A Novel Polygonal Finite Element Method: Virtual Node Method

Science.gov (United States)

Tang, X. H.; Zheng, C.; Zhang, J. H.

2010-05-01

Polygonal finite element method (PFEM), which can construct shape functions on polygonal elements, provides greater flexibility in mesh generation. However, the non-polynomial form of traditional PFEM, such as Wachspress method and Mean Value method, leads to inexact numerical integration. Since the integration technique for non-polynomial functions is immature. To overcome this shortcoming, a great number of integration points have to be used to obtain sufficiently exact results, which increases computational cost. In this paper, a novel polygonal finite element method is proposed and called as virtual node method (VNM). The features of present method can be list as: (1) It is a PFEM with polynomial form. Thereby, Hammer integral and Gauss integral can be naturally used to obtain exact numerical integration; (2) Shape functions of VNM satisfy all the requirements of finite element method. To test the performance of VNM, intensive numerical tests are carried out. It found that, in standard patch test, VNM can achieve significantly better results than Wachspress method and Mean Value method. Moreover, it is observed that VNM can achieve better results than triangular 3-node elements in the accuracy test.

A Family of Multipoint Flux Mixed Finite Element Methods for Elliptic Problems on General Grids

KAUST Repository

Wheeler, Mary F.; Xue, Guangri; Yotov, Ivan

2011-01-01

In this paper, we discuss a family of multipoint flux mixed finite element (MFMFE) methods on simplicial, quadrilateral, hexahedral, and triangular-prismatic grids. The MFMFE methods are locally conservative with continuous normal fluxes, since

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

International Nuclear Information System (INIS)

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

1969-01-01

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

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

International Nuclear Information System (INIS)

Sabir, A.B.

1983-01-01

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

Two-dimensional calculation by finite element method of velocity field and temperature field development in fast reactor fuel assembly. II

International Nuclear Information System (INIS)

Schmid, J.

1985-11-01

A package of updated computer codes for velocity and temperature field calculations for a fast reactor fuel subassembly (or its part) by the finite element method is described. Isoparametric triangular elements of the second degree are used. (author)

SIMULATION OF THE BEHAVIOR OF THE WATER TABLE IN A COASTAL AQUIFER SYSTEM FINITE ELEMENT

Directory of Open Access Journals (Sweden)

Luis Lara Romero

2016-06-01

Full Text Available This paper presents the application of Galerkin method to discretize the model equation of groundwater ow in a conned aquifer semipermeable with tidal boundary conditions on one of its borders, the other borders remain constant. For the simulations was generated a numerical program, Ground Water Finite Element Method, which implements the method of nite elements with triangular elements with three nodes and a degree of freedom per node.

SPLAI: Computational Finite Element Model for Sensor Networks

Directory of Open Access Journals (Sweden)

Ruzana Ishak

2006-01-01

Full Text Available Wireless sensor network refers to a group of sensors, linked by a wireless medium to perform distributed sensing task. The primary interest is their capability in monitoring the physical environment through the deployment of numerous tiny, intelligent, wireless networked sensor nodes. Our interest consists of a sensor network, which includes a few specialized nodes called processing elements that can perform some limited computational capabilities. In this paper, we propose a model called SPLAI that allows the network to compute a finite element problem where the processing elements are modeled as the nodes in the linear triangular approximation problem. Our model also considers the case of some failures of the sensors. A simulation model to visualize this network has been developed using C++ on the Windows environment.

A flat triangular shell element with Loof nodes

DEFF Research Database (Denmark)

Poulsen, Peter Noe; Damkilde, Lars

1996-01-01

In the formulation of flat shell elements it is difficult to achieve inter-element compatibility between membrane and transverse displacements for non-coplanar elements. Many elements lack proper nodal degrees of freedom to model intersections making the assembly of elements troublesome. A flat...... triangular shell element is established by a combination of a new plate bending element DKTL and the well-known linear membrane strain element LST, and for this element the above-mentioned deficiences are avoided. The plate bending element DKTL is based on Discrete Kirchhoff Theory and Loof nodes. The nodal...

Adaptive Finite Volume Method for the Shallow Water Equations on Triangular Grids

Directory of Open Access Journals (Sweden)

Sudi Mungkasi

2016-01-01

Full Text Available This paper presents a numerical entropy production (NEP scheme for two-dimensional shallow water equations on unstructured triangular grids. We implement NEP as the error indicator for adaptive mesh refinement or coarsening in solving the shallow water equations using a finite volume method. Numerical simulations show that NEP is successful to be a refinement/coarsening indicator in the adaptive mesh finite volume method, as the method refines the mesh or grids around nonsmooth regions and coarsens them around smooth regions.

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

Energy Technology Data Exchange (ETDEWEB)

Steibler, P.

2000-07-01

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

High-Order Curvilinear Finite Element Methods for Lagrangian Hydrodynamics [High Order Curvilinear Finite Elements for Lagrangian Hydrodynamics

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

Finite element modeling of tornado missile impact on reinforced concrete wall panels

International Nuclear Information System (INIS)

Zhang, Y.; Vallabhan, C.V.G.; McDonald, J.R.

