics, electromagnetics, ferromagnetic materials science and electrical engineering. The authors present current concepts on ferromagnetic material characterizations and losses. They provide introductory material; highlight basic electromagnetics, present experimental and numerical modeling related to losses and focus on FEM applied to 3D applications. They also explain various formulations, and discuss numerical codes.

  12. On higher order pyramidal finite elements

    Czech Academy of Sciences Publication Activity Database

    Liu, L.; Davies, K.B.; Křížek, Michal; Guan, L.

    2011-01-01

    Roč. 3, č. 2 (2011), s. 131-140 ISSN 2070-0733 R&D Projects: GA AV ČR(CZ) IAA100190803 Institutional research plan: CEZ:AV0Z10190503 Keywords : pyramidal polynomial basis functions * finite element method * composite elements * three-dimensional mortar elements Subject RIV: BA - General Mathematics Impact factor: 0.750, year: 2011

  13. Free vibration of thin axisymmetric structures by a semi-analytical finite element scheme and isoparametric solid elements

    International Nuclear Information System (INIS)

    Akeju, T.A.I.; Kelly, D.W.; Zienkiewicz, O.C.; Kanaka Raju, K.

    1981-01-01

    The eigenvalue equations governing the free vibration of axisymmetric solids are derived by means of a semi-analytical finite element scheme. In particular we investigated the use of an 8-node solid element in structures which exhibit a 'shell-like' behaviour. Bathe-Wilson subspace iteration algorithm is employed for the solution of the equations. The element is shown to give good results for beam and shell vibration problems. It is also utilised to solve a complex solid in the form of an internal component of a modern jet engine. This particular application is of considerable practical importance as the dynamics of such components form a dominant design constraint. (orig./HP)

  14. Computational error estimates for Monte Carlo finite element approximation with log normal diffusion coefficients

    KAUST Repository

    Sandberg, Mattias

    2015-01-07

    The Monte Carlo (and Multi-level Monte Carlo) finite element method can be used to approximate observables of solutions to diffusion equations with log normal distributed diffusion coefficients, e.g. modelling ground water flow. Typical models use log normal diffusion coefficients with H¨older regularity of order up to 1/2 a.s. This low regularity implies that the high frequency finite element approximation error (i.e. the error from frequencies larger than the mesh frequency) is not negligible and can be larger than the computable low frequency error. This talk will address how the total error can be estimated by the computable error.

  15. Finite element method for simulation of the semiconductor devices

    International Nuclear Information System (INIS)

    Zikatanov, L.T.; Kaschiev, M.S.

    1991-01-01

    An iterative method for solving the system of nonlinear equations of the drift-diffusion representation for the simulation of the semiconductor devices is worked out. The Petrov-Galerkin method is taken for the discretization of these equations using the bilinear finite elements. It is shown that the numerical scheme is a monotonous one and there are no oscillations of the solutions in the region of p-n transition. The numerical calculations of the simulation of one semiconductor device are presented. 13 refs.; 3 figs

  16. Validation of High Displacement Piezoelectric Actuator Finite Element Models

    Science.gov (United States)

    Taleghani, B. K.

    2000-01-01

    The paper presents the results obtained by using NASTRAN(Registered Trademark) and ANSYS(Regitered Trademark) finite element codes to predict doming of the THUNDER piezoelectric actuators during the manufacturing process and subsequent straining due to an applied input voltage. To effectively use such devices in engineering applications, modeling and characterization are essential. Length, width, dome height, and thickness are important parameters for users of such devices. Therefore, finite element models were used to assess the effects of these parameters. NASTRAN(Registered Trademark) and ANSYS(Registered Trademark) used different methods for modeling piezoelectric effects. In NASTRAN(Registered Trademark), a thermal analogy was used to represent voltage at nodes as equivalent temperatures, while ANSYS(Registered Trademark) processed the voltage directly using piezoelectric finite elements. The results of finite element models were validated by using the experimental results.

  17. The finite-difference and finite-element modeling of seismic wave propagation and earthquake motion

    International Nuclear Information System (INIS)

    Moszo, P.; Kristek, J.; Galis, M.; Pazak, P.; Balazovijech, M.

    2006-01-01

    Numerical modeling of seismic wave propagation and earthquake motion is an irreplaceable tool in investigation of the Earth's structure, processes in the Earth, and particularly earthquake phenomena. Among various numerical methods, the finite-difference method is the dominant method in the modeling of earthquake motion. Moreover, it is becoming more important in the seismic exploration and structural modeling. At the same time we are convinced that the best time of the finite-difference method in seismology is in the future. This monograph provides tutorial and detailed introduction to the application of the finite-difference, finite-element, and hybrid finite-difference-finite-element methods to the modeling of seismic wave propagation and earthquake motion. The text does not cover all topics and aspects of the methods. We focus on those to which we have contributed. (Author)

  18. L∞-error estimates of a finite element method for the Hamilton-Jacobi-Bellman equations

    International Nuclear Information System (INIS)

    Bouldbrachene, M.

    1994-11-01

    We study the finite element approximation for the solution of the Hamilton-Jacobi-Bellman equations involving a system of quasi-variational inequalities (QVI). We also give the optimal L ∞ -error estimates, using the concepts of subsolutions and discrete regularity. (author). 7 refs

  19. A set of pathological tests to validate new finite elements

    Indian Academy of Sciences (India)

    M. Senthilkumar (Newgen Imaging) 1461 1996 Oct 15 13:05:22

    The finite element method entails several approximations. Hence it ... researchers have designed several pathological tests to validate any new finite element. The .... Three dimensional thick shell elements using a hybrid/mixed formu- lation.

  20. Crack Propagation by Finite Element Method

    Directory of Open Access Journals (Sweden)

    Luiz Carlos H. Ricardo

    2018-01-01

    Full Text Available Crack propagation simulation began with the development of the finite element method; the analyses were conducted to obtain a basic understanding of the crack growth. Today structural and materials engineers develop structures and materials properties using this technique. The aim of this paper is to verify the effect of different crack propagation rates in determination of crack opening and closing stress of an ASTM specimen under a standard suspension spectrum loading from FDandE SAE Keyhole Specimen Test Load Histories by finite element analysis. To understand the crack propagation processes under variable amplitude loading, retardation effects are observed

  1. Finite element analysis of plastic recycling machine designed for ...

    African Journals Online (AJOL)

    ... design was evaluated using finite element analysis (FEA) tool in Solid Works Computer ... Also, a minimum factor of safety value of 5.3 was obtained for shredder shaft ... Machine; Design; Recycling; Sustainability; Finite Element; Simulation ...

  2. An introduction to the UNCLE finite element scheme

    International Nuclear Information System (INIS)

    Enderby, J.A.

    1983-01-01

    UNCLE is a completely general finite element scheme which provides common input, output, equation-solving and other facilities for a family of finite element codes for linear and non-linear stress analysis, heat transfer etc. This report describes the concepts on which UNCLE is based and gives a general account of the facilities provided. (author)

  3. An introduction to the UNCLE finite element scheme

    Energy Technology Data Exchange (ETDEWEB)

    Enderby, J A [UK Atomic Energy Authority, Northern Division, Risley Nuclear Power Development Establishment, Risley, Warrington (United Kingdom)

    1983-05-01

    UNCLE is a completely general finite element scheme which provides common input, output, equation-solving and other facilities for a family of finite element codes for linear and non-linear stress analysis, heat transfer etc. This report describes the concepts on which UNCLE is based and gives a general account of the facilities provided. (author)

  4. A particle finite element method for machining simulations

    Science.gov (United States)

    Sabel, Matthias; Sator, Christian; Müller, Ralf

    2014-07-01

    The particle finite element method (PFEM) appears to be a convenient technique for machining simulations, since the geometry and topology of the problem can undergo severe changes. In this work, a short outline of the PFEM-algorithm is given, which is followed by a detailed description of the involved operations. The -shape method, which is used to track the topology, is explained and tested by a simple example. Also the kinematics and a suitable finite element formulation are introduced. To validate the method simple settings without topological changes are considered and compared to the standard finite element method for large deformations. To examine the performance of the method, when dealing with separating material, a tensile loading is applied to a notched plate. This investigation includes a numerical analysis of the different meshing parameters, and the numerical convergence is studied. With regard to the cutting simulation it is found that only a sufficiently large number of particles (and thus a rather fine finite element discretisation) leads to converged results of process parameters, such as the cutting force.

  5. A finite element primer for beginners the basics

    CERN Document Server

    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

  6. A Stabilized Finite Element Method for Modified Poisson-Nernst-Planck Equations to Determine Ion Flow Through a Nanopore

    Science.gov (United States)

    Chaudhry, Jehanzeb Hameed; Comer, Jeffrey; Aksimentiev, Aleksei; Olson, Luke N.

