Finite element mesh generation
Lo, Daniel SH
2014-01-01
Highlights the Progression of Meshing Technologies and Their ApplicationsFinite Element Mesh Generation provides a concise and comprehensive guide to the application of finite element mesh generation over 2D domains, curved surfaces, and 3D space. Organised according to the geometry and dimension of the problem domains, it develops from the basic meshing algorithms to the most advanced schemes to deal with problems with specific requirements such as boundary conformity, adaptive and anisotropic elements, shape qualities, and mesh optimization. It sets out the fundamentals of popular techniques
Finite element differential forms on cubical meshes
Arnold, Douglas N
2012-01-01
We develop a family of finite element spaces of differential forms defined on cubical meshes in any number of dimensions. The family contains elements of all polynomial degrees and all form degrees. In two dimensions, these include the serendipity finite elements and the rectangular BDM elements. In three dimensions they include a recent generalization of the serendipity spaces, and new H(curl) and H(div) finite element spaces. Spaces in the family can be combined to give finite element subcomplexes of the de Rham complex which satisfy the basic hypotheses of the finite element exterior calculus, and hence can be used for stable discretization of a variety of problems. The construction and properties of the spaces are established in a uniform manner using finite element exterior calculus.
Diffusive mesh relaxation in ALE finite element numerical simulations
Energy Technology Data Exchange (ETDEWEB)
Dube, E.I.
1996-06-01
The theory for a diffusive mesh relaxation algorithm is developed for use in three-dimensional Arbitary Lagrange/Eulerian (ALE) finite element simulation techniques. This mesh relaxer is derived by a variational principle for an unstructured 3D grid using finite elements, and incorporates hourglass controls in the numerical implementation. The diffusive coefficients are based on the geometric properties of the existing mesh, and are chosen so as to allow for a smooth grid that retains the general shape of the original mesh. The diffusive mesh relaxation algorithm is then applied to an ALE code system, and results from several test cases are discussed.
Finite Element Meshes Auto-Generation for the Welted Bifurcation
Institute of Scientific and Technical Information of China (English)
YUANMei; LIYa-ping
2004-01-01
In this paper, firstly, a mathematical model for a specific kind of welted bifurcation is established, the parametric equation for the intersecting curve is resulted in. Secondly, a method for partitioning finite element meshes of the welted bifurcation is put forward, its main idea is that developing the main pipe surface and the branch pipe surface respectively, dividing meshes on each developing plane and obtaining meshes points, then transforming their plane coordinates into space coordinates. Finally, an applied program for finite element meshes auto-generation is simply introduced, which adopt ObjectARX technique and its running result can be shown in AutoCAD. The meshes generated in AutoCAD can be exported conveniently to most of finite element analysis soft wares, and the finite element computing result can satisfy the engineering precision requirement.
Finite element meshing approached as a global minimization process
Energy Technology Data Exchange (ETDEWEB)
WITKOWSKI,WALTER R.; JUNG,JOSEPH; DOHRMANN,CLARK R.; LEUNG,VITUS J.
2000-03-01
The ability to generate a suitable finite element mesh in an automatic fashion is becoming the key to being able to automate the entire engineering analysis process. However, placing an all-hexahedron mesh in a general three-dimensional body continues to be an elusive goal. The approach investigated in this research is fundamentally different from any other that is known of by the authors. A physical analogy viewpoint is used to formulate the actual meshing problem which constructs a global mathematical description of the problem. The analogy used was that of minimizing the electrical potential of a system charged particles within a charged domain. The particles in the presented analogy represent duals to mesh elements (i.e., quads or hexes). Particle movement is governed by a mathematical functional which accounts for inter-particles repulsive, attractive and alignment forces. This functional is minimized to find the optimal location and orientation of each particle. After the particles are connected a mesh can be easily resolved. The mathematical description for this problem is as easy to formulate in three-dimensions as it is in two- or one-dimensions. The meshing algorithm was developed within CoMeT. It can solve the two-dimensional meshing problem for convex and concave geometries in a purely automated fashion. Investigation of the robustness of the technique has shown a success rate of approximately 99% for the two-dimensional geometries tested. Run times to mesh a 100 element complex geometry were typically in the 10 minute range. Efficiency of the technique is still an issue that needs to be addressed. Performance is an issue that is critical for most engineers generating meshes. It was not for this project. The primary focus of this work was to investigate and evaluate a meshing algorithm/philosophy with efficiency issues being secondary. The algorithm was also extended to mesh three-dimensional geometries. Unfortunately, only simple geometries were tested
GPU accelerated spectral finite elements on all-hex meshes
Remacle, J.-F.; Gandham, R.; Warburton, T.
2016-11-01
This paper presents a spectral element finite element scheme that efficiently solves elliptic problems on unstructured hexahedral meshes. The discrete equations are solved using a matrix-free preconditioned conjugate gradient algorithm. An additive Schwartz two-scale preconditioner is employed that allows h-independence convergence. An extensible multi-threading programming API is used as a common kernel language that allows runtime selection of different computing devices (GPU and CPU) and different threading interfaces (CUDA, OpenCL and OpenMP). Performance tests demonstrate that problems with over 50 million degrees of freedom can be solved in a few seconds on an off-the-shelf GPU.
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.
MeshEZW: an image coder using mesh and finite elements
Landais, Thomas; Bonnaud, Laurent; Chassery, Jean-Marc
2003-08-01
In this paper, we present a new method to compress the information in an image, called MeshEZW. The proposed approach is based on the finite elements method, a mesh construction and a zerotree method. The zerotree method is an adaptive of the EZW algorithm with two new symbols for increasing the performance. These steps allow a progressive representation of the image by the automatic construction of a bitstream. The mesh structure is adapted to the image compression domain and is defined to allow video comrpession. The coder is described and some preliminary results are discussed.
A REGIONAL REFINEMENT FOR FINITE ELEMENT MESH DESIGN USING COLLAPSIBLE ELEMENT
Directory of Open Access Journals (Sweden)
Priyo Suprobo
2000-01-01
Full Text Available A practical algorithm for automated mesh design in finite element analysis is developed. A regional mixed mesh improvement procedure is introduced. The error control%2C algorithm implementation%2C code development%2C and the solution accuracy are discussed. Numerical example includes automated mesh designs for plane elastic media with singularities. The efficiency of the procedure is demonstrated. Abstract in Bahasa Indonesia : regional+refinement%2C+mesh+generation%2C+isoparametric+element%2C+collapsible+element
The mesh-matching algorithm: an automatic 3D mesh generator for Finite element structures
Couteau, B; Lavallee, S; Payan, Yohan; Lavallee, St\\'{e}phane
2000-01-01
Several authors have employed Finite Element Analysis (FEA) for stress and strain analysis in orthopaedic biomechanics. Unfortunately, the use of three-dimensional models is time consuming and consequently the number of analysis to be performed is limited. The authors have investigated a new method allowing automatically 3D mesh generation for structures as complex as bone for example. This method called Mesh-Matching (M-M) algorithm generated automatically customized 3D meshes of bones from an already existing model. The M-M algorithm has been used to generate FE models of ten proximal human femora from an initial one which had been experimentally validated. The new meshes seemed to demonstrate satisfying results.
3D unstructured mesh discontinuous finite element hydro
Energy Technology Data Exchange (ETDEWEB)
Prasad, M.K.; Kershaw, D.S.; Shaw, M.J. [Lawrence Livermore National Lab., CA (United States)
1995-07-01
The authors present detailed features of the ICF3D hydrodynamics code used for inertial fusion simulations. This code is intended to be a state-of-the-art upgrade of the well-known fluid code, LASNEX. ICF3D employs discontinuous finite elements on a discrete unstructured mesh consisting of a variety of 3D polyhedra including tetrahedra, prisms, and hexahedra. The authors discussed details of how the ROE-averaged second-order convection was applied on the discrete elements, and how the C++ coding interface has helped to simplify implementing the many physics and numerics modules within the code package. The author emphasized the virtues of object-oriented design in large scale projects such as ICF3D.
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.
A multi-mesh finite element method for Lagrange elements of arbitrary degree
Witkowski, Thomas
2010-01-01
We consider within a finite element approach the usage of different adaptively refined meshes for different variables in systems of nonlinear, time-depended PDEs. To resolve different solution behaviours of these variables, the meshes can be independently adapted. The resulting linear systems are usually much smaller, when compared to the usage of a single mesh, and the overall computational runtime can be more than halved in such cases. Our multi-mesh method works for Lagrange finite elements of arbitrary degree and is independent of the spatial dimension. The approach is well defined, and can be implemented in existing adaptive finite element codes with minimal effort. We show computational examples in 2D and 3D ranging from dendritic growth to solid-solid phase-transitions. A further application comes from fluid dynamics where we demonstrate the applicability of the approach for solving the incompressible Navier-Stokes equations with Lagrange finite elements of the same order for velocity and pressure. The...
Determination of an Initial Mesh Density for Finite Element Computations via Data Mining
Energy Technology Data Exchange (ETDEWEB)
Kanapady, R; Bathina, S K; Tamma, K K; Kamath, C; Kumar, V
2001-07-23
Numerical analysis software packages which employ a coarse first mesh or an inadequate initial mesh need to undergo a cumbersome and time consuming mesh refinement studies to obtain solutions with acceptable accuracy. Hence, it is critical for numerical methods such as finite element analysis to be able to determine a good initial mesh density for the subsequent finite element computations or as an input to a subsequent adaptive mesh generator. This paper explores the use of data mining techniques for obtaining an initial approximate finite element density that avoids significant trial and error to start finite element computations. As an illustration of proof of concept, a square plate which is simply supported at its edges and is subjected to a concentrated load is employed for the test case. Although simplistic, the present study provides insight into addressing the above considerations.
Pamgen, a library for parallel generation of simple finite element meshes.
Energy Technology Data Exchange (ETDEWEB)
Foucar, James G.; Drake, Richard Roy; Hensinger, David M.; Gardiner, Thomas Anthony
2008-04-01
Generating finite-element meshes is a serious bottleneck for large parallel simulations. When mesh generation is limited to serial machines and element counts approach a billion, this bottleneck becomes a roadblock. Pamgen is a parallel mesh generation library that allows on-the-fly scalable generation of hexahedral and quadrilateral finite element meshes for several simple geometries. It has been used to generate more that 1.1 billion elements on 17,576 processors. Pamgen generates an unstructured finite element mesh on each processor at the start of a simulation. The mesh is specified by commands passed to the library as a 'C'-programming language string. The resulting mesh geometry, topology, and communication information can then be queried through an API. pamgen allows specification of boundary condition application regions using sidesets (element faces) and nodesets (collections of nodes). It supports several simple geometry types. It has multiple alternatives for mesh grading. It has several alternatives for the initial domain decomposition. Pamgen makes it easy to change details of the finite element mesh and is very useful for performance studies and scoping calculations.
Bucki, Marek; Payan, Yohan; 10.1016/j.media.2010.02.003
2010-01-01
Finite Element mesh generation remains an important issue for patient specific biomechanical modeling. While some techniques make automatic mesh generation possible, in most cases, manual mesh generation is preferred for better control over the sub-domain representation, element type, layout and refinement that it provides. Yet, this option is time consuming and not suited for intraoperative situations where model generation and computation time is critical. To overcome this problem we propose a fast and automatic mesh generation technique based on the elastic registration of a generic mesh to the specific target organ in conjunction with element regularity and quality correction. This Mesh-Match-and-Repair (MMRep) approach combines control over the mesh structure along with fast and robust meshing capabilities, even in situations where only partial organ geometry is available. The technique was successfully tested on a database of 5 pre-operatively acquired complete femora CT scans, 5 femoral heads partially...
ESCHER: An interactive mesh-generating editor for preparing finite-element input
Oakes, W. R., Jr.
1984-01-01
ESCHER is an interactive mesh generation and editing program designed to help the user create a finite-element mesh, create additional input for finite-element analysis, including initial conditions, boundary conditions, and slidelines, and generate a NEUTRAL FILE that can be postprocessed for input into several finite-element codes, including ADINA, ADINAT, DYNA, NIKE, TSAAS, and ABUQUS. Two important ESCHER capabilities, interactive geometry creation and mesh archival storge are described in detail. Also described is the interactive command language and the use of interactive graphics. The archival storage and restart file is a modular, entity-based mesh data file. Modules of this file correspond to separate editing modes in the mesh editor, with data definition syntax preserved between the interactive commands and the archival storage file. Because ESCHER was expected to be highly interactive, extensive user documentation was provided in the form of an interactive HELP package.
Finite element simulation of stretch forging using a mesh condensation method
Institute of Scientific and Technical Information of China (English)
无
2010-01-01
In order to reduce the computation time of finite element simulations of stretch forging process,a mesh condensation method is presented and applied to a three-dimensional rigid-viscoplastic finite element program.In this method,a conventional mesh for the whole zone of a workpiece is condensed to a computational mesh for the active deformation zone.Two vital problems are solved,which are automatic construction of the computational mesh and treatment of interfaces between the deformation zone and the rigid zone.The mesh condensation method is compared with conventional finite element method by simulations of a six-bite stretch forging process.Some simulation results including forging load,temperature distribution and effective strain distribution are illustrated.The efficiency and accuracy of this method are verified.
ESCHER: An interactive mesh-generating editor for preparing finite-element input
Oakes, W. R., Jr.
1984-01-01
ESCHER is an interactive mesh generation and editing program designed to help the user create a finite-element mesh, create additional input for finite-element analysis, including initial conditions, boundary conditions, and slidelines, and generate a NEUTRAL FILE that can be postprocessed for input into several finite-element codes, including ADINA, ADINAT, DYNA, NIKE, TSAAS, and ABUQUS. Two important ESCHER capabilities, interactive geometry creation and mesh archival storge are described in detail. Also described is the interactive command language and the use of interactive graphics. The archival storage and restart file is a modular, entity-based mesh data file. Modules of this file correspond to separate editing modes in the mesh editor, with data definition syntax preserved between the interactive commands and the archival storage file. Because ESCHER was expected to be highly interactive, extensive user documentation was provided in the form of an interactive HELP package.
A new conformal absorbing boundary condition for finite element meshes and parallelization of FEMATS
Chatterjee, A.; Volakis, J. L.; Nguyen, J.; Nurnberger, M.; Ross, D.
1993-01-01
Some of the progress toward the development and parallelization of an improved version of the finite element code FEMATS is described. This is a finite element code for computing the scattering by arbitrarily shaped three dimensional surfaces composite scatterers. The following tasks were worked on during the report period: (1) new absorbing boundary conditions (ABC's) for truncating the finite element mesh; (2) mixed mesh termination schemes; (3) hierarchical elements and multigridding; (4) parallelization; and (5) various modeling enhancements (antenna feeds, anisotropy, and higher order GIBC).
Finite element based electrostatic-structural coupled analysis with automated mesh morphing
Energy Technology Data Exchange (ETDEWEB)
OWEN,STEVEN J.; ZHULIN,V.I.; OSTERGAARD,D.F.
2000-02-29
A co-simulation tool based on finite element principles has been developed to solve coupled electrostatic-structural problems. An automated mesh morphing algorithm has been employed to update the field mesh after structural deformation. The co-simulation tool has been successfully applied to the hysteric behavior of a MEMS switch.
Design of Finite Element Tools for Coupled Surface and Volume Meshes
Institute of Scientific and Technical Information of China (English)
Daniel K(o)ster; Oliver Kriessl; Kunibert G. Siebert
2008-01-01
Many problems with underlying variational structure involve a coupling of volume with surface effects. A straight-forward approach in a finite element discretization is to make use of the surface triangulation that is naturally induced by the volume triangulation. In an adaptive method one wants to facilitate "matching" local mesh modifications, i.e., local refinement and/or coarsening, of volume and surface mesh with standard tools such that the surface grid is always induced by the volume grid. We describe the concepts behind this approach for bisectional refinement and describe new tools incorporated in the finite element toolbox ALBERTA. We also present several important applications of the mesh coupling.
Adaptive meshing technique applied to an orthopaedic finite element contact problem.
Roarty, Colleen M; Grosland, Nicole M
2004-01-01
Finite element methods have been applied extensively and with much success in the analysis of orthopaedic implants. Recently a growing interest has developed, in the orthopaedic biomechanics community, in how numerical models can be constructed for the optimal solution of problems in contact mechanics. New developments in this area are of paramount importance in the design of improved implants for orthopaedic surgery. Finite element and other computational techniques are widely applied in the analysis and design of hip and knee implants, with additional joints (ankle, shoulder, wrist) attracting increased attention. The objective of this investigation was to develop a simplified adaptive meshing scheme to facilitate the finite element analysis of a dual-curvature total wrist implant. Using currently available software, the analyst has great flexibility in mesh generation, but must prescribe element sizes and refinement schemes throughout the domain of interest. Unfortunately, it is often difficult to predict in advance a mesh spacing that will give acceptable results. Adaptive finite-element mesh capabilities operate to continuously refine the mesh to improve accuracy where it is required, with minimal intervention by the analyst. Such mesh adaptation generally means that in certain areas of the analysis domain, the size of the elements is decreased (or increased) and/or the order of the elements may be increased (or decreased). In concept, mesh adaptation is very appealing. Although there have been several previous applications of adaptive meshing for in-house FE codes, we have coupled an adaptive mesh formulation with the pre-existing commercial programs PATRAN (MacNeal-Schwendler Corp., USA) and ABAQUS (Hibbit Karlson and Sorensen, Pawtucket, RI). In doing so, we have retained several attributes of the commercial software, which are very attractive for orthopaedic implant applications.
A study on moving mesh finite element solution of the porous medium equation
Ngo, Cuong; Huang, Weizhang
2017-02-01
An adaptive moving mesh finite element method is studied for the numerical solution of the porous medium equation with and without variable exponents and absorption. The method is based on the moving mesh partial differential equation approach and employs its newly developed implementation. The implementation has several improvements over the traditional one, including its explicit, compact form of the mesh velocities, ease to program, and less likelihood of producing singular meshes. Three types of metric tensor that correspond to uniform and arclength-based and Hessian-based adaptive meshes are considered. The method shows first-order convergence for uniform and arclength-based adaptive meshes, and second-order convergence for Hessian-based adaptive meshes. It is also shown that the method can be used for situations with complex free boundaries, emerging and splitting of free boundaries, and the porous medium equation with variable exponents and absorption. Two-dimensional numerical results are presented.
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.
Tangle-Free Finite Element Mesh Motion for Ablation Problems
Droba, Justin
2016-01-01
In numerical simulations involving boundaries that evolve in time, the primary challenge is updating the computational mesh to reflect the physical changes in the domain. In particular, the fundamental objective for any such \\mesh motion" scheme is to maintain mesh quality and suppress unphysical geometric anamolies and artifacts. External to a physical process of interest, mesh motion is an added component that determines the specifics of how to move the mesh given certain limited information from the main system. This paper develops a set of boundary conditions designed to eliminate tangling and internal collision within the context of PDE-based mesh motion (linear elasticity). These boundary conditions are developed for two- and three-dimensional meshes. The paper presents detailed algorithms for commonly occuring topological scenarios and explains how to apply them appropriately. Notably, the techniques discussed herein make use of none of the specifics of any particular formulation of mesh motion and thus are more broadly applicable. The two-dimensional algorithms are validated by an extensive verification procedure. Finally, many examples of diverse geometries in both two- and three-dimensions are shown to showcase the capabilities of the tangle-free boundary conditions.
Design of computer-generated beam-shaping holograms by iterative finite-element mesh adaption.
Dresel, T; Beyerlein, M; Schwider, J
1996-12-10
Computer-generated phase-only holograms can be used for laser beam shaping, i.e., for focusing a given aperture with intensity and phase distributions into a pregiven intensity pattern in their focal planes. A numerical approach based on iterative finite-element mesh adaption permits the design of appropriate phase functions for the task of focusing into two-dimensional reconstruction patterns. Both the hologram aperture and the reconstruction pattern are covered by mesh mappings. An iterative procedure delivers meshes with intensities equally distributed over the constituting elements. This design algorithm adds new elementary focuser functions to what we call object-oriented hologram design. Some design examples are discussed.
Finite Macro-Element Mesh Deformation in a Structured Multi-Block Navier-Stokes Code
Bartels, Robert E.
2005-01-01
A mesh deformation scheme is developed for a structured multi-block Navier-Stokes code consisting of two steps. The first step is a finite element solution of either user defined or automatically generated macro-elements. Macro-elements are hexagonal finite elements created from a subset of points from the full mesh. When assembled, the finite element system spans the complete flow domain. Macro-element moduli vary according to the distance to the nearest surface, resulting in extremely stiff elements near a moving surface and very pliable elements away from boundaries. Solution of the finite element system for the imposed boundary deflections generally produces smoothly varying nodal deflections. The manner in which distance to the nearest surface has been found to critically influence the quality of the element deformation. The second step is a transfinite interpolation which distributes the macro-element nodal deflections to the remaining fluid mesh points. The scheme is demonstrated for several two-dimensional applications.
A mesh re-zoning technique for finite element simulations of metal forming processes
Cheng, J.-C.; Kikuchi, N.
1986-01-01
Based on some fundamental properties of finite element approximations, a mesh re-zoning scheme is proposed for finite element simulations of metal forming problems. It is demonstrated that this technique is indispensable in analyzing many difficult forming processes, especially when there exist corners or very irregular shapes on the boundaries. The algorithm is tested by a backward extrusion process and direct extrusion through a square die.
Selection of finite-element mesh parameters in modeling the growth of hydraulic fracturing cracks
Kurguzov, V. D.
2016-12-01
The effect of the mesh geometry on the accuracy of solutions obtained by the finite-element method for problems of linear fracture mechanics is investigated. The guidelines have been formulated for constructing an optimum mesh for several routine problems involving elements with linear and quadratic approximation of displacements. The accuracy of finite-element solutions is estimated based on the degree of the difference between the calculated stress-intensity factor (SIF) and its value obtained analytically. In problems of hydrofracturing of oil-bearing formation, the pump-in pressure of injected water produces a distributed load on crack flanks as opposed to standard fracture mechanics problems that have analytical solutions, where a load is applied to the external boundaries of the computational region and the cracks themselves are kept free from stresses. Some model pressure profiles, as well as pressure profiles taken from real hydrodynamic computations, have been considered. Computer models of cracks with allowance for the pre-stressed state, fracture toughness, and elastic properties of materials are developed in the MSC.Marc 2012 finite-element analysis software. The Irwin force criterion is used as a criterion of brittle fracture and the SIFs are computed using the Cherepanov-Rice invariant J-integral. The process of crack propagation in a linearly elastic isotropic body is described in terms of the elastic energy release rate G and modeled using the VCCT (Virtual Crack Closure Technique) approach. It has been found that the solution accuracy is sensitive to the mesh configuration. Several parameters that are decisive in constructing effective finite-element meshes, namely, the minimum element size, the distance between mesh nodes in the vicinity of a crack tip, and the ratio of the height of an element to its length, have been established. It has been shown that a mesh that consists of only small elements does not improve the accuracy of the solution.
ZONE: a finite element mesh generator. [In FORTRAN IV for CDC 7600
Energy Technology Data Exchange (ETDEWEB)
Burger, M. J.
1976-05-01
The ZONE computer program is a finite-element mesh generator which produces the nodes and element description of any two-dimensional geometry. The geometry is subdivided into a mesh of quadrilateral and triangular zones arranged sequentially in an ordered march through the geometry. The order of march can be chosen so that the minimum bandwidth is obtained. The node points are defined in terms of the x and y coordinates in a global rectangular coordinate system. The zones generated are quadrilaterals or triangles defined by four node points in a counterclockwise sequence. Node points defining the outside boundary are generated to describe pressure boundary conditions. The mesh that is generated can be used as input to any two-dimensional as well as any axisymmetrical structure program. The output from ZONE is essentially the input file to NAOS, HONDO, and other axisymmetric finite element programs. 14 figures. (RWR)
Li, Xianping
2010-01-01
Heterogeneous anisotropic diffusion problems arise in the various areas of science and engineering including plasma physics, petroleum engineering, and image processing. Standard numerical methods can produce spurious oscillations when they are used to solve those problems. A common approach to avoid this difficulty is to design a proper numerical scheme and/or a proper mesh so that the numerical solution validates the discrete counterpart (DMP) of the maximum principle satisfied by the continuous solution. A well known mesh condition for the DMP satisfaction by the linear finite element solution of isotropic diffusion problems is the non-obtuse angle condition that requires the dihedral angles of mesh elements to be non-obtuse. In this paper, a generalization of the condition, the so-called anisotropic non-obtuse angle condition, is developed for the finite element solution of heterogeneous anisotropic diffusion problems. The new condition is essentially the same as the existing one except that the dihedral ...
Finite element model for linear-elastic mixed mode loading using adaptive mesh strategy
Institute of Scientific and Technical Information of China (English)
无
2008-01-01
An adaptive mesh finite element model has been developed to predict the crack propagation direction as well as to calculate the stress intensity factors (SIFs), under linear-elastic assumption for mixed mode loading application. The finite element mesh is generated using the advancing front method. In order to suit the requirements of the fracture analysis, the generation of the background mesh and the construction of singular elements have been added to the developed program. The adaptive remeshing process is carried out based on the posteriori stress error norm scheme to obtain an optimal mesh. Previous works of the authors have proposed techniques for adaptive mesh generation of 2D cracked models. Facilitated by the singular elements, the displacement extrapolation technique is employed to calculate the SIF. The fracture is modeled by the splitting node approach and the trajectory follows the successive linear extensions of each crack increment. The SIFs values for two different case studies were estimated and validated by direct comparisons with other researchers work.
A MIXED FINITE ELEMENT METHOD ON A STAGGERED MESH FOR NAVIER-STOKES EQUATIONS
Institute of Scientific and Technical Information of China (English)
Houde Han; Ming Yan
2008-01-01
In this paper, we introduce a mixed finite element method on a staggered mesh for the numerical solution of the steady state Navier-Stokes equations in which the two components of the velocity and the pressure are defined on three different meshes. This method is a conforming quadrilateral Q1 × Q1 - P0 element approximation for the Navier-Stokes equations. First-order error estimates are obtained for both the velocity and the pressure.Numerical examples are presented to illustrate the effectiveness of the proposed method.
Charged particle tracking through electrostatic wire meshes using the finite element method
Devlin, L. J.; Karamyshev, O.; Welsch, C. P.
2016-06-01
Wire meshes are used across many disciplines to accelerate and focus charged particles, however, analytical solutions are non-exact and few codes exist which simulate the exact fields around a mesh with physical sizes. A tracking code based in Matlab-Simulink using field maps generated using finite element software has been developed which tracks electrons or ions through electrostatic wire meshes. The fields around such a geometry are presented as an analytical expression using several basic assumptions, however, it is apparent that computational calculations are required to obtain realistic values of electric potential and fields, particularly when multiple wire meshes are deployed. The tracking code is flexible in that any quantitatively describable particle distribution can be used for both electrons and ions as well as other benefits such as ease of export to other programs for analysis. The code is made freely available and physical examples are highlighted where this code could be beneficial for different applications.
Charged particle tracking through electrostatic wire meshes using the finite element method
Energy Technology Data Exchange (ETDEWEB)
Devlin, L. J.; Karamyshev, O.; Welsch, C. P., E-mail: carsten.welsch@cockcroft.ac.uk [The Cockcroft Institute, Daresbury Laboratory, Warrington (United Kingdom); Department of Physics, University of Liverpool, Liverpool (United Kingdom)
2016-06-15
Wire meshes are used across many disciplines to accelerate and focus charged particles, however, analytical solutions are non-exact and few codes exist which simulate the exact fields around a mesh with physical sizes. A tracking code based in Matlab-Simulink using field maps generated using finite element software has been developed which tracks electrons or ions through electrostatic wire meshes. The fields around such a geometry are presented as an analytical expression using several basic assumptions, however, it is apparent that computational calculations are required to obtain realistic values of electric potential and fields, particularly when multiple wire meshes are deployed. The tracking code is flexible in that any quantitatively describable particle distribution can be used for both electrons and ions as well as other benefits such as ease of export to other programs for analysis. The code is made freely available and physical examples are highlighted where this code could be beneficial for different applications.
MAPVAR - A Computer Program to Transfer Solution Data Between Finite Element Meshes
Energy Technology Data Exchange (ETDEWEB)
Wellman, G.W.
1999-03-01
MAPVAR, as was the case with its precursor programs, MERLIN and MERLIN II, is designed to transfer solution results from one finite element mesh to another. MAPVAR draws heavily from the structure and coding of MERLIN II, but it employs a new finite element data base, EXODUS II, and offers enhanced speed and new capabilities not available in MERLIN II. In keeping with the MERLIN II documentation, the computational algorithms used in MAPVAR are described. User instructions are presented. Example problems are included to demonstrate the operation of the code and the effects of various input options.
Mesh Partitioning Algorithm Based on Parallel Finite Element Analysis and Its Actualization
Directory of Open Access Journals (Sweden)
Lei Zhang
2013-01-01
Full Text Available In parallel computing based on finite element analysis, domain decomposition is a key technique for its preprocessing. Generally, a domain decomposition of a mesh can be realized through partitioning of a graph which is converted from a finite element mesh. This paper discusses the method for graph partitioning and the way to actualize mesh partitioning. Relevant softwares are introduced, and the data structure and key functions of Metis and ParMetis are introduced. The writing, compiling, and testing of the mesh partitioning interface program based on these key functions are performed. The results indicate some objective law and characteristics to guide the users who use the graph partitioning algorithm and software to write PFEM program, and ideal partitioning effects can be achieved by actualizing mesh partitioning through the program. The interface program can also be used directly by the engineering researchers as a module of the PFEM software. So that it can reduce the application of the threshold of graph partitioning algorithm, improve the calculation efficiency, and promote the application of graph theory and parallel computing.
CONVERGENCE OF A MIXED FINITE ELEMENT FOR THE STOKES PROBLEM ON ANISOTROPIC MESHES
Institute of Scientific and Technical Information of China (English)
Qingshan Li; Huixia Sun; Shaochun Chen
2008-01-01
The main aim of this paper is to study the convergence properties of a low order mixed finite element for the Stokes problem under anisotropic meshes. We discuss the anisotropic convergence and superconvergence independent of the aspect ratio. Without the shape regularity assumption and inverse assumption on the meshes, the optimal error estimates and natural superconvergence at central points are obtained. The global superconvergence for the gradient of the velocity and the pressure is derived with the aid of a suitable postprocessing method. Furthermore, we develop a simple method to obtain the superclose properties which improves the results of the previous works.
Institute of Scientific and Technical Information of China (English)
谢小平; 周天孝
2003-01-01
The combined hybrid finite element method is of an intrinsic mechanism of enhancing coarse-mesh-accuracy of lower order displacement schemes. It was confirmed that the combined hybrid scheme without energy error leads to enhancement of accuracy at coarse meshes, and that the combination parameter plays an important role in the enhancement. As an improvement of conforming bilinear Q4-plane element, the combined hybrid method adopted the most convenient quadrilateral displacements-stress mode, i. e.,the mode of compatible isoparametric bilinear displacements and pure constant stresses. By adjusting the combined parameter, the optimized version of the combined hybrid element was obtained and numerical tests indicated that this parameter-adjusted version behaves much better than Q4-element and is of high accuracy at coarse meshes. Due to elimination of stress parameters at the elemental level, this combined hybrid version is of the same computational cost as that of Q4 -element.
A mass-redistributed finite element method (MR-FEM) for acoustic problems using triangular mesh
He, Z. C.; Li, Eric; Liu, G. R.; Li, G. Y.; Cheng, A. G.
2016-10-01
The accuracy of numerical results using standard finite element method (FEM) in acoustic problems will deteriorate with increasing frequency due to the "dispersion error". Such dispersion error depends on the balance between the "stiffness" and "mass" of discretization equation systems. This paper reports an improved finite element method (FEM) for solving acoustic problems by re-distributing the mass in the mass matrix to "tune" the balance, aiming to minimize the dispersion errors. This is done by shifting the integration point locations when computing the entries of the mass matrix, while ensuring the mass conservation. The new method is verified through the detailed numerical error analysis, and a strategy is also proposed for the best mass redistribution in terms of minimizing dispersion error. The relative dispersion error of present mass-redistributed finite element method (MR-FEM) is found to be much smaller than the FEM solution, in both theoretical prediction and numerical examination. The present MR-FEM works well by using the linear triangular elements that can be generated automatically, which enables automation in computation and saving computational cost in mesh generation. Numerical examples demonstrate the advantages of MR-FEM, in comparison with the standard FEM using the same triangular meshes and quadrilateral meshes.
Institute of Scientific and Technical Information of China (English)
Dongyang Shi; Yucheng Peng; Shaochun Chen
2006-01-01
The main aim of this paper is to study the approximation to viscoelasticity type equations with a Crouzeix-Raviart type nonconforming finite element on the anisotropic meshes. The superclose property of the exact solution and the optimal error estimate of its derivative with respect to time are derived by using some novel techniques. Moreover,employing a postprocessing technique, the global superconvergence property for the discretization error of the postprocessed discrete solution to the solution itself is studied.
A 3D moving mesh Finite Element Method for two-phase flows
Anjos, G. R.; Borhani, N.; Mangiavacchi, N.; Thome, J. R.
2014-08-01
A 3D ALE Finite Element Method is developed to study two-phase flow phenomena using a new discretization method to compute the surface tension forces. The computational method is based on the Arbitrary Lagrangian-Eulerian formulation (ALE) and the Finite Element Method (FEM), creating a two-phase method with an improved model for the liquid-gas interface. An adaptive mesh update procedure is also proposed for effective management of the mesh to remove, add and repair elements, since the computational mesh nodes move according to the flow. The ALE description explicitly defines the two-phase interface position by a set of interconnected nodes which ensures a sharp representation of the boundary, including the role of the surface tension. The proposed methodology for computing the curvature leads to accurate results with moderate programming effort and computational cost. Static and dynamic tests have been carried out to validate the method and the results have compared well to analytical solutions and experimental results found in the literature, demonstrating that the new proposed methodology provides good accuracy to describe the interfacial forces and bubble dynamics. This paper focuses on the description of the proposed methodology, with particular emphasis on the discretization of the surface tension force, the new remeshing technique, and the validation results. Additionally, a microchannel simulation in complex geometry is presented for two elongated bubbles.
Bucki, M; Bucki, Marek; Payan, Yohan
2005-01-01
In this paper, we address the problem of automatic mesh generation for finite elements modeling of anatomical organs for which a volumetric data set is available. In the first step a set of characteristic outlines of the organ is defined manually or automatically within the volume. The outlines define the "key frames" that will guide the procedure of surface reconstruction. Then, based on this information, and along with organ surface curvature information extracted from the volume data, a 3D scalar field is generated. This field allows a 3D reconstruction of the organ: as an iso-surface model, using a marching cubes algorithm; or as a 3D mesh, using a grid "immersion" technique, the field value being used as the outside/inside test. The final reconstruction respects the various topological changes that occur within the organ, such as holes and branching elements.
Atlas-Based Automatic Generation of Subject-Specific Finite Element Tongue Meshes.
Bijar, Ahmad; Rohan, Pierre-Yves; Perrier, Pascal; Payan, Yohan
2016-01-01
Generation of subject-specific 3D finite element (FE) models requires the processing of numerous medical images in order to precisely extract geometrical information about subject-specific anatomy. This processing remains extremely challenging. To overcome this difficulty, we present an automatic atlas-based method that generates subject-specific FE meshes via a 3D registration guided by Magnetic Resonance images. The method extracts a 3D transformation by registering the atlas' volume image to the subject's one, and establishes a one-to-one correspondence between the two volumes. The 3D transformation field deforms the atlas' mesh to generate the subject-specific FE mesh. To preserve the quality of the subject-specific mesh, a diffeomorphic non-rigid registration based on B-spline free-form deformations is used, which guarantees a non-folding and one-to-one transformation. Two evaluations of the method are provided. First, a publicly available CT-database is used to assess the capability to accurately capture the complexity of each subject-specific Lung's geometry. Second, FE tongue meshes are generated for two healthy volunteers and two patients suffering from tongue cancer using MR images. It is shown that the method generates an appropriate representation of the subject-specific geometry while preserving the quality of the FE meshes for subsequent FE analysis. To demonstrate the importance of our method in a clinical context, a subject-specific mesh is used to simulate tongue's biomechanical response to the activation of an important tongue muscle, before and after cancer surgery.
Least-squares finite-element scheme for the lattice Boltzmann method on an unstructured mesh.
Li, Yusong; LeBoeuf, Eugene J; Basu, P K
2005-10-01
A numerical model of the lattice Boltzmann method (LBM) utilizing least-squares finite-element method in space and the Crank-Nicolson method in time is developed. This method is able to solve fluid flow in domains that contain complex or irregular geometric boundaries by using the flexibility and numerical stability of a finite-element method, while employing accurate least-squares optimization. Fourth-order accuracy in space and second-order accuracy in time are derived for a pure advection equation on a uniform mesh; while high stability is implied from a von Neumann linearized stability analysis. Implemented on unstructured mesh through an innovative element-by-element approach, the proposed method requires fewer grid points and less memory compared to traditional LBM. Accurate numerical results are presented through two-dimensional incompressible Poiseuille flow, Couette flow, and flow past a circular cylinder. Finally, the proposed method is applied to estimate the permeability of a randomly generated porous media, which further demonstrates its inherent geometric flexibility.
DISCONTINUITY-CAPTURING FINITE ELEMENT COMPUTATION OF UNSTEADY FLOW WITH ADAPTIVE UNSTRUCTURED MESH
Institute of Scientific and Technical Information of China (English)
DONG Genjin; LU Xiyun; ZHUANG Lixian
2004-01-01
A discontinuity-capturing scheme of finite element method (FEM) is proposed. The unstructured-grid technique combined with a new type of adaptive mesh approach is developed for both compressible and incompressible unsteady flows, which exhibits the capability of capturing the shock waves and/or thin shear layers accurately in an unsteady viscous flow at high Reynolds number.In particular, a new testing variable, i.e., the disturbed kinetic energy E, is suggested and used in the adaptive mesh computation, which is universally applicable to the capturing of both shock waves and shear layers in the inviscid flow and viscous flow at high Reynolds number. Based on several calculated examples, this approach has been proved to be effective and efficient for the calculations of compressible and incompressible flows.
A local level set method based on a finite element method for unstructured meshes
Energy Technology Data Exchange (ETDEWEB)
Ngo, Long Cu; Choi, Hyoung Gwon [School of Mechanical Engineering, Seoul National University of Science and Technology, Seoul (Korea, Republic of)
2016-12-15
A local level set method for unstructured meshes has been implemented by using a finite element method. A least-square weighted residual method was employed for implicit discretization to solve the level set advection equation. By contrast, a direct re-initialization method, which is directly applicable to the local level set method for unstructured meshes, was adopted to re-correct the level set function to become a signed distance function after advection. The proposed algorithm was constructed such that the advection and direct reinitialization steps were conducted only for nodes inside the narrow band around the interface. Therefore, in the advection step, the Gauss–Seidel method was used to update the level set function using a node-by-node solution method. Some benchmark problems were solved by using the present local level set method. Numerical results have shown that the proposed algorithm is accurate and efficient in terms of computational time.
Park, B. Y.; Roberts, B. L.; Sobolik, S. R.
2016-12-01
The U.S. Strategic Petroleum Reserve (SPR) stores crude oil in 60 caverns located at four sites located along the Gulf Coast. As a matter of normal operation of caverns in a salt dome, the continuous mechanical creep of salt, along with the change in internal cavern and casing pressure due to cavern closure and fluid exchanges, impose several mechanical conditions on the skin, well, and casing of a cavern that could potentially create damage. Sandia, on behalf of DOE, is evaluating the structural integrity of the salt surrounding existing caverns in the Bayou Choctaw (BC) salt dome in Louisiana. In reality, the geometry, spacing, and depths of the caverns are irregular. It is not easy to realize the naturally and artificially formed cavern and salt dome for numerical analysis. It is harder to convert the geometries into the meshed mass consisting of only hexahedral finite elements. A three-dimensional (3D) finite element mesh capturing realistic geometries of the Bayou Choctaw site has been constructed using the seismic and sonar survey data obtained from the field (see Figures below). The mesh consists of hexahedral elements because the salt constitutive model is coded using hexahedral elements. Techniques to reduce the number of elements as much as possible to save on computer run time while maintaining computational accuracy are also developed. These methodologies could also be applied to construct computational meshes for the Big Hill, Bryan Mound, and West Hackberry SPR sites. The methodology could be applied to the complicated shape masses for not only various civil and geological structures but also biological applications such as artificial limbs. The newly developed mesh is expected to provide more accurate solutions of geotechnical concerns that arise due to the close proximity of the caverns to each other or to the edge of salt. Also, there are nine abandoned caverns, one of which is believed to be in a quasi-stable condition. Stability issues for these
Directory of Open Access Journals (Sweden)
Abdulnaser M. Alshoaibi
2009-01-01
Full Text Available The purpose of this study is on the determination of 2D crack paths and surfaces as well as on the evaluation of the stress intensity factors as a part of the damage tolerant assessment. Problem statement: The evaluation of SIFs and crack tip singular stresses for arbitrary fracture structure are a challenging problem, involving the calculation of the crack path and the crack propagation rates at each step especially under mixed mode loading. Approach: This study was provided a finite element code which produces results comparable to the current available commercial software. Throughout the simulation of crack propagation an automatic adaptive mesh was carried out in the vicinity of the crack front nodes and in the elements which represent the higher stresses distribution. The finite element mesh was generated using the advancing front method. The adaptive remising process carried out based on the posteriori stress error norm scheme to obtain an optimal mesh. The onset criterion of crack propagation was based on the stress intensity factors which provide as the most important parameter that must be accurately estimated. Facilitated by the singular elements, the displacement extrapolation technique is employed to calculate the stress intensity factor. Crack direction is predicted using the maximum circumferential stress theory. The fracture was modeled by the splitting node approach and the trajectory follows the successive linear extensions of each crack increment. The propagation process is driven by Linear Elastic Fracture Mechanics (LEFM approach with minimum user interaction. Results: In evaluating the accuracy of the estimated stress intensity factors and the crack path predictions, the results were compared with sets of experimental data, benchmark analytical solutions as well as numerical results of other researchers. Conclusion/Recommendations: The assessment indicated that the program was highly reliable to evaluate the stress intensity
Danaila, Ionut; Hecht, Frédéric
2009-01-01
to appear in J. Computational Physics; Numerical computations of stationary states of fast-rotating Bose-Einstein condensates require high spatial resolution due to the presence of a large number of quantized vortices. In this paper we propose a low-order finite element method with mesh adaptivity by metric control, as an alternative approach to the commonly used high order (finite difference or spectral) approximation methods. The mesh adaptivity is used with two different numerical algorith...
Danaila, Ionut; Hecht, Frédéric
2010-01-01
Numerical computations of stationary states of fast-rotating Bose-Einstein condensates re- quire high spatial resolution due to the presence of a large number of quantized vortices. In this paper we propose a low-order finite element method with mesh adaptivity by metric con- trol, as an alternative approach to the commonly used high order (finite difference or spectral) approximation methods. The mesh adaptivity is used with two different numerical algorithms to compute stationary vortex sta...
Danaila, Ionut; Hecht, Frédéric
2010-01-01
to appear in J. Computational Physics; Numerical computations of stationary states of fast-rotating Bose-Einstein condensates require high spatial resolution due to the presence of a large number of quantized vortices. In this paper we propose a low-order finite element method with mesh adaptivity by metric control, as an alternative approach to the commonly used high order (finite difference or spectral) approximation methods. The mesh adaptivity is used with two different numerical algorith...
De Corato, M.; Slot, J. J. M.; Hütter, M.; D'Avino, G.; Maffettone, P. L.; Hulsen, M. A.
2016-07-01
In this paper, we present a finite element implementation of fluctuating hydrodynamics with a moving boundary fitted mesh for treating the suspended particles. The thermal fluctuations are incorporated into the continuum equations using the Landau and Lifshitz approach [1]. The proposed implementation fulfills the fluctuation-dissipation theorem exactly at the discrete level. Since we restrict the equations to the creeping flow case, this takes the form of a relation between the diffusion coefficient matrix and friction matrix both at the particle and nodal level of the finite elements. Brownian motion of arbitrarily shaped particles in complex confinements can be considered within the present formulation. A multi-step time integration scheme is developed to correctly capture the drift term required in the stochastic differential equation (SDE) describing the evolution of the positions of the particles. The proposed approach is validated by simulating the Brownian motion of a sphere between two parallel plates and the motion of a spherical particle in a cylindrical cavity. The time integration algorithm and the fluctuating hydrodynamics implementation are then applied to study the diffusion and the equilibrium probability distribution of a confined circle under an external harmonic potential.
Energy Technology Data Exchange (ETDEWEB)
De Corato, M., E-mail: marco.decorato@unina.it [Dipartimento di Ingegneria Chimica, dei Materiali e della Produzione Industriale, Università di Napoli Federico II, Piazzale Tecchio 80, 80125 Napoli (Italy); Slot, J.J.M., E-mail: j.j.m.slot@tue.nl [Department of Mathematics and Computer Science, Eindhoven University of Technology, PO Box 513, 5600 MB Eindhoven (Netherlands); Hütter, M., E-mail: m.huetter@tue.nl [Department of Mechanical Engineering, Eindhoven University of Technology, PO Box 513, 5600 MB Eindhoven (Netherlands); D' Avino, G., E-mail: gadavino@unina.it [Dipartimento di Ingegneria Chimica, dei Materiali e della Produzione Industriale, Università di Napoli Federico II, Piazzale Tecchio 80, 80125 Napoli (Italy); Maffettone, P.L., E-mail: pierluca.maffettone@unina.it [Dipartimento di Ingegneria Chimica, dei Materiali e della Produzione Industriale, Università di Napoli Federico II, Piazzale Tecchio 80, 80125 Napoli (Italy); Hulsen, M.A., E-mail: m.a.hulsen@tue.nl [Department of Mechanical Engineering, Eindhoven University of Technology, PO Box 513, 5600 MB Eindhoven (Netherlands)
2016-07-01
In this paper, we present a finite element implementation of fluctuating hydrodynamics with a moving boundary fitted mesh for treating the suspended particles. The thermal fluctuations are incorporated into the continuum equations using the Landau and Lifshitz approach [1]. The proposed implementation fulfills the fluctuation–dissipation theorem exactly at the discrete level. Since we restrict the equations to the creeping flow case, this takes the form of a relation between the diffusion coefficient matrix and friction matrix both at the particle and nodal level of the finite elements. Brownian motion of arbitrarily shaped particles in complex confinements can be considered within the present formulation. A multi-step time integration scheme is developed to correctly capture the drift term required in the stochastic differential equation (SDE) describing the evolution of the positions of the particles. The proposed approach is validated by simulating the Brownian motion of a sphere between two parallel plates and the motion of a spherical particle in a cylindrical cavity. The time integration algorithm and the fluctuating hydrodynamics implementation are then applied to study the diffusion and the equilibrium probability distribution of a confined circle under an external harmonic potential.