1993-01-01

This paper describes a finite element model for the impact of large tornado-generated missiles with reinforced concrete wall panels. The analysis predicts the dynamic response of a wall panel when impacted by a missile with a large contact area such as an automobile. Quadratic finite elements are used to discretize the domain of the wall panel. Fundamental assumptions are based on the Mindlin and the related Reinsser plate theories. An 'embedded' model is employed to account for the reinforcing bars. The nonlinear behavior of concrete and steel bars are analyzed by means of time-dependent constitutive relationships. A model is proposed to describe the initial and subsequent yield surfaces of concrete material, which avoids underestimation of the effect of high hydrostatic stresses on the yielding behavior of concrete. Ottosen's four-parameter failure criterion is used to define the failure surface of concrete. A crack monitoring algorithm accounts for post-cracking and post-crushing behavior of concrete. Explicit time step integration of nonlinear dynamic equations are carried out using the finite element discretization of a concrete wall panel. As a practical application of the analysis technique, the contact failure pressure for a particular panel geometry can be calculated. The contact failure pressure and the elapsed time to failure after missile contact define a rectangular or triangular impulse loading to produce failure of the panel. Since automobile crashes are known to produce triangular impulse loads, the two pulses (failure and impact) can be compared to determine if a particular impact will fail the panels. Thus, a particular concrete panel can be analyzed to determine if it will fail under a postulated missile impact

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

KAUST Repository

Saad, Bilal Mohammed; Saad, Mazen Naufal B M

2014-01-01

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

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

KAUST Repository

Saad, Bilal Mohammed

2014-06-28

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

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)

Effectiveness of Rotation-free Triangular and Quadrilateral Shell Elements in Sheet-metal Forming Simulations

International Nuclear Information System (INIS)

Brunet, M.; Sabourin, F.

2005-01-01

This paper is concerned with the effectiveness of triangular 3-node shell element without rotational d.o.f. and the extension to a new 4-node quadrilateral shell element called S4 with only 3 translational degrees of freedom per node and one-point integration. The curvatures are computed resorting to the surrounding elements. Extension from rotation-free triangular element to a quadrilateral element requires internal curvatures in order to avoid singular bending stiffness. Two numerical examples with regular and irregular meshes are performed to show the convergence and accuracy. Deep-drawing of a box, spring-back analysis of a U-shape strip sheet and the crash simulation of a beam-box complete the demonstration of the bending capabilities of the proposed rotation-free triangular and quadrilateral elements

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

OpenAIRE

Ochoa-Avendaño, J.; Garzon-Alvarado, D. A.; Linero, Dorian L.; Cerrolaza, M.

2017-01-01

This paper presents the formulation, implementation, and validation of a simplified qualitative model to determine the crack path of solids considering static loads, infinitesimal strain, and plane stress condition. This model is based on finite element method with a special meshing technique, where nonlinear link elements are included between the faces of the linear triangular elements. The stiffness loss of some link elements represents the crack opening. Three experimental tests of bending...

Solution of two-dimensional neutron diffusion equation for triangular region by finite Fourier transformation

International Nuclear Information System (INIS)

Kobayashi, Keisuke; Ishibashi, Hideo

1978-01-01

A two-dimensional neutron diffusion equation for a triangular region is shown to be solved by the finite Fourier transformation. An application of the Fourier transformation to the diffusion equation for triangular region yields equations whose unknowns are the expansion coefficients of the neutron flux and current in Fourier series or Legendre polynomials expansions only at the region boundary. Some numerical calculations have revealed that the present technique gives accurate results. It is shown also that the solution using the expansion in Legendre polynomials converges with relatively few terms even if the solution in Fourier series exhibits the Gibbs' phenomenon. (auth.)

Higher Order Lagrange Finite Elements In M3D

International Nuclear Information System (INIS)

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

2004-01-01

The M3D code has been using linear finite elements to represent multilevel MHD on 2-D poloidal planes. Triangular higher order elements, up to third order, are constructed here in order to provide M3D the capability to solve highly anisotropic transport problems. It is found that higher order elements are essential to resolve the thin transition layer characteristic of the anisotropic transport equation, particularly when the strong anisotropic direction is not aligned with one of the Cartesian coordinates. The transition layer is measured by the profile width, which is zero for infinite anisotropy. It is shown that only higher order schemes have the ability to make this layer converge towards zero when the anisotropy gets stronger and stronger. Two cases are considered. One has the strong transport direction partially aligned with one of the element edges, the other doesn't have any alignment. Both cases have the strong transport direction misaligned with the grid line by some angles

Comparative study on triangular and quadrilateral meshes by a finite-volume method with a central difference scheme

KAUST Repository

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.

Comparative study on triangular and quadrilateral meshes by a finite-volume method with a central difference scheme

KAUST Repository

Yu, Guojun; Yu, Bo; Sun, Shuyu; Tao, Wenquan

2012-01-01

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.