    2013-01-01

    The conventional Poisson-Nernst-Planck equations do not account for the finite size of ions explicitly. This leads to solutions featuring unrealistically high ionic concentrations in the regions subject to external potentials, in particular, near highly charged surfaces. A modified form of the Poisson-Nernst-Planck equations accounts for steric effects and results in solutions with finite ion concentrations. Here, we evaluate numerical methods for solving the modified Poisson-Nernst-Planck equations by modeling electric field-driven transport of ions through a nanopore. We describe a novel, robust finite element solver that combines the applications of the Newton's method to the nonlinear Galerkin form of the equations, augmented with stabilization terms to appropriately handle the drift-diffusion processes. To make direct comparison with particle-based simulations possible, our method is specifically designed to produce solutions under periodic boundary conditions and to conserve the number of ions in the solution domain. We test our finite element solver on a set of challenging numerical experiments that include calculations of the ion distribution in a volume confined between two charged plates, calculations of the ionic current though a nanopore subject to an external electric field, and modeling the effect of a DNA molecule on the ion concentration and nanopore current. PMID:24363784

  7. Automation of finite element methods

    CERN Document Server

    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.

  8. 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...

  9. 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.

  10. Guided waves dispersion equations for orthotropic multilayered pipes solved using standard finite elements code.

    Science.gov (United States)

    Predoi, Mihai Valentin

    2014-09-01

    The dispersion curves for hollow multilayered cylinders are prerequisites in any practical guided waves application on such structures. The equations for homogeneous isotropic materials have been established more than 120 years ago. The difficulties in finding numerical solutions to analytic expressions remain considerable, especially if the materials are orthotropic visco-elastic as in the composites used for pipes in the last decades. Among other numerical techniques, the semi-analytical finite elements method has proven its capability of solving this problem. Two possibilities exist to model a finite elements eigenvalue problem: a two-dimensional cross-section model of the pipe or a radial segment model, intersecting the layers between the inner and the outer radius of the pipe. The last possibility is here adopted and distinct differential problems are deduced for longitudinal L(0,n), torsional T(0,n) and flexural F(m,n) modes. Eigenvalue problems are deduced for the three modes classes, offering explicit forms of each coefficient for the matrices used in an available general purpose finite elements code. Comparisons with existing solutions for pipes filled with non-linear viscoelastic fluid or visco-elastic coatings as well as for a fully orthotropic hollow cylinder are all proving the reliability and ease of use of this method. Copyright © 2014 Elsevier B.V. All rights reserved.

  11. Finite element simulation and testing of ISW CFRP anchorage

    DEFF Research Database (Denmark)

    Schmidt, Jacob Wittrup; Goltermann, Per; Hertz, Kristian Dahl

    2013-01-01

    is modelled in the 3D finite Element program ABAQUS, just as digital image correlation (DIC) testing was performed to verify the finite element simulation. Also a new optimized design was produced to ensure that the finite element simulation and anchorage behaviour correlated well. It is seen....... This paper presents a novel mechanical integrated sleeve wedge anchorage which seem very promising when perusing the scope of ultimate utilization of CFRP 8mm rods (with a tension capacity of approximately 140kN). Compression transverse to the CFRP is evaluated to prevent premature failure. The anchorage...

  12. A holistic 3D finite element simulation model for thermoelectric power generator element

    International Nuclear Information System (INIS)

    Wu, Guangxi; Yu, Xiong

    2014-01-01

    Highlights: • Development of a holistic simulation model for the thermoelectric energy harvester. • Account for delta Seebeck coefficient and carrier charge densities variations. • Solution of thermo-electric coupling problem with finite element method. • Model capable of predicting phenomena not captured by traditional models. • A simulation tool for design of innovative TEM materials and structures. - Abstract: Harvesting the thermal energy stored in the ambient environment provides a potential sustainable energy source. Thermoelectric power generators have advantages of having no moving parts, being durable, and light-weighted. These unique features are advantageous for many applications (i.e., carry-on medical devices, embedded infrastructure sensors, aerospace, transportation, etc.). To ensure the efficient applications of thermoelectric energy harvesting system, the behaviors of such systems need to be fully understood. Finite element simulations provide important tools for such purpose. Although modeling the performance of thermoelectric modules has been conducted by many researchers, due to the complexity in solving the coupled problem, the influences of the effective Seebeck coefficient and carrier density variations on the performance of thermoelectric system are generally neglected. This results in an overestimation of the power generator performance under strong-ionization temperature region. This paper presents an advanced simulation model for thermoelectric elements that considers the effects of both factors. The mathematical basis of this model is firstly presented. Finite element simulations are then implemented on a thermoelectric power generator unit. The characteristics of the thermoelectric power generator and their relationship to its performance are discussed under different working temperature regions. The internal physics processes of the TEM harvester are analyzed from the results of computational simulations. The new model

  13. Hydrothermal analysis in engineering using control volume finite element method

    CERN Document Server

    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),

  14. A multiscale mortar multipoint flux mixed finite element method

    KAUST Repository

    Wheeler, Mary Fanett; Xue, Guangri; Yotov, Ivan

    2012-01-01

    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

  15. Development and validation of a weight-bearing finite element model for total knee replacement.

    Science.gov (United States)

    Woiczinski, M; Steinbrück, A; Weber, P; Müller, P E; Jansson, V; Schröder, Ch

    2016-01-01

    Total knee arthroplasty (TKA) is a successful procedure for osteoarthritis. However, some patients (19%) do have pain after surgery. A finite element model was developed based on boundary conditions of a knee rig. A 3D-model of an anatomical full leg was generated from magnetic resonance image data and a total knee prosthesis was implanted without patella resurfacing. In the finite element model, a restarting procedure was programmed in order to hold the ground reaction force constant with an adapted quadriceps muscle force during a squat from 20° to 105° of flexion. Knee rig experimental data were used to validate the numerical model in the patellofemoral and femorotibial joint. Furthermore, sensitivity analyses of Young's modulus of the patella cartilage, posterior cruciate ligament (PCL) stiffness, and patella tendon origin were performed. Pearson's correlations for retropatellar contact area, pressure, patella flexion, and femorotibial ap-movement were near to 1. Lowest root mean square error for retropatellar pressure, patella flexion, and femorotibial ap-movement were found for the baseline model setup with Young's modulus of 5 MPa for patella cartilage, a downscaled PCL stiffness of 25% compared to the literature given value and an anatomical origin of the patella tendon. The results of the conducted finite element model are comparable with the experimental results. Therefore, the finite element model developed in this study can be used for further clinical investigations and will help to better understand the clinical aspects after TKA with an unresurfaced patella.

  16. Development and applications of two finite element groundwater flow and contaminant transport models: FEWA and FEMA

    International Nuclear Information System (INIS)

    Yeh, G.T.; Wong, K.V.; Craig, P.M.; Davis, E.C.

    1985-01-01

    This paper presents the construction, verification, and application of two groundwater flow and contaminant transport models: A Finite Element Model of Water Flow through Aquifers (FEWA) and A Finite Element Model of Material Transport through Aquifers (FEMA). The construction is based on the finite element approximation of partial differential equations of groundwater flow (FEWA) and of solute movement (FEMA). The particular features of FEWA and FEMA are their versatility and flexibility for dealing with nearly all vertically integrated two-dimensional problems. The models were verified against both analytical solutions and widely used US Geological Survey finite difference approximations. They were then applied for calibration and validation, using data obtained in experiments at the Engineering Test Facility at Oak Ridge National Laboratory. Results indicated that the models are valid for this specific site. To demonstrate the versatility anf flexibility of the models, they were applied to two hypothetical, but realistic, complex problems and three field sites across the United States. In these applications the models yielded good agreement with the field data for all three sites. Finally, the predictive capabilities of the models were demonstrated using data obtained at the Hialeah Preston site in Florida. This case illustrates the capability of FEWA and FEMA as predictive tools and their usefulness in the management of groundwater flow and contaminant transport. 25 refs

  17. Investigation of High-Speed Cryogenic Machining Based on Finite Element Approach

    Directory of Open Access Journals (Sweden)

    Pooyan Vahidi Pashaki

    Full Text Available Abstract The simulation of cryogenic machining process because of using a three-dimensional model and high process duration time in the finite element method, have been studied rarely. In this study, to overcome this limitation, a 2.5D finite element model using the commercial finite element software ABAQUS has been developed for the cryogenic machining process and by considering more realistic assumptions, the chip formation procedure investigated. In the proposed method, the liquid nitrogen has been used as a coolant. At the modeling of friction during the interaction of tools - chip, the Coulomb law has been used. In order to simulate the behavior of plasticity and failure criterion, Johnson-Cook model was used, and unlike previous investigations, thermal and mechanical properties of materials as a function of temperature were applied to the software. After examining accuracy of the model with present experimental data, the effect of parameters such as rake angle and the cutting speed as well as dry machining of aluminum alloy by the use of coupled dynamic temperature solution has been studied. Results indicated that at the cutting velocity of 10 m/s, cryogenic cooling has caused into decreasing 60 percent of tools temperature in comparison with the dry cooling. Furthermore, a chip which has been made by cryogenic machining were connected and without fracture in contrast to dry machining.