Institute of Scientific and Technical Information of China (English)
SHI Dong-yang; WANG Hui-min; LI Zhi-yan
2009-01-01
A lumped mass approximation scheme of a low order Crouzeix-Raviart type nonconforming triangular finite element is proposed to a kind of nonlinear parabolic integro-differential equations. The L2 error estimate is derived on anisotropic meshes without referring to the traditional nonclassical elliptic projection.
Bishnu P. Lamichhane
2013-01-01
We consider a mixed finite element method for approximating the solution of nearly incompressible elasticity and Stokes equations. The finite element method is based on quadrilateral and hexahedral triangulation using primal and dual meshes. We use the standard bilinear and trilinear finite element space enriched with element-wise defined bubble functions with respect to the primal mesh for the displacement or velocity, whereas the pressure space is discretised by using a piecewise constant f...
Castro-Mateos, Isaac; Pozo, Jose M.; Lazary, Aron; Frangi, Alejandro F.
2016-03-01
Computational medicine aims at developing patient-specific models to help physicians in the diagnosis and treatment selection for patients. The spine, and other skeletal structures, is an articulated object, composed of rigid bones (vertebrae) and non-rigid parts (intervertebral discs (IVD), ligaments and muscles). These components are usually extracted from different image modalities, involving patient repositioning. In the case of the spine, these models require the segmentation of IVDs from MR and vertebrae from CT. In the literature, there exists a vast selection of segmentations methods, but there is a lack of approaches to align the vertebrae and IVDs. This paper presents a method to create patient-specific finite element meshes for biomechanical simulations, integrating rigid and non-rigid parts of articulated objects. First, the different parts are aligned in a complete surface model. Vertebrae extracted from CT are rigidly repositioned in between the IVDs, initially using the IVDs location and then refining the alignment using the MR image with a rigid active shape model algorithm. Finally, a mesh morphing algorithm, based on B-splines, is employed to map a template finite-element (volumetric) mesh to the patient-specific surface mesh. This morphing reduces possible misalignments and guarantees the convexity of the model elements. Results show that the accuracy of the method to align vertebrae into MR, together with IVDs, is similar to that of the human observers. Thus, this method is a step forward towards the automation of patient-specific finite element models for biomechanical simulations.
Energy Technology Data Exchange (ETDEWEB)
Spear, A. D. [Department of Mechanical Engineering, University of Utah, Salt Lake City UT USA; Hochhalter, J. D. [NASA Langley Research Center, Hampton VA USA; Cerrone, A. R. [GE Global Research Center, Niskayuna NY USA; Li, S. F. [Lawrence Livermore National Laboratory, Livermore CA USA; Lind, J. F. [Lawrence Livermore National Laboratory, Livermore CA USA; Suter, R. M. [Department of Physics, Carnegie Mellon University, Pittsburgh PA USA; Ingraffea, A. R. [School of Civil & Environmental Engineering, Cornell University, Ithaca NY USA
2016-04-27
In an effort to reproduce computationally the observed evolution of microstructurally small fatigue cracks (MSFCs), a method is presented for generating conformal, finite-element (FE), volume meshes from 3D measurements of MSFC propagation. The resulting volume meshes contain traction-free surfaces that conform to incrementally measured 3D crack shapes. Grain morphologies measured using near-field high-energy X-ray diffraction microscopy are also represented within the FE volume meshes. Proof-of-concept simulations are performed to demonstrate the utility of the mesh-generation method. The proof-of-concept simulations employ a crystal-plasticity constitutive model and are performed using the conformal FE meshes corresponding to successive crack-growth increments. Although the simulations for each crack increment are currently independent of one another, they need not be, and transfer of material-state information among successive crack-increment meshes is discussed. The mesh-generation method was developed using post-mortem measurements, yet it is general enough that it can be applied to in-situ measurements of 3D MSFC propagation.
Elgeti, Stefanie
2015-01-01
Fluid flow applications can involve a number of coupled problems. One is the simulation of free-surface flows, which require the solution of a free-boundary problem. Within this problem, the governing equations of fluid flow are coupled with a domain deformation approach. This work reviews five of those approaches: interface tracking using a boundary-conforming mesh and, in the interface capturing context, the level-set method, the volume-of-fluid method, particle methods, as well as the phase-field method. The history of each method is presented in combination with the most recent developments in the field. Particularly, the topics of extended finite elements (XFEM) and NURBS-based methods, such as Isogeometric Analysis (IGA), are addressed. For illustration purposes, two applications have been chosen: two-phase flow involving drops or bubbles and sloshing tanks. The challenges of these applications, such as the geometrically correct representation of the free surface or the incorporation of surface tension ...
Institute of Scientific and Technical Information of China (English)
Sutthisak Phongthanapanich; Suthee Traivivatana; Parinya Boonmaruth; Pramote Dechaumphai
2006-01-01
Based on flux-based formulation,a nodeless variable element method is developed to analyze two-dimensional steady-state and transient heat transfer problems.The nodeless variable element employs quadratic interpolation functions to provide higher solution accuracy without necessity to actually generate additional nodes.The flux-based formulation is applied to reduce the complexity in deriving the finite element equations as compared to the conventional finite element method.The solution accuracy is further improved by implementing an adaptive meshing technique to generate finite element mesh that can adapt and move along corresponding to the solution behavior.The technique generates small elements in the regions of steep solution gradients to provide accurate solution,and mean while it generates larger elements in the other regions where the solution gradients are slight to reduce the computational time and the computer memory.The effectiveness of the combined procedure is demonstrated by heat transfer problems that have exact solutions.These problems are:(a) a steady-state heat conduction analysis in a square plate subjected to a highly localized surface heating,and (b) a transient heat conduction analysis in a long pate subjected to a moving heat source.
Energy Technology Data Exchange (ETDEWEB)
Lipnikov, Konstantin [Los Alamos National Laboratory; Agouzal, Abdellatif [UNIV DE LYON; Vassilevski, Yuri [Los Alamos National Laboratory
2009-01-01
We present a new technology for generating meshes minimizing the interpolation and discretization errors or their gradients. The key element of this methodology is construction of a space metric from edge-based error estimates. For a mesh with N{sub h} triangles, the error is proportional to N{sub h}{sup -1} and the gradient of error is proportional to N{sub h}{sup -1/2} which are optimal asymptotics. The methodology is verified with numerical experiments.
Adaptive Meshing Technique Applied to an Orthopaedic Finite Element Contact Problem
Roarty, Colleen M; Grosland, Nicole M.
2004-01-01
Finite element methods have been applied extensively and with much success in the analysis of orthopaedic implants.6,7,12,13,15 Recently a growing interest has developed, in the orthopaedic biomechanics community, in how numerical models can be constructed for the optimal solution of problems in contact mechanics. New developments in this area are of paramount importance in the design of improved implants for orthopaedic surgery. Finite element and other computational techniques are widely ap...
Gonzales, Matthew J; Sturgeon, Gregory; Krishnamurthy, Adarsh; Hake, Johan; Jonas, René; Stark, Paul; Rappel, Wouter-Jan; Narayan, Sanjiv M; Zhang, Yongjie; Segars, W Paul; McCulloch, Andrew D
2013-07-01
High-order cubic Hermite finite elements have been valuable in modeling cardiac geometry, fiber orientations, biomechanics, and electrophysiology, but their use in solving three-dimensional problems has been limited to ventricular models with simple topologies. Here, we utilized a subdivision surface scheme and derived a generalization of the "local-to-global" derivative mapping scheme of cubic Hermite finite elements to construct bicubic and tricubic Hermite models of the human atria with extraordinary vertices from computed tomography images of a patient with atrial fibrillation. To an accuracy of 0.6 mm, we were able to capture the left atrial geometry with only 142 bicubic Hermite finite elements, and the right atrial geometry with only 90. The left and right atrial bicubic Hermite meshes were G1 continuous everywhere except in the one-neighborhood of extraordinary vertices, where the mean dot products of normals at adjacent elements were 0.928 and 0.925. We also constructed two biatrial tricubic Hermite models and defined fiber orientation fields in agreement with diagrammatic data from the literature using only 42 angle parameters. The meshes all have good quality metrics, uniform element sizes, and elements with aspect ratios near unity, and are shared with the public. These new methods will allow for more compact and efficient patient-specific models of human atrial and whole heart physiology. Copyright © 2013 Elsevier B.V. All rights reserved.
Cai, Hongzhu; Hu, Xiangyun; Li, Jianhui; Endo, Masashi; Xiong, Bin
2017-02-01
We solve the 3D controlled-source electromagnetic (CSEM) problem using the edge-based finite element method. The modeling domain is discretized using unstructured tetrahedral mesh. We adopt the total field formulation for the quasi-static variant of Maxwell's equation and the computation cost to calculate the primary field can be saved. We adopt a new boundary condition which approximate the total field on the boundary by the primary field corresponding to the layered earth approximation of the complicated conductivity model. The primary field on the modeling boundary is calculated using fast Hankel transform. By using this new type of boundary condition, the computation cost can be reduced significantly and the modeling accuracy can be improved. We consider that the conductivity can be anisotropic. We solve the finite element system of equations using a parallelized multifrontal solver which works efficiently for multiple source and large scale electromagnetic modeling.
Bibel, George; Lewicki, David G. (Technical Monitor)
2002-01-01
A procedure was developed to perform tooth contact analysis between a face gear meshing with a spur pinion using finite element analysis. The face gear surface points from a previous analysis were used to create a connected tooth solid model without gaps or overlaps. The face gear surface points were used to create a five tooth face gear Patran model (with rim) using Patran PCL commands. These commands were saved in a series of session files suitable for Patran input. A four tooth spur gear that meshes with the face gear was designed and constructed with Patran PCL commands. These commands were also saved in a session files suitable for Patran input. The orientation of the spur gear required for meshing with the face gear was determined. The required rotations and translations are described and built into the session file for the spur gear. The Abaqus commands for three-dimensional meshing were determined and verified for a simplified model containing one spur tooth and one face gear tooth. The boundary conditions, loads, and weak spring constraints were determined to make the simplified model work. The load steps and load increments to establish contact and obtain a realistic load was determined for the simplified two tooth model. Contact patterns give some insight into required mesh density. Building the two gears in two different local coordinate systems and rotating the local coordinate systems was verified as an easy way to roll the gearset through mesh. Due to limitation of swap space, disk space and time constraints of the summer period, the larger model was not completed.
Institute of Scientific and Technical Information of China (English)
Jun Liu; Zheng Nan; Ping Yi
2012-01-01
In the last decade,three dimensional discontinuous deformation analyses (3D DDA) has attracted more and more attention of researchers and geotechnical engineers worldwide.The original DDA formulation utilizes a linear displacement function to describe the block movement and deformation,which would cause block expansion under rigid body rotation and thus limit its capability to model block deformation.In this paper,3D DDA is coupled with tetrahedron finite elements to tackle these two problems.Tetrahedron is the simplest in the 3D domain and makes it easy to implement automatic discretization,even for complex topology shape.Furthermore,element faces will remain planar and element edges will remain straight after deformation for tetrahedron finite elements and polyhedral contact detection schemes can be used directly.The matrices of equilibrium equations for this coupled method are given in detail and an effective contact searching algorithm is suggested.Validation is conducted by comparing the results of the proposed coupled method with that of physical model tests using one of the most common failure modes,i.e.,wedge failure.Most of the failure modes predicted by the coupled method agree with the physical model results except for 4 cases out of the total 65 cases.Finally,a complex rockslide example demonstrates the robustness and versatility of the coupled method.
Energy Technology Data Exchange (ETDEWEB)
Svyatskiy, Daniil [Los Alamos National Laboratory; Shashkov, Mikhail [Los Alamos National Laboratory; Kuzmin, D [DORTMUND UNIV
2008-01-01
A new approach to the design of constrained finite element approximations to second-order elliptic problems is introduced. This approach guarantees that the finite element solution satisfies the discrete maximum principle (DMP). To enforce these monotonicity constrains the sufficient conditions for elements of the stiffness matrix are formulated. An algebraic splitting of the stiffness matrix is employed to separate the contributions of diffusive and antidiffusive numerical fluxes, respectively. In order to prevent the formation of spurious undershoots and overshoots, a symmetric slope limiter is designed for the antidiffusive part. The corresponding upper and lower bounds are defined using an estimate of the steepest gradient in terms of the maximum and minimum solution values at surrounding nodes. The recovery of nodal gradients is performed by means of a lumped-mass L{sub 2} projection. The proposed slope limiting strategy preserves the consistency of the underlying discrete problem and the structure of the stiffness matrix (symmetry, zero row and column sums). A positivity-preserving defect correction scheme is devised for the nonlinear algebraic system to be solved. Numerical results and a grid convergence study are presented for a number of anisotropic diffusion problems in two space dimensions.
A parallel geometric multigrid method for finite elements on octree meshes
Energy Technology Data Exchange (ETDEWEB)
Sampath, Rahul S [ORNL; Biros, George [University of Texas, Austin
2010-01-01
In this article, we present a parallel geometric multigrid algorithm for solving variable-coefficient elliptic partial differential equations on the unit box (with Dirichlet or Neumann boundary conditions) using highly nonuniform, octree-based, conforming finite element discretizations. Our octrees are 2:1 balanced, that is, we allow no more than one octree-level difference between octants that share a face, edge, or vertex. We describe a parallel algorithm whose input is an arbitrary 2:1 balanced fine-grid octree and whose output is a set of coarser 2:1 balanced octrees that are used in the multigrid scheme. Also, we derive matrix-free schemes for the discretized finite element operators and the intergrid transfer operations. The overall scheme is second-order accurate for sufficiently smooth right-hand sides and material properties; its complexity for nearly uniform trees is {Omicron}(N/n{sub p} log N/n{sub p}) + {Omicron}(n{sub p} log n{sub p}), where N is the number of octree nodes and n{sub p} is the number of processors. Our implementation uses the Message Passing Interface standard. We present numerical experiments for the Laplace and Navier (linear elasticity) operators that demonstrate the scalability of our method. Our largest run was a highly nonuniform, 8-billion-unknown, elasticity calculation using 32,000 processors on the Teragrid system, 'Ranger,' at the Texas Advanced Computing Center. Our implementation is publically available in the Dendro library, which is built on top of the PETSc library from Argonne National Laboratory.
Kimura, Satoshi; Candy, Adam S.; Holland, Paul R.; Piggott, Matthew D.; Jenkins, Adrian
2013-07-01
Several different classes of ocean model are capable of representing floating glacial ice shelves. We describe the incorporation of ice shelves into Fluidity-ICOM, a nonhydrostatic finite-element ocean model with the capacity to utilize meshes that are unstructured and adaptive in three dimensions. This geometric flexibility offers several advantages over previous approaches. The model represents melting and freezing on all ice-shelf surfaces including vertical faces, treats the ice shelf topography as continuous rather than stepped, and does not require any smoothing of the ice topography or any of the additional parameterisations of the ocean mixed layer used in isopycnal or z-coordinate models. The model can also represent a water column that decreases to zero thickness at the 'grounding line', where the floating ice shelf is joined to its tributary ice streams. The model is applied to idealised ice-shelf geometries in order to demonstrate these capabilities. In these simple experiments, arbitrarily coarsening the mesh outside the ice-shelf cavity has little effect on the ice-shelf melt rate, while the mesh resolution within the cavity is found to be highly influential. Smoothing the vertical ice front results in faster flow along the smoothed ice front, allowing greater exchange with the ocean than in simulations with a realistic ice front. A vanishing water-column thickness at the grounding line has little effect in the simulations studied. We also investigate the response of ice shelf basal melting to variations in deep water temperature in the presence of salt stratification.
有限元混合网格的压缩%Compression of finite element hybrid mesh
Institute of Scientific and Technical Information of China (English)
曾建江; 陈文亮; 翟建军
2005-01-01
A method for encoding and compressing finite element models is proposed.The model may be various non-simple topological structures and contain any combinations of beams,triangular elements and quadrilateral elements.First the model is subdivided into simple meshes that are orientable and manifold.Based on the Edgebreaker algorithm,13 labelled pairs are introduced for quadrilateral meshes and five other labelled pairs are introduced for triangles.Then the connectivity information of mixed triangle/quadrilateral meshes is coded in a direct manner.Two other bits are used to record the wireframe information.For the pure wireframe model,Taubin s method is extended to compress it.The compression algorithm is implemented and evaluated.Experiments with several models show that the method achieves excellent compression ratios.%提出了一个对有限元模型进行编码压缩的方法.该模型的拓扑结构可以是任意型式,允许包含四边形单元、三角形单元和梁(杆)单元.有限元模型首先分解成一系列的可定向的流形模型.基于Edgebreaker算法,针对四边形网格遍历的情况引入13对标记,同时对混合网格中的三角形用5对标记来表示.这样,混合网格的连接信息可以采用一种直接的方式进行编码.然后再使用2比特位记录模型中的线框信息.对于完全线框模型,采用扩展后的Taubin方法进行压缩.该压缩算法已经实现并进行了测试.多个复杂模型的压缩实验表明该方法具有很好的压缩效率.
Pearson, Ian T.; Mottram, J. Toby
2012-01-01
A new modelling methodology is presented that enables the stiffness of adhesively bonded single lap-joints to be included in the finite element analysis of whole vehicle bodies. This work was driven by the need to significantly reduce computing resources for vehicle analysis. To achieve this goal the adhesive bond line and adherends are modelled by a relatively ‘small’ number of shell elements to replace the usual solid element mesh for a reliable analysis. Previous work in Part 1 has provide...
Sarkis, C.; Silva, L.; Gandin, Ch-A.; Plapp, M.
2016-03-01
Dendritic growth is computed with automatic adaptation of an anisotropic and unstructured finite element mesh. The energy conservation equation is formulated for solid and liquid phases considering an interface balance that includes the Gibbs-Thomson effect. An equation for a diffuse interface is also developed by considering a phase field function with constant negative value in the liquid and constant positive value in the solid. Unknowns are the phase field function and a dimensionless temperature, as proposed by [1]. Linear finite element interpolation is used for both variables, and discretization stabilization techniques ensure convergence towards a correct non-oscillating solution. In order to perform quantitative computations of dendritic growth on a large domain, two additional numerical ingredients are necessary: automatic anisotropic unstructured adaptive meshing [2,[3] and parallel implementations [4], both made available with the numerical platform used (CimLib) based on C++ developments. Mesh adaptation is found to greatly reduce the number of degrees of freedom. Results of phase field simulations for dendritic solidification of a pure material in two and three dimensions are shown and compared with reference work [1]. Discussion on algorithm details and the CPU time will be outlined.
Kashefi, A
2016-01-01
Coarse grid projection (CGP) methodology is a novel multigrid method for systems involving decoupled nonlinear evolution equations and linear elliptic Poisson equations. The nonlinear equations are solved on a fine grid and the linear equations are solved on a corresponding coarsened grid. Mapping operators execute data transfer between the grids. The CGP framework is constructed upon spatial and temporal discretization schemes. This framework has been established for finite volume/difference discretizations as well as explicit time integration methods. In this article we present for the first time a version of CGP for finite element discretizations, which uses a semi-implicit time integration scheme. The mapping functions correspond to the finite-element shape functions. With the novel data structure introduced, the mapping computational cost becomes insignificant. We apply CGP to pressure-correction schemes used for the incompressible Navier-Stokes flow computations. This version is validated on standard te...
Salinas, P.; Jackson, M.; Pavlidis, D.; Pain, C.; Adam, A.; Xie, Z.; Percival, J. R.
2015-12-01
We present a new, high-order, control-volume-finite-element (CVFE) method with discontinuous representation for pressure and velocity to simulate multiphase flow in heterogeneous porous media. Time is discretized using an adaptive, fully implicit method. Heterogeneous geologic features are represented as volumes bounded by surfaces. Within these volumes, termed geologic domains, the material properties are constant. A given model typically contains numerous such geologic domains. Our approach conserves mass and does not require the use of CVs that span domain boundaries. Computational efficiency is increased by use of dynamic mesh optimization, in which an unstructured mesh adapts in space and time to key solution fields, such as pressure, velocity or saturation, whilst preserving the geometry of the geologic domains. Up-, cross- or down-scaling of material properties during mesh optimization is not required, as the properties are uniform within each geologic domain. We demonstrate that the approach, amongst other features, accurately preserves sharp saturation changes associated with high aspect ratio geologic domains such as fractures and mudstones, allowing efficient simulation of flow in highly heterogeneous models. Moreover, accurate solutions are obtained at significantly lower computational cost than an equivalent fine, fixed mesh and conventional CVFE methods. The use of implicit time integration allows the method to efficiently converge using highly anisotropic meshes without having to reduce the time-step. The work is significant for two key reasons. First, it resolves a long-standing problem associated with the use of classical CVFE methods to model flow in highly heterogeneous porous media, in which CVs span boundaries between domains of contrasting material properties. Second, it reduces computational cost/increases solution accuracy through the use of dynamic mesh optimization and time-stepping with large Courant number.
Institute of Scientific and Technical Information of China (English)
Wei Gao; Ru-Xun Liu; Hong Li
2012-01-01
This paper proposes a hybrid vertex-centered finite volume/finite element method for sol ution of the two dimensional (2D) incompressible Navier-Stokes equations on unstructured grids.An incremental pressure fractional step method is adopted to handle the velocity-pressure coupling.The velocity and the pressure are collocated at the node of the vertex-centered control volume which is formed by joining the centroid of cells sharing the common vertex.For the temporal integration of the momentum equations,an implicit second-order scheme is utilized to enhance the computational stability and eliminate the time step limit due to the diffusion term.The momentum equations are discretized by the vertex-centered finite volume method (FVM) and the pressure Poisson equation is solved by the Galerkin finite element method (FEM).The momentum interpolation is used to damp out the spurious pressure wiggles.The test case with analytical solutions demonstrates second-order accuracy of the current hybrid scheme in time and space for both velocity and pressure.The classic test cases,the lid-driven cavity flow,the skew cavity flow and the backward-facing step flow,show that numerical results are in good agreement with the published benchmark solutions.
Directory of Open Access Journals (Sweden)
Hamid R. Nikraz
2007-01-01
Full Text Available Fracture mechanics is a branch of mechanics, which deals with the cracked body. Every construction material that currently in use inevitably is not flawless. The pre-existing crack may grow to cause structure failure due to low stress, which acts to a structure. Stress intensity factor (K is a single parameter in fracture mechanics, which can be used to examine if a crack, would propagate in a cracked structure under particular loading condition. Finite element method is used to analyze the cracked body to provide the displacements data around the crack tip (at quarter point elements due to load prescribed, for stress intensity factor determination. Two methods of stress intensity factor calculation, Quarter Point Displacement Technique (QPDT and Displacement Correlation Technique (DCT, were evaluated. A series of standard fracture testing were undertaken to provide the fracture load data (Pf, which coupled with the stress intensity factor analytical formula to calculate fracture toughness. The results showed that under a particular mesh arrangement, the result of finite element analysis could deviate from the analytical formula calculation result. The QPDT method is suitable for compact tension specimen but DCT seemed to be not. For cracked beam analysis, the QPDT and DCT calculations were in good agreement with the analytical formula as long as coupled with the appropriate mesh arrangement around the crack tip.
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.
CONVERGENCE ANALYSIS FOR A NONCONFORMING MEMBRANE ELEMENT ON ANISOTROPIC MESHES
Institute of Scientific and Technical Information of China (English)
Dong-yang Shi; Shao-chun Chen; Ichiro Hagiwara
2005-01-01
Regular assumption of finite element meshes is a basic condition of most analysis of finite element approximations both for conventional conforming elements and nonconforming elements. The aim of this paper is to present a novel approach of dealing with the approximation of a four-degree nonconforming finite element for the second order elliptic problems on the anisotropic meshes. The optimal error estimates of energy norm and L2-norm without the regular assumption or quasi-uniform assumption are obtained based on some new special features of this element discovered herein. Numerical results are given to demonstrate validity of our theoretical analysis.
Institute of Scientific and Technical Information of China (English)
林甲富; 林群
2004-01-01
In this paper, superconvergence of the lowest order Raviart-Thomas mixed finite element approximation for second order Neumann boundary value problem on fishbone shape meshes is analyzed. The main term of the error between the exact solution and the finite element interpolating function is determined by Bramble-Hilbert lemma on the individual finite element. A part of the main term of the error on two adjacent finite elements can be cancelled along the special direction, and thus the higher order error estimate is obtained on the whole domain by summation. Compared with the general finite element error estimate,the convergence rate can be increased from order one to order two in L2-norm by postprocessing superconvergence technique.
基于三角形连接的有限元网格划分%Finite Element Mesh Division Based on Triangle Conjunction
Institute of Scientific and Technical Information of China (English)
许文彬; 张华良
2011-01-01
文中创新地提出了三角形连接的有限元网格划分的算法,但是三角形并不是有限元计算的基本单元,而是根据已经生成的三角形生成较为规整的四边形.在实际的项目过程中,创新地提出了三种有效的算法,并利用C++面向对象的MFC程序设计和编写.本程序可以从模型文件读取边界以及点约束和线约束特征数据,程序自动计算出一个较为合理的边界间距值,并且根据需要人工或自动选择一种划分算法,从而自动完成高质量的四边形网格划分.三种算法皆可以处理大量数据点和线,并且划分速度较为高效.本程序模块成功应用于有限元计算软件中.%Creatively proposed the finite element mesh division method based on triangle conjunction. However, the created triangles are not the basic units of the finite calculation. The created triangles will generate regular quadrilaterals. In the real projects,creatively put forwards three effective algorithms and use C++ object-oriented designing method and MFC framework to programme the algorithm. This programme can read boundary information, point restrain and line restrain datas from the model file. The programme will calculate a reasonable boundary interval,and then select a division algorithm manually or automatically, thus complete the high-qualified quadrilateral mesh division. Three algorithms can deal large amount of point and line data,meanwhile, the division speed is highly effective. Finally, this programme module has been successfully applied to the finite element calculation software.
Institute of Scientific and Technical Information of China (English)
吴景珠; 石东洋
2005-01-01
In this paper, the nonconforming mortar finite element with a class of meshes is studied without considering the global regularity condition or quasi-uniformly assumption.Meanwhile, the superclose result coincides with conventional methods is obtained by means of integral identities techniques.
Institute of Scientific and Technical Information of China (English)
杨乔; 石东洋
2006-01-01
In this paper we mainly discuss the nonconforming finite element method for second order elliptic boundary value problems on anisotropic meshes. By changing the discretization form(i.e., by use of numerical quadrature in the procedure of computing the left load ), we obtain the optimal estimate O(h), which is as same as in the traditional finite element analysis when the load f∈H1(Ω)∩C0(Ω) which is weaker than the previous studies. The results obtained in this paper are also valid to the conforming triangular element and nonconforming Carey's element.
The finite cell method for polygonal meshes: poly-FCM
Duczek, Sascha; Gabbert, Ulrich
2016-10-01
In the current article, we extend the two-dimensional version of the finite cell method (FCM), which has so far only been used for structured quadrilateral meshes, to unstructured polygonal discretizations. Therefore, the adaptive quadtree-based numerical integration technique is reformulated and the notion of generalized barycentric coordinates is introduced. We show that the resulting polygonal (poly-)FCM approach retains the optimal rates of convergence if and only if the geometry of the structure is adequately resolved. The main advantage of the proposed method is that it inherits the ability of polygonal finite elements for local mesh refinement and for the construction of transition elements (e.g. conforming quadtree meshes without hanging nodes). These properties along with the performance of the poly-FCM are illustrated by means of several benchmark problems for both static and dynamic cases.
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.
Unified Framework for Finite Element Assembly
Alnæs, Martin Sandve; Mardal, Kent-Andre; Skavhaug, Ola; Langtangen, Hans Petter; 10.1504/IJCSE.2009.029160
2012-01-01
At the heart of any finite element simulation is the assembly of matrices and vectors from discrete variational forms. We propose a general interface between problem-specific and general-purpose components of finite element programs. This interface is called Unified Form-assembly Code (UFC). A wide range of finite element problems is covered, including mixed finite elements and discontinuous Galerkin methods. We discuss how the UFC interface enables implementations of variational form evaluation to be independent of mesh and linear algebra components. UFC does not depend on any external libraries, and is released into the public domain.
DOLFIN: Automated Finite Element Computing
Logg, Anders; 10.1145/1731022.1731030
2011-01-01
We describe here a library aimed at automating the solution of partial differential equations using the finite element method. By employing novel techniques for automated code generation, the library combines a high level of expressiveness with efficient computation. Finite element variational forms may be expressed in near mathematical notation, from which low-level code is automatically generated, compiled and seamlessly integrated with efficient implementations of computational meshes and high-performance linear algebra. Easy-to-use object-oriented interfaces to the library are provided in the form of a C++ library and a Python module. This paper discusses the mathematical abstractions and methods used in the design of the library and its implementation. A number of examples are presented to demonstrate the use of the library in application code.
Finite elements 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
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.
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.
System Supporting Automatic Generation of Finite Element Using Image Information
Institute of Scientific and Technical Information of China (English)
J; Fukuda
2002-01-01
A mesh generating system has been developed in orde r to prepare large amounts of input data which are needed for easy implementation of a finite element analysis. This system consists of a Pre-Mesh Generator, an Automatic Mesh Generator and a Mesh Modifier. Pre-Mesh Generator produces the shape and sub-block information as input data of Automatic Mesh Generator by c arrying out various image processing with respect to the image information of th e drawing input using scanner. Automatic Mesh Generato...
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.
A finite element parametric modeling technique of aircraft wing structures
Institute of Scientific and Technical Information of China (English)
Tang Jiapeng; Xi Ping; Zhang Baoyuan; Hu Bifu
2013-01-01
A finite element parametric modeling method of aircraft wing structures is proposed in this paper because of time-consuming characteristics of finite element analysis pre-processing. The main research is positioned during the preliminary design phase of aircraft structures. A knowledge-driven system of fast finite element modeling is built. Based on this method, employing a template parametric technique, knowledge including design methods, rules, and expert experience in the process of modeling is encapsulated and a finite element model is established automatically, which greatly improves the speed, accuracy, and standardization degree of modeling. Skeleton model, geometric mesh model, and finite element model including finite element mesh and property data are established on parametric description and automatic update. The outcomes of research show that the method settles a series of problems of parameter association and model update in the pro-cess of finite element modeling which establishes a key technical basis for finite element parametric analysis and optimization design.
准双曲面齿轮动态啮合性能的有限元分析研究%Finite element analysis for dynamic meshing of a pair of hypoid gears
Institute of Scientific and Technical Information of China (English)
唐进元; 彭方进
2011-01-01
研究准双曲面齿轮动态啮合有限元分析模型的构建方法,建立了合理的有限元模型.基于接触动力学的基本理论和显式有限元分析方法,对准双曲面齿轮的动态啮合性能进行了研究,得到啮合接触冲击特性、齿面接触区域、齿面接触应力及齿根弯曲应力等在轮齿动态啮合过程中的变化规律.以转速和负载两个典型的工作条件为变量,建立对比分析模型,研究转速和负载对准双曲面齿轮动态啮合性能的影响.转速对准双曲面齿轮动态啮合性能影响显著,而负载对准双面齿轮的动态啮合性能影响则跟转速有关,随着转速的增大,相同的负载变化对动态啮合性能的影响逐渐减弱.%The method to build a finite element model for dynamic meshing analysis of a pair of hypoid gears was discussed. A reasonable finite element model was introduced. Based on the theory of nonlinear dynamics and finite element explicit algorithm, the characteristics of the hypoid gears in dynamic meshing were studied. The laws of gear motion, the contact area, the contact stress and the tooth root bending stress in dynamic meshing of hypoid gears were obtained. The two typical working factors; votating speed and load were taken as variables. The influences of rotating speed and load on the dynamic meshing characteristics were discussed. The contrast study showed that rotational speed has an obvious influence on the characteristics of the hypoid gears in dynamic meshing, and the influence of load is related to the rotational speed; as the rotational speed increases, the influence of the same load change on the dynamic meshing characteristics gradually decreases.
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.
A coarse-mesh nodal method-diffusive-mesh finite difference method
Energy Technology Data Exchange (ETDEWEB)
Joo, H.; Nichols, W.R.
1994-05-01
Modern nodal methods have been successfully used for conventional light water reactor core analyses where the homogenized, node average cross sections (XSs) and the flux discontinuity factors (DFs) based on equivalence theory can reliably predict core behavior. For other types of cores and other geometries characterized by tightly-coupled, heterogeneous core configurations, the intranodal flux shapes obtained from a homogenized nodal problem may not accurately portray steep flux gradients near fuel assembly interfaces or various reactivity control elements. This may require extreme values of DFs (either very large, very small, or even negative) to achieve a desired solution accuracy. Extreme values of DFs, however, can disrupt the convergence of the iterative methods used to solve for the node average fluxes, and can lead to a difficulty in interpolating adjacent DF values. Several attempts to remedy the problem have been made, but nothing has been satisfactory. A new coarse-mesh nodal scheme called the Diffusive-Mesh Finite Difference (DMFD) technique, as contrasted with the coarse-mesh finite difference (CMFD) technique, has been developed to resolve this problem. This new technique and the development of a few-group, multidimensional kinetics computer program are described in this paper.
Error computation for adaptive finite element analysis
Khan, A A; Memon, I R; Ming, X Y
2002-01-01
The paper gives a simple numerical procedure for computations of errors generated by the discretisation process of finite element method. The procedure given is based on the ZZ error estimator which is believed to be reasonable accurate and thus can be readily implemented in any existing finite element codes. The devised procedure not only estimates the global energy norm error but also evaluates the local errors in individual elements. In the example, the given procedure is combined with an adaptive refinement procedure, which provides guidance for optimal mesh designing and allows the user to obtain a desired accuracy with a limited number of interaction. (author)
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.
The Application of Mesh Variables Mapping to Finite Element Analysis%网格变量映射方法在有限元分析中的应用
Institute of Scientific and Technical Information of China (English)
李洲; 杨旭静
2012-01-01
The stamping forming and crash simulations of vehicle body panels have different requirements on the mesh of finite element analysis model. For achieving the transfer of variables between different types of mesh model, a new mesh variables mapping technique based on inverse isoparametric mapping algorithm is proposed, in which the real state variables ( such as thickness, stress and strain) of panel after the change in material properties during sheet metal forming process are accurately mapped into the model for crash simulation by accurately locating the nodes of crash simulation model in stamping model and the interpolation of node variables between mesh models. This method is applied to the crash simulation for a car front bumper and the results show that the method can well realize the mesh preprocessing in finite element analysis and accurately transfer mesh variables, while introducing stamping effects into crash simulation and hence improve the efficiency and accuracy of vehicle crash simulation.%汽车车身零件的冲压成形和碰撞两种仿真对有限元模型网格的要求不同.为了实现不同类型网格模型之间变量的传递,提出了一种基于等参元逆变换的网格变量映射新方法.该方法通过碰撞模型节点在冲压模型中的精确定位和网格模型之间节点变量的插值,将板料冲压过程中材料性能变化后的实际状态变量(如厚度、应力和应变)精确映射到碰撞仿真模型中.将该方法应用于某轿车前保险杠碰撞仿真的结果表明,该映射方法能很好地实现有限元分析的网格前处理,在精确传递网格变量的同时将冲压效应引入碰撞仿真中,从而提高汽车碰撞仿真的效率和精度.
Trew, Mark L; Smaill, Bruce H; Bullivant, David P; Hunter, Peter J; Pullan, Andrew J
2005-12-01
A generalized finite difference (GFD) method is presented that can be used to solve the bi-domain equations modeling cardiac electrical activity. Classical finite difference methods have been applied by many researchers to the bi-domain equations. However, these methods suffer from the limitation of requiring computational meshes that are structured and orthogonal. Finite element or finite volume methods enable the bi-domain equations to be solved on unstructured meshes, although implementations of such methods do not always cater for meshes with varying element topology. The GFD method solves the bi-domain equations on arbitrary and irregular computational meshes without any need to specify element basis functions. The method is useful as it can be easily applied to activation problems using existing meshes that have originally been created for use by finite element or finite difference methods. In addition, the GFD method employs an innovative approach to enforcing nodal and non-nodal boundary conditions. The GFD method performs effectively for a range of two and three-dimensional test problems and when computing bi-domain electrical activation moving through a fully anisotropic three-dimensional model of canine ventricles.
Scalable, Finite Element Analysis of Electromagnetic Scattering and Radiation
Cwik, T.; Lou, J.; Katz, D.
1997-01-01
In this paper a method for simulating electromagnetic fields scattered from complex objects is reviewed; namely, an unstructured finite element code that does not use traditional mesh partitioning algorithms.
Sarakorn, Weerachai
2017-04-01
In this research, the finite element (FE) method incorporating quadrilateral elements for solving 2-D MT modeling was presented. The finite element software was developed, employing a paving algorithm to generate the unstructured quadrilateral mesh. The accuracy, efficiency, reliability, and flexibility of our FE forward modeling are presented, compared and discussed. The numerical results indicate that our FE codes using an unstructured quadrilateral mesh provide good accuracy when the local mesh refinement is applied around sites and in the area of interest, with superior results when compared to other FE methods. The reliability of the developed codes was also confirmed when comparing both analytical solutions and COMMEMI2D model. Furthermore, our developed FE codes incorporating an unstructured quadrilateral mesh showed useful and powerful features such as handling irregular and complex subregions and providing local refinement of the mesh for a 2-D domain as closely as unstructured triangular mesh but it requires less number of elements in a mesh.
Footbridge between finite volumes and finite elements with applications to CFD
Pascal, Frédéric; Ghidaglia, Jean-Michel
2001-12-01
The aim of this paper is to introduce a new algorithm for the discretization of second-order elliptic operators in the context of finite volume schemes on unstructured meshes. We are strongly motivated by partial differential equations (PDEs) arising in computational fluid dynamics (CFD), like the compressible Navier-Stokes equations. Our technique consists of matching up a finite volume discretization based on a given mesh with a finite element representation on the same mesh. An inverse operator is also built, which has the desirable property that in the absence of diffusion, one recovers exactly the finite volume solution. Numerical results are also provided. Copyright
Experimental Finite Element Approach for Stress Analysis
Directory of Open Access Journals (Sweden)
Ahmet Erklig
2014-01-01
Full Text Available This study aims to determining the strain gauge location points in the problems of stress concentration, and it includes both experimental and numerical results. Strain gauges were proposed to be positioned to corresponding locations on beam and blocks to related node of elements of finite element models. Linear and nonlinear cases were studied. Cantilever beam problem was selected as the linear case to approve the approach and conforming contact problem was selected as the nonlinear case. An identical mesh structure was prepared for the finite element and the experimental models. The finite element analysis was carried out with ANSYS. It was shown that the results of the experimental and the numerical studies were in good agreement.
On Using Particle Finite Element for Hydrodynamics Problems Solving
Directory of Open Access Journals (Sweden)
E. V. Davidova
2015-01-01
Full Text Available The aim of the present research is to develop software for the Particle Finite Element Method (PFEM and its verification on the model problem of viscous incompressible flow simulation in a square cavity. The Lagrangian description of the medium motion is used: the nodes of the finite element mesh move together with the fluid that allows to consider them as particles of the medium. Mesh cells deform when in time-stepping procedure, so it is necessary to reconstruct the mesh to provide stability of the finite element numerical procedure.Meshing algorithm allows us to obtain the mesh, which satisfies the Delaunay criteria: it is called \\the possible triangles method". This algorithm is based on the well-known Fortune method of Voronoi diagram constructing for a certain set of points in the plane. The graphical representation of the possible triangles method is shown. It is suitable to use generalization of Delaunay triangulation in order to construct meshes with polygonal cells in case of multiple nodes close to be lying on the same circle.The viscous incompressible fluid flow is described by the Navier | Stokes equations and the mass conservation equation with certain initial and boundary conditions. A fractional steps method, which allows us to avoid non-physical oscillations of the pressure, provides the timestepping procedure. Using the finite element discretization and the Bubnov | Galerkin method allows us to carry out spatial discretization.For form functions calculation of finite element mesh with polygonal cells, \
A geometric toolbox for tetrahedral finite element partitions
Brandts, J.; Korotov, S.; Křížek, M.; Axelsson, O.; Karátson, J.
2011-01-01
In this work we present a survey of some geometric results on tetrahedral partitions and their refinements in a unified manner. They can be used for mesh generation and adaptivity in practical calculations by the finite element method (FEM), and also in theoretical finite element (FE) analysis. Spec
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.
THE SUPERCONVERGENCE ANALYSIS OF AN ANISOTROPIC FINITE ELEMENT
Institute of Scientific and Technical Information of China (English)
SHI Dongyang; ZHU Huiqing
2005-01-01
This paper deals with the high accuracy analysis of bilinear finite element on the class of anisotropic rectangular meshes. The inverse inequalities on anisotropic meshes are established. The superclose and the superconvergence are obtained for the second order elliptic problem. A numerical test is given, which coincides with our theoretical analysis.
IFEMS, an Interactive Finite Element Modeling System Using a CAD/CAM System
Mckellip, S.; Schuman, T.; Lauer, S.
1980-01-01
A method of coupling a CAD/CAM system with a general purpose finite element mesh generator is described. The three computer programs which make up the interactive finite element graphics system are discussed.
PHG: A Toolbox for Developing Parallel Adaptive Finite Element Programs
Institute of Scientific and Technical Information of China (English)
ZHANG Linbo
2011-01-01
@@ Significance of the finite element method The finite element method (Feng, 1965) is mainly used for numerical solution of partial differential equations.It consists of partitioning the computational domain into a mesh composed of disjoint smaller sub-domains called elements which cover the whole domain, and approximating the solution in each element using simple functions (usually polynomials) so that the original problem can be turned into a suitable one to be solved on modern computers.The finite element method has a very wide range of applications as one of the most important methods in scientific and engineering computing.In the finite element method, two key factors which can affect the computational efficiency and precision of the computed solution are quality and distribution of the mesh elements.The adaptive finite element method, first proposed by I.Babuska and W.Rheinboldt in 1978 (Babuska et al., 1978), automatically adjusts and optimizes the distribution of mesh elements according to estimation on the distribution of the error of the computed solution, in order to improve the precision of the computed solution.Recent researches show that for many problems with locally singular solutions, by using mathematically rigorous a posteriori error estimates and suitable adaptive strategy, the adaptive finite element method can produce quasi-optimal meshes and dramatically improve the overall computational efficiency.
Essentials of finite element modeling and adaptive refinement
Dow, John O
2012-01-01
Finite Element Analysis is a very popular, computer-based tool that uses a complex system of points called nodes to make a grid called a ""mesh. "" The mesh contains the material and structural properties that define how the structure will react to certain loading conditions, allowing virtual testing and analysis of stresses or changes applied to the material or component design. This groundbreaking text extends the usefulness of finite element analysis by helping both beginners and advanced users alike. It simplifies, improves, and extends both the finite element method while at the same t
Liu, G. R.; Nguyen-Xuan, H.; Nguyen-Thoi, T.; Xu, X.
2009-06-01
A carefully designed procedure is presented to modify the piecewise constant strain field of linear triangular FEM models, and to reconstruct a strain field with an adjustable parameter α. A novel Galerkin-like weakform derived from the Hellinger-Reissner variational principle is proposed for establishing the discretized system equations. The new weak form is very simple, possesses the same good properties of the standard Galerkin weakform, and works particularly well for strain construction methods. A superconvergent alpha finite element method (S αFEM) is then formulated by using the constructed strain field and the Galerkin-like weakform for solid mechanics problems. The implementation of the S αFEM is straightforward and no additional parameters are used. We prove theoretically and show numerically that the S αFEM always achieves more accurate and higher convergence rate than the standard FEM of triangular elements (T3) and even more accurate than the four-node quadrilateral elements (Q4) when the same sets of nodes are used. The S αFEM can always produce both lower and upper bounds to the exact solution in the energy norm for all elasticity problems by properly choosing an α. In addition, a preferable- α approach has also been devised to produce very accurate solutions for both displacement and energy norms and a superconvergent rate in the energy error norm. Furthermore, a model-based selective scheme is proposed to formulate a combined S αFEM/NS-FEM model that handily overcomes the volumetric locking problems. Intensive numerical studies including singularity problems have been conducted to confirm the theory and properties of the S αFEM.
Finite Element Analysis of Deformed Legs of Offshore Platform Structures
Institute of Scientific and Technical Information of China (English)
柳春图; 秦太验; 段梦兰
2002-01-01
The element stiffness matrix of the equivalent beam or pipe element of the deformed leg of the platform is derived bythe finite element method. The stresses and displacements of some damaged components are calculated, and the numeri-cal solutions agree well with those obtained by the fine mesh finite element method. Finally, as an application of thismethod, the stresses of some platform structures are calculated and analyzed.
PRECONDITIONING HIGHER ORDER FINITE ELEMENT SYSTEMS BY ALGEBRAIC MULTIGRID METHOD OF LINEAR ELEMENTS
Institute of Scientific and Technical Information of China (English)
Yun-qing Huang; Shi Shu; Xi-jun Yu
2006-01-01
We present and analyze a robust preconditioned conjugate gradient method for the higher order Lagrangian finite element systems of a class of elliptic problems. An auxiliary linear element stiffness matrix is chosen to be the preconditioner for higher order finite elements. Then an algebraic multigrid method of linear finite element is applied for solving the preconditioner. The optimal condition number which is independent of the mesh size is obtained. Numerical experiments confirm the efficiency of the algorithm.