A fluid-solid finite element method for the analysis of reactor safety problems

International Nuclear Information System (INIS)

Mitra, Santanu; Kumar, Ashutosh; Sinhamahapatra, K.P.

2006-01-01

The work presented herein can broadly be categorized as a fluid-structure interaction problem. The response of a circular cylindrical structure subjected to cross flow is examined using the finite element method for both the liquid and the structure domains. The cylindrical tube is mounted elastically at the ends and is free to move under the action of the unsteady flow-induced forces. The fluid is considered to be acoustic compressible and viscous. A Galerkin finite element method implemented on a triangular mesh is used to solve the time-dependent Navier-Stokes equations. The cylinder motion is modeled using a five-degrees of freedom generalized shell element structural dynamics model. The numerical simulations of the response of the calandria tubes/pressure tubes, adjustor rod and shut-off rod of a nuclear reactor are presented. A few typical results are presented to assess the accuracy and applicability of the developed modules

A finite element method for solving the shallow water equations on the sphere

Science.gov (United States)

Comblen, Richard; Legrand, Sébastien; Deleersnijder, Eric; Legat, Vincent

Within the framework of ocean general circulation modeling, the present paper describes an efficient way to discretize partial differential equations on curved surfaces by means of the finite element method on triangular meshes. Our approach benefits from the inherent flexibility of the finite element method. The key idea consists in a dialog between a local coordinate system defined for each element in which integration takes place, and a nodal coordinate system in which all local contributions related to a vectorial degree of freedom are assembled. Since each element of the mesh and each degree of freedom are treated in the same way, the so-called pole singularity issue is fully circumvented. Applied to the shallow water equations expressed in primitive variables, this new approach has been validated against the standard test set defined by [Williamson, D.L., Drake, J.B., Hack, J.J., Jakob, R., Swarztrauber, P.N., 1992. A standard test set for numerical approximations to the shallow water equations in spherical geometry. Journal of Computational Physics 102, 211-224]. Optimal rates of convergence for the P1NC-P1 finite element pair are obtained, for both global and local quantities of interest. Finally, the approach can be extended to three-dimensional thin-layer flows in a straightforward manner.

A Family of Multipoint Flux Mixed Finite Element Methods for Elliptic Problems on General Grids

KAUST Repository

Wheeler, Mary F.

2011-01-01

In this paper, we discuss a family of multipoint flux mixed finite element (MFMFE) methods on simplicial, quadrilateral, hexahedral, and triangular-prismatic grids. The MFMFE methods are locally conservative with continuous normal fluxes, since they are developed within a variational framework as mixed finite element methods with special approximating spaces and quadrature rules. The latter allows for local flux elimination giving a cell-centered system for the scalar variable. We study two versions of the method: with a symmetric quadrature rule on smooth grids and a non-symmetric quadrature rule on rough grids. Theoretical and numerical results demonstrate first order convergence for problems with full-tensor coefficients. Second order superconvergence is observed on smooth grids. © 2011 Published by Elsevier Ltd.

Basic Finite Element Method

International Nuclear Information System (INIS)

Lee, Byeong Hae

1992-02-01

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

Solution of the multigroup diffusion equation for two-dimensional triangular regions by finite Fourier transformation

International Nuclear Information System (INIS)

Takeshi, Y.; Keisuke, K.

1983-01-01

The multigroup neutron diffusion equation for two-dimensional triangular geometry is solved by the finite Fourier transformation method. Using the zero-th-order equation of the integral equation derived by this method, simple algebraic expressions for the flux are derived and solved by the alternating direction implicit method. In sample calculations for a benchmark problem of a fast breeder reactor, it is shown that the present method gives good results with fewer mesh points than the usual finite difference method

Linear dynamic analysis of arbitrary thin shells modal superposition by using finite element method

International Nuclear Information System (INIS)

Goncalves Filho, O.J.A.

1978-11-01

The linear dynamic behaviour of arbitrary thin shells by the Finite Element Method is studied. Plane triangular elements with eighteen degrees of freedom each are used. The general equations of movement are obtained from the Hamilton Principle and solved by the Modal Superposition Method. The presence of a viscous type damping can be considered by means of percentages of the critical damping. An automatic computer program was developed to provide the vibratory properties and the dynamic response to several types of deterministic loadings, including temperature effects. The program was written in FORTRAN IV for the Burroughs B-6700 computer. (author)

Two-dimensional multigroup finite element calculation of fast reactor in diffusion approximation

International Nuclear Information System (INIS)

Schmid, J.

1986-06-01

When a linear element of triangular shape is used the actual finite element calculation is relatively simple. Extensive programs for mesh generation were written for easy inputting the configuration of reactors. A number of other programs were written for plotting neutron flux fields in individual groups, the power distribution, spatial plotting of fields, etc. The operation of selected programs, data preparation and operating instructions are described and examples given of data and results. All programs are written in GIER ALGOL. The used method and the developed programs have demonstrated that they are a useful instrument for the calculation of criticality and the distribution of neutron flux and power of both fast and thermal reactors. (J.B.)