  18. Global-Local Finite Element Analysis of Bonded Single-Lap Joints

    Science.gov (United States)

    Kilic, Bahattin; Madenci, Erdogan; Ambur, Damodar R.

    2004-01-01

    Adhesively bonded lap joints involve dissimilar material junctions and sharp changes in geometry, possibly leading to premature failure. Although the finite element method is well suited to model the bonded lap joints, traditional finite elements are incapable of correctly resolving the stress state at junctions of dissimilar materials because of the unbounded nature of the stresses. In order to facilitate the use of bonded lap joints in future structures, this study presents a finite element technique utilizing a global (special) element coupled with traditional elements. The global element includes the singular behavior at the junction of dissimilar materials with or without traction-free surfaces.

  19. Spectral decomposition in advection-diffusion analysis by finite element methods

    International Nuclear Information System (INIS)

    Nickell, R.E.; Gartling, D.K.; Strang, G.

    1978-01-01

    In a recent study of the convergence properties of finite element methods in nonlinear fluid mechanics, an indirect approach was taken. A two-dimensional example with a known exact solution was chosen as the vehicle for the study, and various mesh refinements were tested in an attempt to extract information on the effect of the local Reynolds number. However, more direct approaches are usually preferred. In this study one such direct approach is followed, based upon the spectral decomposition of the solution operator. Spectral decomposition is widely employed as a solution technique for linear structural dynamics problems and can be applied readily to linear, transient heat transfer analysis; in this case, the extension to nonlinear problems is of interest. It was shown previously that spectral techniques were applicable to stiff systems of rate equations, while recent studies of geometrically and materially nonlinear structural dynamics have demonstrated the increased information content of the numerical results. The use of spectral decomposition in nonlinear problems of heat and mass transfer would be expected to yield equally increased flow of information to the analyst, and this information could include a quantitative comparison of various solution strategies, meshes, and element hierarchies

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

    Science.gov (United States)

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

    2018-05-01

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

  1. Finite element simulation of laser transmission welding of dissimilar ...

    African Journals Online (AJOL)

    user

    materials between polyvinylidene fluoride and titanium ... finite element (FE) thermal model is developed to simulate the laser ... Keywords: Laser transmission welding, Temperature field, Weld dimension, Finite element analysis, Thermal modeling. 1. .... 4) The heating phenomena due to the phase changes are neglected.

  2. Finite element analysis of tibial fractures

    DEFF Research Database (Denmark)

    Wong, Christian Nai En; Mikkelsen, Mikkel Peter W; Hansen, Leif Berner

    2010-01-01

    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...

  3. Generalized multiscale finite element method. Symmetric interior penalty coupling

    KAUST Repository

    Efendiev, Yalchin R.; Galvis, Juan; Lazarov, Raytcho D.; Moon, M.; Sarkis, Marcus V.

    2013-01-01

    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.

  4. Generalized multiscale finite element method. Symmetric interior penalty coupling

    KAUST Repository

    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.

  5. An evaluation of a translator for finite element data to resistor/capacitor data for the heat diffusion equation

    International Nuclear Information System (INIS)

    Manteufel, R.D.; Klein, D.E.; Yoshimura, H.R.

    1988-01-01

    This paper evaluates a translator for finite element data to resistor/capacitor data (FEM/RC) for the numerical solution of heat diffusion problems. The translator involves the derivation of thermal resistors and capacitors, implicit in the heat balance formulation of the finite difference method. It uses a finite element mesh, which consists of nodes and elements and is implicit in the Galerkin finite element method (GFEM). This hybrid translation method, FEM/RC, has been incorporated in Q/TRAN, a new thermal analysis computer code. This evaluation compares Q/TRAN, HEATING-6, and a research code employing GFEM on a purely mathematical, highly nonlinear steady-state conduction benchmark problem. The evaluation concludes that the FEM/RC technique has numerical characteristics that are consistent with comparable schemes for the benchmark problem. FEM/RC also accurately translates skewed meshes. Because FEM/RC generates resistors and capacitors, it appears to offer a more efficient method than the classical GFEM

  6. Finite element reduction strategy for composite sandwich plates with viscoelastic layers

    Directory of Open Access Journals (Sweden)

    Adriana Amaro Diacenco

    2013-04-01

    Full Text Available Composite materials have been regarded as a convenient strategy in various types of engineering systems such as aeronautical and space structures, as well as architecture and light industry products due to their advantages over the traditional engineering materials, such as their high strength/stiffness relation characteristics and their anti-corrosion properties. This paper is devoted to the finite element modeling of composite laminated structures incorporating viscoelastic materials to the problem of vibration attenuation. However, the typically high dimension of large finite element models of composite structures incorporating viscoelastic materials makes the numerical processes sometimes unfeasible. Within this context, emphasis is placed on a general condensation strategy specially adapted for the case of viscoelastically damped structures, in which a constant (frequency- and temperature-independent reduction basis to be enriched by static residues associated to the applied loads and the viscoelastic forces is used. After presenting the theoretical foundations, the numerical applications of composite plates treated by viscoelastic materials are addressed, and the main features of the methodology are discussed.

  7. Finite element reduction strategy for composite sandwich plates with viscoelastic layers

    Directory of Open Access Journals (Sweden)

    Adriana Amaro Diacenco

    2012-01-01

    Full Text Available Composite materials have been regarded as a convenient strategy in various types of engineering systems such as aeronautical and space structures, as well as architecture and light industry products due to their advantages over the traditional engineering materials, such as their high strength/stiffness relation characteristics and their anti-corrosion properties. This paper is devoted to the finite element modeling of composite laminated structures incorporating viscoelastic materials to the problem of vibration attenuation. However, the typically high dimension of large finite element models of composite structures incorporating viscoelastic materials makes the numerical processes sometimes unfeasible. Within this context, emphasis is placed on a general condensation strategy specially adapted for the case of viscoelastically damped structures, in which a constant (frequency- and temperature-independent reduction basis to be enriched by static residues associated to the applied loads and the viscoelastic forces is used. After presenting the theoretical foundations, the numerical applications of composite plates treated by viscoelastic materials are addressed, and the main features of the methodology are discussed.

  8. Analysing the mechanical performance and growth adaptation of Norway spruce using a non-linear finite-element model and experimental data.

    Science.gov (United States)

    Lundström, T; Jonas, T; Volkwein, A

    2008-01-01

    Thirteen Norway spruce [Picea abies (L.) Karst.] trees of different size, age, and social status, and grown under varying conditions, were investigated to see how they react to complex natural static loading under summer and winter conditions, and how they have adapted their growth to such combinations of load and tree state. For this purpose a non-linear finite-element model and an extensive experimental data set were used, as well as a new formulation describing the degree to which the exploitation of the bending stress capacity is uniform. The three main findings were: material and geometric non-linearities play important roles when analysing tree deflections and critical loads; the strengths of the stem and the anchorage mutually adapt to the local wind acting on the tree crown in the forest canopy; and the radial stem growth follows a mechanically high-performance path because it adapts to prevailing as well as acute seasonal combinations of the tree state (e.g. frozen or unfrozen stem and anchorage) and load (e.g. wind and vertical and lateral snow pressure). Young trees appeared to adapt to such combinations in a more differentiated way than older trees. In conclusion, the mechanical performance of the Norway spruce studied was mostly very high, indicating that their overall growth had been clearly influenced by the external site- and tree-specific mechanical stress.

  9. Accuracy of finite-element models for the stress analysis of multiple-holed moderator blocks

    International Nuclear Information System (INIS)

    Smith, P.D.; Sullivan, R.M.; Lewis, A.C.; Yu, H.J.

    1981-01-01

    Two steps have been taken to quantify and improve the accuracy in the analysis. First, the limitations of various approximation techniques have been studied with the aid of smaller benchmark problems containing fewer holes. Second, a new family of computer programs has been developed for handling such large problems. This paper describes the accuracy studies and the benchmark problems. A review is given of some proposed modeling techniques including local mesh refinement, homogenization, a special-purpose finite element, and substructuring. Some limitations of these approaches are discussed. The new finite element programs and the features that contribute to their efficiency are discussed. These include a standard architecture for out-of-core data processing and an equation solver that operates on a peripheral array processor. The central conclusions of the paper are: (1) modeling approximation methods such as local mesh refinement and homogenization tend to be unreliable, and they should be justified by a fine mesh benchmark analysis; and (2) finite element codes are now available that can achieve accurate solutions at a reasonable cost, and there is no longer a need to employ modeling approximations in the two-dimensional analysis of HTGR fuel elements. 10 figures

  10. A combined finite element-boundary integral formulation for solution of two-dimensional scattering problems via CGFFT. [Conjugate Gradient Fast Fourier Transformation

    Science.gov (United States)

    Collins, Jeffery D.; Volakis, John L.; Jin, Jian-Ming

    1990-01-01

    A new technique is presented for computing the scattering by 2-D structures of arbitrary composition. The proposed solution approach combines the usual finite element method with the boundary-integral equation to formulate a discrete system. This is subsequently solved via the conjugate gradient (CG) algorithm. A particular characteristic of the method is the use of rectangular boundaries to enclose the scatterer. Several of the resulting boundary integrals are therefore convolutions and may be evaluated via the fast Fourier transform (FFT) in the implementation of the CG algorithm. The solution approach offers the principal advantage of having O(N) memory demand and employs a 1-D FFT versus a 2-D FFT as required with a traditional implementation of the CGFFT algorithm. The speed of the proposed solution method is compared with that of the traditional CGFFT algorithm, and results for rectangular bodies are given and shown to be in excellent agreement with the moment method.

