A multipoint flux mixed finite element method on distorted quadrilaterals and hexahedra
Wheeler, Mary
2011-11-06
In this paper, we develop a new mixed finite element method for elliptic problems on general quadrilateral and hexahedral grids that reduces to a cell-centered finite difference scheme. A special non-symmetric quadrature rule is employed that yields a positive definite cell-centered system for the pressure by eliminating local velocities. The method is shown to be accurate on highly distorted rough quadrilateral and hexahedral grids, including hexahedra with non-planar faces. Theoretical and numerical results indicate first-order convergence for the pressure and face fluxes. © 2011 Springer-Verlag.
Bathe, Klaus-Jürgen
2015-01-01
Finite element procedures are now an important and frequently indispensable part of engineering analyses and scientific investigations. This book focuses on finite element procedures that are very useful and are widely employed. Formulations for the linear and nonlinear analyses of solids and structures, fluids, and multiphysics problems are presented, appropriate finite elements are discussed, and solution techniques for the governing finite element equations are given. The book presents general, reliable, and effective procedures that are fundamental and can be expected to be in use for a long time. The given procedures form also the foundations of recent developments in the field.
Finite elements and approximation
Zienkiewicz, O C
2006-01-01
A powerful tool for the approximate solution of differential equations, the finite element is extensively used in industry and research. This book offers students of engineering and physics a comprehensive view of the principles involved, with numerous illustrative examples and exercises.Starting with continuum boundary value problems and the need for numerical discretization, the text examines finite difference methods, weighted residual methods in the context of continuous trial functions, and piecewise defined trial functions and the finite element method. Additional topics include higher o
Advanced finite element technologies
Wriggers, Peter
2016-01-01
The book presents an overview of the state of research of advanced finite element technologies. Besides the mathematical analysis, the finite element development and their engineering applications are shown to the reader. The authors give a survey of the methods and technologies concerning efficiency, robustness and performance aspects. The book covers the topics of mathematical foundations for variational approaches and the mathematical understanding of the analytical requirements of modern finite element methods. Special attention is paid to finite deformations, adaptive strategies, incompressible, isotropic or anisotropic material behavior and the mathematical and numerical treatment of the well-known locking phenomenon. Beyond that new results for the introduced approaches are presented especially for challenging nonlinear problems.
A maximum-principle preserving finite element method for scalar conservation equations
Guermond, Jean-Luc
2014-04-01
This paper introduces a first-order viscosity method for the explicit approximation of scalar conservation equations with Lipschitz fluxes using continuous finite elements on arbitrary grids in any space dimension. Provided the lumped mass matrix is positive definite, the method is shown to satisfy the local maximum principle under a usual CFL condition. The method is independent of the cell type; for instance, the mesh can be a combination of tetrahedra, hexahedra, and prisms in three space dimensions. © 2014 Elsevier B.V.
2010-01-01
Finite element analysis is an engineering method for the numerical analysis of complex structures. This book provides a bird's eye view on this very broad matter through 27 original and innovative research studies exhibiting various investigation directions. Through its chapters the reader will have access to works related to Biomedical Engineering, Materials Engineering, Process Analysis and Civil Engineering. The text is addressed not only to researchers, but also to professional engineers, engineering lecturers and students seeking to gain a better understanding of where Finite Element Analysis stands today.
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.
Solution of Finite Element Equations
DEFF Research Database (Denmark)
Krenk, Steen
An important step in solving any problem by the finite element method is the solution of the global equations. Numerical solution of linear equations is a subject covered in most courses in numerical analysis. However, the equations encountered in most finite element applications have some special...
Massively Parallel Finite Element Programming
Heister, Timo
2010-01-01
Today\\'s large finite element simulations require parallel algorithms to scale on clusters with thousands or tens of thousands of processor cores. We present data structures and algorithms to take advantage of the power of high performance computers in generic finite element codes. Existing generic finite element libraries often restrict the parallelization to parallel linear algebra routines. This is a limiting factor when solving on more than a few hundreds of cores. We describe routines for distributed storage of all major components coupled with efficient, scalable algorithms. We give an overview of our effort to enable the modern and generic finite element library deal.II to take advantage of the power of large clusters. In particular, we describe the construction of a distributed mesh and develop algorithms to fully parallelize the finite element calculation. Numerical results demonstrate good scalability. © 2010 Springer-Verlag.
Finite element computational fluid mechanics
Baker, A. J.
1983-01-01
Finite element analysis as applied to the broad spectrum of computational fluid mechanics is analyzed. The finite element solution methodology is derived, developed, and applied directly to the differential equation systems governing classes of problems in fluid mechanics. The heat conduction equation is used to reveal the essence and elegance of finite element theory, including higher order accuracy and convergence. The algorithm is extended to the pervasive nonlinearity of the Navier-Stokes equations. A specific fluid mechanics problem class is analyzed with an even mix of theory and applications, including turbulence closure and the solution of turbulent flows.
quadratic spline finite element method
Directory of Open Access Journals (Sweden)
A. R. Bahadir
2002-01-01
Full Text Available The problem of heat transfer in a Positive Temperature Coefficient (PTC thermistor, which may form one element of an electric circuit, is solved numerically by a finite element method. The approach used is based on Galerkin finite element using quadratic splines as shape functions. The resulting system of ordinary differential equations is solved by the finite difference method. Comparison is made with numerical and analytical solutions and the accuracy of the computed solutions indicates that the method is well suited for the solution of the PTC thermistor problem.
Green's Functions and Finite Elements
Hartmann, Friedel
2013-01-01
This book elucidates how Finite Element methods look like from the perspective of Green’s functions, and shows new insights into the mathematical theory of Finite Elements. Practically, this new view on Finite Elements enables the reader to better assess solutions of standard programs and to find better model of a given problem. The book systematically introduces the basic concepts how Finite Elements fulfill the strategy of Green’s functions and how approximating of Green’s functions. It discusses in detail the discretization error and shows that are coherent with the strategy of “goal oriented refinement”. The book also gives much attention to the dependencies of FE solutions from the parameter set of the model.
Programming the finite element method
Smith, I M; Margetts, L
2013-01-01
Many students, engineers, scientists and researchers have benefited from the practical, programming-oriented style of the previous editions of Programming the Finite Element Method, learning how to develop computer programs to solve specific engineering problems using the finite element method. This new fifth edition offers timely revisions that include programs and subroutine libraries fully updated to Fortran 2003, which are freely available online, and provides updated material on advances in parallel computing, thermal stress analysis, plasticity return algorithms, convection boundary c
Finite element methods for engineers
Fenner, Roger T
2013-01-01
This book is intended as a textbook providing a deliberately simple introduction to finite element methods in a way that should be readily understandable to engineers, both students and practising professionals. Only the very simplest elements are considered, mainly two dimensional three-noded “constant strain triangles”, with simple linear variation of the relevant variables. Chapters of the book deal with structural problems (beams), classification of a broad range of engineering into harmonic and biharmonic types, finite element analysis of harmonic problems, and finite element analysis of biharmonic problems (plane stress and plane strain). Full Fortran programs are listed and explained in detail, and a range of practical problems solved in the text. Despite being somewhat unfashionable for general programming purposes, the Fortran language remains very widely used in engineering. The programs listed, which were originally developed for use on mainframe computers, have been thoroughly updated for use ...
Moortgat, Joachim
2016-01-01
Problems of interest in hydrogeology and hydrocarbon resources involve complex heterogeneous geological formations. Such domains are most accurately represented in reservoir simulations by unstructured computational grids. Finite element methods accurately describe flow on unstructured meshes with complex geometries, and their flexible formulation allows implementation on different grid types. In this work, we consider for the first time the challenging problem of fully compositional three-phase flow in 3D unstructured grids, discretized by any combination of tetrahedra, prisms, and hexahedra. We employ a mass conserving mixed hybrid finite element (MHFE) method to solve for the pressure and flux fields. The transport equations are approximated with a higher-order vertex-based discontinuous Galerkin (DG) discretization. We show that this approach outperforms a face-based implementation of the same polynomial order. These methods are well suited for heterogeneous and fractured reservoirs, because they provide ...
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.
Finite elements of nonlinear continua
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
Stochastic finite element method with simple random elements
Starkloff, Hans-Jörg
2008-01-01
We propose a variant of the stochastic finite element method, where the random elements occuring in the problem formulation are approximated by simple random elements, i.e. random elements with only a finite number of possible values.
Unconstrained paving and plastering method for generating finite element meshes
Staten, Matthew L.; Owen, Steven J.; Blacker, Teddy D.; Kerr, Robert
2010-03-02
Computer software for and a method of generating a conformal all quadrilateral or hexahedral mesh comprising selecting an object with unmeshed boundaries and performing the following while unmeshed voids are larger than twice a desired element size and unrecognizable as either a midpoint subdividable or pave-and-sweepable polyhedra: selecting a front to advance; based on sizes of fronts and angles with adjacent fronts, determining which adjacent fronts should be advanced with the selected front; advancing the fronts; detecting proximities with other nearby fronts; resolving any found proximities; forming quadrilaterals or unconstrained columns of hexahedra where two layers cross; and establishing hexahedral elements where three layers cross.
Solid finite elements through three decades
Venkatesh, DN; Shrinivasa, U
1994-01-01
conventionally, solid finite elements have been looked upon as just generalizations of two-dimensional finite elements. In this article we trace their development starting from the days of their inception. Keeping in tune with our perceptions on developing finite elements, without taking recourse to any extra variational techniques, we discuss a few of the techniques which have been applied to solid finite elements. Finally we critically examine our own work on formulating solid finite elemen...
Automation of finite element methods
Korelc, Jože
2016-01-01
New finite elements are needed as well in research as in industry environments for the development of virtual prediction techniques. The design and implementation of novel finite elements for specific purposes is a tedious and time consuming task, especially for nonlinear formulations. The automation of this process can help to speed up this process considerably since the generation of the final computer code can be accelerated by order of several magnitudes. This book provides the reader with the required knowledge needed to employ modern automatic tools like AceGen within solid mechanics in a successful way. It covers the range from the theoretical background, algorithmic treatments to many different applications. The book is written for advanced students in the engineering field and for researchers in educational and industrial environments.
Finite elements methods in mechanics
Eslami, M Reza
2014-01-01
This book covers all basic areas of mechanical engineering, such as fluid mechanics, heat conduction, beams, and elasticity with detailed derivations for the mass, stiffness, and force matrices. It is especially designed to give physical feeling to the reader for finite element approximation by the introduction of finite elements to the elevation of elastic membrane. A detailed treatment of computer methods with numerical examples are provided. In the fluid mechanics chapter, the conventional and vorticity transport formulations for viscous incompressible fluid flow with discussion on the method of solution are presented. The variational and Galerkin formulations of the heat conduction, beams, and elasticity problems are also discussed in detail. Three computer codes are provided to solve the elastic membrane problem. One of them solves the Poisson’s equation. The second computer program handles the two dimensional elasticity problems, and the third one presents the three dimensional transient heat conducti...
Linear and Nonlinear Finite Elements.
1983-12-01
Yang, Matrix displacement solution to elastica problems of beams and frames , Internat. J. Solids Structures 9 (1973) 829-842. [51 W.F. Schmidt...nonlinear finite element analysis of beams, frames . arches and axisymmetric shells. Comput. and Structures 7 (1977) 725-735. 171 1. Fried. The Numerical...extension. Near inexten bility is achieved with a high dostic constant . ,p -P+(.(l-)+Q? (3) Lare axial stilness gives rise to strong oscmations in
ANSYS duplicate finite-element checker routine
Ortega, R.
1995-01-01
An ANSYS finite-element code routine to check for duplicated elements within the volume of a three-dimensional (3D) finite-element mesh was developed. The routine developed is used for checking floating elements within a mesh, identically duplicated elements, and intersecting elements with a common face. A space shuttle main engine alternate turbopump development high pressure oxidizer turbopump finite-element model check using the developed subroutine is discussed. Finally, recommendations are provided for duplicate element checking of 3D finite-element models.
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
Nonconforming tetrahedral mixed finite elements for elasticity
Arnold, Douglas N.; Awanou, Gerard; Winther, Ragnar
2012-01-01
This paper presents a nonconforming finite element approximation of the space of symmetric tensors with square integrable divergence, on tetrahedral meshes. Used for stress approximation together with the full space of piecewise linear vector fields for displacement, this gives a stable mixed finite element method which is shown to be linearly convergent for both the stress and displacement, and which is significantly simpler than any stable conforming mixed finite element method. The method ...
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.
A first course in finite elements
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
FEBio: finite elements for biomechanics.
Maas, Steve A; Ellis, Benjamin J; Ateshian, Gerard A; Weiss, Jeffrey A
2012-01-01
In the field of computational biomechanics, investigators have primarily used commercial software that is neither geared toward biological applications nor sufficiently flexible to follow the latest developments in the field. This lack of a tailored software environment has hampered research progress, as well as dissemination of models and results. To address these issues, we developed the FEBio software suite (http://mrl.sci.utah.edu/software/febio), a nonlinear implicit finite element (FE) framework, designed specifically for analysis in computational solid biomechanics. This paper provides an overview of the theoretical basis of FEBio and its main features. FEBio offers modeling scenarios, constitutive models, and boundary conditions, which are relevant to numerous applications in biomechanics. The open-source FEBio software is written in C++, with particular attention to scalar and parallel performance on modern computer architectures. Software verification is a large part of the development and maintenance of FEBio, and to demonstrate the general approach, the description and results of several problems from the FEBio Verification Suite are presented and compared to analytical solutions or results from other established and verified FE codes. An additional simulation is described that illustrates the application of FEBio to a research problem in biomechanics. Together with the pre- and postprocessing software PREVIEW and POSTVIEW, FEBio provides a tailored solution for research and development in computational biomechanics.
Why and how of finite elements
Energy Technology Data Exchange (ETDEWEB)
Ackroyd, R.T. (UKAEA Risley Nuclear Power Development Establishment)
1981-01-01
The development of the finite element method is traced to show how ideas from structural and fluid mechanics, the calculus of variations, functional analysis and the calculus of finite differences have been forged to provide a tool which minimizes the mismatch between the behaviour of a continuous system and that of a discrete model of the system assembled from finite elements. Geometrical flexibility of the model is achieved by the use of polygonal and curved elements. The behaviour of any point of an element is described in terms of its behaviour at discrete points or nodes of the element. In treating neutron transport the finite element method can be applied to phase-space, or the spatial dependence can be treated by the use of finite elements in conjuction with expansions in orthogonal functions for the directional dependence. The maximum principle for the second-order even-parity Boltzmann equations is used to demonstrate the precision and flexibility of the finite element method by solving the problems of a doglegged duct in a shield and a cylindrical fuel element in a square lattice cell. The geometrical interpretation of the boundary-free maximum principle with the aid of a suitable Hilbert space then leads to completely boundary-free weighted residual or Galerkin schemes for both the first- and second-order forms of the Boltzmann equation. Imposing essential boundary conditions leads to classical schemes, a sketch of finite element treatments of the multigroup Boltzmann equation is given.
Finite element bending behaviour of discretely delaminated ...
African Journals Online (AJOL)
user
for large deformations in curved panels including full cylinders by finite element method. Acharyya et al. 2008 used a finite element method for the study of bending behaviour of partially delaminated shallow cylindrical composite shells subjected to uniformly distributed load with various practical boundary conditions.
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...
Why do probabilistic finite element analysis ?
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.
Finite element modeling of quasi-brittle cracks in 2D and 3D with enhanced strain accuracy
Cervera, M.; Barbat, G. B.; Chiumenti, M.
2017-11-01
This paper discusses the finite element modeling of cracking in quasi-brittle materials. The problem is addressed via a mixed strain/displacement finite element formulation and an isotropic damage constitutive model. The proposed mixed formulation is fully general and is applied in 2D and 3D. Also, it is independent of the specific finite element discretization considered; it can be equally used with triangles/tetrahedra, quadrilaterals/hexahedra and prisms. The feasibility and accuracy of the method is assessed through extensive comparison with experimental evidence. The correlation with the experimental tests shows the capacity of the mixed formulation to reproduce the experimental crack path and the force-displacement curves with remarkable accuracy. Both 2D and 3D examples produce results consistent with the documented data. Aspects related to the discrete solution, such as convergence regarding mesh resolution and mesh bias, as well as other related to the physical model, like structural size effect and the influence of Poisson's ratio, are also investigated. The enhanced accuracy of the computed strain field leads to accurate results in terms of crack paths, failure mechanisms and force displacement curves. Spurious mesh dependency suffered by both continuous and discontinuous irreducible formulations is avoided by the mixed FE, without the need of auxiliary tracking techniques or other computational schemes that alter the continuum mechanical problem.
Element-topology-independent preconditioners for parallel finite element computations
Park, K. C.; Alexander, Scott
1992-01-01
A family of preconditioners for the solution of finite element equations are presented, which are element-topology independent and thus can be applicable to element order-free parallel computations. A key feature of the present preconditioners is the repeated use of element connectivity matrices and their left and right inverses. The properties and performance of the present preconditioners are demonstrated via beam and two-dimensional finite element matrices for implicit time integration computations.
Nonconforming finite element methods on quadrilateral meshes
Hu, Jun; Zhang, ShangYou
2013-12-01
It is well-known that it is comparatively difficult to design nonconforming finite elements on quadrilateral meshes by using Gauss-Legendre points on each edge of triangulations. One reason lies in that these degrees of freedom associated to these Gauss-Legendre points are not all linearly independent for usual expected polynomial spaces, which explains why only several lower order nonconforming quadrilateral finite elements can be found in literature. The present paper proposes two families of nonconforming finite elements of any odd order and one family of nonconforming finite elements of any even order on quadrilateral meshes. Degrees of freedom are given for these elements, which are proved to be well-defined for their corresponding shape function spaces in a unifying way. These elements generalize three lower order nonconforming finite elements on quadrilaterals to any order. In addition, these nonconforming finite element spaces are shown to be full spaces which is somehow not discussed for nonconforming finite elements in literature before.
Finite element and finite difference methods in electromagnetic scattering
Morgan, MA
2013-01-01
This second volume in the Progress in Electromagnetic Research series examines recent advances in computational electromagnetics, with emphasis on scattering, as brought about by new formulations and algorithms which use finite element or finite difference techniques. Containing contributions by some of the world's leading experts, the papers thoroughly review and analyze this rapidly evolving area of computational electromagnetics. Covering topics ranging from the new finite-element based formulation for representing time-harmonic vector fields in 3-D inhomogeneous media using two coupled sca
Books and monographs on finite element technology
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.
The Mathematics of Finite Elements and Applications
1993-04-30
adaptive mesh refinement ( AMR ) are nowadays two of the challenging issues in the finite element method (FEM). In this paper a methodology for deriving AMR ...parameters and that of the element refinement parameter are obtained for each case. Finally, the efficiency of the two AMR methodologies studied is...operators approximated. Appropriate error bounds are established. A K MOHAMMED, M H BALUCH and S T GOMAA Finite element modelling of deep beams using a
Electrical machine analysis using finite elements
Bianchi, Nicola
2005-01-01
OUTLINE OF ELECTROMAGNETIC FIELDSVector AnalysisElectromagnetic FieldsFundamental Equations SummaryReferencesBASIC PRINCIPLES OF FINITE ELEMENT METHODSIntroductionField Problems with Boundary ConditionsClassical Method for the Field Problem SolutionThe Classical Residual Method (Galerkin's Method)The Classical Variational Method (Rayleigh-Ritz's Method)The Finite Element MethodReferencesAPPLICATIONS OF THE FINITE ELEMENT METHOD TO TWO-DIMENSIONAL FIELDSIntroductionLinear Interpolation of the Function fApplication of the Variational MethodSimple Descriptions of Electromagnetic FieldsAppendix: I
Finite Element Modeling on Scalable Parallel Computers
Cwik, T.; Zuffada, C.; Jamnejad, V.; Katz, D.
1995-01-01
A coupled finite element-integral equation was developed to model fields scattered from inhomogenous, three-dimensional objects of arbitrary shape. This paper outlines how to implement the software on a scalable parallel processor.
Finite element methods a practical guide
Whiteley, Jonathan
2017-01-01
This book presents practical applications of the finite element method to general differential equations. The underlying strategy of deriving the finite element solution is introduced using linear ordinary differential equations, thus allowing the basic concepts of the finite element solution to be introduced without being obscured by the additional mathematical detail required when applying this technique to partial differential equations. The author generalizes the presented approach to partial differential equations which include nonlinearities. The book also includes variations of the finite element method such as different classes of meshes and basic functions. Practical application of the theory is emphasised, with development of all concepts leading ultimately to a description of their computational implementation illustrated using Matlab functions. The target audience primarily comprises applied researchers and practitioners in engineering, but the book may also be beneficial for graduate students.
Advanced finite element method in structural engineering
Long, Yu-Qiu; Long, Zhi-Fei
2009-01-01
This book systematically introduces the research work on the Finite Element Method completed over the past 25 years. Original theoretical achievements and their applications in the fields of structural engineering and computational mechanics are discussed.
ANSYS mechanical APDL for finite element analysis
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...
Visualization of higher order finite elements.
Energy Technology Data Exchange (ETDEWEB)
Thompson, David C.; Pebay, Philippe Pierre; Crawford, Richard H.; Khardekar, Rahul Vinay
2004-04-01
Finite element meshes are used to approximate the solution to some differential equation when no exact solution exists. A finite element mesh consists of many small (but finite, not infinitesimal or differential) regions of space that partition the problem domain, {Omega}. Each region, or element, or cell has an associated polynomial map, {Phi}, that converts the coordinates of any point, x = ( x y z ), in the element into another value, f(x), that is an approximate solution to the differential equation, as in Figure 1(a). This representation works quite well for axis-aligned regions of space, but when there are curved boundaries on the problem domain, {Omega}, it becomes algorithmically much more difficult to define {Phi} in terms of x. Rather, we define an archetypal element in a new coordinate space, r = ( r s t ), which has a simple, axis-aligned boundary (see Figure 1(b)) and place two maps onto our archetypal element:
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...
The finite element method in electromagnetics
Jin, Jianming
2014-01-01
A new edition of the leading textbook on the finite element method, incorporating major advancements and further applications in the field of electromagnetics The finite element method (FEM) is a powerful simulation technique used to solve boundary-value problems in a variety of engineering circumstances. It has been widely used for analysis of electromagnetic fields in antennas, radar scattering, RF and microwave engineering, high-speed/high-frequency circuits, wireless communication, electromagnetic compatibility, photonics, remote sensing, biomedical engineering, and space exploration. The
Quantum algorithms and the finite element method
Montanaro, Ashley; Pallister, Sam
2015-01-01
The finite element method is used to approximately solve boundary value problems for differential equations. The method discretises the parameter space and finds an approximate solution by solving a large system of linear equations. Here we investigate the extent to which the finite element method can be accelerated using an efficient quantum algorithm for solving linear equations. We consider the representative general question of approximately computing a linear functional of the solution t...
Finite element modeling of the human pelvis
Energy Technology Data Exchange (ETDEWEB)
Carlson, B.
1995-11-01
A finite element model of the human pelvis was created using a commercial wire frame image as a template. To test the final mesh, the model`s mechanical behavior was analyzed through finite element analysis and the results were displayed graphically as stress concentrations. In the future, this grid of the pelvis will be integrated with a full leg model and used in side-impact car collision simulations.
Stabilized Finite Elements in FUN3D
Anderson, W. Kyle; Newman, James C.; Karman, Steve L.
2017-01-01
A Streamlined Upwind Petrov-Galerkin (SUPG) stabilized finite-element discretization has been implemented as a library into the FUN3D unstructured-grid flow solver. Motivation for the selection of this methodology is given, details of the implementation are provided, and the discretization for the interior scheme is verified for linear and quadratic elements by using the method of manufactured solutions. A methodology is also described for capturing shocks, and simulation results are compared to the finite-volume formulation that is currently the primary method employed for routine engineering applications. The finite-element methodology is demonstrated to be more accurate than the finite-volume technology, particularly on tetrahedral meshes where the solutions obtained using the finite-volume scheme can suffer from adverse effects caused by bias in the grid. Although no effort has been made to date to optimize computational efficiency, the finite-element scheme is competitive with the finite-volume scheme in terms of computer time to reach convergence.
Galerkin finite element methods for wave problems
Indian Academy of Sciences (India)
Galerkin ﬁnite element methods for wave problems ... hp-Finite element method; continuous Galerkin methods; wave solutions; Gibbs' phenomenon. ... Department of Aerospace Engineering, Indian Institute of Technology, Kanpur 208 016, India; Institute of High Performance Computing, 1, Science Park Road, Singapore ...
A Nonlocal Finite Element Approach to Nanobeams
Directory of Open Access Journals (Sweden)
Francesco Marotti de Sciarra
2013-01-01
Full Text Available This paper presents a consistent derivation of a new nonlocal finite element procedure in the framework of continuum mechanics and nonlocal thermodynamics for the analysis of bending of nanobeams under transverse loads. This approach is able to provide the overall performance and the influence of specific parameters in the behavior of nanobeams and it is also able to deal with nanomechanical systems by solving a reduced number of algebraic equations. An example shows that the proposed nonlocal finite element procedure, using a mesh composed by only four elements of equal size, provides the exact values in terms of transversal displacement and bending of the nanobeam.
Finite Element Computational Dynamics of Rotating Systems
Directory of Open Access Journals (Sweden)
Jaroslav Mackerle
1999-01-01
Full Text Available This bibliography lists references to papers, conference proceedings and theses/dissertations dealing with finite element analysis of rotor dynamics problems that were published in 1994–1998. It contains 319 citations. Also included, as separate subsections, are finite element analyses of rotor elements – discs, shafts, spindles, and blades. Topics dealing with fracture mechanics, contact and stability problems of rotating machinery are also considered in specific sections. The last part of the bibliography presents papers dealing with specific industrial applications.
Finite element analysis of tibial fractures
DEFF Research Database (Denmark)
Wong, Christian Nai En; Mikkelsen, Mikkel Peter W; Hansen, Leif Berner
2010-01-01
INTRODUCTION: Fractures of the tibial shaft are relatively common injuries. There are indications that tibial shaft fractures share characteristics in terms of site, type and local fracture mechanisms. In this study, we aimed to set up a mathematical, computer-based model using finite element...... of bony healing. The biomechanical results are the basis for fracture healing, biomechanical fall analysis and stability analysis of osteosynthesis. MATERIAL AND METHODS: A finite element model of the bony part of the lower leg was generated on the basis of computed tomography data from the Visible Human...... 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...
Finite element analysis of tibial fractures
DEFF Research Database (Denmark)
Wong, Christian Nai En; Mikkelsen, Mikkel Peter W; Hansen, Leif Berner
2010-01-01
of bony healing. The biomechanical results are the basis for fracture healing, biomechanical fall analysis and stability analysis of osteosynthesis. MATERIAL AND METHODS: A finite element model of the bony part of the lower leg was generated on the basis of computed tomography data from the Visible Human...... 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......INTRODUCTION: Fractures of the tibial shaft are relatively common injuries. There are indications that tibial shaft fractures share characteristics in terms of site, type and local fracture mechanisms. In this study, we aimed to set up a mathematical, computer-based model using finite element...
Quadrilateral finite element mesh coarsening
Staten, Matthew L; Dewey, Mark W; Benzley, Steven E
2012-10-16
Techniques for coarsening a quadrilateral mesh are described. These techniques include identifying a coarsening region within the quadrilateral mesh to be coarsened. Quadrilateral elements along a path through the coarsening region are removed. Node pairs along opposite sides of the path are identified. The node pairs along the path are then merged to collapse the path.
Finite-Element Software for Conceptual Design
DEFF Research Database (Denmark)
Lindemann, J.; Sandberg, G.; Damkilde, Lars
2010-01-01
Using finite-element analysis in conceptual design and teaching has quite different software requirements to that in engineering and research. In teaching and conceptual design the focus is on speed, interactivity and ease of use, whereas accuracy and precision are needed in engineering...... 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...... success in teaching as well as in conceptual design environments such as architecture, industrial design and engineering. The addition of an optimisation algorithm and tablet PC support makes the software even more interesting as a tool for conceptual design....
Finite Element Methods and Their Applications
Chen, Zhangxin
2005-01-01
This book serves as a text for one- or two-semester courses for upper-level undergraduates and beginning graduate students and as a professional reference for people who want to solve partial differential equations (PDEs) using finite element methods. The author has attempted to introduce every concept in the simplest possible setting and maintain a level of treatment that is as rigorous as possible without being unnecessarily abstract. Quite a lot of attention is given to discontinuous finite elements, characteristic finite elements, and to the applications in fluid and solid mechanics including applications to porous media flow, and applications to semiconductor modeling. An extensive set of exercises and references in each chapter are provided.
Finite Element Modeling of Cracks and Joints
Directory of Open Access Journals (Sweden)
Jozef Čížik
2006-12-01
Full Text Available The application of finite element method to the analysis of discontinuous structural systems has received a considerable interest in recent years. Examples of problems in which discontinuities play a prominent role in the physical behaviour of a system are numerous and include various types of contact problems and layered or jointed systems. This paper gives a state-of-the-art report on the different methods developed to date for the finite element modelling of cracks and joints in discontinuous systems. Particular attention, however, has been given to the use of joint/interface elements, since their application is considered to be most appropriate for modelling of all kinds of discontinuities that may present in a structural system. A chronology of development of the main types of joint elements, including their pertinent characteristics, is also given. Advantages and disadvantages of the individual methods and types of joint elements presented are briefly discussed, together with various applications of interest.
Finite elements for analysis and design
Akin, J E; Davenport, J H
1994-01-01
The finite element method (FEM) is an analysis tool for problem-solving used throughout applied mathematics, engineering, and scientific computing. Finite Elements for Analysis and Design provides a thoroughlyrevised and up-to-date account of this important tool and its numerous applications, with added emphasis on basic theory. Numerous worked examples are included to illustrate the material.Key Features* Akin clearly explains the FEM, a numerical analysis tool for problem-solving throughout applied mathematics, engineering and scientific computing* Basic theory has bee
Quadrilateral/hexahedral finite element mesh coarsening
Staten, Matthew L; Dewey, Mark W; Scott, Michael A; Benzley, Steven E
2012-10-16
A technique for coarsening a finite element mesh ("FEM") is described. This technique includes identifying a coarsening region within the FEM to be coarsened. Perimeter chords running along perimeter boundaries of the coarsening region are identified. The perimeter chords are redirected to create an adaptive chord separating the coarsening region from a remainder of the FEM. The adaptive chord runs through mesh elements residing along the perimeter boundaries of the coarsening region. The adaptive chord is then extracted to coarsen the FEM.
FINITE ELEMENT MODEL FOR PREDICTING RESIDUAL ...
African Journals Online (AJOL)
This paper investigates the prediction of residual stresses developed in shielded manual metal arc welding of mild steel plates through Finite Element Model simulation and experiments. The existence of residual stresses that cause fatigue and distortion in welded structures has been responsible for failure of machine parts ...
Finite element modeling of corneal strip extensometry
CSIR Research Space (South Africa)
Botha, N
2012-12-01
Full Text Available symmetric conicoid [19]: (x xo) 2+(y yo) 2+(1+Q)(z zo) 2 2R(z zo) 2 = 0; (2) c SACAM 2012 25 Top view Isometric view Initial corneal curvature z y x x y z Fig. 3: Finite element model of the vertical corneal strip, including the orthogonal...
Fast finite elements for surgery simulation
Bro-Nielsen, Morten
1997-01-01
This paper discusses volumetric deformable models for modeling human body parts and organs in surgery simulation systems. These models are built using finite element models for linear elastic materials. To achieve real-time response condensation has been applied to the system stiffness matrix, and selective matrix vector multiplication has been used to minimize the computational cost
Finite element modelling of solidification phenomena
Indian Academy of Sciences (India)
The process of solidification process is complex in nature and the simulation of such process is required in industry before it is actually undertaken. Finite element method is used to simulate the heat transfer process accompanying the solidification process. The metal and the mould along with the air gap formation is ...
Image segmentation with a finite element method
DEFF Research Database (Denmark)
Bourdin, Blaise
1999-01-01
regularization results, make possible to imagine a finite element resolution method.In a first time, the Mumford-Shah functional is introduced and some existing results are quoted. Then, a discrete formulation for the Mumford-Shah problem is proposed and its $\\Gamma$-convergence is proved. Finally, some...
Fast finite elements for surgery simulation
DEFF Research Database (Denmark)
Bro-Nielsen, Morten
1997-01-01
This paper discusses volumetric deformable models for modeling human body parts and organs in surgery simulation systems. These models are built using finite element models for linear elastic materials. To achieve real-time response condensation has been applied to the system stiffness matrix...
Introduction to finite and spectral element methods using Matlab
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.
Finite Dynamic Elements and Modal Analysis
Directory of Open Access Journals (Sweden)
N.J. Fergusson
1993-01-01
Full Text Available A general modal analysis scheme is derived for forced response that makes use of high accuracy modes computed by the dynamic element method. The new procedure differs from the usual modal analysis in that the modes are obtained from a power series expansion for the dynamic stiffness matrix that includes an extra dynamic correction term in addition to the static stiffness matrix and the consistent mass matrix based on static displacement. A cantilevered beam example is used to demonstrate the relative accuracies of the dynamic element and the traditional finite element methods.
An anisotropic, superconvergent nonconforming plate finite element
Chen, Shaochun; Yin, Li; Mao, Shipeng
2008-10-01
The classical finite element convergence analysis relies on the following regularity condition: there exists a constant c independent of the element K and the mesh such that hK/[rho]K[less-than-or-equals, slant]c, where hK and [rho]K are diameters of K and the biggest ball contained in K, respectively. In this paper, we construct a new, nonconforming rectangular plate element by the double set parameter method. We prove the convergence of this element without the above regularity condition. The key in our proof is to obtain the O(h2) consistency error. We also prove the superconvergence of this element for narrow rectangular meshes. Results of our numerical tests agree well with our analysis.
Finite element simulations with ANSYS workbench 16
Lee , Huei-Huang
2015-01-01
Finite Element Simulations with ANSYS Workbench 16 is a comprehensive and easy to understand workbook. It utilizes step-by-step instructions to help guide readers to learn finite element simulations. Twenty seven real world case studies are used throughout the book. Many of these cases are industrial or research projects the reader builds from scratch. All the files readers may need if they have trouble are available for download on the publishers website. Companion videos that demonstrate exactly how to preform each tutorial are available to readers by redeeming the access code that comes in the book. Relevant background knowledge is reviewed whenever necessary. To be efficient, the review is conceptual rather than mathematical. Key concepts are inserted whenever appropriate and summarized at the end of each chapter. Additional exercises or extension research problems are provided as homework at the end of each chapter. A learning approach emphasizing hands-on experiences spreads through this entire book. A...
Finite element analysis of human joints
Energy Technology Data Exchange (ETDEWEB)
Bossart, P.L.; Hollerbach, K.
1996-09-01
Our work focuses on the development of finite element models (FEMs) that describe the biomechanics of human joints. Finite element modeling is becoming a standard tool in industrial applications. In highly complex problems such as those found in biomechanics research, however, the full potential of FEMs is just beginning to be explored, due to the absence of precise, high resolution medical data and the difficulties encountered in converting these enormous datasets into a form that is usable in FEMs. With increasing computing speed and memory available, it is now feasible to address these challenges. We address the first by acquiring data with a high resolution C-ray CT scanner and the latter by developing semi-automated method for generating the volumetric meshes used in the FEM. Issues related to tomographic reconstruction, volume segmentation, the use of extracted surfaces to generate volumetric hexahedral meshes, and applications of the FEM are described.
FINITE ELEMENT ANALYSIS FOR PERIFLEX COUPLINGS
Directory of Open Access Journals (Sweden)
URDEA Mihaela
2015-06-01
Full Text Available The Periflex shaft couplings with rubber sleeve have a hig elasticity and link two shafts in diesel-engine and electric drives. They are simple from the point of view of construction, easily mounted and dismounted. The main goal of this paper is to present a finite element analysis for the Periflex coupling using the Generative Structural Analysis from CATIA software package. This paper presents important information about how to prepare an assembly for creating a static analysis case and also the important steps for developing a finite element analysis. It is very important that the analysis model should have the same behavior as the real, also the loading model. The results are images corresponding to Von Mises Stresses and Translational Displacement magnitude.
Introduction to nonlinear finite element analysis
Kim, Nam-Ho
2015-01-01
This book introduces the key concepts of nonlinear finite element analysis procedures. The book explains the fundamental theories of the field and provides instructions on how to apply the concepts to solving practical engineering problems. Instead of covering many nonlinear problems, the book focuses on three representative problems: nonlinear elasticity, elastoplasticity, and contact problems. The book is written independent of any particular software, but tutorials and examples using four commercial programs are included as appendices: ANSYS, NASTRAN, ABAQUS, and MATLAB. In particular, the MATLAB program includes all source codes so that students can develop their own material models, or different algorithms. This book also: · Presents clear explanations of nonlinear finite element analysis for elasticity, elastoplasticity, and contact problems · Includes many informative examples of nonlinear analyses so that students can clearly understand the nonlinear theory · ...
FINITE-ELEMENT MODELING OF SALT TECTONICS
Directory of Open Access Journals (Sweden)
Natalia Bakhova
2012-09-01
Full Text Available The two-dimensional thermal model of graben structure in the presence of salt tectonics on the basis of a finite elements method is constructed. The analysis of the thermal field is based on the solution of stationary equation of heat conductivity with variable boundary conditions. The high precision of temperatures distribution and heat flows is received. The decision accuracy is no more than 0,6 %.
Finite element simulation of heat transfer
Bergheau, Jean-Michel
2010-01-01
This book introduces the finite element method applied to the resolution of industrial heat transfer problems. Starting from steady conduction, the method is gradually extended to transient regimes, to traditional non-linearities, and to convective phenomena. Coupled problems involving heat transfer are then presented. Three types of couplings are discussed: coupling through boundary conditions (such as radiative heat transfer in cavities), addition of state variables (such as metallurgical phase change), and coupling through partial differential equations (such as electrical phenomena).? A re
Upstand Finite Element Analysis of Slab Bridges
O'Brien, Eugene J.; Keogh, D.L.
1998-01-01
For slab bridge decks with wide transverse edge cantilevers, the plane grillage analogy is shown to be an inaccurate method of linear elastic analysis due to variations in the vertical position of the neutral axis. The upstand grillage analogy is also shown to give inaccurate results, this time due to inappropriate modelling of in-plane distortions. An alternative method, known as upstand finite element analysis, is proposed which is sufficiently simple to be used on an everyday basis in the ...
Finite element model of needle electrode sensitivity
Høyum, P.; Kalvøy, H.; Martinsen, Ø. G.; Grimnes, S.
2010-04-01
We used the Finite Element (FE) Method to estimate the sensitivity of a needle electrode for bioimpedance measurement. This current conducting needle with insulated shaft was inserted in a saline solution and current was measured at the neutral electrode. FE model resistance and reactance were calculated and successfully compared with measurements on a laboratory model. The sensitivity field was described graphically based on these FE simulations.
Finite element modeling of lipid bilayer membranes
Feng, Feng; Klug, William S.
2006-12-01
A numerical simulation framework is presented for the study of biological membranes composed of lipid bilayers based on the finite element method. The classic model for these membranes employs a two-dimensional-fluid-like elastic constitutive law which is sensitive to curvature, and subjects vesicles to physically imposed constraints on surface area and volume. This model is implemented numerically via the use of C1-conforming triangular Loop subdivision finite elements. The validity of the framework is tested by computing equilibrium shapes from previously-determined axisymmetric shape-phase diagram of lipid bilayer vesicles with homogeneous material properties. Some of the benefits and challenges of finite element modeling of lipid bilayer systems are discussed, and it is indicated how this framework is natural for future investigation of biologically realistic bilayer structures involving nonaxisymmetric geometries, binding and adhesive interactions, heterogeneous mechanical properties, cytoskeletal interactions, and complex loading arrangements. These biologically relevant features have important consequences for the shape mechanics of nonidealized vesicles and cells, and their study requires not simply advances in theory, but also advances in numerical simulation techniques, such as those presented here.
Coupled finite element modeling of piezothermoelastic materials
Senousy, M. S.; Rajapakse, R. K. N. D.; Gadala, M.
2007-04-01
The governing equations of piezo-thermoelastic materials show full coupling between mechanical, electric, and temperature fields. It is often assumed in the literature that in high-frequency oscillations, the coupling between the temperature and mechanical displacement and electric field is small and, therefore, can be neglected. A solution for the temperature field is then determined from an uncoupled equation. A finite element (FE) model that accounts for full coupling between the mechanical, electric, and thermal fields, nonlinear constitutive behavior and heat generation resulting from dielectric losses under alternating driving fields is under development. This paper presents a linear fully coupled model as an early development of the fully coupled nonlinear FE model. In the linear model, a solution for all field variables is obtained simultaneously and compared with the uncoupled solution. The finite element model is based on the weighted-residual principle and uses 2-D four-node isoparametric finite elements with four degrees of freedom per node. A thin piezoelectric square disk is modeled to obtain some preliminary understanding of the coupled fields in a piezoelectric stack actuator.
Finite Element Based Design and Optimization for Piezoelectric Accelerometers
DEFF Research Database (Denmark)
Liu, Bin; Kriegbaum, B.; Yao, Q.
1998-01-01
A systematic Finite Element design and optimisation procedure is implemented for the development of piezoelectric accelerometers. Most of the specifications of accelerometers can be obtained using the Finite Element simulations. The deviations between the simulated and calibrated sensitivities...
Application of finite-element-methods in food processing
DEFF Research Database (Denmark)
Risum, Jørgen
2004-01-01
Presentation of the possible use of finite-element-methods in food processing. Examples from diffusion studies are given.......Presentation of the possible use of finite-element-methods in food processing. Examples from diffusion studies are given....
Finite element modeling for materials engineers using Matlab
Oluwole, Oluleke
2014-01-01
Finite Element Modeling for Materials Engineers Using MATLAB® combines the finite element method with MATLAB to offer materials engineers a fast and code-free way of modeling for many materials processes.
Cojocaru, E.
2009-01-01
The finite element method has become a preeminent simulation technique in electromagnetics. For problems involving anisotropic media and metamaterials, proper algorithms should be developed. It has been proved that discretizing in quadratic triangular elements may lead to an improved accuracy. Here we present a collection of elemental matrices evaluated analytically for quadratic triangular elements. They could be useful for the finite element method in advanced electromagnetics.
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...
Finite element modelling of helmeted head impact under frontal ...
Indian Academy of Sciences (India)
Abstract. Finite element models of the head and helmet were used to study contact forces during frontal impact of the head with a rigid surface. The finite element model of the head consists of skin, skull, cerebro-spinal fluid (CSF), brain, tentorium and falx. The finite element model of the helmet consists of shell and foam.
Adaptive Smoothed Finite Elements (ASFEM) for history dependent material models
Quak, W.; van den Boogaard, Antonius H.; Menary, Gary
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
The Total Number of Parameters in the Finite Element ...