Final Report of the Project "From the finite element method to the virtual element method"

Energy Technology Data Exchange (ETDEWEB)

Manzini, Gianmarco [Los Alamos National Lab. (LANL), Los Alamos, NM (United States); Gyrya, Vitaliy [Los Alamos National Lab. (LANL), Los Alamos, NM (United States)

2017-12-20

The Finite Element Method (FEM) is a powerful numerical tool that is being used in a large number of engineering applications. The FEM is constructed on triangular/tetrahedral and quadrilateral/hexahedral meshes. Extending the FEM to general polygonal/polyhedral meshes in straightforward way turns out to be extremely difficult and leads to very complex and computationally expensive schemes. The reason for this failure is that the construction of the basis functions on elements with a very general shape is a non-trivial and complex task. In this project we developed a new family of numerical methods, dubbed the Virtual Element Method (VEM) for the numerical approximation of partial differential equations (PDE) of elliptic type suitable to polygonal and polyhedral unstructured meshes. We successfully formulated, implemented and tested these methods and studied both theoretically and numerically their stability, robustness and accuracy for diffusion problems, convection-reaction-diffusion problems, the Stokes equations and the biharmonic equations.

High Order Finite Element Method for the Lambda modes problem on hexagonal geometry

International Nuclear Information System (INIS)

Gonzalez-Pintor, S.; Ginestar, D.; Verdu, G.

2009-01-01

A High Order Finite Element Method to approximate the Lambda modes problem for reactors with hexagonal geometry has been developed. This method is based on the expansion of the neutron flux in terms of the modified Dubiner's polynomials on a triangular mesh. This mesh is fixed and the accuracy of the method is improved increasing the degree of the polynomial expansions without the necessity of remeshing. The performance of method has been tested obtaining the dominant Lambda modes of different 2D reactor benchmark problems.

An assessment of finite element synthesis model using 3D FEM

International Nuclear Information System (INIS)

Jagannathan, V.; Rastogi, B.P

1983-01-01

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

Generalized finite elements

International Nuclear Information System (INIS)

Wachspress, E.

2009-01-01

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

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

International Nuclear Information System (INIS)

Fujimura, Toichiro

1996-01-01

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

FINELM: a multigroup finite element diffusion code. Part I

International Nuclear Information System (INIS)

Davierwalla, D.M.

1980-12-01

The author presents a two dimensional code for multigroup diffusion using the finite element method. It was realized that the extensive connectivity which contributes significantly to the accuracy, results in a matrix which, although symmetric and positive definite, is wide band and possesses an irregular profile. Hence, it was decided to introduce sparsity techniques into the code. The introduction of the R-Z geometry lead to a great deal of changes in the code since the rotational invariance of the removal matrices in X-Y geometry did not carry over in R-Z geometry. Rectangular elements were introduced to remedy the inability of the triangles to model essentially one dimensional problems such as slab geometry. The matter is discussed briefly in the text in the section on benchmark problems. This report is restricted to the general theory of the triangular elements and to the sparsity techniques viz. incomplete disections. The latter makes the size of the problem that can be handled independent of core memory and dependent only on disc storage capacity which is virtually unlimited. (Auth.)

Determination of the ultimate load in concrete slabs by the yield line finite element method

International Nuclear Information System (INIS)

Vaz, L.E.; Feijo, B.; Martha, L.F.R.; Lopes, M.M.

1984-01-01

A method for calculating the ultimate load in reinforced concrete slabs is proposed. The method follows the finite element aproach representating the continuum slab as an assembly of rigid triangular plates connected along their sides through yield line elements. This approach leads to the definition of the displacement configuration of the plate only as a function of the transversal displacement at the nodes of the mesh (1 DOF per node) reducing significantly the number of DOF's in relation to the conventional formulation by means of the finite element method (minimum of 3 DOF per node). Nonlinear behaviour of the reinforced concrete section is considered in the definition of the moment rotation curve of the yield lines. The effect of the in plane forces acting in the middle surface of the plate is also taken into account. The validity of the model is verified comparing the numerical solutions with the results of the classical yield line theory. (Author) [pt

Implicit three-dimensional finite-element formulation for the nonlinear structural response of reactor components

International Nuclear Information System (INIS)

Kulak, R.F.; Belytschko, T.B.

1975-09-01

The formulation of a finite-element procedure for the implicit transient and static analysis of plate/shell type structures in three-dimensional space is described. The triangular plate/shell element can sustain both membrane and bending stresses. Both geometric and material nonlinearities can be treated, and an elastic-plastic material law has been incorporated. The formulation permits the element to undergo arbitrarily large rotations and translations; but, in its present form it is restricted to small strains. The discretized equations of motion are obtained by a stiffness method. An implicit integration algorithm based on trapezoidal integration formulas is used to integrate the discretized equations of motion in time. To ensure numerical stability, an iterative solution procedure with equilibrium checks is used

Finite element analysis of inclined nozzle-plate junctions

International Nuclear Information System (INIS)

Dixit, K.B.; Seth, V.K.; Krishnan, A.; Ramamurthy, T.S.; Dattaguru, B.; Rao, A.K.