  11. Discrete-ordinates finite-element method for atmospheric radiative transfer and remote sensing

    International Nuclear Information System (INIS)

    Gerstl, S.A.W.; Zardecki, A.

    1985-01-01

    Advantages and disadvantages of modern discrete-ordinates finite-element methods for the solution of radiative transfer problems in meteorology, climatology, and remote sensing applications are evaluated. After the common basis of the formulation of radiative transfer problems in the fields of neutron transport and atmospheric optics is established, the essential features of the discrete-ordinates finite-element method are described including the limitations of the method and their remedies. Numerical results are presented for 1-D and 2-D atmospheric radiative transfer problems where integral as well as angular dependent quantities are compared with published results from other calculations and with measured data. These comparisons provide a verification of the discrete-ordinates results for a wide spectrum of cases with varying degrees of absorption, scattering, and anisotropic phase functions. Accuracy and computational speed are also discussed. Since practically all discrete-ordinates codes offer a builtin adjoint capability, the general concept of the adjoint method is described and illustrated by sample problems. Our general conclusion is that the strengths of the discrete-ordinates finite-element method outweight its weaknesses. We demonstrate that existing general-purpose discrete-ordinates codes can provide a powerful tool to analyze radiative transfer problems through the atmosphere, especially when 2-D geometries must be considered

  12. Coarse mesh finite element method for boiling water reactor physics analysis

    International Nuclear Information System (INIS)

    Ellison, P.G.

    1983-01-01

    A coarse mesh method is formulated for the solution of Boiling Water Reactor physics problems using two group diffusion theory. No fuel assembly cross-section homogenization is required; water gaps, control blades and fuel pins of varying enrichments are treated explicitly. The method combines constrained finite element discretization with infinite lattice super cell trial functions to obtain coarse mesh solutions for which the only approximations are along the boundaries between fuel assemblies. The method is applied to bench mark Boiling Water Reactor problems to obtain both the eigenvalue and detailed flux distributions. The solutions to these problems indicate the method is useful in predicting detailed power distributions and eigenvalues for Boiling Water Reactor physics problems

  13. Finite Element Analysis of Circular Plate using SolidWorks

    International Nuclear Information System (INIS)

    Kang, Yeo Jin; Jhung, Myung Jo

    2011-01-01

    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

  14. A multiscale mortar multipoint flux mixed finite element method

    KAUST Repository

    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.

  15. Solving the Einstein constraint equations on multi-block triangulations using finite element methods

    Energy Technology Data Exchange (ETDEWEB)

    Korobkin, Oleg; Pazos, Enrique [Department of Physics and Astronomy, Louisiana State University, Baton Rouge, LA 70803 (United States); Aksoylu, Burak [Center for Computation and Technology, Louisiana State University, Baton Rouge, LA 70803 (United States); Holst, Michael [Department of Mathematics, University of California at San Diego 9500 Gilman Drive La Jolla, CA 92093-0112 (United States); Tiglio, Manuel [Department of Physics, University of Maryland, College Park, MD 20742 (United States)

    2009-07-21

    In order to generate initial data for nonlinear relativistic simulations, one needs to solve the Einstein constraints, which can be cast into a coupled set of nonlinear elliptic equations. Here we present an approach for solving these equations on three-dimensional multi-block domains using finite element methods. We illustrate our approach on a simple example of Brill wave initial data, with the constraints reducing to a single linear elliptic equation for the conformal factor psi. We use quadratic Lagrange elements on semi-structured simplicial meshes, obtained by triangulation of multi-block grids. In the case of uniform refinement the scheme is superconvergent at most mesh vertices, due to local symmetry of the finite element basis with respect to local spatial inversions. We show that in the superconvergent case subsequent unstructured mesh refinements do not improve the quality of our initial data. As proof of concept that this approach is feasible for generating multi-block initial data in three dimensions, after constructing the initial data we evolve them in time using a high-order finite-differencing multi-block approach and extract the gravitational waves from the numerical solution.

  16. Solving the Einstein constraint equations on multi-block triangulations using finite element methods

    International Nuclear Information System (INIS)

    Korobkin, Oleg; Pazos, Enrique; Aksoylu, Burak; Holst, Michael; Tiglio, Manuel

    2009-01-01

    In order to generate initial data for nonlinear relativistic simulations, one needs to solve the Einstein constraints, which can be cast into a coupled set of nonlinear elliptic equations. Here we present an approach for solving these equations on three-dimensional multi-block domains using finite element methods. We illustrate our approach on a simple example of Brill wave initial data, with the constraints reducing to a single linear elliptic equation for the conformal factor ψ. We use quadratic Lagrange elements on semi-structured simplicial meshes, obtained by triangulation of multi-block grids. In the case of uniform refinement the scheme is superconvergent at most mesh vertices, due to local symmetry of the finite element basis with respect to local spatial inversions. We show that in the superconvergent case subsequent unstructured mesh refinements do not improve the quality of our initial data. As proof of concept that this approach is feasible for generating multi-block initial data in three dimensions, after constructing the initial data we evolve them in time using a high-order finite-differencing multi-block approach and extract the gravitational waves from the numerical solution.

  17. Finite element computation of multi-physical micropolar transport phenomena from an inclined moving plate in porous media

    Science.gov (United States)

    Shamshuddin, MD.; Anwar Bég, O.; Sunder Ram, M.; Kadir, A.

    2018-02-01

    Non-Newtonian flows arise in numerous industrial transport processes including materials fabrication systems. Micropolar theory offers an excellent mechanism for exploring the fluid dynamics of new non-Newtonian materials which possess internal microstructure. Magnetic fields may also be used for controlling electrically-conducting polymeric flows. To explore numerical simulation of transport in rheological materials processing, in the current paper, a finite element computational solution is presented for magnetohydrodynamic, incompressible, dissipative, radiative and chemically-reacting micropolar fluid flow, heat and mass transfer adjacent to an inclined porous plate embedded in a saturated homogenous porous medium. Heat generation/absorption effects are included. Rosseland's diffusion approximation is used to describe the radiative heat flux in the energy equation. A Darcy model is employed to simulate drag effects in the porous medium. The governing transport equations are rendered into non-dimensional form under the assumption of low Reynolds number and also low magnetic Reynolds number. Using a Galerkin formulation with a weighted residual scheme, finite element solutions are presented to the boundary value problem. The influence of plate inclination, Eringen coupling number, radiation-conduction number, heat absorption/generation parameter, chemical reaction parameter, plate moving velocity parameter, magnetic parameter, thermal Grashof number, species (solutal) Grashof number, permeability parameter, Eckert number on linear velocity, micro-rotation, temperature and concentration profiles. Furthermore, the influence of selected thermo-physical parameters on friction factor, surface heat transfer and mass transfer rate is also tabulated. The finite element solutions are verified with solutions from several limiting cases in the literature. Interesting features in the flow are identified and interpreted.

  18. SPIRIT, Plot of Geometry and Results of 2-D Finite Elements Calculation

    International Nuclear Information System (INIS)

    Lambert, P.

    1977-01-01

    1 - Nature of the physical problem solved: SPIRIT plots the geometry and the results from a 2-D finite elements calculation. 2 - Method of solution: SPIRIT uses the Benson-Lehner graph plotter. The programme will draw each separate element of the mesh according to the description supplied and a complete picture of the mesh is therefore built up. The program can also construct an isothermal distribution using straight lines. Each line is constructed considering each element in isolation. 3 - Restrictions on the complexity of the problem: The program deals only with bodies entirely contained in the first quadrant and the x-coordinates should be less than 20.0

  19. Essential Boundary Conditions with Straight C1 Finite Elements in Curved Domains

    International Nuclear Information System (INIS)

    Ferraro, N.M.; Jardin, S.C.; Luo, X.

    2010-01-01

    The implementation of essential boundary conditions in C1 finite element analysis requires proper treatment of both the boundary conditions on second-order differentials of the solution and the curvature of the domain boundary. A method for the imposition of essential boundary conditions using straight elements (where the elements are not deformed to approximate a curved domain) is described. It is shown that pre-multiplication of the matrix equation by the local rotation matrix at each boundary node is not the optimal transformation. The uniquely optimal transformation is found, which does not take the form of a similarity transformation due to the non-orthogonality of the transformation to curved coordinates.