African Journals Online (AJOL)
Rectangular finite elements are important in Finite Element Method. This paper establishes a general formula for obtaining the total number of parameters associated with any finite element rectangulation of a domain. This number is also the dimension of the trail space as well as the size of the associated linear system.
finite element model for predicting residual stresses in shielded
African Journals Online (AJOL)
eobe
steel plates through Finite Element Model simulation and experiments. The existence of residual stresses that cause ... From the Finite Element Model Simulation, the transverse residual stress in the x. From the Finite Element Model ... cracking (SCC) and hydrogen initiated cracking (HIC). Nigerian Journal of Technology ...
Parallel direct solver for finite element modeling of manufacturing processes
DEFF Research Database (Denmark)
Nielsen, Chris Valentin; Martins, P.A.F.
2017-01-01
The central processing unit (CPU) time is of paramount importance in finite element modeling of manufacturing processes. Because the most significant part of the CPU time is consumed in solving the main system of equations resulting from finite element assemblies, different approaches have been...... developed to optimize solutions and reduce the overall computational costs of large finite element models....
Mixed Finite Element Method for Melt Migration
Taicher, A. L.; Hesse, M. A.; Arbogast, T.
2012-12-01
Multi-phase flow arises during partial melting in the earth mantle, where the porosity is small and material has the characteristics of a compacting porous medium. The equations governing multi-phase flow have been specialized to partially molten materials by McKenzie and Fowler. Their model, also called a Darcy-Stokes system, is highly coupled and non-linear. Melt flow is governed by Darcy's Law while the high temperature, ductile creep of the solid matrix is modeled using viscous non-Newtonian Stokes rheology. In addition, the melt and solid pressures are related through a compaction relation. This nearly elliptic mechanical problem is then coupled with both solute transport and thermal evolution according to the enthalpy method developed by Katz. A suitable numerical method must solve the Darcy-Stokes problem in a manner compatible with the transport problem. Moreover, unlike most porous media problems, partially molten materials transition dynamically from non-porous solid to porous medium. Therefore, a numerical method must also carefully account for the limit of zero porosity. The Darcy-Stokes system for modeling partial melting in the mantle is a novel problem. As far as we know, there currently does not exist a finite element solution in the literature solving these coupled equations. The finite element framework provides support for additional analysis of error and convergence. Moreover, both mesh refinement and anisotropy are naturally incorporated into finite elements. In particular, the mixed finite element method presents a good candidate because it works in both limiting cases: Darcy and incompressible Stokes flow. Mixed methods also produce discretely conservative fluxes that are required for the transport problem to remains stable without violating conservation of mass. Based preliminary investigations in 1D and derived energy estimates, we present a mixed formulation for the Darcy-Stokes system. Next, using novel elements of lowest order and
Finite rotation shells basic equations and finite elements for Reissner kinematics
Wisniewski, K
2010-01-01
This book covers theoretical and computational aspects of non-linear shells. Several advanced topics of shell equations and finite elements - not included in standard textbooks on finite elements - are addressed, and the book includes an extensive bibliography.
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.
Finite Element analysis of jar connections
DEFF Research Database (Denmark)
Kristensen, A.; Toor, Kashif; Solem, Sigurd
2005-01-01
A new tool joint system is considered. Traditionally these rotary connections have been designed with only one shoulder geometry. However, in order to increase the torque rating of the tool joint, a new design is introduced using two shoulders. This design allow reduced tool joint dimensions wher...... whereby down-hole equipment more easily can be fitted. In order to evaluate the validity of the design, finite element analysis have been performed in ANSYS. The results obtained indicate that the new design is valid and further tests can be performed....
Mixed finite elements for global tide models.
Cotter, Colin J; Kirby, Robert C
2016-01-01
We study mixed finite element methods for the linearized rotating shallow water equations with linear drag and forcing terms. By means of a strong energy estimate for an equivalent second-order formulation for the linearized momentum, we prove long-time stability of the system without energy accumulation-the geotryptic state. A priori error estimates for the linearized momentum and free surface elevation are given in [Formula: see text] as well as for the time derivative and divergence of the linearized momentum. Numerical results confirm the theoretical results regarding both energy damping and convergence rates.
System software for the finite element machine
Crockett, T. W.; Knott, J. D.
1985-01-01
The Finite Element Machine is an experimental parallel computer developed at Langley Research Center to investigate the application of concurrent processing to structural engineering analysis. This report describes system-level software which has been developed to facilitate use of the machine by applications researchers. The overall software design is outlined, and several important parallel processing issues are discussed in detail, including processor management, communication, synchronization, and input/output. Based on experience using the system, the hardware architecture and software design are critiqued, and areas for further work are suggested.
Finite element modeling methods for photonics
Rahman, B M Azizur
2013-01-01
The term photonics can be used loosely to refer to a vast array of components, devices, and technologies that in some way involve manipulation of light. One of the most powerful numerical approaches available to engineers developing photonic components and devices is the Finite Element Method (FEM), which can be used to model and simulate such components/devices and analyze how they will behave in response to various outside influences. This resource provides a comprehensive description of the formulation and applications of FEM in photonics applications ranging from telecommunications, astron
Generalized multiscale finite element methods: Oversampling strategies
Efendiev, Yalchin R.
2014-01-01
In this paper, we propose oversampling strategies in the generalized multiscale finite element method (GMsFEM) framework. The GMsFEM, which has been recently introduced in Efendiev et al. (2013b) [Generalized Multiscale Finite Element Methods, J. Comput. Phys., vol. 251, pp. 116-135, 2013], allows solving multiscale parameter-dependent problems at a reduced computational cost by constructing a reduced-order representation of the solution on a coarse grid. The main idea of the method consists of (1) the construction of snapshot space, (2) the construction of the offline space, and (3) construction of the online space (the latter for parameter-dependent problems). In Efendiev et al. (2013b) [Generalized Multiscale Finite Element Methods, J. Comput. Phys., vol. 251, pp. 116-135, 2013], it was shown that the GMsFEM provides a flexible tool to solve multiscale problems with a complex input space by generating appropriate snapshot, offline, and online spaces. In this paper, we develop oversampling techniques to be used in this context (see Hou and Wu (1997) where oversampling is introduced for multiscale finite element methods). It is known (see Hou and Wu (1997)) that the oversampling can improve the accuracy of multiscale methods. In particular, the oversampling technique uses larger regions (larger than the target coarse block) in constructing local basis functions. Our motivation stems from the analysis presented in this paper, which shows that when using oversampling techniques in the construction of the snapshot space and offline space, GMsFEM will converge independent of small scales and high contrast under certain assumptions. We consider the use of a multiple eigenvalue problems to improve the convergence and discuss their relation to single spectral problems that use oversampled regions. The oversampling procedures proposed in this paper differ from those in Hou and Wu (1997). In particular, the oversampling domains are partially used in constructing local
Hybrid finite difference/finite element immersed boundary method.
E Griffith, Boyce; Luo, Xiaoyu
2017-12-01
The immersed boundary method is an approach to fluid-structure interaction that uses a Lagrangian description of the structural deformations, stresses, and forces along with an Eulerian description of the momentum, viscosity, and incompressibility of the fluid-structure system. The original immersed boundary methods described immersed elastic structures using systems of flexible fibers, and even now, most immersed boundary methods still require Lagrangian meshes that are finer than the Eulerian grid. This work introduces a coupling scheme for the immersed boundary method to link the Lagrangian and Eulerian variables that facilitates independent spatial discretizations for the structure and background grid. This approach uses a finite element discretization of the structure while retaining a finite difference scheme for the Eulerian variables. We apply this method to benchmark problems involving elastic, rigid, and actively contracting structures, including an idealized model of the left ventricle of the heart. Our tests include cases in which, for a fixed Eulerian grid spacing, coarser Lagrangian structural meshes yield discretization errors that are as much as several orders of magnitude smaller than errors obtained using finer structural meshes. The Lagrangian-Eulerian coupling approach developed in this work enables the effective use of these coarse structural meshes with the immersed boundary method. This work also contrasts two different weak forms of the equations, one of which is demonstrated to be more effective for the coarse structural discretizations facilitated by our coupling approach. © 2017 The Authors International Journal for Numerical Methods in Biomedical Engineering Published by John Wiley & Sons Ltd.
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.
An algorithm for domain decomposition in finite element analysis
Al-Nasra, M.; Nguyen, D. T.
1991-01-01
A simple and efficient algorithm is described for automatic decomposition of an arbitrary finite element domain into a specified number of subdomains for finite element and substructuring analysis in a multiprocessor computer environment. The algorithm is designed to balance the work loads, to minimize the communication among processors and to minimize the bandwidths of the resulting system of equations. Small- to large-scale finite element models, which have two-node elements (truss, beam element), three-node elements (triangular element) and four-node elements (quadrilateral element), are solved on the Convex computer to illustrate the effectiveness of the proposed algorithm. A FORTRAN computer program is also included.
Finite element analysis of multilayer coextrusion.
Energy Technology Data Exchange (ETDEWEB)
Hopkins, Matthew Morgan; Schunk, Peter Randall; Baer, Thomas A. (Proctor & Gamble Company, West Chester, OH); Mrozek, Randy A. (Army Research Laboratory, Adelphi, MD); Lenhart, Joseph Ludlow (Army Research Laboratory, Adelphi, MD); Rao, Rekha Ranjana; Collins, Robert (Oak Ridge National Laboratory); Mondy, Lisa Ann
2011-09-01
Multilayer coextrusion has become a popular commercial process for producing complex polymeric products from soda bottles to reflective coatings. A numerical model of a multilayer coextrusion process is developed based on a finite element discretization and two different free-surface methods, an arbitrary-Lagrangian-Eulerian (ALE) moving mesh implementation and an Eulerian level set method, to understand the moving boundary problem associated with the polymer-polymer interface. The goal of this work is to have a numerical capability suitable for optimizing and troubleshooting the coextrusion process, circumventing flow instabilities such as ribbing and barring, and reducing variability in layer thickness. Though these instabilities can be both viscous and elastic in nature, for this work a generalized Newtonian description of the fluid is used. Models of varying degrees of complexity are investigated including stability analysis and direct three-dimensional finite element free surface approaches. The results of this work show how critical modeling can be to reduce build test cycles, improve material choices, and guide mold design.
Mixed Finite Element Methods for Melt Migration
Taicher, A. L.
2013-12-01
Multi-phase flow arises during partial melting in the earth mantle, where the porosity is small and material has the characteristics of a compacting porous medium. The equations governing multi-phase flow have been specialized to partially molten materials by McKenzie and Fowler. Their model, also called a Darcy-Stokes system, is highly coupled and non-linear. Melt flow is governed by Darcy's Law while the high temperature, ductile creep of the solid matrix is modeled using viscous non-Newtonian Stokes rheology. In addition, the melt and solid pressures are related through a compaction relation. This nearly elliptic mechanical problem is then coupled with both solute transport and thermal evolution according to the enthalpy method developed by Katz. A suitable numerical method must solve the Darcy-Stokes problem in a manner compatible with the transport problem. Moreover, unlike most porous media problems, partially molten materials transition dynamically from non-porous solid to porous medium so must carefully account for the limit of zero porosity. The Darcy-Stokes system for modeling partial melting in the mantle is a novel problem. As far as we know, there currently does not exist a finite element solution in the literature solving these coupled equations. In particular, the mixed finite element method presents a good candidate because it works in both limiting cases: Darcy and incompressible Stokes flow. We present a mixed formulation for the Darcy-Stokes system. Next, we present novel elements of lowest order and compatible with both Darcy and Stokes flow Finally, we present our 2D mixed FEM code result for solving Stokes and Darcy flow as well as the coupled Darcy-Stokes system the mid-ocean ridge or corner flow problem.
Primitive elements in finite fields with arbitrary trace
Çoban, Mustafa; Coban, Mustafa
2003-01-01
Arithmetic of finite fields is not only important for other branches of mathematics but also widely used in applications such as coding and cryptography. A primitive element of a finite field is of particular interest since it enables one to represent all other elements of the field. Therefore an extensive research has been done on primitive elements, especially those satisfying extra conditions. We are interested in the existence of primitive elements in extensions of finite fields with pres...
Patient-specific finite element modeling of bones.
Poelert, Sander; Valstar, Edward; Weinans, Harrie; Zadpoor, Amir A
2013-04-01
Finite element modeling is an engineering tool for structural analysis that has been used for many years to assess the relationship between load transfer and bone morphology and to optimize the design and fixation of orthopedic implants. Due to recent developments in finite element model generation, for example, improved computed tomography imaging quality, improved segmentation algorithms, and faster computers, the accuracy of finite element modeling has increased vastly and finite element models simulating the anatomy and properties of an individual patient can be constructed. Such so-called patient-specific finite element models are potentially valuable tools for orthopedic surgeons in fracture risk assessment or pre- and intraoperative planning of implant placement. The aim of this article is to provide a critical overview of current themes in patient-specific finite element modeling of bones. In addition, the state-of-the-art in patient-specific modeling of bones is compared with the requirements for a clinically applicable patient-specific finite element method, and judgment is passed on the feasibility of application of patient-specific finite element modeling as a part of clinical orthopedic routine. It is concluded that further development in certain aspects of patient-specific finite element modeling are needed before finite element modeling can be used as a routine clinical tool.
Composite finite element solutions for neutron transport
Energy Technology Data Exchange (ETDEWEB)
Ackroyd, R.T.; Wilson, W.E.
1988-01-01
Composite solutions for neutron transport employ a finite element representation for a spatial dependence of the angular flux and spherical-harmonic expansions for its directional dependence. The orders of the spherical harmonic expansions are varied from region to region, according to the physical characteristics of the regions, so that the massive calculations inherent with high-order expansions can be confined to the regions for which they are essential. The transitions from low- to high-order expansions are made at the interfaces of elements. The K/sup +-/ boundary-free maximum principle provides a convenient means of optimizing a composite approximate solution for the angular flux. The way in which penalty weighting of interfaces is used to optimize composite solutions is investigated theoretically and numerically. The method is illustrated by solutions of two benchmark problems. An estimate for penalty weightings is obtained by deriving a central difference analogue of the even-parity transport equation. This provides also a demonstration of the use of admissible, wildly nonconforming elements in a maximum principle.
Adaptive finite element methods for differential equations
Bangerth, Wolfgang
2003-01-01
These Lecture Notes discuss concepts of `self-adaptivity' in the numerical solution of differential equations, with emphasis on Galerkin finite element methods. The key issues are a posteriori error estimation and it automatic mesh adaptation. Besides the traditional approach of energy-norm error control, a new duality-based technique, the Dual Weighted Residual method for goal-oriented error estimation, is discussed in detail. This method aims at economical computation of arbitrary quantities of physical interest by properly adapting the computational mesh. This is typically required in the design cycles of technical applications. For example, the drag coefficient of a body immersed in a viscous flow is computed, then it is minimized by varying certain control parameters, and finally the stability of the resulting flow is investigated by solving an eigenvalue problem. `Goal-oriented' adaptivity is designed to achieve these tasks with minimal cost. At the end of each chapter some exercises are posed in order ...
Finite-Element Modelling of Biotransistors
Directory of Open Access Journals (Sweden)
Selvaganapathy PR
2010-01-01
Full Text Available Abstract Current research efforts in biosensor design attempt to integrate biochemical assays with semiconductor substrates and microfluidic assemblies to realize fully integrated lab-on-chip devices. The DNA biotransistor (BioFET is an example of such a device. The process of chemical modification of the FET and attachment of linker and probe molecules is a statistical process that can result in variations in the sensed signal between different BioFET cells in an array. In order to quantify these and other variations and assess their importance in the design, complete physical simulation of the device is necessary. Here, we perform a mean-field finite-element modelling of a short channel, two-dimensional BioFET device. We compare the results of this model with one-dimensional calculation results to show important differences, illustrating the importance of the molecular structure, placement and conformation of DNA in determining the output signal.
Adaptive finite element method for shape optimization
Morin, Pedro
2012-01-16
We examine shape optimization problems in the context of inexact sequential quadratic programming. Inexactness is a consequence of using adaptive finite element methods (AFEM) to approximate the state and adjoint equations (via the dual weighted residual method), update the boundary, and compute the geometric functional. We present a novel algorithm that equidistributes the errors due to shape optimization and discretization, thereby leading to coarse resolution in the early stages and fine resolution upon convergence, and thus optimizing the computational effort. We discuss the ability of the algorithm to detect whether or not geometric singularities such as corners are genuine to the problem or simply due to lack of resolution - a new paradigm in adaptivity. © EDP Sciences, SMAI, 2012.
Immersed molecular electrokinetic finite element method
Kopacz, Adrian M.; Liu, Wing K.
2013-07-01
A unique simulation technique has been developed capable of modeling electric field induced detection of biomolecules such as viruses, at room temperatures where thermal fluctuations must be considered. The proposed immersed molecular electrokinetic finite element method couples electrokinetics with fluctuating hydrodynamics to study the motion and deformation of flexible objects immersed in a suspending medium under an applied electric field. The force induced on an arbitrary object due to an electric field is calculated based on the continuum electromechanics and the Maxwell stress tensor. The thermal fluctuations are included in the Navier-Stokes fluid equations via the stochastic stress tensor. Dielectrophoretic and fluctuating forces acting on the particle are coupled through the fluid-structure interaction force calculated within the surrounding environment. This method was used to perform concentration and retention efficacy analysis of nanoscale biosensors using gold particles of various sizes. The analysis was also applied to a human papillomavirus.
Finite Element Based Viscous Numerical Wave Flume
Directory of Open Access Journals (Sweden)
Jianmin Qin
2013-01-01
Full Text Available A two-dimensional numerical wave flume (NWF for viscous fluid flows with free surface is developed in this work. It is based on the upwind finite element solutions of Navier-Stokes equations, CLEAR-volume of fluid method for free surface capture, internal wave maker for wave generation, and sponge layer for wave absorbing. The wave generation and absorption by prescribing velocity boundary conditions along inlet and radiation boundary condition along outlet are also incorporated. The numerical model is validated against several benchmarks, including dam-breaking flow, liquid sloshing in baffled tank, linear water wave propagation and reflection from vertical wall, nonlinear solitary wave fission over sharp step, and wave-induced fluid resonance in narrow gap confined by floating structures. The comparisons with available experimental data, numerical results, and theoretical solutions confirm that the present numerical wave flume has good performance in dealing with complex interface flows and water wave interaction with structures.
Friction welding; Magnesium; Finite element; Shear test.
Directory of Open Access Journals (Sweden)
Leonardo Contri Campanelli
2013-06-01
Full Text Available Friction spot welding (FSpW is one of the most recently developed solid state joining technologies. In this work, based on former publications, a computer aided draft and engineering resource is used to model a FSpW joint on AZ31 magnesium alloy sheets and subsequently submit the assembly to a typical shear test loading, using a linear elastic model, in order to conceive mechanical tests results. Finite element analysis shows that the plastic flow is concentrated on the welded zone periphery where yield strength is reached. It is supposed that “through the weld” and “circumferential pull-out” variants should be the main failure behaviors, although mechanical testing may provide other types of fracture due to metallurgical features.
An advanced finite element model of IPMC
Pugal, D.; Kasemägi, H.; Kruusmaa, M.; Aabloo, A.
2008-03-01
This paper presents an electro-mechanical Finite Element Model of an ionic polymer-metal composite (IPMC) material. Mobile counter ions inside the polymer are drifted by an applied electric field, causing mass imbalance inside the material. This is the main cause of the bending motion of this kind of materials. All foregoing physical effects have been considered as time dependent and modeled with FEM. Time dependent mechanics is modeled with continuum mechanics equations. The model also considers the fact that there is a surface of platinum on both sides of the polymer backbone. The described basic model has been under developement for a while and has been improved over the time. Simulation comparisons with experimental data have shown good harmony. Our previous paper described most of the basic model. Additionally, the model was coupled with equations, which described self-oscillatory behavior of the IPMC material. It included describing electrochemical processes with additional four differential equations. The Finite Element Method turned out to be very reasonable for coupling together and solving all equations as a single package. We were able to achieve reasonably precise model to describe this complicated phenomenon. Our most recent goal has been improving the basic model. Studies have shown that some electrical parameters of an IPMC, such as surface resistance and voltage drop are dependent on the curvature of the IPMC. Therefore the new model takes surface resistance into account to some extent. It has added an extra level of complexity to the model, because now all simulations are done in three dimensional domain. However, the result is advanced visual and numerical behavior of an IPMC with different surface characteristics.
The computation of linear triangular matrices in the finite element ...
African Journals Online (AJOL)
An algorithm is developed for generating the system matrices for the Finite Element Method of solving some classes of second order partial differential equations problems using the linear triangular elements. This algorithm reduces the complexity normally associated with the finite element approximation and makes the ...
Finite element analysis theory and application with ANSYS
Moaveni, Saeed
2015-01-01
For courses in Finite Element Analysis, offered in departments of Mechanical or Civil and Environmental Engineering. While many good textbooks cover the theory of finite element modeling, Finite Element Analysis: Theory and Application with ANSYS is the only text available that incorporates ANSYS as an integral part of its content. Moaveni presents the theory of finite element analysis, explores its application as a design/modeling tool, and explains in detail how to use ANSYS intelligently and effectively. Teaching and Learning Experience This program will provide a better teaching and learning experience-for you and your students. It will help: *Present the Theory of Finite Element Analysis: The presentation of theoretical aspects of finite element analysis is carefully designed not to overwhelm students. *Explain How to Use ANSYS Effectively: ANSYS is incorporated as an integral part of the content throughout the book. *Explore How to Use FEA as a Design/Modeling Tool: Open-ended design problems help stude...
A stabilised nonconforming finite element method for steady incompressible flows
Huang, Pengzhan; Feng, Xinlong; Liu, Demin
2012-02-01
A stabilised nonconforming finite element method for the steady incompressible flow problem with damping based on local Gauss integration is considered in this article. The method combines the nonconforming finite element method with the stabilised strategy. Moreover, the stability and error estimates are analysed. Finally, numerical results are shown to support the developed theory analysis. Compared with some classical, closely related mixed finite element methods, the results of the present method show its better performance than others.
The finite element method its basis and fundamentals
Zienkiewicz, Olek C; Zhu, JZ
2013-01-01
The Finite Element Method: Its Basis and Fundamentals offers a complete introduction to the basis of the finite element method, covering fundamental theory and worked examples in the detail required for readers to apply the knowledge to their own engineering problems and understand more advanced applications. This edition sees a significant rearrangement of the book's content to enable clearer development of the finite element method, with major new chapters and sections added to cover: Weak forms Variational forms Multi-dimensional field prob
Leapfrog/finite element method for fractional diffusion equation.
Zhao, Zhengang; Zheng, Yunying
2014-01-01
We analyze a fully discrete leapfrog/Galerkin finite element method for the numerical solution of the space fractional order (fractional for simplicity) diffusion equation. The generalized fractional derivative spaces are defined in a bounded interval. And some related properties are further discussed for the following finite element analysis. Then the fractional diffusion equation is discretized in space by the finite element method and in time by the explicit leapfrog scheme. For the resulting fully discrete, conditionally stable scheme, we prove an L (2)-error bound of finite element accuracy and of second order in time. Numerical examples are included to confirm our theoretical analysis.
Introduction to finite element analysis using MATLAB and Abaqus
Khennane, Amar
2013-01-01
There are some books that target the theory of the finite element, while others focus on the programming side of things. Introduction to Finite Element Analysis Using MATLAB(R) and Abaqus accomplishes both. This book teaches the first principles of the finite element method. It presents the theory of the finite element method while maintaining a balance between its mathematical formulation, programming implementation, and application using commercial software. The computer implementation is carried out using MATLAB, while the practical applications are carried out in both MATLAB and Abaqus. MA
Ablative Thermal Response Analysis Using the Finite Element Method
Dec John A.; Braun, Robert D.
2009-01-01
A review of the classic techniques used to solve ablative thermal response problems is presented. The advantages and disadvantages of both the finite element and finite difference methods are described. As a first step in developing a three dimensional finite element based ablative thermal response capability, a one dimensional computer tool has been developed. The finite element method is used to discretize the governing differential equations and Galerkin's method of weighted residuals is used to derive the element equations. A code to code comparison between the current 1-D tool and the 1-D Fully Implicit Ablation and Thermal Response Program (FIAT) has been performed.
Wheeler, M.F.
2010-09-06
For many years there have been formulations considered for modeling single phase ow on general hexahedra grids. These include the extended mixed nite element method, and families of mimetic nite di erence methods. In most of these schemes either no rate of convergence of the algorithm has been demonstrated both theoret- ically and computationally or a more complicated saddle point system needs to be solved for an accurate solution. Here we describe a multipoint ux mixed nite element (MFMFE) method [5, 2, 3]. This method is motivated from the multipoint ux approximation (MPFA) method [1]. The MFMFE method is locally conservative with continuous ux approximations and is a cell-centered scheme for the pressure. Compared to the MPFA method, the MFMFE has a variational formulation, since it can be viewed as a mixed nite element with special approximating spaces and quadrature rules. The framework allows han- dling of hexahedral grids with non-planar faces by applying trilinear mappings from physical elements to reference cubic elements. In addition, there are several multi- scale and multiphysics extensions such as the mortar mixed nite element method that allows the treatment of non-matching grids [4]. Extensions to the two-phase oil-water ow are considered. We reformulate the two- phase model in terms of total velocity, capillary velocity, water pressure, and water saturation. We choose water pressure and water saturation as primary variables. The total velocity is driven by the gradient of the water pressure and total mobility. Iterative coupling scheme is employed for the coupled system. This scheme allows treatments of di erent time scales for the water pressure and water saturation. In each time step, we rst solve the pressure equation using the MFMFE method; we then Center for Subsurface Modeling, The University of Texas at Austin, Austin, TX 78712; mfw@ices.utexas.edu. yCenter for Subsurface Modeling, The University of Texas at Austin, Austin, TX 78712; gxue
A coupling procedure for modeling acoustic problems using finite elements and boundary elements
Coyette, J.; Vanderborck, G.; Steichen, W.
1994-01-01
Finite element (FEM) and boundary element (BEM) methods have been used for a long time for the numerical simulation of acoustic problems. The development presented in this paper deals with a general procedure for coupling acoustic finite elements with acoustic boundary elements in order to solve efficiently acoustic problems involving non homogeneous fluids. Emphasis is made on problems where finite elements are used for a confined (bounded) fluid while boundary elements are selected for an e...
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
, of fixed type i.e., an element selected for a specific application and with a given dof configuration. Sze (1996). Admissible matrix formulation for efficient construction of multifield finite element models which employ patch test to identify the con-.
A Finite Element Analysis of Optimal Variable Thickness Sheets
DEFF Research Database (Denmark)
Petersson, Joakim S
1996-01-01
A quasimixed Finite Element (FE) method for maximum stiffness of variablethickness sheets is analysed. The displacement is approximated with ninenode Lagrange quadrilateral elements and the thickness is approximated aselementwise constant. One is guaranteed that the FE displacement solutionswill...
Finite element modelling of composite castellated beam
Directory of Open Access Journals (Sweden)
Frans Richard
2017-01-01
Full Text Available Nowadays, castellated beam becomes popular in building structural as beam members. This is due to several advantages of castellated beam such as increased depth without any additional mass, passing the underfloor service ducts without changing of story elevation. However, the presence of holes can develop various local effects such as local buckling, lateral torsional buckling caused by compression force at the flange section of the steel beam. Many studies have investigated the failure mechanism of castellated beam and one technique which can prevent the beam fall into local failure is the use of reinforced concrete slab as lateral support on castellated beam, so called composite castellated beam. Besides of preventing the local failure of castellated beam, the concrete slab can increase the plasticity moment of the composite castellated beam section which can deliver into increasing the ultimate load of the beam. The aim of this numerical studies of composite castellated beam on certain loading condition (monotonic quasi-static loading. ABAQUS was used for finite element modelling purpose and compared with the experimental test for checking the reliability of the model. The result shows that the ultimate load of the composite castellated beam reached 6.24 times than the ultimate load of the solid I beam and 1.2 times compared the composite beam.
FINITE ELEMENT ANALYSIS OF WOOD ADHESIVE JOINTS
Directory of Open Access Journals (Sweden)
Thomas GEREKE
2016-03-01
Full Text Available Engineered wood products such as glulam or cross-laminated timber are widely established in the construction industry. Their structural behaviour and reliability clearly bases on the adhesive bonding. In order to understand and improve the performance of glued wood members a finite element modelling of standard single lap shear samples was carried out. A three-dimensional model of a longitudinal tensile-shear specimen with quasi-centric load application was developed. The main influences of wood and adhesive parameters on structural performance were identified. Therefore, variations of the elasticity, the annual ring angle, fibre angle, and the interface zone and their effect on the occurring stresses in the adhesive bond line were investigated numerically. The adhesive bond line is most significantly sensitive to the Young´s modulus of the adhesive itself. A variation of the fibre angle of the glued members in the standard test is an essential criterion and to be considered when preparing lap shear specimens. A model with representation of early- and latewood gives a more detailed insight into wooden adhesive joints.
Finite element modelling of X-band RF flanges
Kortelainen, Laurie; Riddone, Germana
A finite element model of different versions of RF flange used in Compact Linear Collider modules was created in ANSYS Workbench software. A 2D idealisation of the assembly was modelled using both plane stress and plane strain elements. Three of the versions were also modelled using 3D elements. A detailed description of finite element models and theoretical background accompanying the models are presented in this thesis.
Hydrothermal analysis in engineering using control volume finite element method
Sheikholeslami, Mohsen
2015-01-01
Control volume finite element methods (CVFEM) bridge the gap between finite difference and finite element methods, using the advantages of both methods for simulation of multi-physics problems in complex geometries. In Hydrothermal Analysis in Engineering Using Control Volume Finite Element Method, CVFEM is covered in detail and applied to key areas of thermal engineering. Examples, exercises, and extensive references are used to show the use of the technique to model key engineering problems such as heat transfer in nanofluids (to enhance performance and compactness of energy systems),
Viscoelastic finite-element analysis of human skull - dura mater ...
African Journals Online (AJOL)
SERVER
2008-03-18
Mar 18, 2008 ... Key words: Viscoelasticity, finite-element analysis (FEA), strain, human skull, dura mater, intracranial pressure. INTRODUCTION. Intracranial pressure (ICP) is the ... We presented the development and validation of a 3D finite-element model intended to better understand the deformation mechanisms of ...
An optimal adaptive finite element method for the Stokes problem
Kondratyuk, Y.; Stevenson, R.
2008-01-01
A new adaptive finite element method for solving the Stokes equations is developed, which is shown to converge with the best possible rate. The method consists of 3 nested loops. The outermost loop consists of an adaptive finite element method for solving the pressure from the (elliptic) Schur
THE PRACTICAL ANALYSIS OF FINITE ELEMENTS METHOD ERRORS
Directory of Open Access Journals (Sweden)
Natalia Bakhova
2011-03-01
Full Text Available Abstract. The most important in the practical plan questions of reliable estimations of finite elementsmethod errors are considered. Definition rules of necessary calculations accuracy are developed. Methodsand ways of the calculations allowing receiving at economical expenditures of computing work the best finalresults are offered.Keywords: error, given the accuracy, finite element method, lagrangian and hermitian elements.
Finite elements modeling of delaminations in composite laminates
DEFF Research Database (Denmark)
Gaiotti, m.; Rizzo, C.M.; Branner, Kim
2011-01-01
The application of composite materials in many structures poses to engineers the problem to create reliable and relatively simple methods, able to estimate the strength of multilayer composite structures. Multilayer composites, like other laminated materials, suffer from layer separation, i.e., d...... by finite elements using different techniques. Results obtained with different finite element models are compared and discussed....
Finite element approach to solution of multidimensional quasi ...
African Journals Online (AJOL)
The functional of a stress field function was established using mixed methods analogous to variational principle, minimum total potential principle and finite element method. The functional of function, Φ(x,y) was formed using Euler equivalent integral and finite element shape function for a function expressed in derivative ...
Finite element analysis of tubular joints in offshore structures ...
African Journals Online (AJOL)
This research work was involved in the finite element tool to determine the ultimate strength of initially uncorked joints, which fail by development of tearing fracture at the weld toe. The local approach methodology in contrast to classical fracture mechanics was used. Finite element analysis was done of T-joint plate ...
About the Finite Element Method Applied to Thick Plates
Directory of Open Access Journals (Sweden)
Mihaela Ibănescu
2006-01-01
Full Text Available The present paper approaches of plates subjected to transverse loads, when the shear force and the actual boundary conditions are considered, by using the Finite Element Method. The isoparametric finite elements create real facilities in formulating the problems and great possibilities in creating adequate computer programs.
A cohesive finite element formulation for modelling fracture and ...
Indian Academy of Sciences (India)
Abstract. In recent years, cohesive zone models have been employed to simulate fracture and delamination in solids. This paper presents in detail the formulation for incorporating cohesive zone models within the framework of a large deformation finite element procedure. A special Ritz-finite element technique is employed ...
Geotechnical Ultimate Limit State Design Using Finite Elements
Brinkgreve, R.B.J.; Post, M.
2015-01-01
Displacement-based finite element calculations are primarily used for serviceability limit state (SLS) analysis, but the finite element method also offers possibilities for ultimate limit state (ULS) design in geotechnical engineering. The combined use of SLS and ULS calculations with partial safety
Analysis of Tube Drawing Process – A Finite Element Approach ...
African Journals Online (AJOL)
In this paper the effect of die semi angle on drawing load in cold tube drawing has been investigated numerically using the finite element method. The equation governing the stress distribution was derived and solved using Galerkin finite element method. An isoparametric formulation for the governing equation was utilized ...
Viscoelastic finite-element analysis of human skull - dura mater ...
African Journals Online (AJOL)
In the work, the dynamic characteristics of the human skull-dura mater system were studied. For the purpose of our analysis, we adopted a model consisted of a hollow sphere. By using the 'Patran and. Ansys' finite element processor, a simplified three-dimensional finite element model (FEM) of a human skull was ...
A cohesive finite element formulation for modelling fracture and ...
Indian Academy of Sciences (India)
In recent years, cohesive zone models have been employed to simulate fracture and delamination in solids. This paper presents in detail the formulation for incorporating cohesive zone models within the framework of a large deformation finite element procedure. A special Ritz-finite element technique is employed to control ...
Finite size effects of a pion matrix element
Energy Technology Data Exchange (ETDEWEB)
Guagnelli, M. [Dipartimento di Fisica, Universita di Roma Tor Vergata and INFN, Sezione di Roma II, Via della Ricerca Scientifica 1, I-00133 Rome (Italy); Jansen, K. [NIC/DESY Zeuthen, Platanenallee 6, D-15738 Zeuthen (Germany); Palombi, F. [Dipartimento di Fisica, Universita di Roma Tor Vergata and INFN, Sezione di Roma II, Via della Ricerca Scientifica 1, I-00133 Rome (Italy); E. Fermi Research Center, c/o Compendio Viminale, pal. F, I-00184 Rome (Italy); Petronzio, R. [Dipartimento di Fisica, Universita di Roma Tor Vergata and INFN, Sezione di Roma II, Via della Ricerca Scientifica 1, I-00133 Rome (Italy); Shindler, A. [NIC/DESY Zeuthen, Platanenallee 6, D-15738 Zeuthen (Germany); Wetzorke, I. [NIC/DESY Zeuthen, Platanenallee 6, D-15738 Zeuthen (Germany)]. E-mail: ines.wetzorke@desy.de
2004-09-09
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.
Finite Element analyses of soil bioengineered slopes
Tamagnini, Roberto; Switala, Barbara Maria; Sudan Acharya, Madhu; Wu, Wei; Graf, Frank; Auer, Michael; te Kamp, Lothar
2014-05-01
Soil Bioengineering methods are not only effective from an economical point of view, but they are also interesting as fully ecological solutions. The presented project is aimed to define a numerical model which includes the impact of vegetation on slope stability, considering both mechanical and hydrological effects. In this project, a constitutive model has been developed that accounts for the multi-phase nature of the soil, namely the partly saturated condition and it also includes the effects of a biological component. The constitutive equation is implemented in the Finite Element (FE) software Comes-Geo with an implicit integration scheme that accounts for the collapse of the soils structure due to wetting. The mathematical formulation of the constitutive equations is introduced by means of thermodynamics and it simulates the growth of the biological system during the time. The numerical code is then applied in the analysis of an ideal rainfall induced landslide. The slope is analyzed for vegetated and non-vegetated conditions. The final results allow to quantitatively assessing the impact of vegetation on slope stability. This allows drawing conclusions and choosing whenever it is worthful to use soil bioengineering methods in slope stabilization instead of traditional approaches. The application of the FE methods show some advantages with respect to the commonly used limit equilibrium analyses, because it can account for the real coupled strain-diffusion nature of the problem. The mechanical strength of roots is in fact influenced by the stress evolution into the slope. Moreover, FE method does not need a pre-definition of any failure surface. FE method can also be used in monitoring the progressive failure of the soil bio-engineered system as it calculates the amount of displacements and strains of the model slope. The preliminary study results show that the formulated equations can be useful for analysis and evaluation of different soil bio
Finite Element Analysis of Fluid-Conveying Timoshenko Pipes
Directory of Open Access Journals (Sweden)
Chih-Liang Chu
1995-01-01
Full Text Available A general finite element formulation using cubic Hermitian interpolation for dynamic analysis of pipes conveying fluid is presented. Both the effects of shearing deformations and rotary inertia are considered. The development retains the use of the classical four degrees-of-freedom for a two-node element. The effect of moving fluid is treated as external distributed forces on the support pipe and the fluid finite element matrices are derived from the virtual work done due to the fluid inertia forces. Finite element matrices for both the support pipe and moving fluid are derived and given explicitly. A numerical example is given to demonstrate the validity of the model.
Wave Scattering in Heterogeneous Media using the Finite Element Method
2016-10-21
AFRL-AFOSR-JP-TR-2016-0086 Wave Scattering in Heterogeneous Media using the Finite Element Method Chiruvai Vendhan INDIAN INSTITUTE OF TECHNOLOGY...Scattering in Heterogeneous Media using the Finite Element Method 5a. CONTRACT NUMBER 5b. GRANT NUMBER FA2386-12-1-4026 5c. PROGRAM ELEMENT NUMBER 61102F 6...heterogeneous ocean acoustic waveguide. 15. SUBJECT TERMS Acoustics, Finite Element Methods , Wave propagation 16. SECURITY CLASSIFICATION OF: 17
Hermitian Mindlin Plate Wavelet Finite Element Method for Load Identification
Xiaofeng Xue; Xuefeng Chen; Xingwu Zhang; Baijie Qiao; Jia Geng
2016-01-01
A new Hermitian Mindlin plate wavelet element is proposed. The two-dimensional Hermitian cubic spline interpolation wavelet is substituted into finite element functions to construct frequency response function (FRF). It uses a system’s FRF and response spectrums to calculate load spectrums and then derives loads in the time domain via the inverse fast Fourier transform. By simulating different excitation cases, Hermitian cubic spline wavelets on the interval (HCSWI) finite elements are used t...
Gleadall, Andrew; Pan, Jingzhe; Ding, Lifeng; Kruft, Marc-Anton; Curcó, David
2015-11-01
Molecular dynamics (MD) simulations are widely used to analyse materials at the atomic scale. However, MD has high computational demands, which may inhibit its use for simulations of structures involving large numbers of atoms such as amorphous polymer structures. An atomic-scale finite element method (AFEM) is presented in this study with significantly lower computational demands than MD. Due to the reduced computational demands, AFEM is suitable for the analysis of Young's modulus of amorphous polymer structures. This is of particular interest when studying the degradation of bioresorbable polymers, which is the topic of an accompanying paper. AFEM is derived from the inter-atomic potential energy functions of an MD force field. The nonlinear MD functions were adapted to enable static linear analysis. Finite element formulations were derived to represent interatomic potential energy functions between two, three and four atoms. Validation of the AFEM was conducted through its application to atomic structures for crystalline and amorphous poly(lactide). Copyright © 2015 Elsevier Ltd. All rights reserved.
A finite element calculation of flux pumping
Campbell, A. M.
2017-12-01
A flux pump is not only a fascinating example of the power of Faraday’s concept of flux lines, but also an attractive way of powering superconducting magnets without large electronic power supplies. However it is not possible to do this in HTS by driving a part of the superconductor normal, it must be done by exceeding the local critical density. The picture of a magnet pulling flux lines through the material is attractive, but as there is no direct contact between flux lines in the magnet and vortices, unless the gap between them is comparable to the coherence length, the process must be explicable in terms of classical electromagnetism and a nonlinear V–I characteristic. In this paper a simple 2D model of a flux pump is used to determine the pumping behaviour from first principles and the geometry. It is analysed with finite element software using the A formulation and FlexPDE. A thin magnet is passed across one or more superconductors connected to a load, which is a large rectangular loop. This means that the self and mutual inductances can be calculated explicitly. A wide strip, a narrow strip and two conductors are considered. Also an analytic circuit model is analysed. In all cases the critical state model is used, so the flux flow resistivity and dynamic resistivity are not directly involved, although an effective resistivity appears when J c is exceeded. In most of the cases considered here is a large gap between the theory and the experiments. In particular the maximum flux transferred to the load area is always less than the flux of the magnet. Also once the threshold needed for pumping is exceeded the flux in the load saturates within a few cycles. However the analytic circuit model allows a simple modification to allow for the large reduction in I c when the magnet is over a conductor. This not only changes the direction of the pumped flux but leads to much more effective pumping.
Ruiz-Baier, Ricardo; Lunati, Ivan
2016-10-01
We present a novel discretization scheme tailored to a class of multiphase models that regard the physical system as consisting of multiple interacting continua. In the framework of mixture theory, we consider a general mathematical model that entails solving a system of mass and momentum equations for both the mixture and one of the phases. The model results in a strongly coupled and nonlinear system of partial differential equations that are written in terms of phase and mixture (barycentric) velocities, phase pressure, and saturation. We construct an accurate, robust and reliable hybrid method that combines a mixed finite element discretization of the momentum equations with a primal discontinuous finite volume-element discretization of the mass (or transport) equations. The scheme is devised for unstructured meshes and relies on mixed Brezzi-Douglas-Marini approximations of phase and total velocities, on piecewise constant elements for the approximation of phase or total pressures, as well as on a primal formulation that employs discontinuous finite volume elements defined on a dual diamond mesh to approximate scalar fields of interest (such as volume fraction, total density, saturation, etc.). As the discretization scheme is derived for a general formulation of multicontinuum physical systems, it can be readily applied to a large class of simplified multiphase models; on the other, the approach can be seen as a generalization of these models that are commonly encountered in the literature and employed when the latter are not sufficiently accurate. An extensive set of numerical test cases involving two- and three-dimensional porous media are presented to demonstrate the accuracy of the method (displaying an optimal convergence rate), the physics-preserving properties of the mixed-primal scheme, as well as the robustness of the method (which is successfully used to simulate diverse physical phenomena such as density fingering, Terzaghi's consolidation
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......Several Carbon Fibre Reinforced Polymers (CFRP) systems have been used successfully for strengthening of structures during the last decades. However, the fracture often occurs in the concrete adherent or in the adhesive interface when used for steel strengthening. As a consequence the CFRP...