1994-01-01
element approximations of singular solutions with quasiuniform meshes the pollution error may be significant (depending on the strength of the singu...3 4. For singular solutions computed using quasi-uniform meshes, the pollution error may be significant and ii%-superconvergence regions may not...superconvergence for singular solutions : L-shaped domain. 3 Fig. 24. Pollution effect and 71%-superconvergence for singular solutions : L-shaped domain meshed
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...
A set of mixed-elements patterns for domain boundary approximation in hexahedral meshes.
Lobos, Claudio
2013-01-01
Hexahedral meshes are largely used by the Finite Element Method in a high variety of simulation problems. One of the most common problems of these type of meshes is to achieve an adequate approximation of curved domains; a feature typically found in the shape of organs. This work introduces a set of mixed-elements patterns, which are employed at the surface of target domain, and allow to conserve hexahedra elsewhere. These patterns are meant to be combined with any meshing technique producing a regular or non-regular hexahedral mesh.
Nonconforming rotated Q1 element on non-tensor product anisotropic meshes
Institute of Scientific and Technical Information of China (English)
MAO; Shipeng; SHI; Zhongci
2006-01-01
In this paper, we consider the nonconforming rotated Q1 element for the second order elliptic problem on the non-tensor product anisotropic meshes, i.e. the anisotropic affine quadrilateral meshes. Though the interpolation error is divergent on the anisotropic meshes,we overcome this difficulty by constructing another proper operator. Then we give the optimal approximation error and the consistency error estimates under the anisotropic affine quadrilateral meshes. The results of this paper provide some hints to derive the anisotropic error of some finite elements whose interpolations do not satisfy the anisotropic interpolation properties. Lastly, a numerical test is carried out, which coincides with our theoretical analysis.
Construction of hexahedral elements mesh capturing realistic geometries of Bayou Choctaw SPR site
Energy Technology Data Exchange (ETDEWEB)
Park, Byoung Yoon [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States); Roberts, Barry L. [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)
2015-09-01
The three-dimensional finite element mesh capturing realistic geometries of Bayou Choctaw site has been constructed using the sonar and seismic survey data obtained from the field. The mesh is consisting of hexahedral elements because the salt constitutive model is coded using hexahedral elements. Various ideas and techniques to construct finite element mesh capturing artificially and naturally formed geometries are provided. The techniques to reduce the number of elements as much as possible to save on computer run time with maintaining the computational accuracy is also introduced. The steps and methodologies could be applied to construct the meshes of Big Hill, Bryan Mound, and West Hackberry strategic petroleum reserve sites. The methodology could be applied to the complicated shape masses for not only various civil and geological structures but also biological applications such as artificial limbs.
A Comparison of Continuous Mass-lumped Finite Elements and Finite Differences for 3D
Zhebel, E.; Minisini, S.; Kononov, A.; Mulder, W.A.
2012-01-01
The finite-difference method is widely used for time-domain modelling of the wave equation because of its ease of implementation of high-order spatial discretization schemes, parallelization and computational efficiency. However, finite elements on tetrahedral meshes are more accurate in complex geo
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
quadratic spline finite element method
Directory of Open Access Journals (Sweden)
A. R. Bahadir
2002-01-01
Full Text Available The problem of heat transfer in a Positive Temperature Coefficient (PTC thermistor, which may form one element of an electric circuit, is solved numerically by a finite element method. The approach used is based on Galerkin finite element using quadratic splines as shape functions. The resulting system of ordinary differential equations is solved by the finite difference method. Comparison is made with numerical and analytical solutions and the accuracy of the computed solutions indicates that the method is well suited for the solution of the PTC thermistor problem.
Finite element computational fluid mechanics
Baker, A. J.
1983-01-01
Finite element analysis as applied to the broad spectrum of computational fluid mechanics is analyzed. The finite element solution methodology is derived, developed, and applied directly to the differential equation systems governing classes of problems in fluid mechanics. The heat conduction equation is used to reveal the essence and elegance of finite element theory, including higher order accuracy and convergence. The algorithm is extended to the pervasive nonlinearity of the Navier-Stokes equations. A specific fluid mechanics problem class is analyzed with an even mix of theory and applications, including turbulence closure and the solution of turbulent flows.
Institute of Scientific and Technical Information of China (English)
庞智晖; 魏秋实; 周广全; 陈鹏; 何伟; 白波; 李颖
2012-01-01
This paper is aimed to acquire high Geometric similar Subject-specific three-dimensional (3D) finite element mesh model of hip joint containing necrotic femoral head according to individual patient's X-ray, CT and MRI by u-sing the image registration and fusion technology. We selected a middle-aged female patient with osteonecrosis of femoral head, obtained the X-ray, CT and MRI images respectively. Then we established 3D solid model separately based on these image data by using Mimics 13.1 and Pro/E 5,1 software. We confirmed the match points and then proceed the 2D image registration after image projection conversion. Finally we showed the 3D finite element mesh model. A highly geometric similar subject-specific 3D finite element mesh model for osteonecrosis of femoral head has been established, which included normal cortical bone, cancellous bone, articular cartilage and necrotic zone, fractured trabecular bone within the femoral head. The model truly reflects the morphological characteristics and relationship of hip joint with osteonecrosis of femoral head, provides a relatively ideal research platform for further bio-mechanical analysis and surgical simulation.%同时基于个体股骨头坏死患者的X-ray、CT和MRI图像,采用图像配准和融合技术对包含坏死股骨头的髋关节进行三维重建,获取具有高度几何相似性的三维有限元网格模型.选择1例中年女性股骨头坏死患者,分别获取X-ray、CT和MRI三套图像,采用Mimics 13.1和Pro/E 5.1软件分别基于这三套数据建立相关三维实体模型,经图像投影转换后,确定图像之间的匹配点,进行二维图像配准,配准后对成功融合的图像进行三维有限元网格模型显示.建立了具有良好几何相似性的髋关节三维有限元网格模型,包括正常皮质骨、松质骨、关节软骨和股骨头坏死区、断裂骨小梁等六部份,较真实地反映了包含坏死股骨头的髋关节的形态特征及毗邻关系,
Directory of Open Access Journals (Sweden)
Konstandinos G. Raptis
2012-01-01
Full Text Available Purpose of this study is the consideration of loading and contact problems encountered at rotating machine elements and especially at toothed gears. The later are some of the most commonly used mechanical components for rotary motion and power transmission. This fact proves the necessity for improved reliability and enhanced service life, which require precise and clear knowledge of the stress field at gear tooth. This study investigates the maximum allowable stresses occurring during spur gear tooth meshing computed using Niemannâs formulas at Highest Point of Single Tooth Contact (HPSTC. Gear material, module, power rating and number of teeth are considered as variable parameters. Furthermore, the maximum allowable stresses for maximum power transmission conditions are considered keeping the other parameters constant. After the application of Niemannâs formulas to both loading cases, the derived results are compared to the respective estimations of Finite Element Method (FEM using ANSYS software. Comparison of the results derived from Niemannâs formulas and FEM show that deviations between the two methods are kept at low level for both loading cases independently of the applied power (either random or maximum and the respective tangential load.
H-VERSION ADAPTIVE FINITE ELEMENT METHOD FOR THREE-DIMENSIONAL SEEPAGE PROBLEM
Institute of Scientific and Technical Information of China (English)
Feng Xue-min; Chen Sheng-hong
2003-01-01
The h-version adaptive finite element method for 3-D seepage problem is presented in this paper.The adaptive system includes 4 modules: 3-D mesh generation, finite element analysis for 3-D seepage, mesh error estimation and post-process.The effectiveness of this system is verified by the given example.
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.
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
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
HANGING NODES IN THE UNIFYING THEORY OF A POSTERIORI FINITE ELEMENT ERROR CONTROL
Institute of Scientific and Technical Information of China (English)
C.Carstensen; Jun Hu
2009-01-01
A unified a posteriori error analysis has been developed in [18,21-23] to analyze the finite element error a posteriori under a universal roof.This paper contributes to the finite element meshes with hanging nodes which are required for local mesh-refining.The twodimensional 1-irregular triangulations into triangles and parallelograms and their combinations are considered with conforming and nonconforming finite element methods named after or by Courant,Q1,Crouzeix-Raviart,Han,Rannacher-Turek,and others for the a posteriori error analysis for triangulations with hanging nodes of degree≤1 which are fundamental for local mesh refinement in self-adaptive finite element discretisations.
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 ...
Second order tensor finite element
Oden, J. Tinsley; Fly, J.; Berry, C.; Tworzydlo, W.; Vadaketh, S.; Bass, J.
1990-01-01
The results of a research and software development effort are presented for the finite element modeling of the static and dynamic behavior of anisotropic materials, with emphasis on single crystal alloys. Various versions of two dimensional and three dimensional hybrid finite elements were implemented and compared with displacement-based elements. Both static and dynamic cases are considered. The hybrid elements developed in the project were incorporated into the SPAR finite element code. In an extension of the first phase of the project, optimization of experimental tests for anisotropic materials was addressed. In particular, the problem of calculating material properties from tensile tests and of calculating stresses from strain measurements were considered. For both cases, numerical procedures and software for the optimization of strain gauge and material axes orientation were developed.
Mimetic finite difference method for the stokes problem on polygonal meshes
Energy Technology Data Exchange (ETDEWEB)
Lipnikov, K [Los Alamos National Laboratory; Beirao Da Veiga, L [DIPARTIMENTO DI MATE; Gyrya, V [PENNSYLVANIA STATE UNIV; Manzini, G [ISTIUTO DI MATEMATICA
2009-01-01
Various approaches to extend the finite element methods to non-traditional elements (pyramids, polyhedra, etc.) have been developed over the last decade. Building of basis functions for such elements is a challenging task and may require extensive geometry analysis. The mimetic finite difference (MFD) method has many similarities with low-order finite element methods. Both methods try to preserve fundamental properties of physical and mathematical models. The essential difference is that the MFD method uses only the surface representation of discrete unknowns to build stiffness and mass matrices. Since no extension inside the mesh element is required, practical implementation of the MFD method is simple for polygonal meshes that may include degenerate and non-convex elements. In this article, we develop a MFD method for the Stokes problem on arbitrary polygonal meshes. The method is constructed for tensor coefficients, which will allow to apply it to the linear elasticity problem. The numerical experiments show the second-order convergence for the velocity variable and the first-order for the pressure.
THE DERIVATIVE PATCH INTERPOLATING RECOVERY TECHNIQUE FOR FINITE ELEMENT APPROXIMATIONS
Institute of Scientific and Technical Information of China (English)
TieZhang; Yan-pingLin; R.J.Tait
2004-01-01
A derivative patch interpolating recovery technique is analyzed for the finite element approximation to the second order elliptic boundary value problems in two dimensional case.It is shown that the convergence rate of the recovered gradient admits superc onvergence on the recovered subdomain, and is two order higher than the optimal global convergence rate (ultracovergence) at an internal node point when even order finite element spaces and local uniform meshes are used.
Institute of Scientific and Technical Information of China (English)
Bahattin Kanber; O.Yavuz Bozkurt
2006-01-01
In this work,the finite element analysis of the elasto-plastic plate bending problems is carried out using transition rectangular plate elements.The shape functions of the transition plate elements are derived based on a practical rule.The transition plate elements are all quadrilateral and can be used to obtain efficient finite element models using minimum number of elements.The mesh convergence rates of the models including the transition elements are compared with the regular element models.To verify the developed elements,simple tests are demonstrated and various elasto-plastic problems are solved.Their results are compared with ANSYS results.
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 ...
Situ, J. J.; Barron, R. M.; Higgins, M.
2011-11-01
Partial differential equations (PDEs) arise in connection with many physical phenomena involving two or more independent variables. Boundary conditions associated with the PDEs are either Dirichlet, Neumann or mixed conditions. Analytical solutions for most of these problems are not easy to obtain, and may not even be posssible. For such reasons, numerical methodologies for solving PDEs have been developed, such as finite element (FE), finite volume (FV) and finite difference (FD) methods. In the present paper, an innovative finite difference formulation, referred to as the cell-centred finite difference (CCFD) method, is proposed. Instead of applying finite difference approximations at the grid points as in the traditional finite difference method, the new methodology implements a finite difference scheme at each cell centroid in a predefined mesh topology. The prominent advantage of the proposed methodology is that it allows finite differencing to be applied on any arbitrary mesh topology, i.e. structured, unstructured or hybrid. The CCFD formulation is developed in this paper and implemented on a test problem to demonstrate its capabilities.
Bessel smoothing filter for spectral-element mesh
Trinh, P. T.; Brossier, R.; Métivier, L.; Virieux, J.; Wellington, P.
2017-06-01
Smoothing filters are extremely important tools in seismic imaging and inversion, such as for traveltime tomography, migration and waveform inversion. For efficiency, and as they can be used a number of times during inversion, it is important that these filters can easily incorporate prior information on the geological structure of the investigated medium, through variable coherent lengths and orientation. In this study, we promote the use of the Bessel filter to achieve these purposes. Instead of considering the direct application of the filter, we demonstrate that we can rely on the equation associated with its inverse filter, which amounts to the solution of an elliptic partial differential equation. This enhances the efficiency of the filter application, and also its flexibility. We apply this strategy within a spectral-element-based elastic full waveform inversion framework. Taking advantage of this formulation, we apply the Bessel filter by solving the associated partial differential equation directly on the spectral-element mesh through the standard weak formulation. This avoids cumbersome projection operators between the spectral-element mesh and a regular Cartesian grid, or expensive explicit windowed convolution on the finite-element mesh, which is often used for applying smoothing operators. The associated linear system is solved efficiently through a parallel conjugate gradient algorithm, in which the matrix vector product is factorized and highly optimized with vectorized computation. Significant scaling behaviour is obtained when comparing this strategy with the explicit convolution method. The theoretical numerical complexity of this approach increases linearly with the coherent length, whereas a sublinear relationship is observed practically. Numerical illustrations are provided here for schematic examples, and for a more realistic elastic full waveform inversion gradient smoothing on the SEAM II benchmark model. These examples illustrate well the
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.
Finite Element Method for Analysis of Material Properties
DEFF Research Database (Denmark)
Rauhe, Jens Christian
description of the material microstructure the finite element models must contain a large number of elements and this problem is solved by using the preconditioned conjugated gradient solver with an Element-By-Element preconditioner. Finite element analysis provides the volume averaged stresses and strains...... and the finite element method. The material microstructure of the heterogeneous material is non-destructively determined using X-ray microtomography. A software program has been generated which uses the X-ray tomographic data as an input for the mesh generation of the material microstructure. To obtain a proper...... which are used for the determination of the effective properties of the heterogeneous material. Generally, the properties determined using the finite element method coupled with X-ray microtomography are in good agreement with both experimentally determined properties and properties determined using...
GLOBAL SUPERCONVERGENCE OF THE MIXED FINITE ELEMENT METHODS FOR 2-D MAXWELL EQUATIONS
Institute of Scientific and Technical Information of China (English)
Jia-fu Lin; Qun Lin
2003-01-01
Superconvergence of the mixed finite element methods for 2-d Maxwell equations isstudied in this paper. Two order of superconvergent factor can be obtained for the k-thNedelec elements on the rectangular meshes.
Accurate finite element modeling of acoustic waves
Idesman, A.; Pham, D.
2014-07-01
In the paper we suggest an accurate finite element approach for the modeling of acoustic waves under a suddenly applied load. We consider the standard linear elements and the linear elements with reduced dispersion for the space discretization as well as the explicit central-difference method for time integration. The analytical study of the numerical dispersion shows that the most accurate results can be obtained with the time increments close to the stability limit. However, even in this case and the use of the linear elements with reduced dispersion, mesh refinement leads to divergent numerical results for acoustic waves under a suddenly applied load. This is explained by large spurious high-frequency oscillations. For the quantification and the suppression of spurious oscillations, we have modified and applied a two-stage time-integration technique that includes the stage of basic computations and the filtering stage. This technique allows accurate convergent results at mesh refinement as well as significantly reduces the numerical anisotropy of solutions. We should mention that the approach suggested is very general and can be equally applied to any loading as well as for any space-discretization technique and any explicit or implicit time-integration method.
ELASTO-PLASTIC FINITE ELEMENT ANALYSIS OF HOOK'S JOINT
Directory of Open Access Journals (Sweden)
Adnan ATICI
1996-03-01
Full Text Available In this study, stress analysis has been done in Hooke's joint by the finite element method. In finite element meshing, isoparametric quadrilateral elements with four nodes has been chosen and Lagrange polynomial has been used as the interpolation function. The special computer program has been written for the automatic mesh generation. In addition the other program has been developed to solve the finite element problems. Elastoplastic stress analysis is done to calculate the residual stresses in hooke's joint. Elasto-plastic stress values are calculated under loading from 400 daN to 1000 daN with increment of 100 daN. In this analysis "The initial stress method" is used.
Finite elements of nonlinear continua
Oden, J T
2000-01-01
Geared toward undergraduate and graduate students, this text extends applications of the finite element method from linear problems in elastic structures to a broad class of practical, nonlinear problems in continuum mechanics. It treats both theory and applications from a general and unifying point of view.The text reviews the thermomechanical principles of continuous media and the properties of the finite element method, and then brings them together to produce discrete physical models of nonlinear continua. The mathematical properties of these models are analyzed, along with the numerical s
FINITE ELEMENT ANALYSIS OF STRUCTURES
Directory of Open Access Journals (Sweden)
PECINGINA OLIMPIA-MIOARA
2015-05-01
Full Text Available The application of finite element method is analytical when solutions can not be applied for deeper study analyzes static, dynamic or other types of requirements in different points of the structures .In practice it is necessary to know the behavior of the structure or certain parts components of the machine under the influence of certain factors static and dynamic . The application of finite element in the optimization of components leads to economic growth , to increase reliability and durability organs studied, thus the machine itself.
Dual Formulations of Mixed Finite Element Methods with Applications.
Gillette, Andrew; Bajaj, Chandrajit
2011-10-01
Mixed finite element methods solve a PDE using two or more variables. The theory of Discrete Exterior Calculus explains why the degrees of freedom associated to the different variables should be stored on both primal and dual domain meshes with a discrete Hodge star used to transfer information between the meshes. We show through analysis and examples that the choice of discrete Hodge star is essential to the numerical stability of the method. Additionally, we define interpolation functions and discrete Hodge stars on dual meshes which can be used to create previously unconsidered mixed methods. Examples from magnetostatics and Darcy flow are examined in detail.
Institute of Scientific and Technical Information of China (English)
刘书田; 董焱章
2013-01-01
Mesh-dependency in simulation results of metamaterial electromagnetic performance was analyzed based on finite element analysis.It is found in the simulation results that the retrieval metamaterial equivalent performance parameters based on S-parameters have a strong dependence on the S-parameters' calculation accuracy,especially in the resonant frequency-domain where S-parameters' error may cause a qualitative error of the electromagnetic parameters.To improve the accuracy when a solution frequency is away from the resonant frequency based on the mesh-adaptive technology,a proper solution frequency needs to be determined for implementing the adaptive mesh of high quality.So a new method was proposed to improve the accuracy of the electromagnetic simulation analysis.In the new method,firstly the electromagnetic parameters could be retrieved from the S-parameters through the Kramers-Kronig relationship with an initial solution frequency,and thus an approximate value of the resonant frequency could be obtained.Afterwards,the adaptive mesh of high quality was achieved,using the approximate value as the solution frequency.Finally the electromagnetic parameters of high accuracy were retrieved from the S-parameters through the frequency-sweep technology.Numerical results show that the new method can effectively improve the accuracy of the simulation analysis and parameters-retrieval methods.%分析了基于有限元方法的超材料电磁性能仿真分析结果对有限元网格的依赖性.通过对仿真结果的分析,发现基于S参数的材料性能参数反演结果对S参数的计算准确度的依赖性巨大,特别是处在谐振频域的S参数误差会导致等效电磁参数的性态误差.针对基于求解频率的网格自适应技术对远离求解频率的谐振频域的分析结果的准确度改善不够这个问题,需要确定合适的求解频率来执行网格自适应.提出了一种改进电磁性能仿真分析准确度的方法,其基本思
MULTIGRID FOR THE MORTAR FINITE ELEMENT FOR PARABOLIC PROBLEM
Institute of Scientific and Technical Information of China (English)
Xue-jun Xu; Jin-ru Chen
2003-01-01
In this paper, a mortar finite element method for parabolic problem is presented. Multigrid method is used for solving the resulting discrete system. It is shown that the multigrid method is optimal, I.e, the convergence rate is independent of the mesh size L and the time step parameter т.
Institute of Scientific and Technical Information of China (English)
唐进元; 刘艳平
2012-01-01
研究正交面齿轮在加载条件下面齿轮啮合的传动性能参数、齿面接触应力和轮齿弯曲应力变化规律的有限元分析计算关键技术,以赫兹接触应力解析公式计算结果为对比,提出接触应力和弯曲应力计算的有限元网格密度确定方法.根据面齿轮重合度,分析面齿轮加载啮合仿真的五齿模型和七齿模型适用场合,给出面齿轮在啮合过程中的齿面接触应力和齿根弯曲应力最大值位置,计算面齿轮多齿模型接触应力及弯曲应力极值,准确得到面齿轮传动的重合度、传动误差、载荷分布系数等传动性能参数,以及载荷对这些传动性能参数的影响规律.研究结果表明,赫兹接触应力解析公式计算的结果合理地确定了有限元模型的网格密度,有限元仿真得到的应力值可靠,传动性能参数的分析结论正确.%The transmission performance, contact stress and bending stress of face-gear drive under torque are studied. Based on the calculated results of Hertz contact theory, a method to get reasonable amounts of grid for finite element method (FEM), is introduced. According to the contact ratio, it investigates the applications of FEM with five teeth, and one with seven teeth, which are used to research on the loaded meshing simulation of face-gear drive. The dangerous positions for contact stress and bending stress of face-gear are found, and their values are given out. The transmission performance of face-gear drive, such as contact ratio, transmission error and the loading distribution coefficient, can be computed by this method. When the face gear is under different torques, their relationship to loadings can be got The results of research turn out that, the grid size of finite element model, which is decided by Hertz contact theory, is reasonable. The values of stresses in the meshing simulation are reliable, and the conclusions about the transmission performance of face-gear drive are
THE SPACE-TIME FINITE ELEMENT METHOD FOR PARABOLIC PROBLEMS
Institute of Scientific and Technical Information of China (English)
李宏; 刘儒勋
2001-01-01
Adaptive space-time finite element method, continuous in space but discontinuous in time for semi-linear parabolic problems is discussed. The approach is based on a combination of finite element and finite difference techniques. The existence and uniqueness of the weak solution are proved without any assumptions on choice of the spacetime meshes. Basic error estimates in L∞ (L2) norm, that is maximum-norm in time, L2norm in space are obtained. The numerical results are given in the last part and the analysis between theoretic and experimental results are obtained.
The Relation of Finite Element and Finite Difference Methods
Vinokur, M.
1976-01-01
Finite element and finite difference methods are examined in order to bring out their relationship. It is shown that both methods use two types of discrete representations of continuous functions. They differ in that finite difference methods emphasize the discretization of independent variable, while finite element methods emphasize the discretization of dependent variable (referred to as functional approximations). An important point is that finite element methods use global piecewise functional approximations, while finite difference methods normally use local functional approximations. A general conclusion is that finite element methods are best designed to handle complex boundaries, while finite difference methods are superior for complex equations. It is also shown that finite volume difference methods possess many of the advantages attributed to finite element methods.
A suitable low-order, eight-node tetrahedral finite element for solids
Energy Technology Data Exchange (ETDEWEB)
Key, S.W.; Heinstein, M.S.; Stone, C.M.; Mello, F.J.; Blanford, M.L.; Budge, K.G.
1998-03-01
To use the all-tetrahedral mesh generation existing today, the authors have explored the creation of a computationally efficient eight-node tetrahedral finite element (a four-node tetrahedral finite element enriched with four mid-face nodal points). The derivation of the element`s gradient operator, studies in obtaining a suitable mass lumping, and the element`s performance in applications are presented. In particular they examine the eight-node tetrahedral finite element`s behavior in longitudinal plane wave propagation, in transverse cylindrical wave propagation, and in simulating Taylor bar impacts. The element samples only constant strain states and, therefore, has 12 hour-glass modes. In this regard it bears similarities to the eight-node, mean-quadrature hexahedral finite element. Comparisons with the results obtained from the mean-quadrature eight-node hexahedral finite element and the four-node tetrahedral finite element are included. Given automatic all-tetrahedral meshing, the eight-node, constant-strain tetrahedral finite element is a suitable replacement for the eight-node hexahedral finite element in those cases where mesh generation requires an inordinate amount of user intervention and direction to obtain acceptable mesh properties.
hp-finite-elements for simulating electromagnetic fields in optical devices with rough textures
Burger, S; Hammerschmidt, M; Herrmann, S; Pomplun, J; Schmidt, F; Wohlfeil, B; Zschiedrich, L
2015-01-01
The finite-element method is a preferred numerical method when electromagnetic fields at high accuracy are to be computed in nano-optics design. Here, we demonstrate a finite-element method using hp-adaptivity on tetrahedral meshes for computation of electromagnetic fields in a device with rough textures. The method allows for efficient computations on meshes with strong variations in element sizes. This enables to use precise geometry resolution of the rough textures. Convergence to highly accurate results is observed.
AN ANISOTROPIC NONCONFORMING FINITE ELEMENT WITH SOME SUPERCONVERGENCE RESULTS
Institute of Scientific and Technical Information of China (English)
Dong-yang Shi; Shi-peng Mao; Shao-chun Chen
2005-01-01
The main aim of this paper is to study the error estimates of a nonconforming finite element with some superconvergence results under anisotropic meshes. The anisotropic interpolation error and consistency error estimates are obtained by using some novel approaches and techniques, respectively. Furthermore, the superclose and a superconvergence estimate on the central points of elements are also obtained without the regularity assumption and quasi-uniform assumption requirement on the meshes. Finally, a numerical test is carried out, which coincides with our theoretical analysis.
Research of Stamp Forming Simulation Based on Finite Element Method
Institute of Scientific and Technical Information of China (English)
SU Xaio-ping; XU Lian
2008-01-01
We point out that the finite element method offers a greta functional improvement for analyzing the stamp forming process of an automobile panel. Using the finite element theory and the simulation method of sheet stamping forming, the element model of sheet forming is built based on software HyperMesh,and the simulation of the product's sheet forming process is analyzed based on software Dynaform. A series of simulation results are obtained. It is clear that the simulation results from the theoretical basis for the product's die design and are useful for selecting process parameters.
Finite 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...
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.
Selective Smoothed Finite Element Method
Institute of Scientific and Technical Information of China (English)
无
2007-01-01
The paper examines three selective schemes for the smoothed finite element method (SFEM) which was formulated by incorporating a cell-wise strain smoothing operation into the standard compatible finite element method (FEM). These selective SFEM schemes were formulated based on three selective integration FEM schemes with similar properties found between the number of smoothing cells in the SFEM and the number of Gaussian integration points in the FEM. Both scheme 1 and scheme 2 are free of nearly incompressible locking, but scheme 2 is more general and gives better results than scheme 1. In addition, scheme 2 can be applied to anisotropic and nonlinear situations, while scheme 1 can only be applied to isotropic and linear situations. Scheme 3 is free of shear locking. This scheme can be applied to plate and shell problems. Results of the numerical study show that the selective SFEM schemes give more accurate results than the FEM schemes.
A Nonconforming Arbitrary Quadrilateral Finite Element Method for Approximating Maxwell's Equations
Institute of Scientific and Technical Information of China (English)
Dongyang Shi; Lifang Pei; Shaochun Chen
2007-01-01
The main aim of this paper is to provide convergence analysis of Quasi-Wilson nonconforming finite element to Maxwell's equations under arbitrary quadrilateral meshes. The error estimates are derived, which are the same as those for conforming elements under conventional regular meshes.
Finite Element Method for Analysis of Material Properties
DEFF Research Database (Denmark)
Rauhe, Jens Christian
The use of cellular and composite materials have in recent years become more and more common in all kinds of structural components and accurate knowledge of the effective properties is therefore essential. In this wok the effective properties are determined using the real material microstructure...... and the finite element method. The material microstructure of the heterogeneous material is non-destructively determined using X-ray microtomography. A software program has been generated which uses the X-ray tomographic data as an input for the mesh generation of the material microstructure. To obtain a proper...... description of the material microstructure the finite element models must contain a large number of elements and this problem is solved by using the preconditioned conjugated gradient solver with an Element-By-Element preconditioner. Finite element analysis provides the volume averaged stresses and strains...
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.
SUPERCONVERGENCE ANALYSIS OF A NONCONFORMING TRIANGULAR ELEMENT ON ANISOTROPIC MESHES
Institute of Scientific and Technical Information of China (English)
Dongyang SHI; Hui LIANG; Caixia WANG
2007-01-01
The class of anisotropic meshes we conceived abandons the regular assumption. Some distinct properties of Carey's element are used to deal with the superconvergence for a class of twodimensional second-order elliptic boundary value problems on anisotropic meshes. The optimal results are obtained and numerical examples are given to confirm our theoretical analysis.
各向异性双二次元的自然超收敛性结果%Anisotropic Biquadratic Finite Element with Some Natural Superconvergence Results
Institute of Scientific and Technical Information of China (English)
李清善; 孙会霞
2007-01-01
The paper studies the convergence and the superconvergence of the biquadratic finite element for Poisson' problem on anisotropic meshes. By detailed analysis, it shows that the biquadratic finite element is anisotropically superconvergent at four Gauss points in the element.
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.
Infinite Possibilities for the Finite Element.
Finlayson, Bruce A.
1981-01-01
Describes the uses of finite element methods in solving problems of heat transfer, fluid flow, etc. Suggests that engineers should know the general concepts and be able to apply the principles of finite element methods. (Author/WB)
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.
RSW Mixed Element Cell-Centered Medium Mesh
National Aeronautics and Space Administration — This RSW gridset is designed as the medium size mixed element grid for use with cell-centered unstructured meshes. UG3 : Grid File Name = rsw_med_mixedcc.b8.ugrid...
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
A LOW ORDER NONCONFORMING ANISOTROPIC FINITE ELEMENT APPROXIMATION TO PARABOLIC PROBLEM
Institute of Scientific and Technical Information of China (English)
Dongyang SHI; Wei GONG
2009-01-01
A low order nonconforming finite element is applied to the parabolic problem with anisotropic meshes. Both the semidiscrete and fully discrete forms are studied. Some superclose properties and superconvergence are obtained through some novel approaches and techniques.
A finite element method for netting application to fish cages and fishing gear
Priour, Daniel
2014-01-01
This book describes a finite element method for netting that describes the relation between forces and deformation of the netting and takes into account forces due to the twine elasticity, the hydrodynamic forces, the catch effect, the mesh opening stiffness.
NATURAL SUPERCONVERGENT POINTS OF EQUILATERAL TRIANGULAR FINITE ELEMENTS-A NUMERICAL EXAMPLE
Institute of Scientific and Technical Information of China (English)
Zhi-min Zhang; Ahmed Naga
2006-01-01
A numerical test case demonstrates that the Lobatto and the Gauss points are not natural superconvergent points of the cubic and the quartic finite elements under equilateral triangular mesh for the Poisson equation.
Least-squares finite-element lattice Boltzmann method.
Li, Yusong; LeBoeuf, Eugene J; Basu, P K
2004-06-01
A new numerical model of the lattice Boltzmann method utilizing least-squares finite element in space and Crank-Nicolson method in time is presented. The new method is able to solve problem domains that contain complex or irregular geometric boundaries by using finite-element method's geometric flexibility and numerical stability, while employing efficient and accurate least-squares optimization. For the pure advection equation on a uniform mesh, the proposed method provides for fourth-order accuracy in space and second-order accuracy in time, with unconditional stability in the time domain. Accurate numerical results are presented through two-dimensional incompressible Poiseuille flow and Couette flow.
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.
Stress analysis of 3D complex geometries using the scaled boundary polyhedral finite elements
Talebi, Hossein; Saputra, Albert; Song, Chongmin
2016-10-01
While dominating the numerical stress analysis of solids, the finite element method requires a mesh to conform to the surface of the geometry. Thus the mesh generation of three dimensional complex structures often require tedious human interventions. In this paper, we present a formulation for arbitrary polyhedral elements based on the scaled boundary finite element method, which reduces the difficulties in automatic mesh generation. We also propose a simple method to generate polyhedral meshes with local refinements. The mesh generation method is based on combining an octree mesh with surfaces defined using signed distance functions. Through several numerical examples, we verify the results, study the convergence behaviour and depict the many advantages and capabilities of the presented method. This contribution is intended to assist us to eventually frame a set of numerical methods and associated tools for the full automation of the engineering analysis where minimal human interaction is needed.
Institute of Scientific and Technical Information of China (English)
Yin-nianHe
2004-01-01
In this article we consider a two-level finite element Galerkin method using mixed finite elements for the two-dimensional nonstationary incompressible Navier-Stokes equations. The method yields a H1-optimal velocity approximation and a L2-optimal pressure approximation. The two-level finite element Galerkin method involves solving one small,nonlinear Navier-Stokes problem on the coarse mesh with mesh size H, one linear Stokes problem on the fine mesh with mesh size h <
Quadratic Serendipity Finite Elements on Polygons Using Generalized Barycentric Coordinates
Rand, Alexander; Bajaj, Chandrajit
2011-01-01
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 satisfying simple geometric criteria, our construction produces 2n 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. Numerical evidence is provided on a trapezoidal quadrilateral mesh, previously not amenable to serendipity constructions, and applications to adaptive meshing are discussed.
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 2n 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.
Multisymplectic Structure-Preserving in Simple Finite Element Method in High Dimensional Case
Institute of Scientific and Technical Information of China (English)
BAI Yong-Qiang; LIU Zhen; PEI Ming; ZHENG Zhu-Jun
2003-01-01
In this paper, we study a finite element scheme of some semi-linear elliptic boundary value problems inhigh-dimensional space. With uniform mesh, we find that, the numerical scheme derived from finite element method cankeep a preserved multisymplectic structure.
Xia, Yi-Ming
2015-01-01
A locking-free rectangular Mindlin plate element with a new multi-resolution analysis (MRA) is proposed and a multireolution finite element method is hence presented. The MRA framework is formulated out of a mutually nesting displacement subspace sequence. The MRA endows the proposed element with the resolution level (RL) to adjust the element node number, thus modulating structural analysis accuracy accordingly. As a result, the traditional 4-node rectangular Mindlin plate element and method is a mono-resolution one and also a special case of the proposed element and method. The meshing for the monoresolution plate element model is based on the empiricism while the RL adjusting for the multiresolution is laid on the rigorous mathematical basis. The accuracy of a structural analysis is actually determined by the RL, not by the mesh. The rational MRA enables the implementation of the multiresolution Mindlin plate element method to be more rational and efficient than that of the conventional monoresolution or o...
Behaviour of Lagrangian triangular mixed fluid finite elements
Indian Academy of Sciences (India)
S Gopalakrishnan; G Devi
2000-02-01
The behaviour of mixed fluid finite elements, formulated based on the Lagrangian frame of reference, is investigated to understand the effects of locking due to incompressibility and irrotational constraints. For this purpose, both linear and quadratic mixed triangular fluid elements are formulated. It is found that there exists a close relationship between the penalty finite element approach that uses reduced/selective numerical integration to alleviate locking, and the mixed finite element approach. That is, performing reduced/selective integration in the penalty approach amounts to reducing the order of pressure interpolation in the mixed finite element approach for obtaining similar results. A number of numerical experiments are performed to determine the optimum degree of interpolation of both the mean pressure and the rotational pressure in order that the twin constraints are satisfied exactly. For this purpose, the benchmark solution of the rigid rectangular tank is used. It is found that, irrespective of the degree of mean and the rotational pressure interpolation, the linear triangle mesh, with or without central bubble function (incompatible mode), locks when both the constraints are enforced simultaneously. However, for quadratic triangle, linear interpolation of the mean pressure and constant rotational pressure ensures exact satisfaction of the constraints and the mesh does not lock. Based on the results obtained from the numerical experiments, a number of important conclusions are arrived at.
Model refinements of transformers via a subproblem finite element method
Dular, Patrick; Kuo-Peng, Patrick; Ferreira Da Luz, Mauricio,; Krähenbühl, Laurent
2015-01-01
International audience; A progressive modeling of transformers is performed via a subproblem finite element method. A complete problem is split into subproblems with different adapted overlapping meshes. Model refinements are performed from ideal to real flux tubes, 1-D to 2-D to 3-D models, linear to nonlinear materials, perfect to real materials, single wire to volume conductor windings, and homogenized to fine models of cores and coils, with any coupling of these changes. The proposed unif...
ON THE ANISOTROPIC ACCURACY ANALYSIS OF ACM'S NONCONFORMING FINITE ELEMENT
Institute of Scientific and Technical Information of China (English)
Dong-yang Shi; Shi-peng Mao; Shao-chun Chen
2005-01-01
The main aim of this paper is to study the superconvergence accuracy analysis of the famous ACM's nonconforming finite element for biharmonic equation under anisotropic meshes. By using some novel approaches and techniques, the optimal anisotropic interpolation error and consistency error estimates are obtained. The global error is of order O(h2). Lastly, some numerical tests are presented to verify the theoretical analysis.
Smooth surface micro finite element modelling of a cancellous bone analogue material.
Leung, S Y; Browne, M; New, A M
2008-01-01
Tetrahedral finite element meshes with smooth surfaces can be created from computed tomography scans of cancellous bone in order to evaluate its mechanical properties. Image processing before creation of the mesh can affect the accuracy of determined mechanical properties. For a cancellous bone analogue, threshold, mesh density and surface smoothing parameters used in mesh generation were varied and the mechanical properties predicted by the resulting meshes were compared to experimental results. This study has shown that threshold selection is vital for accurate determination of volume fraction and resulting mechanical properties.
Error Estimation and h-Adaptivity for Optimal Finite Element Analysis
Cwik, Tom; Lou, John
1997-01-01
The objective of adaptive meshing and automatic error control in finite element analysis is to eliminate the need for the application engineer from re-meshing and re-running design simulations to verify numerical accuracy. The user should only need to enter the component geometry and a coarse finite element mesh. The software will then autonomously and adaptively refine this mesh where needed, reducing the error in the fields to a user prescribed value. The ideal end result of the simulation is a measurable quantity (e.g. scattered field, input impedance), calculated to a prescribed error, in less time and less machine memory than if the user applied typical uniform mesh refinement by hand. It would also allow for the simulation of larger objects since an optimal mesh is created.
Elements with Square Roots in Finite Groups
Institute of Scientific and Technical Information of China (English)
M.S. Lucido; M.R. Pournaki
2005-01-01
In this paper, we study the probability that a randomly chosen element in a finite group has a square root, in particular the simple groups of Lie type of rank 1, the sporadic finite simple groups and the alternating groups.
Conforming finite elements with embedded strong discontinuities
Dias-da-Costa, D.; Alfaiate, J.; Sluys, L.J.; Areias, P.; Fernandes, C.; Julio, E.
2012-01-01
The possibility of embedding strong discontinuities into finite elements allowed the simulation of different problems, namely, brickwork masonry fracture, dynamic fracture, failure in finite strain problems and simulation of reinforcement concrete members. However, despite the significant contributi
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.
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.
Finite element simulation of barge impact into a rigid wall
Directory of Open Access Journals (Sweden)
H.W. Leheta
2014-03-01
Many approaches have been developed in order to obtain these impact loads. In general, collision mechanics for floating units is classified into, external mechanics and internal mechanics. In external mechanics, analytical approaches are used to determine the absorbed energy acting on the vessel from the collision, while in internal mechanics analytical approaches are used to determine the ability of the ship’s structure to withstand the absorbed energy. Due to the difficulty and the highly expected cost to perform model testing and impact data for validation, finite element simulation provides an alternative tool for physical validation. In this study, a simulation of barge impact to a rigid wall is presented using the explicit nonlinear finite element code LS-DYNA3D. A conventional fine mesh finite element barge model is created. Impact results are obtained at two different speeds in order to show the consequence of barge and wall damage.
Nonconforming stabilized combined finite element method for Reissner-Mindlin plate
Institute of Scientific and Technical Information of China (English)
Min-fu FENG; Yan YANG; Tian-xiao ZHOU
2009-01-01
Based on combination of two variational principles, a nonconforming sta-bilized finite element method is presented for the Reissner-Mindlin plates. The method is convergent when the finite element space is energy-compatible. Error estimates are derived. In particular, three finite element spaces are applied in the computation. Nu-merical results show that the method is insensitive to the mesh distortion and has better performence than the MITC4 and DKQ methods. With properly chosen parameters, high accuracy can be obtained at coarse meshes.
Institute of Scientific and Technical Information of China (English)
苏波; 钱若军; 韩向科
2011-01-01
针对流固耦合分析中的移动边界问题,在拟固体二步法的基础上,提出一种新的有限元网格更新方法:第一步(预测步),将流体网格作为指定位移边界条件下的拟固体,进行线弹性分析;第二步(校正步),根据第一步计算得到的应变场,采用主剪应变方法,赋予主剪应变较大的单元以较大的杨氏模量,对所构造的非均质固体进行运动分析,得到理想的更新网格.采用不同算法对不同运动类型(包括平动、转动、变形)和不同运动幅度下的二维、三维网格运动进行计算,结果表明:与一步法和ChiandUssi法相比,文中提出的方法具有较强的适用性,能显著地减小单元的畸变,使网格保持优良的计算性能,适用于大变形流固耦合问题中的网格更新计算.%Based on the pseudo-solid two-step (PSTS) model, a new mesh update method-PSS-PSTS method is proposed to solve moving boundary problems for fluid-structure interaction analysis. In the first step (predictor), a linear pseudo-solid model is first conducted to the fluid mesh subjected to prescribed displacement boundary. In the second step (corrector), based on the strain field computed in the first step, PSS (principal shear strain) method endows the element with greater Young modulus due to its larger principal shear strain, then the motion of the established non-homogeneous solid model is computed and taken as the desired fluid update mesh.Some examples of 2D/3D FEM mesh update under different motion types (translation, rotation and deformation) and different motion scale computed by PSS-PSTS method are studied. The results show that the PSS-PSTS method is highly effective in preventing extremely distorted elements and makes the mesh maintain high computation quality compared with the one-step method and the two-step methods proposed by Chiandussi. It can be used for mesh update computation for fluid-structure interaction problems with large deformation.
Finite element simulation of wheel impact test
Directory of Open Access Journals (Sweden)
S.H. Yang
2008-06-01
Full Text Available Purpose: In order to achieve better performance and quality, the wheel design and manufacturing use a number of wheel tests (rotating bending test, radial fatigue test, and impact test to insure that the wheel meets the safety requirements. The test is very time consuming and expensive. Computer simulation of these tests can significantly reduce the time and cost required to perform a wheel design. In this study, nonlinear dynamic finite element is used to simulate the SAE wheel impact test.Design/methodology/approach: The test fixture used for the impact test consists of a striker with specified weight. The test is intended to simulate actual vehicle impact conditions. The tire-wheel assembly is mounted at 13° angle to the vertical plane with the edge of the weight in line with outer radius of the rim. The striker is dropped from a specified height above the highest point of the tire-wheel assembly and contacts the outboard flange of the wheel.Because of the irregular geometry of the wheel, the finite element model of an aluminium wheel is constructed by tetrahedral element. A mesh convergence study is carried out to ensure the convergence of the mesh model. The striker is assumed to be rigid elements. Initially, the striker contacts the highest area of the wheel, and the initial velocity of the striker is calculated from the impact height. The simulated strains at two locations on the disc are verified by experimental measurements by strain gages. The damage parameter of a wheel during the impact test is a strain energy density from the calculated result.Findings: The prediction of a wheel failure at impact is based on the condition that fracture will occur if the maximum strain energy density of the wheel during the impact test exceeds the total plastic work of the wheel material from tensile test. The simulated results in this work show that the total plastic work can be effectively employed as a fracture criterion to predict a wheel
A Finite Element Method for Simulation of Compressible Cavitating Flows
Shams, Ehsan; Yang, Fan; Zhang, Yu; Sahni, Onkar; Shephard, Mark; Oberai, Assad
2016-11-01
This work focuses on a novel approach for finite element simulations of multi-phase flows which involve evolving interface with phase change. Modeling problems, such as cavitation, requires addressing multiple challenges, including compressibility of the vapor phase, interface physics caused by mass, momentum and energy fluxes. We have developed a mathematically consistent and robust computational approach to address these problems. We use stabilized finite element methods on unstructured meshes to solve for the compressible Navier-Stokes equations. Arbitrary Lagrangian-Eulerian formulation is used to handle the interface motions. Our method uses a mesh adaptation strategy to preserve the quality of the volumetric mesh, while the interface mesh moves along with the interface. The interface jump conditions are accurately represented using a discontinuous Galerkin method on the conservation laws. Condensation and evaporation rates at the interface are thermodynamically modeled to determine the interface velocity. We will present initial results on bubble cavitation the behavior of an attached cavitation zone in a separated boundary layer. We acknowledge the support from Army Research Office (ARO) under ARO Grant W911NF-14-1-0301.
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.
Parallel performance of a preconditioned CG solver for unstructured finite element applications
Energy Technology Data Exchange (ETDEWEB)
Shadid, J.N.; Hutchinson, S.A.; Moffat, H.K. [Sandia National Labs., Albuquerque, NM (United States)
1994-12-31
A parallel unstructured finite element (FE) implementation designed for message passing MIMD machines is described. This implementation employs automated problem partitioning algorithms for load balancing unstructured grids, a distributed sparse matrix representation of the global finite element equations and a parallel conjugate gradient (CG) solver. In this paper a number of issues related to the efficient implementation of parallel unstructured mesh applications are presented. These include the differences between structured and unstructured mesh parallel applications, major communication kernels for unstructured CG solvers, automatic mesh partitioning algorithms, and the influence of mesh partitioning metrics on parallel performance. Initial results are presented for example finite element (FE) heat transfer analysis applications on a 1024 processor nCUBE 2 hypercube. Results indicate over 95% scaled efficiencies are obtained for some large problems despite the required unstructured data communication.