  20. A 2D finite element implementation of the Fleck–Willis strain-gradient flow theory

    DEFF Research Database (Denmark)

    Nielsen, Kim Lau; Niordson, Christian Frithiof

    2013-01-01

    The lay-out of a numerical solution procedure for the strain gradient flow (rate-independent) theory by Fleck and Willis [A mathematical basis for strain-gradient theory – Part II: Tensorial plastic multiplier, 57:1045–1057; 2009, JMPS] has been an open issue, and its finite element implementation...

  1. Supercomputer implementation of finite element algorithms for high speed compressible flows. Progress report, period ending 30 June 1986

    International Nuclear Information System (INIS)

    Thornton, E.A.; Ramakrishnan, R.

    1986-06-01

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

  2. finite element model for predicting residual stresses in shielded

    African Journals Online (AJOL)

    eobe

    This paper investigates the prediction of residual stresses developed ... steel plates through Finite Element Model simulation and experiments. ... The experimental values as measured by the X-Ray diffractometer were of ... Based on this, it can be concluded that Finite Element .... Comparison of Residual Stresses from X.

  3. Finite-Element Modeling of Timber Joints with Punched Metal Plate Fasteners

    DEFF Research Database (Denmark)

    Ellegaard, Peter

    2006-01-01

    The focus of this paper is to describe the idea and the theory behind a finite-element model developed for analysis of timber trusses with punched metal plate fasteners (nail plates). The finite-element model includes the semirigid and nonlinear behavior of the joints (nonlinear nail and plate...... elements) and contact between timber beams, if any (bilinear contact elements). The timber beams have linear-elastic properties. The section forces needed for design of the joints are given directly by the finite-element model, since special elements are used to model the nail groups and the nail plate...... the behavior of the joints very well at lower load levels. At higher load levels the stiffness is overestimated due to development of cracks in the timber and the linear-elastic timber properties in the finite-element model....

  4. Sampling of finite elements for sparse recovery in large scale 3D electrical impedance tomography

    International Nuclear Information System (INIS)

    Javaherian, Ashkan; Moeller, Knut; Soleimani, Manuchehr

    2015-01-01

    This study proposes a method to improve performance of sparse recovery inverse solvers in 3D electrical impedance tomography (3D EIT), especially when the volume under study contains small-sized inclusions, e.g. 3D imaging of breast tumours. Initially, a quadratic regularized inverse solver is applied in a fast manner with a stopping threshold much greater than the optimum. Based on assuming a fixed level of sparsity for the conductivity field, finite elements are then sampled via applying a compressive sensing (CS) algorithm to the rough blurred estimation previously made by the quadratic solver. Finally, a sparse inverse solver is applied solely to the sampled finite elements, with the solution to the CS as its initial guess. The results show the great potential of the proposed CS-based sparse recovery in improving accuracy of sparse solution to the large-size 3D EIT. (paper)

  5. Analytical and finite element modeling of grounding systems

    Energy Technology Data Exchange (ETDEWEB)

    Luz, Mauricio Valencia Ferreira da [University of Santa Catarina (UFSC), Florianopolis, SC (Brazil)], E-mail: mauricio@grucad.ufsc.br; Dular, Patrick [University of Liege (Belgium). Institut Montefiore], E-mail: Patrick.Dular@ulg.ac.be

    2007-07-01

    Grounding is the art of making an electrical connection to the earth. This paper deals with the analytical and finite element modeling of grounding systems. An electrokinetic formulation using a scalar potential can benefit from floating potentials to define global quantities such as electric voltages and currents. The application concerns a single vertical grounding with one, two and three-layer soil, where the superior extremity stays in the surface of the soil. This problem has been modeled using a 2D axi-symmetric electrokinetic formulation. The grounding resistance obtained by finite element method is compared with the analytical one for one-layer soil. With the results of this paper it is possible to show that finite element method is a powerful tool in the analysis of the grounding systems in low frequencies. (author)

  6. Computable error estimates for Monte Carlo finite element approximation of elliptic PDE with lognormal diffusion coefficients

    KAUST Repository

    Hall, Eric

    2016-01-09

    The Monte Carlo (and Multi-level Monte Carlo) finite element method can be used to approximate observables of solutions to diffusion equations with lognormal distributed diffusion coefficients, e.g. modeling ground water flow. Typical models use lognormal diffusion coefficients with H´ older regularity of order up to 1/2 a.s. This low regularity implies that the high frequency finite element approximation error (i.e. the error from frequencies larger than the mesh frequency) is not negligible and can be larger than the computable low frequency error. We address how the total error can be estimated by the computable error.

  7. Eigensolution of finite element problems in a completely connected parallel architecture

    Science.gov (United States)

    Akl, Fred A.; Morel, Michael R.

    1989-01-01

    A parallel algorithm for the solution of the generalized eigenproblem in linear elastic finite element analysis, (K)(phi)=(M)(phi)(omega), where (K) and (M) are of order N, and (omega) is of order q is presented. The parallel algorithm is based on a completely connected parallel architecture in which each processor is allowed to communicate with all other processors. The algorithm has been successfully implemented on a tightly coupled multiple-instruction-multiple-data (MIMD) parallel processing computer, Cray X-MP. A finite element model is divided into m domains each of which is assumed to process n elements. Each domain is then assigned to a processor, or to a logical processor (task) if the number of domains exceeds the number of physical processors. The macro-tasking library routines are used in mapping each domain to a user task. Computational speed-up and efficiency are used to determine the effectiveness of the algorithm. The effect of the number of domains, the number of degrees-of-freedom located along the global fronts and the dimension of the subspace on the performance of the algorithm are investigated. For a 64-element rectangular plate, speed-ups of 1.86, 3.13, 3.18 and 3.61 are achieved on two, four, six and eight processors, respectively.

  8. New Multigrid Method Including Elimination Algolithm Based on High-Order Vector Finite Elements in Three Dimensional Magnetostatic Field Analysis

    Science.gov (United States)

    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.

  9. Robust mixed finite element methods to deal with incompressibility in finite strain in an industrial framework

    International Nuclear Information System (INIS)

    Al-Akhrass, Dina

    2014-01-01

    Simulations in solid mechanics exhibit several difficulties, as dealing with incompressibility, with nonlinearities due to finite strains, contact laws, or constitutive laws. The basic motivation of our work is to propose efficient finite element methods capable of dealing with incompressibility in finite strain context, and using elements of low order. During the three last decades, many approaches have been proposed in the literature to overcome the incompressibility problem. Among them, mixed formulations offer an interesting theoretical framework. In this work, a three-field mixed formulation (displacement, pressure, volumetric strain) is investigated. In some cases, this formulation can be condensed in a two-field (displacement - pressure) mixed formulation. However, it is well-known that the discrete problem given by the Galerkin finite element technique, does not inherit the 'inf-sup' stability condition from the continuous problem. Hence, the interpolation orders in displacement and pressure have to be chosen in a way to satisfy the Brezzi-Babuska stability conditions when using Galerkin approaches. Interpolation orders must be chosen so as to satisfy this condition. Two possibilities are considered: to use stable finite element satisfying this requirement, or to use finite element that does not satisfy this condition, and to add terms stabilizing the FE Galerkin formulation. The latter approach allows the use of equal order interpolation. In this work, stable finite element P2/P1 and P2/P1/P1 are used as reference, and compared to P1/P1 and P1/P1/P1 formulations stabilized with a bubble function or with a VMS method (Variational Multi-Scale) based on a sub-grid-space orthogonal to the FE space. A finite strain model based on logarithmic strain is selected. This approach is extended to three and two field mixed formulations with stable or stabilized elements. These approaches are validated on academic cases and used on industrial cases. (author)

  10. Non-Linear Three Dimensional Finite Elements for Composite Concrete Structures

    Directory of Open Access Journals (Sweden)

    O. Kohnehpooshi

    Full Text Available Abstract The current investigation focused on the development of effective and suitable modelling of reinforced concrete component with and without strengthening. The modelling includes physical and constitutive models. New interface elements have been developed, while modified constitutive law have been applied and new computational algorithm is utilised. The new elements are the Truss-link element to model the interaction between concrete and reinforcement bars, the interface element between two plate bending elements and the interface element to represent the interfacial behaviour between FRP, steel plates and concrete. Nonlinear finite-element (FE codes were developed with pre-processing. The programme was written using FORTRAN language. The accuracy and efficiency of the finite element programme were achieved by analyzing several examples from the literature. The application of the 3D FE code was further enhanced by carrying out the numerical analysis of the three dimensional finite element analysis of FRP strengthened RC beams, as well as the 3D non-linear finite element analysis of girder bridge. Acceptable distributions of slip, deflection, stresses in the concrete and FRP plate have also been found. These results show that the new elements are effective and appropriate to be used for structural component modelling.

  11. ZONE: a finite element mesh generator

    International Nuclear Information System (INIS)

    Burger, M.J.