A finite element conjugate gradient FFT method for scattering
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.
Finite element solution algorithm for incompressible fluid dynamics
Baker, A. J.
1974-01-01
A finite element solution algorithm is established for the two-dimensional Navier-Stokes equations governing the transient motion of a viscous incompressible fluid, i.e., hydrodynamics. Dependent variable transformation renders the differential equation description uniformly elliptic. The finite element algorithm is established using the Galerkin criterion on a local basis within the Method of Weighted Residuals. It is unconstrained with respect to system linearity, computational mesh uniformity or solution domain closure regularity. The finite element matrices are established using a linear 'natural coordinate function' description. Computational solutions using the COMOC computer program illustrate the various features of the algorithm including recirculating flows.
Finite Element Method for Analysis of Material Properties
DEFF Research Database (Denmark)
Rauhe, Jens Christian
The use of cellular and composite materials have in recent years become more and more common in all kinds of structural components and accurate knowledge of the effective properties is therefore essential. In this wok the effective properties are determined using the real material microstructure...... theoretical models. Besides the determination of the effective properties, viscoelastic and damage analysis have been performed on a number of material microstructures....... description of the material microstructure the finite element models must contain a large number of elements and this problem is solved by using the preconditioned conjugated gradient solver with an Element-By-Element preconditioner. Finite element analysis provides the volume averaged stresses and strains...
Page 1 Dynamic behaviour of the Timoshenko beam finite elements ...
Indian Academy of Sciences (India)
Dynamic behaviour of the Timoshenko beam finite elements 193. For quadratic interpolation of both w and @x, the element matrices are of the order 6 × 6 for pure bending case. Interdependent interpolation element (IIE): For this case, the stiffness matrix and load. Vector are given in (25) [and the same as in (74)]. The mass ...
High convergence order finite elements with lumped mass matrix
DEFF Research Database (Denmark)
Jensen, Morten skårup
1996-01-01
A method for deriving hexahedral finite elements with lumped mass matrices for three-dimensional problems is presented. These elements meet the theoretical conditions for high order convergence, and two numerical examples based on the three-dimensional scalar wave equation show that this is also...... the case in practice and that their accuracy is comparable to elements with consistent mass matrices....
Validating Finite Element Models of Assembled Shell Structures
Hoff, Claus
2006-01-01
The validation of finite element models of assembled shell elements is presented. The topics include: 1) Problems with membrane rotations in assembled shell models; 2) Penalty stiffness for membrane rotations; 3) Physical stiffness for membrane rotations using shell elements with 6 dof per node; and 4) Connections avoiding rotations.
Finite element modelling of helmeted head impact under frontal ...
Indian Academy of Sciences (India)
Finite element models of the head and helmet were used to study contact forces during frontal impact of the head with a rigid surface. The ﬁnite element model of the head consists of skin, skull, cerebro-spinal ﬂuid (CSF), brain, tentorium and falx. The ﬁnite element model of the helmet consists of shell and foam liner.
Reliable finite element methods for self-adjoint singular perturbation ...
African Journals Online (AJOL)
It is well known that the standard finite element method based on the space Vh of continuous piecewise linear functions is not reliable in solving singular perturbation problems. It is also known that the solution of a two-point boundaryvalue singular perturbation problem admits a decomposition into a regular part and a finite ...
Finite element analysis of bending performance on polyurethane composite panel
Jia, Minli; Li, Hongqiao; Wang, Xiaoming
2017-09-01
The finite element analysis model of polyurethane composite panel (simply named PCP) is established by using ABAQUS software. In view of the PCPs made of different thickness of surface board, their bending performance is carried out on finite element analysis, and the load-deflection curves which come from it are compared with the experimental results. The results show that the values between finite element analysis and experiment agree well with each other. It can be deduced that the established finite element model is fit to simulate the bending test of PCPs. The simulation not only has certain reference significance to the optimal design for the bending performance of PCPs, but also to the choice of PCPs in the practical project.
Finite element analysis of rotating beams physics based interpolation
Ganguli, Ranjan
2017-01-01
This book addresses the solution of rotating beam free-vibration problems using the finite element method. It provides an introduction to the governing equation of a rotating beam, before outlining the solution procedures using Rayleigh-Ritz, Galerkin and finite element methods. The possibility of improving the convergence of finite element methods through a judicious selection of interpolation functions, which are closer to the problem physics, is also addressed. The book offers a valuable guide for students and researchers working on rotating beam problems – important engineering structures used in helicopter rotors, wind turbines, gas turbines, steam turbines and propellers – and their applications. It can also be used as a textbook for specialized graduate and professional courses on advanced applications of finite element analysis.
Finite element analysis (FEA) analysis of the preflex beam
Wan, Lijuan; Gao, Qilang
2017-10-01
The development of finite element analysis (FEA) has been relatively mature, and is one of the important means of structural analysis. This method changes the problem that the research of complex structure in the past needs to be done by a large number of experiments. Through the finite element method, the numerical simulation of the structure can be used to achieve a variety of static and dynamic simulation analysis of the mechanical problems, it is also convenient to study the parameters of the structural parameters. Combined with a certain number of experiments to verify the simulation model can be completed in the past all the needs of experimental research. The nonlinear finite element method is used to simulate the flexural behavior of the prestressed composite beams with corrugated steel webs. The finite element analysis is used to understand the mechanical properties of the structure under the action of bending load.
Finite element analysis of unnotched charpy impact tests
2008-10-01
This paper describes nonlinear finite element analysis (FEA) to examine the energy to : fracture unnotched Charpy specimens under pendulum impact loading. An oversized, : nonstandard pendulum impactor, called the Bulk Fracture Charpy Machine (BFCM), ...
Finite element model updating using bayesian framework and modal properties
CSIR Research Space (South Africa)
Marwala, T
2005-01-01
Full Text Available Finite element (FE) models are widely used to predict the dynamic characteristics of aerospace structures. These models often give results that differ from measured results and therefore need to be updated to match measured results. Some...
Finite element analyses of railroad tank car head impacts
2008-09-24
This paper describes engineering analyses of a railroad : tank car impacted at its head by a rigid punch. This type of : collision, referred to as a head impact, is examined using : dynamic, nonlinear finite element analysis (FEA). : Commercial softw...
Finite Element Crash Simulations and Impact-Induced Injuries
Directory of Open Access Journals (Sweden)
Jaroslav Mackerle
1999-01-01
Full Text Available This bibliography lists references to papers, conference proceedings and theses/dissertations dealing with finite element simulations of crashes, impact-induced injuries and their protection that were published in 1980–1998. 390 citations are listed.
Vehicle Interior Noise Prediction Using Energy Finite Element Analysis Project
National Aeronautics and Space Administration — It is proposed to develop and implement a computational technique based on Energy Finite Element Analysis (EFEA) for interior noise prediction of advanced aerospace...
Structural analysis with the finite element method linear statics
Oñate, Eugenio
2013-01-01
STRUCTURAL ANALYSIS WITH THE FINITE ELEMENT METHOD Linear Statics Volume 1 : The Basis and Solids Eugenio Oñate The two volumes of this book cover most of the theoretical and computational aspects of the linear static analysis of structures with the Finite Element Method (FEM). The content of the book is based on the lecture notes of a basic course on Structural Analysis with the FEM taught by the author at the Technical University of Catalonia (UPC) in Barcelona, Spain for the last 30 years. Volume1 presents the basis of the FEM for structural analysis and a detailed description of the finite element formulation for axially loaded bars, plane elasticity problems, axisymmetric solids and general three dimensional solids. Each chapter describes the background theory for each structural model considered, details of the finite element formulation and guidelines for the application to structural engineering problems. The book includes a chapter on miscellaneous topics such as treatment of inclined supports, elas...
Finite Element Models for Electron Beam Freeform Fabrication Process Project
National Aeronautics and Space Administration — This Small Business Innovation Research Phase II proposal offers to develop a comprehensive computer simulation methodology based on the finite element method for...
Modelling of fabric draping: Finite elements versus a geometrical method
Lamers, E.A.D.; Wijskamp, Sebastiaan; Akkerman, Remko
2001-01-01
Thermoplastic composite materials can be processed by Rubber Press Forming at elevated temperatures. Process specific boundary conditions are difficult to incorporate in the classical geometric drape simulation methods. Therefore, a fabric reinforced fluid model was implemented in the Finite Element
Finite Element Models for Electron Beam Freeform Fabrication Process Project
National Aeronautics and Space Administration — This Small Business Innovation Research proposal offers to develop the most accurate, comprehensive and efficient finite element models to date for simulation of the...
Generalized multiscale finite element method. Symmetric interior penalty coupling
Efendiev, Yalchin R.
2013-12-01
Motivated by applications to numerical simulations of flows in highly heterogeneous porous media, we develop multiscale finite element methods for second order elliptic equations. We discuss a multiscale model reduction technique in the framework of the discontinuous Galerkin finite element method. We propose two different finite element spaces on the coarse mesh. The first space is based on a local eigenvalue problem that uses an interior weighted L2-norm and a boundary weighted L2-norm for computing the "mass" matrix. The second choice is based on generation of a snapshot space and subsequent selection of a subspace of a reduced dimension. The approximation with these multiscale spaces is based on the discontinuous Galerkin finite element method framework. We investigate the stability and derive error estimates for the methods and further experimentally study their performance on a representative number of numerical examples. © 2013 Elsevier Inc.
Comparison of different precondtioners for nonsymmtric finite volume element methods
Energy Technology Data Exchange (ETDEWEB)
Mishev, I.D.
1996-12-31
We consider a few different preconditioners for the linear systems arising from the discretization of 3-D convection-diffusion problems with the finite volume element method. Their theoretical and computational convergence rates are compared and discussed.
Commercial exploitation of finite element codes for neutron transport
Energy Technology Data Exchange (ETDEWEB)
Ackroyd, R.T.; Issa, J.G.
1989-01-01
The finite element method for neutron transport is in commercial use in the United Kingdom for shielding and criticality problems. It is also applied to time-dependent problems arising in the field of oil-well logging. The present capability of the method is described, and the developments in hand to accelerate calculations are outlined. The codes that have been developed in the United Kingdom are FELTRAN, TRIPAC, and MARC. Complex shapes can be modeled with finite elements as realistically as in Monte Carlo calculations. Thus the finite element and Monte Carlo methods provide an independent means of cross checking a safety assessment for finalized design. The finite element method is particularly useful for scoping design studies, because it gives the angular fluxes everywhere in the system. These fluxes provide guidance on the efficacy of the design features.
Predicting target displacements using ultrasound elastography and finite element modeling
Buijs, J.O. den; Hansen, H.H.G.; Lopata, R.G.P.; Korte, C.L. de; Misra, S.
2011-01-01
Soft tissue displacements during minimally invasive surgical procedures may cause target motion and subsequent misplacement of the surgical tool. A technique is presented to predict target displacements using a combination of ultrasound elastography and finite element (FE) modeling. A cubic
Predicting target displacements using ultrasound elastography and finite element modeling
op den Buijs, J.; Hansen, Hendrik H.G.; Lopata, Richard G.P.; de Korte, Chris L.; Misra, Sarthak
Soft tissue displacements during minimally invasive surgical procedures may cause target motion and subsequent misplacement of the surgical tool. A technique is presented to predict target displacements using a combination of ultrasound elastography and finite element (FE) modeling. A cubic
Finite-element method for above-core structures. [LMFBR
Energy Technology Data Exchange (ETDEWEB)
Kennedy, J.M.; Belytschko, T.B.
1979-12-01
Three-dimensional finite-element models for the treatment of the nonlinear, transient response of a fast breeder reactor's above-core structures are described. For purposes of treating arbitrarily large rotations, node orientations are described by unit vectors and the deformable elements are treated by a corotational formulation in which the coordinate system is embedded in the elements. Deformable elements may be connected either to nodes directly or through rigid bodies. The time integration is carried out by the Newmark ..beta.. method. These features have been incorporated to form the finite-element program SAFE/RAS (Safety Analysis by Finite Elements/Reactor Analysis and Safety Division). Computations are presented for semianalytical comparisons, simple scoping studies, and Stanford Research Institute (SRI) test comparisons.
Symmetric Matrix Fields in the Finite Element Method
Directory of Open Access Journals (Sweden)
Gerard Awanou
2010-07-01
Full Text Available The theory of elasticity is used to predict the response of a material body subject to applied forces. In the linear theory, where the displacement is small, the stress tensor which measures the internal forces is the variable of primal importance. However the symmetry of the stress tensor which expresses the conservation of angular momentum had been a challenge for finite element computations. We review in this paper approaches based on mixed finite element methods.
Finite element modeling of the filament winding process using ABAQUS
Miltenberger, Louis C.
1992-01-01
A comprehensive stress model of the filament winding fabrication process, previously implemented in the finite element program, WACSAFE, was implemented using the ABAQUS finite element software package. This new implementation, referred to as the ABWACSAFE procedure, consists of the ABAQUS software and a pre/postprocessing routine that was developed to prepare necessary ABAQUS input files and process ABAQUS displacement results for stress and strain computation. The ABWACSAF...
Determination of a synchronous generator characteristics via Finite Element Analysis
Directory of Open Access Journals (Sweden)
Kolondzovski Zlatko
2005-01-01
Full Text Available In the paper a determination of characteristics of a small salient pole synchronous generator (SG is presented. Machine characteristics are determined via Finite Element Analysis (FEA and for that purpose is used the software package FEMM Version 3.3. After performing their calculation and analysis, one can conclude that most of the characteristics presented in this paper can be obtained only by using the Finite Element Method (FEM.
Skeletal assessment with finite element analysis: relevance, pitfalls and interpretation.
Campbell, Graeme Michael; Glüer, Claus-C
2017-07-01
Finite element models simulate the mechanical response of bone under load, enabling noninvasive assessment of strength. Models generated from quantitative computed tomography (QCT) incorporate the geometry and spatial distribution of bone mineral density (BMD) to simulate physiological and traumatic loads as well as orthopaedic implant behaviour. The present review discusses the current strengths and weakness of finite element models for application to skeletal biomechanics. In cadaver studies, finite element models provide better estimations of strength compared to BMD. Data from clinical studies are encouraging; however, the superiority of finite element models over BMD measures for fracture prediction has not been shown conclusively, and may be sex and site dependent. Therapeutic effects on bone strength are larger than for BMD; however, model validation has only been performed on untreated bone. High-resolution modalities and novel image processing methods may enhance the structural representation and predictive ability. Despite extensive use of finite element models to study orthopaedic implant stability, accurate simulation of the bone-implant interface and fracture progression remains a significant challenge. Skeletal finite element models provide noninvasive assessments of strength and implant stability. Improved structural representation and implant surface interaction may enable more accurate models of fragility in the future.
A finite element primer for beginners the basics
Zohdi, Tarek I
2014-01-01
The purpose of this primer is to provide the basics of the Finite Element Method, primarily illustrated through a classical model problem, linearized elasticity. The topics covered are:(1) Weighted residual methods and Galerkin approximations,(2) A model problem for one-dimensional?linear elastostatics,(3) Weak formulations in one dimension,(4) Minimum principles in one dimension,(5) Error estimation in one dimension,(5) Construction of Finite Element basis functions in one dimension,(6) Gaussian Quadrature,(7) Iterative solvers and element by element data structures,(8) A model problem for th
A Comparison of Continuous Mass-lumped Finite Elements and Finite Differences for 3D
Zhebel, E.; Minisini, S.; Kononov, A.; Mulder, W.A.
2012-01-01
The finite-difference method is widely used for time-domain modelling of the wave equation because of its ease of implementation of high-order spatial discretization schemes, parallelization and computational efficiency. However, finite elements on tetrahedral meshes are more accurate in complex
Nonconforming finite elements and the Cascade iteration
Stevenson, R.
1999-01-01
We derive sucient conditions under which the Cascade iteration applied to nonconforming nite element discretizations yields an optimal solver. Key ingredients are optimal error estimates of such discretizations, which we therefore study in detail. We derive a new, ecient modied Morley nite element
Finite element thermal analysis of convectively-cooled aircraft structures
Wieting, A. R.; Thornton, E. A.
1981-01-01
The design complexity and size of convectively-cooled engine and airframe structures for hypersonic transports necessitate the use of large general purpose computer programs for both thermal and structural analyses. Generally thermal analyses are based on the lumped-parameter finite difference technique, and structural analyses are based on the finite element technique. Differences in these techniques make it difficult to achieve an efficient interface. It appears, therefore, desirable to conduct an integrated analysis based on a common technique. A summary is provided of efforts by NASA concerned with the development of an integrated thermal structural analysis capability using the finite element method. Particular attention is given to the development of conduction/forced-convection finite element methodology and applications which illustrate the capabilities of the developed concepts.
Finite Element Aircraft Simulation of Turbulence
1997-02-01
A Simulation of Rotor Blade Element Turbulence (SORBET) model has been : developed for realtime aircraft simulation that accommodates stochastic : turbulence and distributed discrete gusts as a function of the terrain. This : model is applicable to c...
Experimental and finite element analysis of fracture criterion in ...
Indian Academy of Sciences (India)
R. Narasimhan (Krishtel eMaging) 1461 1996 Oct 15 13:05:22
z o. (a) θ r. (b). Figure 5. (a) Creation of crack tip elements (3-D, 20-noded structural solid). (b) Determination of stress value at the node having maximum displacement. 6.4 Nonlinear analysis. Elastic-plastic finite element analysis can be considered as an extension of elastic by incorporating extra conditions pertaining to ...
Finite element stress analysis of brick-mortar masonry under ...
African Journals Online (AJOL)
Stress analysis of a brick-mortar couplet as a substitute for brick wall structure has been performed by finite element method, and algorithm for determining the element stiffness matrix for a plane stress problem using the displacement approach was developed. The nodal displacements were derived for the stress in each ...
Stress distributions in finite element analysis of concrete gravity dam ...
African Journals Online (AJOL)
Gravity dams are solid structures built of mass concrete material; they maintain their stability against the design loads from the geometric shape, the mass, and the strength of the concrete. The model was meshed with an 8-node biquadratic plane strain quadrilateral (CPE8R) elements, using ABAQUS, a finite element ...
Behaviour of Lagrangian triangular mixed fluid finite elements
Indian Academy of Sciences (India)
The behaviour of mixed fluid finite elements, formulated based on the Lagrangian frame of reference, is investigated to understand the effects of locking due to incompressibility and irrotational constraints. For this purpose, both linear and quadratic mixed triangular fluid elements are formulated. It is found that there exists a ...
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 ...
Finite element solution of the Boussinesq wave equation | Akpobi ...
African Journals Online (AJOL)
In this work, we investigate a Boussinesq-type flow model for nonlinear dispersive waves by developing a computational model based on the finite element discretisation technique. Hermite interpolation functions were used to interpolate approximation elements. The system is modeled using a time dependent equation.
Calibration of a finite element composite delamination model by experiments
DEFF Research Database (Denmark)
Gaiotti, M.; Rizzo, C.M.; Branner, Kim
2013-01-01
distinct sub-laminates. The work focuses on experimental validation of a finite element model built using the 9-noded MITC9 shell elements, which prevent locking effects and aiming to capture the highly non linear buckling features involved in the problem. The geometry has been numerically defined...
Finite Element Studies on Hollow Steel Columns under Multi ...
African Journals Online (AJOL)
Herein, finite element (FE) modeling of the columns under multi-directional loading is conducted employing ABAQUS FE code in conjunction with the experimental results. To optimize on the program capabilities, the sensitivity of the developed model is appraised with regard to the effect of type of shell element, type of ...
A finite element analysis of the distribution velocity in viscous ...
African Journals Online (AJOL)
In this work we use the finite element method to analyze the distribution of velocity in a viscous incompressible fluid flow using Lagrange interpolation function. The results obtained are highly accurate and converge fast to the exact solution as the number of elements increase.
An implicit discontinuous Galerkin finite element model for water waves
van der Vegt, Jacobus J.W.; Ambati, V.R.; Bokhove, Onno
2005-01-01
We discuss a new higher order accurate discontinuous Galerkin finite element method for non-linear free surface gravity waves. The algorithm is based on an arbitrary Lagrangian Eulerian description of the flow field using deforming elements and a moving mesh, which makes it possible to represent
Finite Element Vibration Analysis of Beams, Plates and Shells
Directory of Open Access Journals (Sweden)
Jaroslav Mackerle
1999-01-01
Full Text Available This bibliography lists references to papers, conference proceedings and theses/dissertations dealing with finite element vibration analysis of beams, plates and shells that were published in 1994–1998. It contains 361 citations. Also included, as separated subsections, are vibration analysis of composite materials and vibration analysis of structural elements with cracks/contacts.
Guo, Hongqiang; Shah, Mitul; Spilker, Robert L
2014-03-01
The study of biphasic soft tissue contact is fundamental to understand the biomechanical behavior of human diarthrodial joints. However, to date, only few biphasic finite element contact analyses for three-dimensional physiological geometries under finite deformation have been developed. The objective of this article is to develop a hyperelastic biphasic contact implementation for finite deformation and sliding problem. An augmented Lagrangian method was used to enforce the continuity of contact traction and fluid pressure across the contact interface. The finite element implementation was based on a general purpose software, COMSOL Multiphysics. The accuracy of the implementation is verified using example problems, for which solutions are available by alternative analyses. The implementation was proven to be robust and able to handle finite deformation and sliding.
Preconditioned CG-solvers and finite element grids
Energy Technology Data Exchange (ETDEWEB)
Bauer, R.; Selberherr, S. [Technical Univ. of Vienna (Austria)
1994-12-31
To extract parasitic capacitances in wiring structures of integrated circuits the authors developed the two- and three-dimensional finite element program SCAP (Smart Capacitance Analysis Program). The program computes the task of the electrostatic field from a solution of Poisson`s equation via finite elements and calculates the energies from which the capacitance matrix is extracted. The unknown potential vector, which has for three-dimensional applications 5000-50000 unknowns, is computed by a ICCG solver. Currently three- and six-node triangular, four- and ten-node tetrahedronal elements are supported.
Tissue-fluid interface analysis using biphasic finite element method.
Unnikrishnan, G U; Unnikrishnan, V U; Reddy, J N
2009-04-01
Numerical studies on fluid-structure interaction have primarily relied on decoupling the solid and fluid sub-domains with the interactions treated as external boundary conditions on the individual sub-domains. The finite element applications for the fluid-structure interactions can be divided into iterative algorithms and sequential algorithms. In this paper, a new computational methodology for the analysis of tissue-fluid interaction problems is presented. The whole computational domain is treated as a single biphasic continuum, and the same space and time discretisation is carried out for the sub-domains using a penalty-based finite element model. This procedure does not require the explicit modelling of additional boundary conditions or interface elements. The developed biphasic interface finite element model is used in analysing blood flow through normal and stenotic arteries. The increase in fluid flow velocity when passing through a stenosed artery and the drop in pressure at the region are captured using this method.
Ship Impact Study: Analytical Approaches and Finite Element Modeling
Directory of Open Access Journals (Sweden)
Pawel Woelke
2012-01-01
Full Text Available The current paper presents the results of a ship impact study conducted using various analytical approaches available in the literature with the results obtained from detailed finite element analysis. Considering a typical container vessel impacting a rigid wall with an initial speed of 10 knots, the study investigates the forces imparted on the struck obstacle, the energy dissipated through inelastic deformation, penetration, local deformation patterns, and local failure of the ship elements. The main objective of the paper is to study the accuracy and generality of the predictions of the vessel collision forces, obtained by means of analytical closed-form solutions, in reference to detailed finite element analyses. The results show that significant discrepancies between simplified analytical approaches and detailed finite element analyses can occur, depending on the specific impact scenarios under consideration.
Galerkin finite element methods for wave problems
Indian Academy of Sciences (India)
One-dimensional wave equation. First, we briefly discuss the Galerkin method that employs piecewise quadratic polynomials for the basis or interpolating functions. We will call this as G2FEM for ease of reference. Here, one would have three quadratic functions for each element (see Reddy 2001, for details). In figure 1, we ...
The Applications of Finite Element Analysis in Proximal Humeral Fractures
Ye, Yongyu; You, Wei; Zhu, Weimin; Cui, Jiaming; Chen, Kang
2017-01-01
Proximal humeral fractures are common and most challenging, due to the complexity of the glenohumeral joint, especially in the geriatric population with impacted fractures, that the development of implants continues because currently the problems with their fixation are not solved. Pre-, intra-, and postoperative assessments are crucial in management of those patients. Finite element analysis, as one of the valuable tools, has been implemented as an effective and noninvasive method to analyze proximal humeral fractures, providing solid evidence for management of troublesome patients. However, no review article about the applications and effects of finite element analysis in assessing proximal humeral fractures has been reported yet. This review article summarized the applications, contribution, and clinical significance of finite element analysis in assessing proximal humeral fractures. Furthermore, the limitations of finite element analysis, the difficulties of more realistic simulation, and the validation and also the creation of validated FE models were discussed. We concluded that although some advancements in proximal humeral fractures researches have been made by using finite element analysis, utility of this powerful tool for routine clinical management and adequate simulation requires more state-of-the-art studies to provide evidence and bases. PMID:29081829
The Applications of Finite Element Analysis in Proximal Humeral Fractures
Directory of Open Access Journals (Sweden)
Yongyu Ye
2017-01-01
Full Text Available Proximal humeral fractures are common and most challenging, due to the complexity of the glenohumeral joint, especially in the geriatric population with impacted fractures, that the development of implants continues because currently the problems with their fixation are not solved. Pre-, intra-, and postoperative assessments are crucial in management of those patients. Finite element analysis, as one of the valuable tools, has been implemented as an effective and noninvasive method to analyze proximal humeral fractures, providing solid evidence for management of troublesome patients. However, no review article about the applications and effects of finite element analysis in assessing proximal humeral fractures has been reported yet. This review article summarized the applications, contribution, and clinical significance of finite element analysis in assessing proximal humeral fractures. Furthermore, the limitations of finite element analysis, the difficulties of more realistic simulation, and the validation and also the creation of validated FE models were discussed. We concluded that although some advancements in proximal humeral fractures researches have been made by using finite element analysis, utility of this powerful tool for routine clinical management and adequate simulation requires more state-of-the-art studies to provide evidence and bases.
Finite element analysis of thrust angle contact ball slewing bearing
Deng, Biao; Guo, Yuan; Zhang, An; Tang, Shengjin
2017-12-01
In view of the large heavy slewing bearing no longer follows the rigid ring hupothesis under the load condition, the entity finite element model of thrust angular contact ball bearing was established by using finite element analysis software ANSYS. The boundary conditions of the model were set according to the actual condition of slewing bearing, the internal stress state of the slewing bearing was obtained by solving and calculation, and the calculated results were compared with the numerical results based on the rigid ring assumption. The results show that more balls are loaded in the result of finite element method, and the maximum contact stresses between the ball and raceway have some reductions. This is because the finite element method considers the ferrule as an elastic body. The ring will produce structure deformation in the radial plane when the heavy load slewing bearings are subjected to external loads. The results of the finite element method are more in line with the actual situation of the slewing bearing in the engineering.
[Application of finite element method in spinal biomechanics].
Liu, Qiang; Zhang, Jun; Sun, Shu-Chun; Wang, Fei
2017-02-25
The finite element model is one of the most important methods in study of modern spinal biomechanics, according to the needs to simulate the various states of the spine, calculate the stress force and strain distribution of the different groups in the state, and explore its principle of mechanics, mechanism of injury, and treatment effectiveness. In addition, in the study of the pathological state of the spine, the finite element is mainly used in the understanding the mechanism of lesion location, evaluating the effects of different therapeutic tool, assisting and completing the selection and improvement of therapeutic tool, in order to provide a theoretical basis for the rehabilitation of spinal lesions. Finite element method can be more provide the service for the patients suffering from spinal correction, operation and individual implant design. Among the design and performance evaluation of the implant need to pay attention to the individual difference and perfect the evaluation system. At present, how to establish a model which is more close to the real situation has been the focus and difficulty of the study of human body's finite element.Although finite element method can better simulate complex working condition, it is necessary to improve the authenticity of the model and the sharing of the group by using many kinds of methods, such as image science, statistics, kinematics and so on. Copyright© 2017 by the China Journal of Orthopaedics and Traumatology Press.
Finite Element Method for Capturing Ultra-relativistic Shocks
Richardson, G. A.; Chung, T. J.
2003-01-01
While finite element methods are used extensively by researchers solving computational fluid dynamics in fields other than astrophysics, their use in astrophysical fluid simulations has been predominantly overlooked. Current simulations using other methods such as finite difference and finite volume (based on finite difference) have shown remarkable results, but these methods are limited by their fundamental properties in aspects that are important for simulations with complex geometries and widely varying spatial and temporal scale differences. We have explored the use of finite element methods for astrophysical fluids in order to establish the validity of using such methods in astrophysical environments. We present our numerical technique applied to solving ultra-relativistic (Lorentz Factor Gamma >> 1) shocks which are prevalent in astrophysical studies including relativistic jets and gamma-ray burst studies. We show our finite element formulation applied to simulations where the Lorentz factor ranges up to 2236 and demonstrate its stability in solving ultra-relativistic flows. Our numerical method is based on the Flowfield Dependent Variation (FDV) Method, unique in that numerical diffusion is derived from physical parameters rather than traditional artificial viscosity methods. Numerical instabilities account for most of the difficulties when capturing shocks in this regime. Our method results in stable solutions and accurate results as compared with other methods.
An Object Oriented, Finite Element Framework for Linear Wave Equations
Energy Technology Data Exchange (ETDEWEB)
Koning, Joseph M. [Univ. of California, Berkeley, CA (United States)
2004-03-01
This dissertation documents an object oriented framework which can be used to solve any linear wave equation. The linear wave equations are expressed in the differential forms language. This differential forms expression allows a strict discrete interpretation of the system. The framework is implemented using the Galerkin Finite Element Method to define the discrete differential forms and operators. Finite element basis functions including standard scalar Nodal and vector Nedelec basis functions are used to implement the discrete differential forms resulting in a mixed finite element system. Discretizations of scalar and vector wave equations in the time and frequency domains will be demonstrated in both differential forms and vector calculi. This framework conserves energy, maintains physical continuity, is valid on unstructured grids, conditionally stable and second order accurate. Examples including linear electrodynamics, acoustics, elasticity and magnetohydrodynamics are demonstrated.
Finite element method for eigenvalue problems in electromagnetics
Reddy, C. J.; Deshpande, Manohar D.; Cockrell, C. R.; Beck, Fred B.
1994-01-01
Finite element method (FEM) has been a very powerful tool to solve many complex problems in electromagnetics. The goal of the current research at the Langley Research Center is to develop a combined FEM/method of moments approach to three-dimensional scattering/radiation problem for objects with arbitrary shape and filled with complex materials. As a first step toward that goal, an exercise is taken to establish the power of FEM, through closed boundary problems. This paper demonstrates the developed of FEM tools for two- and three-dimensional eigenvalue problems in electromagnetics. In section 2, both the scalar and vector finite elements have been used for various waveguide problems to demonstrate the flexibility of FEM. In section 3, vector finite element method has been extended to three-dimensional eigenvalue problems.
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.
Choice of input fields in stochastic finite elements
DEFF Research Database (Denmark)
Ditlevsen, Ove Dalager; Tarp-Johansen, Niels Jacob
1996-01-01
, the flexibility field, as the input to the stochastic finite element model. To answer this question the focus should be on the error of the output of the mechanical model rather than on the input field itself when discretizing the field through replacing it by a field defined in terms of a finite number of random...... and compliance, Stochastic finite elements, Discretization of random fields, Winterstein approximations.......The problem of the arbitrary choice of variables for random field modelling in structural mechanics or in soil mechanics is treated. For example, it is relevant to ask the question of whether it is best to choose a stiffness field along a beam element or to choose its reciprocal field...
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)
Flow Applications of the Least Squares Finite Element Method
Jiang, Bo-Nan
1998-01-01
The main thrust of the effort has been towards the development, analysis and implementation of the least-squares finite element method (LSFEM) for fluid dynamics and electromagnetics applications. In the past year, there were four major accomplishments: 1) special treatments in computational fluid dynamics and computational electromagnetics, such as upwinding, numerical dissipation, staggered grid, non-equal order elements, operator splitting and preconditioning, edge elements, and vector potential are unnecessary; 2) the analysis of the LSFEM for most partial differential equations can be based on the bounded inverse theorem; 3) the finite difference and finite volume algorithms solve only two Maxwell equations and ignore the divergence equations; and 4) the first numerical simulation of three-dimensional Marangoni-Benard convection was performed using the LSFEM.
Finite Element Residual Stress Analysis of Planetary Gear Tooth
Directory of Open Access Journals (Sweden)
Jungang Wang
2013-01-01
Full Text Available A method to simulate residual stress field of planetary gear is proposed. In this method, the finite element model of planetary gear is established and divided to tooth zone and profile zone, whose different temperature field is set. The gear's residual stress simulation is realized by the thermal compression stress generated by the temperature difference. Based on the simulation, the finite element model of planetary gear train is established, the dynamic meshing process is simulated, and influence of residual stress on equivalent stress of addendum, pitch circle, and dedendum of internal and external meshing planetary gear tooth profile is analyzed, according to non-linear contact theory, thermodynamic theory, and finite element theory. The results show that the equivalent stresses of planetary gear at both meshing and nonmeshing surface are significantly and differently reduced by residual stress. The study benefits fatigue cracking analysis and dynamic optimization design of planetary gear train.
Engineering computation of structures the finite element method
Neto, Maria Augusta; Roseiro, Luis; Cirne, José; Leal, Rogério
2015-01-01
This book presents theories and the main useful techniques of the Finite Element Method (FEM), with an introduction to FEM and many case studies of its use in engineering practice. It supports engineers and students to solve primarily linear problems in mechanical engineering, with a main focus on static and dynamic structural problems. Readers of this text are encouraged to discover the proper relationship between theory and practice, within the finite element method: Practice without theory is blind, but theory without practice is sterile. Beginning with elasticity basic concepts and the classical theories of stressed materials, the work goes on to apply the relationship between forces, displacements, stresses and strains on the process of modeling, simulating and designing engineered technical systems. Chapters discuss the finite element equations for static, eigenvalue analysis, as well as transient analyses. Students and practitioners using commercial FEM software will find this book very helpful. It us...
Finite Element Modelling of Cold Formed Stainless Steel Columns
Directory of Open Access Journals (Sweden)
M. Macdonald
2005-01-01
Full Text Available This paper describes the results obtained from a finite element investigation into the load capacity of column members of lipped channel cross-section, cold formed from Type 304 stainless steel, subjected to concentric and eccentric compression loading. The main aims of this investigation were to determine the effects which the non-linearity of the stress-strain behaviour of the material would have on the column behaviour under concentric or eccentric loading. Stress-strain curves derived from tests and design codes are incorporated into non-linear finite element analyses of eccentrically loaded columns and the results obtained are compared with those obtained on the basis of experiments on stainless steel channel columns with the same properties and dimensions. Comparisons of the finite element results and the test results are also made with existing design specifications and conclusions are drawn on the basis of the comparisons.
Finite Element Modeling of the Skew Rolling Process
He, Ming; Sawamiphakdi, Krich; Perez, Anthony J.; Daiger, Kevin P.
2004-06-01
A helical skew rolling process is a continuous hot forming process that produces near net-shape parts from tubing for hard turning or machining to the finished parts. The process can challenge forging processes in a number of applications by its high production rate and ability of forming intricate geometry. Because of its technical complexity, a number of tests have to be performed to improve and validate the design before a part can be put into production. To reduce the design lead-time and cost as well as improving the production quality, developing and implementing the finite element analysis procedures in design is an inevitable step. In literature, it has not been seen that the numerical simulation is applied to the skew rolling process so far. Simulation of the skew rolling is in a complicated three-dimensional metal large-deformation category, characterized by its severe mesh distortion and consistent contact and separation between the workpiece and dies. This paper describes the new development in finite element modeling of the skew rolling process and demonstrates the application of finite element modeling to aid the design of tooling and process parameters. By the use of the DEFORM-3D finite element program, the simulations can predict the geometry and some defects in parts reasonably well agreed with the actual products. However, one of the key issues is simulation time due to the nature of the nonlinear finite element method and the Lagrangian formulation adopted in the DEFORM-3D program. Solving nonlinear algebraic equations in each time step combined with iterative procedures is very computationally demanding and time consuming. Repeatedly reduction in time step size to satisfy the contact criterion prolongs the simulation significantly. Therefore, the improvement in the finite element theories and solving methods is necessary before the simulation can achieve reasonable timing.
FINITE ELEMENT IMPLEMENTATION OF DELAMINATION IN COMPOSITE PLATES
Directory of Open Access Journals (Sweden)
Milan Žmindák
2012-12-01
Full Text Available Modelling of composite structures by finite element (FE codes to effectively model certain critical failure modes such as delamination is limited. Previous efforts to model delamination and debonding failure modes using FE codes have typically relied on ad hoc failure criteria and quasi-static fracture data. Improvements to these modelling procedures can be made by using an approach based on fracture mechanics. A study of modelling delamination using the finite element code ANSYS was conducted. This investigation demonstrates the modelling of composites through improved delamination modelling. Further developments to this approach may be improved.
Fast Stiffness Matrix Calculation for Nonlinear Finite Element Method
Directory of Open Access Journals (Sweden)
Emir Gülümser
2014-01-01
Full Text Available We propose a fast stiffness matrix calculation technique for nonlinear finite element method (FEM. Nonlinear stiffness matrices are constructed using Green-Lagrange strains, which are derived from infinitesimal strains by adding the nonlinear terms discarded from small deformations. We implemented a linear and a nonlinear finite element method with the same material properties to examine the differences between them. We verified our nonlinear formulation with different applications and achieved considerable speedups in solving the system of equations using our nonlinear FEM compared to a state-of-the-art nonlinear FEM.
Parallel computing for the finite element method in MATLAB
Directory of Open Access Journals (Sweden)
Aurimas Šimkus
2013-09-01
Full Text Available In this research, parallel computing capabilities of MATLAB and the capabilities for the finite element method were analyzed. A program for solving a heat transfer problem by the finite element method was implemented. Three different parallel algorithms using CPU and GPU for solving steady state and transient heat transfer problems were proposed and implemented. A maximal speedup of around 2.3 times for steady state and 2 times for transient problem solving time was achieved by using a quad-core CPU.
Ultrasound finite element simulation sensitivity to anisotropic titanium microstructures
Freed, Shaun; Blackshire, James L.; Na, Jeong K.
2016-02-01
Analytical wave models are inadequate to describe complex metallic microstructure interactions especially for near field anisotropic property effects and through geometric features smaller than the wavelength. In contrast, finite element ultrasound simulations inherently capture microstructure influences due to their reliance on material definitions rather than wave descriptions. To better understand and quantify heterogeneous crystal orientation effects to ultrasonic wave propagation, a finite element modeling case study has been performed with anisotropic titanium grain structures. A parameterized model has been developed utilizing anisotropic spheres within a bulk material. The resulting wave parameters are analyzed as functions of both wavelength and sphere to bulk crystal mismatch angle.
FINITE ELEMENT EVALUATION AND OPTIMIZATION OF GEOMETRY WITH DOE
Directory of Open Access Journals (Sweden)
Janko D. Jovanovic
2011-03-01
Full Text Available Since 1960, Taguchi methods have been used for improving the quality of Japanese products with great success. Basic assumption of Taguchi's design for six sigma or robust design is that quality must be designed into a product from the start at both the product and process design stage in order to improve product reliability and manufacturability. This paper deals with case study of product design based on Taguchi's approach that involves parametric optimization of piston rod geometry aiming mass reduction with stress restriction. Finite element analysis software ANSYS Workbench was used to get access to CAD parameters of piston rod within a process of parametric finite element evaluation and optimization.
Discontinuous Galerkin finite element methods for gradient plasticity.
Energy Technology Data Exchange (ETDEWEB)
Garikipati, Krishna. (University of Michigan, Ann Arbor, MI); Ostien, Jakob T.
2010-10-01
In this report we apply discontinuous Galerkin finite element methods to the equations of an incompatibility based formulation of gradient plasticity. The presentation is motivated with a brief overview of the description of dislocations within a crystal lattice. A tensor representing a measure of the incompatibility with the lattice is used in the formulation of a gradient plasticity model. This model is cast in a variational formulation, and discontinuous Galerkin machinery is employed to implement the formulation into a finite element code. Finally numerical examples of the model are shown.
FINITE ELEMENT MODELING OF THIN CIRCULAR SANDWICH PLATES DEFLECTION
Directory of Open Access Journals (Sweden)
K. S. Kurachka
2014-01-01
Full Text Available A mathematical model of a thin circular sandwich plate being under the vertical load is proposed. The model employs the finite element method and takes advantage of an axisymmetric finite element that leads to the small dimension of the resulting stiffness matrix and sufficient accuracy for practical calculations. The analytical expressions for computing local stiffness matrices are found, which can significantly speed up the process of forming the global stiffness matrix and increase the accuracy of calculations. A software is under development and verification. The discrepancy between the results of the mathematical model and those of analytical formulas for homogeneous thin circularsandwich plates does not exceed 7%.
Preconditioning for Mixed Finite Element Formulations of Elliptic Problems
Wildey, Tim
2013-01-01
In this paper, we discuss a preconditioning technique for mixed finite element discretizations of elliptic equations. The technique is based on a block-diagonal approximation of the mass matrix which maintains the sparsity and positive definiteness of the corresponding Schur complement. This preconditioner arises from the multipoint flux mixed finite element method and is robust with respect to mesh size and is better conditioned for full permeability tensors than a preconditioner based on a diagonal approximation of the mass matrix. © Springer-Verlag Berlin Heidelberg 2013.
Finite element solution of two dimensional time dependent heat equation
Maa
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.
Finite element treatment of nonlinear thermal radiation transport
Energy Technology Data Exchange (ETDEWEB)
Oliveira, C.R.E. de; Ackroyd, R.T.; Goddard, A.J.H. (Univ. of London (United Kingdom))
1993-01-01
This paper reports the application of a variational finite element-spherical harmonics method to transient nonlinear radiation transport problems. Apart from its geometric flexibility, the finite element treatment described allows the use of spatially discontinuous trial functions in the variational principles. This permits an economical treatment of steep gradients in the photon intensity distribution and offers greater freedom in the choice of spherical harmonic expansion, potentially allowing the order of the expansion to be varied from region to region according to physical needs. The formulation also easily accomodates, with minor computational overheads, spatially varying cross sections and temperatures.
High-order finite elements for material and geometric nonlinear finite strain problems
Heisserer, Ulrich
2008-01-01
For the simulation of geometric and material nonlinear problems implicit high-order (p-version) displacement-based finite elements are applied. Besides hyperelastic materials a finite strain viscoplasticity model with internal variables is considered. We apply the combination of Backward-Euler integration and Multilevel-Newton algorithm to solve the system of differential-algebraic equations resulting from the space-discretized weak form. For an efficient modeling of the cold isostatic pressi...