An hybrid finite volume finite element method for variable density incompressible flows
Calgaro, Caterina; Creusé, Emmanuel; Goudon, Thierry
2008-04-01
This paper is devoted to the numerical simulation of variable density incompressible flows, modeled by the Navier-Stokes system. We introduce an hybrid scheme which combines a finite volume approach for treating the mass conservation equation and a finite element method to deal with the momentum equation and the divergence free constraint. The breakthrough relies on the definition of a suitable footbridge between the two methods, through the design of compatibility condition. In turn, the method is very flexible and allows to deal with unstructured meshes. Several numerical tests are performed to show the scheme capabilities. In particular, the viscous Rayleigh-Taylor instability evolution is carefully investigated.
An iterative algorithm for finite element analysis
Laouafa, F.; Royis, P.
2004-03-01
In this paper, we state in a new form the algebraic problem arising from the one-field displacement finite element method (FEM). The displacement approach, in this discrete form, can be considered as the dual approach (force or equilibrium) with subsidiary constraints. This approach dissociates the nonlinear operator to the linear ones and their sizes are linear functions of integration rule which is of interest in the case of reduced integration. This new form of the problem leads to an inexpensive improvement of FEM computations, which acts at local, elementary and global levels. We demonstrate the numerical performances of this approach which is independent of the mesh structure. Using the GMRES algorithm we build, for nonsymmetric problems, a new algorithm based upon the discretized field of strain. The new algorithms proposed are more closer to the mechanical problem than the classical ones because all fields appear during the resolution process. The sizes of the different operators arising in these new forms are linear functions of integration rule, which is of great interest in the case of reduced integration.
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
Institute of Scientific and Technical Information of China (English)
梁韬; 孟春玲; 尹一恒; 刘广伟; 余新光
2016-01-01
Objective To explore how to establish a three-dimensional finite element model of basilar invagination and occipitalization of atlas. Methods The CT data of craniovertebral junction in a typical patient with basilar invagination and occipitalization of atlas was collected. Mimics software was used to edit CT pictures and generate the three-dimensional geometric model of atlanto-occipital fusion corpus and axis surface. Then point cloud was exported. Reverse engineering software of Imageware was used to process point cloud data and generate three-dimensional curved surface. The surface model was blocked first and then meshed by Hypermesh software. The mesh model was finally exported by the method of mix-meshing in tetrahedrons and hexahedrons. The mesh model was imported into finite element software of Abaqus. Finite element model was established by adding ligaments, assigning material, defining contact and defining boundary. Results The finite element model of basilar invagination and occipitalization of atlas contained 474,162 elements and 235,524 notes with good geometric similarity. Conclusion The three-dimensional finite element model of basilar invagination and occipitalization of atlas provides the basis for the research on craniovertebral junction malformation, and it can be used for reference of establishment of finite element model in upper cervical spine malformation.%目的：探讨建立颅底陷入合并寰枕融合畸形的三维有限元模型的方法。方法采集1例颅底陷入合并寰枕融合畸形患者的颅颈交界区的CT薄层扫描数据，利用Mimics软件对CT数据进行处理，生成三维几何表面模型，并导出点云；采用逆向工程软件Imageware处理点云数据，生成三维曲面；采用四面体与六面体混合分网的思路，利用HyperMesh对曲面模型先分块再分网，最后导出网格模型；将网格模型导入有限元软件Abaqus，进行韧带添加、材料赋值、接触定义、边界
Superconvergence for rectangular serendipity finite elements
Institute of Scientific and Technical Information of China (English)
CHEN; Chuanmiao(陈传淼)
2003-01-01
Based on an orthogonal expansion and orthogonality correction in an element, superconvergenceat symmetric points for any degree rectangular serendipity finite element approximation to second order ellipticproblem is proved, and its behaviour up to the boundary is also discussed.
Finite elements and finite differences for transonic flow calculations
Hafez, M. M.; Murman, E. M.; Wellford, L. C.
1978-01-01
The paper reviews the chief finite difference and finite element techniques used for numerical solution of nonlinear mixed elliptic-hyperbolic equations governing transonic flow. The forms of the governing equations for unsteady two-dimensional transonic flow considered are the Euler equation, the full potential equation in both conservative and nonconservative form, the transonic small-disturbance equation in both conservative and nonconservative form, and the hodograph equations for the small-disturbance case and the full-potential case. Finite difference methods considered include time-dependent methods, relaxation methods, semidirect methods, and hybrid methods. Finite element methods include finite element Lax-Wendroff schemes, implicit Galerkin method, mixed variational principles, dual iterative procedures, optimal control methods and least squares.
Continuous finite element methods for Hamiltonian systems
Institute of Scientific and Technical Information of China (English)
无
2007-01-01
By applying the continuous finite element methods of ordinary differential equations, the linear element methods are proved having second-order pseudo-symplectic scheme and the quadratic element methods are proved having third-order pseudosymplectic scheme respectively for general Hamiltonian systems, and they both keep energy conservative. The finite element methods are proved to be symplectic as well as energy conservative for linear Hamiltonian systems. The numerical results are in agreement with theory.
Element-topology-independent preconditioners for parallel finite element computations
Park, K. C.; Alexander, Scott
1992-01-01
A family of preconditioners for the solution of finite element equations are presented, which are element-topology independent and thus can be applicable to element order-free parallel computations. A key feature of the present preconditioners is the repeated use of element connectivity matrices and their left and right inverses. The properties and performance of the present preconditioners are demonstrated via beam and two-dimensional finite element matrices for implicit time integration computations.
Element-topology-independent preconditioners for parallel finite element computations
Park, K. C.; Alexander, Scott
1992-01-01
A family of preconditioners for the solution of finite element equations are presented, which are element-topology independent and thus can be applicable to element order-free parallel computations. A key feature of the present preconditioners is the repeated use of element connectivity matrices and their left and right inverses. The properties and performance of the present preconditioners are demonstrated via beam and two-dimensional finite element matrices for implicit time integration computations.
RSW Mixed Element Cell-Centered Fine Mesh
National Aeronautics and Space Administration — This is a RSW mixed-element unstructured fine mesh for cell-centered solvers. UG3 : Grid File Name = rsw_fine_mixedcc.b8.ugrid UG3 : Quad Surface Faces= 28968 UG3 :...
Why do probabilistic finite element analysis ?
Thacker, B H
2008-01-01
The intention of this book is to provide an introduction to performing probabilistic finite element analysis. As a short guideline, the objective is to inform the reader of the use, benefits and issues associated with performing probabilistic finite element analysis without excessive theory or mathematical detail.
Finite-Element Software for Conceptual Design
DEFF Research Database (Denmark)
Lindemann, J.; Sandberg, G.; Damkilde, Lars
2010-01-01
and research. Forcepad is an effort to provide a conceptual design and teaching tool in a finite-element software package. Forcepad is a two-dimensional finite-element application based on the same conceptual model as image editing applications such as Adobe Photoshop or Microsoft Paint. Instead of using...
Non-linear finite element modeling
DEFF Research Database (Denmark)
Mikkelsen, Lars Pilgaard
The note is written for courses in "Non-linear finite element method". The note has been used by the author teaching non-linear finite element modeling at Civil Engineering at Aalborg University, Computational Mechanics at Aalborg University Esbjerg, Structural Engineering at the University...... on the governing equations and methods of implementing....
ADAPTIVE FINITE ELEMENT METHOD FOR HIGH-SPEED FLOW-STRUCTURE INTERACTION
Institute of Scientific and Technical Information of China (English)
Wiroj LIMTRAKARN; Pramote DECHAUMPHAI
2004-01-01
An adaptive finite element method for high-speed flow-structure interaction is presented. The cell-centered finite element method is combined with an adaptive meshing technique to solve the Navier-Stokes equations for high-speed compressible flow behavior. The energy equation and the quasi-static structural equations for aerodynamically heated structures are solved by applying the Galerkin finite element method. The finite element formulation and computational procedure are described. Interactions between the high-speed flow, structural heat transfer, and deformation are studied by two applications of Mach 10 flow over an inclined plate, and Mach 4 flow in a channel.
Self-gravity in curved mesh elements
Huré, Jean-Marc; Hersant, Franck
2014-01-01
The local character of self-gravity along with the number of spatial dimensions are critical issues when computing the potential and forces inside massive systems like stars and disks. This appears from the discretisation scale where each cell of the numerical grid is a self-interacting body in itself. There is apparently no closed-form expression yet giving the potential of a three-dimensional homogeneous cylindrical or spherical cell, in contrast with the Cartesian case. By using Green's theorem, we show that the potential integral for such polar-type 3D sectors -- initially, a volume integral with singular kernel -- can be converted into a regular line-integral running over the lateral contour, thereby generalising a formula already known under axial symmetry. It therefore is a step towards the obtention of another potential/density pair. The new kernel is a finite function of the cell's shape (with the simplest form in cylindrical geometry), and mixes incomplete elliptic integrals, inverse trigonometric a...
New triangular mass-lumped finite elements of degree six for wave propagation
Mulder, W.A.
2013-01-01
Mass-lumped continuous finite elements allow for explicit time stepping with the second-order wave equation if the resulting integration weights are positive and provide sufficient accuracy. To meet these requirements on triangular and tetrahedral meshes, the construction of continuous finite elemen
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
FEMHD: An adaptive finite element method for MHD and edge modelling
Energy Technology Data Exchange (ETDEWEB)
Strauss, H.R.
1995-07-01
This paper describes the code FEMHD, an adaptive finite element MHD code, which is applied in a number of different manners to model MHD behavior and edge plasma phenomena on a diverted tokamak. The code uses an unstructured triangular mesh in 2D and wedge shaped mesh elements in 3D. The code has been adapted to look at neutral and charged particle dynamics in the plasma scrape off region, and into a full MHD-particle code.
Nonlinear dynamics of planetary gears using analytical and finite element models
Ambarisha, Vijaya Kumar; Parker, Robert G.
2007-05-01
Vibration-induced gear noise and dynamic loads remain key concerns in many transmission applications that use planetary gears. Tooth separations at large vibrations introduce nonlinearity in geared systems. The present work examines the complex, nonlinear dynamic behavior of spur planetary gears using two models: (i) a lumped-parameter model, and (ii) a finite element model. The two-dimensional (2D) lumped-parameter model represents the gears as lumped inertias, the gear meshes as nonlinear springs with tooth contact loss and periodically varying stiffness due to changing tooth contact conditions, and the supports as linear springs. The 2D finite element model is developed from a unique finite element-contact analysis solver specialized for gear dynamics. Mesh stiffness variation excitation, corner contact, and gear tooth contact loss are all intrinsically considered in the finite element analysis. The dynamics of planetary gears show a rich spectrum of nonlinear phenomena. Nonlinear jumps, chaotic motions, and period-doubling bifurcations occur when the mesh frequency or any of its higher harmonics are near a natural frequency of the system. Responses from the dynamic analysis using analytical and finite element models are successfully compared qualitatively and quantitatively. These comparisons validate the effectiveness of the lumped-parameter model to simulate the dynamics of planetary gears. Mesh phasing rules to suppress rotational and translational vibrations in planetary gears are valid even when nonlinearity from tooth contact loss occurs. These mesh phasing rules, however, are not valid in the chaotic and period-doubling regions.
The finite element method for the global gravity field modelling
Kollár, Michal; Macák, Marek; Mikula, Karol; Minarechová, Zuzana
2014-05-01
We present a finite element approach for solving the fixed gravimetric boundary-value problem on a global level. To that goal, we have defined the computational domain bounded by the real topography and a chosen satellite level. The boundary-value problem consists of the Laplace equation for the disturbing potential and the Neumann boundary condition given by the gravity disturbances applied on the bottom boundary, and the Dirichlet boundary condition given by the disturbing potential applied on the upper boundary. Afterwards, the computational domain is meshed with several different meshes chosen to avoid the problem of simple spherical meshes that contain a singularity at poles. Our aim has been to show how the right mesh can improve results as well as significantly reduce the computational time. The practical implementation has been done in the FEM software ANSYS using 3D linear elements SOLID70 and for solving the linear system of equations, the preconditioned conjugate gradients method has been chosen. The obtained disturbing potential has been applied to calculate the geopotential value W0.
Finite Element Analysis of the Crack Propagation for Solid Materials
Directory of Open Access Journals (Sweden)
Miloud Souiyah
2009-01-01
Full Text Available Problem statement: The use of fracture mechanics techniques in the assessment of performance and reliability of structure is on increase and the prediction of crack propagation in structure play important part. The finite element method is widely used for the evaluation of SIF for various types of crack configurations. Source code program of two-dimensional finite element model had been developed, to demonstrate the capability and its limitations, in predicting the crack propagation trajectory and the SIF values under linear elastic fracture analysis. Approach: Two different geometries were used on this finite element model in order, to analyze the reliability of this program on the crack propagation in linear and nonlinear elastic fracture mechanics. These geometries were namely; a rectangular plate with crack emanating from square-hole and Double Edge Notched Plate (DENT. Where, both geometries are in tensile loading and under mode I conditions. In addition, the source code program of this model was written by FORTRAN language. Therefore, a Displacement Extrapolation Technique (DET was employed particularly, to predict the crack propagations directions and to, calculate the Stress Intensity Factors (SIFs. Furthermore, the mesh for the finite elements was the unstructured type; generated using the advancing front method. And, the global h-type adaptive mesh was adopted based on the norm stress error estimator. While, the quarter-point singular elements were uniformly generated around the crack tip in the form of a rosette. Moreover, make a comparison between this current study with other relevant and published research study. Results: The application of the source code program of 2-D finite element model showed a significant result on linear elastic fracture mechanics. Based on the findings of the two different geometries from the current study, the result showed a good agreement. And, it seems like very close compare to the other published
Effective Finite Elements for Shell Analysis.
1984-02-20
conjunction with a shallow shell theory . It 2 should be noteJ that contrary to the results of earlier investigators [12,19], use of a shallow shell theory in...the inadequacy of the shallow shell theory for the relatively deep element emerging from such a coarse mesh. A considerable improvement is obtained
Gong, Jian; Volakis, John L.; Nurnberger, Michael W.
1995-01-01
This semi-annual report describes progress up to mid-January 1995. The report contains five sections all dealing with the modeling of spiral and patch antennas recessed in metallic platforms. Of significance is the development of decomposition schemes which separate the different regions of the antenna volume. Substantial effort was devoted to improving the feed model in the context of the finite element method (FEM). Finally, an innovative scheme for truncating finite element meshes is presented.
Ying, Jinyong; Xie, Dexuan
2015-10-01
The Poisson-Boltzmann equation (PBE) is one widely-used implicit solvent continuum model for calculating electrostatics of ionic solvated biomolecule. In this paper, a new finite element and finite difference hybrid method is presented to solve PBE efficiently based on a special seven-overlapped box partition with one central box containing the solute region and surrounded by six neighboring boxes. In particular, an efficient finite element solver is applied to the central box while a fast preconditioned conjugate gradient method using a multigrid V-cycle preconditioning is constructed for solving a system of finite difference equations defined on a uniform mesh of each neighboring box. Moreover, the PBE domain, the box partition, and an interface fitted tetrahedral mesh of the central box can be generated adaptively for a given PQR file of a biomolecule. This new hybrid PBE solver is programmed in C, Fortran, and Python as a software tool for predicting electrostatics of a biomolecule in a symmetric 1:1 ionic solvent. Numerical results on two test models with analytical solutions and 12 proteins validate this new software tool, and demonstrate its high performance in terms of CPU time and memory usage.
Saad, Bilal Mohammed
2014-06-28
We propose and analyze a combined finite volume-nonconforming finite element scheme on general meshes to simulate the two compressible phase flow in porous media. The diffusion term, which can be anisotropic and heterogeneous, is discretized by piecewise linear nonconforming triangular finite elements. The other terms are discretized by means of a cell-centered finite volume scheme on a dual mesh, where the dual volumes are constructed around the sides of the original mesh. The relative permeability of each phase is decentred according the sign of the velocity at the dual interface. This technique also ensures the validity of the discrete maximum principle for the saturation under a non restrictive shape regularity of the space mesh and the positiveness of all transmissibilities. Next, a priori estimates on the pressures and a function of the saturation that denote capillary terms are established. These stabilities results lead to some compactness arguments based on the use of the Kolmogorov compactness theorem, and allow us to derive the convergence of a subsequence of the sequence of approximate solutions to a weak solution of the continuous equations, provided the mesh size tends to zero. The proof is given for the complete system when the density of the each phase depends on its own pressure. © 2014 Springer-Verlag Berlin Heidelberg.
Finite element analysis of optical waveguides
Mabaya, N.; Lagasse, P. E.; Vandenbulcke, P.
1981-06-01
Several finite element programs for the computation of the guided modes of optical waveguides are presented. The advantages and limitations of a very general program for the analysis of anisotropic guides are presented. A possible solution to the problem of the spurious numerical modes, encountered when calculating higher order modes, is proposed. For isotropic waveguides, it is shown that both EH- and HE-type modes can be very accurately approximated by two different scalar finite element programs. Finally, a boundary perturbation method is outlined that makes it possible to calculate the attenuation coefficient of leaky modes in single material guides, starting from a finite element calculation.
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
Will Finite Elements Replace Structural Mechanics?
Ojalvo, I. U.
1984-01-01
This paper presents a personal view regarding the need for a continued interest and activity in structural methods in general, while viewing finite elements and the computer as simply two specific tools for assisting in this endeavor. An attempt is made to provide some insight as to why finite element methods seem to have "won the war," and to give examples of their more (and less) intelligent use. Items addressed include a highlight of unnecessary limitations of many existing standard finite element codes and where it is felt that further development work is needed.
Superconvergence of tricubic block finite elements
Institute of Scientific and Technical Information of China (English)
2009-01-01
In this paper, we first introduce interpolation operator of projection type in three dimen- sions, from which we derive weak estimates for tricubic block finite elements. Then using the estimate for the W 2, 1-seminorm of the discrete derivative Green’s function and the weak estimates, we show that the tricubic block finite element solution uh and the tricubic interpolant of projection type Πh3u have superclose gradient in the pointwise sense of the L∞-norm. Finally, this supercloseness is applied to superconvergence analysis, and the global superconvergence of the finite element approximation is derived.
Linear and Nonlinear Finite Elements.
1983-12-01
Sm (b) aON cipasofa mesh of b~ow elemears as.i (at 71Thoesi(dan (e)iw for 5. mod S... reqecive y. for emada2x2Gaess scheme (brken ink ) and a 3 x 3...8217:I :111d C i rr,,r ! (yr(Itt I’:V il jilt I JI! 1-11 . IL curves iFj. 101 are for a prcsstire that ill~;-. t1-1 Cequal st PS rum. p t,,t tlc cr it
Luboz, V; Swider, P; Payan, Y; Luboz, Vincent; Chabanas, Matthieu; Swider, Pascal; Payan, Yohan
2005-01-01
This paper addresses an important issue raised for the clinical relevance of Computer-Assisted Surgical applications, namely the methodology used to automatically build patient-specific Finite Element (FE) models of anatomical structures. From this perspective, a method is proposed, based on a technique called the Mesh-Matching method, followed by a process that corrects mesh irregularities. The Mesh-Matching algorithm generates patient-specific volume meshes from an existing generic model. The mesh regularization process is based on the Jacobian matrix transform related to the FE reference element and the current element. This method for generating patient-specific FE models is first applied to Computer-Assisted maxillofacial surgery, and more precisely to the FE elastic modelling of patient facial soft tissues. For each patient, the planned bone osteotomies (mandible, maxilla, chin) are used as boundary conditions to deform the FE face model, in order to predict the aesthetic outcome of the surgery. Seven F...
A new multiresolution finite element method based on a multiresolution quadrilateral plate element
Xia, YiMing
2014-01-01
A new multiresolution quadrilateral plate element is proposed and a multiresolution finite element method is hence presented. The multiresolution analysis (MRA) framework is formulated out of a mutually nesting displacement subspace sequence, whose basis functions are constructed of scaling and shifting on the element domain of basic node shape function. The basic node shape function is constructed by extending shape function around a specific node. The MRA endows the proposed element with the resolution level (RL) to adjust the element node number, thus modulating structural analysis accuracy accordingly. As a result, the traditional 4-node quadrilateral plate element and method is a monoresolution one and also a special case of the proposed element and method. The meshing for the monoresolution plate element model is based on the empiricism while the RL adjusting for the multiresolution is laid on the rigorous mathematical basis. The accuracy of a structural analysis is fully determined by the RL, not by th...
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.
Moving Finite Elements in 2-D.
1984-08-06
34 . - ; .-’- . - . -- .- -. . - -.. -- ; -. - - - - - ." . ,- . -••. - - ; . IOSR : TR. SAI-84/1299 (0 N MOVING FINITE ELEMENTS IN 2-I Final Report AFOSR Contract: F4962U-81-C-UO73 Program Manager
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.
Finite element modeling of corneal strip extensometry
CSIR Research Space (South Africa)
Botha, N
2012-12-01
Full Text Available numerically modelled in several studies, this study focusses on accurately modelling the strip extensiometry test. Two methods were considered to simulate the experimental conditions namely, a single phase and a two phase method. A finite element model...
A survey of mixed finite element methods
Brezzi, F.
1987-01-01
This paper is an introduction to and an overview of mixed finite element methods. It discusses the mixed formulation of certain basic problems in elasticity and hydrodynamics. It also discusses special techniques for solving the discrete problem.
Infinite to finite: An overview of finite element analysis
Directory of Open Access Journals (Sweden)
Srirekha A
2010-01-01
Full Text Available The method of finite elements was developed at perfectly right times; growing computer capacities, growing human skills and industry demands for ever faster and cost effective product development providing unlimited possibilities for the researching community. This paper reviews the basic concept, current status, advances, advantages, limitations and applications of finite element method (FEM in restorative dentistry and endodontics. Finite element method is able to reveal the otherwise inaccessible stress distribution within the tooth-restoration complex and it has proven to be a useful tool in the thinking process for the understanding of tooth biomechanics and the biomimetic approach in restorative dentistry. Further improvement of the non-linear FEM solutions should be encouraged to widen the range of applications in dental and oral health science.
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
A NOTE ON FINITE ELEMENT WAVELETS
Institute of Scientific and Technical Information of China (English)
谌秋辉; 陈翰麟
2001-01-01
The refinability and approximation order of finite element multi-scale vector are discussed in [1]. But the coefficients in the conditions of approximation order of finite element multi-scale vector are incorrect there. The main purpose of this note is to make a correction of the error in the main result of [1]. These coefficients are very important for the properties of wavelets, such as vanishing moments and regularity.
Institute of Scientific and Technical Information of China (English)
郑旖; 张为民
2012-01-01
Based on the mathematical expression is the 3D Model of the gear surface established in MAT-LAB.The method of object -oriented programming is applied to the establishment .The average distributed knots of the finite elements are generated at the curve of the tooth surface , which is based on the modular model .And the knots are the Basis of the generation of triangle elements of the tooth surface .% 在 MATLAB 中根据数学解析式建立齿轮齿面的三维模型，并且将面向对象的编程方法运用到数学模型的建立中。在模块化的齿面模型基础上，在齿面曲线上生成平均分布的有限元网格节点，并以生成的节点为基础建立齿面的三角形网格单元。
Finite element modeling of electromagnetic fields and waves using NASTRAN
Moyer, E. Thomas, Jr.; Schroeder, Erwin
1989-01-01
The various formulations of Maxwell's equations are reviewed with emphasis on those formulations which most readily form analogies with Navier's equations. Analogies involving scalar and vector potentials and electric and magnetic field components are presented. Formulations allowing for media with dielectric and conducting properties are emphasized. It is demonstrated that many problems in electromagnetism can be solved using the NASTRAN finite element code. Several fundamental problems involving time harmonic solutions of Maxwell's equations with known analytic solutions are solved using NASTRAN to demonstrate convergence and mesh requirements. Mesh requirements are studied as a function of frequency, conductivity, and dielectric properties. Applications in both low frequency and high frequency are highlighted. The low frequency problems demonstrate the ability to solve problems involving media inhomogeneity and unbounded domains. The high frequency applications demonstrate the ability to handle problems with large boundary to wavelength ratios.
A multilevel finite element method for Fredholm integral eigenvalue problems
Xie, Hehu; Zhou, Tao
2015-12-01
In this work, we proposed a multigrid finite element (MFE) method for solving the Fredholm integral eigenvalue problems. The main motivation for such studies is to compute the Karhunen-Loève expansions of random fields, which play an important role in the applications of uncertainty quantification. In our MFE framework, solving the eigenvalue problem is converted to doing a series of integral iterations and eigenvalue solving in the coarsest mesh. Then, any existing efficient integration scheme can be used for the associated integration process. The error estimates are provided, and the computational complexity is analyzed. It is noticed that the total computational work of our method is comparable with a single integration step in the finest mesh. Several numerical experiments are presented to validate the efficiency of the proposed numerical method.
hp-finite element methods for singular perturbations
Melenk, Jens M
2002-01-01
Many partial differential equations arising in practice are parameter-dependent problems that are of singularly perturbed type. Prominent examples include plate and shell models for small thickness in solid mechanics, convection-diffusion problems in fluid mechanics, and equations arising in semi-conductor device modelling. Common features of these problems are layers and, in the case of non-smooth geometries, corner singularities. Mesh design principles for the efficient approximation of both features by the hp-version of the finite element method (hp-FEM) are proposed in this volume. For a class of singularly perturbed problems on polygonal domains, robust exponential convergence of the hp-FEM based on these mesh design principles is established rigorously.
Institute of Scientific and Technical Information of China (English)
SHI Dong-yang; WANG Cai-xia
2008-01-01
This paper deals with a new nonconforming anisotropic rectangular finite element approximation for the planar elasticity problem with pure displacement boundary condition. By use of the special properties of this element,and by introducing the complementary space and a series of novel techniques,the optimal error estimates of the energy norm and the L2-norm are obtained. The restrictions of regularity assumption and quasi-uniform assumption or the inverse assumption on the meshes required in the conventional finite element methods analysis are to be got rid of and the applicable scope of the nonconforming finite elements is extended.
Finite element analysis of flexible, rotating blades
Mcgee, Oliver G.
1987-01-01
A reference guide that can be used when using the finite element method to approximate the static and dynamic behavior of flexible, rotating blades is given. Important parameters such as twist, sweep, camber, co-planar shell elements, centrifugal loads, and inertia properties are studied. Comparisons are made between NASTRAN elements through published benchmark tests. The main purpose is to summarize blade modeling strategies and to document capabilities and limitations (for flexible, rotating blades) of various NASTRAN elements.
Suvorov, A. S.; Sokov, E. M.; V'yushkina, I. A.
2016-09-01
A new method is presented for the automatic refinement of finite element models of complex mechanical-acoustic systems using the results of experimental studies. The method is based on control of the spectral characteristics via selection of the optimal distribution of adjustments to the stiffness of a finite element mesh. The results of testing the method are given to show the possibility of its use to significantly increase the simulation accuracy of vibration characteristics of bodies with arbitrary spatial configuration.
Algorithms and data structures for massively parallel generic adaptive finite element codes
Bangerth, Wolfgang
2011-12-01
Today\\'s largest supercomputers have 100,000s of processor cores and offer the potential to solve partial differential equations discretized by billions of unknowns. However, the complexity of scaling to such large machines and problem sizes has so far prevented the emergence of generic software libraries that support such computations, although these would lower the threshold of entry and enable many more applications to benefit from large-scale computing. We are concerned with providing this functionality for mesh-adaptive finite element computations. We assume the existence of an "oracle" that implements the generation and modification of an adaptive mesh distributed across many processors, and that responds to queries about its structure. Based on querying the oracle, we develop scalable algorithms and data structures for generic finite element methods. Specifically, we consider the parallel distribution of mesh data, global enumeration of degrees of freedom, constraints, and postprocessing. Our algorithms remove the bottlenecks that typically limit large-scale adaptive finite element analyses. We demonstrate scalability of complete finite element workflows on up to 16,384 processors. An implementation of the proposed algorithms, based on the open source software p4est as mesh oracle, is provided under an open source license through the widely used deal.II finite element software library. © 2011 ACM 0098-3500/2011/12-ART10 $10.00.
Quadrature representation of finite element variational forms
DEFF Research Database (Denmark)
Ølgaard, Kristian Breum; Wells, Garth N.
2012-01-01
This chapter addresses the conventional run-time quadrature approach for the numerical integration of local element tensors associated with finite element variational forms, and in particular automated optimizations that can be performed to reduce the number of floating point operations...
Finite Element Computational Dynamics of Rotating Systems
Directory of Open Access Journals (Sweden)
Jaroslav Mackerle
1999-01-01
Full Text Available This bibliography lists references to papers, conference proceedings and theses/dissertations dealing with finite element analysis of rotor dynamics problems that were published in 1994–1998. It contains 319 citations. Also included, as separate subsections, are finite element analyses of rotor elements – discs, shafts, spindles, and blades. Topics dealing with fracture mechanics, contact and stability problems of rotating machinery are also considered in specific sections. The last part of the bibliography presents papers dealing with specific industrial applications.
MULTIGRID METHODS FOR THE GENERALIZED STOKES EQUATIONS BASED ON MIXED FINITE ELEMENT METHODS
Institute of Scientific and Technical Information of China (English)
Qing-ping Deng; Xiao-ping Feng
2002-01-01
Multigrid methods are developed and analyzed for the generalized stationary Stokes equations which are discretized by various mixed finite element methods. In this paper, the multigrid algorithm, the criterion for prolongation operators and the convergence analysis are all established in an abstract and element-independent fashion. It is proven that the multigrid algorithm converges optimally if the prolongation operator satisfies the criterion.To utilize the abstract result, more than ten well-known mixed finite elements for the Stokes problems are discussed in detail and examples of prolongation operators are constructed explicitly. For nonconforming elements, it is shown that the usual local averaging technique for constructing prolongation operators can be replaced by a computationally cheaper alternative, random choice technique. Moreover, since the algorithm and analysis allows using of nonnested meshes, the abstract result also applies to low order mixed finite elements, which are usually stable only for some special mesh structures.
Institute of Scientific and Technical Information of China (English)
Sutthisak Phongthanapanich; Pramote Dechaumphai
2008-01-01
A nodeless variable element method with the flux-based formulation is developed to analyze two-dimensional thermal-structural problems. The nodeless variable formula-tion provides accurate temperature distributions to yield more accurate thermal stress solutions. The flux-based formula-tion is used to reduce the complexity in deriving the finite element equations as compared to the conventional finite element method. The solution accuracy is further improved by implementing an adaptive meshing technique to generate finite element meshes that can adapt and move along with the transient solution behavior. A version of a nearly opti- mal element size determination is proposed to provide high convergence rate of the predicted solutions. The combined procedure is evaluated by solving several thermal, structural,and thermal stress problems.
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.
Exact finite elements for conduction and convection
Thornton, E. A.; Dechaumphai, P.; Tamma, K. K.
1981-01-01
An appproach for developing exact one dimensional conduction-convection finite elements is presented. Exact interpolation functions are derived based on solutions to the governing differential equations by employing a nodeless parameter. Exact interpolation functions are presented for combined heat transfer in several solids of different shapes, and for combined heat transfer in a flow passage. Numerical results demonstrate that exact one dimensional elements offer advantages over elements based on approximate interpolation functions. Previously announced in STAR as N81-31507
Domain decomposition based iterative methods for nonlinear elliptic finite element problems
Energy Technology Data Exchange (ETDEWEB)
Cai, X.C. [Univ. of Colorado, Boulder, CO (United States)
1994-12-31
The class of overlapping Schwarz algorithms has been extensively studied for linear elliptic finite element problems. In this presentation, the author considers the solution of systems of nonlinear algebraic equations arising from the finite element discretization of some nonlinear elliptic equations. Several overlapping Schwarz algorithms, including the additive and multiplicative versions, with inexact Newton acceleration will be discussed. The author shows that the convergence rate of the Newton`s method is independent of the mesh size used in the finite element discretization, and also independent of the number of subdomains into which the original domain in decomposed. Numerical examples will be presented.
Gao, Yongchang; Jin, Zhongmin; Wang, Ling; Wang, Manyi
2015-06-01
An explicit finite element method was developed to predict the dynamic behavior of the contact mechanics for a hip implant under normal walking conditions. Two key parameters of mesh sensitivity and time steps were examined to balance the accuracy and computational cost. Both the maximum contact pressure and accumulated sliding distance showed good agreement with those in the previous studies using the implicit finite element analysis and analytical methods. Therefore, the explicit finite element method could be used to predict the contact pressure and accumulated sliding distance for an artificial hip joint simultaneously in dynamic manner.
Fracture Capabilities in Grizzly with the extended Finite Element Method (X-FEM)
Energy Technology Data Exchange (ETDEWEB)
Dolbow, John [Idaho National Lab. (INL), Idaho Falls, ID (United States); Zhang, Ziyu [Idaho National Lab. (INL), Idaho Falls, ID (United States); Spencer, Benjamin [Idaho National Lab. (INL), Idaho Falls, ID (United States); Jiang, Wen [Idaho National Lab. (INL), Idaho Falls, ID (United States)
2015-09-01
Efforts are underway to develop fracture mechanics capabilities in the Grizzly code to enable it to be used to perform deterministic fracture assessments of degraded reactor pressure vessels (RPVs). A capability was previously developed to calculate three-dimensional interaction- integrals to extract mixed-mode stress-intensity factors. This capability requires the use of a finite element mesh that conforms to the crack geometry. The eXtended Finite Element Method (X-FEM) provides a means to represent a crack geometry without explicitly fitting the finite element mesh to it. This is effected by enhancing the element kinematics to represent jump discontinuities at arbitrary locations inside of the element, as well as the incorporation of asymptotic near-tip fields to better capture crack singularities. In this work, use of only the discontinuous enrichment functions was examined to see how accurate stress intensity factors could still be calculated. This report documents the following work to enhance Grizzly’s engineering fracture capabilities by introducing arbitrary jump discontinuities for prescribed crack geometries; X-FEM Mesh Cutting in 3D: to enhance the kinematics of elements that are intersected by arbitrary crack geometries, a mesh cutting algorithm was implemented in Grizzly. The algorithm introduces new virtual nodes and creates partial elements, and then creates a new mesh connectivity; Interaction Integral Modifications: the existing code for evaluating the interaction integral in Grizzly was based on the assumption of a mesh that was fitted to the crack geometry. Modifications were made to allow for the possibility of a crack front that passes arbitrarily through the mesh; and Benchmarking for 3D Fracture: the new capabilities were benchmarked against mixed-mode three-dimensional fracture problems with known analytical solutions.
Latest Trends in Finite Element Analysis
Directory of Open Access Journals (Sweden)
L. S. Madhav
1996-01-01
Full Text Available This paper highlights the advances in computer graphics and the computational power of the processors which have promoted a method of analysis, applicable to almost all the fields of engineering. The advantages of the computers have been judiciously used in the design of algorithms, based on the principles of finite difference, finite element, boundary element, etc., intended for the analysis of engineering components. The concept of finite element method which has been generalised with the availability of commercial software, is also reviewed with a special emphasis on the future trends. The modelling and visualisation techniques have also been discussed with an inner perspective on future of visual display of multidimensional complex information. The application of these techniques in some fields is also indicated.
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.
Higher-order adaptive finite-element methods for Kohn-Sham density functional theory
Motamarri, Phani; Leiter, Kenneth; Knap, Jaroslaw; Gavini, Vikram
2012-01-01
We present an efficient computational approach to perform real-space electronic structure calculations using an adaptive higher-order finite-element discretization of Kohn-Sham density-functional theory (DFT).To this end, we develop an \\emph{a priori} mesh adaption technique to construct a close to optimal finite-element discretization of the problem. We further propose an efficient solution strategy for solving the discrete eigenvalue problem by using spectral finite-elements in conjunction with Gauss-Lobatto quadrature, and a Chebyshev acceleration technique for computing the occupied eigenspace. Using the proposed solution procedure, we investigate the computational efficiency afforded by higher-order finite-element discretizations of the Kohn-Sham DFT problem. Our studies suggest that staggering computational savings---of the order of $1000-$fold---can be realized, for both all-electron and pseudopotential calculations, by using higher-order finite-element discretizations. On all the benchmark systems stu...
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
A Novel Virtual Node Hexahedral Element with Exact Integration and Octree Meshing
Directory of Open Access Journals (Sweden)
Logah Perumal
2016-01-01
Full Text Available The method presented in this work is a 3-dimensional polyhedral finite element (3D PFEM based on virtual node method. Novel virtual node polyhedral elements (termed as VPHE are developed here, particularly virtual node hexahedral element (termed as VHE. Stiffness matrices of these polyhedral elements consist of simple polynomials. Thus, a new algorithm is introduced in this paper, which enables exact integration of monomials without a need for high number of integration points and weights. The number of nodes for VHE elements is not restricted, as opposed to the conventional hexahedral elements. This feature enables formulation of transition elements (termed as T-VHE which are useful to adaptive computation. Performances of the new VHE elements in solid mechanics and conductive heat transfer phenomena are examined through numerical simulations. The new T-VHE elements are utilized in octree mesh. The VHE elements are found to produce good results and T-VHE elements help to reduce number of global nodes for the analysis.
Nonlinear explicit transient finite element analysis on the Intel Delta
Energy Technology Data Exchange (ETDEWEB)
Plaskacz, E.J. [Argonne National Lab., IL (United States); Ramirez, M.R.; Gupta, S. [Johns Hopkins Univ., Baltimore, MD (United States). Dept. of Civil Engineering
1993-03-01
Many large scale finite element problems are intractable on current generation production supercomputers. High-performance computer architectures offer effective avenues to bridge the gap between computational needs and the power of computational hardware. The biggest challenge lies in the substitution of the key algorithms in an application program with redesigned algorithms which exploit the new architectures and use better or more appropriate numerical techniques. A methodology for implementing nonlinear finite element analysis on a homogeneous distributed processing network is discussed. The method can also be extended to heterogeneous networks comprised of different machine architectures provided that they have a mutual communication interface. This unique feature has greatly facilitated the port of the code to the 8-node Intel Touchstone Gamma and then the 512-node Intel Touchstone Delta. The domain is decomposed serially in a preprocessor. Separate input files are written for each subdomain. These files are read in by local copies of the program executable operating in parallel. Communication between processors is addressed utilizing asynchronous and synchronous message passing. The basic kernel of message passing is the internal force exchange which is analogous to the computed interactions between sections of physical bodies in static stress analysis. Benchmarks for the Intel Delta are presented. Performance exceeding 1 gigaflop was attained. Results for two large-scale finite element meshes are presented.
Nonlinear explicit transient finite element analysis on the Intel Delta
Energy Technology Data Exchange (ETDEWEB)
Plaskacz, E.J. (Argonne National Lab., IL (United States)); Ramirez, M.R.; Gupta, S. (Johns Hopkins Univ., Baltimore, MD (United States). Dept. of Civil Engineering)
1993-01-01
Many large scale finite element problems are intractable on current generation production supercomputers. High-performance computer architectures offer effective avenues to bridge the gap between computational needs and the power of computational hardware. The biggest challenge lies in the substitution of the key algorithms in an application program with redesigned algorithms which exploit the new architectures and use better or more appropriate numerical techniques. A methodology for implementing nonlinear finite element analysis on a homogeneous distributed processing network is discussed. The method can also be extended to heterogeneous networks comprised of different machine architectures provided that they have a mutual communication interface. This unique feature has greatly facilitated the port of the code to the 8-node Intel Touchstone Gamma and then the 512-node Intel Touchstone Delta. The domain is decomposed serially in a preprocessor. Separate input files are written for each subdomain. These files are read in by local copies of the program executable operating in parallel. Communication between processors is addressed utilizing asynchronous and synchronous message passing. The basic kernel of message passing is the internal force exchange which is analogous to the computed interactions between sections of physical bodies in static stress analysis. Benchmarks for the Intel Delta are presented. Performance exceeding 1 gigaflop was attained. Results for two large-scale finite element meshes are presented.
Kou, Jisheng
2017-06-09
In this paper, a new three-field weak formulation for Stokes problems is developed, and from this, a dual-mixed finite element method is proposed on a rectangular mesh. In the proposed mixed methods, the components of stress tensor are approximated by piecewise constant functions or Q1 functions, while the velocity and pressure are discretized by the lowest-order Raviart-Thomas element and the piecewise constant functions, respectively. Using quadrature rules, we demonstrate that this scheme can be reduced into a finite volume method on staggered grid, which is extensively used in computational fluid mechanics and engineering.
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 simulation of stress intensity factors in elastic-plastic crack growth
Institute of Scientific and Technical Information of China (English)
ALSHOAIBI Abdulnaser M.; ARIFFIN Ahmad Kamal
2006-01-01
A finite element program developed elastic-plastic crack propagation simulation using Fortran language. At each propagation step, the adaptive mesh is automatically refined based on a posteriori h-type refinement using norm stress error estimator. A rosette of quarter-point elements is then constructed around the crack tip to facilitate the prediction of crack growth based on the maximum normal stress criterion and to calculate stress intensity factors under plane stress and plane strain conditions.Crack was modelled to propagate through the inter-element in the mesh. Some examples are presented to show the results of the implementation.
Numerical computation of transonic flows by finite-element and finite-difference methods
Hafez, M. M.; Wellford, L. C.; Merkle, C. L.; Murman, E. M.
1978-01-01
Studies on applications of the finite element approach to transonic flow calculations are reported. Different discretization techniques of the differential equations and boundary conditions are compared. Finite element analogs of Murman's mixed type finite difference operators for small disturbance formulations were constructed and the time dependent approach (using finite differences in time and finite elements in space) was examined.
Finite element based simulation of dry sliding wear
Hegadekatte, V.; Huber, N.; Kraft, O.
2005-01-01
In order to predict wear and eventually the life-span of complex mechanical systems, several hundred thousand operating cycles have to be simulated. Therefore, a finite element (FE) post-processor is the optimum choice, considering the computational expense. A wear simulation approach based on Archard's wear law is implemented in an FE post-processor that works in association with a commercial FE package, ABAQUS, for solving the general deformable-deformable contact problem. Local wear is computed and then integrated over the sliding distance using the Euler integration scheme. The wear simulation tool works in a loop and performs a series of static FE-simulations with updated surface geometries to get a realistic contact pressure distribution on the contacting surfaces. It will be demonstrated that this efficient approach can simulate wear on both two-dimensional and three-dimensional surface topologies. The wear on both the interacting surfaces is computed using the contact pressure distribution from a two-dimensional or three-dimensional simulation, depending on the case. After every wear step the geometry is re-meshed to correct the deformed mesh due to wear, thus ensuring a fairly uniform mesh for further processing. The importance and suitability of such a wear simulation tool will be enunciated in this paper.
A Minimum-Residual Finite Element Method for the Convection-Diffusion Equation
2013-05-01
examples of nonstan- dard discretizations include higher order continuity basis functions (splines and NURBS [34]), and discontinuous functions (DG...analysis: CAD, finite elements, NURBS , exact geometry and mesh refinement. Computer Methods in Applied Mechanics and Engineering, 194(39–41):4135
Simulation of wind effects on tall structures by finite element method
Ebrahimi, Masood
2016-06-01
In the present study finite element method is used to predict the wind forces on a tall structure. The governing equations of mass and momentum with boundary conditions are solved. The κ- ɛ turbulence model is utilized to calculate the turbulence viscosity. The results are independent from the generated mesh. The numerical results are validated with American Society of Civil Engineering standards.
Automated volumetric grid generation for finite element modeling of human hand joints
Energy Technology Data Exchange (ETDEWEB)
Hollerbach, K.; Underhill, K. [Lawrence Livermore National Lab., CA (United States); Rainsberger, R. [XYZ Scientific Applications, Inc., Livermore, CA (United States)
1995-02-01
We are developing techniques for finite element analysis of human joints. These techniques need to provide high quality results rapidly in order to be useful to a physician. The research presented here increases model quality and decreases user input time by automating the volumetric mesh generation step.
Directory of Open Access Journals (Sweden)
Paulo Cesar Plaisant Junior
2011-09-01
Full Text Available Finite element models are proposed to the micromechanical analysis of a representative volume of composite materials. A detailed description of the meshes, boundary conditions, and loadings are presented. An illustrative application is given to evaluate stress amplification factors within a representative volume of the unidirectional carbon fiber composite plate. The results are discussed and compared to the numerical findings.
Space-time discontinuous Galerkin finite element method for inviscid gas dynamics
van der Ven, H.; van der Vegt, Jacobus J.W.; Bouwman, E.G.; Bathe, K.J.
2003-01-01
In this paper an overview is given of the space-time discontinuous Galerkin finite element method for the solution of the Euler equations of gas dynamics. This technique is well suited for problems which require moving meshes to deal with changes in the domain boundary. The method is demonstrated
Implementation of a finite-element approximation of the Mumford-Shah functional
DEFF Research Database (Denmark)
Bourdin, Blaise; Chambolle, Antonin
1999-01-01
We present and detail a method for the numerical solving of the Mumford-Shah problem, based on a finite element method and on adaptive meshes. We start with a formulation introduced by A. Chambolle and G. Dal Maso, detail its numerical implementation and then propose a variant which is proved to ...