    1976-05-01

    The ZONE computer program is a finite-element mesh generator which produces the nodes and element description of any two-dimensional geometry. The geometry is subdivided into a mesh of quadrilateral and triangular zones arranged sequentially in an ordered march through the geometry. The order of march can be chosen so that the minimum bandwidth is obtained. The node points are defined in terms of the x and y coordinates in a global rectangular coordinate system. The zones generated are quadrilaterals or triangles defined by four node points in a counterclockwise sequence. Node points defining the outside boundary are generated to describe pressure boundary conditions. The mesh that is generated can be used as input to any two-dimensional as well as any axisymmetrical structure program. The output from ZONE is essentially the input file to NAOS, HONDO, and other axisymmetric finite element programs. 14 figures

  12. Discontinuous finite elements applied to solution of problems about heat transfer in heterogeneous media

    International Nuclear Information System (INIS)

    Ferreira, Monica Barcellos Jansen; Carmo, Eduardo Gomes Dutra do

    2000-01-01

    Heat transfer problems in heterogenous media with large variation of thermal conductivity are notorious for the difficulties in obtaining good numerical results. In this work it is proposed an application of a new mixed discontinuous finite element formulation to this class of problems, which produces good results without the need of high mesh refinement. Stability and consistency aspects are considered and numerical results are presented to show the efficacy of the method. (author)

  13. Finite element implementation and numerical issues of strain gradient plasticity with application to metal matrix composites

    DEFF Research Database (Denmark)

    Frederiksson, Per; Gudmundson, Peter; Mikkelsen, Lars Pilgaard

    2009-01-01

    A framework of finite element equations for strain gradient plasticity is presented. The theoretical framework requires plastic strain degrees of freedom in addition to displacements and a plane strain version is implemented into a commercial finite element code. A couple of different elements...... of quadrilateral type are examined and a few numerical issues are addressed related to these elements as well as to strain gradient plasticity theories in general. Numerical results are presented for an idealized cell model of a metal matrix composite under shear loading. It is shown that strengthening due...... to fiber size is captured but strengthening due to fiber shape is not. A few modelling aspects of this problem are discussed as well. An analytic solution is also presented which illustrates similarities to other theories....

  14. Modeling hemodynamics in intracranial aneurysms: Comparing accuracy of CFD solvers based on finite element and finite volume schemes.

    Science.gov (United States)

    Botti, Lorenzo; Paliwal, Nikhil; Conti, Pierangelo; Antiga, Luca; Meng, Hui

    2018-06-01

    Image-based computational fluid dynamics (CFD) has shown potential to aid in the clinical management of intracranial aneurysms (IAs) but its adoption in the clinical practice has been missing, partially due to lack of accuracy assessment and sensitivity analysis. To numerically solve the flow-governing equations CFD solvers generally rely on two spatial discretization schemes: Finite Volume (FV) and Finite Element (FE). Since increasingly accurate numerical solutions are obtained by different means, accuracies and computational costs of FV and FE formulations cannot be compared directly. To this end, in this study we benchmark two representative CFD solvers in simulating flow in a patient-specific IA model: (1) ANSYS Fluent, a commercial FV-based solver and (2) VMTKLab multidGetto, a discontinuous Galerkin (dG) FE-based solver. The FV solver's accuracy is improved by increasing the spatial mesh resolution (134k, 1.1m, 8.6m and 68.5m tetrahedral element meshes). The dGFE solver accuracy is increased by increasing the degree of polynomials (first, second, third and fourth degree) on the base 134k tetrahedral element mesh. Solutions from best FV and dGFE approximations are used as baseline for error quantification. On average, velocity errors for second-best approximations are approximately 1cm/s for a [0,125]cm/s velocity magnitude field. Results show that high-order dGFE provide better accuracy per degree of freedom but worse accuracy per Jacobian non-zero entry as compared to FV. Cross-comparison of velocity errors demonstrates asymptotic convergence of both solvers to the same numerical solution. Nevertheless, the discrepancy between under-resolved velocity fields suggests that mesh independence is reached following different paths. This article is protected by copyright. All rights reserved.

  15. SAFE-PLANE, Stress Analysis of Planar Structure by Finite Elements Method

    International Nuclear Information System (INIS)

    Cornell, D.C.; Reich, Morris

    1967-01-01

    1 - Description of problem or function: SAFE-PLANE is applied to two- dimensional structures of arbitrary geometry under in-plane loads. Either plane stress or plane strain conditions may be imposed. Mechanical and thermal loads are permitted. 2 - Method of solution: The finite-element method is used to construct a mathematical model by assembling discrete elements. The total potential energy of the structure is determined and subsequently minimized by iteration on components of the displacement field until static equilibrium of the structure is attained. Strains and stresses are computed from the resulting displacements. 3 - Restrictions on the complexity of the problem: Multi-material structures with varying rigidities converge very slowly. Not valid for incompressible materials. Maximum number of nodal points = 675. Maximum number of elements = 1350

  16. Efficient solution of the non-linear Reynolds equation for compressible fluid using the finite element method

    DEFF Research Database (Denmark)

    Larsen, Jon Steffen; Santos, Ilmar

    2015-01-01

    An efficient finite element scheme for solving the non-linear Reynolds equation for compressible fluid coupled to compliant structures is presented. The method is general and fast and can be used in the analysis of airfoil bearings with simplified or complex foil structure models. To illustrate...

  17. SAFE-AXISYM, Stress Analysis of Axisymmetric Composite Structure by Finite Elements Method

    International Nuclear Information System (INIS)

    Cornell, D.C.

    1967-01-01

    1 - Nature of physical problem solved: SAFE-AXISYM is a program for the analysis of multi-material axisymmetric composite structures. It is designed for the analysis of heterogeneous structures such as reinforced and/or prestressed concrete vessels. The structure is assumed to be linearly elastic, and only bodies of revolution subjected to axisymmetric loading can be treated. 2 - Method of solution: SAFE-AXISYM uses a finite element method with a modified Gauss-Seidel iteration scheme. A reference grid subdivides the structure into ring-like small, finite elements, the vertices of which are called nodes. The grid may be generated by hand, by the computer or by a combination of the two methods. Each node has two degrees of freedom, translation in the and in the axial direction. Both zero and non-zero fixed displacement constraints may be assumed, and the loading condition may be mechanical and/or thermal. 3 - Restrictions on the complexity of the problem: Multi-material structures with varying rigidities converge very slowly. Not valid for incompressible materials. Maximum number of nodes = 475. Maximum number of elements = 1100

  18. SEACAS Theory Manuals: Part III. Finite Element Analysis in Nonlinear Solid Mechanics

    Energy Technology Data Exchange (ETDEWEB)

    Laursen, T.A.; Attaway, S.W.; Zadoks, R.I.

    1999-03-01

    This report outlines the application of finite element methodology to large deformation solid mechanics problems, detailing also some of the key technological issues that effective finite element formulations must address. The presentation is organized into three major portions: first, a discussion of finite element discretization from the global point of view, emphasizing the relationship between a virtual work principle and the associated fully discrete system, second, a discussion of finite element technology, emphasizing the important theoretical and practical features associated with an individual finite element; and third, detailed description of specific elements that enjoy widespread use, providing some examples of the theoretical ideas already described. Descriptions of problem formulation in nonlinear solid mechanics, nonlinear continuum mechanics, and constitutive modeling are given in three companion reports.

  19. Mixed spectral finite elements and perfectly matched layers for elastic waves in time domain; Elements finis mixtes spectraux et couches absorbantes parfaitement adaptees pour la propagation d'ondes elastiques en regime transitoire

    Energy Technology Data Exchange (ETDEWEB)

    Fauqueux, S.

    2003-02-01

    We consider the propagation of elastic waves in unbounded domains. A new formulation of the linear elasticity system as an H (div) - L{sup 2} system enables us to use the 'mixed spectral finite element method', This new method is based on the definition of new spaces of approximation and the use of mass-lumping. It leads to an explicit scheme with reduced storage and provides the same solution as the spectral finite element method. Then, we model unbounded domains by using Perfectly Matched Layers. Instabilities in the PML in the case of particular 2D elastic media are pointed out and investigated. The numerical method is validated and tested in the case of acoustic and elastic realistic models. A plane wave analysis gives results about numerical dispersion and shows that meshes adapted to the physical and geometrical properties of the media are more accurate than the others. Then, an extension of the method to fluid-solid coupling is introduced for 2D seismic propagation. (author)

  20. An object-oriented class design for the generalized finite element method programming

    Directory of Open Access Journals (Sweden)

    Dorival Piedade Neto

    Full Text Available The Generalized Finite Element Method (GFEM is a numerical method based on the Finite Element Method (FEM, presenting as its main feature the possibility of improving the solution by means of local enrichment functions. In spite of its advantages, the method demands a complex data structure, which can be especially benefited by the Object-Oriented Programming (OOP. Even though the OOP for the traditional FEM has been extensively described in the technical literature, specific design issues related to the GFEM are yet little discussed and not clearly defined. In the present article it is described an Object-Oriented (OO class design for the GFEM, aiming to achieve a computational code that presents a flexible class structure, circumventing the difficulties associated to the method characteristics. The proposed design is evaluated by means of some numerical examples, computed using a code implemented in Python programming language.