A multiscale mortar multipoint flux mixed finite element method
Wheeler, Mary Fanett
2012-02-03
In this paper, we develop a multiscale mortar multipoint flux mixed finite element method for second order elliptic problems. The equations in the coarse elements (or subdomains) are discretized on a fine grid scale by a multipoint flux mixed finite element method that reduces to cell-centered finite differences on irregular grids. The subdomain grids do not have to match across the interfaces. Continuity of flux between coarse elements is imposed via a mortar finite element space on a coarse grid scale. With an appropriate choice of polynomial degree of the mortar space, we derive optimal order convergence on the fine scale for both the multiscale pressure and velocity, as well as the coarse scale mortar pressure. Some superconvergence results are also derived. The algebraic system is reduced via a non-overlapping domain decomposition to a coarse scale mortar interface problem that is solved using a multiscale flux basis. Numerical experiments are presented to confirm the theory and illustrate the efficiency and flexibility of the method. © EDP Sciences, SMAI, 2012.
A direct implementation for influence lines in finite element software
DEFF Research Database (Denmark)
Jepsen, Michael S.; Damkilde, Lars
2014-01-01
The use of influence lines is a recognized method for determining the critical design load conditions and this paper shows a direct method for applying influence lines in any structural finite element software. The main idea is to equate displacement or angular discontinuities with nodal forces...... to consistent nodal forces, which makes it very suitable for implementation in finite element schemes and applicable for all element types, such as shell, plates, beams etc. This paper derives the consistent nodal forces for angular, lateral and axial displacement discontinuities for a Bernoulli-Euler beam...... element. To exemplify the new approach the response function of the pre-stressing cables for a cable-stay bridge subjected to a truck loading is studied....
Electric field calculations in brain stimulation based on finite elements
DEFF Research Database (Denmark)
Windhoff, Mirko; Opitz, Alexander; Thielscher, Axel
2013-01-01
The need for realistic electric field calculations in human noninvasive brain stimulation is undisputed to more accurately determine the affected brain areas. However, using numerical techniques such as the finite element method (FEM) is methodologically complex, starting with the creation...... elements. The latter is crucial to guarantee the numerical robustness of the FEM calculations. The pipeline will be released as open-source, allowing for the first time to perform realistic field calculations at an acceptable methodological complexity and moderate costs....
Analysis of Finite Element Methods for Vector Laplacians on Surfaces
Hansbo, Peter; Larson, Mats G.; Larsson, Karl
2016-01-01
We develop a finite element method for the vector Laplacian based on the covariant derivative of tangential vector fields on surfaces embedded in $\\mathbb{R}^3$. Closely related operators arise in models of flow on surfaces as well as elastic membranes and shells. The method is based on standard continuous parametric Lagrange elements with one order higher polynomial degree for the mapping. The tangent condition is weakly enforced using a penalization term. We derive error estimates that take...
Choice of input fields in stochastic finite elements
DEFF Research Database (Denmark)
Ditlevsen, Ove Dalager; Tarp-Johansen, Niels Jacob
1999-01-01
, the flexibility field, as the input to the stochastic finite element model. To answer this question the focus should be on the error of the output of the mechanical model rather than on the input field itself when discretizing the held through replacing it by a field defined in terms of a finite number of random......The problem of the arbitrary choice of variables for random field modelling in structural mechanics or in soil mechanics is treated. For example, it is relevant to ask the question of whether it is best to choose a stiffness field along a beam element or to choose its reciprocal field...... variables. Several reported discretization methods define these random variables as integrals of the product of the held and some suitable weight functions. In particular, the weight functions can be Dirac delta functions whereby the random variables become the field values at a finite set of given points...
Mesh considerations for finite element blast modelling in biomechanics.
Panzer, Matthew B; Myers, Barry S; Bass, Cameron R
2013-01-01
Finite element (FE) modelling is a popular tool for studying human body response to blast exposure. However, blast modelling is a complex problem owing to more numerous fluid-structure interactions (FSIs) and the high-frequency loading that accompanies blast exposures. This study investigates FE mesh design for blast modelling using a sphere in a closed-ended shock tube meshed with varying element sizes using both tetrahedral and hexahedral elements. FSI was consistent for sphere-to-fluid element ratios between 0.25 and 4, and acceleration response was similar for both element types (R(2) = 0.997). Tetrahedral elements were found to become increasingly volatile following shock loading, causing higher pressures and stresses than predicted with the hexahedral elements. Deviatoric stress response was dependent on the sphere mesh size (p tube mesh size (p blast models.
Finite element simulation of laser transmission welding of dissimilar ...
African Journals Online (AJOL)
Now-a-days, metal to plastic micro-welding is of great interest in the field of biomedical and electronics applications. Laser transmission welding (LTW) has emerged as the most suitable technique for such applications. In this paper, a three-dimensional finite element (FE) thermal model is developed to simulate the laser ...
finite element model for predicting residual stresses in shielded
African Journals Online (AJOL)
eobe
*Corresponding author, Tel: +234-803-563-5419. FINITE ELEMENT MODEL FOR PREDICTING RESIDUAL STRESSES IN. SHIELDED MANUAL METAL ARC WELDING OF MILD STEEL PLATES. SHIELDED MANUAL METAL ARC WELDING OF MILD STEEL PLATES. I. U. Musa1,*, M. O. Afolayan. O. Afolayan2 and I. M. ...
Finite element modelling of fibre-reinforced brittle materials
Kullaa, J.
1997-01-01
The tensile constitutive behaviour of fibre-reinforced brittle materials can be extended to two or three dimensions by using the finite element method with crack models. The three approaches in this study include the smeared and discrete crack concepts and a multi-surface plasticity model. The
Efficient tetrahedral remeshing of feature models for finite element analysis
Sypkens Smit, M.; Bronsvoort, W.F.
2009-01-01
Finite element analysis is nowadays widely used for product testing. At various moments during the design phase, aspects of the physical behaviour of the product are simulated by performing an analysis of the model. For each analysis, a mesh needs to be created that represents the geometry of the
2-D Finite Element Analysis of Massive RC Structures
DEFF Research Database (Denmark)
Saabye Ottosen, Niels
1982-01-01
Nonlinear analysis of concrete structures using finite elements is discussed. The applications include a thick-walled top-closure for a pressure vessel as well as the delicate problems of beams failing in shear. The top-closure analysis evaluates the effect of two different failure criteria...
An Eulerean Finite element Model for Penetration in Layered Soil
van den Berg, Peter; de Borst, Rene; Huetink, Han
1996-01-01
An Eulerean large-strain finite element formulation is presented to simulate static soil penetration. The method is an extension of the Updated Lagrangean description to an Eulerean formulation taking into account convection of deformation-history-dependent properties as well as material properties.
A Monte Carlo adapted finite element method for dislocation ...
Indian Academy of Sciences (India)
Home; Journals; Journal of Earth System Science; Volume 126; Issue 7. A Monte Carlo adapted finite element method for dislocation ... However, geological features of a fault cannot be measured exactly, and therefore these features and data involve uncertainties. This paper presents a Monte Carlo based random model of ...
Finite element crash simulations of the human body: Passive and ...
Indian Academy of Sciences (India)
Abstract. Conventional dummy based testing procedures suffer from known limitations. This report addresses issues in finite element human body models in evaluating pedestrian and occupant crash safety measures. A review of material properties of soft tissues and characterization methods show a scarcity of material.
Viscoelastic finite-element analysis of human skull - dura mater ...
African Journals Online (AJOL)
SERVER
2008-03-18
Mar 18, 2008 ... 1981). MATERIALS AND METHODS. In order to determine the influence of the viscoelastic nature of the human skull and dura mater on their deformation, we made the finite-element analysis of cranial cavity with the ICP scope from 1.5 to 5 kPa respectively. By ignoring the viscoelasticity of human skull.
Superconvergence for tetrahedral quadratic finite element methods for elliptic equations
Brandts, J.H.; Krizek, M.
2005-01-01
For a model elliptic boundary value problem we will prove that on strongly regular families of uniform tetrahedral partitions of the domain, the gradient of the quadratic finite element approximation is superclose to the gradient of the quadratic Lagrange interpolant of the exact solution. This
Finite element analysis of thermal stress distribution in different ...
African Journals Online (AJOL)
Purpose: Cervical lesions are restored with class V preparation. The aim of this study was to use a three-dimensional finite element method to carry out a thermal analysis of the temperature and stress distributions of three different restorative materials used for class V cavities of maxillary molar teeth. Materials and Methods: ...
A 2-dimensional finite element simulation of cooling in castings ...
African Journals Online (AJOL)
In this work we present a 2 dimensional finite element simulation of the cooling process in castings. A one way coupling +technique was used to predict the behavior of thermal strains and stresses from the temperature history of casting. The temperature distribution across the casting at different times, the cooling pattern of ...
Finite element analysis of boron diffusion in wooden Poles
DEFF Research Database (Denmark)
Krabbenhøft, Kristian; Hoffmeyer, Preben; Bechgaard, Carl
2004-01-01
The problem of describing the migration of dissolved boron in wood is treated with special reference to the commonly used remedial treatment of wooden poles. The governing equations are derived and discussed together with some of the material parameters required. The equations are solved by the f...... by the finite element method and, finally, results showing the effect of different treatment strategies are presented....
Piezoelectric Accelerometers Modification Based on the Finite Element Method
DEFF Research Database (Denmark)
Liu, Bin; Kriegbaum, B.
2000-01-01
The paper describes the modification of piezoelectric accelerometers using a Finite Element (FE) method. Brüel & Kjær Accelerometer Type 8325 is chosen as an example to illustrate the advanced accelerometer development procedure. The deviation between the measurement and FE simulation results...
Finite Element Analysis of a Free-Standing Staircase | Ajagbe ...
African Journals Online (AJOL)
The existing approximate analytical methods of analyzing free-standing stairs fail to predict the distribution of any stress resultant and the actual three dimensional behavior of the stair slab system. A more rationale but simple and accurate method of analysis based on finite element method is presented. Plate flexural ...
Finite Element Analysis of Boron Diffusion in Wooden Poles
DEFF Research Database (Denmark)
Krabbenhøft, Kristian; Hoffmeyer, Preben; Bechgaard, Carl
2004-01-01
The problem of describing the migration of dissolved boron in wood is treated with special reference to the commonly used remedial treatment of wooden poles. The governing equations are derived and discussed together with some of the material parameters required. The equations are solved by the f...... by the finite element method and, finally, results showing the effect of different treatment strategies are presented....
Stochastic Finite Elements in Reliability-Based Structural Optimization
DEFF Research Database (Denmark)
Sørensen, John Dalsgaard; Engelund, S.
1995-01-01
Application of stochastic finite elements in structural optimization is considered. It is shown how stochastic fields modelling e.g. the modulus of elasticity can be discretized in stochastic variables and how a sensitivity analysis of the reliability of a structural system with respect...
Finite element modelling of elastic intraplate stresses due to ...
Indian Academy of Sciences (India)
Finite element modelling of elastic intraplate stresses due to heterogeneities in crustal density and mechanical properties for the Jabalpur earthquake region, central India. A Manglik1,∗. , S Thiagarajan. 1. , A V Mikhailova. 2 and Yu Rebetsky. 2. 1. National Geophysical Research Institute, Uppal Road, Hyderabad 500 007, ...
An Orthogonal Residual Procedure for Nonlinear Finite Element Equations
DEFF Research Database (Denmark)
Krenk, S.
A general and robust solution procedure for nonlinear finite element equations with limit points is developed. At each equilibrium iteration the magnitude of the load is adjusted such that the residual force is orthogonal to the current displacement increment from the last equilibrium state...
Beam section stiffness properties usig 3D finite elements
DEFF Research Database (Denmark)
Couturier, Philippe; Krenk, Steen; Høgsberg, Jan Becker
2013-01-01
The cross-section properties of a beam is characterized by a six by six stiffness matrix, relating the six generalized strains to the conjugate section forces. The problem is formulated as a single-layer finite element model of a slice of the beam, on which the six deformation modes are imposed via...
Review on finite element method | Erhunmwun | Journal of Applied ...
African Journals Online (AJOL)
In this work, we have discussed what Finite Element Method (FEM) is, its historical development, advantages and its future. The eventual intension of using FEM is to determine the nodal solution of a particular problem under study. The power of FEM is its ability to discretize complex problems and analyse it part by part.
Stochastic Finite Elements in Reliability-Based Structural Optimization
DEFF Research Database (Denmark)
Sørensen, John Dalsgaard; Engelund, S.
Application of stochastic finite elements in structural optimization is considered. It is shown how stochastic fields modelling e.g. the modulus of elasticity can be discretized in stochastic variables and how a sensitivity analysis of the reliability of a structural system with respect...
Appendix F : finite element analysis of end region.
2013-03-01
FE (finite element) modeling was conducted to 1) provide a better understanding of the : elastic behavior of the end region prior to cracking and 2) to evaluate the effects of bearing pad : stiffness and width on end region elastic stresses. The FEA ...
Finite element analysis of ship structural connections (fracture of ships)
African Journals Online (AJOL)
The stress analysis for a right angled welded joint is characterized with some level of difficulty when assessing results from finite element analysis. Setting up the model itself and undertaking the analysis needs some skill and also takes longer time to interpret the results. This paper, reports of some work done to derive ...
Finite element concept to derive isostatic residual maps-Application ...
Indian Academy of Sciences (India)
A new space-domain operator based on the shape function concept of finite element analysis has been developed to derive the residual maps of the Gorda Plate of western United States. The technique does not require explicit assumptions on isostatic models. Besides delineating the Gorda Plate boundary, the residual ...
Nonlinear Finite Element Analysis of Pull-Out Test
DEFF Research Database (Denmark)
Saabye Ottesen, N
1981-01-01
A specific pull-out test used to determine in-situ concrete compressive strength is analyzed. This test consists of a steel disc that is extracted from the structure. The finite element analysis considers cracking as well as strain hardening and softening in the pre- and post-failure region...
Finite Element Modelling Of Solidification Of Zinc Alloy | Osinkolu ...
African Journals Online (AJOL)
The solidification process of Zinc alloy is modelled by solving heat transfer equations with the aid of finite element method (FEM) using appropriate boundary conditions at the mould walls. The commercial software, Matlab, has been used to model the solidification process. The temperature profiles for each casting condition ...
Finite element analysis of one–dimensional hydrodynamic ...
African Journals Online (AJOL)
In this research work, we consider the one dimensional hydrodynamic dispersion of a reactive solute in electroosmotic flow. We present results demonstrating the utility of finite element methods to simulate and visualize hydrodynamic dispersion in the electroosmotic flow. From examination of concentration profile, effective ...
Feasibility Study of a Knowledge Based Finite Element Modeling Assistant.
1988-02-01
computer graphics, computer-aided design, computer vision , etc. and in- terest. in representing and reasoning about shapes and spatial relations is...descriptions. Arificial Intelligence 14:1-39, 1980. [Taig 86] Ian C. Taig. Expert Aids to Finite Element System Applications. In D. Srram and R. Adey
Finite Elements Approximate Flows of Compressible Viscous Melt ...
African Journals Online (AJOL)
The processing over flow encountered while generating finite elements was assumed to arise as a result of increasing wave interference. Although the flow frequency was found to be increasing, it was insufficient for improving the prescribed energy level. Conclusively, it was assumed that the flow of the fluid being ...
The finite element method in computational fluid mechanics
Baker, A. J.
1977-01-01
A finite element solution algorithm is established for a general statement of the time-averaged Navier-Stokes equations governing multi-dimensional turbulent flows. Numerical results are presented which evaluate factors affecting solution accuracy for a broad spectrum of linear and non-linear problem classes.
Finite element analysis of bone loss around failing implants
Wolff, J.; Narra, N.; Antalainen, A.K.; Valášek, J.; Kaiser, J.; Sandór, G.K.; Marcián, P.
2014-01-01
Dental implants induce diverse forces on their surrounding bone. However, when excessive unphysiological forces are applied, resorption of the neighbouring bone may occur. The aim of this study was to assess possible causes of bone loss around failing dental implants using finite element analysis. A
(ajst) finite element analysis of a fluid-structure
African Journals Online (AJOL)
6th International Conference on Pressure. Surges, Cambridge, England C2. [9] Wiggert, D. C., Tijsseling, A. S. Fluid transients and fluid-structure interaction in flexible liquid-filled piping. 2001. ASME Applied Mechanics Reviews. Vol. 54. PP455-481. [10] Zienkiewicz O. C. and Taylor, R. L. The finite element method 1989.
Finite element investigation of the prestressed jointed concrete ...
African Journals Online (AJOL)
Precast prestressed concrete pavement (PCP) technology is of recent origin, and the information on PCP performance is not available in literature. This research presents a finite-element analysis of the potential benefits of prestressing on the jointed concrete pavements (JCP). With using a 3-dimensional (3D) ...
Surface processing methods for point sets using finite elements
Clarenz, Ulrich; Rumpf, Martin; Telea, Alexandru
2004-01-01
We present a framework for processing point-based surfaces via partial differential equations (PDEs). Our framework efficiently and effectively brings well-known PDE-based processing techniques to the field of point-based surfaces. At the core of our method is a finite element discretization of PDEs
On angle conditions in the finite element method
Brandts, J.; Hannukainen, A.; Korotov, S.; Krizek, M.
2011-01-01
Abstract Angle conditions play an important role in the analysis of the finite element method. They enable us to derive the optimal interpolation order and prove convergence of this method, to derive various a posteriori error estimates, to perform regular mesh refinements, etc. In 1968, Miloˇs
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.
Design, development and use of the finite element machine
Adams, L. M.; Voigt, R. C.
1983-01-01
Some of the considerations that went into the design of the Finite Element Machine, a research asynchronous parallel computer are described. The present status of the system is also discussed along with some indication of the type of results that were obtained.
Implicit extrapolation methods for multilevel finite element computations
Energy Technology Data Exchange (ETDEWEB)
Jung, M.; Ruede, U. [Technische Universitaet Chemnitz-Zwickau (Germany)
1994-12-31
The finite element package FEMGP has been developed to solve elliptic and parabolic problems arising in the computation of magnetic and thermomechanical fields. FEMGP implements various methods for the construction of hierarchical finite element meshes, a variety of efficient multilevel solvers, including multigrid and preconditioned conjugate gradient iterations, as well as pre- and post-processing software. Within FEMGP, multigrid {tau}-extrapolation can be employed to improve the finite element solution iteratively to higher order. This algorithm is based on an implicit extrapolation, so that the algorithm differs from a regular multigrid algorithm only by a slightly modified computation of the residuals on the finest mesh. Another advantage of this technique is, that in contrast to explicit extrapolation methods, it does not rely on the existence of global error expansions, and therefore neither requires uniform meshes nor global regularity assumptions. In the paper the authors will analyse the {tau}-extrapolation algorithm and present experimental results in the context of the FEMGP package. Furthermore, the {tau}-extrapolation results will be compared to higher order finite element solutions.
Finite element analysis of moisture migration, creep, shrinkage and cracking
Zijl, G.P.A.G. van; Borst, R. de; Rots, J.G.
1999-01-01
A finite element formulation is presented for the analysis of moisture migra-tion, creep, shrinkage and cracking in cementitious materials. A one-way coupled approach is followed, where the pore humidity, the driving force for shrinkage, is solved for from a diffusion equation. The evolution of the
Finite element analyses of wood laminated composite poles
Cheng Piao; Todd F. Shupe; R.C. Tang; Chung Y. Hse
2005-01-01
Finite element analyses using ANSYS were conducted on orthotropic, polygonal, wood laminated composite poles subjected to a body force and a concentrated load at the free end. Deflections and stress distributions of small-scale and full-size composite poles were analyzed and compared to the results obtained in an experimental study. The predicted deflection for both...
Efficient implicit finite element analysis of sheet forming processes
van den Boogaard, Antonius H.; Meinders, Vincent T.; Huetink, Han
2003-01-01
The computation time for implicit finite element analyses tends to increase disproportionally with increasing problem size. This is due to the repeated solution of linear sets of equations, if direct solvers are used. By using iterative linear equation solvers the total analysis time can be reduced
Hands on applied finite element analysis application with ANSYS
Arslan, Mehmet Ali
2015-01-01
Hands on Applied Finite Element Analysis Application with Ansys is truly an extraordinary book that offers practical ways of tackling FEA problems in machine design and analysis. In this book, 35 good selection of example problems have been presented, offering students the opportunity to apply their knowledge to real engineering FEA problem solutions by guiding them with real life hands on experience.
Finite Element Vibration and Dynamic Response Analysis of Engineering Structures
Directory of Open Access Journals (Sweden)
Jaroslav Mackerle
2000-01-01
Full Text Available This bibliography lists references to papers, conference proceedings, and theses/dissertations dealing with finite element vibration and dynamic response analysis of engineering structures that were published from 1994 to 1998. It contains 539 citations. The following types of structures are included: basic structural systems; ground structures; ocean and coastal structures; mobile structures; and containment structures.
The future of the finite element method in geotechnics
Brinkgreve, R.B.J.
2012-01-01
In this presentation a vision is given on tlie fiiture of the finite element method (FEM) for geotechnical engineering and design. In the past 20 years the FEM has proven to be a powerful method for estimating deformation, stability and groundwater flow in geoteclmical stmctures. Much has been
Dedicated finite elements for electrode thin films on quartz resonators.
Srivastava, Sonal A; Yong, Yook-Kong; Tanaka, Masako; Imai, Tsutomu
2008-08-01
The accuracy of the finite element analysis for thickness shear quartz resonators is a function of the mesh resolution; the finer the mesh resolution, the more accurate the finite element solution. A certain minimum number of elements are required in each direction for the solution to converge. This places a high demand on memory for computation, and often the available memory is insufficient. Typically the thickness of the electrode films is very small compared with the thickness of the resonator itself; as a result, electrode elements have very poor aspect ratios, and this is detrimental to the accuracy of the result. In this paper, we propose special methods to model the electrodes at the crystal interface of an AT cut crystal. This reduces the overall problem size and eliminates electrode elements having poor aspect ratios. First, experimental data are presented to demonstrate the effects of electrode film boundary conditions on the frequency-temperature curves of an AT cut plate. Finite element analysis is performed on a mesh representing the resonator, and the results are compared for testing the accuracy of the analysis itself and thus validating the results of analysis. Approximations such as lumping and Guyan reduction are then used to model the electrode thin films at the electrode interface and their results are studied. In addition, a new approximation called merging is proposed to model electrodes at the electrode interface.
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.
An efficient structural finite element for inextensible flexible risers
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.
Finite element and discontinuous Galerkin methods for transient wave equations
Cohen, Gary
2017-01-01
This monograph presents numerical methods for solving transient wave equations (i.e. in time domain). More precisely, it provides an overview of continuous and discontinuous finite element methods for these equations, including their implementation in physical models, an extensive description of 2D and 3D elements with different shapes, such as prisms or pyramids, an analysis of the accuracy of the methods and the study of the Maxwell’s system and the important problem of its spurious free approximations. After recalling the classical models, i.e. acoustics, linear elastodynamics and electromagnetism and their variational formulations, the authors present a wide variety of finite elements of different shapes useful for the numerical resolution of wave equations. Then, they focus on the construction of efficient continuous and discontinuous Galerkin methods and study their accuracy by plane wave techniques and a priori error estimates. A chapter is devoted to the Maxwell’s system and the important problem ...
Foundations of finite element applications to neutron transport
Energy Technology Data Exchange (ETDEWEB)
Ackroyd, R.T. [Imperial Coll. of Science and Technology, London (United Kingdom). Dept. of Mechanical Engineering
1995-06-01
The use of finite elements in neutron transport gives deterministic treatments a geometrical capability with a flexibility comparable to that achievable by the stochastic Monte Carlo method. The principles used in obtaining solutions can be used also to assess the accuracy of numerical solutions. These assessment methods are illustrated by close bracketing bounds for local error and disadvantage factors. Principles are described for the steady state which guarantee neutron conservation for the whole finite element mesh. Some new principles are described which guarantee neutron conservation over each element of a mesh. For time dependent transport a principle guarantees neutron conservation with time over the whole mesh. The paper concludes with a sketch of fundamental work with the potential to exploit recent developments in computer architecture. (author).
Evaluation of Concrete Cylinder Tests Using Finite Elements
DEFF Research Database (Denmark)
Saabye Ottosen, Niels
1984-01-01
Nonlinear axisymmetric finite element analyses are performed on the uniaxial compressive test of concrete cylinders. The models include thick steel loading plates, and cylinders with height‐to‐diameter ratios (h/d) ranging from 1‐3 are treated. A simple constitutive model of the concrete...... uniaxial strength the use of geometrically matched loading plates seems to be advantageous. Finally, it is observed that for variations of the element size within limits otherwise required to obtain a realistic analysis, the results are insensitive to the element size....
Finite-size scaling for quantum criticality using the finite-element method.
Antillon, Edwin; Wehefritz-Kaufmann, Birgit; Kais, Sabre
2012-03-01
Finite size scaling for the Schrödinger equation is a systematic approach to calculate the quantum critical parameters for a given Hamiltonian. This approach has been shown to give very accurate results for critical parameters by using a systematic expansion with global basis-type functions. Recently, the finite-element method was shown to be a powerful numerical method for ab initio electronic-structure calculations with a variable real-space resolution. In this work, we demonstrate how to obtain quantum critical parameters by combining the finite-element method (FEM) with finite size scaling (FSS) using different ab initio approximations and exact formulations. The critical parameters could be atomic nuclear charges, internuclear distances, electron density, disorder, lattice structure, and external fields for stability of atomic, molecular systems and quantum phase transitions of extended systems. To illustrate the effectiveness of this approach we provide detailed calculations of applying FEM to approximate solutions for the two-electron atom with varying nuclear charge; these include Hartree-Fock, local density approximation, and an "exact" formulation using FEM. We then use the FSS approach to determine its critical nuclear charge for stability; here, the size of the system is related to the number of elements used in the calculations. Results prove to be in good agreement with previous Slater-basis set calculations and demonstrate that it is possible to combine finite size scaling with the finite-element method by using ab initio calculations to obtain quantum critical parameters. The combined approach provides a promising first-principles approach to describe quantum phase transitions for materials and extended systems.
Finite element analysis of structures through unified formulation
Carrera, Erasmo; Petrolo, Marco; Zappino, Enrico
2014-01-01
The finite element method (FEM) is a computational tool widely used to design and analyse complex structures. Currently, there are a number of different approaches to analysis using the FEM that vary according to the type of structure being analysed: beams and plates may use 1D or 2D approaches, shells and solids 2D or 3D approaches, and methods that work for one structure are typically not optimized to work for another. Finite Element Analysis of Structures Through Unified Formulation deals with the FEM used for the analysis of the mechanics of structures in the case of linear elasticity. The novelty of this book is that the finite elements (FEs) are formulated on the basis of a class of theories of structures known as the Carrera Unified Formulation (CUF). It formulates 1D, 2D and 3D FEs on the basis of the same ''fundamental nucleus'' that comes from geometrical relations and Hooke''s law, and presents both 1D and 2D refined FEs that only have displacement variables as in 3D elements. It also covers 1D...
A tool for finite element deflection analysis of wings
Energy Technology Data Exchange (ETDEWEB)
Carlen, Ingemar
2005-03-01
A first version (ver 0.1) of a new tool for finite element deflection analysis of wind turbine blades is presented. The software is called SOLDE (SOLid blaDE), and was developed as a Matlab shell around the free finite element codes CGX (GraphiX - pre-processor), and CCX (CrunchiX - solver). In the present report a brief description of SOLDE is given, followed by a basic users guide. The main features of SOLDE are: - Deflection analysis of wind turbine blades, including 3D effects and warping. - Accurate prediction of eigenmodes and eigenfrequencies. - Derivation of 2-node slender elements for use in various aeroelastic analyses. The main differences between SOLDE and other similar tools can be summarised as: - SOLDE was developed without a graphical user interface or a traditional text file input deck. Instead the input is organised as Matlab data structures that have to be formed by a user provided pre-processor. - SOLDE uses a solid representation of the geometry instead of a thin shell approximation. The benefit is that the bending-torsion couplings will automatically be correctly captured. However, a drawback with the current version is that the equivalent orthotropic shell idealisation violates the local bending characteristics, which makes the model useless for buckling analyses. - SOLDE includes the free finite element solver CCX, and thus no expensive commercial software (e.g. Ansys, or Nastran) is required to produce results.
FINITE ELEMENT MODELING OF DELAMINATION PROCESS ON COMPOSITE LAMINATE USING COHESIVE ELEMENTS
Directory of Open Access Journals (Sweden)
S. Huzn
2013-06-01
Full Text Available The implementation of cohesive elements for studying the delamination process in composite laminates is presented in this paper. The commercially available finite element software ABAQUS provides the cohesive element model used in this study. Cohesive elements with traction-separation laws consist of an initial linear elastic phase, followed by a linear softening that simulates the debonding of the interface after damage initiation is inserted at the interfaces between the laminas. Simulation results from two types of composite laminate specimen, i.e., a double cantilever beam and an L-shape, show that the delamination process on laminated composites begin with debonding phenomena. These results indicate that the implementation of cohesive elements in modeling the process of delamination in laminated composite materials, using the finite element method, has been successful. Cohesive elements are able to model the phenomenon of delamination in the specimens used in this study.
Multibody Finite Element Method and Application in Hydraulic Structure Analysis
Directory of Open Access Journals (Sweden)
Chao Su
2015-01-01
Full Text Available Multibody finite element method is proposed for analysis of contact problems in hydraulic structure. This method is based on the block theory of discontinuous deformation analysis (DDA method and combines advantages of finite element method (FEM and the displacement compatibility equation in classical elastic mechanics. Each single block is analyzed using FEM in corresponding local coordinate system and all contacting blocks need to satisfy the displacement compatibility requirement between any two blocks in a blocky system. It is proved that this method is very efficient and practical to overcome the limitations in DDA method when tackling contact problems, such as the overlap problem and the equal strain assumption. In this paper, detailed theoretical basis and formulations are given. Two numerical examples are performed to verify the proposed method successfully. Furthermore, this method is adopted to study the stability issues of underground houses of a large hydropower station.
Introduction to assembly of finite element methods on graphics processors
Cecka, Cristopher; Lew, Adrian; Darve, Eric
2010-06-01
Recently, graphics processing units (GPUs) have had great success in accelerating numerical computations. We present their application to computations on unstructured meshes such as those in finite element methods. Multiple approaches in assembling and solving sparse linear systems with NVIDIA GPUs and the Compute Unified Device Architecture (CUDA) are presented and discussed. Multiple strategies for efficient use of global, shared, and local memory, methods to achieve memory coalescing, and optimal choice of parameters are introduced. We find that with appropriate preprocessing and arrangement of support data, the GPU coprocessor achieves speedups of 30x or more in comparison to a well optimized serial implementation on the CPU. We also find that the optimal assembly strategy depends on the order of polynomials used in the finite-element discretization.
Finite element solution of transient fluid-structure interaction problems
Everstine, Gordon C.; Cheng, Raymond S.; Hambric, Stephen A.
1991-01-01
A finite element approach using NASTRAN is developed for solving time-dependent fluid-structure interaction problems, with emphasis on the transient scattering of acoustic waves from submerged elastic structures. Finite elements are used for modeling both structure and fluid domains to facilitate the graphical display of the wave motion through both media. For the liquid, the use of velocity potential as the fundamental unknown results in a symmetric matrix equation. The approach is illustrated for the problem of transient scattering from a submerged elastic spherical shell subjected to an incident tone burst. The use of an analogy between the equations of elasticity and the wave equation of acoustics, a necessary ingredient to the procedure, is summarized.
Assembly of finite element methods on graphics processors
Cecka, Cris
2010-08-23
Recently, graphics processing units (GPUs) have had great success in accelerating many numerical computations. We present their application to computations on unstructured meshes such as those in finite element methods. Multiple approaches in assembling and solving sparse linear systems with NVIDIA GPUs and the Compute Unified Device Architecture (CUDA) are created and analyzed. Multiple strategies for efficient use of global, shared, and local memory, methods to achieve memory coalescing, and optimal choice of parameters are introduced. We find that with appropriate preprocessing and arrangement of support data, the GPU coprocessor using single-precision arithmetic achieves speedups of 30 or more in comparison to a well optimized double-precision single core implementation. We also find that the optimal assembly strategy depends on the order of polynomials used in the finite element discretization. © 2010 John Wiley & Sons, Ltd.
Domain Decomposition Solvers for Frequency-Domain Finite Element Equations
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.
Finite Element Analysis of Electrically Excited Quartz Tuning Fork Devices
Oria, Roger; Otero, Jorge; González, Laura; Botaya, Luis; Carmona, Manuel; Puig-Vidal, Manel
2013-01-01
Quartz Tuning Fork (QTF)-based Scanning Probe Microscopy (SPM) is an important field of research. A suitable model for the QTF is important to obtain quantitative measurements with these devices. Analytical models have the limitation of being based on the double cantilever configuration. In this paper, we present an electromechanical finite element model of the QTF electrically excited with two free prongs. The model goes beyond the state-of-the-art of numerical simulations currently found in the literature for this QTF configuration. We present the first numerical analysis of both the electrical and mechanical behavior of QTF devices. Experimental measurements obtained with 10 units of the same model of QTF validate the finite element model with a good agreement. PMID:23722828
Finite Element Analysis of Electrically Excited Quartz Tuning Fork Devices
Directory of Open Access Journals (Sweden)
Manel Puig-Vidal
2013-05-01
Full Text Available Quartz Tuning Fork (QTF-based Scanning Probe Microscopy (SPM is an important field of research. A suitable model for the QTF is important to obtain quantitative measurements with these devices. Analytical models have the limitation of being based on the double cantilever configuration. In this paper, we present an electromechanical finite element model of the QTF electrically excited with two free prongs. The model goes beyond the state-of-the-art of numerical simulations currently found in the literature for this QTF configuration. We present the first numerical analysis of both the electrical and mechanical behavior of QTF devices. Experimental measurements obtained with 10 units of the same model of QTF validate the finite element model with a good agreement.
The finite element method and applications in engineering using ANSYS
Madenci, Erdogan
2015-01-01
This textbook offers theoretical and practical knowledge of the finite element method. The book equips readers with the skills required to analyze engineering problems using ANSYS®, a commercially available FEA program. Revised and updated, this new edition presents the most current ANSYS® commands and ANSYS® screen shots, as well as modeling steps for each example problem. This self-contained, introductory text minimizes the need for additional reference material by covering both the fundamental topics in finite element methods and advanced topics concerning modeling and analysis. It focuses on the use of ANSYS® through both the Graphics User Interface (GUI) and the ANSYS® Parametric Design Language (APDL). Extensive examples from a range of engineering disciplines are presented in a straightforward, step-by-step fashion. Key topics include: • An introduction to FEM • Fundamentals and analysis capabilities of ANSYS® • Fundamentals of discretization and approximation functions • Modeling techniq...
A finite element model of ferroelectric/ferroelastic polycrystals
Energy Technology Data Exchange (ETDEWEB)
HWANG,STEPHEN C.; MCMEEKING,ROBERT M.
2000-02-17
A finite element model of polarization switching in a polycrystalline ferroelectric/ferroelastic ceramic is developed. It is assumed that a crystallite switches if the reduction in potential energy of the polycrystal exceeds a critical energy barrier per unit volume of switching material. Each crystallite is represented by a finite element with the possible dipole directions assigned randomly subject to crystallographic constraints. The model accounts for both electric field induced (i.e. ferroelectric) switching and stress induced (i.e. ferroelastic) switching with piezoelectric interactions. Experimentally measured elastic, dielectric, and piezoelectric constants are used consistently, but different effective critical energy barriers are selected phenomenologically. Electric displacement versus electric field, strain versus electric field, stress versus strain, and stress versus electric displacement loops of a ceramic lead lanthanum zirconate titanate (PLZT) are modeled well below the Curie temperature.
Finite element solution theory for three-dimensional boundary flows
Baker, A. J.
1974-01-01
A finite element algorithm is derived for the numerical solution of a three-dimensional flow field described by a system of initial-valued, elliptic boundary value partial differential equations. The familiar three-dimensional boundary layer equations belong to this description when diffusional processes in only one coordinate direction are important. The finite element algorithm transforms the original description into large order systems of ordinary differential equations written for the dependent variables discretized at node points of an arbitrarily irregular computational lattice. The generalized elliptic boundary conditions is piecewise valid for each dependent variable on boundaries that need not explicitly coincide with coordinate surfaces. Solutions for sample problems in laminar and turbulent boundary flows illustrate favorable solution accuracy, convergence, and versatility.
Solution strategies for implicit nonlinear finite element analysis
Energy Technology Data Exchange (ETDEWEB)
Engelmann, B.E.; Whirley, R.G.
1991-08-08
The development of effective solution strategies to solve the global nonlinear equations which arise in implicit finite element analysis is an important area of research. Efficient strategies make good use of computational resources, and allow larger and more complex analysis models to be studies. Robust algorithms are essential to handle the complex nonlinearities which arise in many engineering applications, such as metalforming process simulation. Our research indicates that robustness can be best achieved in a general setting through adaptive solution strategies. This adaptivity and flexibility has been incorporated into an implicit nonlinear finite element code, NIKE2D. Temporal and algorithmic adaptivity is achieved through the development of ISLAND (Interactive Solution Language for an Adaptive Nike Driver). These new solution control features make NIKE2D a smart code,'' and permit many new and challenging problems to be addressed. 3 refs.
Solution strategies for implicit nonlinear finite element analysis
Energy Technology Data Exchange (ETDEWEB)
Engelmann, B.E.; Whirley, R.G.
1991-08-08
The development of effective solution strategies to solve the global nonlinear equations which arise in implicit finite element analysis is an important area of research. Efficient strategies make good use of computational resources, and allow larger and more complex analysis models to be studies. Robust algorithms are essential to handle the complex nonlinearities which arise in many engineering applications, such as metalforming process simulation. Our research indicates that robustness can be best achieved in a general setting through adaptive solution strategies. This adaptivity and flexibility has been incorporated into an implicit nonlinear finite element code, NIKE2D. Temporal and algorithmic adaptivity is achieved through the development of ISLAND (Interactive Solution Language for an Adaptive Nike Driver). These new solution control features make NIKE2D a ``smart code,`` and permit many new and challenging problems to be addressed. 3 refs.
Finite-element modelling of multilayer X-ray optics.
Cheng, Xianchao; Zhang, Lin
2017-05-01
Multilayer optical elements for hard X-rays are an attractive alternative to crystals whenever high photon flux and moderate energy resolution are required. Prediction of the temperature, strain and stress distribution in the multilayer optics is essential in designing the cooling scheme and optimizing geometrical parameters for multilayer optics. The finite-element analysis (FEA) model of the multilayer optics is a well established tool for doing so. Multilayers used in X-ray optics typically consist of hundreds of periods of two types of materials. The thickness of one period is a few nanometers. Most multilayers are coated on silicon substrates of typical size 60 mm × 60 mm × 100-300 mm. The high aspect ratio between the size of the optics and the thickness of the multilayer (10 7 ) can lead to a huge number of elements for the finite-element model. For instance, meshing by the size of the layers will require more than 10 16 elements, which is an impossible task for present-day computers. Conversely, meshing by the size of the substrate will produce a too high element shape ratio (element geometry width/height > 10 6 ), which causes low solution accuracy; and the number of elements is still very large (10 6 ). In this work, by use of ANSYS layer-functioned elements, a thermal-structural FEA model has been implemented for multilayer X-ray optics. The possible number of layers that can be computed by presently available computers is increased considerably.
Finite-element modelling of multilayer X-ray optics
Energy Technology Data Exchange (ETDEWEB)
Cheng, Xianchao; Zhang, Lin
2017-04-11
Multilayer optical elements for hard X-rays are an attractive alternative to crystals whenever high photon flux and moderate energy resolution are required. Prediction of the temperature, strain and stress distribution in the multilayer optics is essential in designing the cooling scheme and optimizing geometrical parameters for multilayer optics. The finite-element analysis (FEA) model of the multilayer optics is a well established tool for doing so. Multilayers used in X-ray optics typically consist of hundreds of periods of two types of materials. The thickness of one period is a few nanometers. Most multilayers are coated on silicon substrates of typical size 60 mm × 60 mm × 100–300 mm. The high aspect ratio between the size of the optics and the thickness of the multilayer (10^{7}) can lead to a huge number of elements for the finite-element model. For instance, meshing by the size of the layers will require more than 10^{16}elements, which is an impossible task for present-day computers. Conversely, meshing by the size of the substrate will produce a too high element shape ratio (element geometry width/height > 10^{6}), which causes low solution accuracy; and the number of elements is still very large (10^{6}). In this work, by use of ANSYS layer-functioned elements, a thermal-structural FEA model has been implemented for multilayer X-ray optics. The possible number of layers that can be computed by presently available computers is increased considerably.
OOFEM – An Object Oriented Framework for Finite Element Analysis
Directory of Open Access Journals (Sweden)
B. Patzák
2004-01-01
Full Text Available This paper presents the design principles and structure of the object-oriented finite element software OOFEM, which has been under active development for several years. The main advantages of the presented framework include modular design, extensibility, and robustness. The code itself is freely available and is distributed under GNU public license. It provides tools for linear and nonlinear analysis of mechanical and transport problems on sequential and parallel computers.
The Applications of Finite Element Analysis in Proximal Humeral Fractures
Yongyu Ye; Wei You; Weimin Zhu; Jiaming Cui; Kang Chen; Daping Wang
2017-01-01
Proximal humeral fractures are common and most challenging, due to the complexity of the glenohumeral joint, especially in the geriatric population with impacted fractures, that the development of implants continues because currently the problems with their fixation are not solved. Pre-, intra-, and postoperative assessments are crucial in management of those patients. Finite element analysis, as one of the valuable tools, has been implemented as an effective and noninvasive method to analyze...
Customized finite element modelling of the human cornea
Irene Simonini; Anna Pandolfi
2015-01-01
Aim To construct patient-specific solid models of human cornea from ocular topographer data, to increase the accuracy of the biomechanical and optical estimate of the changes in refractive power and stress caused by photorefractive keratectomy (PRK). Method Corneal elevation maps of five human eyes were taken with a rotating Scheimpflug camera combined with a Placido disk before and after refractive surgery. Patient-specific solid models were created and discretized in finite elements to esti...
[Three dimensional mathematical model of tooth for finite element analysis].