1979-01-01

Estimation of stress concentration at nozzle to plate or shell junctions is a significant problem in the stress analysis of nuclear reactors. The topic is a subject matter of extensive investigations and earlier considerable success has been reported on analysis for the cases when the nozzle is perpendicular to the plate or is radial to the shell. Analytical methods for the estimation of stress concentrations for the practical situations when the intersecting nozzle is inclined to the plate or is non-radial to the shell is rather scanty. Specific complications arise in dealing with the junction region when the nozzle with circular cross-section meets the non-circular cut-out on the plate or shell. In this paper a finite element analysis is developed for inclined nozzles and results are presented for nozzle-plate junctions. A method of analysis is developed with a view to achieving simultaneously accuracy of results and simplicity in the choice of elements and their connectivity. The circular nozzle is treated by axisymmetric conical shell elements. The nozzle portion in the region around the junction and the flat plate is dealt with by triangular flat shell elements. Special transition elements are developed for joining the flat shell elements with the axisymmetric elements under non-axisymmetric loading. A substructure method of analysis is adopted which achieves considerable economy in handling the structure and also conveniently combines the different types of elements in the structure. (orig.)

Solution of 2D and 3D hexagonal geometry benchmark problems by using the finite element diffusion code DIFGEN

International Nuclear Information System (INIS)

Gado, J.

1986-02-01

The four group, 2D and 3D hexagonal geometry HTGR benchmark problems and a 2D hexagonal geometry PWR (WWER) benchmark problem have been solved by using the finite element diffusion code DIFGEN. The hexagons (or hexagonal prisms) were subdivided into first order or second order triangles or quadrilaterals (or triangular or quadrilateral prisms). In the 2D HTGR case of the number of the inserted absorber rods was also varied (7, 6, 0 or 37 rods). The calculational results are in a good agreement with the results of other calculations. The larger systematic series of DIFGEN calculations have given a quantitative picture on the convergence properties of various finite element modellings of hexagonal grids in DIFGEN. (orig.)

Finite Element Method Analysis of An Out Flow With Free Surface In Transition Zones

Science.gov (United States)

Saoula, R. Iddir S.; Mokhtar, K. Ait

The object of this work is to present this part of the fluid mechanics that relates to out-flows of the fluid to big speeds in transitions. Results usually gotten by the classic processes can only have a qualitative aspect. The method fluently used for the count of these out-flows to big speeds is the one of characteristics, this approach remains interesting so much that doesn't appear within the out-flow of intersections of shock waves, as well as of reflections of these. In the simple geometry case, the method of finite differences satisfying result, But when the complexity of this geometry imposes itself, it is the method of finite elements that is proposed to solve this type of prob- lem, in particular for problems Trans critic. The goal of our work is to analyse free surface flows in channels no prismatic has oblong transverse section in zone of tran- sition. (Convergent, divergent). The basic mathematical model of this study is Saint Venant derivatives partial equations. To solve these equations we use the finite ele- ment method, the element of reference is the triangular element with 6 nodes which are quadratic in speed and linear in height (pressure). Our results and their obtains by others are very close to experimental results.

Massively Parallel Finite Element Programming

KAUST Repository

Heister, Timo; Kronbichler, Martin; Bangerth, Wolfgang

2010-01-01

Today's large finite element simulations require parallel algorithms to scale on clusters with thousands or tens of thousands of processor cores. We present data structures and algorithms to take advantage of the power of high performance computers in generic finite element codes. Existing generic finite element libraries often restrict the parallelization to parallel linear algebra routines. This is a limiting factor when solving on more than a few hundreds of cores. We describe routines for distributed storage of all major components coupled with efficient, scalable algorithms. We give an overview of our effort to enable the modern and generic finite element library deal.II to take advantage of the power of large clusters. In particular, we describe the construction of a distributed mesh and develop algorithms to fully parallelize the finite element calculation. Numerical results demonstrate good scalability. © 2010 Springer-Verlag.

Massively Parallel Finite Element Programming

KAUST Repository

Heister, Timo

2010-01-01

Today\\'s large finite element simulations require parallel algorithms to scale on clusters with thousands or tens of thousands of processor cores. We present data structures and algorithms to take advantage of the power of high performance computers in generic finite element codes. Existing generic finite element libraries often restrict the parallelization to parallel linear algebra routines. This is a limiting factor when solving on more than a few hundreds of cores. We describe routines for distributed storage of all major components coupled with efficient, scalable algorithms. We give an overview of our effort to enable the modern and generic finite element library deal.II to take advantage of the power of large clusters. In particular, we describe the construction of a distributed mesh and develop algorithms to fully parallelize the finite element calculation. Numerical results demonstrate good scalability. © 2010 Springer-Verlag.

Finite element computational fluid mechanics

International Nuclear Information System (INIS)

Baker, A.J.