  1. FEAST: a two-dimensional non-linear finite element code for calculating stresses

    International Nuclear Information System (INIS)

    Tayal, M.

    1986-06-01

    The computer code FEAST calculates stresses, strains, and displacements. The code is two-dimensional. That is, either plane or axisymmetric calculations can be done. The code models elastic, plastic, creep, and thermal strains and stresses. Cracking can also be simulated. The finite element method is used to solve equations describing the following fundamental laws of mechanics: equilibrium; compatibility; constitutive relations; yield criterion; and flow rule. FEAST combines several unique features that permit large time-steps in even severely non-linear situations. The features include a special formulation for permitting many finite elements to simultaneously cross the boundary from elastic to plastic behaviour; accomodation of large drops in yield-strength due to changes in local temperature and a three-step predictor-corrector method for plastic analyses. These features reduce computing costs. Comparisons against twenty analytical solutions and against experimental measurements show that predictions of FEAST are generally accurate to ± 5%

  2. Numerical solutions of magnetohydrodynamic stability of axisymmetric toroidal plasmas using cubic B-spline finite element method

    International Nuclear Information System (INIS)

    Cheng, C.Z.

    1988-12-01

    A nonvariational ideal MHD stability code (NOVA) has been developed. In a general flux coordinate (/psi/, θ, /zeta/) system with an arbitrary Jacobian, the NOVA code employs Fourier expansions in the generalized poloidal angle θ and generalized toroidal angle /zeta/ directions, and cubic-B spline finite elements in the radial /psi/ direction. Extensive comparisons with these variational ideal MHD codes show that the NOVA code converges faster and gives more accurate results. An extended version of NOVA is developed to integrate non-Hermitian eigenmode equations due to energetic particles. The set of non-Hermitian integro-differential eigenmode equations is numerically solved by the NOVA-K code. We have studied the problems of the stabilization of ideal MHD internal kink modes by hot particle pressure and the excitation of ''fishbone'' internal kink modes by resonating with the energetic particle magnetic drift frequency. Comparisons with analytical solutions show that the values of the critical β/sub h/ from the analytical theory can be an order of magnitude different from those computed by the NOVA-K code. 24 refs., 11 figs., 1 tab

  3. 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...

  4. A Finite Element Solution of Lateral Periodic Poisson–Boltzmann Model for Membrane Channel Proteins

    Science.gov (United States)

    Xu, Jingjie; Lu, Benzhuo

    2018-01-01

    Membrane channel proteins control the diffusion of ions across biological membranes. They are closely related to the processes of various organizational mechanisms, such as: cardiac impulse, muscle contraction and hormone secretion. Introducing a membrane region into implicit solvation models extends the ability of the Poisson–Boltzmann (PB) equation to handle membrane proteins. The use of lateral periodic boundary conditions can properly simulate the discrete distribution of membrane proteins on the membrane plane and avoid boundary effects, which are caused by the finite box size in the traditional PB calculations. In this work, we: (1) develop a first finite element solver (FEPB) to solve the PB equation with a two-dimensional periodicity for membrane channel proteins, with different numerical treatments of the singular charges distributions in the channel protein; (2) add the membrane as a dielectric slab in the PB model, and use an improved mesh construction method to automatically identify the membrane channel/pore region even with a tilt angle relative to the z-axis; and (3) add a non-polar solvation energy term to complete the estimation of the total solvation energy of a membrane protein. A mesh resolution of about 0.25 Å (cubic grid space)/0.36 Å (tetrahedron edge length) is found to be most accurate in linear finite element calculation of the PB solvation energy. Computational studies are performed on a few exemplary molecules. The results indicate that all factors, the membrane thickness, the length of periodic box, membrane dielectric constant, pore region dielectric constant, and ionic strength, have individually considerable influence on the solvation energy of a channel protein. This demonstrates the necessity to treat all of those effects in the PB model for membrane protein simulations. PMID:29495644

  5. Fracture Capabilities in Grizzly with the extended Finite Element Method (X-FEM)

    Energy Technology Data Exchange (ETDEWEB)

    Dolbow, John [Idaho National Lab. (INL), Idaho Falls, ID (United States); Zhang, Ziyu [Idaho National Lab. (INL), Idaho Falls, ID (United States); Spencer, Benjamin [Idaho National Lab. (INL), Idaho Falls, ID (United States); Jiang, Wen [Idaho National Lab. (INL), Idaho Falls, ID (United States)

    2015-09-01

    Efforts are underway to develop fracture mechanics capabilities in the Grizzly code to enable it to be used to perform deterministic fracture assessments of degraded reactor pressure vessels (RPVs). A capability was previously developed to calculate three-dimensional interaction- integrals to extract mixed-mode stress-intensity factors. This capability requires the use of a finite element mesh that conforms to the crack geometry. The eXtended Finite Element Method (X-FEM) provides a means to represent a crack geometry without explicitly fitting the finite element mesh to it. This is effected by enhancing the element kinematics to represent jump discontinuities at arbitrary locations inside of the element, as well as the incorporation of asymptotic near-tip fields to better capture crack singularities. In this work, use of only the discontinuous enrichment functions was examined to see how accurate stress intensity factors could still be calculated. This report documents the following work to enhance Grizzly’s engineering fracture capabilities by introducing arbitrary jump discontinuities for prescribed crack geometries; X-FEM Mesh Cutting in 3D: to enhance the kinematics of elements that are intersected by arbitrary crack geometries, a mesh cutting algorithm was implemented in Grizzly. The algorithm introduces new virtual nodes and creates partial elements, and then creates a new mesh connectivity; Interaction Integral Modifications: the existing code for evaluating the interaction integral in Grizzly was based on the assumption of a mesh that was fitted to the crack geometry. Modifications were made to allow for the possibility of a crack front that passes arbitrarily through the mesh; and Benchmarking for 3D Fracture: the new capabilities were benchmarked against mixed-mode three-dimensional fracture problems with known analytical solutions.

  6. Numerical simulation of subwoofer array congurations using the Finite Element Method

    Directory of Open Access Journals (Sweden)

    Xavier Banyuls-Juan

    2017-08-01

    Full Text Available Teaching in the Master of Acoustic Engineering includes contents that require the modeling of acoustic systems of two types: simple systems through analytical theory and complex models using simulation techniques. In the present work, we describe an example of complex acoustic sources modeling using the finite element method: subwoofer sound radiation in different configurations. Numerical simulations in the frequency domain can calculate the radiation pattern of systems that do not have a simple analytical solution.

  7. Development of a partitioned finite volume-finite element fluid-structure interaction scheme for strongly-coupled problems

    CSIR Research Space (South Africa)

    Suliman, Ridhwaan

    2012-07-01

    Full Text Available -linear deformations are accounted for. As will be demonstrated, the finite volume approach exhibits similar disad- vantages to the linear Q4 finite element formulation when undergoing bending. An enhanced finite volume approach is discussed and compared with finite...

  8. The finite element analysis program MSC Marc/Mentat a first introduction

    CERN Document Server

    Öchsner, Andreas

    2016-01-01

    Based on simple examples, this book offers a short introduction to the general-purpose finite element program MSC Marc, a specialized program for non-linear problems (implicit solver) distributed by the MSC Software Corporation, which is commonly used in academia and industry. Today the documentation of all finite element programs includes a variety of step-by-step examples of differing complexity, and in addition, all software companies offer professional workshops on different topics. As such, rather than competing with these, the book focuses on providing simple examples, often single-element problems, which can easily be related to the theory that is discussed in finite element lectures. This makes it an ideal companion book to classical introductory courses on the finite element method.

  9. A finite element thermohydrodynamic analyis of profile bore bearing

    International Nuclear Information System (INIS)

    Shah Nor bin Basri

    1994-01-01

    A finite element-based method is presented for analysing the thermohydrodynamic (THD) behaviour of profile bore bearing. A variational statement for the governing equation is derived and used to formulate a non-linear quadrilateral finite element of serendipity family. The predicted behaviour is compared with experimental evidence where possible and favorable correlation is obtained

  10. 2.5-D frequency-domain viscoelastic wave modelling using finite-element method

    Science.gov (United States)

    Zhao, Jian-guo; Huang, Xing-xing; Liu, Wei-fang; Zhao, Wei-jun; Song, Jian-yong; Xiong, Bin; Wang, Shang-xu

    2017-10-01

    2-D seismic modelling has notable dynamic information discrepancies with field data because of the implicit line-source assumption, whereas 3-D modelling suffers from a huge computational burden. The 2.5-D approach is able to overcome both of the aforementioned limitations. In general, the earth model is treated as an elastic material, but the real media is viscous. In this study, we develop an accurate and efficient frequency-domain finite-element method (FEM) for modelling 2.5-D viscoelastic wave propagation. To perform the 2.5-D approach, we assume that the 2-D viscoelastic media are based on the Kelvin-Voigt rheological model and a 3-D point source. The viscoelastic wave equation is temporally and spatially Fourier transformed into the frequency-wavenumber domain. Then, we systematically derive the weak form and its spatial discretization of 2.5-D viscoelastic wave equations in the frequency-wavenumber domain through the Galerkin weighted residual method for FEM. Fixing a frequency, the 2-D problem for each wavenumber is solved by FEM. Subsequently, a composite Simpson formula is adopted to estimate the inverse Fourier integration to obtain the 3-D wavefield. We implement the stiffness reduction method (SRM) to suppress artificial boundary reflections. The results show that this absorbing boundary condition is valid and efficient in the frequency-wavenumber domain. Finally, three numerical models, an unbounded homogeneous medium, a half-space layered medium and an undulating topography medium, are established. Numerical results validate the accuracy and stability of 2.5-D solutions and present the adaptability of finite-element method to complicated geographic conditions. The proposed 2.5-D modelling strategy has the potential to address modelling studies on wave propagation in real earth media in an accurate and efficient way.