Puskar, Tatjana; Vasiljević, Darko; Marković, Dubravka; Jevremović, Danimir; Pantelić, Dejan; Savić-Sević, Svetlana; Murić, Branka
2010-01-01
The mathematical model of the abutment tooth is the starting point of the finite element analysis of stress and deformation of dental structures. The simplest and easiest way is to form a model according to the literature data of dimensions and morphological characteristics of teeth. Our method is based on forming 3D models using standard geometrical forms (objects) in programmes for solid modeling. Forming the mathematical model of abutment of the second upper premolar for finite element analysis of stress and deformation of dental structures. The abutment tooth has a form of a complex geometric object. It is suitable for modeling in programs for solid modeling SolidWorks. After analysing the literature data about the morphological characteristics of teeth, we started the modeling dividing the tooth (complex geometric body) into simple geometric bodies (cylinder, cone, pyramid,...). Connecting simple geometric bodies together or substricting bodies from the basic body, we formed complex geometric body, tooth. The model is then transferred into Abaqus, a computational programme for finite element analysis. Transferring the data was done by standard file format for transferring 3D models ACIS SAT. Using the programme for solid modeling SolidWorks, we developed three models of abutment of the second maxillary premolar: the model of the intact abutment, the model of the endodontically treated tooth with two remaining cavity walls and the model of the endodontically treated tooth with two remaining walls and inserted post. Mathematical models of the abutment made according to the literature data are very similar with the real abutment and the simplifications are minimal. These models enable calculations of stress and deformation of the dental structures. The finite element analysis provides useful information in understanding biomechanical problems and gives guidance for clinical research.
The Development of Piezoelectric Accelerometers Using Finite Element Analysis
DEFF Research Database (Denmark)
Liu, Bin
1999-01-01
This paper describes the application of Finite Element (FE) approach for the development of piezoelectric accelerometers. An accelerometer is simulated using the FE approach as an example. Good agreement is achieved between simulated results and calibrated results. It is proved that the FE modeling...... can be effectively used to predict the specifications of the accelerometer, especially when modification of the accelerometer is required. The FE developing technology forms the bases of fast responsiveness and flexible customized design of piezoelectric accelerometers....
Building Finite Element Models to Investigate Zebrafish Jaw Biomechanics.
Brunt, Lucy H; Roddy, Karen A; Rayfield, Emily J; Hammond, Chrissy L
2016-12-03
Skeletal morphogenesis occurs through tightly regulated cell behaviors during development; many cell types alter their behavior in response to mechanical strain. Skeletal joints are subjected to dynamic mechanical loading. Finite element analysis (FEA) is a computational method, frequently used in engineering that can predict how a material or structure will respond to mechanical input. By dividing a whole system (in this case the zebrafish jaw skeleton) into a mesh of smaller 'finite elements', FEA can be used to calculate the mechanical response of the structure to external loads. The results can be visualized in many ways including as a 'heat map' showing the position of maximum and minimum principal strains (a positive principal strain indicates tension while a negative indicates compression. The maximum and minimum refer the largest and smallest strain). These can be used to identify which regions of the jaw and therefore which cells are likely to be under particularly high tensional or compressional loads during jaw movement and can therefore be used to identify relationships between mechanical strain and cell behavior. This protocol describes the steps to generate Finite Element models from confocal image data on the musculoskeletal system, using the zebrafish lower jaw as a practical example. The protocol leads the reader through a series of steps: 1) staining of the musculoskeletal components, 2) imaging the musculoskeletal components, 3) building a 3 dimensional (3D) surface, 4) generating a mesh of Finite Elements, 5) solving the FEA and finally 6) validating the results by comparison to real displacements seen in movements of the fish jaw.
Finite groups with three conjugacy class sizes of some elements
Indian Academy of Sciences (India)
Abstract. Let G be a finite group. We prove as follows: Let G be a p-solvable group for a fixed prime p. If the conjugacy class sizes of all elements of primary and biprimary orders of G are {1, pa, n} with a and n two positive integers and (p, n) = 1, then G is p-nilpotent or G has abelian Sylow p-subgroups. Keywords. Conjugacy ...
Least-squares finite element method for fluid dynamics
Jiang, Bo-Nan; Povinelli, Louis A.
1989-01-01
An overview is given of new developments of the least squares finite element method (LSFEM) in fluid dynamics. Special emphasis is placed on the universality of LSFEM; the symmetry and positiveness of the algebraic systems obtained from LSFEM; the accommodation of LSFEM to equal order interpolations for incompressible viscous flows; and the natural numerical dissipation of LSFEM for convective transport problems and high speed compressible flows. The performance of LSFEM is illustrated by numerical examples.
Better Finite-Element Analysis of Composite Shell Structures
Clarke, Gregory
2007-01-01
A computer program implements a finite-element-based method of predicting the deformations of thin aerospace structures made of isotropic materials or anisotropic fiber-reinforced composite materials. The technique and corresponding software are applicable to thin shell structures in general and are particularly useful for analysis of thin beamlike members having open cross-sections (e.g. I-beams and C-channels) in which significant warping can occur.
Discontinuous Galerkin Finite Element Method for Parabolic Problems
Kaneko, Hideaki; Bey, Kim S.; Hou, Gene J. W.
2004-01-01
In this paper, we develop a time and its corresponding spatial discretization scheme, based upon the assumption of a certain weak singularity of parallel ut(t) parallel Lz(omega) = parallel ut parallel2, for the discontinuous Galerkin finite element method for one-dimensional parabolic problems. Optimal convergence rates in both time and spatial variables are obtained. A discussion of automatic time-step control method is also included.
Application of Finite Element Method to Analyze Inflatable Waveguide Structures
Deshpande, M. D.
1998-01-01
A Finite Element Method (FEM) is presented to determine propagation characteristics of deformed inflatable rectangular waveguide. Various deformations that might be present in an inflatable waveguide are analyzed using the FEM. The FEM procedure and the code developed here are so general that they can be used for any other deformations that are not considered in this report. The code is validated by applying the present code to rectangular waveguide without any deformations and comparing the numerical results with earlier published results.
Three dimensional mathematical model of tooth for finite element analysis
Directory of Open Access Journals (Sweden)
Puškar Tatjana
2010-01-01
Full Text Available Introduction. The mathematical model of the abutment tooth is the starting point of the finite element analysis of stress and deformation of dental structures. The simplest and easiest way is to form a model according to the literature data of dimensions and morphological characteristics of teeth. Our method is based on forming 3D models using standard geometrical forms (objects in programmes for solid modeling. Objective. Forming the mathematical model of abutment of the second upper premolar for finite element analysis of stress and deformation of dental structures. Methods. The abutment tooth has a form of a complex geometric object. It is suitable for modeling in programs for solid modeling SolidWorks. After analyzing the literature data about the morphological characteristics of teeth, we started the modeling dividing the tooth (complex geometric body into simple geometric bodies (cylinder, cone, pyramid,.... Connecting simple geometric bodies together or substricting bodies from the basic body, we formed complex geometric body, tooth. The model is then transferred into Abaqus, a computational programme for finite element analysis. Transferring the data was done by standard file format for transferring 3D models ACIS SAT. Results. Using the programme for solid modeling SolidWorks, we developed three models of abutment of the second maxillary premolar: the model of the intact abutment, the model of the endodontically treated tooth with two remaining cavity walls and the model of the endodontically treated tooth with two remaining walls and inserted post. Conclusion Mathematical models of the abutment made according to the literature data are very similar with the real abutment and the simplifications are minimal. These models enable calculations of stress and deformation of the dental structures. The finite element analysis provides useful information in understanding biomechanical problems and gives guidance for clinical research.
Evaluation of a Nonlinear Finite Element Program - ABAQUS.
1983-03-15
Elastic-plastic material and small deformation Material Properties: A Ramberg - Osgood stress-strain curve was assumed to represent the strain-hardening...NONLINEAR FINITE ELEMENT PROGRAM - ABAQUS T. Y. Chang S. M. Wang Department of Civil Engineering The University of Akron Akron, Ohio 44325 August 1, 1982... ABAQUS T. Y. Chang S. M. Wang Department of Civil Engineering The University of Akron Akron, Ohio 44325 August 1, 1982 (Revised on March 15, 1983
Piezoelectric theory for finite element analysis of ultrasonic motors
Energy Technology Data Exchange (ETDEWEB)
Emery, J.D.; Mentesana, C.P.
1997-06-01
The authors present the fundamental equations of piezoelectricity and references. They show how a second form of the equations and a second set of coefficients can be found, through inversions involving the elasticity tensor. They show how to compute the clamped permittivity matrix from the unclamped matrix. The authors list the program pzansys.ftn and present examples of its use. This program does the conversions and calculations needed by the finite element program ANSYS.
Convergence of a residual based artificial viscosity finite element method
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.
Free vibration analysis of dragonfly wings using finite element method
M Darvizeh; A Darvizeh; H Rajabi; A Rezaei
2016-01-01
In the present work, investigations on the microstructure and mechanicalproperties of the dragonfly wing are carried out and numerical modelingbased on Finite Element Method (FEM) is developed to predict Flightcharacteristics of dragonfly wings. Vibrational behavior of wings typestructures is immensely important in analysis, design and manufacturing ofsimilar engineering structures. For this purpose natural frequencies andmode shapes are calculated. In addition, the kind of deformation in eac...
Finite element solver for 3-D compressible viscous flows
Reddy, K. C.; Reddy, J. N.
1986-12-01
The space shuttle main engine (SSME) has extremely complex internal flow structure. The geometry of the flow domain is three-dimensional with complicated topology. The flow is compressible, viscous, and turbulent with large gradients in flow quantities and regions of recirculations. The analysis of the flow field in SSME involves several tedious steps. One is the geometrical modeling of the particular zone of the SSME being studied. Accessing the geometry definition, digitalizing it, and developing surface interpolations suitable for an interior grid generator require considerable amount of manual labor. There are several types of grid generators available with some general-purpose finite element programs. An efficient and robust computational scheme for solving 3D Navier-Stokes equations has to be implemented. Post processing software has to be adapted to visualize and analyze the computed 3D flow field. The progress made in a project to develop software for the analysis of the flow is discussed. The technical approach to the development of the finite element scheme and the relaxation procedure are discussed. The three dimensional finite element code for the compressible Navier-Stokes equations is listed.
Statistical osteoporosis models using composite finite elements: a parameter study.
Wolfram, Uwe; Schwen, Lars Ole; Simon, Ulrich; Rumpf, Martin; Wilke, Hans-Joachim
2009-09-18
Osteoporosis is a widely spread disease with severe consequences for patients and high costs for health care systems. The disease is characterised by a loss of bone mass which induces a loss of mechanical performance and structural integrity. It was found that transverse trabeculae are thinned and perforated while vertical trabeculae stay intact. For understanding these phenomena and the mechanisms leading to fractures of trabecular bone due to osteoporosis, numerous researchers employ micro-finite element models. To avoid disadvantages in setting up classical finite element models, composite finite elements (CFE) can be used. The aim of the study is to test the potential of CFE. For that, a parameter study on numerical lattice samples with statistically simulated, simplified osteoporosis is performed. These samples are subjected to compression and shear loading. Results show that the biggest drop of compressive stiffness is reached for transverse isotropic structures losing 32% of the trabeculae (minus 89.8% stiffness). The biggest drop in shear stiffness is found for an isotropic structure also losing 32% of the trabeculae (minus 67.3% stiffness). The study indicates that losing trabeculae leads to a worse drop of macroscopic stiffness than thinning of trabeculae. The results further demonstrate the advantages of CFEs for simulating micro-structured samples.
Thermal buckling comparative analysis using Different FE (Finite Element) tools
Energy Technology Data Exchange (ETDEWEB)
Banasiak, Waldemar; Labouriau, Pedro [INTECSEA do Brasil, Rio de Janeiro, RJ (Brazil); Burnett, Christopher [INTECSEA UK, Surrey (United Kingdom); Falepin, Hendrik [Fugro Engineers SA/NV, Brussels (Belgium)
2009-12-19
High operational temperature and pressure in offshore pipelines may lead to unexpected lateral movements, sometimes call lateral buckling, which can have serious consequences for the integrity of the pipeline. The phenomenon of lateral buckling in offshore pipelines needs to be analysed in the design phase using FEM. The analysis should take into account many parameters, including operational temperature and pressure, fluid characteristic, seabed profile, soil parameters, coatings of the pipe, free spans etc. The buckling initiation force is sensitive to small changes of any initial geometric out-of-straightness, thus the modeling of the as-laid state of the pipeline is an important part of the design process. Recently some dedicated finite elements programs have been created making modeling of the offshore environment more convenient that has been the case with the use of general purpose finite element software. The present paper aims to compare thermal buckling analysis of sub sea pipeline performed using different finite elements tools, i.e. general purpose programs (ANSYS, ABAQUS) and dedicated software (SAGE Profile 3D) for a single pipeline resting on an the seabed. The analyses considered the pipeline resting on a flat seabed with a small levels of out-of straightness initiating the lateral buckling. The results show the quite good agreement of results of buckling in elastic range and in the conclusions next comparative analyses with sensitivity cases are recommended. (author)
Coupling nonlinear Stokes and Darcy flow using mortar finite elements
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.
A phenomenological finite element model of stereolithography processing
Energy Technology Data Exchange (ETDEWEB)
Chambers, R.S.; Guess, T.R.; Hinnerichs, T.D.
1996-03-01
In the stereolithography process, three dimensional parts are built layer by layer using a laser to selectively cure slices of a photocurable resin, one on top of another. As the laser spot passes over the surface of the resin, the ensuing chemical reaction causes the resin to shrink and stiffen during solidification. When laser paths cross or when new layers are cured on top of existing layers, residual stresses are generated as the cure shrinkage of the freshly gelled resin is constrained by the adjoining previously-cured material. These internal stresses can cause curling in the compliant material. A capability for performing finite element analyses of the stereolithography process has been developed. Although no attempt has been made to incorporate all the physics of the process, a numerical platform suitable for such development has been established. A methodology and code architecture have been structured to allow finite elements to be birthed (activated) according to a prescribed order mimicking the procedure by which a laser is used to cure and build-up surface layers of resin to construct a three dimensional geometry. In its present form, the finite element code incorporates a simple phenomenological viscoelastic material model of solidification that is based on the shrinkage and relaxation observed following isolated, uncoupled laser exposures. The phenomenological material model has been used to analyze the curl in a simple cantilever beam and to make qualitative distinctions between two contrived build styles.
Fluid-structure finite-element vibrational analysis
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.
Energy Technology Data Exchange (ETDEWEB)
Dohrmann, C.R.; Heinstein, M.W.; Jung, J.; Key, S.W.
1999-01-01
This report documents a collection of papers on a family of uniform strain tetrahedral finite elements and their connection to different element types. Also included in the report are two papers which address the general problem of connecting dissimilar meshes in two and three dimensions. Much of the work presented here was motivated by the development of the tetrahedral element described in the report "A Suitable Low-Order, Eight-Node Tetrahedral Finite Element For Solids," by S. W. Key {ital et al.}, SAND98-0756, March 1998. Two basic issues addressed by the papers are: (1) the performance of alternative tetrahedral elements with uniform strain and enhanced uniform strain formulations, and (2) the proper connection of tetrahedral and other element types when two meshes are "tied" together to represent a single continuous domain.
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
Energy Technology Data Exchange (ETDEWEB)
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.
Bause, Markus; Radu, Florin A; Köcher, Uwe
2017-01-01
Variational time discretization schemes are getting of increasing importance for the accurate numerical approximation of transient phenomena. The applicability and value of mixed finite element methods in space for simulating transport processes have been demonstrated in a wide class of works. We consider a family of continuous Galerkin-Petrov time discretization schemes that is combined with a mixed finite element approximation of the spatial variables. The existence and uniqueness of the semidiscrete approximation and of the fully discrete solution are established. For this, the Banach-Nečas-Babuška theorem is applied in a non-standard way. Error estimates with explicit rates of convergence are proved for the scalar and vector-valued variable. An optimal order estimate in space and time is proved by duality techniques for the scalar variable. The convergence rates are analyzed and illustrated by numerical experiments, also on stochastically perturbed meshes.
National Research Council Canada - National Science Library
W.R. Azzam
2015-01-01
.... This technique is investigated numerically using finite element analysis. A four story reinforced concrete building that rests on a raft foundation is idealized as a two-dimensional model with and without skirts...
Shear deformable finite beam elements for composite box beams
Kim, Nam-Il; Choi, Dong-Ho
2014-04-01
The shear deformable thin-walled composite beams with closed cross-sections have been developed for coupled flexural, torsional, and buckling analyses. A theoretical model applicable to the thin-walled laminated composite box beams is presented by taking into account all the structural couplings coming from the material anisotropy and the shear deformation effects. The current composite beam includes the transverse shear and the restrained warping induced shear deformation by using the first-order shear deformation beam theory. Seven governing equations are derived for the coupled axial-flexural-torsional-shearing buckling based on the principle of minimum total potential energy. Based on the present analytical model, three different types of finite composite beam elements, namely, linear, quadratic and cubic elements are developed to analyze the flexural, torsional, and buckling problems. In order to demonstrate the accuracy and superiority of the beam theory and the finite beam elements developed by this study, numerical solutions are presented and compared with the results obtained by other researchers and the detailed three-dimensional analysis results using the shell elements of ABAQUS. Especially, the influences of the modulus ratio and the simplified assumptions in stress-strain relations on the deflection, twisting angle, and critical buckling loads of composite box beams are investigated. [Figure not available: see fulltext.
Simulating Space Capsule Water Landing with Explicit Finite Element Method
Wang, John T.; Lyle, Karen H.
2007-01-01
A study of using an explicit nonlinear dynamic finite element code for simulating the water landing of a space capsule was performed. The finite element model contains Lagrangian shell elements for the space capsule and Eulerian solid elements for the water and air. An Arbitrary Lagrangian Eulerian (ALE) solver and a penalty coupling method were used for predicting the fluid and structure interaction forces. The space capsule was first assumed to be rigid, so the numerical results could be correlated with closed form solutions. The water and air meshes were continuously refined until the solution was converged. The converged maximum deceleration predicted is bounded by the classical von Karman and Wagner solutions and is considered to be an adequate solution. The refined water and air meshes were then used in the models for simulating the water landing of a capsule model that has a flexible bottom. For small pitch angle cases, the maximum deceleration from the flexible capsule model was found to be significantly greater than the maximum deceleration obtained from the corresponding rigid model. For large pitch angle cases, the difference between the maximum deceleration of the flexible model and that of its corresponding rigid model is smaller. Test data of Apollo space capsules with a flexible heat shield qualitatively support the findings presented in this paper.
The Blended Finite Element Method for Multi-fluid Plasma Modeling
2016-07-01
Briefing Charts 3. DATES COVERED (From - To) 07 June 2016 - 01 July 2016 4. TITLE AND SUBTITLE The Blended Finite Element Method for Multi-fluid Plasma...BLENDED FINITE ELEMENT METHOD FOR MULTI-FLUID PLASMA MODELING Éder M. Sousa1, Uri Shumlak2 1ERC INC., IN-SPACE PROPULSION BRANCH (RQRS) AIR FORCE RESEARCH...MULTI-FLUID PLASMA MODEL 2 BLENDED FINITE ELEMENT METHOD Blended Finite Element Method Nodal Continuous Galerkin Modal Discontinuous Galerkin Model
1984-07-01
Ackroyd , R. T. "A Finite Element Technique for the Even Parity Neutron Transport Equation," The Mathematics of Finite Elements and...state transport equation. In 1972 a more detailed examination of the use of finite elements to solve neutron diffusion problems was provided by Kaper...79, 269-277 (1981). Ukai, S., "Solution of the Multi-dimensional Neutron Transport Equation by Finite Element Methods,"
Interpolation functions in control volume finite element method
Abbassi, H.; Turki, S.; Nasrallah, S. Ben
The main contribution of this paper is the study of interpolation functions in control volume finite element method used in equal order and applied to an incompressible two-dimensional fluid flow. Especially, the exponential interpolation function expressed in the elemental local coordinate system is compared to the classic linear interpolation function expressed in the global coordinate system. A quantitative comparison is achieved by the application of these two schemes to four flows that we know the analytical solutions. These flows are classified in two groups: flows with privileged direction and flows without. The two interpolation functions are applied to a triangular element of the domain then; a direct comparison of the results given by each interpolation function to the exact value is easily realized. The two functions are also compared when used to solve the discretized equations over the entire domain. Stability of the numerical process and accuracy of solutions are compared.
3D finite element simulations of high velocity projectile impact
Directory of Open Access Journals (Sweden)
Ožbolt Joško
2015-01-01
Full Text Available An explicit three-dimensional (3D finite element (FE code is developed for the simulation of high velocity impact and fragmentation events. The rate sensitive microplane material model, which accounts for large deformations and rate effects, is used as a constitutive law. In the code large deformation frictional contact is treated by forward incremental Lagrange multiplier method. To handle highly distorted and damaged elements the approach based on the element deletion is employed. The code is then used in 3D FE simulations of high velocity projectile impact. The results of the numerical simulations are evaluated and compared with experimental results. It is shown that it realistically predicts failure mode and exit velocities for different geometries of plain concrete slab. Moreover, the importance of some relevant parameters, such as contact friction, rate sensitivity, bulk viscosity and deletion criteria are addressed.
Acoustic Finite Element Calculations in the Time Domain
DEFF Research Database (Denmark)
Jensen, Morten Skaarup
The use of the finite element method (FEM) for making predictions for acoustic fields in the time domain is investigated. First, an introduction to FEM for acoustics is given. This includes a description of important present day algorithms and a derivation of FEM. The overall performance...... of these algorithms is then examined with particular emphasis on accuracy and computational costs. It is shown that the most important error is one that takes the form of a falsely predicted dispersion. The dispersion error can be reduced by using smaller elements and time steps, but this is very costly. Attempts...... and consequences of the dispersion error has been obtained. This led to a new method for determining the optimum element and time step size. The method is valuable because the present way of doing this is not theoretically well-founded....
Finite Element Modeling of Scattering from Underwater Proud and Buried Military Munitions
2017-02-28
FINAL REPORT Finite Element Modeling of Scattering from Underwater Proud and Buried Military Munitions SERDP Project MR-2408 JULY 2017...solution and the red dash-dot line repre- sents the coupled finite -boundary element solution. . . . . . . . . . . . . . . . . . 11 3 The scattering...dot line represents the coupled finite -boundary element solution. . . . . . . . 11 i 4 The scattering amplitude as a function of the receiver angle for
Analysis of a non-standard mixed finite element method with applications to superconvergence
Brandts, J.H.
2009-01-01
We show that a non-standard mixed finite element method proposed by Barrios and Gatica in 2007, is a higher order perturbation of the least-squares mixed finite element method. Therefore, it is also superconvergent whenever the least-squares mixed finite element method is superconvergent.
Energy Technology Data Exchange (ETDEWEB)
Sung, Jin Il [Hyosung Co., Ltd., Seoul (Korea, Republic of); Yoo, Jeong Hoon [Yonsei Univ., Seoul (Korea, Republic of)
2002-07-01
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.
Finite Element and Plate Theory Modeling of Acoustic Emission Waveforms
Prosser, W. H.; Hamstad, M. A.; Gary, J.; OGallagher, A.
1998-01-01
A comparison was made between two approaches to predict acoustic emission waveforms in thin plates. A normal mode solution method for Mindlin plate theory was used to predict the response of the flexural plate mode to a point source, step-function load, applied on the plate surface. The second approach used a dynamic finite element method to model the problem using equations of motion based on exact linear elasticity. Calculations were made using properties for both isotropic (aluminum) and anisotropic (unidirectional graphite/epoxy composite) materials. For simulations of anisotropic plates, propagation along multiple directions was evaluated. In general, agreement between the two theoretical approaches was good. Discrepancies in the waveforms at longer times were caused by differences in reflections from the lateral plate boundaries. These differences resulted from the fact that the two methods used different boundary conditions. At shorter times in the signals, before reflections, the slight discrepancies in the waveforms were attributed to limitations of Mindlin plate theory, which is an approximate plate theory. The advantages of the finite element method are that it used the exact linear elasticity solutions, and that it can be used to model real source conditions and complicated, finite specimen geometries as well as thick plates. These advantages come at a cost of increased computational difficulty, requiring lengthy calculations on workstations or supercomputers. The Mindlin plate theory solutions, meanwhile, can be quickly generated on personal computers. Specimens with finite geometry can also be modeled. However, only limited simple geometries such as circular or rectangular plates can easily be accommodated with the normal mode solution technique. Likewise, very limited source configurations can be modeled and plate theory is applicable only to thin plates.
Ko, William L.; Olona, Timothy; Muramoto, Kyle M.
1990-01-01
Different finite element models previously set up for thermal analysis of the space shuttle orbiter structure are discussed and their shortcomings identified. Element density criteria are established for the finite element thermal modelings of space shuttle orbiter-type large, hypersonic aircraft structures. These criteria are based on rigorous studies on solution accuracies using different finite element models having different element densities set up for one cell of the orbiter wing. Also, a method for optimization of the transient thermal analysis computer central processing unit (CPU) time is discussed. Based on the newly established element density criteria, the orbiter wing midspan segment was modeled for the examination of thermal analysis solution accuracies and the extent of computation CPU time requirements. The results showed that the distributions of the structural temperatures and the thermal stresses obtained from this wing segment model were satisfactory and the computation CPU time was at the acceptable level. The studies offered the hope that modeling the large, hypersonic aircraft structures using high-density elements for transient thermal analysis is possible if a CPU optimization technique was used.
Phase-change techniques for finite element conduction codes
Energy Technology Data Exchange (ETDEWEB)
Lemmon, E C
1979-01-01
A method employing integral averaging techniques is proposed to aid conduction finite element code users in approximating multidimensional phase change problems such as: (a) liquid solidification under action of surface heat removal such as ice production or solidification of a casting, (b) thermal/chemical decomposition of a solid without removal of degraded material from the remaining virgin material such as charring of wood or reinforced plastics, (c) ablation of solids where the products of decomposition are removed on formation such as melting glass or subliming teflon. Of prime interest to the method is the determination of the amount of material solidified, decomposed, melted or sublimed and the location of the phase change interface as a function of time as it moves through the one-, two-, or three-dimensional finite element mesh. As the interface moves through each element, the energy involved in the phase change process and the difference in heat capacity and conductivity of two phases is accounted for. A method is also included to accommodate convective heat transfer at the moving phase change interface.
Curved Thermopiezoelectric Shell Structures Modeled by Finite Element Analysis
Lee, Ho-Jun
2000-01-01
"Smart" structures composed of piezoelectric materials may significantly improve the performance of aeropropulsion systems through a variety of vibration, noise, and shape-control applications. The development of analytical models for piezoelectric smart structures is an ongoing, in-house activity at the NASA Glenn Research Center at Lewis Field focused toward the experimental characterization of these materials. Research efforts have been directed toward developing analytical models that account for the coupled mechanical, electrical, and thermal response of piezoelectric composite materials. Current work revolves around implementing thermal effects into a curvilinear-shell finite element code. This enhances capabilities to analyze curved structures and to account for coupling effects arising from thermal effects and the curved geometry. The current analytical model implements a unique mixed multi-field laminate theory to improve computational efficiency without sacrificing accuracy. The mechanics can model both the sensory and active behavior of piezoelectric composite shell structures. Finite element equations are being implemented for an eight-node curvilinear shell element, and numerical studies are being conducted to demonstrate capabilities to model the response of curved piezoelectric composite structures (see the figure).
Power flows and Mechanical Intensities in structural finite element analysis
Hambric, Stephen A.
1989-01-01
The identification of power flow paths in dynamically loaded structures is an important, but currently unavailable, capability for the finite element analyst. For this reason, methods for calculating power flows and mechanical intensities in finite element models are developed here. Formulations for calculating input and output powers, power flows, mechanical intensities, and power dissipations for beam, plate, and solid element types are derived. NASTRAN is used to calculate the required velocity, force, and stress results of an analysis, which a post-processor then uses to calculate power flow quantities. The SDRC I-deas Supertab module is used to view the final results. Test models include a simple truss and a beam-stiffened cantilever plate. Both test cases showed reasonable power flow fields over low to medium frequencies, with accurate power balances. Future work will include testing with more complex models, developing an interactive graphics program to view easily and efficiently the analysis results, applying shape optimization methods to the problem with power flow variables as design constraints, and adding the power flow capability to NASTRAN.
Tadepalli, Srinivas C; Erdemir, Ahmet; Cavanagh, Peter R
2011-08-11
Finite element analysis has been widely used in the field of foot and footwear biomechanics to determine plantar pressures as well as stresses and strains within soft tissue and footwear materials. When dealing with anatomical structures such as the foot, hexahedral mesh generation accounts for most of the model development time due to geometric complexities imposed by branching and embedded structures. Tetrahedral meshing, which can be more easily automated, has been the approach of choice to date in foot and footwear biomechanics. Here we use the nonlinear finite element program Abaqus (Simulia, Providence, RI) to examine the advantages and disadvantages of tetrahedral and hexahedral elements under compression and shear loading, material incompressibility, and frictional contact conditions, which are commonly seen in foot and footwear biomechanics. This study demonstrated that for a range of simulation conditions, hybrid hexahedral elements (Abaqus C3D8H) consistently performed well while hybrid linear tetrahedral elements (Abaqus C3D4H) performed poorly. On the other hand, enhanced quadratic tetrahedral elements with improved stress visualization (Abaqus C3D10I) performed as well as the hybrid hexahedral elements in terms of contact pressure and contact shear stress predictions. Although the enhanced quadratic tetrahedral element simulations were computationally expensive compared to hexahedral element simulations in both barefoot and footwear conditions, the enhanced quadratic tetrahedral element formulation seems to be very promising for foot and footwear applications as a result of decreased labor and expedited model development, all related to facilitated mesh generation. Copyright © 2011. Published by Elsevier Ltd.
Interpreting finite element results for brittle materials in endodontic restorations
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González-Lluch Carmen
2011-06-01
Full Text Available Abstract Background Finite element simulation has been used in last years for analysing the biomechanical performance of post-core restorations in endodontics, but results of these simulations have been interpreted in most of the works using von Mises stress criterion. However, the validity of this failure criterion for brittle materials, which are present in these restorations, is questionable. The objective of the paper is to analyse how finite element results for brittle materials of endodontic restorations should be interpreted to obtain correct conclusions about the possible failure in the restoration. Methods Different failure criteria (Von Mises, Rankine, Coulomb-Mohr, Modified Mohr and Christensen and material strength data (diametral tensile strength and flexural strength were considered in the study. Three finite element models (FEM were developed to simulate an endodontic restoration and two typical material tests: diametral tensile test and flexural test. Results Results showed that the Christensen criterion predicts similar results as the Von Mises criterion for ductile components, while it predicts similar results to all other criteria for brittle components. The different criteria predict different failure points for the diametral tensile test, all of them under multi-axial stress states. All criteria except Von Mises predict failure for flexural test at the same point of the specimen, with this point under uniaxial tensile stress. Conclusions From the results it is concluded that the Christensen criterion is recommended for FEM result interpretation in endodontic restorations and that the flexural test is recommended to estimate tensile strength instead of the diametral tensile test.
Generalized Potential Energy Finite Elements for Modeling Molecular Nanostructures.
Chatzieleftheriou, Stavros; Adendorff, Matthew R; Lagaros, Nikos D
2016-10-24
The potential energy of molecules and nanostructures is commonly calculated in the molecular mechanics formalism by superimposing bonded and nonbonded atomic energy terms, i.e. bonds between two atoms, bond angles involving three atoms, dihedral angles involving four atoms, nonbonded terms expressing the Coulomb and Lennard-Jones interactions, etc. In this work a new, generalized numerical simulation is presented for studying the mechanical behavior of three-dimensional nanostructures at the atomic scale. The energy gradient and Hessian matrix of such assemblies are usually computed numerically; a potential energy finite element model is proposed herein where these two components are expressed analytically. In particular, generalized finite elements are developed that express the interactions among atoms in a manner equivalent to that invoked in simulations performed based on the molecular dynamics method. Thus, the global tangent stiffness matrix for any nanostructure is formed as an assembly of the generalized finite elements and is directly equivalent to the Hessian matrix of the potential energy. The advantages of the proposed model are identified in terms of both accuracy and computational efficiency. In the case of popular force fields (e.g., CHARMM), the computation of the Hessian matrix by implementing the proposed method is of the same order as that of the gradient. This analysis can be used to minimize the potential energy of molecular systems under nodal loads in order to derive constitutive laws for molecular systems where the entropy and solvent effects are neglected and can be approximated as solids, such as double stranded DNA nanostructures. In this context, the sequence dependent stretch modulus for some typical base pairs step is calculated.
Finite Element Analysis of Boron Diffusion in Wooden Poles
DEFF Research Database (Denmark)
Krabbenhøft, Kristian; Hoffmeyer, P.; Bechgaard, C.
2003-01-01
The problem of describing the migration of dissolved boron in wood is treated with special reference to the commonly used remedial treatment of wooden poles. The governing equations are derived and discussed together with some of the material parameters required. The equations are solved by the f......The problem of describing the migration of dissolved boron in wood is treated with special reference to the commonly used remedial treatment of wooden poles. The governing equations are derived and discussed together with some of the material parameters required. The equations are solved...... by the finite element method and, finally, results showing the effect of different treatment strategies are presented....
Galerkin finite-element simulation of a geothermal reservoir
Mercer, J.W.; Pinder, G.F.
1973-01-01
The equations describing fluid flow and energy transport in a porous medium can be used to formulate a mathematical model capable of simulating the transient response of a hot-water geothermal reservoir. The resulting equations can be solved accurately and efficiently using a numerical scheme which combines the finite element approach with the Galerkin method of approximation. Application of this numerical model to the Wairakei geothermal field demonstrates that hot-water geothermal fields can be simulated using numerical techniques currently available and under development. ?? 1973.
The Iris biometric feature segmentation using finite element method
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David Ibitayo LANLEGE
2015-05-01
Full Text Available This manuscript presents a method for segmentation of iris images based on a deformable contour (active contour paradigm. The deformable contour is a novel approach in image segmentation. A type of active contour is the Snake. Snake is a parametric curve defined within the domain of the image. Snake properties are specified through a function called energy functional. This means they consist of packets of energy which expressed as partial Differential Equations. The partial Differential Equation is the controlling engine of the active contour since this project, the Finite Element Method (Standard Galerkin Method implementation for deformable model is presented.
Finite element analysis of a single lap joint
Heistermann, Christine; Heistermann, Tim; Limam, Marouene; Veljkovic, Milan, ed. lit.
2012-01-01
A single shear lap joint of steel grade S355 is modelled with finite elements to investigate the influence of externally applied tensile loading on the loss of pretension in the engaged bolts. Additionally, a parameter study is performed to understand the effect of various steel grades on the loss of pretension. It is found that the slip resistance of the specimen depends on the steel grade of the clamped plates. Besides, the final resistance of the single shear lap joint has been found to in...
Modeling of coal stockpiles using a finite elements method
Energy Technology Data Exchange (ETDEWEB)
Ozdeniz, A.H.; Sensogut, C. [Dumlupinar University, Kutahya (Turkey)
2008-07-01
In the case of coal stockpiles finding suitable environmental conditions, spontaneous combustion phenomenon will be unavoidable. In this study, an industrial-sized stockpile having a shape of triangle prism was constituted in a coal stockyard of Western Lignite Corporation (WLC), Turkey. The parameters of time, humidity and temperature of air, atmospheric pressure, velocity and direction of wind values that are effective on coal stockpile were measured in a continuous manner. These experimental works were transferred into a computer media in order to obtain similar outcomes by carrying out 2-dimensional analysis of the stockpile with Finite Elements Method (FEM). The performed experimental studies and obtained results were then compared.
Piezoelectric Analysis of Saw Sensor Using Finite Element Method
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Vladimír KUTIŠ
2013-06-01
Full Text Available In this contribution modeling and simulation of surface acoustic waves (SAW sensor using finite element method will be presented. SAW sensor is made from piezoelectric GaN layer and SiC substrate. Two different analysis types are investigated - modal and transient. Both analyses are only 2D. The goal of modal analysis, is to determine the eigenfrequency of SAW, which is used in following transient analysis. In transient analysis, wave propagation in SAW sensor is investigated. Both analyses were performed using FEM code ANSYS.
Assessing performance and validating finite element simulations using probabilistic knowledge
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Dolin, Ronald M.; Rodriguez, E. A. (Edward A.)
2002-01-01
Two probabilistic approaches for assessing performance are presented. The first approach assesses probability of failure by simultaneously modeling all likely events. The probability each event causes failure along with the event's likelihood of occurrence contribute to the overall probability of failure. The second assessment method is based on stochastic sampling using an influence diagram. Latin-hypercube sampling is used to stochastically assess events. The overall probability of failure is taken as the maximum probability of failure of all the events. The Likelihood of Occurrence simulation suggests failure does not occur while the Stochastic Sampling approach predicts failure. The Likelihood of Occurrence results are used to validate finite element predictions.
Stress Reduction of Pickup Truck Chassis Using Finite Element Method
Kurdi, O.; Yob, M. S.; Dasson, S. R.; Barrathi, S.; Altayeb, A. A.; Yulianti, I.
2017-04-01
This paper performed stress reduction of the chassis of single cab pick truck using Finite Element Method (FEM). The first step was to evaluate and identify the critical area or maximum values of the static stress and its locations. The second stage of this project was dealing with designing a new chassis based on the Tata model, and then the final stage was a validation of numerical results with both experiments and analytical calculation to get the desired chassis that have strong and high-quality design.
Finite Element Modeling Techniques for Analysis of VIIP
Feola, Andrew J.; Raykin, J.; Gleason, R.; Mulugeta, Lealem; Myers, Jerry G.; Nelson, Emily S.; Samuels, Brian C.; Ethier, C. Ross
2015-01-01
Visual Impairment and Intracranial Pressure (VIIP) syndrome is a major health concern for long-duration space missions. Currently, it is thought that a cephalad fluid shift in microgravity causes elevated intracranial pressure (ICP) that is transmitted along the optic nerve sheath (ONS). We hypothesize that this in turn leads to alteration and remodeling of connective tissue in the posterior eye which impacts vision. Finite element (FE) analysis is a powerful tool for examining the effects of mechanical loads in complex geometries. Our goal is to build a FE analysis framework to understand the response of the lamina cribrosa and optic nerve head to elevations in ICP in VIIP.
Finite element method for time-space-fractional Schrodinger equation
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Xiaogang Zhu
2017-07-01
Full Text Available In this article, we develop a fully discrete finite element method for the nonlinear Schrodinger equation (NLS with time- and space-fractional derivatives. The time-fractional derivative is described in Caputo's sense and the space-fractional derivative in Riesz's sense. Its stability is well derived; the convergent estimate is discussed by an orthogonal operator. We also extend the method to the two-dimensional time-space-fractional NLS and to avoid the iterative solvers at each time step, a linearized scheme is further conducted. Several numerical examples are implemented finally, which confirm the theoretical results as well as illustrate the accuracy of our methods.
Finite element discretization of two immiscible fluids with surface tension
Bernardi, Christine; Maarouf, Sarra; Yakoubi, Driss
2015-01-01
We consider a model for the flow of two immiscible fluids where the surface tension between both of them is taken into account. We first write the variational formulation of the problem and investigate its well-posedness. Next, we consider a finite element discretization of it and prove optimal a priori error estimates. Numerical experiments confirm its good properties. Résumé. Nous considérons un mod ele pour l'´ ecoulement de deux fluides immiscibles o` u la tension de surface entre les deu...
Finite element solvers for incompressible fluid flows and heat transfer
Sohn, Jeong L.; Kim, Yongmo; Chung, T. J.
1989-01-01
Two different finite-element solvers for incompressible viscous flow, i.e., the mixed interpolation method and the SIMPLE-type iterative method, are compared and tested with some benchmark problems. The advantages of the SIMPLE-type iterative method are the decoupling of the governing equations and the use of equal-order interpolation functions for both velocity and pressure. Even though there is a significant difference between the two methods in terms of the pressure field, similar solutions are obtained for the velocity field.
Analysis of anelastic flow and numerical treatment via finite elements
Energy Technology Data Exchange (ETDEWEB)
Martinez, M.J.
1994-05-01
In this report, we reconsider the various approximations made to the full equations of motion and energy transport for treating low-speed flows with significant temperature induced property variations. This entails assessment of the development of so-called anelastic for low-Mach number flows outside the range of validity of the Boussinesq equations. An integral part of this assessment is the development of a finite element-based numerical scheme for obtaining approximate numerical solutions to this class of problems. Several formulations were attempted and are compared.
Finite Element Approach for Coupled Striplines Embedded in Dielectric Material
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Matthew N.O. Sadiku
2013-03-01
Full Text Available In this paper, we present finite element method (FEM to investigate the quasi-static analysis of two dimensional (2D shielded two coupled stripline structures for microelectronic devices. In the proposed method, we specifically determine the values of capacitance per unit length and inductance per unit length of shielded two vertically coupled striplines and shielded two coupled striplines embedded in dielectric material. Extensive simulation results are presented, and some comparative results are given by other methods and found them to be in excellent agreement. Furthermore, we determine the quasi-TEM spectral for the potential distribution of these shielded two coupled striplines.
Methods and framework for visualizing higher-order finite elements.
Schroeder, William J; Bertel, François; Malaterre, Mathieu; Thompson, David; Pébay, Philippe P; O'Bara, Robert; Tendulkar, Saurabh
2006-01-01
The finite element method is an important, widely used numerical technique for solving partial differential equations. This technique utilizes basis functions for approximating the geometry and the variation of the solution field over finite regions, or elements, of the domain. These basis functions are generally formed by combinations of polynomials. In the past, the polynomial order of the basis has been low-typically of linear and quadratic order. However, in recent years so-called p and hp methods have been developed, which may elevate the order of the basis to arbitrary levels with the aim of accelerating the convergence of the numerical solution. The increasing complexity of numerical basis functions poses a significant challenge to visualization systems. In the past, such systems have been loosely coupled to simulation packages, exchanging data via file transfer, and internally reimplementing the basis functions in order to perform interpolation and implement visualization algorithms. However, as the basis functions become more complex and, in some cases, proprietary in nature, it becomes increasingly difficult if not impossible to reimplement them within the visualization system. Further, most visualization systems typically process linear primitives, in part to take advantage of graphics hardware and, in part, due to the inherent simplicity of the resulting algorithms. Thus, visualization of higher-order finite elements requires tessellating the basis to produce data compatible with existing visualization systems. In this paper, we describe adaptive methods that automatically tessellate complex finite element basis functions using a flexible and extensible software framework. These methods employ a recursive, edge-based subdivision algorithm driven by a set of error metrics including geometric error, solution error, and error in image space. Further, we describe advanced pretessellation techniques that guarantees capture of the critical points of the
Analysis of Waveguide Junction Discontinuities Using Finite Element Method
Deshpande, Manohar D.
1997-01-01
A Finite Element Method (FEM) is presented to determine reflection and transmission coefficients of rectangular waveguide junction discontinuities. An H-plane discontinuity, an E-plane ridge discontinuity, and a step discontinuity in a concentric rectangular waveguide junction are analyzed using the FEM procedure. Also, reflection and transmission coefficients due to presence of a gap between two sections of a rectangular waveguide are determined using the FEM. The numerical results obtained by the present method are in excellent agreement with the earlier published results. The numerical results obtained by the FEM are compared with the numerical results obtained using the Mode Matching Method (MMM) and also with the measured data.