1983-01-01

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

Block-triangular preconditioners for PDE-constrained optimization

KAUST Repository

Rees, Tyrone

2010-11-26

In this paper we investigate the possibility of using a block-triangular preconditioner for saddle point problems arising in PDE-constrained optimization. In particular, we focus on a conjugate gradient-type method introduced by Bramble and Pasciak that uses self-adjointness of the preconditioned system in a non-standard inner product. We show when the Chebyshev semi-iteration is used as a preconditioner for the relevant matrix blocks involving the finite element mass matrix that the main drawback of the Bramble-Pasciak method-the appropriate scaling of the preconditioners-is easily overcome. We present an eigenvalue analysis for the block-triangular preconditioners that gives convergence bounds in the non-standard inner product and illustrates their competitiveness on a number of computed examples. Copyright © 2010 John Wiley & Sons, Ltd.

Block-triangular preconditioners for PDE-constrained optimization

KAUST Repository

Rees, Tyrone; Stoll, Martin

2010-01-01

In this paper we investigate the possibility of using a block-triangular preconditioner for saddle point problems arising in PDE-constrained optimization. In particular, we focus on a conjugate gradient-type method introduced by Bramble and Pasciak that uses self-adjointness of the preconditioned system in a non-standard inner product. We show when the Chebyshev semi-iteration is used as a preconditioner for the relevant matrix blocks involving the finite element mass matrix that the main drawback of the Bramble-Pasciak method-the appropriate scaling of the preconditioners-is easily overcome. We present an eigenvalue analysis for the block-triangular preconditioners that gives convergence bounds in the non-standard inner product and illustrates their competitiveness on a number of computed examples. Copyright © 2010 John Wiley & Sons, Ltd.

Hierarchical Material Properties in Finite Element Analysis: The Oilfield Infrastructure Problem.

Science.gov (United States)

Weiss, C. J.; Wilson, G. A.

2017-12-01

Geophysical simulation of low-frequency electromagnetic signals within built environments such as urban centers and industrial landscapes facilities is a challenging computational problem because strong conductors (e.g., pipes, fences, rail lines, rebar, etc.) are not only highly conductive and/or magnetic relative to the surrounding geology, but they are very small in one or more of their physical length coordinates. Realistic modeling of such structures as idealized conductors has long been the standard approach; however this strategy carries with it computational burdens such as cumbersome implementation of internal boundary conditions, and limited flexibility for accommodating realistic geometries. Another standard approach is "brute force" discretization (often coupled with an equivalent medium model) whereby 100's of millions of voxels are used to represent these strong conductors, but at the cost of extreme computation times (and mesh design) for a simulation result when possible. To minimize these burdens, a new finite element scheme (Weiss, Geophysics, 2017) has been developed in which the material properties reside on a hierarchy of geometric simplicies (i.e., edges, facets and volumes) within an unstructured tetrahedral mesh. This allows thin sheet—like structures, such as subsurface fractures, to be economically represented by a connected set of triangular facets, for example, that freely conform to arbitrary "real world" geometries. The same holds thin pipe/wire-like structures, such as casings or pipelines. The hierarchical finite element scheme has been applied to problems in electro- and magnetostatics for oilfield problems where the elevated, but finite, conductivity and permeability of the steel-cased oil wells must be properly accounted for, yielding results that are otherwise unobtainable, with run times as low as a few 10s of seconds. Extension of the hierarchical finite element concept to broadband electromagnetics is presently underway, as

Finite elements and approximation

CERN Document Server

Zienkiewicz, O C

2006-01-01

A powerful tool for the approximate solution of differential equations, the finite element is extensively used in industry and research. This book offers students of engineering and physics a comprehensive view of the principles involved, with numerous illustrative examples and exercises.Starting with continuum boundary value problems and the need for numerical discretization, the text examines finite difference methods, weighted residual methods in the context of continuous trial functions, and piecewise defined trial functions and the finite element method. Additional topics include higher o

A first course in finite elements

CERN Document Server

Fish, Jacob

2007-01-01

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

An element-based finite-volume method approach for naturally fractured compositional reservoir simulation

Energy Technology Data Exchange (ETDEWEB)

Marcondes, Francisco [Federal University of Ceara, Fortaleza (Brazil). Dept. of Metallurgical Engineering and Material Science], e-mail: marcondes@ufc.br; Varavei, Abdoljalil; Sepehrnoori, Kamy [The University of Texas at Austin (United States). Petroleum and Geosystems Engineering Dept.], e-mails: varavei@mail.utexas.edu, kamys@mail.utexas.edu

2010-07-01

An element-based finite-volume approach in conjunction with unstructured grids for naturally fractured compositional reservoir simulation is presented. In this approach, both the discrete fracture and the matrix mass balances are taken into account without any additional models to couple the matrix and discrete fractures. The mesh, for two dimensional domains, can be built of triangles, quadrilaterals, or a mix of these elements. However, due to the available mesh generator to handle both matrix and discrete fractures, only results using triangular elements will be presented. The discrete fractures are located along the edges of each element. To obtain the approximated matrix equation, each element is divided into three sub-elements and then the mass balance equations for each component are integrated along each interface of the sub-elements. The finite-volume conservation equations are assembled from the contribution of all the elements that share a vertex, creating a cell vertex approach. The discrete fracture equations are discretized only along the edges of each element and then summed up with the matrix equations in order to obtain a conservative equation for both matrix and discrete fractures. In order to mimic real field simulations, the capillary pressure is included in both matrix and discrete fracture media. In the implemented model, the saturation field in the matrix and discrete fractures can be different, but the potential of each phase in the matrix and discrete fracture interface needs to be the same. The results for several naturally fractured reservoirs are presented to demonstrate the applicability of the method. (author)

Modelling optimization involving different types of elements in finite element analysis

International Nuclear Information System (INIS)

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

2013-01-01

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

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...