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

    Science.gov (United States)

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

    2017-07-01

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

  12. Hualien forced vibration calculation with a finite element model

    International Nuclear Information System (INIS)

    Wang, F.; Gantenbein, F.; Nedelec, M.; Duretz, Ch.

    1995-01-01

    The forced vibration tests of the Hualien mock-up were useful to validate finite element models developed for soil-structure interaction. In this paper the two sets of tests with and without backfill were analysed. the methods used are based on finite element modeling for the soil. Two approaches were considered: calculation of soil impedance followed by the calculation of the transfer functions with a model taking into account the superstructure and the impedance; direct calculation of the soil-structure transfer functions, with the soil and the structure being represented in the same model by finite elements. Blind predictions and post-test calculations are presented and compared with the test results. (author). 4 refs., 8 figs., 2 tabs

  13. Stream function-vorticity finite elements and the resolution of the Navier-Stokes equations

    International Nuclear Information System (INIS)

    Almeida, R.C.C. de.

    1987-07-01

    A stream function-vorticity finite element formulation for the solution of the Navier-Stokes equations is proposed. The present work shows a procedure to solve the problem posed by the no-slip conditions on solid frontiers which can also be applied to flow problems in a multi-connected domain. Moreover, a methodology to solve the pressure is developed using the stream function-vorticity approximate solution. Numerical experiments were conducted for some steady and unsteady problems and the performance of the proposed methods is discussed. (author) [pt

  14. A Finite Element Theory for Predicting the Attenuation of Extended-Reacting Liners

    Science.gov (United States)

    Watson, W. R.; Jones, M. G.

    2009-01-01

    A non-modal finite element theory for predicting the attenuation of an extended-reacting liner containing a porous facesheet and located in a no-flow duct is presented. The mathematical approach is to solve separate wave equations in the liner and duct airway and to couple these two solutions by invoking kinematic constraints at the facesheet that are consistent with a continuum theory of fluid motion. Given the liner intrinsic properties, a weak Galerkin finite element formulation with cubic polynomial basis functions is used as the basis for generating a discrete system of acoustic equations that are solved to obtain the coupled acoustic field. A state-of-the-art, asymmetric, parallel, sparse equation solver is implemented that allows tens of thousands of grid points to be analyzed. A grid refinement study is presented to show that the predicted attenuation converges. Excellent comparison of the numerically predicted attenuation to that of a mode theory (using a Haynes 25 metal foam liner) is used to validate the computational approach. Simulations are also presented for fifteen porous plate, extended-reacting liners. The construction of some of the porous plate liners suggest that they should behave as resonant liners while the construction of others suggest that they should behave as broadband attenuators. In each case the finite element theory is observed to predict the proper attenuation trend.

  15. Finite element model updating of concrete structures based on imprecise probability

    Science.gov (United States)

    Biswal, S.; Ramaswamy, A.

    2017-09-01

    Imprecise probability based methods are developed in this study for the parameter estimation, in finite element model updating for concrete structures, when the measurements are imprecisely defined. Bayesian analysis using Metropolis Hastings algorithm for parameter estimation is generalized to incorporate the imprecision present in the prior distribution, in the likelihood function, and in the measured responses. Three different cases are considered (i) imprecision is present in the prior distribution and in the measurements only, (ii) imprecision is present in the parameters of the finite element model and in the measurement only, and (iii) imprecision is present in the prior distribution, in the parameters of the finite element model, and in the measurements. Procedures are also developed for integrating the imprecision in the parameters of the finite element model, in the finite element software Abaqus. The proposed methods are then verified against reinforced concrete beams and prestressed concrete beams tested in our laboratory as part of this study.

  16. GOMESH, Finite Elements Structure Plot with Triangular Mesh

    International Nuclear Information System (INIS)

    Draper, J.

    1977-01-01

    1 - Nature of the physical problem solved: Graphical representation of calculations on structures with finite subdivision. 2 - Method of solution: GOMESH treats meshes with triangular basic elements. The program uses the same punched cards as those required for the input to the 'STAG' series of stress analysis codes and can prepare three basic mesh diagrams which differ in their mode of numbering. One objective of using these diagrams is to show up errors in the card deck by making them visually recognisable. Furthermore, digital tests are made within the program to check that certain requirements have been observed in the production of the lattice. The program 'GOMESH', can provide, superimposed in the graphical representation, stress and temperature values in numerical form, can represent the displacement of the mesh before and after a specified irradiation time, and give the directions and sense of the principal stresses occurring in the individual elements, in the form of arrows of varying length

  17. Finite Element Analysis of Mechanical Characteristics of Dropped Eggs Based on Fluid-Solid Coupling Theory

    Directory of Open Access Journals (Sweden)

    Song Haiyan

    2017-01-01

    Full Text Available It is important to study the properties and mechanics of egg drop impacts in order to reduce egg loss during processing and logistics and to provide a basis for the protective packaging of egg products. In this paper, we present the results of our study of the effects of the structural parameters on the mechanical properties of an egg using a finite element model of the egg. Based on Fluid-Solid coupling theory, a finite element model of an egg was constructed using ADINA, a finite element calculation and analysis software package. To simplify the model, the internal fluid of the egg was considered to be a homogeneous substance. The egg drop impact was simulated by the coupling solution, and the feasibility of the model was verified by comparison with the experimental results of a drop test. In summary, the modeling scheme was shown to be feasible and the simulation results provide a theoretical basis for the optimum design of egg packaging and egg processing equipment.

  18. A three-dimensional cell-based smoothed finite element method for elasto-plasticity

    International Nuclear Information System (INIS)

    Lee, Kye Hyung; Im, Se Yong; Lim, Jae Hyuk; Sohn, Dong Woo

    2015-01-01

    This work is concerned with a three-dimensional cell-based smoothed finite element method for application to elastic-plastic analysis. The formulation of smoothed finite elements is extended to cover elastic-plastic deformations beyond the classical linear theory of elasticity, which has been the major application domain of smoothed finite elements. The finite strain deformations are treated with the aid of the formulation based on the hyperelastic constitutive equation. The volumetric locking originating from the nearly incompressible behavior of elastic-plastic deformations is remedied by relaxing the volumetric strain through the mean value. The comparison with the conventional finite elements demonstrates the effectiveness and accuracy of the present approach.

  19. A three-dimensional cell-based smoothed finite element method for elasto-plasticity

    Energy Technology Data Exchange (ETDEWEB)

    Lee, Kye Hyung; Im, Se Yong [KAIST, Daejeon (Korea, Republic of); Lim, Jae Hyuk [KARI, Daejeon (Korea, Republic of); Sohn, Dong Woo [Korea Maritime and Ocean University, Busan (Korea, Republic of)

    2015-02-15

    This work is concerned with a three-dimensional cell-based smoothed finite element method for application to elastic-plastic analysis. The formulation of smoothed finite elements is extended to cover elastic-plastic deformations beyond the classical linear theory of elasticity, which has been the major application domain of smoothed finite elements. The finite strain deformations are treated with the aid of the formulation based on the hyperelastic constitutive equation. The volumetric locking originating from the nearly incompressible behavior of elastic-plastic deformations is remedied by relaxing the volumetric strain through the mean value. The comparison with the conventional finite elements demonstrates the effectiveness and accuracy of the present approach.

  20. On accuracy of the wave finite element predictions of wavenumbers and power flow: A benchmark problem

    Science.gov (United States)

    Søe-Knudsen, Alf; Sorokin, Sergey

    2011-06-01

    This rapid communication is concerned with justification of the 'rule of thumb', which is well known to the community of users of the finite element (FE) method in dynamics, for the accuracy assessment of the wave finite element (WFE) method. An explicit formula linking the size of a window in the dispersion diagram, where the WFE method is trustworthy, with the coarseness of a FE mesh employed is derived. It is obtained by the comparison of the exact Pochhammer-Chree solution for an elastic rod having the circular cross-section with its WFE approximations. It is shown that the WFE power flow predictions are also valid within this window.