Extended Finite Element Method for Fracture Analysis of Structures
Mohammadi, Soheil
2008-01-01
This important textbook provides an introduction to the concepts of the newly developed extended finite element method (XFEM) for fracture analysis of structures, as well as for other related engineering applications.One of the main advantages of the method is that it avoids any need for remeshing or geometric crack modelling in numerical simulation, while generating discontinuous fields along a crack and around its tip. The second major advantage of the method is that by a small increase in number of degrees of freedom, far more accurate solutions can be obtained. The method has recently been
Finite element analysis of thumb carpometacarpal joint implants
Energy Technology Data Exchange (ETDEWEB)
Nielsen, C.
1995-11-01
The thumb carpometacarpal joint is frequently replaced in women who have developed severe osteoarthritis of the hand. A new, privately developed implant design consists of two components, trapezial and metacarpal, each with a saddle-shaped articulating surface. A three dimensional finite element model of this implant has been developed to analyze stresses on the device. The first simulations using the model involve loading the implant with forces normal to the trapezial component. Preliminary results show contact stress distributions at the particulating surfaces of the implant.
2D Finite Element Model of a CIGS Module
Energy Technology Data Exchange (ETDEWEB)
Janssen, G.J.M.; Slooff, L.H.; Bende, E.E. [ECN Solar Energy, P.O.Box 1, NL-1755 ZG Petten (Netherlands)
2012-06-15
The performance of thin-film CIGS (Copper indium gallium selenide) modules is often limited due to inhomogeneities in CIGS layers. A 2-dimensional Finite Element Model for CIGS modules is presented that predicts the impact of such inhomogeneities on the module performance. Results are presented of a module with a region of poor diode characteristics. It is concluded that according to this model the effects of poor diodes depend strongly on their location in the module and on their dispersion over the module surface. Due to its generic character the model can also be applied to other series connections of photovoltaic cells.
Finite Element Assembly Using an Embedded Domain Specific Language
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Bart Janssens
2015-01-01
Full Text Available In finite element methods, numerical simulation of the problem requires the generation of a linear system based on an integral form of a problem. Using C++ meta-programming techniques, a method is developed that allows writing code that stays close to the mathematical formulation. We explain the specifics of our method, which relies on the Boost.Proto framework to simplify the evaluation of our language. Some practical examples are elaborated, together with an analysis of the performance. The abstraction overhead is quantified using benchmarks.
[Finite Element Analysis of Intravascular Stent Based on ANSYS Software].
Shi, Gengqiang; Song, Xiaobing
2015-10-01
This paper adopted UG8.0 to bulid the stent and blood vessel models. The models were then imported into the finite element analysis software ANSYS. The simulation results of ANSYS software showed that after endothelial stent implantation, the velocity of the blood was slow and the fluctuation of velocity was small, which meant the flow was relatively stable. When blood flowed through the endothelial stent, the pressure gradually became smaller, and the range of the pressure was not wide. The endothelial shear stress basically unchanged. In general, it can be concluded that the endothelial stents have little impact on the flow of blood and can fully realize its function.
A Dual Orthogonality Procedure for Nonlinear Finite Element Equations
DEFF Research Database (Denmark)
Krenk, S.; Hededal, O.
In the orthogonal residual procedure for solution of nonlinear finite element equations the load is adjusted in each equilibrium iteration to satisfy an orthogonality condition to the current displacement increment. It is here shown that the quasi-newton formulation of the orthogonal residual...... method consists of a simple one-term correction of the displacement subincrement, and that this correction leads to orthogonality between the corrected displacement subincrement and the current increment of the internal force vector, thus defining a dual orthogonality algorithm. It is demonstrated how...
Applications of finite-element scaling analysis in primatology.
Richtsmeier, J T
1989-01-01
The study of biological shape in three dimensions using landmark data can now be accomplished using several alternative methods. This report focuses on the use of finite-element scaling analysis in primate craniofacial morphology. The method is particularly useful in its ability to localize the differences between forms, thereby indicating those loci that differ most between specimens. Several examples of this feature are provided from primatological research. Particulars of the methods are also discussed in an attempt to provide the reader with cautionary knowledge for prudent application of the method in future research.
Stochastic Finite Element Method in Geotechnical Engineering. Spectral Approach
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Auvinet-Guichard G.
2013-01-01
Full Text Available This paper presents the mathematical tools in which the formulation of Spectral Stochastic Finite Element Method is based. The usefulness of this method to model the spatial variability of heterogeneous materials, and in particular of soils, is illustrated by a practical example in which the propagation of the uncertainty on the deformation modulus to the computed displacement field is assessed. The influence of the correlation length on the distribution of uncertainty is set forth. Finally, the advantages of the method in geotechnical engineering are evaluated and some conclusions are presented.
An introduction to the mathematical theory of finite elements
Oden, J T
2011-01-01
This introduction to the theory of Sobolev spaces and Hilbert space methods in partial differential equations is geared toward readers of modest mathematical backgrounds. It offers coherent, accessible demonstrations of the use of these techniques in developing the foundations of the theory of finite element approximations.J. T. Oden is Director of the Institute for Computational Engineering & Sciences (ICES) at the University of Texas at Austin, and J. N. Reddy is a Professor of Engineering at Texas A&M University. They developed this essentially self-contained text from their seminars and co
Free vibration analysis of dragonfly wings using finite element method
Directory of Open Access Journals (Sweden)
M Darvizeh
2016-04-01
Full Text Available In the present work, investigations on the microstructure and mechanicalproperties of the dragonfly wing are carried out and numerical modelingbased on Finite Element Method (FEM is developed to predict Flightcharacteristics of dragonfly wings. Vibrational behavior of wings typestructures is immensely important in analysis, design and manufacturing ofsimilar engineering structures. For this purpose natural frequencies andmode shapes are calculated. In addition, the kind of deformation in eachmode shape evaluated and the ratio between numerical natural frequencyand experimental natural frequency presented as damping ratio. Theresults obtain from present method are in good agreement with sameexperimental methods.
An 8-node tetrahedral finite element suitable for explicit transient dynamic simulations
Energy Technology Data Exchange (ETDEWEB)
Key, S.W.; Heinstein, M.W.; Stone, C.M. [Sandia National Labs., Albuquerque, NM (United States)
1997-12-31
Considerable effort has been expended in perfecting the algorithmic properties of 8-node hexahedral finite elements. Today the element is well understood and performs exceptionally well when used in modeling three-dimensional explicit transient dynamic events. However, the automatic generation of all-hexahedral meshes remains an elusive achievement. The alternative of automatic generation for all-tetrahedral finite element is a notoriously poor performer, and the 10-node quadratic tetrahedral finite element while a better performer numerically is computationally expensive. To use the all-tetrahedral mesh generation extant today, the authors have explored the creation of a quality 8-node tetrahedral finite element (a four-node tetrahedral finite element enriched with four midface nodal points). The derivation of the element`s gradient operator, studies in obtaining a suitable mass lumping and the element`s performance in applications are presented. In particular, they examine the 80node tetrahedral finite element`s behavior in longitudinal plane wave propagation, in transverse cylindrical wave propagation, and in simulating Taylor bar impacts. The element only samples constant strain states and, therefore, has 12 hourglass modes. In this regard, it bears similarities to the 8-node, mean-quadrature hexahedral finite element. Given automatic all-tetrahedral meshing, the 8-node, constant-strain tetrahedral finite element is a suitable replacement for the 8-node hexahedral finite element and handbuilt meshes.
Comparing finite elements and finite differences for developing diffusive models of glioma growth.
Roniotis, Alexandros; Marias, Kostas; Sakkalis, Vangelis; Stamatakos, Georgios; Zervakis, Michalis
2010-01-01
Glioma is the most aggressive type of brain tumor. Several mathematical models have been developed during the last two decades, towards simulating the mechanisms that govern the development of glioma. The most common models use the diffusion-reaction equation (DRE) for simulating the spatiotemporal variation of tumor cell concentration. The proposed diffusive models have mainly used finite differences (FDs) or finite elements (FEs) for the approximation of the solution of the partial differential DRE. This paper presents experimental results on the comparison of the FEs and FDs, especially focused on the glioma model case. It is studied how the different meshes of brain can affect computational consistency, simulation time and efficiency of the model. The experiments have been studied on a test case, for which there is a known algebraic expression of the solution. Thus, it is possible to calculate the error that the different models yield.
Stupkiewicz, Stanisław
2009-10-01
Soft elastohydrodynamic lubrication (EHL) problem is studied for a reciprocating elastomeric seal with full account of finite configuration changes. The fluid part is described by the Reynolds equation which is formulated on the deformed boundary of the seal treated as a hyperelastic body. The paper is concerned with the finite element (FE) treatment of this soft EHL problem. Displacement-based FE discretization is applied for the solid part. The Reynolds equation is discretized using the FE method or, alternatively, the discontinuous Galerkin method, both employing higher-order interpolation of pressure. The performance of both methods is assessed by studying convergence and stability of the solution for a benchmark problem of an O-ring seal. It is shown that the solution may exhibit spurious oscillations which occur in severe lubrication conditions. Mesh refinement results in reduction of these oscillations, while increasing the pressure interpolation order or application of the discontinuous Galerkin method does not help significantly.
Finite-element model of the active organ of Corti
Elliott, Stephen J.; Baumgart, Johannes
2016-01-01
The cochlear amplifier that provides our hearing with its extraordinary sensitivity and selectivity is thought to be the result of an active biomechanical process within the sensory auditory organ, the organ of Corti. Although imaging techniques are developing rapidly, it is not currently possible, in a fully active cochlea, to obtain detailed measurements of the motion of individual elements within a cross section of the organ of Corti. This motion is predicted using a two-dimensional finite-element model. The various solid components are modelled using elastic elements, the outer hair cells (OHCs) as piezoelectric elements and the perilymph and endolymph as viscous and nearly incompressible fluid elements. The model is validated by comparison with existing measurements of the motions within the passive organ of Corti, calculated when it is driven either acoustically, by the fluid pressure or electrically, by excitation of the OHCs. The transverse basilar membrane (BM) motion and the shearing motion between the tectorial membrane and the reticular lamina are calculated for these two excitation modes. The fully active response of the BM to acoustic excitation is predicted using a linear superposition of the calculated responses and an assumed frequency response for the OHC feedback. PMID:26888950
Reliability-Based Shape Optimization using Stochastic Finite Element Methods
DEFF Research Database (Denmark)
Enevoldsen, Ib; Sørensen, John Dalsgaard; Sigurdsson, G.
1991-01-01
(7). In this paper a reliability-based shape optimization problem is formulated with the total expected cost as objective function and some requirements for the reliability measures (element or systems reliability measures) as constraints, see section 2. As design variables sizing variables......Application of first-order reliability methods FORM (see Madsen, Krenk & Lind [8)) in structural design problems has attracted growing interest in recent years, see e.g. Frangopol [4), Murotsu, Kishi, Okada, Yonezawa & Taguchi [9) and Sørensen [14). In probabilistically based optimal design...... stochastic fields (e.g. loads and material parameters such as Young's modulus and the Poisson ratio). In this case stochastic finite element techniques combined with FORM analysis can be used to obtain measures of the reliability of the structural systems, see Der Kiureghian & Ke (6) and Liu & Der Kiureghian...
Model Reduction in Dynamic Finite Element Analysis of Lightweight Structures
DEFF Research Database (Denmark)
Flodén, Ola; Persson, Kent; Sjöström, Anders
2012-01-01
models may be created by assembling models of floor and wall structures into large models of complete buildings. When assembling the floor and wall models, the number of degrees of freedom quickly increases to exceed the limits of computer capacity, at least in a reasonable amount of computational time....... The objective of the analyses presented in this paper is to evaluate methods for model reduction of detailed finite element models of floor and wall structures and to investigate the influence of reducing the number of degrees of freedom and computational cost on the dynamic response of the models in terms....... The drawback of component mode synthesis compared to modelling with structural elements is the increased computational cost, although the number of degrees of freedom is small in comparison, as a result of the large bandwidth of the system matrices....
Multiscale finite-element method for linear elastic geomechanics
Castelletto, Nicola; Hajibeygi, Hadi; Tchelepi, Hamdi A.
2017-02-01
The demand for accurate and efficient simulation of geomechanical effects is widely increasing in the geoscience community. High resolution characterizations of the mechanical properties of subsurface formations are essential for improving modeling predictions. Such detailed descriptions impose severe computational challenges and motivate the development of multiscale solution strategies. We propose a multiscale solution framework for the geomechanical equilibrium problem of heterogeneous porous media based on the finite-element method. After imposing a coarse-scale grid on the given fine-scale problem, the coarse-scale basis functions are obtained by solving local equilibrium problems within coarse elements. These basis functions form the restriction and prolongation operators used to obtain the coarse-scale system for the displacement-vector. Then, a two-stage preconditioner that couples the multiscale system with a smoother is derived for the iterative solution of the fine-scale linear system. Various numerical experiments are presented to demonstrate accuracy and robustness of the method.
QUADRATIC SERENDIPITY FINITE ELEMENTS ON POLYGONS USING GENERALIZED BARYCENTRIC COORDINATES.
Rand, Alexander; Gillette, Andrew; Bajaj, Chandrajit
2014-01-01
We introduce a finite element construction for use on the class of convex, planar polygons and show it obtains a quadratic error convergence estimate. On a convex n -gon, our construction produces 2 n basis functions, associated in a Lagrange-like fashion to each vertex and each edge midpoint, by transforming and combining a set of n ( n + 1)/2 basis functions known to obtain quadratic convergence. The technique broadens the scope of the so-called 'serendipity' elements, previously studied only for quadrilateral and regular hexahedral meshes, by employing the theory of generalized barycentric coordinates. Uniform a priori error estimates are established over the class of convex quadrilaterals with bounded aspect ratio as well as over the class of convex planar polygons satisfying additional shape regularity conditions to exclude large interior angles and short edges. Numerical evidence is provided on a trapezoidal quadrilateral mesh, previously not amenable to serendipity constructions, and applications to adaptive meshing are discussed.
OXYGEN PRESSURE REGULATOR DESIGN AND ANALYSIS THROUGH FINITE ELEMENT MODELING
Directory of Open Access Journals (Sweden)
Asterios KOSMARAS
2017-05-01
Full Text Available Oxygen production centers produce oxygen in high pressure that needs to be defused. A regulator is designed and analyzed in the current paper for medical use in oxygen production centers. This study aims to design a new oxygen pressure regulator and perform an analysis using Finite Element Modeling in order to evaluate its working principle. In the design procedure,the main elements and the operating principles of a pressure regulator are taking into account. The regulator is designed and simulations take place in order to assessthe proposed design. Stress analysis results are presented for the main body of the regulator, as well as, flow analysis to determine some important flow characteristics in the inlet and outlet of the regulator.
Multigrid waveform relaxation on spatial finite element meshes
Energy Technology Data Exchange (ETDEWEB)
Janssen, J. [Katholieke Universiteit Leuven (Belgium); Vandewalle, S. [Caltech, Pasadena, CA (United States)
1994-12-31
The authors shall discuss the numerical solution of a parabolic partial differential equation {partial_derivative}u/{partial_derivative}t(x,t) = Lu(x,t) + f(x,t), x{element_of}{Omega}, t>0, (1) supplied with a boundary condition and given initial values. The spatial finite element discretization of (1) on a discrete grid {Omega}{sub h} leads to an initial value problem of the form B{dot u} + Au = f, u(0) = u{sub o}, t > 0, (2) with B a non-singular matrix. The waveform relaxation method is a method for solving ordinary differential equations. It differs from most standard iterative techniques in that it is a continuous-time method, iterating with functions in time, and thereby well-suited for parallel computation.
Fracture and Fragmentation of Simplicial Finite Elements Meshes using Graphs
Energy Technology Data Exchange (ETDEWEB)
Mota, A; Knap, J; Ortiz, M
2006-10-18
An approach for the topological representation of simplicial finite element meshes as graphs is presented. It is shown that by using a graph, the topological changes induced by fracture reduce to a few, local kernel operations. The performance of the graph representation is demonstrated and analyzed, using as reference the 3D fracture algorithm by Pandolfi and Ortiz [22]. It is shown that the graph representation initializes in O(N{sub E}{sup 1.1}) time and fractures in O(N{sub I}{sup 1.0}) time, while the reference implementation requires O(N{sub E}{sup 2.1}) time to initialize and O(N{sub I}{sup 1.9}) time to fracture, where NE is the number of elements in the mesh and N{sub I} is the number of interfaces to fracture.
Dynamic stability of a rotor blade using finite element analysis
Sivaneri, N. T.; Chopra, I.
1981-01-01
The aeroelastic stability of flap bending, lead-lag bending, and torsion of a helicopter rotor blade in hover is examined using a finite element formulation based on the principle of virtual work. Quasi-steady two-dimensional airfoil theory is used to obtain the aerodynamic loads. The rotor blade is discretized into beam elements, each with ten modal degrees of freedom. The resulting nonlinear equations of motion are solved for steady-state blade deflections through an iterative procedure. The flutter solution is calculated assuming blade motion to be a small perturbation about the steady solution. The normal mode method based on the coupled rotating natural modes about the steady deflections is used to reduce the number of equations in the flutter eigenanalysis. Results are presented for hingeless and articulated rotor blade configurations.
Finite element analysis for bearingless rotor blade aeroelasticity
Sivaneri, N. T.; Chopra, I.
1982-01-01
A conventional articulated rotor blade has mechanical flap and lag hinges, a lag damper, and a pitch bearing. In connection with an interest in designs of greater mechanical simplicity and increased maintainability, hingeless and bearingless rotors have been developed. A hingeless blade lacks the hinges and is cantilevered at the hub. It does have a pitch bearing for pitch control. A bearingless design eliminates the hinges and the pitch bearing as well. In the present investigation of bearingless rotor blade characteristics, finite element analysis has been successfully applied to determine the solutions of the nonlinear trim equations and the linearized flutter equations of multiple-load-path blades. The employed formulation is based on Hamilton's principle. The spatial dependence of the equations of motion is discretized by dividing the flexbeams, the torque tube, and the outboard into a number of elements.
Structural optimisation of cage induction motors using finite element analysis
Palko, S.
The current trend in motor design is to have highly efficient, low noise, low cost, and modular motors with a high power factor. High torque motors are useful in applications like servo motors, lifts, cranes, and rolling mills. This report contains a detailed review of different optimization methods applicable in various design problems. Special attention is given to the performance of different methods, when they are used with finite element analysis (FEA) as an objective function, and accuracy problems arising from the numerical simulations. Also an effective method for designing high starting torque and high efficiency motors is presented. The method described in this work utilizes FEA combined with algorithms for the optimization of the slot geometry. The optimization algorithm modifies the position of the nodal points in the element mesh. The number of independent variables ranges from 14 to 140 in this work.
A nonlinear dynamic corotational finite element model for submerged pipes
de Vries, F. H.; Geijselaers, H. J. M.; van den Boogaard, A. H.; Huisman, A.
2017-12-01
A three dimensional finite element model is built to compute the motions of a pipe that is being laid on the seabed. This process is geometrically nonlinear, therefore co-rotational beam elements are used. The pipe is subject to static and dynamic forces. Static forces are due to gravity, current and buoyancy. The dynamic forces exerted by the water are incorporated using Morison’s equation. The dynamic motions are computed using implicit time integration. For this the Hilber-Hughes-Taylor method is selected. The Newton-Raphson iteration scheme is used to solve the equations in every time step. During laying, the pipe is connected to the pipe laying vessel, which is subject to wave motion. Response amplitude operators are used to determine the motions of the ship and thus the motions of the top end of the pipe.
Model Reduction in Dynamic Finite Element Analysis of Lightweight Structures
DEFF Research Database (Denmark)
Flodén, Ola; Persson, Kent; Sjöström, Anders
2012-01-01
. The objective of the analyses presented in this paper is to evaluate methods for model reduction of detailed finite element models of floor and wall structures and to investigate the influence of reducing the number of degrees of freedom and computational cost on the dynamic response of the models in terms....... The drawback of component mode synthesis compared to modelling with structural elements is the increased computational cost, although the number of degrees of freedom is small in comparison, as a result of the large bandwidth of the system matrices.......The application of wood as a construction material when building multi-storey buildings has many advantages, e.g., light weight, sustainability and low energy consumption during the construction and lifecycle of the building. However, compared to heavy structures, it is a greater challenge to build...
Practical Aspects of Finite Element Method Applications in Dentistry
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Grbović Aleksandar
2017-07-01
Full Text Available The use of numerical methods, such as finite element method (FEM, has been widely adopted in solving structural problems with complex geometry under external loads when analytical solutions are unachievable. Basic idea behind FEM is to divide the complex body geometry into smaller and simpler domains, called finite elements, and then to formulate solution for each element instead of seeking a solution for the entire domain. After finding the solutions for all elements they can be combined to obtain a solution for the whole domain. This numerical method is mostly used in engineering, but it is also useful for studying the biomechanical properties of materials used in medicine and the influence of mechanical forces on the biological systems. Since its introduction in dentistry four decades ago, FEM became powerful tool for the predictions of stress and strain distribution on teeth, dentures, implants and surrounding bone. FEM can indicate aspects of biomaterials and human tissues that can hardly be measured in vivo and can predict the stress distribution in the contact areas which are not accessible, such as areas between the implant and cortical bone, denture and gingiva, or around the apex of the implant in trabecular bone. Aim of this paper is to present - using results of several successful FEM studies - the usefulness of this method in solving dentistry problems, as well as discussing practical aspects of FEM applications in dentistry. Some of the method limitations, such as impossibility of complete replication of clinical conditions and need for simplified assumptions regarding loads and materials modeling, are also presented. However, the emphasis is on FE modelling of teeth, bone, dentures and implants and their modifications according to the requirements. All presented studies have been carried out in commercial software for FE analysis ANSYS Workbench.
Automating the generation of finite element dynamical cores with Firedrake
Ham, David; Mitchell, Lawrence; Homolya, Miklós; Luporini, Fabio; Gibson, Thomas; Kelly, Paul; Cotter, Colin; Lange, Michael; Kramer, Stephan; Shipton, Jemma; Yamazaki, Hiroe; Paganini, Alberto; Kärnä, Tuomas
2017-04-01
The development of a dynamical core is an increasingly complex software engineering undertaking. As the equations become more complete, the discretisations more sophisticated and the hardware acquires ever more fine-grained parallelism and deeper memory hierarchies, the problem of building, testing and modifying dynamical cores becomes increasingly complex. Here we present Firedrake, a code generation system for the finite element method with specialist features designed to support the creation of geoscientific models. Using Firedrake, the dynamical core developer writes the partial differential equations in weak form in a high level mathematical notation. Appropriate function spaces are chosen and time stepping loops written at the same high level. When the programme is run, Firedrake generates high performance C code for the resulting numerics which are executed in parallel. Models in Firedrake typically take a tiny fraction of the lines of code required by traditional hand-coding techniques. They support more sophisticated numerics than are easily achieved by hand, and the resulting code is frequently higher performance. Critically, debugging, modifying and extending a model written in Firedrake is vastly easier than by traditional methods due to the small, highly mathematical code base. Firedrake supports a wide range of key features for dynamical core creation: A vast range of discretisations, including both continuous and discontinuous spaces and mimetic (C-grid-like) elements which optimally represent force balances in geophysical flows. High aspect ratio layered meshes suitable for ocean and atmosphere domains. Curved elements for high accuracy representations of the sphere. Support for non-finite element operators, such as parametrisations. Access to PETSc, a world-leading library of programmable linear and nonlinear solvers. High performance adjoint models generated automatically by symbolically reasoning about the forward model. This poster will present
Finite element and analytical models for twisted and coiled actuator
Tang, Xintian; Liu, Yingxiang; Li, Kai; Chen, Weishan; Zhao, Jianguo
2018-01-01
Twisted and coiled actuator (TCA) is a class of recently discovered artificial muscle, which is usually made by twisting and coiling polymer fibers into spring-like structures. It has been widely studied since discovery due to its impressive output characteristics and bright prospects. However, its mathematical models describing the actuation in response to the temperature are still not fully developed. It is known that the large tensile stroke is resulted from the untwisting of the twisted fiber when heated. Thus, the recovered torque during untwisting is a key parameter in the mathematical model. This paper presents a simplified model for the recovered torque of TCA. Finite element method is used for evaluating the thermal stress of the twisted fiber. Based on the results of the finite element analyses, the constitutive equations of twisted fibers are simplified to develop an analytic model of the recovered torque. Finally, the model of the recovered torque is used to predict the deformation of TCA under varying temperatures and validated against experimental results. This work will enhance our understanding of the deformation mechanism of TCAs, which will pave the way for the closed-loop position control.
A finite element model for ultrafast laser-lamellar keratoplasty.
Fernández, D Cabrera; Niazy, A M; Kurtz, R M; Djotyan, G P; Juhasz, T
2006-01-01
A biomechanical model of the human cornea is employed in a finite element formulation for simulating the effects of Ultrafast Laser-Lamellar Keratoplasty. Several computer simulations were conducted to study curvature changes of the central corneal zone under various physiological and surgical factors. These factors included the combined effect of corneal flap and residual stromal bed thickness on corneal curvature; the effect of the shape of the lenticle on the surgical procedure outcomes and the effect of flap thickness on stress distribution in the cornea. The results were validated by comparing computed refractive power changes with clinical results. The effect of flap thickness on the amount of central flattening indicates that for flap thickness values 28% over the corneal thickness, central corneal flattening decreases. Moreover, the change in corneal curvature induced by subtraction of a plano-convex lenticle under a uniform flap, naturally imply a smaller change in the structure of the anterior layers of the cornea, but a bigger deformation in the structure of the posterior layers that are left behind the resection of the lenticle. In addition, the model also verified that the corneal curvature increased peripherally with simultaneous thinning centrally after subtraction of corneal tissue. This result shows that not only the treated zone is affected by the surgery, indicating the important role of the biomechanical response of the corneal tissue to refractive surgery, which is unaccounted for in current ablation algorithms. The results illustrate the potentialities of finite element modeling as an aid to the surgeon in evaluating variables.
Muscle-driven finite element simulation of human foot movements.
Spyrou, L A; Aravas, N
2012-01-01
This paper describes a finite element scheme for realistic muscle-driven simulation of human foot movements. The scheme is used to simulate human ankle plantar flexion. A three-dimensional anatomically detailed finite element model of human foot and lower leg is developed and the idea of generating natural foot movement based entirely on the contraction of the plantar flexor muscles is used. The bones, ligaments, articular cartilage, muscles, tendons, as well as the rest soft tissues of human foot and lower leg are included in the model. A realistic three-dimensional continuum constitutive model that describes the biomechanical behaviour of muscles and tendons is used. Both the active and passive properties of muscle tissue are accounted for. The materials for bones and ligaments are considered as homogeneous, isotropic and linearly elastic, whereas the articular cartilage and the rest soft tissues (mainly fat) are defined as hyperelastic materials. The model is used to estimate muscle tissue deformations as well as stresses and strains that develop in the lower leg muscles during plantar flexion of the ankle. Stresses and strains that develop in Achilles tendon during such a movement are also investigated.
Domain decomposition solvers for nonlinear multiharmonic finite element equations
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.
Modelling of Shaft Orbiting with 3-D Solid Finite Elements
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J. Yu
1999-01-01
Full Text Available A 3-D solid finite element model which can include bending, torsional, axial and other motions is proposed to analyse dynamic responses of shafts. For uniform shafts, this model shows consistency with beam theories when bending vibration is examined. For non-uniform shafts such as tapered ones, however, this model gives much more reliable and accurate results than beam theories which use an assumption that plane sections remain plane. Reduction procedures can be applied which involve only small matrix operations for such a system with a large number of degrees of freedom. The equations of motion have been consistently derived in a rotating frame. Shaft orbiting motion is then defined in this frame, giving a clear view of its trajectories. Forced responses due to excitation in the rotating frame have been examined to find some characteristics of the orbiting shaft. Resonant orbiting frequencies, i.e., natural frequencies of rotating shafts, can be determined in terms of the rotating or fixed frame. Trajectories of transverse displacements have been found to be varying with the forcing frequencies. At resonance, a uniform shaft will only have forward or backward orbiting motion with circular orbits. For other forcing frequencies, however, even a uniform shaft could present both forward and backward orbiting motions with non-circular orbits at different locations along its length. It is anticipated that modelling of shaft orbiting in the rotating frame with the proposed 3-D solid finite elements will lead to accurate dynamic stress evaluation.
Finite Element Modeling of the Posterior Eye in Microgravity
Feola, Andrew; Raykin, Julia; Mulugeta, Lealem; Gleason, Rudolph; Myers, Jerry G.; Nelson, Emily S.; Samuels, Brian; Ethier, C. Ross
2015-01-01
Microgravity experienced during spaceflight affects astronauts in various ways, including weakened muscles and loss of bone density. Recently, visual impairment and intracranial pressure (VIIP) syndrome has become a major concern for space missions lasting longer than 30 days. Astronauts suffering from VIIP syndrome have changes in ocular anatomical and visual impairment that persist after returning to earth. It is hypothesized that a cephalad fluid shift in microgravity may increase the intracranial pressure (ICP), which leads to an altered biomechanical environment of the posterior globe and optic nerve sheath (ONS).Currently, there is a lack of knowledge of how elevated ICP may lead to vision impairment and connective tissue changes in VIIP. Our goal was to develop a finite element model to simulate the acute effects of elevated ICP on the posterior eye and optic nerve sheath. We used a finite element (FE) analysis approach to understand the response of the lamina cribrosa and optic nerve to the elevations in ICP thought to occur in microgravity and to identify which tissue components have the greatest impact on strain experienced by optic nerve head tissues.
Mixed Generalized Multiscale Finite Element Methods and Applications
Chung, Eric T.
2015-03-03
In this paper, we present a mixed generalized multiscale finite element method (GMsFEM) for solving flow in heterogeneous media. Our approach constructs multiscale basis functions following a GMsFEM framework and couples these basis functions using a mixed finite element method, which allows us to obtain a mass conservative velocity field. To construct multiscale basis functions for each coarse edge, we design a snapshot space that consists of fine-scale velocity fields supported in a union of two coarse regions that share the common interface. The snapshot vectors have zero Neumann boundary conditions on the outer boundaries, and we prescribe their values on the common interface. We describe several spectral decompositions in the snapshot space motivated by the analysis. In the paper, we also study oversampling approaches that enhance the accuracy of mixed GMsFEM. A main idea of oversampling techniques is to introduce a small dimensional snapshot space. We present numerical results for two-phase flow and transport, without updating basis functions in time. Our numerical results show that one can achieve good accuracy with a few basis functions per coarse edge if one selects appropriate offline spaces. © 2015 Society for Industrial and Applied Mathematics.
Finite element stress analysis of stainless steel crowns.
Prabhakar, Attiguppe R; Yavagal, Chandrashekar M; Chakraborty, Amrita; Sugandhan, S
2015-01-01
Though stainless steel crowns (SSCs) have often been stated as the best restorative modality, there are limited studies demonstrating its efficacy in restoring the functional integrity of the primary dentition. Hence has arisen, the necessity to establish the supremacy of SSCs. Evaluation of the efficacy of SSC to with stand compressive (0°), shearing (90°), and torsional (45°) stress when used as a restorative material. The study design employed four finite element models, each with differing amounts of tooth structure, which were exported to ANSYS software and subjected to an average simulated bite force of 245N. Four maxillary deciduous primary molars restored with SSCs (3M ESPE) were subjected to spiral computed tomography (CT) in order to obtain three-dimensional (3D) images, which were then converted into finite element models. They were each subjected to forces along the long axis of the tooth and at 45°and 90°. The maximal equivalent von Mises stress was demonstrated in the SSCs of all the models with only a minimal amount observed in the underlying dentine. In all situations, the maximal equivalent von Mises stress was well below the ultimate tensile strength values of stainless steel and dentine. Even at maximal physiologic masticatory force levels, a grossly destructed tooth restored with SSC is able to resist deformation.
Finite Element Stress Analysis of Stainless Steel Crowns
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Attiguppe R Prabhakar
2015-01-01
Full Text Available Background: Though stainless steel crowns (SSCs have often been stated as the best restorative modality, there are limited studies demonstrating its efficacy in restoring the functional integrity of the primary dentition. Hence has arisen, the necessity to establish the supremacy of SSCs. Aim: Evaluation of the efficacy of SSC to with stand compressive (0°, shearing (90°, and torsional (45° stress when used as a restorative material. Settings and Design: The study design employed four finite element models, each with differing amounts of tooth structure, which were exported to ANSYS software and subjected to an average simulated bite force of 245N. Materials and Methods: Four maxillary deciduous primary molars restored with SSCs (3M ESPE were subjected to spiral computed tomography (CT in order to obtain three-dimensional (3D images, which were then converted into finite element models. They were each subjected to forces along the long axis of the tooth and at 45°and 90°. Results: The maximal equivalent von Mises stress was demonstrated in the SSCs of all the models with only a minimal amount observed in the underlying dentine. In all situations, the maximal equivalent von Mises stress was well below the ultimate tensile strength values of stainless steel and dentine. Conclusion: Even at maximal physiologic masticatory force levels, a grossly destructed tooth restored with SSC is able to resist deformation.
Adaptive Finite Element Methods for Elliptic Problems with Discontinuous Coefficients
Bonito, Andrea
2013-01-01
Elliptic PDEs with discontinuous diffusion coefficients occur in application domains such as diffusions through porous media, electromagnetic field propagation on heterogeneous media, and diffusion processes on rough surfaces. The standard approach to numerically treating such problems using finite element methods is to assume that the discontinuities lie on the boundaries of the cells in the initial triangulation. However, this does not match applications where discontinuities occur on curves, surfaces, or manifolds, and could even be unknown beforehand. One of the obstacles to treating such discontinuity problems is that the usual perturbation theory for elliptic PDEs assumes bounds for the distortion of the coefficients in the L∞ norm and this in turn requires that the discontinuities are matched exactly when the coefficients are approximated. We present a new approach based on distortion of the coefficients in an Lq norm with q < ∞ which therefore does not require the exact matching of the discontinuities. We then use this new distortion theory to formulate new adaptive finite element methods (AFEMs) for such discontinuity problems. We show that such AFEMs are optimal in the sense of distortion versus number of computations, and report insightful numerical results supporting our analysis. © 2013 Societ y for Industrial and Applied Mathematics.
Investigation of Apple Vibration Characteristics Using Finite Element Modal Analysis
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R Mirzaei
2013-02-01
Full Text Available The most important quality indicator of fruits is the flesh firmness which is well correlated to their young’s modulus. In this research variation of vibration characteristics (shape modes, natural frequency of apple due to change of material characteristics (density, young's models, Poisson ratio and apple volume was investigated using Finite Element simulation. An image processing technique was used to obtain an unsymmetrical and non-spherical geometric model of apple. The exact three-dimensional shape of the fruit was created by determining the coordinates of apple surface and forming uneven rotational curvatures. Modal analysis with no boundary constraints has been applied. The first 20 Eigen frequencies and the corresponding mode shape were determined. Six rigid body modes possess zero resonant frequency which is related to the degree of freedom of a rigid body in space indicated the validity of finite element model. The modal analysis results showed that resonant frequency increased by increasing young's modulus of the fruit, while it decreased by increasing apple density. First mode torsion has a mean resonant frequency of 584 Hz. Variations of natural frequency due to change in young's modulus, density, and Poisson ratio were 80%, 11% and 4%, respectively. Coefficient of variation of resonant frequency in response to changing young's modulus was 2-3 times of that of density which shows the greatest effect of young modulus changes on natural frequency of fruits. Consequently with determination of fruits' natural frequency, their young modulus and firmness can be estimated.
Finite element analysis of the Roquefort diagnostic canister
Energy Technology Data Exchange (ETDEWEB)
Pratuch, S.M.
1985-08-01
This document reports on the development of a simple finite element model of the Roquefort diagnostic canister. It describes the means in which the model was used to predict the canister deflection when simply supported as well as the corresponding forces, moments, and stresses in the cable trays and lifting fixtures. Also included in the report are the results of the line of sight (LOS) hardware modeling which was used to size the LOS hardware to bulkhead connections. Three canister load configurations - bare frame, bare frame plus lead shielding, and bare frame, lead, plus LOS hardware - were studied during the analysis and are presented in this report. In addition, the results of a fourth canister configuration (using the same loads as that of the third load case), initiated because of the presence of near-yield stresses in the third load configuration and the subsequent addition of cable tray stiffeners, are also included. Throughout the analysis, three computer codes were used: SLIC, to generate the canister mesh, GEMINI, to conduct the finite element data, and TAURUS, to create the figures presented in this report.
The mixed finite element multigrid method for stokes equations.
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 Q2-Q1 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.
Scientific use of the finite element method in Orthodontics
Knop, Luegya; Gandini, Luiz Gonzaga; Shintcovsk, Ricardo Lima; Gandini, Marcia Regina Elisa Aparecida Schiavon
2015-01-01
INTRODUCTION: The finite element method (FEM) is an engineering resource applied to calculate the stress and deformation of complex structures, and has been widely used in orthodontic research. With the advantage of being a non-invasive and accurate method that provides quantitative and detailed data on the physiological reactions possible to occur in tissues, applying the FEM can anticipate the visualization of these tissue responses through the observation of areas of stress created from applied orthodontic mechanics. OBJECTIVE: This article aims at reviewing and discussing the stages of the finite element method application and its applicability in Orthodontics. RESULTS: FEM is able to evaluate the stress distribution at the interface between periodontal ligament and alveolar bone, and the shifting trend in various types of tooth movement when using different types of orthodontic devices. Therefore, it is necessary to know specific software for this purpose. CONCLUSIONS: FEM is an important experimental method to answer questions about tooth movement, overcoming the disadvantages of other experimental methods. PMID:25992996
SENSITIVITY ANALYSIS OF CONCRETE PERFORMANCE USING FINITE ELEMENT APPROACH
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Y. H. Parjoko
2012-06-01
Full Text Available This study aims to understand the effect of applying several parameters: different axle load configuration, concrete properties, subgrade properties, slab thickness, joint characteristics, shoulder construction, bounded HMA overlay on concrete pavement, and bounded and unbounded CTB foundation over subgrade on the fatigue and erosion related distresses in concrete pavements. KENSLAB, an elaborate finite element program is used to determine the concrete pavement responses: stresses and deflection under the defined parameters. The results obtained using this software is relatively close to known theoretical Westergaard solutions. Several other findings related to pavement performance and behavior are made through this study. Multiple axle configurations is less damaging than single axle configuration in terms of fatigue life. Increasing the thickness is very effective in reducing the edge stress. Using concrete with higher modulus of elasticity brings only a small increase to the edge stress. Increasing the slab thickness is the most effective way to increase the fatigue life. Increasing subgrade modulus is more effective in reducing corner deflection than decreasing edge stress. The availability of tied shoulder construction gives significant impact in both reducing edge stress and corner deflection. The debonding condition between layers has a significant effect on pavement responses. Keywords: Concrete pavement, fatigue failure, erosion failure, finite element, KENSLAB.
Using optimisation for calibrating finite element models for adobe walls
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Wilson Rodríguez Calderón
2010-07-01
Full Text Available This paper presents a proposal for applying optimisation schemes to calibrating 3D linear and non-linear finite element models for analysing structural walls made out of adobe. The calibration was based on laboratory data and that from previous research. Simulation and calibration involves a deep study of the conceptual model of adobe’s structural behaviour, mathematical and nu- merical models and the interrelationship with optimisation schemes arising from minimising an objective function. This is defined in terms of design variables and is restricted by the values of state variables. Both were obtained from the finite element model developed at ANSYS. The optimisation scheme with which the model was automatically calibrated required a macro to be pro- grammed using an APDL language package. This research was aimed at implementing nonlinear computational models for the structural analysis of walls based on experimental data; this provided a tool for assessing the behaviour of adobe walls with grea- ter security so that decisions can be made to make structural rehabilitation feasible and efficient.
Finite element simulation of articular contact mechanics with quadratic tetrahedral elements.
Maas, Steve A; Ellis, Benjamin J; Rawlins, David S; Weiss, Jeffrey A
2016-03-21
Although it is easier to generate finite element discretizations with tetrahedral elements, trilinear hexahedral (HEX8) elements are more often used in simulations of articular contact mechanics. This is due to numerical shortcomings of linear tetrahedral (TET4) elements, limited availability of quadratic tetrahedron elements in combination with effective contact algorithms, and the perceived increased computational expense of quadratic finite elements. In this study we implemented both ten-node (TET10) and fifteen-node (TET15) quadratic tetrahedral elements in FEBio (www.febio.org) and compared their accuracy, robustness in terms of convergence behavior and computational cost for simulations relevant to articular contact mechanics. Suitable volume integration and surface integration rules were determined by comparing the results of several benchmark contact problems. The results demonstrated that the surface integration rule used to evaluate the contact integrals for quadratic elements affected both convergence behavior and accuracy of predicted stresses. The computational expense and robustness of both quadratic tetrahedral formulations compared favorably to the HEX8 models. Of note, the TET15 element demonstrated superior convergence behavior and lower computational cost than both the TET10 and HEX8 elements for meshes with similar numbers of degrees of freedom in the contact problems that we examined. Finally, the excellent accuracy and relative efficiency of these quadratic tetrahedral elements was illustrated by comparing their predictions with those for a HEX8 mesh for simulation of articular contact in a fully validated model of the hip. These results demonstrate that TET10 and TET15 elements provide viable alternatives to HEX8 elements for simulation of articular contact mechanics. Copyright © 2016 Elsevier Ltd. All rights reserved.