Structural modeling techniques by finite element method

International Nuclear Information System (INIS)

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

1991-01-01

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

Element-topology-independent preconditioners for parallel finite element computations

Science.gov (United States)

Park, K. C.; Alexander, Scott

1992-01-01

A family of preconditioners for the solution of finite element equations are presented, which are element-topology independent and thus can be applicable to element order-free parallel computations. A key feature of the present preconditioners is the repeated use of element connectivity matrices and their left and right inverses. The properties and performance of the present preconditioners are demonstrated via beam and two-dimensional finite element matrices for implicit time integration computations.

Invariants of triangular Lie algebras

International Nuclear Information System (INIS)

Boyko, Vyacheslav; Patera, Jiri; Popovych, Roman

2007-01-01

Triangular Lie algebras are the Lie algebras which can be faithfully represented by triangular matrices of any finite size over the real/complex number field. In the paper invariants ('generalized Casimir operators') are found for three classes of Lie algebras, namely those which are either strictly or non-strictly triangular, and for so-called special upper triangular Lie algebras. Algebraic algorithm of Boyko et al (2006 J. Phys. A: Math. Gen.39 5749 (Preprint math-ph/0602046)), developed further in Boyko et al (2007 J. Phys. A: Math. Theor.40 113 (Preprint math-ph/0606045)), is used to determine the invariants. A conjecture of Tremblay and Winternitz (2001 J. Phys. A: Math. Gen.34 9085), concerning the number of independent invariants and their form, is corroborated

Probabilistic finite elements

Science.gov (United States)

Belytschko, Ted; Wing, Kam Liu

1987-01-01

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

Finite element and finite difference methods in electromagnetic scattering

CERN Document Server

Morgan, MA

2013-01-01

This second volume in the Progress in Electromagnetic Research series examines recent advances in computational electromagnetics, with emphasis on scattering, as brought about by new formulations and algorithms which use finite element or finite difference techniques. Containing contributions by some of the world's leading experts, the papers thoroughly review and analyze this rapidly evolving area of computational electromagnetics. Covering topics ranging from the new finite-element based formulation for representing time-harmonic vector fields in 3-D inhomogeneous media using two coupled sca

Electrical machine analysis using finite elements

CERN Document Server

Bianchi, Nicola

2005-01-01

OUTLINE OF ELECTROMAGNETIC FIELDSVector AnalysisElectromagnetic FieldsFundamental Equations SummaryReferencesBASIC PRINCIPLES OF FINITE ELEMENT METHODSIntroductionField Problems with Boundary ConditionsClassical Method for the Field Problem SolutionThe Classical Residual Method (Galerkin's Method)The Classical Variational Method (Rayleigh-Ritz's Method)The Finite Element MethodReferencesAPPLICATIONS OF THE FINITE ELEMENT METHOD TO TWO-DIMENSIONAL FIELDSIntroductionLinear Interpolation of the Function fApplication of the Variational MethodSimple Descriptions of Electromagnetic FieldsAppendix: I

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

International Nuclear Information System (INIS)

Chiong, Irene; Song Chongmin

2010-01-01

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

FINITE ELEMENT MODEL FOR PREDICTING RESIDUAL ...

African Journals Online (AJOL)

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

Finite element methods a practical guide

CERN Document Server

Whiteley, Jonathan

2017-01-01

This book presents practical applications of the finite element method to general differential equations. The underlying strategy of deriving the finite element solution is introduced using linear ordinary differential equations, thus allowing the basic concepts of the finite element solution to be introduced without being obscured by the additional mathematical detail required when applying this technique to partial differential equations. The author generalizes the presented approach to partial differential equations which include nonlinearities. The book also includes variations of the finite element method such as different classes of meshes and basic functions. Practical application of the theory is emphasised, with development of all concepts leading ultimately to a description of their computational implementation illustrated using Matlab functions. The target audience primarily comprises applied researchers and practitioners in engineering, but the book may also be beneficial for graduate students.

Finite element analysis of piezoelectric materials

International Nuclear Information System (INIS)

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

1999-01-01

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

Finite rotation shells basic equations and finite elements for Reissner kinematics

CERN Document Server

Wisniewski, K

2010-01-01

This book covers theoretical and computational aspects of non-linear shells. Several advanced topics of shell equations and finite elements - not included in standard textbooks on finite elements - are addressed, and the book includes an extensive bibliography.