A moving mesh finite difference method for equilibrium radiation diffusion equations
Energy Technology Data Exchange (ETDEWEB)
Yang, Xiaobo, E-mail: xwindyb@126.com [Department of Mathematics, College of Science, China University of Mining and Technology, Xuzhou, Jiangsu 221116 (China); Huang, Weizhang, E-mail: whuang@ku.edu [Department of Mathematics, University of Kansas, Lawrence, KS 66045 (United States); Qiu, Jianxian, E-mail: jxqiu@xmu.edu.cn [School of Mathematical Sciences and Fujian Provincial Key Laboratory of Mathematical Modeling and High-Performance Scientific Computing, Xiamen University, Xiamen, Fujian 361005 (China)
2015-10-01
An efficient moving mesh finite difference method is developed for the numerical solution of equilibrium radiation diffusion equations in two dimensions. The method is based on the moving mesh partial differential equation approach and moves the mesh continuously in time using a system of meshing partial differential equations. The mesh adaptation is controlled through a Hessian-based monitor function and the so-called equidistribution and alignment principles. Several challenging issues in the numerical solution are addressed. Particularly, the radiation diffusion coefficient depends on the energy density highly nonlinearly. This nonlinearity is treated using a predictor–corrector and lagged diffusion strategy. Moreover, the nonnegativity of the energy density is maintained using a cutoff method which has been known in literature to retain the accuracy and convergence order of finite difference approximation for parabolic equations. Numerical examples with multi-material, multiple spot concentration situations are presented. Numerical results show that the method works well for radiation diffusion equations and can produce numerical solutions of good accuracy. It is also shown that a two-level mesh movement strategy can significantly improve the efficiency of the computation.
Orthodontic treatment: Introducing finite element analysis
Driel, W.D. van; Leeuwen, E.J. van
1998-01-01
The aim of orthodontic treatment is the displacement of teeth by means ofspecial appliances, like braces and brackets. Through these appliances the orthodontist can apply a set of forces to the teeth which wilt result in its displacement through the jawbone. Finite Element analysis of this process e
Interval Finite Element Analysis of Wing Flutter
Institute of Scientific and Technical Information of China (English)
Wang Xiaojun; Qiu Zhiping
2008-01-01
The influences of uncertainties in structural parameters on the flutter speed of wing are studied. On the basis of the deterministic flutter analysis model of wing, the uncertainties in structural parameters are considered and described by interval numbers. By virtue of first-order Taylor series expansion, the lower and upper bound curves of the transient decay rate coefficient versus wind velocity are given. So the interval estimation of the flutter critical wind speed of wing can be obtained, which is more reasonable than the point esti- mation obtained by the deterministic flutter analysis and provides the basis for the further non-probabilistic interval reliability analysis of wing flutter. The flow chart for interval finite element model of flutter analysis of wing is given. The proposed interval finite element model and the stochastic finite element model for wing flutter analysis are compared by the examples of a three degrees of freedorn airfoil and fuselage and a 15° swepthack wing, and the results have shown the effectiveness and feasibility of the presented model. The prominent advantage of the proposed interval finite element model is that only the bounds of uncertain parameters axe required, and the probabilistic distribution densities or other statistical characteristics are not needed.
Fast finite elements for surgery simulation
DEFF Research Database (Denmark)
Bro-Nielsen, Morten
1997-01-01
This paper discusses volumetric deformable models for modeling human body parts and organs in surgery simulation systems. These models are built using finite element models for linear elastic materials. To achieve real-time response condensation has been applied to the system stiffness matrix, an...
Watanabe, Ikumu; Terada, Kenjiro; Neto, Eduardo Alberto de Souza; Perić, Djordje
The objective of this contribution is to develop an elastic-plastic-damage constitutive model for crystal grain and to incorporate it with two-scale finite element analyses based on mathematical homogenization method, in order to characterize the macroscopic tensile strength of polycrystalline metals. More specifically, the constitutive model for single crystal is obtained by combining hyperelasticity, a rate-independent single crystal plasticity and a continuum damage model. The evolution equations, stress update algorithm and consistent tangent are derived within the framework of standard elastoplasticity at finite strain. By employing two-scale finite element analysis, the ductile behaviour of polycrystalline metals and corresponding tensile strength are evaluated. The importance of finite element formulation is examined by comparing performance of several finite elements and their convergence behaviour is assessed with mesh refinement. Finally, the grain size effect on yield and tensile strength is analysed in order to illustrate the versatility of the proposed two-scale model.
Directory of Open Access Journals (Sweden)
Matthew R. McCurry
2015-06-01
Full Text Available The reliability of finite element analysis (FEA in biomechanical investigations depends upon understanding the influence of model assumptions. In producing finite element models, surface mesh resolution is influenced by the resolution of input geometry, and influences the resolution of the ensuing solid mesh used for numerical analysis. Despite a large number of studies incorporating sensitivity studies of the effects of solid mesh resolution there has not yet been any investigation into the effect of surface mesh resolution upon results in a comparative context. Here we use a dataset of crocodile crania to examine the effects of surface resolution on FEA results in a comparative context. Seven high-resolution surface meshes were each down-sampled to varying degrees while keeping the resulting number of solid elements constant. These models were then subjected to bite and shake load cases using finite element analysis. The results show that incremental decreases in surface resolution can result in fluctuations in strain magnitudes, but that it is possible to obtain stable results using lower resolution surface in a comparative FEA study. As surface mesh resolution links input geometry with the resulting solid mesh, the implication of these results is that low resolution input geometry and solid meshes may provide valid results in a comparative context.
A Floating Node Method for the Modelling of Discontinuities Within a Finite Element
Pinho, Silvestre T.; Chen, B. Y.; DeCarvalho, Nelson V.; Baiz, P. M.; Tay, T. E.
2013-01-01
This paper focuses on the accurate numerical representation of complex networks of evolving discontinuities in solids, with particular emphasis on cracks. The limitation of the standard finite element method (FEM) in approximating discontinuous solutions has motivated the development of re-meshing, smeared crack models, the eXtended Finite Element Method (XFEM) and the Phantom Node Method (PNM). We propose a new method which has some similarities to the PNM, but crucially: (i) does not introduce an error on the crack geometry when mapping to natural coordinates; (ii) does not require numerical integration over only part of a domain; (iii) can incorporate weak discontinuities and cohesive cracks more readily; (iv) is ideally suited for the representation of multiple and complex networks of (weak, strong and cohesive) discontinuities; (v) leads to the same solution as a finite element mesh where the discontinuity is represented explicitly; and (vi) is conceptually simpler than the PNM.
Finite element analysis of dynamic response and structure borne noise of gearbox
Institute of Scientific and Technical Information of China (English)
LIU Wen; LIN Teng-jiao; LI Run-fang; DU Xue-song
2007-01-01
A dynamic finite element method combined with finite element mixed formula for contact problem is used to analyze the dynamic characteristics of gear system. Considering the stiffness excitation, error excitation and meshing shock excitation, the dynamic finite element model is established for the entire gear system which includes gears, shafts, bearings and gearbox housing. By the software of I-DEAS, the natural frequency, normal mode, dynamic time-domain response, frequency-domain response and one-third octave velocity grade structure borne noise of gear system are studied by the method of theoretical modal analysis and dynamic response analysis. The maximum values of vibration and structure borne noise are occurred at the mesh frequency of output grade gearing.
Jacob, Anaïs; Mehmanparast, Ali
2016-07-01
The effects of microstructure, grain and grain boundary (GB) properties on predicted damage paths and indicative crack propagation direction have been examined for a polycrystalline material using mesoscale finite element simulations. Numerical analyses were carried out on a compact tension specimen geometry containing granular mesh structures with random grain shapes and sizes of average diameter 100μm. Nanoindentation tests were performed to investigate the dependency of mesoscale hardness measurements on the indentation location with respect to grain and GB regions. Finite element results have shown that under tensile loading conditions, the predicted damage paths are very sensitive to the granular mesh structure, GB properties and individual grain properties. Furthermore, finite element results have revealed that the cracking mode (i.e., transgranular/intergranular) and maximum crack deviation angle are strongly dependent on the material microstructures employed in simulations.
On Hybrid and mixed finite element methods
Pian, T. H. H.
1981-01-01
Three versions of the assumed stress hybrid model in finite element methods and the corresponding variational principles for the formulation are presented. Examples of rank deficiency for stiffness matrices by the hybrid stress model are given and their corresponding kinematic deformation modes are identified. A discussion of the derivation of general semi-Loof elements for plates and shells by the hybrid stress method is given. It is shown that the equilibrium model by Fraeijs de Veubeke can be derived by the approach of the hybrid stress model as a special case of semi-Loof elements.
Finite Dynamic Elements and Modal Analysis
Directory of Open Access Journals (Sweden)
N.J. Fergusson
1993-01-01
Full Text Available A general modal analysis scheme is derived for forced response that makes use of high accuracy modes computed by the dynamic element method. The new procedure differs from the usual modal analysis in that the modes are obtained from a power series expansion for the dynamic stiffness matrix that includes an extra dynamic correction term in addition to the static stiffness matrix and the consistent mass matrix based on static displacement. A cantilevered beam example is used to demonstrate the relative accuracies of the dynamic element and the traditional finite element methods.
Revolution in Orthodontics: Finite element analysis
Singh, Johar Rajvinder; Kambalyal, Prabhuraj; Jain, Megha; Khandelwal, Piyush
2016-01-01
Engineering has not only developed in the field of medicine but has also become quite established in the field of dentistry, especially Orthodontics. Finite element analysis (FEA) is a computational procedure to calculate the stress in an element, which performs a model solution. This structural analysis allows the determination of stress resulting from external force, pressure, thermal change, and other factors. This method is extremely useful for indicating mechanical aspects of biomaterials and human tissues that can hardly be measured in vivo. The results obtained can then be studied using visualization software within the finite element method (FEM) to view a variety of parameters, and to fully identify implications of the analysis. This is a review to show the applications of FEM in Orthodontics. It is extremely important to verify what the purpose of the study is in order to correctly apply FEM. PMID:27114948
Finite element analysis of tibial fractures
DEFF Research Database (Denmark)
Wong, Christian Nai En; Mikkelsen, Mikkel Peter W; Hansen, Leif Berner
2010-01-01
INTRODUCTION: Fractures of the tibial shaft are relatively common injuries. There are indications that tibial shaft fractures share characteristics in terms of site, type and local fracture mechanisms. In this study, we aimed to set up a mathematical, computer-based model using finite element...... analysis of the bones of the lower leg to examine if such a model is adequate for prediction of fracture locations and patterns. In future studies, we aim to use these biomechanical results to examine fracture prevention, among others, and to simulate different types of osteosynthesis and the process...... Project. The data consisted of 21,219 3D elements with a cortical shell and a trabecular core. Three types of load of torsion, a direct lateral load and axial compression were applied. RESULTS: The finite element linear static analysis resulted in relevant fracture localizations and indicated relevant...
Boscheri, Walter; Dumbser, Michael
2017-10-01
We present a new family of high order accurate fully discrete one-step Discontinuous Galerkin (DG) finite element schemes on moving unstructured meshes for the solution of nonlinear hyperbolic PDE in multiple space dimensions, which may also include parabolic terms in order to model dissipative transport processes, like molecular viscosity or heat conduction. High order piecewise polynomials of degree N are adopted to represent the discrete solution at each time level and within each spatial control volume of the computational grid, while high order of accuracy in time is achieved by the ADER approach, making use of an element-local space-time Galerkin finite element predictor. A novel nodal solver algorithm based on the HLL flux is derived to compute the velocity for each nodal degree of freedom that describes the current mesh geometry. In our algorithm the spatial mesh configuration can be defined in two different ways: either by an isoparametric approach that generates curved control volumes, or by a piecewise linear decomposition of each spatial control volume into simplex sub-elements. Each technique generates a corresponding number of geometrical degrees of freedom needed to describe the current mesh configuration and which must be considered by the nodal solver for determining the grid velocity. The connection of the old mesh configuration at time tn with the new one at time t n + 1 provides the space-time control volumes on which the governing equations have to be integrated in order to obtain the time evolution of the discrete solution. Our numerical method belongs to the category of so-called direct Arbitrary-Lagrangian-Eulerian (ALE) schemes, where a space-time conservation formulation of the governing PDE system is considered and which already takes into account the new grid geometry (including a possible rezoning step) directly during the computation of the numerical fluxes. We emphasize that our method is a moving mesh method, as opposed to total
HyperMesh-based Finite Element Analysis of A Special Vehicle Frame%基于Hyper Mesh的某液压减震车车架有限元分析
Institute of Scientific and Technical Information of China (English)
周青; 陈靖芯; 李红; 郑再象
2015-01-01
The three dimensional design model of a special vehicle frame was set up and simplified ,and the CAE model of the frame was built using HyperMesh software ,then the static analysis was carried out in the conditions of blending and torsion .The simulation results can be used to guide the further optimization analysis of the frame structure .%建立某特种车车架的三维设计模型，对模型进行必要的简化，利用 HyperMesh软件建立车架的CAE模型，并对此模型进行弯曲工况和扭转工况下的静力学分析，用于指导后续车架结构的进一步优化。
Hambli, Ridha
2011-01-01
The aim of this paper is to develop a multiscale hierarchical hybrid model based on finite element analysis and neural network computation to link mesoscopic scale (trabecular network level) and macroscopic (whole bone level) to simulate bone remodelling process. Because whole bone simulation considering the 3D trabecular level is time consuming, the finite element calculation is performed at macroscopic level and a trained neural network are employed as numerical devices for substituting the finite element code needed for the mesoscale prediction. The bone mechanical properties are updated at macroscopic scale depending on the morphological organization at the mesoscopic computed by the trained neural network. The digital image-based modeling technique using m-CT and voxel finite element mesh is used to capture 2 mm3 Representative Volume Elements at mesoscale level in a femur head. The input data for the artificial neural network are a set of bone material parameters, boundary conditions and the applied str...
Narayanaswami, R.
1973-01-01
A new higher order triangular plate-bending finite element is presented which possesses high accuracy for practical mesh subdivisions and which uses only translations and rotations as grid point degrees of freedom. The element has 18 degrees of freedom, the transverse displacement and two rotations at the vertices and mid-side grid points of the triangle. The transverse displacement within the element is approximated by a quintic polynomial; the bending strains thus vary cubically within the element. Transverse shear flexibility is taken into account in the stiffness formulation. Two examples of static and dynamic analysis are included to show the behavior of the element.
Coarse-grained molecular dynamics: Nonlinear finite elements and finite temperature
Energy Technology Data Exchange (ETDEWEB)
Rudd, R E; Broughton, J Q
2005-05-30
Coarse-grained molecular dynamics (CGMD) is a technique developed as a concurrent multiscale model that couples conventional molecular dynamics (MD) to a more coarse-grained description of the periphery. The coarse-grained regions are modeled on a mesh in a formulation that generalizes conventional finite element modeling (FEM) of continuum elasticity. CGMD is derived solely from the MD model, however, and has no continuum parameters. As a result, it provides a coupling that is smooth and provides control of errors that arise at the coupling between the atomistic and coarse-grained regions. In this article, we elaborate on the formulation of CGMD, describing in detail how CGMD is applied to anharmonic solids and finite temperature simulations. As tests of CGMD, we present in detail the calculation of the phonon spectra for solid argon and tantalum in 3D, demonstrating how CGMD provides a better description of the elastic waves than that provided by FEM. We also present elastic wave scattering calculations that show the elastic wave scattering is more benign in CGMD than FEM. We also discuss the dependence of scattering on the properties of the mesh. We introduce a rigid approximation to CGMD that eliminates internal relaxation, similar to the Quasicontinuum technique, and compare it to the full CGMD.
SURFACE FINITE ELEMENTS FOR PARABOLIC EQUATIONS
Institute of Scientific and Technical Information of China (English)
G. Dziuk; C.M. Elliott
2007-01-01
In this article we define a surface finite element method (SFEM) for the numerical solution of parabolic partial differential equations on hypersurfaces Γ in (R)n+1. The key idea is based on the approximation of Γ by a polyhedral surface Γh consisting of a union of simplices (triangles for n = 2, intervals for n = 1) with vertices on Γ. A finite element space of functions is then defined by taking the continuous functions on Γh which are linear affine on each simplex of the polygonal surface. We use surface gradients to define weak forms of elliptic operators and naturally generate weak formulations of elliptic and parabolic equations on Γ. Our finite element method is applied to weak forms of the equations. The computation of the mass and element stiffness matrices are simple and straightforward.We give an example of error bounds in the case of semi-discretization in space for a fourth order linear problem. Numerical experiments are described for several linear and nonlinear partial differential equations. In particular the power of the method is demonstrated by employing it to solve highly nonlinear second and fourth order problems such as surface Allen-Cahn and Cahn-Hilliard equations and surface level set equations for geodesic mean curvature flow.
Energy Technology Data Exchange (ETDEWEB)
Cwik, T.; Jamnejad, V.; Zuffada, C. [California Institute of Technology, Pasadena, CA (United States)
1994-12-31
The usefulness of finite element modeling follows from the ability to accurately simulate the geometry and three-dimensional fields on the scale of a fraction of a wavelength. To make this modeling practical for engineering design, it is necessary to integrate the stages of geometry modeling and mesh generation, numerical solution of the fields-a stage heavily dependent on the efficient use of a sparse matrix equation solver, and display of field information. The stages of geometry modeling, mesh generation, and field display are commonly completed using commercially available software packages. Algorithms for the numerical solution of the fields need to be written for the specific class of problems considered. Interior problems, i.e. simulating fields in waveguides and cavities, have been successfully solved using finite element methods. Exterior problems, i.e. simulating fields scattered or radiated from structures, are more difficult to model because of the need to numerically truncate the finite element mesh. To practically compute a solution to exterior problems, the domain must be truncated at some finite surface where the Sommerfeld radiation condition is enforced, either approximately or exactly. Approximate methods attempt to truncate the mesh using only local field information at each grid point, whereas exact methods are global, needing information from the entire mesh boundary. In this work, a method that couples three-dimensional finite element (FE) solutions interior to the bounding surface, with an efficient integral equation (IE) solution that exactly enforces the Sommerfeld radiation condition is developed. The bounding surface is taken to be a surface of revolution (SOR) to greatly reduce computational expense in the IE portion of the modeling.
Finite element modeling of permanent magnet devices
Brauer, J. R.; Larkin, L. A.; Overbye, V. D.
1984-03-01
New techniques are presented for finite element modeling of permanent magnets in magnetic devices such as motors and generators. These techniques extend a previous sheet-current permanent magnet model that applies only for straight line B-H loops and rectangular-shaped magnets. Here Maxwell's equations are used to derive the model of a permanent magnet having a general curved B-H loop and any geometric shape. The model enables a nonlinear magnetic finite element program to use Newton-Raphson iteration to solve for saturable magnetic fields in a wide variety of devices containing permanent magnets and steels. The techniques are applied to a brushless dc motor with irregular-shaped permanent magnets. The calculated motor torque agrees well with measured torque.
Finite element modelling of solidification phenomena
Indian Academy of Sciences (India)
K N Seetharamu; R Paragasam; Ghulam A Quadir; Z A Zainal; B Sathya Prasad; T Sundararajan
2001-02-01
The process of solidification process is complex in nature and the simulation of such process is required in industry before it is actually undertaken. Finite element method is used to simulate the heat transfer process accompanying the solidification process. The metal and the mould along with the air gap formation is accounted in the heat transfer simulation. Distortion of the casting is caused due to non-uniform shrinkage associated with the process. Residual stresses are induced in the final castings. Simulation of the shrinkage and the thermal stresses are also carried out using finite element methods. The material behaviour is considered as visco-plastic. The simulations are compared with available experimental data and the comparison is found to be good. Special considerations regarding the simulation of solidification process are also brought out.
Finite element simulations with ANSYS workbench 16
Lee , Huei-Huang
2015-01-01
Finite Element Simulations with ANSYS Workbench 16 is a comprehensive and easy to understand workbook. It utilizes step-by-step instructions to help guide readers to learn finite element simulations. Twenty seven real world case studies are used throughout the book. Many of these cases are industrial or research projects the reader builds from scratch. All the files readers may need if they have trouble are available for download on the publishers website. Companion videos that demonstrate exactly how to preform each tutorial are available to readers by redeeming the access code that comes in the book. Relevant background knowledge is reviewed whenever necessary. To be efficient, the review is conceptual rather than mathematical. Key concepts are inserted whenever appropriate and summarized at the end of each chapter. Additional exercises or extension research problems are provided as homework at the end of each chapter. A learning approach emphasizing hands-on experiences spreads through this entire book. A...
Quantum Finite Elements for Lattice Field Theory
Brower, Richard C; Gasbarro, Andrew; Raben, Timothy; Tan, Chung-I; Weinberg, Evan
2016-01-01
Viable non-perturbative methods for lattice quantum field theories on curved manifolds are difficult. By adapting features from the traditional finite element methods (FEM) and Regge Calculus, a new simplicial lattice Quantum Finite Element (QFE) Lagrangian is constructed for fields on a smooth Riemann manifold. To reach the continuum limit additional counter terms must be constructed to cancel the ultraviolet distortions. This is tested by the comparison of phi 4-th theory at the Wilson-Fisher fixed point with the exact Ising (c =1/2) CFT on a 2D Riemann sphere. The Dirac equation is also constructed on a simplicial lattice approximation to a Riemann manifold by introducing a lattice vierbein and spin connection on each link. Convergence of the QFE Dirac equation is tested against the exact solution for the 2D Riemann sphere. Future directions and applications to Conformal Field Theories are suggested.
Finite element modelling of SAW correlator
Tikka, Ajay C.; Al-Sarawi, Said F.; Abbott, Derek
2007-12-01
Numerical simulations of SAW correlators so far are limited to delta function and equivalent circuit models. These models are not accurate as they do not replicate the actual behaviour of the device. Manufacturing a correlator to specifically realise a different configuration is both expensive and time consuming. With the continuous improvement in computing capacity, switching to finite element modelling would be more appropriate. In this paper a novel way of modelling a SAW correlator using finite element analysis is presented. This modelling approach allows the consideration of different code implementation and device structures. This is demonstrated through simulation results for a 5×2-bit Barker sequence encoded SAW correlator. These results show the effect of both bulk and leaky modes on the device performance at various operating frequencies. Moreover, the ways in which the gain of the correlator can be optimised though variation of design parameters will also be outlined.
FINITE ELEMENT ANALYSIS FOR PERIFLEX COUPLINGS
Directory of Open Access Journals (Sweden)
URDEA Mihaela
2015-06-01
Full Text Available The Periflex shaft couplings with rubber sleeve have a hig elasticity and link two shafts in diesel-engine and electric drives. They are simple from the point of view of construction, easily mounted and dismounted. The main goal of this paper is to present a finite element analysis for the Periflex coupling using the Generative Structural Analysis from CATIA software package. This paper presents important information about how to prepare an assembly for creating a static analysis case and also the important steps for developing a finite element analysis. It is very important that the analysis model should have the same behavior as the real, also the loading model. The results are images corresponding to Von Mises Stresses and Translational Displacement magnitude.
Finite Element Simulation of Metal Quenching
Institute of Scientific and Technical Information of China (English)
方刚; 曾攀
2004-01-01
The evolution of the phase transformation and the resulting internal stresses and strains in metallic parts during quenching were modeled numerically. The numerical simulation of the metal quenching process was based on the metallo-thermo-mechanical theory using the finite element method to couple the temperature, phase transformation, and stress-strain fields. The numerical models are presented for the heat treatment and kinetics of the phase transformation. The finite element models and the phase transition kinetics accurately predict the distribution of the microstructure volume fractions, the temperature, the distortion, and the stress-strain relation during quenching. The two examples used to validate the models are the quenching of a small gear and of a large turbine rotor. The simulation results for the martensite phase volume fraction, the stresses, and the distortion in the gear agree well with the experimental data. The models can be used to optimize the quenching conditions to ensure product quality.
FINITE ELEMENT METHODS FOR SOBOLEV EQUATIONS
Institute of Scientific and Technical Information of China (English)
Tang Liu; Yan-ping Lin; Ming Rao; J. R. Cannon
2002-01-01
A new high-order time-stepping finite element method based upon the high-order numerical integration formula is formulated for Sobolev equations, whose computations consist of an iteration procedure coupled with a system of two elliptic equations. The optimal and superconvergence error estimates for this new method axe derived both in space and in time. Also, a class of new error estimates of convergence and superconvergence for the time-continuous finite element method is demonstrated in which there are no time derivatives of the exact solution involved, such that these estimates can be bounded by the norms of the known data. Moreover, some useful a-posteriori error estimators are given on the basis of the superconvergence estimates.
Finite element analysis of tibial fractures
DEFF Research Database (Denmark)
Wong, Christian Nai En; Mikkelsen, Mikkel Peter W; Hansen, Leif Berner
2010-01-01
INTRODUCTION: Fractures of the tibial shaft are relatively common injuries. There are indications that tibial shaft fractures share characteristics in terms of site, type and local fracture mechanisms. In this study, we aimed to set up a mathematical, computer-based model using finite element...... analysis of the bones of the lower leg to examine if such a model is adequate for prediction of fracture locations and patterns. In future studies, we aim to use these biomechanical results to examine fracture prevention, among others, and to simulate different types of osteosynthesis and the process...... of bony healing. The biomechanical results are the basis for fracture healing, biomechanical fall analysis and stability analysis of osteosynthesis. MATERIAL AND METHODS: A finite element model of the bony part of the lower leg was generated on the basis of computed tomography data from the Visible Human...
Multiphase Transformer Modelling using Finite Element Method
Directory of Open Access Journals (Sweden)
Nor Azizah Mohd Yusoff
2015-03-01
Full Text Available In the year of 1970 saw the starting invention of the five-phase motor as the milestone in advanced electric motor. Through the years, there are many researchers, which passionately worked towards developing for multiphase drive system. They developed a static transformation system to obtain a multiphase supply from the available three-phase supply. This idea gives an influence for further development in electric machines as an example; an efficient solution for bulk power transfer. This paper highlighted the detail descriptions that lead to five-phase supply with fixed voltage and frequency by using Finite-Element Method (FEM. Identifying of specification on a real transformer had been done before applied into software modeling. Therefore, Finite-Element Method provides clearly understandable in terms of visualize the geometry modeling, connection scheme and output waveform.
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 · ...
The finite element modeling of spiral ropes
Institute of Scientific and Technical Information of China (English)
Juan Wu
2014-01-01
Accurate understanding the behavior of spiral rope is complicated due to their complex geometry and complex contact conditions between the wires. This study proposed the finite element models of spiral ropes subjected to tensile loads. The parametric equations developed in this paper were implemented for geometric modeling of ropes. The 3D geometric models with different twisting manner, equal diameters of wires were generated in details by using Pro/ENGINEER software. The results of the present finite element analysis were on an acceptable level of accuracy as compared with those of theoretical and experimental data. Further development is ongoing to analysis the equivalent stresses induced by twisting manner of cables. The twisting manner of wires was important to spiral ropes in the three wire layers and the outer twisting manner of wires should be contrary to that of the second layer, no matter what is the first twisting manner of wires.
Finite element contact analysis of fractal surfaces
Energy Technology Data Exchange (ETDEWEB)
Sahoo, Prasanta; Ghosh, Niloy [Department of Mechanical Engineering, Jadavpur University, Kolkata 700032 (India)
2007-07-21
The present study considers finite element analysis of non-adhesive, frictionless elastic/elastic-plastic contact between a rigid flat plane and a self-affine fractal rough surface using the commercial finite element package ANSYS. Three-dimensional rough surfaces are generated using a modified two-variable Weierstrass-Mandelbrot function with given fractal parameters. Parametric studies are done to consider the general relations between contact properties and key material and surface parameters. The present analysis is validated with available experimental results in the literature. Non-dimensional contact area and displacement are obtained as functions of non-dimensional load for varying fractal surface parameters in the case of elastic contact and for varying rates of strain hardening in the case of elastic-plastic contact of fractal surfaces.
Adaptive Mixed Finite Element Methods for Parabolic Optimal Control Problems
Zuliang Lu
2011-01-01
We will investigate the adaptive mixed finite element methods for parabolic optimal control problems. The state and the costate are approximated by the lowest-order Raviart-Thomas mixed finite element spaces, and the control is approximated by piecewise constant elements. We derive a posteriori error estimates of the mixed finite element solutions for optimal control problems. Such a posteriori error estimates can be used to construct more efficient and reliable adaptive mixed finite element ...
Finite element simulation of heat transfer
Bergheau, Jean-Michel
2010-01-01
This book introduces the finite element method applied to the resolution of industrial heat transfer problems. Starting from steady conduction, the method is gradually extended to transient regimes, to traditional non-linearities, and to convective phenomena. Coupled problems involving heat transfer are then presented. Three types of couplings are discussed: coupling through boundary conditions (such as radiative heat transfer in cavities), addition of state variables (such as metallurgical phase change), and coupling through partial differential equations (such as electrical phenomena).? A re
Finite Element Simulation for Interfacial Evolutions
Institute of Scientific and Technical Information of China (English)
JianmingHUANG; WeiYANG
1998-01-01
A three-dimensional finite element scheme based upon a weak statement of the classical theory is explored to simulate migration of interfaces in materials under linear evaporation and condensation kinetics,The present scheme is exemplified by two cases:facet formation of single crystals;and the evolution of a tri-crystal film on a substrate where the effect of multiple kinetics is demonstrated.
FINITE-ELEMENT MODELING OF SALT TECTONICS
Directory of Open Access Journals (Sweden)
Natalia Bakhova
2012-09-01
Full Text Available The two-dimensional thermal model of graben structure in the presence of salt tectonics on the basis of a finite elements method is constructed. The analysis of the thermal field is based on the solution of stationary equation of heat conductivity with variable boundary conditions. The high precision of temperatures distribution and heat flows is received. The decision accuracy is no more than 0,6 %.
Finite element model of needle electrode sensitivity
Høyum, P.; Kalvøy, H.; Martinsen, Ø. G.; Grimnes, S.
2010-04-01
We used the Finite Element (FE) Method to estimate the sensitivity of a needle electrode for bioimpedance measurement. This current conducting needle with insulated shaft was inserted in a saline solution and current was measured at the neutral electrode. FE model resistance and reactance were calculated and successfully compared with measurements on a laboratory model. The sensitivity field was described graphically based on these FE simulations.
Quick finite elements for electromagnetic waves
Pelosi, Giuseppe; Selleri, Stefano
2009-01-01
This practical book and accompanying software enables you to quickly and easily work out challenging microwave engineering and high-frequency electromagnetic problems using the finite element method (FEM) Using clear, concise text and dozens of real-world application examples, the book provides a detailed description of FEM implementation, while the software provides the code and tools needed to solve the three major types of EM problems: guided propagation, scattering, and radiation.
EXODUS II: A finite element data model
Energy Technology Data Exchange (ETDEWEB)
Schoof, L.A.; Yarberry, V.R.
1994-09-01
EXODUS II is a model developed to store and retrieve data for finite element analyses. It is used for preprocessing (problem definition), postprocessing (results visualization), as well as code to code data transfer. An EXODUS II data file is a random access, machine independent, binary file that is written and read via C, C++, or Fortran library routines which comprise the Application Programming Interface (API).
Finite element methods for incompressible flow problems
John, Volker
2016-01-01
This book explores finite element methods for incompressible flow problems: Stokes equations, stationary Navier-Stokes equations, and time-dependent Navier-Stokes equations. It focuses on numerical analysis, but also discusses the practical use of these methods and includes numerical illustrations. It also provides a comprehensive overview of analytical results for turbulence models. The proofs are presented step by step, allowing readers to more easily understand the analytical techniques.
Finite Element Analysis of Reverberation Chambers
Bunting, Charles F.; Nguyen, Duc T.
2000-01-01
The primary motivating factor behind the initiation of this work was to provide a deterministic means of establishing the validity of the statistical methods that are recommended for the determination of fields that interact in -an avionics system. The application of finite element analysis to reverberation chambers is the initial step required to establish a reasonable course of inquiry in this particularly data-intensive study. The use of computational electromagnetics provides a high degree of control of the "experimental" parameters that can be utilized in a simulation of reverberating structures. As the work evolved there were four primary focus areas they are: 1. The eigenvalue problem for the source free problem. 2. The development of a complex efficient eigensolver. 3. The application of a source for the TE and TM fields for statistical characterization. 4. The examination of shielding effectiveness in a reverberating environment. One early purpose of this work was to establish the utility of finite element techniques in the development of an extended low frequency statistical model for reverberation phenomena. By employing finite element techniques, structures of arbitrary complexity can be analyzed due to the use of triangular shape functions in the spatial discretization. The effects of both frequency stirring and mechanical stirring are presented. It is suggested that for the low frequency operation the typical tuner size is inadequate to provide a sufficiently random field and that frequency stirring should be used. The results of the finite element analysis of the reverberation chamber illustrate io-W the potential utility of a 2D representation for enhancing the basic statistical characteristics of the chamber when operating in a low frequency regime. The basic field statistics are verified for frequency stirring over a wide range of frequencies. Mechanical stirring is shown to provide an effective frequency deviation.
Nonlinear Finite Element Analysis of Ocean Cables
Institute of Scientific and Technical Information of China (English)
Nam-Il KIM; Sang-Soo JEON; Moon-Young KIM
2004-01-01
This study has focused on developing numerical procedures for the dynamic nonlinear analysis of cable structures subjected to wave forces and ground motions in the ocean. A geometrically nonlinear finite element procedure using the isoparametric curved cable element based on the Lagrangian formulation is briefly summarized. A simple and accurate method to determine the initial equilibrium state of cable systems associated with self-weights, buoyancy and the motion of end points is presented using the load incremental method combined with penalty method. Also the Newmark method is used for dynamic nonlinear analysis of ocean cables. Numerical examples are presented to validate the present numerical method.
Directory of Open Access Journals (Sweden)
Amaziane Brahim
2014-07-01
Full Text Available In this paper, we consider adaptive numerical simulation of miscible displacement problems in porous media, which are modeled by single phase flow equations. A vertex-centred finite volume method is employed to discretize the coupled system: the Darcy flow equation and the diffusion-convection concentration equation. The convection term is approximated with a Godunov scheme over the dual finite volume mesh, whereas the diffusion-dispersion term is discretized by piecewise linear conforming finite elements. We introduce two kinds of indicators, both of them of residual type. The first one is related to time discretization and is local with respect to the time discretization: thus, at each time, it provides an appropriate information for the choice of the next time step. The second is related to space discretization and is local with respect to both the time and space variable and the idea is that at each time it is an efficient tool for mesh adaptivity. An error estimation procedure evaluates where additional refinement is needed and grid generation procedures dynamically create or remove fine-grid patches as resolution requirements change. The method was implemented in the software MELODIE, developed by the French Institute for Radiological Protection and Nuclear Safety (IRSN, Institut de Radioprotection et de Sûreté Nucléaire. The algorithm is then used to simulate the evolution of radionuclide migration from the waste packages through a heterogeneous disposal, demonstrating its capability to capture complex behavior of the resulting flow.
Tangential stress analysis of myocardial wall by finite element method
Institute of Scientific and Technical Information of China (English)
Guan Qiu; Jiang Cao; Wang Xiaoyan; Chen Shengyong; Guan Fang
2011-01-01
A novel method is presented to build the triangular surface model and calculate the tangential stress and strain of myocardial wall ,which can be further used to reflect the left ventricle twisting-a sensitive index to assess the systolic and diastolic function of heart. Firstly, a point distribution model is used to obtain the feature points of the ventricular surface in medical images. Secondly, the surface model is constructed by triangular mesh, and then the subdivision strategy is introduced to refine the model. Thirdly, plane projection and finite element method ( FEM ) are applied to calculate the tangential stress and strain. Finally, the distribution of tangential modulus of elasticity is discussed. The stimulation results show that the proposed method can be used to compute the tangential stress and strain of myocardial wall effectively and the computing result is consistent with the results mentioned in the literatures.
A Lagrange multiplier based divide and conquer finite element algorithm
Farhat, C.
1991-01-01
A novel domain decomposition method based on a hybrid variational principle is presented. Prior to any computation, a given finite element mesh is torn into a set of totally disconnected submeshes. First, an incomplete solution is computed in each subdomain. Next, the compatibility of the displacement field at the interface nodes is enforced via discrete, polynomial and/or piecewise polynomial Lagrange multipliers. In the static case, each floating subdomain induces a local singularity that is resolved very efficiently. The interface problem associated with this domain decomposition method is, in general, indefinite and of variable size. A dedicated conjugate projected gradient algorithm is developed for solving the latter problem when it is not feasible to explicitly assemble the interface operator. When implemented on local memory multiprocessors, the proposed methodology requires less interprocessor communication than the classical method of substructuring. It is also suitable for parallel/vector computers with shared memory and compares favorably with factorization based parallel direct methods.
Finite Element Method in Machining Processes
Markopoulos, Angelos P
2013-01-01
Finite Element Method in Machining Processes provides a concise study on the way the Finite Element Method (FEM) is used in the case of manufacturing processes, primarily in machining. The basics of this kind of modeling are detailed to create a reference that will provide guidelines for those who start to study this method now, but also for scientists already involved in FEM and want to expand their research. A discussion on FEM, formulations and techniques currently in use is followed up by machining case studies. Orthogonal cutting, oblique cutting, 3D simulations for turning and milling, grinding, and state-of-the-art topics such as high speed machining and micromachining are explained with relevant examples. This is all supported by a literature review and a reference list for further study. As FEM is a key method for researchers in the manufacturing and especially in the machining sector, Finite Element Method in Machining Processes is a key reference for students studying manufacturing processes but al...
Melis, Matthew E.
1990-01-01
COMGEN (Composite Model Generator) is an interactive FORTRAN program which can be used to create a wide variety of finite element models of continuous fiber composite materials at the micro level. It quickly generates batch or session files to be submitted to the finite element pre- and postprocessor PATRAN based on a few simple user inputs such as fiber diameter and percent fiber volume fraction of the composite to be analyzed. In addition, various mesh densities, boundary conditions, and loads can be assigned easily to the models within COMGEN. PATRAN uses a session file to generate finite element models and their associated loads which can then be translated to virtually any finite element analysis code such as NASTRAN or MARC.
Kaltenbacher, Manfred
2015-01-01
Like the previous editions also the third edition of this book combines the detailed physical modeling of mechatronic systems and their precise numerical simulation using the Finite Element (FE) method. Thereby, the basic chapter concerning the Finite Element (FE) method is enhanced, provides now also a description of higher order finite elements (both for nodal and edge finite elements) and a detailed discussion of non-conforming mesh techniques. The author enhances and improves many discussions on principles and methods. In particular, more emphasis is put on the description of single fields by adding the flow field. Corresponding to these field, the book is augmented with the new chapter about coupled flow-structural mechanical systems. Thereby, the discussion of computational aeroacoustics is extended towards perturbation approaches, which allows a decomposition of flow and acoustic quantities within the flow region. Last but not least, applications are updated and restructured so that the book meets mode...
An efficient wavelet finite element method in fault prognosis of incipient crack
Institute of Scientific and Technical Information of China (English)
无
2006-01-01
The method of constructing any scale wavelet finite element (WFE) based on the one-dimensional or two-dimensional Daubechies scaling functions was presented, and the corresponding WFE adaptive lifting algorithm was given. In order to obtain the nested increasing approximate subspaces of multiscale finite element, the Daubechies scaling functions with the properties of multi-resolution analysis were employed as the finite element interpolating functions. Thus, the WFE could adaptively mesh the singularity domain caused by local cracks, which resulted in better approximate solutions than the traditional finite element methods. The calculations of natural frequencies of cracked beam were used to check the accuracy of given methods. In addition, the results of cracked cantilever beam and engineering application were satisfied. So, the current methods can provide effective tools in the numerical modeling of the fault prognosis of incipient crack.
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.
Relativistic Vlasov-Maxwell modelling using finite volumes and adaptive mesh refinement
Wettervik, Benjamin Svedung; Siminos, Evangelos; Fülöp, Tünde
2016-01-01
The dynamics of collisionless plasmas can be modelled by the Vlasov-Maxwell system of equations. An Eulerian approach is needed to accurately describe processes that are governed by high energy tails in the distribution function, but is of limited efficiency for high dimensional problems. The use of an adaptive mesh can reduce the scaling of the computational cost with the dimension of the problem. Here, we present a relativistic Eulerian Vlasov-Maxwell solver with block-structured adaptive mesh refinement in one spatial and one momentum dimension. The discretization of the Vlasov equation is based on a high-order finite volume method. A flux corrected transport algorithm is applied to limit spurious oscillations and ensure the physical character of the distribution function. We demonstrate a speed-up by a factor of five, because of the use of an adaptive mesh, in a typical scenario involving laser-plasma interaction in the self-induced transparency regime.
Isogeometric finite element approximation of minimal surfaces based on extended loop subdivision
Pan, Qing; Chen, Chong; Xu, Guoliang
2017-08-01
In this paper, we investigate the formulation of isogeometric analysis for minimal surface models on planar bounded domains by extended Loop surface subdivision approach. The exactness of the physical domain of interest is fixed on the coarsest level of the triangular discretization with any topological structure, which is thought of as the initial control mesh of Loop subdivision. By performing extended Loop subdivision, the control mesh can be repeatedly refined, and the geometry is described as an infinite set of quartic box-spline while maintaining its original exactness. The limit function representation of extended Loop subdivision forms our finite element space, which possesses C1 smoothness and the flexibility of mesh topology. We establish its inverse inequalities which resemble the ones of general finite element spaces. We develop the approximation estimate with the aid of H1 convergence property of the corresponding linear models. It enables us to overcome the difficulty of proving the boundedness of the gradient of finite element solutions appearing in the coefficient of minimal surface models. Numerical examples are given with the comparison to the classical linear finite element method which is consistent with our theoretical results.
Finite Element Based Design and Optimization for Piezoelectric Accelerometers
DEFF Research Database (Denmark)
Liu, Bin; Kriegbaum, B.; Yao, Q.
1998-01-01
A systematic Finite Element design and optimisation procedure is implemented for the development of piezoelectric accelerometers. Most of the specifications of accelerometers can be obtained using the Finite Element simulations. The deviations between the simulated and calibrated sensitivities...
Application of finite-element-methods in food processing
DEFF Research Database (Denmark)
Risum, Jørgen
2004-01-01
Presentation of the possible use of finite-element-methods in food processing. Examples from diffusion studies are given.......Presentation of the possible use of finite-element-methods in food processing. Examples from diffusion studies are given....
Finite element modeling for materials engineers using Matlab
Oluwole, Oluleke
2014-01-01
Finite Element Modeling for Materials Engineers Using MATLAB® combines the finite element method with MATLAB to offer materials engineers a fast and code-free way of modeling for many materials processes.
Finite Element Analysis of Reinforced Concrete Plate Impacted by Block
Institute of Scientific and Technical Information of China (English)
LUO Xiaoyang; Pascal PERROTIN; YAN Quansheng
2006-01-01
A new concept of structurally dissipating rock-shed (SDR) was developed by the lab of Tonello IC and LOCIE-ESIGEC (France).To decide the dimension of the plate used in SDR,an ANSYS model which could simulate the impact of rock in the centre of the plate was established by Fabien Delhomme.By using this model,some finite element analyses are carried out in the present paper Firstly,a plate impacted by a block is numerically simulated,the numerical results obtained from different mesh sizes are compared and the accuracy of the finite element model is verified.Then,the dynamic response of the plate impacted at the boundary and in the medium part is computed.By analyzing the stress in rebar,the most dangerous region of impact of plate was found.For a rectangular plate,the most dangerous region is at the corner of the plate when a block drops in.Finally,the whole deformation process of the plate under dropping block was simulated and a simplified definition (effect zone) to describe the deformation process in different positions of plate was given.From this study,it is found that the impact only affects heavily within the effect zone.
A new parallel algorithm for contact detection in finite element methods
Energy Technology Data Exchange (ETDEWEB)
Hendrickson, B.; Plimpton, S.; Attaway, S.; Vaughan, C.; Gardner, D.
1996-03-01
In finite-element, transient dynamics simulations, physical objects are typically modeled as Lagrangian meshes because the meshes can move and deform with the objects as they undergo stress. In many simulations, such as computations of impacts or explosions, portions of the deforming mesh come in contact with each other as the simulation progresses. These contacts must be detected and the forces they impart to the mesh must be computed at each timestep to accurately capture the physics of interest. While the finite-element portion of these computations is readily parallelized, the contact detection problem is difficult to implement efficiently on parallel computers and has been a bottleneck to achieving high performance on large parallel machines. In this paper we describe a new parallel algorithm for detecting contacts. Our approach differs from previous work in that we use two different parallel decompositions, a static one for the finite element analysis and dynamic one for contact detection. We present results for this algorithm in a parallel version of the transient dynamics code PRONTO-3D running on a large Intel Paragon.
Stochastic finite elements: Where is the physics?
Directory of Open Access Journals (Sweden)
Ostoja-Starzewski Martin
2011-01-01
Full Text Available The micromechanics based on the Hill-Mandel condition indicates that the majority of stochastic finite element methods hinge on random field (RF models of material properties (such as Hooke’s law having no physical content, or even at odds with physics. At the same time, that condition allows one to set up the RFs of stiffness and compliance tensors in function of the mesoscale and actual random microstructure of the given material. The mesoscale is defined through a Statistical Volume Element (SVE, i.e. a material domain below the Representative Volume Element (RVE level. The paper outlines a procedure for stochastic scale-dependent homogenization leading to a determination of mesoscale one-point and two-point statistics and, thus, a construction of analytical RF models.
Adaptive Finite Element Method Assisted by Stochastic Simulation of Chemical Systems
Cotter, Simon L.
2013-01-01
Stochastic models of chemical systems are often analyzed by solving the corresponding Fokker-Planck equation, which is a drift-diffusion partial differential equation for the probability distribution function. Efficient numerical solution of the Fokker-Planck equation requires adaptive mesh refinements. In this paper, we present a mesh refinement approach which makes use of a stochastic simulation of the underlying chemical system. By observing the stochastic trajectory for a relatively short amount of time, the areas of the state space with nonnegligible probability density are identified. By refining the finite element mesh in these areas, and coarsening elsewhere, a suitable mesh is constructed and used for the computation of the stationary probability density. Numerical examples demonstrate that the presented method is competitive with existing a posteriori methods. © 2013 Society for Industrial and Applied Mathematics.