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Dobrev, Veselin A. [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States); Kolev, Tzanio V. [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States); Rieben, Robert N. [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)
2012-09-20
The numerical approximation of the Euler equations of gas dynamics in a movingLagrangian frame is at the heart of many multiphysics simulation algorithms. Here, we present a general framework for high-order Lagrangian discretization of these compressible shock hydrodynamics equations using curvilinear finite elements. This method is an extension of the approach outlined in [Dobrev et al., Internat. J. Numer. Methods Fluids, 65 (2010), pp. 1295--1310] and can be formulated for any finite dimensional approximation of the kinematic and thermodynamic fields, including generic finite elements on two- and three-dimensional meshes with triangular, quadrilateral, tetrahedral, or hexahedral zones. We discretize the kinematic variables of position and velocity using a continuous high-order basis function expansion of arbitrary polynomial degree which is obtained via a corresponding high-order parametric mapping from a standard reference element. This enables the use of curvilinear zone geometry, higher-order approximations for fields within a zone, and a pointwise definition of mass conservation which we refer to as strong mass conservation. Moreover, we discretize the internal energy using a piecewise discontinuous high-order basis function expansion which is also of arbitrary polynomial degree. This facilitates multimaterial hydrodynamics by treating material properties, such as equations of state and constitutive models, as piecewise discontinuous functions which vary within a zone. To satisfy the Rankine--Hugoniot jump conditions at a shock boundary and generate the appropriate entropy, we introduce a general tensor artificial viscosity which takes advantage of the high-order kinematic and thermodynamic information available in each zone. Finally, we apply a generic high-order time discretization process to the semidiscrete equations to develop the fully discrete numerical algorithm. Our method can be viewed as the high-order generalization of the so-called staggered
High-order finite element methods for cardiac monodomain simulations
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Kevin P Vincent
2015-08-01
Full Text Available Computational modeling of tissue-scale cardiac electrophysiology requires numerically converged solutions to avoid spurious artifacts. The steep gradients inherent to cardiac action potential propagation necessitate fine spatial scales and therefore a substantial computational burden. The use of high-order interpolation methods has previously been proposed for these simulations due to their theoretical convergence advantage. In this study, we compare the convergence behavior of linear Lagrange, cubic Hermite, and the newly proposed cubic Hermite-style serendipity interpolation methods for finite element simulations of the cardiac monodomain equation. The high-order methods reach converged solutions with fewer degrees of freedom and longer element edge lengths than traditional linear elements. Additionally, we propose a dimensionless number, the cell Thiele modulus, as a more useful metric for determining solution convergence than element size alone. Finally, we use the cell Thiele modulus to examine convergence criteria for obtaining clinically useful activation patterns for applications such as patient-specific modeling where the total activation time is known a priori.
High-order finite element methods for cardiac monodomain simulations
Vincent, Kevin P.; Gonzales, Matthew J.; Gillette, Andrew K.; Villongco, Christopher T.; Pezzuto, Simone; Omens, Jeffrey H.; Holst, Michael J.; McCulloch, Andrew D.
2015-01-01
Computational modeling of tissue-scale cardiac electrophysiology requires numerically converged solutions to avoid spurious artifacts. The steep gradients inherent to cardiac action potential propagation necessitate fine spatial scales and therefore a substantial computational burden. The use of high-order interpolation methods has previously been proposed for these simulations due to their theoretical convergence advantage. In this study, we compare the convergence behavior of linear Lagrange, cubic Hermite, and the newly proposed cubic Hermite-style serendipity interpolation methods for finite element simulations of the cardiac monodomain equation. The high-order methods reach converged solutions with fewer degrees of freedom and longer element edge lengths than traditional linear elements. Additionally, we propose a dimensionless number, the cell Thiele modulus, as a more useful metric for determining solution convergence than element size alone. Finally, we use the cell Thiele modulus to examine convergence criteria for obtaining clinically useful activation patterns for applications such as patient-specific modeling where the total activation time is known a priori. PMID:26300783
Sutural strain in orthopedic headgear therapy: a finite element analysis.
Holberg, Christof; Holberg, Nikola; Rudzki-Janson, Ingrid
2008-07-01
The goal of this study was to analyze the strains induced in the sutures of the midface and the cranial base by headgear therapy involving orthopedic forces. Does the mechanical signal induced in the sutures sufficiently account for a growth-influencing effect? A finite element model of the viscerocranium and the neurocranium was used. It consisted of 53,555 tetrahedral elements and 97,550 nodes. The strain induced in the sutures of the cranial base and the midface when applying orthopedic headgear forces of 5 and 10 N was computed and recorded with an interactive measurement tool. The magnitude and the distribution of the measured strains depended on the level and the direction of the acting force. Overall, the strain values measured at the sutures of the midface and the cranial base were moderate. The measured peak values at a load of 5 N per side were usually just below 20 microstrain irrespective of the force direction. A characteristic distribution of strain values appeared on the anatomical structures of the midface and the cranial base for each vector direction. The measurements based on the finite element method provided a good overview of the approximate magnitudes of sutural strains with orthopedic headgear therapy. The signal arriving in the sutures is apparently well below threshold, since the maximum measured strains in most sutures were about 100 fold lower than the minimal effective strain. A skeletal effect of the orthopedic headgear due to a mechanical effect on sutural growth cannot be confirmed from these results. The good clinical efficacy of headgear therapy with orthopedic forces is apparently based mainly on dentoalveolar effects, whereas the skeletal effect due to inhibition of sutural growth is somewhat questionable.
Applications of finite element simulation in orthopedic and trauma surgery
Herrera, Antonio; Ibarz, Elena; Cegoñino, José; Lobo-Escolar, Antonio; Puértolas, Sergio; López, Enrique; Mateo, Jesús; Gracia, Luis
2012-01-01
Research in different areas of orthopedic and trauma surgery requires a methodology that allows both a more economic approach and the ability to reproduce different situations in an easy way. Simulation models have been introduced recently in bioengineering and could become an essential tool in the study of any physiological unity, regardless of its complexity. The main problem in modeling with finite elements simulation is to achieve an accurate reproduction of the anatomy and a perfect correlation of the different structures, in any region of the human body. Authors have developed a mixed technique, joining the use of a three-dimensional laser scanner Roland Picza captured together with computed tomography (CT) and 3D CT images, to achieve a perfect reproduction of the anatomy. Finite element (FE) simulation lets us know the biomechanical changes that take place after hip prostheses or osteosynthesis implantation and biological responses of bone to biomechanical changes. The simulation models are able to predict changes in bone stress distribution around the implant, so allowing preventing future pathologies. The development of a FE model of lumbar spine is another interesting application of the simulation. The model allows research on the lumbar spine, not only in physiological conditions but also simulating different load conditions, to assess the impact on biomechanics. Different degrees of disc degeneration can also be simulated to determine the impact on adjacent anatomical elements. Finally, FE models may be useful to test different fixation systems, i.e., pedicular screws, interbody devices or rigid fixations compared with the dynamic ones. We have also developed models of lumbar spine and hip joint to predict the occurrence of osteoporotic fractures, based on densitometric determinations and specific biomechanical models, including approaches from damage and fracture mechanics. FE simulations also allow us to predict the behavior of orthopedic splints
Coupled Finite Volume and Finite Element Method Analysis of a Complex Large-Span Roof Structure
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.
A hybrid finite volume - finite element method for bulk-surface coupled problems
Chernyshenko, Alexey Y.; Olshanskii, Maxim A.; Vassilevski, Yuri V.
2018-01-01
The paper develops a hybrid method for solving a system of advection-diffusion equations in a bulk domain coupled to advection-diffusion equations on an embedded surface. A monotone nonlinear finite volume method for equations posed in the bulk is combined with a trace finite element method for equations posed on the surface. In our approach, the surface is not fitted by the mesh and is allowed to cut through the background mesh in an arbitrary way. Moreover, a triangulation of the surface into regular shaped elements is not required. The background mesh is an octree grid with cubic cells. As an example of an application, we consider the modeling of contaminant transport in fractured porous media. One standard model leads to a coupled system of advection-diffusion equations in a bulk (matrix) and along a surface (fracture). A series of numerical experiments with both steady and unsteady problems and different embedded geometries illustrate the numerical properties of the hybrid approach. The method demonstrates great flexibility in handling curvilinear or branching lower dimensional embedded structures.
Coupled Finite Volume and Finite Element Method Analysis of a Complex Large-Span Roof Structure
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Szafran J.
2017-12-01
Full Text Available 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.
Nakamura, Keiko; Tajima, Kiyoshi; Chen, Ker-Kong; Nagamatsu, Yuki; Kakigawa, Hiroshi; Masumi, Shin-ich
2013-12-01
This study focused on the application of novel finite-element analysis software for constructing a finite-element model from the computed tomography data of a human dentulous mandible. The finite-element model is necessary for evaluating the mechanical response of the alveolar part of the mandible, resulting from occlusal force applied to the teeth during biting. Commercially available patient-specific general computed tomography-based finite-element analysis software was solely applied to the finite-element analysis for the extraction of computed tomography data. The mandibular bone with teeth was extracted from the original images. Both the enamel and the dentin were extracted after image processing, and the periodontal ligament was created from the segmented dentin. The constructed finite-element model was reasonably accurate using a total of 234,644 nodes and 1,268,784 tetrahedral and 40,665 shell elements. The elastic moduli of the heterogeneous mandibular bone were determined from the bone density data of the computed tomography images. The results suggested that the software applied in this study is both useful and powerful for creating a more accurate three-dimensional finite-element model of a dentulous mandible from the computed tomography data without the need for any other software.
A suitable low-order, eight-node tetrahedral finite element for solids
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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.
Suryanto, A.; van Groesen, Embrecht W.C.; Hammer, Manfred; Hoekstra, Hugo
We present a simple numerical scheme based on the finite element method (FEM) using transparent-influx boundary conditions to study the nonlinear optical response of a finite one-dimensional grating with Kerr medium. Restricting first to the linear case, we improve the standard FEM to get a fourth
Frehner, Marcel; Schmalholz, Stefan M.; Saenger, Erik H.; Steeb, Holger Karl
2008-01-01
Two-dimensional scattering of elastic waves in a medium containing a circular heterogeneity is investigated with an analytical solution and numerical wave propagation simulations. Different combinations of finite difference methods (FDM) and finite element methods (FEM) are used to numerically solve
Zhebel, E.; Minisini, S.; Kononov, A.; Mulder, W.A.
2013-01-01
With the rapid developments in parallel compute architectures, algorithms for seismic modeling and imaging need to be reconsidered in terms of parallelization. The aim of this paper is to compare scalability of seismic modeling algorithms: finite differences, continuous mass-lumped finite elements
On Round-off Error for Adaptive Finite Element Methods
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.
Finite element analysis on badminton racket design parameters
Nasruddin, Fakhrizal Azmy; Syahrom, Ardiyansyah; Abdul Kadir, Mohammed Rafiq; Omar, Abdul Hafidz; Öchsner, Andreas
2016-01-01
This work identifies the characteristics of racket design parameters that influence racket performance. It presents the finite element analysis of several designs of badminton rackets and compares them to experimental results for validation. Designing a racket requires a comprehensive understanding of racket performance characteristics. Essentially, racket performance is related to the sweet spot, which is the spot on the racket head that produces the most power and control when it strikes a shuttlecock. Determining a coefficient of restitution can help to identify the sweet spot on a racket. By analyzing several head shape designs, it becomes apparent that isometric head shape rackets produce better coefficients of restitution compared to oval and round ones. It is recommended that the racket design consist of low string tension, stiffer racket shafts and bigger head size in order to produce higher shuttlecock speed.
Strong Superconvergence of Finite Element Methods for Linear Parabolic Problems
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Kening Wang
2009-01-01
Full Text Available We study the strong superconvergence of a semidiscrete finite element scheme for linear parabolic problems on =Ω×(0,], where Ω is a bounded domain in ℛ(≤4 with piecewise smooth boundary. We establish the global two order superconvergence results for the error between the approximate solution and the Ritz projection of the exact solution of our model problem in 1,(Ω and ( with 2≤<∞ and the almost two order superconvergence in 1,∞(Ω and ∞(. Results of the =∞ case are also included in two space dimensions (=1 or 2. By applying the interpolated postprocessing technique, similar results are also obtained on the error between the interpolation of the approximate solution and the exact solution.
Dynamic visual cryptography on deformable finite element grids
Aleksiene, S.; Vaidelys, M.; Aleksa, A.; Ragulskis, M.
2017-07-01
Dynamic visual cryptography scheme based on time averaged moiré fringes on deformable finite element grids is introduced in this paper. A predefined Eigenshape function is used for the selection of the pitch of the moiré grating. The relationship between the pitch of moiré grating, the roots of the zero order Bessel function of the first kind and the amplitude of harmonic oscillations is derived and validated by computational experiments. Phase regularization algorithm is used in the entire area of the cover image in order to embed the secret image and to avoid large fluctuations of the moiré grating. Computational simulations are used to demonstrate the efficiency and the applicability of the proposed image hiding technique.
Finite element method application for turbulent and transitional flow
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Sváček Petr
2016-01-01
Full Text Available This paper is interested in numerical simulations of the interaction of the fluid flow with an airfoil. Particularly, the problem of the turbulent flow around the airfoil with elastic support is considered. The main attention is paid to the numerical approximation of the flow problem using the finite element approximations. The laminar - turbulence transition of the flow on the surface airfoil is considered. The chois of the transition model is discussed. The transition model based on the two equation k−ω turbulence model is used. The structure motion is described with the aid of two degrees of freedom. The motion of the computational domain is treated with the aid of the arbitrary Lagrangian-Eulerian method. Numerical results are shown.
Finite elements in fracture mechanics theory, numerics, applications
Kuna, Meinhard
2013-01-01
Fracture mechanics has established itself as an important discipline of growing interest to those working to assess the safety, reliability and service life of engineering structures and materials. In order to calculate the loading situation at cracks and defects, nowadays numerical techniques like finite element method (FEM) have become indispensable tools for a broad range of applications. The present monograph provides an introduction to the essential concepts of fracture mechanics, its main goal being to procure the special techniques for FEM analysis of crack problems, which have to date only been mastered by experts. All kinds of static, dynamic and fatigue fracture problems are treated in two- and three-dimensional elastic and plastic structural components. The usage of the various solution techniques is demonstrated by means of sample problems selected from practical engineering case studies. The primary target group includes graduate students, researchers in academia and engineers in practice.
Finite element modelling of cornea mechanics: a review.
Nejad, Talisa Mohammad; Foster, Craig; Gongal, Dipika
2014-01-01
The cornea is a transparent tissue in front of the eye that refracts light and facilitates vision. A slight change in the geometry of the cornea remarkably affects the optical power. Because of this sensitivity, biomechanical study of the cornea can reveal much about its performance and function. In vivo and in vitro studies have been conducted to investigate the mechanics of the cornea and determine its characteristics. Numerical techniques such as the finite element method (FEM) have been extensively implemented as effective and noninvasive methods for analyzing corneal mechanics and possible disorders. This article reviews the use of FEM for assessing the mechanical behavior of the cornea. Different applications of FEM in corneal disease studies, surgical predictions, impact simulations, and clinical applications have been reviewed. Some suggestions for the future of this type of modeling in the area of corneal mechanics are also discussed.
Investigation of ferrocement channels using experimental and finite element analysis
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Hamid Eskandari
2015-12-01
Full Text Available It is necessary to design and calculate tensile reinforcement for ferrocement channels with various spans used in different structures such as rural houses and mosques. However, such analysis is challenging due to the application of different types of wire meshes, dissimilar tensile and compressive reinforcement, and mechanical properties of the mortar. The present study provided an experimental sample to assess deflection in a standard ferrocement channel (span: 4.5 m; width: 70 cm. The Abaqus Unified finite element analysis (FEA has been also used to model the ferrocement channel by various system supports and beam spans. The obtained results indicated the acceptable accuracy of FE simulations in the estimation of experimental values. Such models can thus be used as quick, simple, and inexpensive methods to calculate the optimal deflection of ferrocement channels for various spans and sizes of tensile reinforcement.
Finite element discretization of Darcy's equations with pressure dependent porosity
Girault, Vivette
2010-02-23
We consider the flow of a viscous incompressible fluid through a rigid homogeneous porous medium. The permeability of the medium depends on the pressure, so that the model is nonlinear. We propose a finite element discretization of this problem and, in the case where the dependence on the pressure is bounded from above and below, we prove its convergence to the solution and propose an algorithm to solve the discrete system. In the case where the dependence on the pressure is exponential, we propose a splitting scheme which involves solving two linear systems, but parts of the analysis of this method are still heuristic. Numerical tests are presented, which illustrate the introduced methods. © 2010 EDP Sciences, SMAI.
Simulating dynamic plastic continuous neural networks by finite elements.
Joghataie, Abdolreza; Torghabehi, Omid Oliyan
2014-08-01
We introduce dynamic plastic continuous neural network (DPCNN), which is comprised of neurons distributed in a nonlinear plastic medium where wire-like connections of neural networks are replaced with the continuous medium. We use finite element method to model the dynamic phenomenon of information processing within the DPCNNs. During the training, instead of weights, the properties of the continuous material at its different locations and some properties of neurons are modified. Input and output can be vectors and/or continuous functions over lines and/or areas. Delay and feedback from neurons to themselves and from outputs occur in the DPCNNs. We model a simple form of the DPCNN where the medium is a rectangular plate of bilinear material, and the neurons continuously fire a signal, which is a function of the horizontal displacement.
Finite Element Based HWB Centerbody Structural Optimization and Weight Prediction
Gern, Frank H.
2012-01-01
This paper describes a scalable structural model suitable for Hybrid Wing Body (HWB) centerbody analysis and optimization. The geometry of the centerbody and primary wing structure is based on a Vehicle Sketch Pad (VSP) surface model of the aircraft and a FLOPS compatible parameterization of the centerbody. Structural analysis, optimization, and weight calculation are based on a Nastran finite element model of the primary HWB structural components, featuring centerbody, mid section, and outboard wing. Different centerbody designs like single bay or multi-bay options are analyzed and weight calculations are compared to current FLOPS results. For proper structural sizing and weight estimation, internal pressure and maneuver flight loads are applied. Results are presented for aerodynamic loads, deformations, and centerbody weight.
Studying apple bruise using a finite element method analysis
Pascoal-Faria, P.; Alves, N.
2017-07-01
Apple bruise damage from harvesting, handling, transporting and sorting is considered to be the major source of reduced fruit quality, resulting in a loss of profits for the entire fruit industry. Bruising is defined as damage and discoloration of fruit flesh, usually with no breach of the skin. The three factors which can physically cause fruit bruising are vibration, compression load and impact. The last one is the main source of bruise damage. Therefore, prediction of the level of damage, stress distribution and deformation of the fruits under external force has become a very important task. To address these problems a finite element analysis has been developed for studying Portuguese Royal Gala apple bruise. The results obtained will be suitable to apple distributors and sellers and will allow a reduction of the impact caused by bruise damage in apple annual production.
Finite-element lattice Boltzmann simulations of contact line dynamics
Matin, Rastin; Krzysztof Misztal, Marek; Hernández-García, Anier; Mathiesen, Joachim
2018-01-01
The lattice Boltzmann method has become one of the standard techniques for simulating a wide range of fluid flows. However, the intrinsic coupling of momentum and space discretization restricts the traditional lattice Boltzmann method to regular lattices. Alternative off-lattice Boltzmann schemes exist for both single- and multiphase flows that decouple the velocity discretization from the underlying spatial grid. The current study extends the applicability of these off-lattice methods by introducing a finite element formulation that enables simulating contact line dynamics for partially wetting fluids. This work exemplifies the implementation of the scheme and furthermore presents benchmark experiments that show the scheme reduces spurious currents at the liquid-vapor interface by at least two orders of magnitude compared to a nodal implementation and allows for predicting the equilibrium states accurately in the range of moderate contact angles.
Finite Element Analysis of PMMA Stretch Blow Molding
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Afef Bougharriou
2014-01-01
Full Text Available The electric bubbles are a useful product made of PMMA material. They are produced by the stretch blow molding process. Thickness, which reflects the quality of the electric bubble, is a crucial parameter that deserves special attention for the molding process. In this work, finite element simulations of the stretch blow molding process are performed aiming at the determination of the preform geometry to ensure homogeneous thickness of the finished product. The geometrical parameters of the preform are optimized allowing a better homogeneity thickness compared to existing data. The predicted parameters allow the improvement of the thickness distribution. The standard deviation of the thickness is reduced to about 95% compared to the existing bubble.
Generalized multiscale finite element methods. nonlinear elliptic equations
Efendiev, Yalchin R.
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.
A mixed finite element method for nonlinear diffusion equations
Burger, Martin
2010-01-01
We propose a mixed finite element method for a class of nonlinear diffusion equations, which is based on their interpretation as gradient flows in optimal transportation metrics. We introduce an appropriate linearization of the optimal transport problem, which leads to a mixed symmetric formulation. This formulation preserves the maximum principle in case of the semi-discrete scheme as well as the fully discrete scheme for a certain class of problems. In addition solutions of the mixed formulation maintain exponential convergence in the relative entropy towards the steady state in case of a nonlinear Fokker-Planck equation with uniformly convex potential. We demonstrate the behavior of the proposed scheme with 2D simulations of the porous medium equations and blow-up questions in the Patlak-Keller-Segel model. © American Institute of Mathematical Sciences.
Finite Element Approach to Analysis of Axisymmetric Reverse Drawing Process
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Keran, Z.
2006-01-01
Full Text Available The intention of this research is to make analyze of deep drawing Cr-Ni stainless steel process. The research is related to forces that appear in machine tool during the process and also to material stress and its behaviour. The results are taken from two sources and their comparison is made. The first source of results are experiments made on hydraulic press, and the other source are results obtained by creation of finite element model (FEM and process simulation on MSC Marc Mentat program package. The measurements are made in cases of different reduction coefficient and different tool material. Comparison that is given is related to punch and pressure plate forces, and the state of material stress for each reduction coefficient is observed too. Datasheets and force diagrams present the results, and material stress can be seen on figures that are result of the simulation.
NON-LINEAR FINITE ELEMENT MODELING OF DEEP DRAWING PROCESS
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Hasan YILDIZ
2004-03-01
Full Text Available Deep drawing process is one of the main procedures used in different branches of industry. Finding numerical solutions for determination of the mechanical behaviour of this process will save time and money. In die surfaces, which have complex geometries, it is hard to determine the effects of parameters of sheet metal forming. Some of these parameters are wrinkling, tearing, and determination of the flow of the thin sheet metal in the die and thickness change. However, the most difficult one is determination of material properties during plastic deformation. In this study, the effects of all these parameters are analyzed before producing the dies. The explicit non-linear finite element method is chosen to be used in the analysis. The numerical results obtained for non-linear material and contact models are also compared with the experiments. A good agreement between the numerical and the experimental results is obtained. The results obtained for the models are given in detail.
Finite element analyses of a linear-accelerator electron gun
Energy Technology Data Exchange (ETDEWEB)
Iqbal, M., E-mail: muniqbal.chep@pu.edu.pk, E-mail: muniqbal@ihep.ac.cn [Centre for High Energy Physics, University of the Punjab, Lahore 45590 (Pakistan); Institute of High Energy Physics, Chinese Academy of Sciences, Beijing 100049 (China); Wasy, A. [Department of Mechanical Engineering, Changwon National University, Changwon 641773 (Korea, Republic of); Islam, G. U. [Centre for High Energy Physics, University of the Punjab, Lahore 45590 (Pakistan); Zhou, Z. [Institute of High Energy Physics, Chinese Academy of Sciences, Beijing 100049 (China)
2014-02-15
Thermo-structural analyses of the Beijing Electron-Positron Collider (BEPCII) linear-accelerator, electron gun, were performed for the gun operating with the cathode at 1000 °C. The gun was modeled in computer aided three-dimensional interactive application for finite element analyses through ANSYS workbench. This was followed by simulations using the SLAC electron beam trajectory program EGUN for beam optics analyses. The simulations were compared with experimental results of the assembly to verify its beam parameters under the same boundary conditions. Simulation and test results were found to be in good agreement and hence confirmed the design parameters under the defined operating temperature. The gun is operating continuously since commissioning without any thermal induced failures for the BEPCII linear accelerator.
Finite element analyses of a linear-accelerator electron gun
Iqbal, M.; Wasy, A.; Islam, G. U.; Zhou, Z.
2014-02-01
Thermo-structural analyses of the Beijing Electron-Positron Collider (BEPCII) linear-accelerator, electron gun, were performed for the gun operating with the cathode at 1000 °C. The gun was modeled in computer aided three-dimensional interactive application for finite element analyses through ANSYS workbench. This was followed by simulations using the SLAC electron beam trajectory program EGUN for beam optics analyses. The simulations were compared with experimental results of the assembly to verify its beam parameters under the same boundary conditions. Simulation and test results were found to be in good agreement and hence confirmed the design parameters under the defined operating temperature. The gun is operating continuously since commissioning without any thermal induced failures for the BEPCII linear accelerator.
Thermo-Elastic Finite Element Analyses of Annular Nuclear Fuels
Kwon, Y. D.; Kwon, S. B.; Rho, K. T.; Kim, M. S.; Song, H. J.
In this study, we tried to examine the pros and cons of the annular type of fuel concerning mainly with the temperatures and stresses of pellet and cladding. The inner and outer gaps between pellet and cladding may play an important role on the temperature distribution and stress distribution of fuel system. Thus, we tested several inner and outer gap cases, and we evaluated the effect of gaps on fuel systems. We conducted thermo-elastic-plastic-creep analyses using an in-house thermo-elastic-plastic-creep finite element program that adopted the 'effective-stress-function' algorithm. Most analyses were conducted until the gaps disappeared; however, certain analyses lasted for 1582 days, after which the fuels were replaced. Further study on the optimal gaps sizes for annular nuclear fuel systems is still required.
Finite Element Thermal Study of the Linac4 Plasma Generatora
Faircloth, D; Kuchler, D; Lettry, L; Scrivens, R; CERN. Geneva. BE Department
2010-01-01
The temperature distribution and heat flow at equilibrium of the plasma generator of the RF-powered non-cesiated Linac4 H- ion source have been studied with a finite element model. It is shown that the equilibrium temperatures obtained in the Linac4 nominal operation mode (100 kW RF power, 2 Hz, 0.4 ms pulse duration) are within material specifications except for the magnet cage, where a redesign may be necessary. To assess the upgrade of the Linac4 source for operation in the high-power operation mode of SPL, an extrapolation of the heat load towards 100 kW RF power, 50 Hz repetition rate and 0.4 ms pulse duration has been performed. The results indicate that a significant improvement of the source cooling is required to allow for operation in HP-SPL.
Finite element modelling of cornea mechanics: a review
Directory of Open Access Journals (Sweden)
Talisa Mohammad Nejad
2014-01-01
Full Text Available The cornea is a transparent tissue in front of the eye that refracts light and facilitates vision. A slight change in the geometry of the cornea remarkably affects the optical power. Because of this sensitivity, biomechanical study of the cornea can reveal much about its performance and function. In vivo and in vitro studies have been conducted to investigate the mechanics of the cornea and determine its characteristics. Numerical techniques such as the finite element method (FEM have been extensively implemented as effective and noninvasive methods for analyzing corneal mechanics and possible disorders. This article reviews the use of FEM for assessing the mechanical behavior of the cornea. Different applications of FEM in corneal disease studies, surgical predictions, impact simulations, and clinical applications have been reviewed. Some suggestions for the future of this type of modeling in the area of corneal mechanics are also discussed.
Model order reduction techniques with applications in finite element analysis
Qu, Zu-Qing
2004-01-01
Despite the continued rapid advance in computing speed and memory the increase in the complexity of models used by engineers persists in outpacing them. Even where there is access to the latest hardware, simulations are often extremely computationally intensive and time-consuming when full-blown models are under consideration. The need to reduce the computational cost involved when dealing with high-order/many-degree-of-freedom models can be offset by adroit computation. In this light, model-reduction methods have become a major goal of simulation and modeling research. Model reduction can also ameliorate problems in the correlation of widely used finite-element analyses and test analysis models produced by excessive system complexity. Model Order Reduction Techniques explains and compares such methods focusing mainly on recent work in dynamic condensation techniques: - Compares the effectiveness of static, exact, dynamic, SEREP and iterative-dynamic condensation techniques in producing valid reduced-order mo...
Hybrid finite element and Brownian dynamics method for charged particles
Energy Technology Data Exchange (ETDEWEB)
Huber, Gary A., E-mail: ghuber@ucsd.edu; Miao, Yinglong [Howard Hughes Medical Institute, University of California San Diego, La Jolla, California 92093-0365 (United States); Zhou, Shenggao [Department of Mathematics and Mathematical Center for Interdiscipline Research, Soochow University, 1 Shizi Street, Suzhou, 215006 Jiangsu (China); Li, Bo [Department of Mathematics and Quantitative Biology Graduate Program, University of California, San Diego, 9500 Gilman Drive, La Jolla, California 92093-0112 (United States); McCammon, J. Andrew [Howard Hughes Medical Institute, University of California San Diego, La Jolla, California 92093 (United States); Department of Chemistry and Biochemistry, University of California San Diego, La Jolla, California 92093-0365 (United States); Department of Pharmacology, University of California San Diego, La Jolla, California 92093-0636 (United States)
2016-04-28
Diffusion is often the rate-determining step in many biological processes. Currently, the two main computational methods for studying diffusion are stochastic methods, such as Brownian dynamics, and continuum methods, such as the finite element method. A previous study introduced a new hybrid diffusion method that couples the strengths of each of these two methods, but was limited by the lack of interactions among the particles; the force on each particle had to be from an external field. This study further develops the method to allow charged particles. The method is derived for a general multidimensional system and is presented using a basic test case for a one-dimensional linear system with one charged species and a radially symmetric system with three charged species.
Obtaining local reciprocal lattice vectors from finite-element analysis.
Sutter, John P; Connolley, Thomas; Hill, Tim P; Huang, Houcheng; Sharp, Doug W; Drakopoulos, Michael
2008-11-01
Finite-element analysis is frequently used by engineers at synchrotron beamlines to calculate the elastic deformation of a single crystal undergoing mechanical bending or thermal load. ANSYS Workbench software is widely used for such simulations. However, although ANSYS Workbench software provides useful information on the displacements, strains and stresses within the crystal, it does not yield the local reciprocal lattice vectors that would be required for X-ray diffraction calculations. To bridge this gap, a method based on the shape functions and interpolation procedures of the software itself has been developed. An application to the double-crystal bent Laue monochromator being designed for the I12 (JEEP) wiggler beamline at the Diamond Light Source is presented.
A vortex model for Darrieus turbine using finite element techniques
Energy Technology Data Exchange (ETDEWEB)
Ponta, Fernando L. [Universidad de Buenos Aires, Dept. de Electrotecnia, Grupo ISEP, Buenos Aires (Argentina); Jacovkis, Pablo M. [Universidad de Buenos Aires, Dept. de Computacion and Inst. de Calculo, Buenos Aires (Argentina)
2001-09-01
Since 1970 several aerodynamic prediction models have been formulated for the Darrieus turbine. We can identify two families of models: stream-tube and vortex. The former needs much less computation time but the latter is more accurate. The purpose of this paper is to show a new option for modelling the aerodynamic behaviour of Darrieus turbines. The idea is to combine a classic free vortex model with a finite element analysis of the flow in the surroundings of the blades. This avoids some of the remaining deficiencies in classic vortex models. The agreement between analysis and experiment when predicting instantaneous blade forces and near wake flow behind the rotor is better than the one obtained in previous models. (Author)
Finite element structural study of the VGOT wind turbine
Energy Technology Data Exchange (ETDEWEB)
Otero, A.D. [University of Buenos Aires (Argentina). College of Engineering; Ponta, F.L. [University of Illinois, Urbana, IL (United States). Dept. of Theoretical and Applied Mechanics
2004-07-01
We analyse the implementation of the finite element method to simulate the structural behaviour of the blade-wagons of variable-geometry oval-trajectory (VGOT) Darrieus wind turbines. The key feature of a VGOT machine is that each blade, instead of rotating around a central vertical axis, slides over rails mounted on a wagon formed by a tubular reticulated structure supported by standard train bogies. The structure should be designed to absorb the efforts in the vertical and traverse directions of the railroad due to the aerodynamic loads, the weight of the components and the centrifugal acceleration along the curved tracks. We show some results for the tip deflection and the tip torsion of the blade, the frontal and lateral angle variations in the blade bottom and the Von Misses tensions of five sample beams, all of them in function of the trajectory-length parameter; and some examples of the deformed configuration of the reticulated structure. (author)
Finite element analysis of osteoporosis models based on synchrotron radiation
Xu, W.; Xu, J.; Zhao, J.; Sun, J.
2016-04-01
With growing pressure of social aging, China has to face the increasing population of osteoporosis patients as well as the whole world. Recently synchrotron radiation has become an essential tool for biomedical exploration with advantage of high resolution and high stability. In order to study characteristic changes in different stages of primary osteoporosis, this research focused on the different periods of osteoporosis of rats based on synchrotron radiation. Both bone histomorphometry analysis and finite element analysis were then carried on according to the reconstructed three dimensional models. Finally, the changes of bone tissue in different periods were compared quantitatively. Histomorphometry analysis showed that the structure of the trabecular in osteoporosis degraded as the bone volume decreased. For femurs, the bone volume fraction (Bone volume/ Total volume, BV/TV) decreased from 69% to 43%. That led to the increase of the thickness of trabecular separation (from 45.05μ m to 97.09μ m) and the reduction of the number of trabecular (from 7.99 mm-1 to 5.97mm-1). Simulation of various mechanical tests with finite element analysis (FEA) indicated that, with the exacerbation of osteoporosis, the bones' ability of resistance to compression, bending and torsion gradually became weaker. The compression stiffness of femurs decreased from 1770.96 Fμ m-1 to 697.41 Fμ m-1, the bending and torsion stiffness were from 1390.80 Fμ m-1 to 566.11 Fμ m-1 and from 2957.28N.m/o to 691.31 N.m/o respectively, indicated the decrease of bone strength, and it matched the histomorphometry analysis. This study suggested that FEA and synchrotron radiation were excellent methods for analysing bone strength conbined with histomorphometry analysis.
A finite element approach to x-ray optics design
Honkanen, A. P.; Ferrero, C.; Guigay, J. P.; Mocella, V.
2017-05-01
Dynamical diffraction in a deformed (often bent) crystal is described by the Takagi equations 1 which, in general, have to be solved numerically on a regular 2-D grid of points representing a planar cross section of the crystal in which the diffraction of an incident X-ray wavefront occurs . Presently, the majority of numerical approaches are based on a finite difference solving scheme2-4 which can be easily implemented on a regular Cartesian grid but is not suitable for deformed meshes. In this case, the inner deformed crystal structure can be taken into account, but not the shape of the crystal surface if this differs substantially from a planar profile 5,6. Conversely, a finite element method (FEM) can be easily applied to a deformed mesh and serves very well to the purpose of modelling any incident wave on an arbitrarily shaped entrance surface 7 e.g. that of a bent crystal or a crystal submitted to a strong heat load 8-10. For instance, the cylindrical shape of the surface of a strongly bent crystal plate can easily be taken into account in a FEM calculation. Bent crystals are often used as focusing optical elements in Xray beamlines 11-13. In the following, we show the implementation of a general numerical framework for describing the propagation of X-rays inside a crystal based on the solution of the Takagi equations via the COMSOL Multiphysics FEM software package (www.comsol.com). A cylindrically bent crystal will be taken as an example to illustrate the capabilities of the new approach.
Finite element simulation of thickness changes in laminate during thermoforming
White, K. D.; Sherwood, J. A.
2017-10-01
This paper discusses a numerical investigation of thickness changes of Dyneema HB80, a cross-ply thermoplastic lamina, during a helmet thermoforming process. The main mode of deformation during the preform phase of manufacture is in-plane shearing of the fabric. A laminate undergoes varying degrees of shear to conform to the geometric variations over the surface of the preform shape. Decreases in areal coverage that occur with increases in the local shear angle will lead to a resulting increase in local thickness. During the consolidation phase, multiple preform layers are compressed in a set of matched tools, and the compounding of the thickness variations can adversely affect the uniformity of pressure distribution between matched die tooling. Pressure variations over the surface of the part can lead to incomplete consolidation of the ply stack, as well as weakened, resin-rich areas. Because wrinkling of the composite reinforcement, incomplete consolidation and resin-rich areas can result in a compromised structural performance, it is important that the manufacturing process be well understood so it can be designed to mitigate formation of such defects. In the current work, the material properties derived from shear, bending and tensile tests are implemented in a finite element model of the cross-ply lamina. The finite element model uses a hybrid discrete mesoscopic approach, and deep-draw forming of the material is simulated to investigate its formability to a hemispherical geometry. Thickening of the lamina resulting from shear deformation is investigated and incorporated into models single-layer preform simulations. The simulation results are used to inform the design of multiple-layer preforms to mitigate the development of thin regions and out-of-plane waves to ensure complete, uniform consolidation.
Fast Gravitational Field Model Using Adaptive Orthogonal Finite Element Approximation
Younes, A.; Macomber, B.; Woollands, R.; Probe, A.; Bai, X.; Junkins, J.
2013-09-01
Recent research has addressed the issue that high degree and order gravity expansions involve tens of thousands of terms in a theoretically infinite order spherical harmonic expansion (some gravity models extend to degree and order 200 with over 30,000 terms) which in principle must be computed at every integration step to obtain the acceleration consistent with the gravity model. We propose to evaluate these gravity model interpolation models and use them in conjunction with the modified Picard path approximation methods. It was decided to consider analogous orthogonal approximation methods to interpolate, an FEM model, high (degree, order) gravity fields, by replacing the global spherical harmonic series by a family of locally precise orthogonal polynomial approximations for efficient computation. Our preliminary results showed that time to compute the state of the art (degree and order 200) spherical harmonic gravity is reduced by 4 to 5 orders of magnitude while maintaining > 9 digits of accuracy. Most of the gain is due to adopting the orthogonal FEM approach, but radial adaptation of the approximation degree gains an additional order of magnitude speedup. The efficient data base storage/access of the local coefficients is studied, which utilizes porting the algorithm to the NVIDIA GPU. This paper will address the accuracy and efficiency in both a C++ serial PC architecture as well as a PC/GPU architecture. The Adaptive Orthogonal Finite Element Gravity Model (AOFEGM) is expected to have broad potential for speeding the trajectory propagation algorithms; for example, used in conjunction with orthogonal Finite Element Model (FEM) gravity approximations, the Chebyshev-Picard path approximation enables truly revolutionary speedups in orbit propagation without accuracy loss.
Multiscale Finite Element Methods for Flows on Rough Surfaces
Efendiev, Yalchin
2013-01-01
In this paper, we present the Multiscale Finite Element Method (MsFEM) for problems on rough heterogeneous surfaces. We consider the diffusion equation on oscillatory surfaces. Our objective is to represent small-scale features of the solution via multiscale basis functions described on a coarse grid. This problem arises in many applications where processes occur on surfaces or thin layers. We present a unified multiscale finite element framework that entails the use of transformations that map the reference surface to the deformed surface. The main ingredients of MsFEM are (1) the construction of multiscale basis functions and (2) a global coupling of these basis functions. For the construction of multiscale basis functions, our approach uses the transformation of the reference surface to a deformed surface. On the deformed surface, multiscale basis functions are defined where reduced (1D) problems are solved along the edges of coarse-grid blocks to calculate nodalmultiscale basis functions. Furthermore, these basis functions are transformed back to the reference configuration. We discuss the use of appropriate transformation operators that improve the accuracy of the method. The method has an optimal convergence if the transformed surface is smooth and the image of the coarse partition in the reference configuration forms a quasiuniform partition. In this paper, we consider such transformations based on harmonic coordinates (following H. Owhadi and L. Zhang [Comm. Pure and Applied Math., LX(2007), pp. 675-723]) and discuss gridding issues in the reference configuration. Numerical results are presented where we compare the MsFEM when two types of deformations are used formultiscale basis construction. The first deformation employs local information and the second deformation employs a global information. Our numerical results showthat one can improve the accuracy of the simulations when a global information is used. © 2013 Global-Science Press.
Finite Element Analysis of Patella Alta: A Patellofemoral Instability Model
Duchman, Kyle R.; Grosland, Nicole M.; Bollier, Matthew J.
2017-01-01
Abstract Background: This study aims to provide biomechanical data on the effect of patella height in the setting of medial patellofemoral ligament (MPFL) reconstruction using finite element analysis. The study will also examine patellofemoral joint biomechanics using variable femoral insertion sites for MPFL reconstruction. Methods: A previously validated finite element knee model was modified to study patella alta and baja by translating the patella a given distance to achieve each patella height ratio. Additionally, the models were modified to study various femoral insertion sites of the MPFL (anatomic, anterior, proximal, and distal) for each patella height model, resulting in 32 unique scenarios available for investigation. Results: In the setting of patella alta, the patellofemoral contact area decreased, resulting in a subsequent increase in maximum patellofemoral contact pressures as compared to the scenarios with normal patellar height. Additionally, patella alta resulted in decreased lateral restraining forces in the native knee scenario as well as following MPFL reconstruction. Changing femoral insertion sites had a variable effect on patellofemoral contact pressures; however, distal and anterior femoral tunnel malpositioning in the setting of patella alta resulted in grossly elevated maximum patellofemoral contact pressures as compared to other scenarios. Conclusions: Patella alta after MPFL reconstruction results in decreased lateral restraining forces and patellofemoral contact area and increased maximum patellofemoral contact pressures. When the femoral MPFL tunnel is malpositioned anteriorly or distally on the femur, the maximum patellofemoral contact pressures increase with severity of patella alta. Clinical Relevance: When evaluating patients with patellofemoral instability, it is important to recognize patella alta as a potential aggravating factor. Failure to address patella alta in the setting of MPFL femoral tunnel malposition may result in
Generalized multiscale finite element methods (GMsFEM)
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.
Nitinol Embolic Protection Filters: Design Investigation by Finite Element Analysis
Conti, Michele; de Beule, Matthieu; Mortier, Peter; van Loo, Denis; Verdonck, Pascal; Vermassen, Frank; Segers, Patrick; Auricchio, Ferdinando; Verhegghe, Benedict
2009-08-01
The widespread acceptance of carotid artery stenting (CAS) to treat carotid artery stenosis and its effectiveness compared with surgical counterpart, carotid endarterectomy (CEA), is still a matter of debate. Transient or permanent neurological deficits may develop in patients undergoing CAS due to distal embolization or hemodynamic changes. Design, development, and usage of embolic protection devices (EPDs), such as embolic protection filters, appear to have a significant impact on the success of CAS. Unfortunately, some drawbacks, such as filtering failure, inability to cross tortuous high-grade stenoses, malpositioning and vessel injury, still remain and require design improvement. Currently, many different designs of such devices are available on the rapidly growing dedicated market. In spite of such a growing commercial interest, there is a significant need for design tools as well as for careful engineering investigations and design analyses of such nitinol devices. The present study aims to investigate the embolic protection filter design by finite element analysis. We first developed a parametrical computer-aided design model of an embolic filter based on micro-CT scans of the Angioguard™ XP (Cordis Endovascular, FL) EPD by means of the open source pyFormex software. Subsequently, we used the finite element method to simulate the deployment of the nitinol filter as it exits the delivery sheath. Comparison of the simulations with micro-CT images of the real device exiting the catheter showed excellent correspondence with our simulations. Finally, we evaluated circumferential basket-vessel wall apposition of a 4 mm size filter in a straight vessel of different sizes and shape. We conclude that the proposed methodology offers a useful tool to evaluate and to compare current or new designs of EPDs. Further simulations will investigate vessel wall apposition in a realistic tortuous anatomy.
Neutral solute transport across osteochondral interface: A finite element approach.