3-D finite element cyclic symmetric and contact stress analysis for a complete gear train
Yin, Zeyong; Xu, Youliang; Gao, Xiangqun; Wei, Gang
1992-10-01
A complete gear train of a reduction gearbox is the object of finite element stress analysis. One of the basic segments of the complete gear train is taken as the computational model in the light of the cyclic symmetry of the gear train; meanwhile, the contact transmission forces between the corresponding meshed teeth are considered in the analysis of the model. For simplicity, the corresponding meshed lines are used instead of the actual contact surfaces. Both torque and centrifugal loads are involved in the analysis. The stresses in all the parts of a complete gear train can be determined by one analysis. The computed results show that the contact force on a meshed tooth is correlative not only to the length of the meshed line, but also to its position. It is shown that the neglect of the stress resulted from centrifugal load is inappropriate to a high speed gear train.
TRIM: A finite-volume MHD algorithm for an unstructured adaptive mesh
Energy Technology Data Exchange (ETDEWEB)
Schnack, D.D.; Lottati, I.; Mikic, Z. [Science Applications International Corp., San Diego, CA (United States)] [and others
1995-07-01
The authors describe TRIM, a MHD code which uses finite volume discretization of the MHD equations on an unstructured adaptive grid of triangles in the poloidal plane. They apply it to problems related to modeling tokamak toroidal plasmas. The toroidal direction is treated by a pseudospectral method. Care was taken to center variables appropriately on the mesh and to construct a self adjoint diffusion operator for cell centered variables.
Schwing, Alan Michael
For computational fluid dynamics, the governing equations are solved on a discretized domain of nodes, faces, and cells. The quality of the grid or mesh can be a driving source for error in the results. While refinement studies can help guide the creation of a mesh, grid quality is largely determined by user expertise and understanding of the flow physics. Adaptive mesh refinement is a technique for enriching the mesh during a simulation based on metrics for error, impact on important parameters, or location of important flow features. This can offload from the user some of the difficult and ambiguous decisions necessary when discretizing the domain. This work explores the implementation of adaptive mesh refinement in an implicit, unstructured, finite-volume solver. Consideration is made for applying modern computational techniques in the presence of hanging nodes and refined cells. The approach is developed to be independent of the flow solver in order to provide a path for augmenting existing codes. It is designed to be applicable for unsteady simulations and refinement and coarsening of the grid does not impact the conservatism of the underlying numerics. The effect on high-order numerical fluxes of fourth- and sixth-order are explored. Provided the criteria for refinement is appropriately selected, solutions obtained using adapted meshes have no additional error when compared to results obtained on traditional, unadapted meshes. In order to leverage large-scale computational resources common today, the methods are parallelized using MPI. Parallel performance is considered for several test problems in order to assess scalability of both adapted and unadapted grids. Dynamic repartitioning of the mesh during refinement is crucial for load balancing an evolving grid. Development of the methods outlined here depend on a dual-memory approach that is described in detail. Validation of the solver developed here against a number of motivating problems shows favorable
A class of hybrid finite element methods for electromagnetics: A review
Volakis, J. L.; Chatterjee, A.; Gong, J.
1993-01-01
Integral equation methods have generally been the workhorse for antenna and scattering computations. In the case of antennas, they continue to be the prominent computational approach, but for scattering applications the requirement for large-scale computations has turned researchers' attention to near neighbor methods such as the finite element method, which has low O(N) storage requirements and is readily adaptable in modeling complex geometrical features and material inhomogeneities. In this paper, we review three hybrid finite element methods for simulating composite scatterers, conformal microstrip antennas, and finite periodic arrays. Specifically, we discuss the finite element method and its application to electromagnetic problems when combined with the boundary integral, absorbing boundary conditions, and artificial absorbers for terminating the mesh. Particular attention is given to large-scale simulations, methods, and solvers for achieving low memory requirements and code performance on parallel computing architectures.
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.
Zeng, X.; Scovazzi, G.
2016-06-01
We present a monolithic arbitrary Lagrangian-Eulerian (ALE) finite element method for computing highly transient flows with strong shocks. We use a variational multiscale (VMS) approach to stabilize a piecewise-linear Galerkin formulation of the equations of compressible flows, and an entropy artificial viscosity to capture strong solution discontinuities. Our work demonstrates the feasibility of VMS methods for highly transient shock flows, an area of research for which the VMS literature is extremely scarce. In addition, the proposed monolithic ALE method is an alternative to the more commonly used Lagrangian+remap methods, in which, at each time step, a Lagrangian computation is followed by mesh smoothing and remap (conservative solution interpolation). Lagrangian+remap methods are the methods of choice in shock hydrodynamics computations because they provide nearly optimal mesh resolution in proximity of shock fronts. However, Lagrangian+remap methods are not well suited for imposing inflow and outflow boundary conditions. These issues offer an additional motivation for the proposed approach, in which we first perform the mesh motion, and then the flow computations using the monolithic ALE framework. The proposed method is second-order accurate and stable, as demonstrated by extensive numerical examples in two and three space dimensions.
Finite element modeling methods for photonics
Rahman, B M Azizur
2013-01-01
The term photonics can be used loosely to refer to a vast array of components, devices, and technologies that in some way involve manipulation of light. One of the most powerful numerical approaches available to engineers developing photonic components and devices is the Finite Element Method (FEM), which can be used to model and simulate such components/devices and analyze how they will behave in response to various outside influences. This resource provides a comprehensive description of the formulation and applications of FEM in photonics applications ranging from telecommunications, astron
Finite element simulation of asphalt fatigue testing
DEFF Research Database (Denmark)
Ullidtz, Per; Kieler, Thomas Lau; Kargo, Anders
1997-01-01
damage mechanics.The paper describes how continuum damage mechanics may be used with a finite element program to explain the progressive deterioration of asphalt mixes under laboratory fatigue testing. Both constant stress and constant strain testing are simulated, and compared to the actual results from...... three point and four point fatigue test on different mixes. It is shown that the same damage law, based on energy density, may be used to explain the gradual deterioration under constant stress as well as under constant strain testing.Some of the advantages of using this method for interpreting fatigue...
The serendipity family of finite elements
Arnold, Douglas N
2011-01-01
We give a new, simple, dimension-independent definition of the serendipity finite element family. The shape functions are the span of all monomials which are linear in at least s-r of the variables where s is the degree of the monomial or, equivalently, whose superlinear degree (total degree with respect to variables entering at least quadratically) is at most r. The degrees of freedom are given by moments of degree at most r-2d on each face of dimension d. We establish unisolvence and a geometric decomposition of the space.
Generalized multiscale finite element methods: Oversampling strategies
Efendiev, Yalchin R.
2014-01-01
In this paper, we propose oversampling strategies in the generalized multiscale finite element method (GMsFEM) framework. The GMsFEM, which has been recently introduced in Efendiev et al. (2013b) [Generalized Multiscale Finite Element Methods, J. Comput. Phys., vol. 251, pp. 116-135, 2013], allows solving multiscale parameter-dependent problems at a reduced computational cost by constructing a reduced-order representation of the solution on a coarse grid. The main idea of the method consists of (1) the construction of snapshot space, (2) the construction of the offline space, and (3) construction of the online space (the latter for parameter-dependent problems). In Efendiev et al. (2013b) [Generalized Multiscale Finite Element Methods, J. Comput. Phys., vol. 251, pp. 116-135, 2013], it was shown that the GMsFEM provides a flexible tool to solve multiscale problems with a complex input space by generating appropriate snapshot, offline, and online spaces. In this paper, we develop oversampling techniques to be used in this context (see Hou and Wu (1997) where oversampling is introduced for multiscale finite element methods). It is known (see Hou and Wu (1997)) that the oversampling can improve the accuracy of multiscale methods. In particular, the oversampling technique uses larger regions (larger than the target coarse block) in constructing local basis functions. Our motivation stems from the analysis presented in this paper, which shows that when using oversampling techniques in the construction of the snapshot space and offline space, GMsFEM will converge independent of small scales and high contrast under certain assumptions. We consider the use of a multiple eigenvalue problems to improve the convergence and discuss their relation to single spectral problems that use oversampled regions. The oversampling procedures proposed in this paper differ from those in Hou and Wu (1997). In particular, the oversampling domains are partially used in constructing local
Finite element modelingof spherical induction actuator
Galary, Grzegorz
2005-01-01
The thesis deals with finite element method simulations of the two-degree of freedom spherical induction actuator performed using the 2D and 3D models. In some cases non-linear magnetization curves, rotor movement and existence of higher harmonics are taken into account. The evolution of the model leading to its simplification is presented. Several rotor structures are tested, namely the one-layer, two-layers and two-layers-with-teeth rotor. The study of some rotor parameters, i.e. t...
A finite element model of ultrasonic extrusion
Energy Technology Data Exchange (ETDEWEB)
Lucas, M [Department of Mechanical Engineering, University of Glasgow, G12 8QQ (United Kingdom); Daud, Y, E-mail: m.lucas@mech.gla.ac.u [College of Science and Technology, UTM City Campus, Kuala Lumpur (Malaysia)
2009-08-01
Since the 1950's researchers have carried out investigations into the effects of applying ultrasonic excitation to metals undergoing elastic and plastic deformation. Experiments have been conducted where ultrasonic excitation is superimposed in complex metalworking operations such as wire drawing and extrusion, to identify the benefits of ultrasonic vibrations. This study presents a finite element analysis of ultrasonic excitation applied to the extrusion of a cylindrical aluminium bar. The effects of friction on the extrusion load are reported for the two excitation configurations of radially and axially applied ultrasonic vibrations and the results are compared with experimental data reported in the literature.
A finite element model of ultrasonic extrusion
Lucas, M.; Daud, Y.
2009-08-01
Since the 1950's researchers have carried out investigations into the effects of applying ultrasonic excitation to metals undergoing elastic and plastic deformation. Experiments have been conducted where ultrasonic excitation is superimposed in complex metalworking operations such as wire drawing and extrusion, to identify the benefits of ultrasonic vibrations. This study presents a finite element analysis of ultrasonic excitation applied to the extrusion of a cylindrical aluminium bar. The effects of friction on the extrusion load are reported for the two excitation configurations of radially and axially applied ultrasonic vibrations and the results are compared with experimental data reported in the literature.
Iterative methods for mixed finite element equations
Nakazawa, S.; Nagtegaal, J. C.; Zienkiewicz, O. C.
1985-01-01
Iterative strategies for the solution of indefinite system of equations arising from the mixed finite element method are investigated in this paper with application to linear and nonlinear problems in solid and structural mechanics. The augmented Hu-Washizu form is derived, which is then utilized to construct a family of iterative algorithms using the displacement method as the preconditioner. Two types of iterative algorithms are implemented. Those are: constant metric iterations which does not involve the update of preconditioner; variable metric iterations, in which the inverse of the preconditioning matrix is updated. A series of numerical experiments is conducted to evaluate the numerical performance with application to linear and nonlinear model problems.
Mixed finite elements for global tide models
Cotter, Colin J
2014-01-01
We study mixed finite element methods for the linearized rotating shallow water equations with linear drag and forcing terms. By means of a strong energy estimate for an equivalent second-order formulation for the linearized momentum, we prove long-time stability of the system without energy accumulation -- the geotryptic state. A priori error estimates for the linearized momentum and free surface elevation are given in $L^2$ as well as for the time derivative and divergence of the linearized momentum. Numerical results confirm the theoretical results regarding both energy damping and convergence rates.
Finite Element Analysis of a Four-Cylinder Four Stroke Gasoline Engine Crankshaft
Directory of Open Access Journals (Sweden)
Parman Setyamartana
2014-07-01
Full Text Available Stress analysis of a crankshaft using traditional method is complicated and needs modification by considering its stress concentration factors. To solve this problem, the crankshaft strength of a four-cylinder four stroke gasoline engine is modeled and analyzed using finite element method (FEM in this paper. For this purpose, the crankshaft is modeled using CATIA software in detail. Then, the model is imported in ANSYS. In the recent software, the model is meshed into a number of finite elements. After defining the boundary and loading conditions, the stresses occur in the crankshaft are analyzed in order to identify critical locations on it.
ADAPTIVE FINITE ELEMENT METHOD FOR ANALYSIS OF POLLUTANT DISPERSION IN SHALLOW WATER
Institute of Scientific and Technical Information of China (English)
Somboon Otarawanna; Pramote Dechaumphai
2005-01-01
A finite element method for analysis of pollutant dispersion in shallow water is presented. The analysis is divided into two parts: ( 1 ) computation of the velocity flow field and water surface elevation, and (2) computation of the pollutant concentration field from the dispersion model. The method was combined with an adaptive meshing technique to increase the solution accuracy ,as well as to reduce the computational time and computer memory. The finite element formulation and the computer programs were validated by several examples that have known solutions. In addition, the capability of the combined method was demonstrated by analyzing pollutant dispersion in Chao Phraya River near the gulf of Thailand.
Hall, Eric
2016-01-09
The Monte Carlo (and Multi-level Monte Carlo) finite element method can be used to approximate observables of solutions to diffusion equations with lognormal distributed diffusion coefficients, e.g. modeling ground water flow. Typical models use lognormal diffusion coefficients with H´ older regularity of order up to 1/2 a.s. This low regularity implies that the high frequency finite element approximation error (i.e. the error from frequencies larger than the mesh frequency) is not negligible and can be larger than the computable low frequency error. We address how the total error can be estimated by the computable error.
Sandberg, Mattias
2015-01-07
The Monte Carlo (and Multi-level Monte Carlo) finite element method can be used to approximate observables of solutions to diffusion equations with log normal distributed diffusion coefficients, e.g. modelling ground water flow. Typical models use log normal diffusion coefficients with H¨older regularity of order up to 1/2 a.s. This low regularity implies that the high frequency finite element approximation error (i.e. the error from frequencies larger than the mesh frequency) is not negligible and can be larger than the computable low frequency error. This talk will address how the total error can be estimated by the computable error.
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
Mesoscale dynamic coupling of finite- and discrete-element methods for fluid-particle interactions.
Srivastava, S; Yazdchi, K; Luding, S
2014-08-06
A new method for two-way fluid-particle coupling on an unstructured mesoscopically coarse mesh is presented. In this approach, we combine a (higher order) finite-element method (FEM) on the moving mesh for the fluid with a soft sphere discrete-element method for the particles. The novel feature of the proposed scheme is that the FEM mesh is a dynamic Delaunay triangulation based on the positions of the moving particles. Thus, the mesh can be multi-purpose: it provides (i) a framework for the discretization of the Navier-Stokes equations, (ii) a simple tool for detecting contacts between moving particles, (iii) a basis for coarse-graining or upscaling, and (iv) coupling with other physical fields (temperature, electromagnetic, etc.). This approach is suitable for a wide range of dilute and dense particulate flows, because the mesh resolution adapts with particle density in a given region. Two-way momentum exchange is implemented using semi-empirical drag laws akin to other popular approaches; for example, the discrete particle method, where a finite-volume solver on a coarser, fixed grid is used. We validate the methodology with several basic test cases, including single- and double-particle settling with analytical and empirical expectations, and flow through ordered and random porous media, when compared against finely resolved FEM simulations of flow through fixed arrays of particles.
Higher-order adaptive finite-element methods for Kohn–Sham density functional theory
Energy Technology Data Exchange (ETDEWEB)
Motamarri, P. [Department of Mechanical Engineering, University of Michigan, Ann Arbor, MI 48109 (United States); Nowak, M.R. [Department of Electrical Engineering, University of Michigan, Ann Arbor, MI 48109 (United States); Leiter, K.; Knap, J. [U.S. Army Research Labs, Aberdeen Proving Ground, Aberdeen, MD 21001 (United States); Gavini, V., E-mail: vikramg@umich.edu [Department of Mechanical Engineering, University of Michigan, Ann Arbor, MI 48109 (United States)
2013-11-15
We present an efficient computational approach to perform real-space electronic structure calculations using an adaptive higher-order finite-element discretization of Kohn–Sham density-functional theory (DFT). To this end, we develop an a priori mesh-adaption technique to construct a close to optimal finite-element discretization of the problem. We further propose an efficient solution strategy for solving the discrete eigenvalue problem by using spectral finite-elements in conjunction with Gauss–Lobatto quadrature, and a Chebyshev acceleration technique for computing the occupied eigenspace. The proposed approach has been observed to provide a staggering 100–200-fold computational advantage over the solution of a generalized eigenvalue problem. Using the proposed solution procedure, we investigate the computational efficiency afforded by higher-order finite-element discretizations of the Kohn–Sham DFT problem. Our studies suggest that staggering computational savings—of the order of 1000-fold—relative to linear finite-elements can be realized, for both all-electron and local pseudopotential calculations, by using higher-order finite-element discretizations. On all the benchmark systems studied, we observe diminishing returns in computational savings beyond the sixth-order for accuracies commensurate with chemical accuracy, suggesting that the hexic spectral-element may be an optimal choice for the finite-element discretization of the Kohn–Sham DFT problem. A comparative study of the computational efficiency of the proposed higher-order finite-element discretizations suggests that the performance of finite-element basis is competing with the plane-wave discretization for non-periodic local pseudopotential calculations, and compares to the Gaussian basis for all-electron calculations to within an order of magnitude. Further, we demonstrate the capability of the proposed approach to compute the electronic structure of a metallic system containing 1688
Simulation of Needle-Type Corona Electrodes by the Finite Element Method
Institute of Scientific and Technical Information of China (English)
YANG Shi-you; Jose Marcio MACHADO; Nancy Mieko ABE; Angelo PASSARO
2007-01-01
This paper describes a software tool,called LEVSOFT,suitable for the electric field simulations of corona electrodes by the Finite Element Method (FEM).Special attention was paid to the user friendly construction of geometries with corners and sharp points,and to the fast generation of highly refined triangular meshes and field maps.The execution of selfadaptive meshes was also implemented.These customized features make the code attractive for the simulation of needle-type corona electrodes.Some case examples involving needle type electrodes are presented.
2013-01-01
The face load factor is a common coefficient used in gear design standards that takes into account the uneven distribution of load across the face width of the gears caused by the mesh misalignment. In this paper, a finite element model that includes the gears and the corresponding shafts is proposed. The results obtained from the application of finite element analysis to this model are compared with those obtained from application of the ISO Standard 6336 coefficient-based method (Method C)....
Finite element modeling of blast lung injury in sheep.
Gibbons, Melissa M; Dang, Xinglai; Adkins, Mark; Powell, Brian; Chan, Philemon
2015-04-01
A detailed 3D finite element model (FEM) of the sheep thorax was developed to predict heterogeneous and volumetric lung injury due to blast. A shared node mesh of the sheep thorax was constructed from a computed tomography (CT) scan of a sheep cadaver, and while most material properties were taken from literature, an elastic-plastic material model was used for the ribs based on three-point bending experiments performed on sheep rib specimens. Anesthetized sheep were blasted in an enclosure, and blast overpressure data were collected using the blast test device (BTD), while surface lung injury was quantified during necropsy. Matching blasts were simulated using the sheep thorax FEM. Surface lung injury in the FEM was matched to pathology reports by setting a threshold value of the scalar output termed the strain product (maximum value of the dot product of strain and strain-rate vectors over all simulation time) in the surface elements. Volumetric lung injury was quantified by applying the threshold value to all elements in the model lungs, and a correlation was found between predicted volumetric injury and measured postblast lung weights. All predictions are made for the left and right lungs separately. This work represents a significant step toward the prediction of localized and heterogeneous blast lung injury, as well as volumetric injury, which was not recorded during field testing for sheep.
Energy Technology Data Exchange (ETDEWEB)
Bailey, T S; Adams, M L; Chang, J H
2008-10-01
We present a new spatial discretization of the discrete-ordinates transport equation in two-dimensional cylindrical (RZ) geometry for arbitrary polygonal meshes. This discretization is a discontinuous finite element method that utilizes the piecewise linear basis functions developed by Stone and Adams. We describe an asymptotic analysis that shows this method to be accurate for many problems in the thick diffusion limit on arbitrary polygons, allowing this method to be applied to radiative transfer problems with these types of meshes. We also present numerical results for multiple problems on quadrilateral grids and compare these results to the well-known bi-linear discontinuous finite element method.
Finite Element Flow Simulations of the EUROLIFT DLR-F11 High Lift Configuration
Chitale, Kedar C; Martin, Jeff; Jansen, Kenneth E
2014-01-01
This paper presents flow simulation results of the EUROLIFT DLR-F11 multi-element wing configuration, obtained with a highly scalable finite element solver, PHASTA. This work was accomplished as a part of the 2nd high lift prediction workshop. In-house meshes were constructed with increasing mesh density for analysis. A solution adaptive approach was used as an alternative and its effectiveness was studied by comparing its results with the ones obtained with other meshes. Comparisons between the numerical solution obtained with unsteady RANS turbulence model and available experimental results are provided for verification and discussion. Based on the observations, future direction for adaptive research and simulations with higher fidelity turbulence models is outlined.
Finite element analysis of bolted flange connections
Hwang, D. Y.; Stallings, J. M.
1994-06-01
A 2-D axisymmetric finite element model and a 3-D solid finite element model of a high pressure bolted flange joint were generated to investigate the stress behaviors. This investigation includes comparisons for axisymmetric loading of both the 2-D and 3-D models, the effects of non-axisymmetric bolt pretensions in the 3-D models, and the differences between 2-D and 3-D models subjected to non-axisymmetric loading. Comparisons indicated differences in von Mises stress up to 12% at various points due to the non-axisymmetric bolt pretensions. Applied bending moments were converted to equivalent axial forces for use in the 2-D model. It was found that the largest von Mises stresses in 3-D model did not occur on the side of the connection where the bending stresses and applied axial stresses were additive. Hence, in the 2-D model where the equivalent axial force (for bending moment) and applied axial forces were added, the 2-D model under estimated the maximum von Mises stress obtained from the 3-D model by 30%.
Impeller deflection and modal finite element analysis.
Energy Technology Data Exchange (ETDEWEB)
Spencer, Nathan A.
2013-10-01
Deflections of an impeller due to centripetal forces are calculated using finite element analysis. The lateral, or out of plane, deflections are an important design consideration for this particular impeller because it incorporates an air bearing with critical gap tolerances. The target gap distance is approximately 10 microns at a rotational velocity of 2500 rpm. The centripetal forces acting on the impeller cause it deflect in a concave fashion, decreasing the initial gap distance as a function of radial position. This deflection is characterized for a previous and updated impeller design for comparative purposes. The impact of design options such as material selection, geometry dimensions, and operating rotational velocity are also explored, followed by a sensitivity study with these parameters bounded by specific design values. A modal analysis is also performed to calculate the impeller's natural frequencies which are desired to be avoided during operation. The finite element modeling techniques continue to be exercised by the impeller design team to address specific questions and evaluate conceptual designs, some of which are included in the Appendix.
A multigrid solution method for mixed hybrid finite elements
Energy Technology Data Exchange (ETDEWEB)
Schmid, W. [Universitaet Augsburg (Germany)
1996-12-31
We consider the multigrid solution of linear equations arising within the discretization of elliptic second order boundary value problems of the form by mixed hybrid finite elements. Using the equivalence of mixed hybrid finite elements and non-conforming nodal finite elements, we construct a multigrid scheme for the corresponding non-conforming finite elements, and, by this equivalence, for the mixed hybrid finite elements, following guidelines from Arbogast/Chen. For a rectangular triangulation of the computational domain, this non-conforming schemes are the so-called nodal finite elements. We explicitly construct prolongation and restriction operators for this type of non-conforming finite elements. We discuss the use of plain multigrid and the multilevel-preconditioned cg-method and compare their efficiency in numerical tests.
Kim, Jaehwan; Jung, Eunmi; Choi, Seung-Bok
2002-07-01
This paper presents a numerical modeling technique of piezoelectric transducers by taking into account wave radiation and scattering. It is based on the finite element modeling. Coupling problems between piezoelectric and elastic materials as well as fluid and structure systems associated with the modeling of piezoelectric underwater acoustic sensors are formulated. In the finite element modeling of unbounded acoustic fluid, IWEE (Infinite Wave Envelop Element) is adopted to take into account the infinite domain. The IWEE code is added to an in-house finite element program, and commercial pre and post-processor are used for mesh generation and to see the output. The validation of the numerical modeling is proved through an example, and scattering and radiation analysis of Tonpilz transducer is performed. The scattered wave on the sensor is calculated, and the sensor response, so called RVS (Receiving Voltage Sensitivity) is predicted.
Smoothing Algorithm for Planar and Surface Mesh Based on Element Geometric Deformation
Directory of Open Access Journals (Sweden)
Shuli Sun
2015-01-01
Full Text Available Smoothing is one of the basic procedures for improvement of mesh quality. In this paper, a novel and efficient smoothing approach for planar and surface mesh based on element geometric deformation is developed. The presented approach involves two main stages. The first stage is geometric deformation of all the individual elements through a specially designed two-step stretching-shrinking operation (SSO, which is performed by moving the vertices of each element according to a certain rule in order to get better shape of the element. The second stage is to determine the position of each node of the mesh by a weighted average strategy according to quality changes of its adjacent elements. The suggested SSO-based smoothing algorithm works efficiently for triangular mesh and can be naturally expanded to quadrilateral mesh, arbitrary polygonal mesh, and mixed mesh. Combined with quadratic error metric (QEM, this approach may be also applied to improve the quality of surface mesh. The proposed method is simple to program and inherently very suitable for parallelization, especially on graphic processing unit (GPU. Results of numerical experiments demonstrate the effectiveness and potential of this method.
Mosler, J.; Ortiz, M.
2009-01-01
A variational h-adaptive finite element formulation is proposed. The distinguishing feature of this method is that mesh refinement and coarsening are governed by the same minimization principle characterizing the underlying physical problem. Hence, no error estimates are invoked at any stage of the adaption procedure. As a consequence, linearity of the problem and a corresponding Hilbert-space functional framework are not required and the proposed formulation can be applied to hig...
Efficient Assembly of H(div) and H(curl) Conforming Finite Elements
Rognes, Marie; Logg, Anders; 10.1137/08073901X
2012-01-01
In this paper, we discuss how to efficiently evaluate and assemble general finite element variational forms on H(div) and H(curl). The proposed strategy relies on a decomposition of the element tensor into a precomputable reference tensor and a mesh-dependent geometry tensor. Two key points must then be considered: the appropriate mapping of basis functions from a reference element, and the orientation of geometrical entities. To address these issues, we extend here a previously presented representation theorem for affinely mapped elements to Piola-mapped elements. We also discuss a simple numbering strategy that removes the need to contend with directions of facet normals and tangents. The result is an automated, efficient, and easy-to-use implementation that allows a user to specify finite element variational forms on H(div) and H(curl) in close to mathematical notation.
Nonlinear tracking in a diffusion process with a Bayesian filter and the finite element method
DEFF Research Database (Denmark)
Pedersen, Martin Wæver; Thygesen, Uffe Høgsbro; Madsen, Henrik
2011-01-01
A new approach to nonlinear state estimation and object tracking from indirect observations of a continuous time process is examined. Stochastic differential equations (SDEs) are employed to model the dynamics of the unobservable state. Tracking problems in the plane subject to boundaries...... become complicated using SMC because Monte Carlo randomness is introduced. The finite element (FE) method solves the Kolmogorov equations of the SDE numerically on a triangular unstructured mesh for which boundary conditions to the state-space are simple to incorporate. The FE approach to nonlinear state...... estimation is suited for off-line data analysis because the computed smoothed state densities, maximum a posteriori parameter estimates and state sequence are deterministic conditional on the finite element mesh and the observations. The proposed method is conceptually similar to existing point...
Anisotropic Finite Element Modeling Based on a Harmonic Field for Patient-Specific Sclera
Directory of Open Access Journals (Sweden)
Xu Jia
2017-01-01
Full Text Available Purpose. This study examined the influence of anisotropic material for human sclera. Method. First, the individual geometry of patient-specific sclera was reproduced from a laser scan. Then, high quality finite element modeling of individual sclera was performed using a convenient automatic hexahedral mesh generator based on harmonic field and integrated with anisotropic material assignment function. Finally, comparison experiments were designed to investigate the effects of anisotropy on finite element modeling of sclera biomechanics. Results. The experimental results show that the presented approach can generate high quality anisotropic hexahedral mesh for patient-specific sclera. Conclusion. The anisotropy shows significant differences for stresses and strain distribution and careful consideration should be given to its use in biomechanical FE studies.
Anisotropic Finite Element Modeling Based on a Harmonic Field for Patient-Specific Sclera.
Jia, Xu; Liao, Shenghui; Duan, Xuanchu; Zheng, Wanqiu; Zou, Beiji
2017-01-01
Purpose. This study examined the influence of anisotropic material for human sclera. Method. First, the individual geometry of patient-specific sclera was reproduced from a laser scan. Then, high quality finite element modeling of individual sclera was performed using a convenient automatic hexahedral mesh generator based on harmonic field and integrated with anisotropic material assignment function. Finally, comparison experiments were designed to investigate the effects of anisotropy on finite element modeling of sclera biomechanics. Results. The experimental results show that the presented approach can generate high quality anisotropic hexahedral mesh for patient-specific sclera. Conclusion. The anisotropy shows significant differences for stresses and strain distribution and careful consideration should be given to its use in biomechanical FE studies.
Real-Time Nonlinear Finite Element Computations on GPU - Application to Neurosurgical Simulation.
Joldes, Grand Roman; Wittek, Adam; Miller, Karol
2010-12-15
Application of biomechanical modeling techniques in the area of medical image analysis and surgical simulation implies two conflicting requirements: accurate results and high solution speeds. Accurate results can be obtained only by using appropriate models and solution algorithms. In our previous papers we have presented algorithms and solution methods for performing accurate nonlinear finite element analysis of brain shift (which includes mixed mesh, different non-linear material models, finite deformations and brain-skull contacts) in less than a minute on a personal computer for models having up to 50.000 degrees of freedom. In this paper we present an implementation of our algorithms on a Graphics Processing Unit (GPU) using the new NVIDIA Compute Unified Device Architecture (CUDA) which leads to more than 20 times increase in the computation speed. This makes possible the use of meshes with more elements, which better represent the geometry, are easier to generate, and provide more accurate results.
Mesh locking effects in the finite volume solution of 2-D anisotropic diffusion equations
Manzini, Gianmarco; Putti, Mario
2007-01-01
Strongly anisotropic diffusion equations require special techniques to overcome or reduce the mesh locking phenomenon. We present a finite volume scheme that tries to approximate with the best possible accuracy the quantities that are of importance in discretizing anisotropic fluxes. In particular, we discuss the crucial role of accurate evaluations of the tangential components of the gradient acting tangentially to the control volume boundaries, that are called into play by anisotropic diffusion tensors. To obtain the sought characteristics from the proposed finite volume method, we employ a second-order accurate reconstruction scheme which is used to evaluate both normal and tangential cell-interface gradients. The experimental results on a number of different meshes show that the scheme maintains optimal convergence rates in both L2 and H1 norms except for the benchmark test considering full Neumann boundary conditions on non-uniform grids. In such a case, a severe locking effect is experienced and documented. However, within the range of practical values of the anisotropy ratio, the scheme is robust and efficient. We postulate and verify experimentally the existence of a quadratic relationship between the anisotropy ratio and the mesh size parameter that guarantees optimal and sub-optimal convergence rates.
Method to geometrically personalize a detailed finite-element model of the spine.
Lalonde, Nadine Michèle; Petit, Yvan; Aubin, Carl-Eric; Wagnac, Eric; Arnoux, Pierre-Jean
2013-07-01
To date, developing geometrically personalized and detailed solid finite-element models (FEMs) of the spine remains a challenge, notably due to multiple articulations and complex geometries. To answer this problem, a methodology based on a free-form deformation technique (kriging) was developed to deform a detailed reference finite-element mesh of the spine (including discs and ligaments) to the patient-specific geometry of 10- and 82-year-old asymptomatic spines. Different kriging configurations were tested: with or without smoothing, and control points on or surrounding the entire mesh. Based on the results, it is recommended to use surrounding control points and smoothing. The mean node to surface distance between the deformed and target geometries was 0.3±1.1 mm. Most elements met the mesh quality criteria (95%) after deformation, without interference at the articular facets. The method's novelty lies in the deformation of the entire spine at once, as opposed to deforming each vertebra separately, with surrounding control points and smoothing. This enables the transformation of reference vertebrae and soft tissues to obtain complete and personalized FEMs of the spine with minimal postprocessing to optimize the mesh.
Energy Technology Data Exchange (ETDEWEB)
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
Yu, Guojun
2012-10-01
In this article, comparative studies on computational accuracies and convergence rates of triangular and quadrilateral meshes are carried out in the frame work of the finite-volume method. By theoretical analysis, we conclude that the number of triangular cells needs to be 4/3 times that of quadrilateral cells to obtain similar accuracy. The conclusion is verified by a number of numerical examples. In addition, the convergence rates of the triangular meshes are found to be slower than those of the quadrilateral meshes when the same accuracy is obtained with these two mesh types. © 2012 Taylor and Francis Group, LLC.
hp-finite element method for simulating light scattering from complex 3D structures
Burger, S; Pomplun, J; Herrmann, S; Schmidt, F
2015-01-01
Methods for solving Maxwell's equations are integral part of optical metrology and computational lithography setups. Applications require accurate geometrical resolution, high numerical accuracy and/or low computation times. We present a finite-element based electromagnetic field solver relying on unstructured 3D meshes and adaptive hp-refinement. We apply the method for simulating light scattering off arrays of high aspect-ratio nano-posts and FinFETs.
Mathematical and Finite Element Modeling of Micro-Modification for Marine Gear
Xiongxi Wu; Qifeng Gao; Zesong Li
2015-01-01
Based on the computer simulation technique, this paper used the professional gear design software MASTA and finite element software ANSYS combined with the method of gear micro-modification to redesign the gear profile and eventually realized the optimization design of gear micro-modification. Then the gear transmission model of one-level reducer was established to simulate and analyze the contact equivalent stress, transmission error, and meshing impact before and after gear modification. By...
Superconvergence of a New Nonconforming Mixed Finite Element Scheme for Elliptic Problem
Directory of Open Access Journals (Sweden)
Lifang Pei
2013-01-01
Full Text Available A new nonconforming mixed finite element scheme for the second-order elliptic problem is proposed based on a new mixed variational form. It has the lowest degrees of freedom on rectangular meshes. The superclose property is proven by employing integral identity technique. Then global superconvergence result is derived through interpolation postprocessing operators. At last, some numerical experiments are carried out to verify the theoretical analysis.
Straightened cervical lordosis causes stress concentration: a finite element model study.
Wei, Wei; Liao, Shenhui; Shi, Shiyuan; Fei, Jun; Wang, Yifan; Chen, Chunyue
2013-03-01
In this study, we propose a finite element analysis of the complete cervical spine with straightened and normal physiological curvature by using a specially designed modelling system. An accurate finite element model is established to recommend plausible approaches to treatment of cervical spondylosis through the finite element analysis results. There are few reports of biomechanics influence of the straightened cervical curve. It is difficult to measure internal responses of cervical spine directly. However, the finite element method has been reported to have the capability to quantify both external and internal responses to mechanical loading, such as the strain and stress distribution of spinal components. We choose a subject with a straightened cervical spine from whom to collect the CT scan data, which formed the basis of the finite element analysis. By using a specially designed modelling system, a high quality finite element model of the complete cervical spine with straightened curvature was generated, which was then mapped to reconstruct a normal physiological curvature model by a volumetric mesh deformation method based on discrete differential properties. Then, the same boundary conditions were applied to do a comparison. The result demonstrated that the active movement range of straightened cervical spine decreased by 24-33 %, but the stress increased by 5-95 %. The stress was concentrated at the facet joint cartilage, uncovertebral joint and the disk. The results suggest that cervical lordosis may have a direct impact on cervical spondylosis treatment. These results may be useful for clinical treatment of cervical spondylosis with straightened curvature.
Institute of Scientific and Technical Information of China (English)
ZHOU Guoxiang; CHEN Yinchao; SHEN Guoqiang
2001-01-01
The paper presents an efficient andfast non-uniform, orthogonal mesh generation algo-rithm for the analysis and design of cylindrical mi-crowave devices and integrated circuits using thecylindrical finite-difference time-domain (CFDTD)methods. By using this algorithm, we can easily gen-erate a suitable CFDTD grid fitting for the devel-oped CFDTD Maxwell's solver. In the paper, wewill introduce in detail the algorithm and the graph-ical functions of the corresponding software package,CylinMesh. In addition, we will illustrate the algo-rithm by demonstrating various one, two, and three-dimensional grid patterns for a double-layered cylin-drical microstrip stepped-impedance low pass filter.
Directory of Open Access Journals (Sweden)
Zhao Tang
2016-04-01
Full Text Available The crashworthiness of a railway vehicle relates to its passive safety performance. Due to mesh distortion and difficulty in controlling the hourglass energy, conventional finite element methods face great challenges in crashworthiness simulation of large-scale complex railway vehicle models. Meshfree methods such as element-free Galerkin method offer an alternative approach to overcome those limitations but have proved time-consuming. In this article, a coupled finite element/meshfree method is proposed to study the crashworthiness of railway vehicles. A representative scenario, in which the leading vehicle of a high-speed train impacts to a rigid wall, is simulated with the coupled finite element/element-free Galerkin method in LS-DYNA. We have compared the conventional finite element method and the coupled finite element/element-free Galerkin method with the simulation results of different levels of discretization. Our work showed that coupled finite element/element-free Galerkin method is a suitable alternative of finite element method to handle the nonlinear deformation in full-size railway vehicle crashworthiness simulation. The coupled method can reduce the hourglass energy in finite element simulation, to produce robust simulation.
FINITE ELEMENT MODELING OF PROBLEMS OF GEOMECHANICS AND GEOPHYSICS
Directory of Open Access Journals (Sweden)
Vlasov Alexander Nikolaevich
2012-10-01
Full Text Available In the article, the authors consider some classes of problems of geomechanics that are resolved through the application of SIMULIA ABAQUS software. The tasks associated with the assessment of the zone of influence of structures produced on surrounding buildings and structures in the dense urban environment, as well as the tectonic and physical simulation of rifts with the purpose of identification of deformations of the Earth surface and other defects of lithospheric plates. These seemingly different types of tasks can be grouped together on the basis of common characteristics due to the complexity of numerical modeling problems of geomechanics and geophysics. Non-linearity of physical processes, complexity of the geological structure and variable thickness of layers, bed thinning layers, lenses, as well as singular elements, make it hard to consolidate different elements (for example, engineering and geological elements and associated structures of buildings in a single model. In this regard, software SIMULIA ABAQUS looks attractive, since it provides a highly advanced finite-element modeling technique, including a convenient hexahedral mesh generator, a wide range of models of elastic and plastic strain of materials, and the ability to work with certain geometric areas that interrelate through the mechanism of contacting surface pairs that have restrictions. It is noteworthy that the research also facilitates development of personal analytical methods designated for the assessment of physical and mechanical properties of heterogeneous materials as well as new solutions applicable in the vicinity of singular elements of the area that may be used in modeling together with ABAQUS software.
Test Simulation using Finite Element Method
Energy Technology Data Exchange (ETDEWEB)
Ali, M B; Abdullah, S; Nuawi, M Z; Ariffin, A K, E-mail: abgbas@yahoo.com [Department of Mechanical and Materials Engineering, Faculty of Engineering and Built Environment Universiti Kebangsaan Malaysia 43600 Bangi, Selangor (Malaysia)
2011-02-15
The dynamic responses of the standard Charpy impact machine are experimentally studied using the relevant data acquisition system, for the purpose of obtaining the impact response. For this reason, the numerical analysis by means of the finite element method has been used for experiment findings. Modelling of the charpy test was performed in order to obtain strain in the striker during the test. Two types of standard charpy specimens fabricated from different materials, i.e. aluminium 6061 and low carbon steel 1050, were used for the impact simulation testing. The related parameters on between different materials, energy absorbed, strain signal, power spectrum density (PSD) and the relationship between those parameters was finally correlated and discussed.
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.
Friction welding; Magnesium; Finite element; Shear test.
Directory of Open Access Journals (Sweden)
Leonardo Contri Campanelli
2013-06-01
Full Text Available Friction spot welding (FSpW is one of the most recently developed solid state joining technologies. In this work, based on former publications, a computer aided draft and engineering resource is used to model a FSpW joint on AZ31 magnesium alloy sheets and subsequently submit the assembly to a typical shear test loading, using a linear elastic model, in order to conceive mechanical tests results. Finite element analysis shows that the plastic flow is concentrated on the welded zone periphery where yield strength is reached. It is supposed that “through the weld” and “circumferential pull-out” variants should be the main failure behaviors, although mechanical testing may provide other types of fracture due to metallurgical features.
Finite element methods in resistivity logging
Lovell, J. R.
1993-09-01
Resistivity measurements are used in geophysical logging to help determine hydrocarbon reserves. The derivation of formation parameters from resistivity measurements is a complicated nonlinear procedure often requiring additional geological information. This requires an excellent understanding of tool physics, both to design new tools and interpret the measurements of existing tools. The Laterolog measurements in particular are difficult to interpret because the response is very nonlinear as a function of electrical conductivity, unlike Induction measurements. Forward modeling of the Laterolog is almost invariably done with finite element codes which require the inversion of large sparse matrices. Modern techniques can be used to accelerate this inversion. Moreover, an understanding of the tool physics can help refine these numerical techniques.
Optimizing the Evaluation of Finite Element Matrices
Kirby, Robert C; Logg, Anders; Scott, L Ridgway; 10.1137/040607824
2012-01-01
Assembling stiffness matrices represents a significant cost in many finite element computations. We address the question of optimizing the evaluation of these matrices. By finding redundant computations, we are able to significantly reduce the cost of building local stiffness matrices for the Laplace operator and for the trilinear form for Navier-Stokes. For the Laplace operator in two space dimensions, we have developed a heuristic graph algorithm that searches for such redundancies and generates code for computing the local stiffness matrices. Up to cubics, we are able to build the stiffness matrix on any triangle in less than one multiply-add pair per entry. Up to sixth degree, we can do it in less than about two. Preliminary low-degree results for Poisson and Navier-Stokes operators in three dimensions are also promising.
Nonlinear Finite Element Analysis of Sloshing
Directory of Open Access Journals (Sweden)
Siva Srinivas Kolukula
2013-01-01
Full Text Available The disturbance on the free surface of the liquid when the liquid-filled tanks are excited is called sloshing. This paper examines the nonlinear sloshing response of the liquid free surface in partially filled two-dimensional rectangular tanks using finite element method. The liquid is assumed to be inviscid, irrotational, and incompressible; fully nonlinear potential wave theory is considered and mixed Eulerian-Lagrangian scheme is adopted. The velocities are obtained from potential using least square method for accurate evaluation. The fourth-order Runge-Kutta method is employed to advance the solution in time. A regridding technique based on cubic spline is employed to avoid numerical instabilities. Regular harmonic excitations and random excitations are used as the external disturbance to the container. The results obtained are compared with published results to validate the numerical method developed.
Adaptive finite element 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.
A shell finite element model of the pelvic floor muscles.
d'Aulignac, D; Martins, J A C; Pires, E B; Mascarenhas, T; Jorge, R M Natal
2005-10-01
The pelvic floor gives support to the organs in the abdominal cavity. Using the dataset made public in (Janda et al. J. Biomech. (2003) 36(6), pp. 749-757), we have reconstructed the geometry of one of the most important parts of the pelvic floor, the levator ani, using NURB surfaces. Once the surface is triangulated, the corresponding mesh is used in a finite element analysis with shell elements. Based on the 3D behavior of the muscle we have constructed a shell that takes into account the direction of the muscle fibers and the incompressibility of the tissue. The constitutive model for the isotropic strain energy and the passive strain energy stored in the fibers is adapted from Humphrey's model for cardiac muscles. To this the active behavior of the skeletal muscle is added. We present preliminary results of a simulation of the levator ani muscle under pressure and with active contraction. This research aims at helping simulate the damages to the pelvic floor that can occur after childbirth.
Directory of Open Access Journals (Sweden)
Aiwen Wang
2012-01-01
Full Text Available We investigate an Oseen two-level stabilized finite-element method based on the local pressure projection for the 2D/3D steady Navier-Stokes equations by the lowest order conforming finite-element pairs (i.e., Q1−P0 and P1−P0. Firstly, in contrast to other stabilized methods, they are parameter free, no calculation of higher-order derivatives and edge-based data structures, implemented at the element level with minimal cost. In addition, the Oseen two-level stabilized method involves solving one small nonlinear Navier-Stokes problem on the coarse mesh with mesh size H, a large general Stokes equation on the fine mesh with mesh size h=O(H2. The Oseen two-level stabilized finite-element method provides an approximate solution (uh,ph with the convergence rate of the same order as the usual stabilized finite-element solutions, which involves solving a large Navier-Stokes problem on a fine mesh with mesh size h. Therefore, the method presented in this paper can save a large amount of computational time. Finally, numerical tests confirm the theoretical results. Conclusion can be drawn that the Oseen two-level stabilized finite-element method is simple and efficient for solving the 2D/3D steady Navier-Stokes equations.
CUBIT mesh generation environment. Volume 1: Users manual
Energy Technology Data Exchange (ETDEWEB)
Blacker, T.D.; Bohnhoff, W.J.; Edwards, T.L. [and others
1994-05-01
The CUBIT mesh generation environment is a two- and three-dimensional finite element mesh generation tool which is being developed to pursue the goal of robust and unattended mesh generation--effectively automating the generation of quadrilateral and hexahedral elements. It is a solid-modeler based preprocessor that meshes volume and surface solid models for finite element analysis. A combination of techniques including paving, mapping, sweeping, and various other algorithms being developed are available for discretizing the geometry into a finite element mesh. CUBIT also features boundary layer meshing specifically designed for fluid flow problems. Boundary conditions can be applied to the mesh through the geometry and appropriate files for analysis generated. CUBIT is specifically designed to reduce the time required to create all-quadrilateral and all-hexahedral meshes. This manual is designed to serve as a reference and guide to creating finite element models in the CUBIT environment.
POD-Galerkin reduced-order modeling with adaptive finite element snapshots
Ullmann, Sebastian; Rotkvic, Marko; Lang, Jens
2016-11-01
We consider model order reduction by proper orthogonal decomposition (POD) for parametrized partial differential equations, where the underlying snapshots are computed with adaptive finite elements. We address computational and theoretical issues arising from the fact that the snapshots are members of different finite element spaces. We propose a method to create a POD-Galerkin model without interpolating the snapshots onto their common finite element mesh. The error of the reduced-order solution is not necessarily Galerkin orthogonal to the reduced space created from space-adapted snapshot. We analyze how this influences the error assessment for POD-Galerkin models of linear elliptic boundary value problems. As a numerical example we consider a two-dimensional convection-diffusion equation with a parametrized convective direction. To illustrate the applicability of our techniques to non-linear time-dependent problems, we present a test case of a two-dimensional viscous Burgers equation with parametrized initial data.
Hydro-mechanical modeling of impermeable discontinuity in rock by extended finite element method
Institute of Scientific and Technical Information of China (English)
郑安兴; 罗先启
2015-01-01
The extended finite element method(XFEM) is a numerical method for modeling discontinuities within the classical finite element framework. The computation mesh in XFEM is independent of the discontinuities, such that remeshing for moving discontinuities can be overcome. The extended finite element method is presented for hydro-mechanical modeling of impermeable discontinuities in rock. The governing equation of XFEM for hydraulic fracture modeling is derived by the virtual work principle of the fracture problem considering the water pressure on crack surface. The coupling relationship between water pressure gradient on crack surface and fracture opening width is obtained by semi-analytical and semi-numerical method. This method simplifies coupling analysis iteration and improves computational precision. Finally, the efficiency of the proposed method for modeling hydraulic fracture problems is verified by two examples and the advantages of the XFEM for hydraulic fracturing analysis are displayed.
Wang, Wansheng; Chen, Long; Zhou, Jie
2016-05-01
A postprocessing technique for mixed finite element methods for the Cahn-Hilliard equation is developed and analyzed. Once the mixed finite element approximations have been computed at a fixed time on the coarser mesh, the approximations are postprocessed by solving two decoupled Poisson equations in an enriched finite element space (either on a finer grid or a higher-order space) for which many fast Poisson solvers can be applied. The nonlinear iteration is only applied to a much smaller size problem and the computational cost using Newton and direct solvers is negligible compared with the cost of the linear problem. The analysis presented here shows that this technique remains the optimal rate of convergence for both the concentration and the chemical potential approximations. The corresponding error estimate obtained in our paper, especially the negative norm error estimates, are non-trivial and different with the existing results in the literatures.
Directory of Open Access Journals (Sweden)
Liu Tian-Yuan
2016-01-01
Full Text Available Blade is one of the core components of turbine machinery. The reliability of blade is directly related to the normal operation of plant unit. However, with the increase of blade length and flow rate, non-linear effects such as finite deformation must be considered in strength computation to guarantee enough accuracy. Parallel computation is adopted to improve the efficiency of classical nonlinear finite element method and shorten the blade design period. So it is of extraordinary importance for engineering practice. In this paper, the dynamic partial differential equations and the finite element method forms for turbine blades under centrifugal load and flow load are given firstly. Then, according to the characteristics of turbine blade model, the classical method is optimized based on central processing unit + graphics processing unit heterogeneous parallel computation. Finally, the numerical experiment validations are performed. The computation speed of the algorithm proposed in this paper is compared with the speed of ANSYS. For the rectangle plate model with mesh number of 10 k to 4000 k, a maximum speed-up of 4.31 can be obtained. For the real blade-rim model with mesh number of 500 k, the speed-up of 4.54 times can be obtained.
DYNAMIC MODELLING OF BAR-GEAR MIXED MULTIBODY SYSTEMS USING A SPECIFIC FINITE ELEMENT METHOD
Institute of Scientific and Technical Information of China (English)
无
1999-01-01
A new dynamic model for mixed, flexible bar and gear multibody systems is developed based on a specific finite element method, and a new gear-element is proposed. The gear-element can take into account the time variant stiffness, the gear errors and mass unbalance. The model for geared multibody systems can couple the gear meshing and the flexibility of all contained components. The kinematic and dynamic analyses of the geared multibody systems are expounded and illustrated on an example composed of three gears, two bars and one slider.
Interpolation theory of anisotropic finite elements and applications
Institute of Scientific and Technical Information of China (English)
CHEN ShaoChun; XIAO LiuChao
2008-01-01
Interpolation theory is the foundation of finite element methods. In this paper, after reviewing some existed interpolation theorems of anisotropic finite element methods, we present a new way to analyse the interpolation error of anisotropic elements based on Newton's formula of polynomial interpolation as well as its applications.
Convergence of adaptive finite element methods for eigenvalue problems
Garau, Eduardo M.; Morin, Pedro; Zuppa, Carlos
2008-01-01
In this article we prove convergence of adaptive finite element methods for second order elliptic eigenvalue problems. We consider Lagrange finite elements of any degree and prove convergence for simple as well as multiple eigenvalues under a minimal refinement of marked elements, for all reasonable marking strategies, and starting from any initial triangulation.
Interpolation theory of anisotropic finite elements and applications
Institute of Scientific and Technical Information of China (English)
2008-01-01
Interpolation theory is the foundation of finite element methods.In this paper,after reviewing some existed interpolation theorems of anisotropic finite element methods,we present a new way to analyse the interpolation error of anisotropic elements based on Newton’s formula of polynomial interpolation as well as its applications.
Institute of Scientific and Technical Information of China (English)
Niphon Wansophark; Pramote Dechaumphai
2008-01-01
A streamline upwind finite element method using 6-node triangular element is presented.The method is applied to the convection term of the governing transport equation directly along local streamlines.Several convective-diffusion examples are used to evaluate efficiency of the method.Results show that the method is monotonic and does not produce any oscillation.In addition,an adaptive meshing technique is combined with the method to further increase accuracy of the solution,and at the same time,to minimize computational time and computer memory requirement.
Finite Element Program Generator and Its Application in Engineering
Institute of Scientific and Technical Information of China (English)
WANShui; HUHong; CHENJian-pin
2004-01-01
A completely new finite element software, Finite ElementProgram Generator (FEPG), is introduced and its designing thought and organizing structure is presented.FEPG uses the method of components and the technique of artificial intelligence to generate finite element program automatically by a computer according to the general principles of mathematic and internal rules of finite element method,as is similar to the deduction of mathematics.FEPG breaks through the limitation of present finite element software,which only applies to special discipline,while FEPG is suitable for all kinds of differential equations solved by finite element method.Now FEPG has been applied to superconductor research,electromagnetic field study,petroleum exploration,transportation,structure engineering,water conservancy,ship mechanics, solid-liquid coupling problems and liquid dynamics,etc.in China.
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...
Energy Technology Data Exchange (ETDEWEB)
Steibler, P.
2000-07-01
The unsteady, turbulent flow is to be calculated in a complex geometry. For this purpose a stabilized finite element formulation in which the same functions for velocity and pressure are used is developed. Thus the process remains independent of the type of elements. This simplifies the application. Above all, it is easier to deal with the boundary conditions. The independency from the elements is also achieved by the extended uzawa-algorithm which uses quadratic functions for velocity and an element-constant pressure. This method is also programmed. In order to produce the unstructured grids, an algorithm is implemented which produces meshes consisting of triangular and tetrahedral elements with flow-dependent adaptation. With standard geometries both calculation methods are compared with results. Finally the flow in a draft tube of a Kaplan turbine is calculated and compared with results from model tests. (orig.) [German] Die instationaere, turbulente Stroemung in einer komplexen Geometrie soll berechnet werden. Dazu wird eine Stabilisierte Finite Element Formulierung entwickelt, bei der die gleichen Ansatzfunktionen fuer Geschwindigkeiten und Druck verwendet werden. Das Verfahren wird damit unabhaengig von der Form der Elemente. Dies vereinfacht die Anwendung. Vor allem wird der Umgang mit den Randbedingungen erleichert. Die Elementunabhaengigkeit erreicht man auch mit dem erweiterten Uzawa-Algorithmus, welcher quadratische Ansatzfunktionen fuer die Geschwindigkeiten und elementweisen konstanten Druck verwendet. Dieses Verfahren wird ebenso implementiert. Zur Erstellung der unstrukturierten Gitter wird ein Algorithmus erzeugt, der Netze aus Dreiecks- und Tetraederelementen erstellt, welche stroemungsabhaengige Groessen besitzen koennen. Anhand einiger Standardgeometrien werden die beiden Berechnungsmethoden mit Ergebnissen aus der Literatur verglichen. Als praxisrelevantes Beispiel wird abschliessend die Stroemung in einem Saugrohr einer Kaplanturbine berechnet
DEFF Research Database (Denmark)
Cai, Hongzhu; Xiong, Bin; Han, Muran
2014-01-01
This paper presents a linear edge-based finite element method for numerical modeling of 3D controlled-source electromagnetic data in an anisotropic conductive medium. We use a nonuniform rectangular mesh in order to capture the rapid change of diffusive electromagnetic field within the regions...... of anomalous conductivity and close to the location of the source. In order to avoid the source singularity, we solve Maxwell's equation with respect to anomalous electric field. The nonuniform rectangular mesh can be transformed to hexahedral mesh in order to simulate the bathymetry effect. The sparse system...
Novel high-performance element in the electromagnetic finite-element method--node-edge element
Institute of Scientific and Technical Information of China (English)
Sheng Xinqing; Peng Zhen
2008-01-01
It is known in the computational electromagnetics (CEM) that the node element has a relative well-conditioned matrix,but suffers from the spurious solution problem; whereas the edge element has no spurious solutions,but usually produces an ill-conditioned matrix.Particularly,when the mesh is over dense,the iterative solution of the matrix equation from edge element converges very slowly.Based on the node element and edge element,a node-edge element is presented,which has no spurious solutions and better-conditioned matrix.Numerical experiments demonstrate that the proposed node-edge element is more efficient than now-widely used edge element.
Institute of Scientific and Technical Information of China (English)
无
2011-01-01
The scaled boundary finite element method(SBFEM) is a semi-analytical numerical method,which models an analysis domain by a small number of large-sized subdomains and discretises subdomain boundaries only.In a subdomain,all fields of state variables including displacement,stress,velocity and acceleration are semi-analytical,and the kinetic energy,strain energy and energy error are all integrated semi-analytically.These advantages are taken in this study to develop a posteriori h-hierarchical adaptive SBFEM for transient elastodynamic problems using a mesh refinement procedure which subdivides subdomains.Because only a small number of subdomains are subdivided,mesh refinement is very simple and efficient,and mesh mapping to transfer state variables from an old mesh to a new one is also very simple but accurate.Two 2D examples with stress wave propagation were modelled.The results show that the developed method is capable of capturing propagation of steep stress regions and calculating accurate dynamic responses,using only a fraction of degrees of freedom required by adaptive finite element method.
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
Impact of new computing systems on finite element computations
Noor, A. K.; Storassili, O. O.; Fulton, R. E.
1983-01-01
Recent advances in computer technology that are likely to impact finite element computations are reviewed. The characteristics of supersystems, highly parallel systems, and small systems (mini and microcomputers) are summarized. The interrelations of numerical algorithms and software with parallel architectures are discussed. A scenario is presented for future hardware/software environment and finite element systems. A number of research areas which have high potential for improving the effectiveness of finite element analysis in the new environment are identified.
Institute of Scientific and Technical Information of China (English)
Jayantha Pasdunkorale A.; Ian W. Turner
2005-01-01
An unstructured mesh finite volume discretisation method for simulating diffusion in anisotropic media in two-dimensional space is discussed. This technique is considered as an extension of the fully implicit hybrid control-volume finite-element method and it retains the local continuity of the flux at the control volume faces. A least squares function reconstruction technique together with a new flux decomposition strategy is used to obtain an accurate flux approximation at the control volume face, ensuring that the overall accuracy of the spatial discretisation maintains second order. This paper highlights that the new technique coincides with the traditional shape function technique when the correction term is neglected and that it significantly increases the accuracy of the previous linear scheme on coarse meshes when applied to media that exhibit very strong to extreme anisotropy ratios. It is concluded that the method can be used on both regular and irregular meshes,and appears independent of the mesh quality.
Dynamic Response of a Planetary Gear System Using a Finite Element/Contact Mechanics Model
Parker, Robert G.; Agashe, Vinayak; Vijayakar, Sandeep M.
2000-01-01
The dynamic response of a helicopter planetary gear system is examined over a wide range of operating speeds and torques. The analysis tool is a unique, semianalytical finite element formulation that admits precise representation of the tooth geometry and contact forces that are crucial in gear dynamics. Importantly, no a priori specification of static transmission error excitation or mesh frequency variation is required; the dynamic contact forces are evaluated internally at each time step. The calculated response shows classical resonances when a harmonic of mesh frequency coincides with a natural frequency. However, peculiar behavior occurs where resonances expected to be excited at a given speed are absent. This absence of particular modes is explained by analytical relationships that depend on the planetary configuration and mesh frequency harmonic. The torque sensitivity of the dynamic response is examined and compared to static analyses. Rotation mode response is shown to be more sensitive to input torque than translational mode response.
A unified multigrid solver for the Navier-Stokes equations on mixed element meshes
Mavriplis, D. J.; Venkatakrishnan, V.
1995-01-01
A unified multigrid solution technique is presented for solving the Euler and Reynolds-averaged Navier-Stokes equations on unstructured meshes using mixed elements consisting of triangles and quadrilaterals in two dimensions, and of hexahedra, pyramids, prisms, and tetrahedra in three dimensions. While the use of mixed elements is by no means a novel idea, the contribution of the paper lies in the formulation of a complete solution technique which can handle structured grids, block structured grids, and unstructured grids of tetrahedra or mixed elements without any modification. This is achieved by discretizing the full Navier-Stokes equations on tetrahedral elements, and the thin layer version of these equations on other types of elements, while using a single edge-based data-structure to construct the discretization over all element types. An agglomeration multigrid algorithm, which naturally handles meshes of any types of elements, is employed to accelerate convergence. An automatic algorithm which reduces the complexity of a given triangular or tetrahedral mesh by merging candidate triangular or tetrahedral elements into quadrilateral or prismatic elements is also described. The gains in computational efficiency afforded by the use of non-simplicial meshes over fully tetrahedral meshes are demonstrated through several examples.
Radial flow of slightly compressible fluids: A finite element-finite ...
African Journals Online (AJOL)
Journal of the Nigerian Association of Mathematical Physics ... Open Access DOWNLOAD FULL TEXT Subscription or Fee Access. Radial flow of slightly compressible fluids: A finite element-finite differences approach. JA Akpobi, ED Akpobi ...
Fix, G. J.; Rose, M. E.
1983-01-01
A least squares formulation of the system divu = rho, curlu = zeta is surveyed from the viewpoint of both finite element and finite difference methods. Closely related arguments are shown to establish convergence estimates.
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).
Institute of Scientific and Technical Information of China (English)
YUAN Si; HE Xue-feng
2006-01-01
Based on the newly-developed element energy projection (EEP) method for computation of super-convergent results in one-dimensional finite element method (FEM),the task of self-adaptive FEM analysis was converted into the task of adaptive piecewise polynomial interpolation. As a result, a satisfactory FEM mesh can be obtained, and further FEM analysis on this mesh would immediately produce an FEM solution which usually satisfies the user specified error tolerance. Even though the error tolerance was not completely satisfied, one or two steps of further local refinements would be sufficient.This strategy was found to be very simple, rapid, cheap and efficient. Taking the elliptical ordinary differential equation of second order as the model problem, the fundamental idea,implementation strategy and detailed algorithm are described. Representative numerical examples are given to show the effectiveness and reliability of the proposed approach.
Introduction to finite element analysis using MATLAB and Abaqus
Khennane, Amar
2013-01-01
There are some books that target the theory of the finite element, while others focus on the programming side of things. Introduction to Finite Element Analysis Using MATLAB(R) and Abaqus accomplishes both. This book teaches the first principles of the finite element method. It presents the theory of the finite element method while maintaining a balance between its mathematical formulation, programming implementation, and application using commercial software. The computer implementation is carried out using MATLAB, while the practical applications are carried out in both MATLAB and Abaqus. MA
Ablative Thermal Response Analysis Using the Finite Element Method
Dec John A.; Braun, Robert D.
2009-01-01
A review of the classic techniques used to solve ablative thermal response problems is presented. The advantages and disadvantages of both the finite element and finite difference methods are described. As a first step in developing a three dimensional finite element based ablative thermal response capability, a one dimensional computer tool has been developed. The finite element method is used to discretize the governing differential equations and Galerkin's method of weighted residuals is used to derive the element equations. A code to code comparison between the current 1-D tool and the 1-D Fully Implicit Ablation and Thermal Response Program (FIAT) has been performed.
An improved optimal elemental method for updating finite element models
Institute of Scientific and Technical Information of China (English)
Duan Zhongdong(段忠东); Spencer B.F.; Yan Guirong(闫桂荣); Ou Jinping(欧进萍)
2004-01-01
The optimal matrix method and optimal elemental method used to update finite element models may not provide accurate results. This situation occurs when the test modal model is incomplete, as is often the case in practice. An improved optimal elemental method is presented that defines a new objective function, and as a byproduct, circumvents the need for mass normalized modal shapes, which are also not readily available in practice. To solve the group of nonlinear equations created by the improved optimal method, the Lagrange multiplier method and Matlab function fmincon are employed. To deal with actual complex structures,the float-encoding genetic algorithm (FGA) is introduced to enhance the capability of the improved method. Two examples, a 7-degree of freedom (DOF) mass-spring system and a 53-DOF planar frame, respectively, are updated using the improved method.Thc example results demonstrate the advantages of the improved method over existing optimal methods, and show that the genetic algorithm is an effective way to update the models used for actual complex structures.
Wang, Ji; Sun, Qiang; Wu, Rongxing; Huang, Bin; Du, Jianke; Xiang, Wei
2015-01-01
The finite element analysis of high frequency vibrations of quartz crystal plates is a necessary process required in the design of quartz crystal resonators of precision types for applications in filters and sensors. The anisotropic materials and extremely high frequency in radiofrequency range of resonators determine that vibration frequency spectra are complicated with strong couplings of large number of different vibration modes representing deformations which do not appear in usual structural problems. For instance, the higher-order thickness-shear vibrations usually representing the sharp deformation of thin plates in the thickness direction, expecting the analysis is to be done with refined meshing schemes along the relatively small thickness and consequently the large plane area. To be able to represent the precise vibration mode shapes, a very large number of elements are needed in the finite element analysis with either the three-dimensional theory or the higher-order plate theory, although considera...
A HIGH ORDER ADAPTIVE FINITE ELEMENT METHOD FOR SOLVING NONLINEAR HYPERBOLIC CONSERVATION LAWS
Institute of Scientific and Technical Information of China (English)
Zhengfu Xu; Jinchao Xu; Chi-Wang Shu
2011-01-01
In this note,we apply the h-adaptive streamline diffusion finite element method with a small mesh-dependent artificial viscosity to solve nonlinear hyperbolic partial differential equations,with the objective of achieving high order accuracy and mesh efficiency.We compute the numerical solution to a steady state Burgers equation and the solution to a converging-diverging nozzle problem.The computational results verify that,by suitably choosing the artificial viscosity coefficient and applying the adaptive strategy based on a posterior error estimate by Johnson et al.,an order of N-3/2 accuracy can be obtained when continuous piecewise linear elements are used,where N is the number of elements.
ADER-WENO finite volume schemes with space-time adaptive mesh refinement
Dumbser, Michael; Zanotti, Olindo; Hidalgo, Arturo; Balsara, Dinshaw S.
2013-09-01
We present the first high order one-step ADER-WENO finite volume scheme with adaptive mesh refinement (AMR) in multiple space dimensions. High order spatial accuracy is obtained through a WENO reconstruction, while a high order one-step time discretization is achieved using a local space-time discontinuous Galerkin predictor method. Due to the one-step nature of the underlying scheme, the resulting algorithm is particularly well suited for an AMR strategy on space-time adaptive meshes, i.e. with time-accurate local time stepping. The AMR property has been implemented 'cell-by-cell', with a standard tree-type algorithm, while the scheme has been parallelized via the message passing interface (MPI) paradigm. The new scheme has been tested over a wide range of examples for nonlinear systems of hyperbolic conservation laws, including the classical Euler equations of compressible gas dynamics and the equations of magnetohydrodynamics (MHD). High order in space and time have been confirmed via a numerical convergence study and a detailed analysis of the computational speed-up with respect to highly refined uniform meshes is also presented. We also show test problems where the presented high order AMR scheme behaves clearly better than traditional second order AMR methods. The proposed scheme that combines for the first time high order ADER methods with space-time adaptive grids in two and three space dimensions is likely to become a useful tool in several fields of computational physics, applied mathematics and mechanics.
Energy Technology Data Exchange (ETDEWEB)
Kim, S. [Purdue Univ., West Lafayette, IN (United States)
1994-12-31
Parallel iterative procedures based on domain decomposition techniques are defined and analyzed for the numerical solution of wave propagation by finite element and finite difference methods. For finite element methods, in a Lagrangian framework, an efficient way for choosing the algorithm parameter as well as the algorithm convergence are indicated. Some heuristic arguments for finding the algorithm parameter for finite difference schemes are addressed. Numerical results are presented to indicate the effectiveness of the methods.
A parallel direct solver for the self-adaptive hp Finite Element Method
Paszyński, Maciej R.
2010-03-01
In this paper we present a new parallel multi-frontal direct solver, dedicated for the hp Finite Element Method (hp-FEM). The self-adaptive hp-FEM generates in a fully automatic mode, a sequence of hp-meshes delivering exponential convergence of the error with respect to the number of degrees of freedom (d.o.f.) as well as the CPU time, by performing a sequence of hp refinements starting from an arbitrary initial mesh. The solver constructs an initial elimination tree for an arbitrary initial mesh, and expands the elimination tree each time the mesh is refined. This allows us to keep track of the order of elimination for the solver. The solver also minimizes the memory usage, by de-allocating partial LU factorizations computed during the elimination stage of the solver, and recomputes them for the backward substitution stage, by utilizing only about 10% of the computational time necessary for the original computations. The solver has been tested on 3D Direct Current (DC) borehole resistivity measurement simulations problems. We measure the execution time and memory usage of the solver over a large regular mesh with 1.5 million degrees of freedom as well as on the highly non-regular mesh, generated by the self-adaptive h p-FEM, with finite elements of various sizes and polynomial orders of approximation varying from p = 1 to p = 9. From the presented experiments it follows that the parallel solver scales well up to the maximum number of utilized processors. The limit for the solver scalability is the maximum sequential part of the algorithm: the computations of the partial LU factorizations over the longest path, coming from the root of the elimination tree down to the deepest leaf. © 2009 Elsevier Inc. All rights reserved.
AbouEisha, Hassan M.
2017-07-13
We consider a class of two-and three-dimensional h-refined meshes generated by an adaptive finite element method. We introduce an element partition tree, which controls the execution of the multi-frontal solver algorithm over these refined grids. We propose and study algorithms with polynomial computational cost for the optimization of these element partition trees. The trees provide an ordering for the elimination of unknowns. The algorithms automatically optimize the element partition trees using extensions of dynamic programming. The construction of the trees by the dynamic programming approach is expensive. These generated trees cannot be used in practice, but rather utilized as a learning tool to propose fast heuristic algorithms. In this first part of our paper we focus on the dynamic programming approach, and draw a sketch of the heuristic algorithm. The second part will be devoted to a more detailed analysis of the heuristic algorithm extended for the case of hp-adaptive
Institute of Scientific and Technical Information of China (English)
DUAN Huoyuan; LIANG Guoping
2001-01-01
Following Part I., we study the stabilized finite element method for the incom pressible Navier-Stokes equations. It is shown that this new methodology is stable and has an optimal error estimates for all mesh Peclet number, allowing any combination of velocity and pressure interpolation.
Directory of Open Access Journals (Sweden)
Dalissier E.
2013-12-01
Full Text Available The objective of the ComPASS project is to develop a parallel multiphase Darcy flow simulator adapted to general unstructured polyhedral meshes (in a general sense with possibly non planar faces and to the parallelization of advanced finite volume discretizations with various choices of the degrees of freedom such as cell centres, vertices, or face centres. The main targeted applications are the simulation of CO2 geological storage, nuclear waste repository and reservoir simulations. The CEMRACS 2012 summer school devoted to high performance computing has been an ideal framework to start this collaborative project. This paper describes what has been achieved during the four weeks of the CEMRACS project which has been focusing on the implementation of basic features of the code such as the distributed unstructured polyhedral mesh, the synchronization of the degrees of freedom, and the connection to scientific libraries including the partitioner METIS, the visualization tool PARAVIEW, and the parallel linear solver library PETSc. The parallel efficiency of this first version of the ComPASS code has been validated on a toy parabolic problem using the Vertex Approximate Gradient finite volume spatial discretization with both cell and vertex degrees of freedom, combined with an Euler implicit time integration.
Solid Modeling and Finite Element Analysis of an Overhead Crane Bridge
Directory of Open Access Journals (Sweden)
C. Alkin
2005-01-01
Full Text Available The design of an overhead crane bridge with a double box girder has been investigated and a case study of a crane with 35 ton capacity and 13 m span length has been conducted. In the initial phase of the case study, conventional design calculations proposed by F. E. M. Rules and DIN standards were performed to verify the stress and deflection levels. The crane design was modeled using both solids and surfaces. Finite element meshes with 4-node tetrahedral and 4-node quadrilateral shell elements were generated from the solid and shell models, respectively. After a comparison of the finite element analyses, the conventional calculations and performance of the existing crane, the analysis with quadratic shell elements was found to give the most realistic results. As a result of this study, a design optimization method for an overhead crane is proposed.
SULEC: Benchmarking a new ALE finite-element code
Buiter, S.; Ellis, S.
2012-04-01
We have developed a 2-D/3-D arbitrary lagrangian-eulerian (ALE) finite-element code, SULEC, based on known techniques from literature. SULEC is successful in tackling many of the problems faced by numerical models of lithosphere and mantle processes, such as the combination of viscous, elastic, and plastic rheologies, the presence of a free surface, the contrast in viscosity between lithosphere and the underlying asthenosphere, and the occurrence of large deformations including viscous flow and offset on shear zones. The aim of our presentation is (1) to describe SULEC, and (2) to present a set of analytical and numerical benchmarks that we use to continuously test our code. SULEC solves the incompressible momentum equation coupled with the energy equation. It uses a structured mesh that is built of quadrilateral or brick elements that can vary in size in all dimensions, allowing to achieve high resolutions where required. The elements are either linear in velocity with constant pressure, or quadratic in velocity with linear pressure. An accurate pressure field is obtained through an iterative penalty (Uzawa) formulation. Material properties are carried on tracer particles that are advected through the Eulerian mesh. Shear elasticity is implemented following the approach of Moresi et al. [J. Comp. Phys. 184, 2003], brittle materials deform following a Drucker-Prager criterion, and viscous flow is by temperature- and pressure-dependent power-law creep. The top boundary of our models is a true free surface (with free surface stabilisation) on which simple surface processes models may be imposed. We use a set of benchmarks that test viscous, viscoelastic, elastic and plastic deformation, temperature advection and conduction, free surface behaviour, and pressure computation. Part of our benchmark set is automated allowing easy testing of new code versions. Examples include Poiseuille flow, Couette flow, Stokes flow, relaxation of viscous topography, viscous pure shear
Gong, J.; Ozdemir, T.; Volakis, J; Nurnberger, M.
1995-01-01
Year 1 progress can be characterized with four major achievements which are crucial toward the development of robust, easy to use antenna analysis code on doubly conformal platforms. (1) A new FEM code was developed using prismatic meshes. This code is based on a new edge based distorted prism and is particularly attractive for growing meshes associated with printed slot and patch antennas on doubly conformal platforms. It is anticipated that this technology will lead to interactive, simple to use codes for a large class of antenna geometries. Moreover, the codes can be expanded to include modeling of the circuit characteristics. An attached report describes the theory and validation of the new prismatic code using reference calculations and measured data collected at the NASA Langley facilities. The agreement between the measured and calculated data is impressive even for the coated patch configuration. (2) A scheme was developed for improved feed modeling in the context of FEM. A new approach based on the voltage continuity condition was devised and successfully tested in modeling coax cables and aperture fed antennas. An important aspect of this new feed modeling approach is the ability to completely separate the feed and antenna mesh regions. In this manner, different elements can be used in each of the regions leading to substantially improved accuracy and meshing simplicity. (3) A most important development this year has been the introduction of the perfectly matched interface (PMI) layer for truncating finite element meshes. So far the robust boundary integral method has been used for truncating the finite element meshes. However, this approach is not suitable for antennas on nonplanar platforms. The PMI layer is a lossy anisotropic absorber with zero reflection at its interface. (4) We were able to interface our antenna code FEMA_CYL (for antennas on cylindrical platforms) with a standard high frequency code. This interface was achieved by first generating
Finite element simulations of thin-film composite BAW resonators.
Makkonen, T; Holappa, A; Ellä, J; Salomaa, M M
2001-09-01
A finite element method (FEM) formulation is presented for the numerical solution of the electroelastic equations that govern the linear forced vibrations of piezoelectric media. A harmonic time dependence is assumed. Both of the approaches, that of solving the field problem (harmonic analysis) and that of solving the corresponding eigenvalue problem (modal analysis), are described. A FEM software package has been created from scratch. Important aspects central to the efficient implementation of FEM are explained, such as memory management and solving the generalized piezoelectric eigenvalue problem. Algorithms for reducing the required computer memory through optimization of the matrix profile, as well as Lanczos algorithm for the solution of the eigenvalue problem are linked into the software from external numerical libraries. Our FEM software is applied to detailed numerical modeling of thin-film bulk acoustic wave (BAW) composite resonators. Comparison of results from 2D and full 39 simulations of a resonator are presented. In particular, 3D simulations are used to investigate the effect of the top electrode shape on the resonator electrical response. The validity of the modeling technique is demonstrated by comparing the simulated and measured displacement profiles at several frequencies. The results show that useful information on the performance of the thin-film resonators can be obtained even with relatively coarse meshes and, consequently, moderate computational resources.
FINITE ELEMENT ANALYSIS FOR OPTIMIZING ANTENNA FOR MICROWAVE COAGULATION THERAPY
Directory of Open Access Journals (Sweden)
MARWAHA S.
2012-08-01
Full Text Available Microwave coagulation therapy (MCT is emerging as an attractive modality for thermal therapy of soft tissues targeted in short periods of time, making it particularly suitable for ablation of hepatic and other tumors. In this field of microwave coagulation therapy, the use of minimally invasive antenna is recognized as a very promising technique for the treatment of small tumors because a very thin antenna can be easily inserted inside the body and precisely localized using the advanced 3D imaging techniques and surgical robots. The authors investigated the microwave coaxial antenna operating at 2.45 GHz by varying the slots size for the removal of liver tumor. The analysis was done using 2D finite element modeling. By several optimization steps the antenna is simulated and optimized by comparing the values of specific absorption rate (SAR, mesh statistics and temperature distributions in tissue generated by the antenna with the variations of dimensions of slot from 1 mm to 1.7 mm.
MORTAR FINITE VOLUME METHOD WITH ADINI ELEMENT FOR BIHARMONIC PROBLEM
Institute of Scientific and Technical Information of China (English)
Chun-jia Bi; Li-kang Li
2004-01-01
In this paper, we construct and analyse a mortar finite volume method for the dis-cretization for the biharmonic problem in R2. This method is based on the mortar-type Adini nonconforming finite element spaces. The optimal order H2-seminorm error estimate between the exact solution and the mortar Adini finite volume solution of the biharmonic equation is established.
Finite Element Analysis (FEA) in Design and Production.
Waggoner, Todd C.; And Others
1995-01-01
Finite element analysis (FEA) enables industrial designers to analyze complex components by dividing them into smaller elements, then assessing stress and strain characteristics. Traditionally mainframe based, FEA is being increasingly used in microcomputers. (SK)
A Finite Element Analysis of Optimal Variable Thickness Sheets
DEFF Research Database (Denmark)
Petersson, Joakim S
1996-01-01
A quasimixed Finite Element (FE) method for maximum stiffness of variablethickness sheets is analysed. The displacement is approximated with ninenode Lagrange quadrilateral elements and the thickness is approximated aselementwise constant. One is guaranteed that the FE displacement solutionswill...
Finite element simulation of asphalt fatigue testing
DEFF Research Database (Denmark)
Ullidtz, Per; Kieler, Thomas Lau; Kargo, Anders
1997-01-01
The traditional interpretation of fatigue tests on asphalt mixes has been in terms of a logarithmic linear relationship between the constant stress or strain amplitude and the number of load repetitions to cause failure, often defined as a decrease in modulus to half the initial value. To accomod......The traditional interpretation of fatigue tests on asphalt mixes has been in terms of a logarithmic linear relationship between the constant stress or strain amplitude and the number of load repetitions to cause failure, often defined as a decrease in modulus to half the initial value....... To accomodate non-constant stress or strain, a mode factor may be introduced or the dissipated energy may be used instead of stress or strain.Cracking of asphalt (or other materials) may be described as a process consisting of three phases. In phase one diffuse microcracking is formed in the material...... damage mechanics.The paper describes how continuum damage mechanics may be used with a finite element program to explain the progressive deterioration of asphalt mixes under laboratory fatigue testing. Both constant stress and constant strain testing are simulated, and compared to the actual results from...
Finite Element Simulation for Springback Prediction Compensation
Directory of Open Access Journals (Sweden)
Agus Dwi Anggono
2011-01-01
Full Text Available An accurate modelling of the sheet metal deformations including the springback prediction is one of the key factors in the efficient utilisation of Finite Element Method (FEM process simulation in industrial application. Assuming that springback can be predicted accurately, there still remains the problem of how to use such results to appear at a suitable die design to produce a target part shape. It is this second step of springback compensation that is addressed in the current work. This paper presents an evaluation of a standard benchmark model defined as Benchmark II of Numisheet 2008, S-channel model with various drawbeads and blank holder force (BHF. The tool geometry modified based on springback calculation for a part to compensate springback. The result shows that the combination of the smooth bead with BHF of 650 kN resulted in the minimum springback and the tool compensation was successfully to accommodate the springback errors.
Studying a dental pathology by finite elements
Directory of Open Access Journals (Sweden)
Fernando Mejía Umaña
2010-04-01
Full Text Available Abfractives lesions or abfractions are non-cavity lesions of dental structures in which a biomechanical factor has been identified as being the most probable cause for it occurring. Even throught such lesion can be presented in any tooth, it occurs more frequently in people aged over 35. This article presents some results obtained by the Universidad Nacional de Colombia's multidisciplinary research group for studying "dental material's structure and propierties". The introduction describes such lesion's characteristics and possible causes. The results of various modelling exercises using finite elements (in two and three dimensions are presented regarding a first premolar tooth subjected to normal mastication load and also to abnormal loads produced by occlusion problems. The most important findings (accompanied by clinical observations were that: areas of high concentration of forces were identified where lesions were frequently presented, associated with loads whose line of action did not pass through the central part of the section of tooth at cervical level; a direct relationship between facets of wear being orientated with the direction of forces produced by a high concentration of force; and the presence of high compression forces in the cervical region.
Finite element modeling of retinal prosthesis mechanics
Basinger, B. C.; Rowley, A. P.; Chen, K.; Humayun, M. S.; Weiland, J. D.
2009-10-01
Epiretinal prostheses used to treat degenerative retina diseases apply stimulus via an electrode array fixed to the ganglion cell side of the retina. Mechanical pressure applied by these arrays to the retina, both during initial insertion and throughout chronic use, could cause sufficient retinal damage to reduce the device's effectiveness. In order to understand and minimize potential mechanical damage, we have used finite element analysis to model mechanical interactions between an electrode array and the retina in both acute and chronic loading configurations. Modeling indicates that an acute tacking force distributes stress primarily underneath the tack site and heel edge of the array, while more moderate chronic stresses are distributed more evenly underneath the array. Retinal damage in a canine model chronically implanted with a similar array occurred in correlating locations, and model predictions correlate well with benchtop eyewall compression tests. This model provides retinal prosthesis researchers with a tool to optimize the mechanical electrode array design, but the techniques used here represent a unique effort to combine a modifiable device and soft biological tissues in the same model and those techniques could be extended to other devices that come into mechanical contact with soft neural tissues.
Intra Plate Stresses Using Finite Element Modelling
Directory of Open Access Journals (Sweden)
Jayalakshmi S.
2016-10-01
Full Text Available One of the most challenging problems in the estimation of seismic hazard is the ability to quantify seismic activity. Empirical models based on the available earthquake catalogue are often used to obtain activity of source regions. The major limitation with this approach is the lack of sufficient data near a specified source. The non-availability of data poses difficulties in obtaining distribution of earthquakes with large return periods. Such events recur over geological time scales during which tectonic processes, including mantle convection, formation of faults and new plate boundaries, are likely to take place. The availability of geometries of plate boundaries, plate driving forces, lithospheric stress field and GPS measurements has provided numerous insights on the mechanics of tectonic plates. In this article, a 2D finite element model of Indo-Australian plate is developed with the focus of representing seismic activity in India. The effect of large scale geological features including sedimentary basins, fold belts and cratons on the stress field in India is explored in this study. In order to address long term behaviour, the orientation of stress field and tectonic faults of the present Indo-Australian plate are compared with a reconstructed stress field from the early Miocene (20 Ma.
Hill, Jon; Piggott, M. D.; Ham, David A.; Popova, E. E.; Srokosz, M. A.
2012-10-01
Research into the use of unstructured mesh methods for ocean modelling has been growing steadily in the last few years. One advantage of using unstructured meshes is that one can concentrate resolution where it is needed. In addition, dynamic adaptive mesh optimisation (DAMO) strategies allow resolution to be concentrated when this is required. Despite the advantage that DAMO gives in terms of improving the spatial resolution where and when required, small-scale turbulence in the oceans still requires parameterisation. A two-equation, generic length scale (GLS) turbulence model (one equation for turbulent kinetic energy and another for a generic turbulence length-scale quantity) adds this parameterisation and can be used in conjunction with adaptive mesh techniques. In this paper, an implementation of the GLS turbulence parameterisation is detailed in a non-hydrostatic, finite-element, unstructured mesh ocean model, Fluidity-ICOM. The implementation is validated by comparing to both a laboratory-scale experiment and real-world observations, on both fixed and adaptive meshes. The model performs well, matching laboratory and observed data, with resolution being adjusted as necessary by DAMO. Flexibility in the prognostic fields used to construct the error metric used in DAMO is required to ensure best performance. Moreover, the adaptive mesh models perform as well as fixed mesh models in terms of root mean square error to observation or theoretical mixed layer depths, but uses fewer elements and hence has a reduced computational cost.
Vande Geest, Jonathan P; Simon, B R; Rigby, Paul H; Newberg, Tyler P
2011-04-01
Finite element models (FEMs) including characteristic large deformations in highly nonlinear materials (hyperelasticity and coupled diffusive/convective transport of neutral mobile species) will allow quantitative study of in vivo tissues. Such FEMs will provide basic understanding of normal and pathological tissue responses and lead to optimization of local drug delivery strategies. We present a coupled porohyperelastic mass transport (PHEXPT) finite element approach developed using a commercially available ABAQUS finite element software. The PHEXPT transient simulations are based on sequential solution of the porohyperelastic (PHE) and mass transport (XPT) problems where an Eulerian PHE FEM is coupled to a Lagrangian XPT FEM using a custom-written FORTRAN program. The PHEXPT theoretical background is derived in the context of porous media transport theory and extended to ABAQUS finite element formulations. The essential assumptions needed in order to use ABAQUS are clearly identified in the derivation. Representative benchmark finite element simulations are provided along with analytical solutions (when appropriate). These simulations demonstrate the differences in transient and steady state responses including finite deformations, total stress, fluid pressure, relative fluid, and mobile species flux. A detailed description of important model considerations (e.g., material property functions and jump discontinuities at material interfaces) is also presented in the context of finite deformations. The ABAQUS-based PHEXPT approach enables the use of the available ABAQUS capabilities (interactive FEM mesh generation, finite element libraries, nonlinear material laws, pre- and postprocessing, etc.). PHEXPT FEMs can be used to simulate the transport of a relatively large neutral species (negligible osmotic fluid flux) in highly deformable hydrated soft tissues and tissue-engineered materials.
Directory of Open Access Journals (Sweden)
Sascha M. Schnepp
2012-01-01
Full Text Available An extension of the framework of the Finite Integration Technique (FIT including dynamic and adaptive mesh refinement is presented. After recalling the standard formulation of the FIT, the proposed mesh adaptation procedure is described. Besides the linear interpolation approach, a novel interpolation technique based on specialized spline functions for approximating the discrete electromagnetic field solution during mesh adaptation is introduced. The standard FIT on a fixed mesh and the new adaptive approach are applied to a simulation test case with a known analytical solution. The numerical accuracy of the two methods is shown to be comparable. The dynamic mesh approach is, however, much more efficient. This is demonstrated with the full scale modeling of the complete rf gun at the Photo Injector Test Facility DESY Zeuthen (PITZ on a single computer. Results of a detailed design study addressing the effects of individual components of the gun onto the beam emittance using a fully self-consistent approach are presented.
Schnepp, Sascha M; Weiland, Thomas
2011-01-01
An extension of the framework of the Finite Integration Technique (FIT) including dynamic and adaptive mesh refinement is presented. After recalling the standard formulation of the FIT, the proposed mesh adaptation procedure is described. Besides the linear interpolation approach, a novel interpolation technique based on specialized spline functions for approximating the discrete electromagnetic field solution during mesh adaptation is introduced. The standard FIT on a fixed mesh and the new adaptive approach are applied to a simulation test case with known analytical solution. The numerical accuracy of the two methods are shown to be comparable. The dynamic mesh approach is, however, much more efficient. This is also demonstrated for the full scale modeling of the complete RF gun at the Photo Injector Test Facility DESY Zeuthen (PITZ) on a single computer. Results of a detailed design study addressing the effects of individual components of the gun onto the beam emittance using a fully self-consistent approa...
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),
Vibration Analysis of Beams by Spline Finite Element
Institute of Scientific and Technical Information of China (English)
YANG Hao; SUN Li
2011-01-01
In this paper,the spline finite element method is developed to investigate free vibration problems of beams.The cubic B-spline functions are used to construct the displacement field.The assembly of elements and the introduction of boundary conditions follow the standard finite element procedure.The results under various boundary conditions are compared with those obtained by the exact method and the finite difference method.It shows that the results are in excellent agreement with the analytical results and much more accurate than the results obtained by the finite difference method,especially for higher order modes.
Three-dimensional finite element analysis of the human temporomandibular joint disc.
Beek, M; Koolstra, J H; van Ruijven, L J; van Eijden, T M
2000-03-01
A three-dimensional finite element model of the articular disc of the human temporomandibular joint has been developed. The geometry of the articular cartilage and articular disc surfaces in the joint was measured using a magnetic tracking device. First, polynomial functions were fitted through the coordinates of these scattered measurements. Next, the polynomial description was transformed into a triangulated description to allow application of an automatic mesher. Finally, a finite element mesh of the articular disc was created by filling the geometry with tetrahedral elements. The articulating surfaces of the mandible and skull were modeled by quadrilateral patches. The finite element mesh and the patches were combined to create a three-dimensional model in which unrestricted sliding of the disc between the articulating surfaces was allowed. Simulation of statical joint loading at the closed jaw position predicted that the stress and strain distributions were located primarily in the intermediate zone of the articular disc with the highest values in the lateral part. Furthermore, it was predicted that considerable deformations occurred for relatively small joint loads and that relatively large variations in the direction of joint loading had little influence on the distribution of the deformations.
Finite Element Model of Cardiac Electrical Conduction.
Yin, John Zhihao
1994-01-01
In this thesis, we develop mathematical models to study electrical conduction of the heart. One important pattern of wave propagation of electrical excitation in the heart is reentry which is believed to be the underlying mechanism of some dangerous cardiac arhythmias such as ventricular tachycardia and ventricular fibrillation. We present in this thesis a new ionic channel model of the ventricular cardiac cell membrane to study the microscopic electrical properties of myocardium. We base our model on recent single channel experiment data and a simple physical diffusion model of the calcium channel. Our ionic channel model of myocardium has simpler differential equations and fewer parameters than previous models. Further more, our ionic channel model achieves better results in simulating the strength-interval curve when we connect the membrane patch model to form a one dimensional cardiac muscle strand. We go on to study a finite element model which uses multiple states and non-nearest neighbor interactions to include curvature and dispersion effects. We create a generalized lattice randomization to overcome the artifacts generated by the interaction between the local dynamics and the regularities of the square lattice. We show that the homogeneous model does not display spontaneous wavefront breakup in a reentrant wave propagation once the lattice artifacts have been smoothed out by lattice randomization with a randomization scale larger than the characteristic length of the interaction. We further develop a finite 3-D 3-state heart model which employs a probability interaction rule. This model is applied to the simulation of Body Surface Laplacian Mapping (BSLM) using a cylindrical volume conductor as the torso model. We show that BSLM has a higher spatial resolution than conventional mapping methods in revealing the underlying electrical activities of the heart. The results of these studies demonstrate that mathematical modeling and computer simulation are very
A NURBS-based generalized finite element scheme for 3D simulation of heterogeneous materials
Safdari, Masoud; Najafi, Ahmad R.; Sottos, Nancy R.; Geubelle, Philippe H.
2016-08-01
A 3D NURBS-based interface-enriched generalized finite element method (NIGFEM) is introduced to solve problems with complex discontinuous gradient fields observed in the analysis of heterogeneous materials. The method utilizes simple structured meshes of hexahedral elements that do not necessarily conform to the material interfaces in heterogeneous materials. By avoiding the creation of conforming meshes used in conventional FEM, the NIGFEM leads to significant simplification of the mesh generation process. To achieve an accurate solution in elements that are crossed by material interfaces, the NIGFEM utilizes Non-Uniform Rational B-Splines (NURBS) to enrich the solution field locally. The accuracy and convergence of the NIGFEM are tested by solving a benchmark problem. We observe that the NIGFEM preserves an optimal rate of convergence, and provides additional advantages including the accurate capture of the solution fields in the vicinity of material interfaces and the built-in capability for hierarchical mesh refinement. Finally, the use of the NIGFEM in the computational analysis of heterogeneous materials is discussed.