Arbabi, Vahid; Pouran, Behdad; Weinans, Harrie; Zadpoor, Amir A
2016-12-08
Investigation of the solute transfer across articular cartilage and subchondral bone plate could nurture the understanding of the mechanisms of osteoarthritis (OA) progression. In the current study, we approached the transport of neutral solutes in human (slight OA) and equine (healthy) samples using both computed tomography and biphasic-solute finite element modeling. We developed a multi-zone biphasic-solute finite element model (FEM) accounting for the inhomogeneity of articular cartilage (superficial, middle and deep zones) and subchondral bone plate. Fitting the FEM model to the concentration-time curves of the cartilage and the equilibrium concentration of the subchondral plate/calcified cartilage enabled determination of the diffusion coefficients in the superficial, middle and deep zones of cartilage and subchondral plate. We found slightly higher diffusion coefficients for all zones in the human samples as compared to the equine samples. Generally the diffusion coefficient in the superficial zone of human samples was about 3-fold higher than the middle zone, the diffusion coefficient of the middle zone was 1.5-fold higher than that of the deep zone, and the diffusion coefficient of the deep zone was 1.5-fold higher than that of the subchondral plate/calcified cartilage. Those ratios for equine samples were 9, 2 and 1.5, respectively. Regardless of the species considered, there is a gradual decrease of the diffusion coefficient as one approaches the subchondral plate, whereas the rate of decrease is dependent on the type of species. Copyright © 2016 Elsevier Ltd. All rights reserved.
Finite element methodology for transient conduction/forced-convection thermal analysis
Thornton, E. A.; Wieting, A. R.
1979-01-01
Finite element methodology for steady state thermal analysis of convectively cooled structures has been extended for transient analysis. The finite elements are based on representing the fluid passages by fluid bulk-temperature nodes and fluid-solid interface nodes. The formulation of the finite element equations for a typical flow passage is based on the weighted residual method with upwind weighting functions. Computer implementation of the convective finite element methodology using explicit and implicit time integration algorithms is described. Accuracy and efficiency of the methodology is evaluated by comparisons with analytical solutions and finite-difference lumped-parameter analyses. The comparative analyses demonstrate that finite element conduction/conduction methodology may be used to predict transient temperatures with an accuracy equal or superior to the lumped-parameter finite-difference method.
Overview of adaptive finite element analysis in computational geodynamics
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
Energy Technology Data Exchange (ETDEWEB)
Manzini, Gianmarco [Los Alamos National Laboratory
2012-07-13
We develop and analyze a new family of virtual element methods on unstructured polygonal meshes for the diffusion problem in primal form, that use arbitrarily regular discrete spaces V{sub h} {contained_in} C{sup {alpha}} {element_of} N. The degrees of freedom are (a) solution and derivative values of various degree at suitable nodes and (b) solution moments inside polygons. The convergence of the method is proven theoretically and an optimal error estimate is derived. The connection with the Mimetic Finite Difference method is also discussed. Numerical experiments confirm the convergence rate that is expected from the theory.
Thermomechanical finite element analysis of hot water boiler structure
Directory of Open Access Journals (Sweden)
Živković Dragoljub S.
2012-01-01
Full Text Available The paper presents an application of the Finite Elements Method for stress and strain analysis of the hot water boiler structure. The aim of the research was to investigate the influence of the boiler scale on the thermal stresses and strains of the structure of hot water boilers. Results show that maximum thermal stresses appear in the zone of the pipe carrying wall of the first reversing chamber. This indicates that the most critical part of the boiler are weld spots of the smoke pipes and pipe carrying plate, which in the case of significant scale deposits can lead to cracks in the welds and water leakage from the boiler. The nonlinear effects were taken into account by defining the bilinear isotropic hardening model for all boiler elements. Temperature dependency was defined for all relevant material properties, i. e. isotropic coefficient of thermal expansion, Young’s modulus, and isotropic thermal conductivity. The verification of the FEA model was performed by comparing the measured deformations of the hot water boiler with the simulation results. As a reference object, a Viessmann - Vitomax 200 HW boiler was used, with the installed power of 18.2 MW. CAD modeling was done within the Autodesk Inventor, and stress and strain analysis was performed in the ANSYS Software.
Flexural Modeling of the Andean System Using Finite Element Method
Sacek, V.; Ussami, N.
2007-05-01
The general equation of flexure of the lithosphere in cartesian coordinates is solved using a numerical Finite Element Method (FEM) with triangular elements in non-structured meshes. This alternative way to model bending of thin elastic plates lying over an inviscid fluid allows taking into account lateral variation of rigidity, plate discontinuities and full 3-D representation of loads. The numerical solution was initially compared with the analytical solution of bending of an elastic plate loaded by an uniformally distributed load. The method was applied to model flexure of a plate due to curved orogenic belts and the results were compared with solutions obtained if a 2-D approximation of plates and loads was considered. The proposed numerical method was applied to study flexural deformation of the western edge of the South American lithospheric plate due to the loads of the Andean mountains, using Te =75 km for both continuous and broken plates. The predicted forebulges agree with the observed distribution of positive gravity anomalies paralleling the negative gravity anomalies associated with the high topography of the Andes. Maximum amplitudes of forebulges correlate with Purus Arch in Solimões basin (W Brazil) and the Chaco Pampeana plain (Argentina), and between these two regions, a saddle point occurs over the Pantanal wetland (SW Brazil).
Tensegrity finite element models of mechanical tests of individual cells.
Bursa, Jiri; Lebis, Radek; Holata, Jakub
2012-01-01
A three-dimensional finite element model of a vascular smooth muscle cell is based on models published recently; it comprehends elements representing cell membrane, cytoplasm and nucleus, and a complex tensegrity structure representing the cytoskeleton. In contrast to previous models of eucaryotic cells, this tensegrity structure consists of several parts. Its external and internal parts number 30 struts, 60 cables each, and their nodes are interconnected by 30 radial members; these parts represent cortical, nuclear and deep cytoskeletons, respectively. This arrangement enables us to simulate load transmission from the extracellular space to the nucleus or centrosome via membrane receptors (focal adhesions); the ability of the model was tested by simulation of some mechanical tests with isolated vascular smooth muscle cells. Although material properties of components defined on the basis of the mechanical tests are ambiguous, modelling of different types of tests has shown the ability of the model to simulate substantial global features of cell behaviour, e.g. "action at a distance effect" or the global load-deformation response of the cell under various types of loading. Based on computational simulations, the authors offer a hypothesis explaining the scatter of experimental results of indentation tests. © 2012 – IOS Press and the authors. All rights reserved
Architecting the Finite Element Method Pipeline for the GPU.
Fu, Zhisong; Lewis, T James; Kirby, Robert M; Whitaker, Ross T
2014-02-01
The finite element method (FEM) is a widely employed numerical technique for approximating the solution of partial differential equations (PDEs) in various science and engineering applications. Many of these applications benefit from fast execution of the FEM pipeline. One way to accelerate the FEM pipeline is by exploiting advances in modern computational hardware, such as the many-core streaming processors like the graphical processing unit (GPU). In this paper, we present the algorithms and data-structures necessary to move the entire FEM pipeline to the GPU. First we propose an efficient GPU-based algorithm to generate local element information and to assemble the global linear system associated with the FEM discretization of an elliptic PDE. To solve the corresponding linear system efficiently on the GPU, we implement a conjugate gradient method preconditioned with a geometry-informed algebraic multi-grid (AMG) method preconditioner. We propose a new fine-grained parallelism strategy, a corresponding multigrid cycling stage and efficient data mapping to the many-core architecture of GPU. Comparison of our on-GPU assembly versus a traditional serial implementation on the CPU achieves up to an 87 × speedup. Focusing on the linear system solver alone, we achieve a speedup of up to 51 × versus use of a comparable state-of-the-art serial CPU linear system solver. Furthermore, the method compares favorably with other GPU-based, sparse, linear solvers.
Busto, S.; Ferrín, J. L.; Toro, E. F.; Vázquez-Cendón, M. E.
2018-01-01
In this paper the projection hybrid FV/FE method presented in [1] is extended to account for species transport equations. Furthermore, turbulent regimes are also considered thanks to the k-ε model. Regarding the transport diffusion stage new schemes of high order of accuracy are developed. The CVC Kolgan-type scheme and ADER methodology are extended to 3D. The latter is modified in order to profit from the dual mesh employed by the projection algorithm and the derivatives involved in the diffusion term are discretized using a Galerkin approach. The accuracy and stability analysis of the new method are carried out for the advection-diffusion-reaction equation. Within the projection stage the pressure correction is computed by a piecewise linear finite element method. Numerical results are presented, aimed at verifying the formal order of accuracy of the scheme and to assess the performance of the method on several realistic test problems.
National Research Council Canada - National Science Library
Zeng, Langqing; Wei, Haifeng; Liu, Yanjie; Zhang, Wen; Pan, Yao; Zhang, Wei; Zhang, Changqing; Zeng, Bingfang; Chen, Yunfeng
2015-01-01
.... This study aimed to present a biomechanical finite element analysis of biomechanical characteristics involved in TEN fixation and reconstruction plate fixation for midshaft clavicular fractures...
Interface fatigue crack propagation in sandwich X-joints – Part II: Finite element modeling
DEFF Research Database (Denmark)
Moslemian, Ramin; Berggreen, Christian
2013-01-01
The aim of the second and final part of this study is to simulate fatigue crack growth in the tested Sandwich Tear Test specimens, described in Part I, using the finite element method. To accelerate the simulation, a cycle jump method is utilized and implemented in the finite element routine....... The proposed method is based on conducting finite element analysis for a set of cycles to establish a trend line, extrapolating the trend line spanning many cycles, and use the extrapolated state as initial state for additional finite element simulations. The measured da/dN relations of the face/core interface...
Structured Extended Finite Element Methods of Solids Defined by Implicit Surfaces
Energy Technology Data Exchange (ETDEWEB)
Belytschko, T; Mish, K; Moes, N; Parimi, C
2002-11-17
A paradigm is developed for generating structured finite element models from solid models by means of implicit surface definitions. The implicit surfaces are defined by radial basis functions. Internal features, such as material interfaces, sliding interfaces and cracks are treated by enrichment techniques developed in the extended finite element method (X-FEM). Methods for integrating the weak form for such models are proposed. These methods simplify the generation of finite element models. Results presented for several examples show that the accuracy of this method is comparable to standard unstructured finite element methods.
Global-Local Finite Element Analysis of Bonded Single-Lap Joints
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.
FEWA: a Finite Element model of Water flow through Aquifers
Energy Technology Data Exchange (ETDEWEB)
Yeh, G.T.; Huff, D.D.
1983-11-01
This report documents the implementation and demonstration of a Finite Element model of Water flow through Aquifers (FEWA). The particular features of FEWA are its versatility and flexibility to deal with as many real-world problems as possible. Point as well as distributed sources/sinks are included to represent recharges/pumpings and rainfall infiltrations. All sources/sinks can be transient or steady state. Prescribed hydraulic head on the Dirichlet boundaries and fluxes on Neumann or Cauchy boundaries can be time-dependent or constant. Source/sink strength over each element and node, hydraulic head at each Dirichlet boundary node, and flux at each boundary segment can vary independently of each other. Either completely confined or completely unconfined aquifers, or partially confined and partially unconfined aquifers can be dealt with effectively. Discretization of a compound region with very irregular curved boundaries is made easy by including both quadrilateral and triangular elements in the formulation. Large-field problems can be solved efficiently by including a pointwise iterative solution strategy as an optional alternative to the direct elimination solution method for the matrix equation approximating the partial differential equation of groundwater flow. FEWA also includes transient flow through confining leaky aquifers lying above and/or below the aquifer of interest. The model is verified against three simple cases to which analytical solutions are available. It is then demonstrated by two examples of how the model can be applied to heterogeneous and anisotropic aquifers with transient boundary conditions, time-dependent sources/sinks, and confining aquitards for a confined aquifer of variable thickness and for a free surface problem in an unconfined aquifer, respectively. 20 references, 25 figures, 8 tables.
Conley, Rebecca; Delaney, Tristan J.; Jiao, Xiangmin
2016-11-01
The finite element methods (FEM) are important techniques in engineering for solving partial differential equations, but they depend heavily on element shape quality for stability and good performance. In this paper, we introduce the Adaptive Extended Stencil Finite Element Method (AES-FEM) as a means for overcoming this dependence on element shape quality. Our method replaces the traditional basis functions with a set of generalized Lagrange polynomial (GLP) basis functions, which we construct using local weighted least-squares approximations. The method preserves the theoretical framework of FEM, and allows imposing essential boundary conditions and integrating the stiffness matrix in the same way as the classical FEM. In addition, AES-FEM can use higher-degree polynomial basis functions than the classical FEM, while virtually preserving the sparsity pattern of the stiffness matrix. We describe the formulation and implementation of AES-FEM, and analyze its consistency and stability. We present numerical experiments in both 2D and 3D for the Poison equation and a time-independent convection-diffusion equation. The numerical results demonstrate that AES-FEM is more accurate than linear FEM, is also more efficient than linear FEM in terms of error versus runtime, and enables much better stability and faster convergence of iterative solvers than linear FEM over poor-quality meshes
Finite Element Models for Electron Beam Freeform Fabrication Process
Chandra, Umesh
2012-01-01
Electron beam freeform fabrication (EBF3) is a member of an emerging class of direct manufacturing processes known as solid freeform fabrication (SFF); another member of the class is the laser deposition process. Successful application of the EBF3 process requires precise control of a number of process parameters such as the EB power, speed, and metal feed rate in order to ensure thermal management; good fusion between the substrate and the first layer and between successive layers; minimize part distortion and residual stresses; and control the microstructure of the finished product. This is the only effort thus far that has addressed computer simulation of the EBF3 process. The models developed in this effort can assist in reducing the number of trials in the laboratory or on the shop floor while making high-quality parts. With some modifications, their use can be further extended to the simulation of laser, TIG (tungsten inert gas), and other deposition processes. A solid mechanics-based finite element code, ABAQUS, was chosen as the primary engine in developing these models whereas a computational fluid dynamics (CFD) code, Fluent, was used in a support role. Several innovative concepts were developed, some of which are highlighted below. These concepts were implemented in a number of new computer models either in the form of stand-alone programs or as user subroutines for ABAQUS and Fluent codes. A database of thermo-physical, mechanical, fluid, and metallurgical properties of stainless steel 304 was developed. Computing models for Gaussian and raster modes of the electron beam heat input were developed. Also, new schemes were devised to account for the heat sink effect during the deposition process. These innovations, and others, lead to improved models for thermal management and prediction of transient/residual stresses and distortions. Two approaches for the prediction of microstructure were pursued. The first was an empirical approach involving the
Evaluation of finite element formulations for transient conduction forced-convection analysis
Thornton, E. A.; Wieting, A. R.
1979-01-01
Numerical studies clarifying the advantages and disavantages of conventional versus upwind convective finite elements are presented along with lumped versus consistent formulations for practical conduction forced-convection analysis. A finite-element procedure for treatment of negligible capacitance fluid nodes is presented. The procedure is based on procedures used in finite-element structural dynamics to treat nodes with negligible structural mass. Two finite-element programs and a finite-difference lumped-parameter program used in the studies are discussed. Evaluation studies utilizing three convection and two combined conduction-convection problems are then presented and discussed. Additionally, the computational time saving offered by the finite element procedure is considered for a practical combined conduction-convection problem.
Chung, T. J. (Editor); Karr, Gerald R. (Editor)
1989-01-01
Recent advances in computational fluid dynamics are examined in reviews and reports, with an emphasis on finite-element methods. Sections are devoted to adaptive meshes, atmospheric dynamics, combustion, compressible flows, control-volume finite elements, crystal growth, domain decomposition, EM-field problems, FDM/FEM, and fluid-structure interactions. Consideration is given to free-boundary problems with heat transfer, free surface flow, geophysical flow problems, heat and mass transfer, high-speed flow, incompressible flow, inverse design methods, MHD problems, the mathematics of finite elements, and mesh generation. Also discussed are mixed finite elements, multigrid methods, non-Newtonian fluids, numerical dissipation, parallel vector processing, reservoir simulation, seepage, shallow-water problems, spectral methods, supercomputer architectures, three-dimensional problems, and turbulent flows.
Physical Constraint Finite Element Model for Medical Image Registration.
Zhang, Jingya; Wang, Jiajun; Wang, Xiuying; Gao, Xin; Feng, Dagan
2015-01-01
Due to being derived from linear assumption, most elastic body based non-rigid image registration algorithms are facing challenges for soft tissues with complex nonlinear behavior and with large deformations. To take into account the geometric nonlinearity of soft tissues, we propose a registration algorithm on the basis of Newtonian differential equation. The material behavior of soft tissues is modeled as St. Venant-Kirchhoff elasticity, and the nonlinearity of the continuum represents the quadratic term of the deformation gradient under the Green- St.Venant strain. In our algorithm, the elastic force is formulated as the derivative of the deformation energy with respect to the nodal displacement vectors of the finite element; the external force is determined by the registration similarity gradient flow which drives the floating image deforming to the equilibrium condition. We compared our approach to three other models: 1) the conventional linear elastic finite element model (FEM); 2) the dynamic elastic FEM; 3) the robust block matching (RBM) method. The registration accuracy was measured using three similarities: MSD (Mean Square Difference), NC (Normalized Correlation) and NMI (Normalized Mutual Information), and was also measured using the mean and max distance between the ground seeds and corresponding ones after registration. We validated our method on 60 image pairs including 30 medical image pairs with artificial deformation and 30 clinical image pairs for both the chest chemotherapy treatment in different periods and brain MRI normalization. Our method achieved a distance error of 0.320±0.138 mm in x direction and 0.326±0.111 mm in y direction, MSD of 41.96±13.74, NC of 0.9958±0.0019, NMI of 1.2962±0.0114 for images with large artificial deformations; and average NC of 0.9622±0.008 and NMI of 1.2764±0.0089 for the real clinical cases. Student's t-test demonstrated that our model statistically outperformed the other methods in comparison (p
Physical Constraint Finite Element Model for Medical Image Registration.
Directory of Open Access Journals (Sweden)
Jingya Zhang
Full Text Available Due to being derived from linear assumption, most elastic body based non-rigid image registration algorithms are facing challenges for soft tissues with complex nonlinear behavior and with large deformations. To take into account the geometric nonlinearity of soft tissues, we propose a registration algorithm on the basis of Newtonian differential equation. The material behavior of soft tissues is modeled as St. Venant-Kirchhoff elasticity, and the nonlinearity of the continuum represents the quadratic term of the deformation gradient under the Green- St.Venant strain. In our algorithm, the elastic force is formulated as the derivative of the deformation energy with respect to the nodal displacement vectors of the finite element; the external force is determined by the registration similarity gradient flow which drives the floating image deforming to the equilibrium condition. We compared our approach to three other models: 1 the conventional linear elastic finite element model (FEM; 2 the dynamic elastic FEM; 3 the robust block matching (RBM method. The registration accuracy was measured using three similarities: MSD (Mean Square Difference, NC (Normalized Correlation and NMI (Normalized Mutual Information, and was also measured using the mean and max distance between the ground seeds and corresponding ones after registration. We validated our method on 60 image pairs including 30 medical image pairs with artificial deformation and 30 clinical image pairs for both the chest chemotherapy treatment in different periods and brain MRI normalization. Our method achieved a distance error of 0.320±0.138 mm in x direction and 0.326±0.111 mm in y direction, MSD of 41.96±13.74, NC of 0.9958±0.0019, NMI of 1.2962±0.0114 for images with large artificial deformations; and average NC of 0.9622±0.008 and NMI of 1.2764±0.0089 for the real clinical cases. Student's t-test demonstrated that our model statistically outperformed the other methods in
Final Report of the Project "From the finite element method to the virtual element method"
Energy Technology Data Exchange (ETDEWEB)
Manzini, Gianmarco [Los Alamos National Lab. (LANL), Los Alamos, NM (United States); Gyrya, Vitaliy [Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
2017-12-20
The Finite Element Method (FEM) is a powerful numerical tool that is being used in a large number of engineering applications. The FEM is constructed on triangular/tetrahedral and quadrilateral/hexahedral meshes. Extending the FEM to general polygonal/polyhedral meshes in straightforward way turns out to be extremely difficult and leads to very complex and computationally expensive schemes. The reason for this failure is that the construction of the basis functions on elements with a very general shape is a non-trivial and complex task. In this project we developed a new family of numerical methods, dubbed the Virtual Element Method (VEM) for the numerical approximation of partial differential equations (PDE) of elliptic type suitable to polygonal and polyhedral unstructured meshes. We successfully formulated, implemented and tested these methods and studied both theoretically and numerically their stability, robustness and accuracy for diffusion problems, convection-reaction-diffusion problems, the Stokes equations and the biharmonic equations.
Energy Technology Data Exchange (ETDEWEB)
Helldoerfer, Bastian
2009-07-01
Many technical failures are caused by cracks. As a consequence fracture mechanical assessment becomes more and more important during the design of security-relevant components. The simulation of stable crackgrowth provides an essential contribution for understanding these failures and as a consequence for preventing these. In order to benefit from the advantages of the Boundary Element Method (BEM) in the field of fracture mechanical problems as well as from the numerical advantages of the Finite Element Methode (FEM) a combined simulation technique is applied within this work. Here the domain containing the crackfront is discretized with boundary elements, the remaining structure is meshed with finite elements. The direct coupling of both techniques is achieved by applying the Symmetric Galerkin BEM (SGBEM) leading to a stiffness formulation for the boundary element domain. The nonlinearity of crackgrowth requires an incremental simulation procedure. In each increment the state of stress has to be obtained firstly, whereon the fracture mechanical assessment within the framework of linear elastic fracture mechanics is carried out based on the results of the boundary element domain only. The simulation of stable crackgrowth is implemented within a predictor/corrector scheme. For increasing the efficiency several approaches were put into practice, e.g. the parallelization of the SGBEM-code, integrated submodel computations and the adaptive enlargement of the boundary element domain. Using ABAQUS it is shown exemplarily how to combine the boundary element based crackgrowth module with commercial FE-Systems. A series of examples underline the efficiency of the presented simulation technique. (orig.)
Membrane finite element method for simulating fluid flow in porous medium
Directory of Open Access Journals (Sweden)
Mei-li Zhan
2009-06-01
Full Text Available A new membrane finite element method for modeling fluid flow in a porous medium is presented in order to quickly and accurately simulate the geo-membrane fabric used in civil engineering. It is based on discontinuous finite element theory, and can be easily coupled with the normal Galerkin finite element method. Based on the saturated seepage equation, the element coefficient matrix of the membrane element method is derived, and a geometric transform relation for the membrane element between a global coordinate system and a local coordinate system is obtained. A method for the determination of the fluid flux conductivity of the membrane element is presented. This method provides a basis for determining discontinuous parameters in discontinuous finite element theory. An anti-seepage problem regarding the foundation of a building is analyzed by coupling the membrane finite element method with the normal Galerkin finite element method. The analysis results demonstrate the utility and superiority of the membrane finite element method in fluid flow analysis of a porous medium.
Directory of Open Access Journals (Sweden)
Shouyan Jiang
2017-01-01
Full Text Available We model the fluid flow within the crack as one-dimensional flow and assume that the flow is laminar; the fluid is incompressible and accounts for the time-dependent rate of crack opening. Here, we discretise the flow equation by finite volume methods. The extended finite element methods are used for solving solid medium with crack under dynamic loads. Having constructed the approximation of dynamic extended finite element methods, the derivation of governing equation for dynamic extended finite element methods is presented. The implicit time algorithm is elaborated for the time descritisation of dominant equation. In addition, the interaction integral method is given for evaluating stress intensity factors. Then, the coupling model for modelling hydraulic fracture can be established by the extended finite element methods and the finite volume methods. We compare our present numerical results with our experimental results for verifying the proposed model. Finally, we investigate the water pressure distribution along crack surface and the effect of water pressure distribution on the fracture property.
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.
Bivariate C^1 quadratic finite elements and vertex splines
Chui, Charles K.; He, Tian Xiao
1990-01-01
Following work of Heindl and of Powell and Sabin, each triangle of an arbitrary (regular) triangulation Δ of a polygonal region Ω in {R^2} is subdivided into twelve triangles, using the three medians, yielding the refinement hat Δ of Δ , so that {C^1} quadratic finite elements can be constructed. In this paper, we derive the Bezier nets of these elements in terms of the parameters that describe function and first partial derivative values at the vertices and values of the normal derivatives at the midpoints of the edges of Δ . Consequently, bivariate {C^1} quadratic (generalized) vertex splines on Δ have an explicit formulation. Here, a generalized vertex spline is one which is a piecewise polynomial on the refined grid partition hat Δ and has support that contains at most one vertex of the original partition Δ in its interior. The collection of all {C^1} quadratic generalized vertex splines on Δ so constructed is shown to form a basis of S_2^1(hat Δ ) , the vector space of all functions on {C^1}(Ω ) whose restrictions to each triangular cell of the partition hat Δ are quadratic polynomials. A subspace with the basis given by appropriately chosen generalized vertex splines with exactly one vertex of Δ in the interior of their supports, that reproduces all quadratic polynomials, is identified, and hence, has approximation order three. Quasi-interpolation formulas using this subspace are obtained. In addition, a constructive procedure that yields a locally supported basis of yet another subspace with dimension given by the number of vertices of Δ , that has approximation order three, is given.
A cut finite element method for the Bernoulli free boundary value problem
National Research Council Canada - National Science Library
Burman, Erik; Elfverson, Daniel; Hansbo, Peter; Larson, Mats G; Larsson, Karl
2017-01-01
We develop a cut finite element method for the Bernoulli free boundary problem. The free boundary, represented by an approximate signed distance function on a fixed background mesh, is allowed to intersect elements in an arbitrary fashion...
Vibration analysis of composite pipes using the finite element method with B-spline wavelets
Energy Technology Data Exchange (ETDEWEB)
Oke, Wasiu A.; Khulief, Yehia A. [King Fahd University of Petroleum and Minerals, Dhahran (Saudi Arabia)
2016-02-15
A finite element formulation using the B-spline wavelets on the interval is developed for modeling the free vibrations of composite pipes. The composite FRP pipe element is treated as a beam element. The finite pipe element is constructed in the wavelet space and then transformed to the physical space. Detailed expressions of the mass and stiffness matrices are derived for the composite pipe using the Bspline scaling and wavelet functions. Both Euler-Bernoulli and Timoshenko beam theories are considered. The generalized eigenvalue problem is formulated and solved to obtain the modal characteristics of the composite pipe. The developed wavelet-based finite element discretization scheme utilizes significantly less elements compared to the conventional finite element method for modeling composite pipes. Numerical solutions are obtained to demonstrate the accuracy of the developed element, which is verified by comparisons with some available results in the literature.
Randomized Oversampling for Generalized Multiscale Finite Element Methods
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.
Finite element analysis of CFRP reinforced silo structure design method
Yuan, Long; Xu, Xinsheng
2017-11-01
Because of poor construction, there is a serious problem of concrete quality in the silo project, which seriously affects the safe use of the structure. Concrete quality problems are mainly seen in three aspects: concrete strength cannot meet the design requirements, concrete cracking phenomenon is serious, and the unreasonable concrete vibration leads to a lot of honeycombs and surface voids. Silos are usually reinforced by carbon fiber cloth in order to ensure the safe use of silos. By the example of an alumina silo in a fly ash plant in Binzhou, Shandong Province, the alumina silo project was tested and examined on site. According to filed test results, the actual concrete strength was determined, and the damage causes of the silo was analysed. Then, a finite element analysis model of this silo was established, the CFRP cloth reinforcement method was adopted to strengthen the silo, and other technology like additional reinforcement, rebar planting, carbon fiber bonding technology was also expounded. The research of this paper is of great significance to the design and construction of silo structure.
Mixed finite-element formulations in piezoelectricity and flexoelectricity
Mao, Sheng; Purohit, Prashant K.; Aravas, Nikolaos
2016-06-01
Flexoelectricity, the linear coupling of strain gradient and electric polarization, is inherently a size-dependent phenomenon. The energy storage function for a flexoelectric material depends not only on polarization and strain, but also strain-gradient. Thus, conventional finite-element methods formulated solely on displacement are inadequate to treat flexoelectric solids since gradients raise the order of the governing differential equations. Here, we introduce a computational framework based on a mixed formulation developed previously by one of the present authors and a colleague. This formulation uses displacement and displacement-gradient as separate variables which are constrained in a `weighted integral sense' to enforce their known relation. We derive a variational formulation for boundary-value problems for piezo- and/or flexoelectric solids. We validate this computational framework against available exact solutions. Our new computational method is applied to more complex problems, including a plate with an elliptical hole, stationary cracks, as well as tension and shear of solids with a repeating unit cell. Our results address several issues of theoretical interest, generate predictions of experimental merit and reveal interesting flexoelectric phenomena with potential for application.
Finite Element Modeling of scattered electromagnetic waves for stroke analysis.
Priyadarshini, N; Rajkumar, E R
2013-01-01
Stroke has become one of the leading causes of mortality worldwide and about 800 in every 100,000 people suffer from stroke each year. The occurrence of stroke is ranked third among the causes of acute death and first among the causes for neurological dysfunction. Currently, Neurological examinations followed by medical imaging with CT, MRI or Angiography are used to provide better identification of the location and the type of the stroke, however they are neither fast, cost-effective nor portable. Microwave technology has emerged to complement these modalities to diagnose stroke as it is sensitive to the differences between the distinct dielectric properties of the brain tissues and blood. This paper investigates the possibility of diagnosing the type of stroke using Finite Element Analysis (FEA). The object of interest is a simulated head phantom with stroke, created with its specifying material characteristics like electrical conductivity and relative permittivity. The phantom is then placed in an electromagnetic field generated by a dipole antenna radiating at 1 GHz. The FEM forward model solver computes the scattered electromagnetic field by finding the solution for the Maxwell's wave equation in the head volume. Subsequently the inverse scattering problem is solved using the Contrast Source Inversion (CSI) method to reconstruct the dielectric profile of the head phantom.
Finite element analysis on seismic performance of EWECS composite column
Directory of Open Access Journals (Sweden)
Fauzan
2017-01-01
Full Text Available A new hybrid Engineering Wood Encased Concrete-Steel (EWECS structural system is developed in Japan to solve the limitation of story number for wooden structure. In this structural system, the EWECS column consist of concrete encased steel (CES core and wood panel as a column cover. An experimental study has been done to investigate the seismic performance of the EWECS column, which is compared with CES column without concrete cover. The main parameter is the presence of wood panel. In order to validate the experimental results, a 3D finite element (FE model is built by using ANSYS APDL v.14. The FE results indicate that FE EWECS column model has excellent performance, which has a stable spindle-shape hysteresis loops. The presence of wood panel contributes to improve the maximum flexural capacity of the EWECS column about 13%. In addition, the stress distribution on the FE models has good correlation with failure mode of the EWECS column specimens. Generally, the numerical results are able to accurately simulate the seismic behaviour of the EWECS column on test results.
Finite element analysis of instability-related delamination growth
Whitcomb, J. D.
1981-01-01
A parametric study of postbuckled through-width delaminations in laminated coupons was performed. A finite element analysis was developed to analyze the coupons as a combination of linear and geometrically nonlinear components. Because most of the coupon configuration studied behaves linearly, the mixed linear and nonlinear analysis greatly reduced computational costs. The analysis was verified by comparing numerical with exact solutions for simple hypothetical problems. In addition, measured lateral deflections of postbuckled through-width delaminations in laminated coupons were compared with predicted deflections. In the parametric study, stress distributions and strain-energy release rates were calculated for various delamination lengths, delamination depths, applied loads, and lateral deflections. Also, a small number of coupons with through-width delaminations were fatigue tested to obtain delamination growth data. Calculated strain-energy release rates were compared with the observed growth rates to determine the relative importance of the Mode 1 and Mode 2 components of energy release. Growth process was dominated by G sub I.
Prototype Mixed Finite Element Hydrodynamics Capability in ARES
Energy Technology Data Exchange (ETDEWEB)
Rieben, R N
2008-07-10
This document describes work on a prototype Mixed Finite Element Method (MFEM) hydrodynamics algorithm in the ARES code, and its application to a set of standard test problems. This work is motivated by the need for improvements to the algorithms used in the Lagrange hydrodynamics step to make them more robust. We begin by identifying the outstanding issues with traditional numerical hydrodynamics algorithms followed by a description of the proposed method and how it may address several of these longstanding issues. We give a theoretical overview of the proposed MFEM algorithm as well as a summary of the coding additions and modifications that were made to add this capability to the ARES code. We present results obtained with the new method on a set of canonical hydrodynamics test problems and demonstrate significant improvement in comparison to results obtained with traditional methods. We conclude with a summary of the issues still at hand and motivate the need for continued research to develop the proposed method into maturity.
Modelling Micro-Vibrations By Finite Element Model Approach
Soula, Laurent; Laduree, Gregory
2012-07-01
With payloads requiring more and more severe environment stability and spacecrafts becoming more and more sensitive to internal mechanical disturbances, micro-vibrations are a key contributor to the performance of new missions. To help predict such behaviour by analyses and verify it by testing, a “METhodology for Analysis of structure-borne MICro- vibrations” is being defined in the frame of the above- named ESA R&D study (METAMIC). This methodology is soon to be validated by a full-test campaign. Meanwhile, this paper proposes a description of the current processes using the Finite Element Models, which start from the perturbation source. Based on ASTRIUM experience, a classification of disturbance sources is proposed. Three different types are selected to illustrate the modelling and the micro- vibrations characterization performed by tests: momentum wheels, cryo-coolers, and stepper motor mechanisms. The perturbation is then to be implemented into system modelling in order to predict its propagation and effect on overall performance. The main assumptions made on structure modelling have to be identified as well as the level of coupling with the disturbance sources has to be anticipated. Most of the questions a project should ask to deal with micro- vibrations are tackled, with the objective to identify all uncertainties, limitations, and validity domains for micro-vibrations prediction.
Beyond first-order finite element schemes in micromagnetics
Energy Technology Data Exchange (ETDEWEB)
Kritsikis, E., E-mail: kritsikis@math.univ-paris13.fr [Laboratoire d' analyse, géométrie et applications, université Paris 13, CNRS UMR 7539, 93430 Villetaneuse (France); Vaysset, A.; Buda-Prejbeanu, L.D. [SPINTEC, INAC, UMR CEA/CNRS/UJF-Grenoble 1/Grenoble-INP, F-38054 Grenoble (France); Alouges, F. [CMAP, CNRS and École polytechnique, F-91128 Palaiseau (France); Toussaint, J.-C. [Institut Néel, CNRS and université Joseph Fourier, F-38042 Grenoble (France)
2014-01-01
Magnetization dynamics in ferromagnetic materials is ruled by the Landau–Lifshitz–Gilbert equation (LLG). Reliable schemes must conserve the magnetization norm, which is a nonconvex constraint, and be energy-decreasing unless there is pumping. Some of the authors previously devised a convergent finite element scheme that, by choice of an appropriate test space – the tangent plane to the magnetization – reduces to a linear problem at each time step. The scheme was however first-order in time. We claim it is not an intrinsic limitation, and the same approach can lead to efficient micromagnetic simulation. We show how the scheme order can be increased, and the nonlocal (magnetostatic) interactions be tackled in logarithmic time, by the fast multipole method or the non-uniform fast Fourier transform. Our implementation is called feeLLGood. A test-case of the National Institute of Standards and Technology is presented, then another one relevant to spin-transfer effects (the spin-torque oscillator)
Beyond first-order finite element schemes in micromagnetics
Kritsikis, E.; Vaysset, A.; Buda-Prejbeanu, L. D.; Alouges, F.; Toussaint, J.-C.
2014-01-01
Magnetization dynamics in ferromagnetic materials is ruled by the Landau-Lifshitz-Gilbert equation (LLG). Reliable schemes must conserve the magnetization norm, which is a nonconvex constraint, and be energy-decreasing unless there is pumping. Some of the authors previously devised a convergent finite element scheme that, by choice of an appropriate test space - the tangent plane to the magnetization - reduces to a linear problem at each time step. The scheme was however first-order in time. We claim it is not an intrinsic limitation, and the same approach can lead to efficient micromagnetic simulation. We show how the scheme order can be increased, and the nonlocal (magnetostatic) interactions be tackled in logarithmic time, by the fast multipole method or the non-uniform fast Fourier transform. Our implementation is called feeLLGood. A test-case of the National Institute of Standards and Technology is presented, then another one relevant to spin-transfer effects (the spin-torque oscillator).
Calibration under uncertainty for finite element models of masonry monuments
Energy Technology Data Exchange (ETDEWEB)
Atamturktur, Sezer,; Hemez, Francois,; Unal, Cetin
2010-02-01
Historical unreinforced masonry buildings often include features such as load bearing unreinforced masonry vaults and their supporting framework of piers, fill, buttresses, and walls. The masonry vaults of such buildings are among the most vulnerable structural components and certainly among the most challenging to analyze. The versatility of finite element (FE) analyses in incorporating various constitutive laws, as well as practically all geometric configurations, has resulted in the widespread use of the FE method for the analysis of complex unreinforced masonry structures over the last three decades. However, an FE model is only as accurate as its input parameters, and there are two fundamental challenges while defining FE model input parameters: (1) material properties and (2) support conditions. The difficulties in defining these two aspects of the FE model arise from the lack of knowledge in the common engineering understanding of masonry behavior. As a result, engineers are unable to define these FE model input parameters with certainty, and, inevitably, uncertainties are introduced to the FE model.
Design Through Manufacturing: The Solid Model - Finite Element Analysis Interface
Rubin, Carol
2003-01-01
State-of-the-art computer aided design (CAD) presently affords engineers the opportunity to create solid models of machine parts which reflect every detail of the finished product. Ideally, these models should fulfill two very important functions: (1) they must provide numerical control information for automated manufacturing of precision parts, and (2) they must enable analysts to easily evaluate the stress levels (using finite element analysis - FEA) for all structurally significant parts used in space missions. Today's state-of-the-art CAD programs perform function (1) very well, providing an excellent model for precision manufacturing. But they do not provide a straightforward and simple means of automating the translation from CAD to FEA models, especially for aircraft-type structures. The research performed during the fellowship period investigated the transition process from the solid CAD model to the FEA stress analysis model with the final goal of creating an automatic interface between the two. During the period of the fellowship a detailed multi-year program for the development of such an interface was created. The ultimate goal of this program will be the development of a fully parameterized automatic ProE/FEA translator for parts and assemblies, with the incorporation of data base management into the solution, and ultimately including computational fluid dynamics and thermal modeling in the interface.
FEMA: a Finite Element Model of Material Transport through Aquifers
Energy Technology Data Exchange (ETDEWEB)
Yeh, G.T.; Huff, D.D.
1985-01-01
This report documents the construction, verification, and demonstration of a Finite Element Model of Material Transport through Aquifers (FEMA). The particular features of FEMA are its versatility and flexibility to deal with as many real-world problems as possible. Mechanisms included in FEMA are: carrier fluid advection, hydrodynamic dispersion and molecular diffusion, radioactive decay, sorption, source/sinks, and degradation due to biological, chemical as well as physical processes. Three optional sorption models are embodied in FEMA. These are linear isotherm and Freundlich and Langmuir nonlinear isotherms. Point as well as distributed source/sinks are included to represent artificial injection/withdrawals and natural infiltration of precipitation. All source/sinks can be transient or steady state. Prescribed concentration on the Dirichlet boundary, given gradient on the Neumann boundary segment, and flux at each Cauchy boundary segment can vary independently of each other. The aquifer may consist of as many formations as desired. Either completely confined or completely unconfined or partially confined and partially unconfined aquifers can be dealt with effectively. FEMA also includes transient leakage to or from the aquifer of interest through confining beds from or to aquifers lying below and/or above.
Spectral Analysis of Large Finite Element Problems by Optimization Methods
Directory of Open Access Journals (Sweden)
Luca Bergamaschi
1994-01-01
Full Text Available Recently an efficient method for the solution of the partial symmetric eigenproblem (DACG, deflated-accelerated conjugate gradient was developed, based on the conjugate gradient (CG minimization of successive Rayleigh quotients over deflated subspaces of decreasing size. In this article four different choices of the coefficient βk required at each DACG iteration for the computation of the new search direction Pk are discussed. The “optimal” choice is the one that yields the same asymptotic convergence rate as the CG scheme applied to the solution of linear systems. Numerical results point out that the optimal βk leads to a very cost effective algorithm in terms of CPU time in all the sample problems presented. Various preconditioners are also analyzed. It is found that DACG using the optimal βk and (LLT−1 as a preconditioner, L being the incomplete Cholesky factor of A, proves a very promising method for the partial eigensolution. It appears to be superior to the Lanczos method in the evaluation of the 40 leftmost eigenpairs of five finite element problems, and particularly for the largest problem, with size equal to 4560, for which the speed gain turns out to fall between 2.5 and 6.0, depending on the eigenpair level.
Modelling cell motility and chemotaxis with evolving surface finite elements.
Elliott, Charles M; Stinner, Björn; Venkataraman, Chandrasekhar
2012-11-07
We present a mathematical and a computational framework for the modelling of cell motility. The cell membrane is represented by an evolving surface, with the movement of the cell determined by the interaction of various forces that act normal to the surface. We consider external forces such as those that may arise owing to inhomogeneities in the medium and a pressure that constrains the enclosed volume, as well as internal forces that arise from the reaction of the cells' surface to stretching and bending. We also consider a protrusive force associated with a reaction-diffusion system (RDS) posed on the cell membrane, with cell polarization modelled by this surface RDS. The computational method is based on an evolving surface finite-element method. The general method can account for the large deformations that arise in cell motility and allows the simulation of cell migration in three dimensions. We illustrate applications of the proposed modelling framework and numerical method by reporting on numerical simulations of a model for eukaryotic chemotaxis and a model for the persistent movement of keratocytes in two and three space dimensions. Movies of the simulated cells can be obtained from http://homepages.warwick.ac.uk/∼maskae/CV_Warwick/Chemotaxis.html.
A hybrid finite-difference and analytic element groundwater model
Haitjema, Henk M.; Feinstein, Daniel T.; Hunt, Randall J.; Gusyev, Maksym
2010-01-01
Regional finite-difference models tend to have large cell sizes, often on the order of 1–2 km on a side. Although the regional flow patterns in deeper formations may be adequately represented by such a model, the intricate surface water and groundwater interactions in the shallower layers are not. Several stream reaches and nearby wells may occur in a single cell, precluding any meaningful modeling of the surface water and groundwater interactions between the individual features. We propose to replace the upper MODFLOW layer or layers, in which the surface water and groundwater interactions occur, by an analytic element model (GFLOW) that does not employ a model grid; instead, it represents wells and surface waters directly by the use of point-sinks and line-sinks. For many practical cases it suffices to provide GFLOW with the vertical leakage rates calculated in the original coarse MODFLOW model in order to obtain a good representation of surface water and groundwater interactions. However, when the combined transmissivities in the deeper (MODFLOW) layers dominate, the accuracy of the GFLOW solution diminishes. For those cases, an iterative coupling procedure, whereby the leakages between the GFLOW and MODFLOW model are updated, appreciably improves the overall solution, albeit at considerable computational cost. The coupled GFLOW–MODFLOW model is applicable to relatively large areas, in many cases to the entire model domain, thus forming an attractive alternative to local grid refinement or inset models.