Finite element analysis for general elastic multi-structures
Institute of Scientific and Technical Information of China (English)
无
2006-01-01
A finite element method is introduced to solve the general elastic multi-structure problem, in which the displacements on bodies, the longitudinal displacements on plates and the longitudinal displacements on beams are discretized using conforming linear elements, the rotational angles on beams are discretized using conforming elements of second order, the transverse displacements on plates and beams are discretized by the Morley elements and the Hermite elements of third order, respectively. The generalized Korn's inequality is established on related nonconforming element spaces, which implies the unique solvability of the finite element method. Finally, the optimal error estimate in the energy norm is derived for the method.
THE PRACTICAL ANALYSIS OF FINITE ELEMENTS METHOD ERRORS
Directory of Open Access Journals (Sweden)
Natalia Bakhova
2011-03-01
Full Text Available Abstract. The most important in the practical plan questions of reliable estimations of finite elementsmethod errors are considered. Definition rules of necessary calculations accuracy are developed. Methodsand ways of the calculations allowing receiving at economical expenditures of computing work the best finalresults are offered.Keywords: error, given the accuracy, finite element method, lagrangian and hermitian elements.
Finite Element Modelling of Seismic Liquefaction in Soils
Galavi, V.; Petalas, A.; Brinkgreve, R.B.J.
2013-01-01
Numerical aspects of seismic liquefaction in soils as implemented in the finite element code, PLAXIS, is described in this paper. After description of finite element equations of dynamic problems, three practical dynamic boundary conditions, namely viscous boundary tractions, tied degrees of freedom
Parallel direct solver for finite element modeling of manufacturing processes
DEFF Research Database (Denmark)
Nielsen, Chris Valentin; Martins, P.A.F.
2017-01-01
The central processing unit (CPU) time is of paramount importance in finite element modeling of manufacturing processes. Because the most significant part of the CPU time is consumed in solving the main system of equations resulting from finite element assemblies, different approaches have been...
Finite element models applied in active structural acoustic control
Oude Nijhuis, Marco H.H.; Boer, de André; Rao, Vittal S.
2002-01-01
This paper discusses the modeling of systems for active structural acoustic control. The finite element method is applied to model structures including the dynamics of piezoelectric sensors and actuators. A model reduction technique is presented to make the finite element model suitable for controll
Viscoelastic finite-element analysis of human skull - dura mater ...
African Journals Online (AJOL)
SERVER
2008-03-18
Mar 18, 2008 ... In the work, the dynamic characteristics of the human skull-dura mater ... Ansys' finite element processor, a simplified three-dimensional finite element ... brain, cerebrospinal fluid (CSF), and the brain's blood ... ICP is often not preventable. .... The creep of linear viscoelastic solid can be simulated by the.
ALTERNATING DIRECTION FINITE ELEMENT METHOD FOR SOME REACTION DIFFUSION MODELS
Institute of Scientific and Technical Information of China (English)
江成顺; 刘蕴贤; 沈永明
2004-01-01
This paper is concerned with some nonlinear reaction - diffusion models. To solve this kind of models, the modified Laplace finite element scheme and the alternating direction finite element scheme are established for the system of patrical differential equations. Besides, the finite difference method is utilized for the ordinary differential equation in the models. Moreover, by the theory and technique of prior estimates for the differential equations, the convergence analyses and the optimal L2- norm error estimates are demonstrated.
OBJECT-ORIENTED FINITE ELEMENT ANALYSIS AND PROGRAMMING IN VC + +
Institute of Scientific and Technical Information of China (English)
马永其; 冯伟
2002-01-01
The design of finite element analysis program using object-oriented programming(OOP) techniques is presented. The objects, classes and the subclasses used in theprogramming are explained. The system of classes library of finite element analysis programand Windows-type Graphical User Interfaces by VC + + and its MFC are developed. Thereliability, reusability and extensibility of program are enhanced. It is a reference todevelop the large-scale, versatile and powerful systems of object-oriented finite elementsoftware.
Semi-automatic computer construction of three-dimensional shapes for the finite element method.
Aharon, S; Bercovier, M
1993-12-01
Precise estimation of spatio-temporal distribution of ions (or other constitutives) in three-dimensional geometrical configuration plays a major role in biology. Since a direct experimental information regarding the free intracellular Ca2+ spatio-temporal distribution is not available to date, mathematical models have been developed. Most of the existing models are based on the classical numerical method of finite-difference (FD). Using this method one is limited when dealing with complicated geometry, general boundary conditions and variable or non-linear material properties. These difficulties are easily solved when the finite-element-method (FEM) is employed. The first step in the implementation of the FEM procedure is the mesh generation which is the single most tedious, time consuming task and vulnerable to mistake. In order to overcome these limitations we developed a new interface called AUTOMESH. This tool is used as a preprocessor program which generates two- and three-dimensional meshes for some known and often-used shapes in neurobiology. AUTOMESH creates an appropriate mesh by using the mesh generator commercial tool of FIDAP.
Finite element simulation of thick sheet thermoforming
Mercier, Daniel
This PhD was organized as collaboration between Lehigh University and the Ecole des Mines d'Albi on the subject: "Numerical simulation of thick sheet thermoforming". The research applications cover a wide range of products from thermoforming, e.g., packaging, automobile parts, appliance parts, large-scale panels and covers. Due to the special nature of this PhD, and the requirements of each hosting institutes, the research was split accordingly into two parts: At Lehigh University, under the supervision of Prof. Herman F. Nied, a full three-dimensional finite element program was developed in order to simulate the mechanical deformation during the process of thermoforming. The material behavior is considered hyperelastic with the property of incompressibility. The deformed structure may exhibit symmetries and may use a large choice of boundary conditions. A contact procedure for molds and/or displacements caused by a plug was implemented to complete the similarity with the thermoforming process. The research focused on simulating the observed nonlinear behaviors and their instabilities. The author emphasized the impact of large deformation on the numerical results and demonstrated the need for a remeshing capability. At the Ecole des Mines d'Albi, under the supervision of Prof. Fabrice Schmidt, an equi-biaxial rheometer was developed and built in order to determine the material properties during the process of thermoforming. Thermoplastic materials consist of long macromolecular chains that when stretched, during the process of sheet extrusion, exhibit a transversal isotropic behavior. The rheometer technique is the inflation of a circular membrane made of extruded thermoplastics. The resulting strain is identified by video analysis during the membrane inflation. This dissertation focused on technical issues related to heating with the goal of overcoming the difficulty of producing a homogeneous temperature distribution.
Finite element analysis of posterior cervical fixation.
Duan, Y; Wang, H H; Jin, A M; Zhang, L; Min, S X; Liu, C L; Qiu, S J; Shu, X Q
2015-02-01
Despite largely, used in the past, biomechanical test, to investigate the fixation techniques of subaxial cervical spine, information is lacking about the internal structural response to external loading. It is not yet clear which technique represents the best choice and whether stabilization devices can be efficient and beneficial for three-column injuries (TCI). The different posterior cervical fixation techniques (pedicle screw PS, lateral mass screw LS, and transarticular screw TS) have respective indications. A detailed, geometrically accurate, nonlinear C3-C7 finite element model (FEM) had been successfully developed and validated. Then three FEMs were reconstructed from different fixation techniques after C4-C6 TCI. A compressive preload of 74N combined with a pure moment of 1.8 Nm in flexion, extension, left-right lateral bending, and left-right axial rotation was applied to the FEMs. The ROM results showed that there were obvious significant differences when comparing the different fixation techniques. PS and TS techniques can provide better immediate stabilization, compared to LS technique. The stress results showed that the variability of von Mises stress in the TS fixation device was minimum and LS fixation device was maximum. Furthermore, the screws inserted by TS technique had high stress concentration at the middle part of the screws. Screw inserted by PS and LS techniques had higher stress concentration at the actual cap-rod-screw interface. The research considers that spinal surgeon should first consider using the TS technique to treat cervical TCI. If PS technique is used, we should eventually prolong the need for external bracing in order to reduce the higher risk of fracture on fixation devices. If LS technique is used, we should add anterior cervical operation for acquire a better immediate stabilization. Copyright © 2014 Elsevier Masson SAS. All rights reserved.
Directory of Open Access Journals (Sweden)
Yong Zhao
1996-01-01
Full Text Available The large strain ratcheting in cyclic plasticity of a typical pressurized pipe elbow in a realistic nuclear piping system was investigated in a more quantitative manner than previously. The elbow was modeled using a fine mesh of shell elements that can provide the completed information of detailed time varying strain distributions in the whole elbow area. The nonlinear time history stress analyses performed were based on a pseudostatic concept using the vector-valued stochastic displacement response time series loaded at the elbow ends. The response time series were synthesized using a simulation approach based on the random vibration analyses of the piping system and its supporting building. After a finite element mesh convergence study, parametric analyses were conducted that included the effects due to the magnitude changes in excitation level, internal pressure, material yield stress, and material strain hardening.
Thermal Analysis of Thin Plates Using the Finite Element Method
Er, G. K.; Iu, V. P.; Liu, X. L.
2010-05-01
The isotropic thermal plate is analyzed with finite element method. The solution procedure is presented. The elementary stiffness matrix and loading vector are derived rigorously with variation principle and the principle of minimum potential energy. Numerical results are obtained based on the derived equations and tested with available exact solutions. The problems in the finite element analysis are figured out. It is found that the finite element solutions can not converge as the number of elements increases around the corners of the plate. The derived equations presented in this paper are fundamental for our further study on more complicated thermal plate analysis.
Finite Element Analysis of Fluid-Conveying Timoshenko Pipes
Directory of Open Access Journals (Sweden)
Chih-Liang Chu
1995-01-01
Full Text Available A general finite element formulation using cubic Hermitian interpolation for dynamic analysis of pipes conveying fluid is presented. Both the effects of shearing deformations and rotary inertia are considered. The development retains the use of the classical four degrees-of-freedom for a two-node element. The effect of moving fluid is treated as external distributed forces on the support pipe and the fluid finite element matrices are derived from the virtual work done due to the fluid inertia forces. Finite element matrices for both the support pipe and moving fluid are derived and given explicitly. A numerical example is given to demonstrate the validity of the model.
Davis, Matthew L; Moreno, Daniel P; Vavalle, Nicholas A; Gayzik, F Scott
2013-01-01
Motor vehicle crashes commonly result in blunt abdominal trauma. Approximately 19,000 such injuries occur each year in the United States. While finite element models of the human body are becoming an important tool for injury assessment, their reliability depends on the accuracy of the material models used. Recently, Samur et al. proposed a hyperelastic and viscoelastic material model of the liver. The aim of this study was to compare the results of a computational model using this material law to uniaxial tension and compression data from biomechanical tests on liver samples by Kemper et al. In this study, the liver samples were modeled using the finite element method. Both the tension and compression test specimen geometries were created from descriptions in the literature. Each sample was meshed using four approaches: fine hexahedral, coarse hexahedral, fine tetrahedral, and coarse tetrahedral. The average element edge lengths of the coarse and fine meshes were 5 mm and 2.5 mm respectively. The samples were loaded in both tension and compression at four rates: 0.01 strain/sec, 0.1 strain/sec, 1 strain/sec, and 10 strain/sec. For each mesh type (n=4), strain rate (n=4), and loading condition (n=2), 32 simulations in total, the results were plotted against the published experimental data. The results were quantitatively evaluated for magnitude and phase agreement with the experimental data using an objective comparison software package, CORA. The model predicted the tensile response of the liver sample more accurately than the compressive response with an average CORA size error factor of 0.66 versus 0.19 for the compressive model (1 is a perfect match). The fine tetrahedral, fine hexahedral, and coarse hexahedral meshes predicted a similar response. The worst performing mesh was the coarse tetrahedral mesh, which had an average size error factor of 8.6% higher than the fine tetrahedral simulations. The peak stress in both tension and compression varied as a
Institute of Scientific and Technical Information of China (English)
LV Wei-Guo; CHU Zhao-Tan; ZHAO Xiao-Qing; FAN Yu-Xiu; SONG Ruo-Long; HAN Wei
2009-01-01
The vector finite element method of tetrahedral elements is used to model 3D electromagnetic wave logging response. The tangential component of the vector field at the mesh edges is used as a degree of freedom to overcome the shortcomings of node-based finite element methods. The algorithm can simulate inhomogeneous media with arbitrary distribution of conductivity and magnetic permeability. The electromagnetic response of well logging tools are studied in dipping bed layers with the borehole and invasion included. In order to simulate realistic logging tools, we take the transmitter antennas consisting of circular wire loops instead of magnetic dipoles. We also investigate the apparent resistivity of inhomogeneous formation for different dip angles.
Robbins, Joshua; Voth, Thomas E.
2007-12-01
The eXtended Finite Element Method (X-FEM) is a finite-element based discretization technique developed originally to model dynamic crack propagation [1]. Since that time the method has been used for modeling physics ranging from static meso-scale material failure to dendrite growth. Here we adapt the recent advances of Vitali and Benson [2] and Song et al. [3] to model dynamic loading of a polycrystalline material. We use demonstration problems to examine the method's efficacy for modeling the dynamic response of polycrystalline materials at the meso-scale. Specifically, we use the X-FEM to model grain boundaries. This approach allows us to i) eliminate ad-hoc mixture rules for multi-material elements and ii) avoid explicitly meshing grain boundaries.
Unconditionally stable concurrent procedures for transient finite-element analysis
Ortiz, Michael; Nour-Omid, Bahram
1989-01-01
A family of algorithms was outlined which would appear to be particularly well-suited for implementation in a parallel environment. This is due to the fact that for any partition of the mesh each subdomain in the partition can be processed over a time step simultaneously and independently of the rest. The method eliminates the need for assembling and factorizing large global arrays while retaining the unconditional stability properties of the algorithms used at the local level. To critically appraise the proposed methodology, two limiting cases were considered: element-by-element mesh partitions, and coarse mesh partitions. It was concluded that while the proposed methodology can be useful in sequential machines, it would appear to be promising as it bears on computation. It should also be emphasized that extensions of the method to nonlinear problems are possible.
An Improved Moving Mesh Algorithm
Institute of Scientific and Technical Information of China (English)
无
2001-01-01
we consider an iterative algorithm of mesh optimization for finite element solution, and give an improved moving mesh strategy that reduces rapidly the complexity and cost of solving variational problems.A numerical result is presented for a 2-dimensional problem by the improved algorithm.
A finite-element toolbox for the stationary Gross-Pitaevskii equation with rotation
Vergez, Guillaume; Danaila, Ionut; Auliac, Sylvain; Hecht, Frédéric
2016-12-01
We present a new numerical system using classical finite elements with mesh adaptivity for computing stationary solutions of the Gross-Pitaevskii equation. The programs are written as a toolbox for FreeFem++ (www.freefem.org), a free finite-element software available for all existing operating systems. This offers the advantage to hide all technical issues related to the implementation of the finite element method, allowing to easily code various numerical algorithms. Two robust and optimized numerical methods were implemented to minimize the Gross-Pitaevskii energy: a steepest descent method based on Sobolev gradients and a minimization algorithm based on the state-of-the-art optimization library Ipopt. For both methods, mesh adaptivity strategies are used to reduce the computational time and increase the local spatial accuracy when vortices are present. Different run cases are made available for 2D and 3D configurations of Bose-Einstein condensates in rotation. An optional graphical user interface is also provided, allowing to easily run predefined cases or with user-defined parameter files. We also provide several post-processing tools (like the identification of quantized vortices) that could help in extracting physical features from the simulations. The toolbox is extremely versatile and can be easily adapted to deal with different physical models.
Finite element method for thermal analysis of concentrating solar receivers
Shtrakov, Stanko; Stoilov, Anton
2006-01-01
Application of finite element method and heat conductivity transfer model for calculation of temperature distribution in receiver for dish-Stirling concentrating solar system is described. The method yields discretized equations that are entirely local to the elements and provides complete geometric flexibility. A computer program solving the finite element method problem is created and great number of numerical experiments is carried out. Illustrative numerical results are given for an array...
Multiphase control volume finite element simulations of fractured reservoirs
Fu, Yao
With rapid evolution of hardware and software techniques in energy sector, reservoir simulation has become a powerful tool for field development planning and reservoir management. Many of the widely used commercial simulators were originally designed for structured grids and implemented with finite difference method (FDM). In recent years, technical advances in griding, fluid modeling, linear solver, reservoir and geological modeling, etc. have created new opportunities. At the same time, new reservoir simulation technology is required for solving large-scale heterogeneous problems. A three-dimensional, three-phase black-oil reservoir simulator has been developed using the control volume finite element (CVFE) formulation. Flux-based upstream weighting is employed to ensure flux continuity. The CVFE method is embedded in a fully-implicit formulation. State-of-the-art parallel, linear solvers are used. The implementation takes the advantages of object-oriented programming capabilities of C++ to provide maximum reuse and extensibility for future students. The results from the simulator have excellent agreement with those from commercial simulators. The convergence properties of the new simulator are verified using the method of manufactured solutions. The pressure and saturation solutions are verified to be first-order convergent as expected. The efficiency of the simulators and their capability to handle real large-scale field models are improved by implementing the models in parallel. Another aspect of the work dealt with multiphase flow of fractured reservoirs was performed. The discrete-fracture model is implemented in the simulator. Fractures and faults are represented by lines and planes in two- and three-dimensional spaces, respectively. The difficult task of generating an unstructured mesh for complex domains with fractures and faults is accomplished in this study. Applications of this model for two-phase and three-phase simulations in a variety of fractured
Fakhari, Abbas; Lee, Taehun
2014-03-01
An adaptive-mesh-refinement (AMR) algorithm for the finite-difference lattice Boltzmann method (FDLBM) is presented in this study. The idea behind the proposed AMR is to remove the need for a tree-type data structure. Instead, pointer attributes are used to determine the neighbors of a certain block via appropriate adjustment of its children identifications. As a result, the memory and time required for tree traversal are completely eliminated, leaving us with an efficient algorithm that is easier to implement and use on parallel machines. To allow different mesh sizes at separate parts of the computational domain, the Eulerian formulation of the streaming process is invoked. As a result, there is no need for rescaling the distribution functions or using a temporal interpolation at the fine-coarse grid boundaries. The accuracy and efficiency of the proposed FDLBM AMR are extensively assessed by investigating a variety of vorticity-dominated flow fields, including Taylor-Green vortex flow, lid-driven cavity flow, thin shear layer flow, and the flow past a square cylinder.
ADER-WENO Finite Volume Schemes with Space-Time Adaptive Mesh Refinement
Dumbser, Michael; Hidalgo, Arturo; Balsara, Dinshaw S
2012-01-01
We present the first high order one-step ADER-WENO finite volume scheme with Adaptive Mesh Refinement (AMR) in multiple space dimensions. High order spatial accuracy is obtained through a WENO reconstruction, while a high order one-step time discretization is achieved using a local space-time discontinuous Galerkin predictor method. Due to the one-step nature of the underlying scheme, the resulting algorithm is particularly well suited for an AMR strategy on space-time adaptive meshes, i.e.with time-accurate local time stepping. The AMR property has been implemented 'cell-by-cell', with a standard tree-type algorithm, while the scheme has been parallelized via the Message Passing Interface (MPI) paradigm. The new scheme has been tested over a wide range of examples for nonlinear systems of hyperbolic conservation laws, including the classical Euler equations of compressible gas dynamics and the equations of magnetohydrodynamics (MHD). High order in space and time have been confirmed via a numerical convergenc...
Finite element modeling of mass transport in high-Péclet cardiovascular flows
Hansen, Kirk; Arzani, Amirhossein; Shadden, Shawn
2016-11-01
Mass transport plays an important role in many important cardiovascular processes, including thrombus formation and atherosclerosis. These mass transport problems are characterized by Péclet numbers of up to 108, leading to several numerical difficulties. The presence of thin near-wall concentration boundary layers requires very fine mesh resolution in these regions, while large concentration gradients within the flow cause numerical stabilization issues. In this work, we will discuss some guidelines for solving mass transport problems in cardiovascular flows using a stabilized Galerkin finite element method. First, we perform mesh convergence studies in a series of idealized and patient-specific geometries to determine the required near-wall mesh resolution for these types of problems, using both first- and second-order tetrahedral finite elements. Second, we investigate the use of several boundary condition types at outflow boundaries where backflow during some parts of the cardiac cycle can lead to convergence issues. Finally, we evaluate the effect of reducing Péclet number by increasing mass diffusivity as has been proposed by some researchers. This work was supported by the NSF GRFP and NSF Career Award #1354541.
Multiphase flow through porous media: an adaptive control volume finite element formulation
Mostaghimi, P.; Tollit, B.; Gorman, G.; Neethling, S.; Pain, C.
2012-12-01
Accurate modeling of multiphase flow in porous media is of great importance in a wide range of applications in science and engineering. We have developed a numerical scheme which employs an implicit pressure explicit saturation (IMPES) algorithm for the temporal discretization of the governing equations. The saturation equation is spatially discretized using a node centered control volume method on an unstructured finite element mesh. The face values are determined through an upwind scheme. The pressure equation is spatially discretized using a continuous control volume finite element method (CV-FEM) to achieve consistency with the discrete saturation equation. The numerical simulation is implemented in Fluidity, an open source and general purpose fluid simulator capable of solving a number of different governing equations for fluid flow and accompanying field equations on arbitrary unstructured meshes. The model is verified against the Buckley-Leverett problem where a quasi-analytical solution is available. We discuss the accuracy and the order of convergence of the scheme. We demonstrate the scheme for modeling multiphase flow in a synthetic heterogeneous porous medium along with the use of anisotropic mesh adaptivity to control local solution errors and increase computational efficiency. The adaptive method is also used to simulate two-phase flow in heap leaching, an industrial mining process, where the flow of the leaching solution is gravitationally dominated. Finally we describe the extension of the developed numerical scheme for simulation of flow in multiscale fractured porous media and its capability to model the multiscale characterization of flow in full scale.
Pieczynska-Kozlowska, Joanna
2014-05-01
One of a geotechnical problem in the area of Wroclaw is an anthropogenic embankment layer delaying to the depth of 4-5m, arising as a result of historical incidents. In such a case an assumption of bearing capacity of strip footing might be difficult. The standard solution is to use a deep foundation or foundation soil replacement. However both methods generate significant costs. In the present paper the authors focused their attention on the influence of anthropogenic embankment variability on bearing capacity. Soil parameters were defined on the basis of CPT test and modeled as 2D anisotropic random fields and the assumption of bearing capacity were made according deterministic finite element methods. Many repeated of the different realizations of random fields lead to stable expected value of bearing capacity. The algorithm used to estimate the bearing capacity of strip footing was the random finite element method (e.g. [1]). In traditional approach of bearing capacity the formula proposed by [2] is taken into account. qf = c'Nc + qNq + 0.5γBN- γ (1) where: qf is the ultimate bearing stress, cis the cohesion, qis the overburden load due to foundation embedment, γ is the soil unit weight, Bis the footing width, and Nc, Nq and Nγ are the bearing capacity factors. The method of evaluation the bearing capacity of strip footing based on finite element method incorporate five parameters: Young's modulus (E), Poisson's ratio (ν), dilation angle (ψ), cohesion (c), and friction angle (φ). In the present study E, ν and ψ are held constant while c and φ are randomized. Although the Young's modulus does not affect the bearing capacity it governs the initial elastic response of the soil. Plastic stress redistribution is accomplished using a viscoplastic algorithm merge with an elastic perfectly plastic (Mohr - Coulomb) failure criterion. In this paper a typical finite element mesh was assumed with 8-node elements consist in 50 columns and 20 rows. Footings width B
ImageParser: a tool for finite element generation from three-dimensional medical images
Directory of Open Access Journals (Sweden)
Yamada T
2004-10-01
Full Text Available Abstract Background The finite element method (FEM is a powerful mathematical tool to simulate and visualize the mechanical deformation of tissues and organs during medical examinations or interventions. It is yet a challenge to build up an FEM mesh directly from a volumetric image partially because the regions (or structures of interest (ROIs may be irregular and fuzzy. Methods A software package, ImageParser, is developed to generate an FEM mesh from 3-D tomographic medical images. This software uses a semi-automatic method to detect ROIs from the context of image including neighboring tissues and organs, completes segmentation of different tissues, and meshes the organ into elements. Results The ImageParser is shown to build up an FEM model for simulating the mechanical responses of the breast based on 3-D CT images. The breast is compressed by two plate paddles under an overall displacement as large as 20% of the initial distance between the paddles. The strain and tangential Young's modulus distributions are specified for the biomechanical analysis of breast tissues. Conclusion The ImageParser can successfully exact the geometry of ROIs from a complex medical image and generate the FEM mesh with customer-defined segmentation information.
Robbins, Joshua; Voth, Thomas
2007-06-01
The eXtended Finite Element Method (X-FEM) is a finite element based discretization technique developed originally to model dynamic crack propagation [1]. Since that time the method has been used for modeling physics ranging from static mesoscale material failure to dendrite growth. Here we adapt the recent advances of Benson et al. [2] and Belytchko et al. [3] to model shock loading of polycrystalline material. Through several demonstration problems we evaluate the method for modeling the shock response of polycrystalline materials at the mesoscale. Specifically, we use the X-FEM to model grain boundaries. This approach allows us to i) eliminate ad-hoc mixture rules for multi-material elements and ii) avoid explicitly meshing grain boundaries. ([1] N. Moes, J. Dolbow, J and T. Belytschko, 1999,``A finite element method for crack growth without remeshing,'' International Journal for Numerical Methods in Engineering, 46, 131-150. [2] E. Vitali, and D. J. Benson, 2006, ``An extended finite element formulation for contact in multi-material arbitrary Lagrangian-Eulerian calculations,'' International Journal for Numerical Methods in Engineering, 67, 1420-1444. [3] J-H Song, P. M. A. Areias and T. Belytschko, 2006, ``A method for dynamic crack and shear band propagation with phantom nodes,'' International Journal for Numerical Methods in Engineering, 67, 868-893.)
Finite Element Simulation of Blanking Process
Directory of Open Access Journals (Sweden)
Afzal Ahmed
2012-10-01
daya penembusan sebanyak 42%. Daya tebukan yang diukur melalui eksperimen dan simulasi kekal pada kira-kira 90kN melepasi penembusan punch sebanyak 62%. Apabila ketebalan keputusan kunci ditambah, ketinggian retak dikurangkan dan ini meningkatkan kualiti pengosongan.KEYWORDS: simulation; finite element simulation; blanking; computer aided manufacturing
Zhang, Hong
2016-01-01
An adaptive moving mesh finite difference method is presented to solve two types of equations with dynamic capillary pressure term in porous media. One is the non-equilibrium Richards Equation and the other is the modified Buckley-Leverett equation. The governing equations are discretized with an adaptive moving mesh finite difference method in the space direction and an implicit-explicit method in the time direction. In order to obtain high quality meshes, an adaptive time-dependent monitor function with directional control is applied to redistribute the mesh grid in every time step, and a diffusive mechanism is used to smooth the monitor function. The behaviors of the central difference flux, the standard local Lax-Friedrich flux and the local Lax-Friedrich flux with reconstruction are investigated by solving a 1D modified Buckley-Leverett equation. With the moving mesh technique, good mesh quality and high numerical accuracy are obtained. A collection of one-dimensional and two-dimensional numerical experi...
Effective Stiffness: Generalizing Effective Resistance Sampling to Finite Element Matrices
Avron, Haim
2011-01-01
We define the notion of effective stiffness and show that it can used to build sparsifiers, algorithms that sparsify linear systems arising from finite-element discretizations of PDEs. In particular, we show that sampling $O(n\\log n)$ elements according to probabilities derived from effective stiffnesses yields an high quality preconditioner that can be used to solve the linear system in a small number of iterations. Effective stiffness generalizes the notion of effective resistance, a key ingredient of recent progress in developing nearly linear symmetric diagonally dominant (SDD) linear solvers. Solving finite elements problems is of considerably more interest than the solution of SDD linear systems, since the finite element method is frequently used to numerically solve PDEs arising in scientific and engineering applications. Unlike SDD systems, which are relatively easy to precondition, there has been limited success in designing fast solvers for finite element systems, and previous algorithms usually tar...
Energy Technology Data Exchange (ETDEWEB)
Kleinstreuer, C.; Patterson, M.R.
1980-05-01
A two- or three-dimensional finite difference mesh generator capable of discretizing subrectangular flow regions (planar coordinates) with arbitrarily shaped bottom contours (vertical dimension) was developed. This economical, interactive computer code, written in FORTRAN IV and employing DISSPLA software together with graphics terminal, generates first a planar rectangular grid of variable element density according to the geometry and local kinematic flow patterns of a given fluid flow problem. Then subrectangular areas are deleted to produce canals, tributaries, bays, and the like. For three-dimensional problems, arbitrary bathymetric profiles (river beds, channel cross section, ocean shoreline profiles, etc.) are approximated with grid lines forming steps of variable spacing. Furthermore, the code works as a preprocessor numbering the discrete elements and the nodal points. Prescribed values for the principal variables can be automatically assigned to solid as well as kinematic boundaries. Cabinet drawings aid in visualizing the complete flow domain. Input data requirements are necessary only to specify the spacing between grid lines, determine land regions that have to be excluded, and to identify boundary nodes. 15 figures, 2 tables.
Lu, Chang; Han, Ke; Li, Jing; Wang, Bing; Lu, Guo-hua
2008-05-01
To establish a 3-dimensional finite element model. The coordinate data of the vertebras were obtained from the CT scan images of Chinese 50th percentile healthy male adult volunteers' cervical spine, converted into point cloud data, and stored as ASCII file using Mimics software. CATIA software was used to preprocess and Geomagic software was used to establish the geometry model of the C0 approximately C7 cervical spine. The geometry model was meshed by Hypermesh software. Mapped mesh method was used to mesh cortical bone, trabecular bone, intervertebral disk, ligaments, etc. Some material parameters were defined from other available material parameters using proportion and function scale method. The model had 22 512 solid elements and 14 180 shell/membrane elements. The model was validated by the cervical spine drop test. The model has good biofidelity and can be used to study the dynamic response and injury mechanism of the cervical spine in the car accidents.
A mixed finite element for the analysis of laminated plates
Putcha, N. S.; Reddy, J. N.
1983-01-01
A new mixed shear-flexible finite element based on the Hellinger-Reissner's variational principle is developed. The element is constructed using a mixed formulation of the shear deformation theory of laminated composite plates, and consists of three displacements, two shear rotations, and three moments as the independent degrees of freedom. The numerical convergence and accuracy characteristics of the element are investigated for bending of laminated anisotropic composite plates. The element is relatively simple to construct and has better accuracy and convergence features when compared to other conventional finite elements.
Chabanas, Matthieu; Luboz, Vincent; Payan, Yohan
2003-06-01
This paper addresses the prediction of face soft tissue deformations resulting from bone repositioning in maxillofacial surgery. A generic 3D Finite Element model of the face soft tissues was developed. Face muscles are defined in the mesh as embedded structures, with different mechanical properties (transverse isotropy, stiffness depending on muscle contraction). Simulations of face deformations under muscle actions can thus be performed. In the context of maxillofacial surgery, this generic soft-tissue model is automatically conformed to patient morphology by elastic registration, using skin and skull surfaces segmented from a CT scan. Some elements of the patient mesh could be geometrically distorted during the registration, which disables Finite Element analysis. Irregular elements are thus detected and automatically regularized. This semi-automatic patient model generation is robust, fast and easy to use. Therefore it seems compatible with clinical use. Six patient models were successfully built, and simulations of soft tissue deformations resulting from bone displacements performed on two patient models. Both the adequation of the models to the patient morphologies and the simulations of post-operative aspects were qualitatively validated by five surgeons. Their conclusions are that the models fit the morphologies of the patients, and that the predicted soft tissue modifications are coherent with what they would expect.
Institute of Scientific and Technical Information of China (English)
无
2006-01-01
In this paper, we study the semi-discrete mortar upwind finite volume element method with the Crouzeix-Raviart element for the parabolic convection diffusion problems.It is proved that the semi-discrete mortar upwind finite volume element approximations derived are convergent in the H1- and L2-norms.
Development of an hp-version finite element method for computational optimal control
Hodges, Dewey H.; Warner, Michael S.
1993-01-01
The purpose of this research effort was to begin the study of the application of hp-version finite elements to the numerical solution of optimal control problems. Under NAG-939, the hybrid MACSYMA/FORTRAN code GENCODE was developed which utilized h-version finite elements to successfully approximate solutions to a wide class of optimal control problems. In that code the means for improvement of the solution was the refinement of the time-discretization mesh. With the extension to hp-version finite elements, the degrees of freedom include both nodal values and extra interior values associated with the unknown states, co-states, and controls, the number of which depends on the order of the shape functions in each element. One possible drawback is the increased computational effort within each element required in implementing hp-version finite elements. We are trying to determine whether this computational effort is sufficiently offset by the reduction in the number of time elements used and improved Newton-Raphson convergence so as to be useful in solving optimal control problems in real time. Because certain of the element interior unknowns can be eliminated at the element level by solving a small set of nonlinear algebraic equations in which the nodal values are taken as given, the scheme may turn out to be especially powerful in a parallel computing environment. A different processor could be assigned to each element. The number of processors, strictly speaking, is not required to be any larger than the number of sub-regions which are free of discontinuities of any kind.
On the Development of the SIMon Finite Element Head Model.
Takhounts, Erik G; Eppinger, Rolf H; Campbell, J Quinn; Tannous, Rabih E; Power, Erik D; Shook, Lauren S
2003-10-01
The SIMon (Simulated Injury Monitor) software package is being developed to advance the interpretation of injury mechanisms based on kinematic and kinetic data measured in the advanced anthropomorphic test dummy (AATD) and applying the measured dummy response to the human mathematical models imbedded in SIMon. The human finite element head model (FEHM) within the SIMon environment is presented in this paper. Three-dimensional head kinematic data in the form of either a nine accelerometer array or three linear CG head accelerations combined with three angular velocities serves as an input to the model. Three injury metrics are calculated: Cumulative strain damage measure (CSDM) - a correlate for diffuse axonal injury (DAI); Dilatational damage measure (DDM) - to estimate the potential for contusions; and Relative motion damage measure (RMDM) - a correlate for acute subdural hematoma (ASDH). During the development, the SIMon FEHM was tuned using cadaveric neutral density targets (NDT) data and further validated against the other available cadaveric NDT data and animal brain injury experiments. The hourglass control methods, integration schemes, mesh density, and contact stiffness penalty coefficient were parametrically altered to investigate their effect on the model's response. A set of numerical and physical parameters was established that allowed a satisfactory prediction of the motion of the brain with respect to the skull, when compared with the NDT data, and a proper separation of injury/no injury cases, when compared with the brain injury data. Critical limits for each brain injury metric were also established. Finally, the SIMon FEHM performance was compared against HIC15 through the use of NHTSA frontal and side impact crash test data. It was found that the injury metrics in the current SIMon model predicted injury in all cases where HIC15 was greater than 700 and several cases from the side impact test data where HIC15 was relatively small. Side impact was
Institute of Scientific and Technical Information of China (English)
Chang-feng Ma
2004-01-01
This paper provides an convergence analysis of a fractional-step projection method for the controlled-source electromagnetic induction problems in heterogenous electrically conducting media by means of finite element approximations. Error estimates in finite time are given. And it is verified that provided the time step τ is sufficiently small, the proposed algorithm yields for finite time T an error of (O)(hs + τ) in the L2-norm for the magnetic field H, where h is the mesh size and 1/2 ＜ s ≤ 1.
Non-regularised Inverse Finite Element Analysis for 3D Traction Force Microscopy
Munoz, Jose J
2016-01-01
The tractions that cells exert on a gel substrate from the observed displacements is an increasingly attractive and valuable information in biomedical experiments. The computation of these tractions requires in general the solution of an inverse problem. Here, we resort to the discretisation with finite elements of the associated direct variational formulation, and solve the inverse analysis using a least square approach. This strategy requires the minimisation of an error functional, which is usually regularised in order to obtain a stable system of equations with a unique solution. In this paper we show that for many common three-dimensional geometries, meshes and loading conditions, this regularisation is unnecessary. In these cases, the computational cost of the inverse problem becomes equivalent to a direct finite element problem. For the non-regularised functional, we deduce the necessary and sufficient conditions that the dimensions of the interpolated displacement and traction fields must preserve in ...
Energy Technology Data Exchange (ETDEWEB)
Bailey, T S; Chang, J H; Warsa, J S; Adams, M L
2010-12-22
We present a new spatial discretization of the discrete-ordinates transport equation in two-dimensional Cartesian (X-Y) geometry for arbitrary polygonal meshes. The discretization is a discontinuous finite element method (DFEM) that utilizes piecewise bi-linear (PWBL) basis functions, which are formally introduced in this paper. We also present a series of numerical results on quadrilateral and polygonal grids and compare these results to a variety of other spatial discretizations that have been shown to be successful on these grid types. Finally, we note that the properties of the PWBL basis functions are such that the leading-order piecewise bi-linear discontinuous finite element (PWBLD) solution will satisfy a reasonably accurate diffusion discretization in the thick diffusion limit, making the PWBLD method a viable candidate for many different classes of transport problems.
Superconvergence of mixed finite element approximations to 3-D Maxwell's equations in metamaterials
Huang, Yunqing
2011-09-01
Numerical simulation of metamaterials has attracted more and more attention since 2000, after the first metamaterial with negative refraction index was successfully constructed. In this paper we construct a fully-discrete leap-frog type finite element scheme to solve the three-dimensional time-dependent Maxwell\\'s equations when metamaterials are involved. First, we obtain some superclose results between the interpolations of the analytical solutions and finite element solutions obtained using arbitrary orders of Raviart-Thomas-Nédélec mixed spaces on regular cubic meshes. Then we prove the superconvergence result in the discrete l2 norm achieved for the lowest-order Raviart-Thomas-Nédélec space. To our best knowledge, such superconvergence results have never been obtained elsewhere. Finally, we implement the leap-frog scheme and present numerical results justifying our theoretical analysis. © 2011 Elsevier Inc.
Guo, Hongbo; He, Xiaowei; Liu, Muhan; Zhang, Zeyu; Hu, Zhenhua; Tian, Jie
2017-03-01
Cerenkov luminescence tomography (CLT), as a promising optical molecular imaging modality, can be applied to cancer diagnostic and therapeutic. Most researches about CLT reconstruction are based on the finite element method (FEM) framework. However, the quality of FEM mesh grid is still a vital factor to restrict the accuracy of the CLT reconstruction result. In this paper, we proposed a multi-grid finite element method framework, which was able to improve the accuracy of reconstruction. Meanwhile, the multilevel scheme adaptive algebraic reconstruction technique (MLS-AART) based on a modified iterative algorithm was applied to improve the reconstruction accuracy. In numerical simulation experiments, the feasibility of our proposed method were evaluated. Results showed that the multi-grid strategy could obtain 3D spatial information of Cerenkov source more accurately compared with the traditional single-grid FEM.
Leser, William P.; Yuan, Fuh-Gwo; Leser, William P.
2013-01-01
A method of numerically estimating dynamic Green's functions using the finite element method is proposed. These Green's functions are accurate in a limited frequency range dependent on the mesh size used to generate them. This range can often match or exceed the frequency sensitivity of the traditional acoustic emission sensors. An algorithm is also developed to characterize an acoustic emission source by obtaining information about its strength and temporal dependence. This information can then be used to reproduce the source in a finite element model for further analysis. Numerical examples are presented that demonstrate the ability of the band-limited Green's functions approach to determine the moment tensor coefficients of several reference signals to within seven percent, as well as accurately reproduce the source-time function.
Densification simulation of compacted Al powders using multi-particle finite element method
Institute of Scientific and Technical Information of China (English)
Kyung-Hun LEE; Jung-Min LEE; Byung-Min KIM
2009-01-01
The powder compaction simulations were performed to demonstrate deformation behavior of particles and estimate the effect of different punch speeds and particle diameters on the relative density of powder by a multi-particle finite element model(MPFEM). Individual particle discretized with a finite element mesh allows for a full description of the contact mechanics. In order to verify the reliability of compaction simulation by MPFEM, the compaction tests of porous aluminum with average particle size of 20 μm and 3 μm were performed at different ram speeds of 5, 15, 30 and 60 mm/min by MTS servo-hydraulic tester. The results show that the slow ram speed is of great advantage for powder densification in low compaction force due to sufficient particle rearrangement and compaction force increases with decrease in average particle size of aluminum.
Gradient plasticity crack tip characterization by means of the extended finite element method
Martínez-Pañeda, E.; Natarajan, S.; Bordas, S.
2017-01-01
Strain gradient plasticity theories are being widely used for fracture assessment, as they provide a richer description of crack tip fields by incorporating the influence of geometrically necessary dislocations. Characterizing the behavior at the small scales involved in crack tip deformation requires, however, the use of a very refined mesh within microns to the crack. In this work a novel and efficient gradient-enhanced numerical framework is developed by means of the extended finite element method (X-FEM). A mechanism-based gradient plasticity model is employed and the approximation of the displacement field is enriched with the stress singularity of the gradient-dominated solution. Results reveal that the proposed numerical methodology largely outperforms the standard finite element approach. The present work could have important implications on the use of microstructurally-motivated models in large scale applications. The non-linear X-FEM code developed in MATLAB can be downloaded from http://www.empaneda.com/codes.
Performance of synchrotron X-ray monochromators under heat load Part 1 finite element modeling
Zhang, L; Migliore, J S; Mocella, V; Ferrero, C; Freund, A K
2001-01-01
In this paper we present the details of the finite element modeling (FEM) procedure used to calculate the thermal deformation generated by the X-ray power absorbed in silicon crystals. Different parameters were varied systematically such as the beam footprint on the crystal, the reflection order and the white beam slit settings. Moreover, the influence of various cooling parameters such as the cooling coefficient and the temperature of the coolant were studied. The finite element meshing was carefully optimized to generate a deformation output that could be easily read by a diffraction simulation code. Comparison with the experiments shows that the peak-to-valley slope error calculated by the FEM is an excellent approximation of the rocking curve width for a liquid nitrogen cooled silicon (3 3 3) crystal, and a quite good approximation for significantly deformed silicon (1 1 1) crystals.
Partitions of nonzero elements of a finite field into pairs
Karasev, R N
2010-01-01
In this paper we prove two theorems. Informally, they claim that the nonzero elements of a finite field with odd characteristic can be partitioned into pairs with prescribed difference (maybe, with some alternatives) in each pair. We also consider some generalizations of these results to packing translates in a finite or infinite field.
A new weak Galerkin finite element method for elliptic interface problems
Mu, Lin; Wang, Junping; Ye, Xiu; Zhao, Shan
2016-11-01
A new weak Galerkin (WG) finite element method is introduced and analyzed in this paper for solving second order elliptic equations with discontinuous coefficients and interfaces. Comparing with the existing WG algorithm for solving the same type problems, the present WG method has a simpler variational formulation and fewer unknowns. Moreover, the new WG algorithm allows the use of finite element partitions consisting of general polytopal meshes and can be easily generalized to high orders. Optimal order error estimates in both H1 and L2 norms are established for the present WG finite element solutions. Extensive numerical experiments have been conducted to examine the accuracy, flexibility, and robustness of the proposed WG interface approach. In solving regular elliptic interface problems, high order convergences are numerically confirmed by using piecewise polynomial basis functions of high degrees. Moreover, the WG method is shown to be able to accommodate very complicated interfaces, due to its flexibility in choosing finite element partitions. Finally, in dealing with challenging problems with low regularities, the piecewise linear WG method is capable of delivering a second order of accuracy in L∞ norm for both C1 and H2 continuous solutions.
A Stable Parametric Finite Element Discretization of Two-Phase Navier--Stokes Flow
Barrett, John W; Nürnberg, Robert
2013-01-01
We present a parametric finite element approximation of two-phase flow. This free boundary problem is given by the Navier--Stokes equations in the two phases, which are coupled via jump conditions across the interface. Using a novel variational formulation for the interface evolution gives rise to a natural discretization of the mean curvature of the interface. The parametric finite element approximation of the evolving interface is then coupled to a standard finite element approximation of the two-phase Navier--Stokes equations in the bulk. Here enriching the pressure approximation space with the help of an XFEM function ensures good volume conservation properties for the two phase regions. In addition, the mesh quality of the parametric approximation of the interface in general does not deteriorate over time, and an equidistribution property can be shown for a semidiscrete continuous-in-time variant of our scheme in two space dimensions. Moreover, our finite element approximation can be shown to be uncondit...
Finite element modelling of internal and multiple localized cracks
Saloustros, Savvas; Pelà, Luca; Cervera, Miguel; Roca, Pere
2017-02-01
Tracking algorithms constitute an efficient numerical technique for modelling fracture in quasi-brittle materials. They succeed in representing localized cracks in the numerical model without mesh-induced directional bias. Currently available tracking algorithms have an important limitation: cracking originates either from the boundary of the discretized domain or from predefined "crack-root" elements and then propagates along one orientation. This paper aims to circumvent this drawback by proposing a novel tracking algorithm that can simulate cracking starting at any point of the mesh and propagating along one or two orientations. This enhancement allows the simulation of structural case-studies experiencing multiple cracking. The proposed approach is validated through the simulation of a benchmark example and an experimentally tested structural frame under in-plane loading. Mesh-bias independency of the numerical solution, computational cost and predicted collapse mechanisms with and without the tracking algorithm are discussed.
Finite element analysis of constrained total Condylar Knee Prosthesis
Energy Technology Data Exchange (ETDEWEB)
NONE
1998-07-13
selected for production. Because of unanticipated delays in the CRADA funding, the knee design had to be finalized before the analysis could be accomplished. Thus, the scope of work was modified by the industrial partner. It was decided that it would be most beneficial to perform FEA that would closely replicate the lab tests that had been done as the basis of the design. Exactech was responsible for transmitting the component geometries to Livermore, as well as providing complete data from the quasi-static laboratory loading tests that were performed on various designs. LLNL was responsible for defining the basic finite element mesh and carrying out the analysis. We performed the initial computer simulation and verified model integrity, using the laboratory data. After performing the parametric studies, the results were reviewed with Exactech. Also, the results were presented at the Orthopedic Research Society meeting in a poster session.