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.

A spatial discretization of the MHD equations based on the finite volume - spectral method

International Nuclear Information System (INIS)

Miyoshi, Takahiro

2000-05-01

Based on the finite volume - spectral method, we present new discretization formulae for the spatial differential operators in the full system of the compressible MHD equations. In this approach, the cell-centered finite volume method is adopted in a bounded plane (poloidal plane), while the spectral method is applied to the differential with respect to the periodic direction perpendicular to the poloidal plane (toroidal direction). Here, an unstructured grid system composed of the arbitrary triangular elements is utilized for constructing the cell-centered finite volume method. In order to maintain the divergence free constraint of the magnetic field numerically, only the poloidal component of the rotation is defined at three edges of the triangular element. This poloidal component is evaluated under the assumption that the toroidal component of the operated vector times the radius, RA φ , is linearly distributed in the element. The present method will be applied to the nonlinear MHD dynamics in an realistic torus geometry without the numerical singularities. (author)

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.

Why do probabilistic finite element analysis ?

CERN Document Server

Thacker, Ben H

2008-01-01

The intention of this book is to provide an introduction to performing probabilistic finite element analysis. As a short guideline, the objective is to inform the reader of the use, benefits and issues associated with performing probabilistic finite element analysis without excessive theory or mathematical detail.

An efficient finite element solution for gear dynamics

International Nuclear Information System (INIS)

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

2010-01-01

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

The Numerical Simulation of the Crack Elastoplastic Extension Based on the Extended Finite Element Method

Directory of Open Access Journals (Sweden)

Xia Xiaozhou

2013-01-01

Full Text Available In the frame of the extended finite element method, the exponent disconnected function is introduced to reflect the discontinuous characteristic of crack and the crack tip enrichment function which is made of triangular basis function, and the linear polar radius function is adopted to describe the displacement field distribution of elastoplastic crack tip. Where, the linear polar radius function form is chosen to decrease the singularity characteristic induced by the plastic yield zone of crack tip, and the triangle basis function form is adopted to describe the displacement distribution character with the polar angle of crack tip. Based on the displacement model containing the above enrichment displacement function, the increment iterative form of elastoplastic extended finite element method is deduced by virtual work principle. For nonuniform hardening material such as concrete, in order to avoid the nonsymmetry characteristic of stiffness matrix induced by the non-associate flowing of plastic strain, the plastic flowing rule containing cross item based on the least energy dissipation principle is adopted. Finally, some numerical examples show that the elastoplastic X-FEM constructed in this paper is of validity.

A New Triangular Hybrid Displacement Function Element for Static and Free Vibration Analyses of Mindlin-Reissner Plate

Directory of Open Access Journals (Sweden)

Jun-Bin Huang

Full Text Available Abstract A new 3-node triangular hybrid displacement function Mindlin-Reissner plate element is developed. Firstly, the modified variational functional of complementary energy for Mindlin-Reissner plate, which is eventually expressed by a so-called displacement function F, is proposed. Secondly, the locking-free formulae of Timoshenko’s beam theory are chosen as the deflection, rotation, and shear strain along each element boundary. Thirdly, seven fundamental analytical solutions of the displacement function F are selected as the trial functions for the assumed resultant fields, so that the assumed resultant fields satisfy all governing equations in advance. Finally, the element stiffness matrix of the new element, denoted by HDF-P3-7β, is derived from the modified principle of complementary energy. Together with the diagonal inertia matrix of the 3-node triangular isoparametric element, the proposed element is also successfully generalized to the free vibration problems. Numerical results show that the proposed element exhibits overall remarkable performance in all benchmark problems, especially in the free vibration analyses.

Finite element analysis theory and application with ANSYS

CERN Document Server

Moaveni, Saeed

2015-01-01

For courses in Finite Element Analysis, offered in departments of Mechanical or Civil and Environmental Engineering. While many good textbooks cover the theory of finite element modeling, Finite Element Analysis: Theory and Application with ANSYS is the only text available that incorporates ANSYS as an integral part of its content. Moaveni presents the theory of finite element analysis, explores its application as a design/modeling tool, and explains in detail how to use ANSYS intelligently and effectively. Teaching and Learning Experience This program will provide a better teaching and learning experience-for you and your students. It will help: *Present the Theory of Finite Element Analysis: The presentation of theoretical aspects of finite element analysis is carefully designed not to overwhelm students. *Explain How to Use ANSYS Effectively: ANSYS is incorporated as an integral part of the content throughout the book. *Explore How to Use FEA as a Design/Modeling Tool: Open-ended design problems help stude...

Finite element application to global reactor analysis

International Nuclear Information System (INIS)

Schmidt, F.A.R.

1981-01-01

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

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...

Books and monographs on finite element technology

Science.gov (United States)

Noor, A. K.

1985-01-01

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

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

Directory of Open Access Journals (Sweden)

J. Ochoa-Avendaño

2017-01-01

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

Probabilistic finite elements for fracture mechanics

Science.gov (United States)

Besterfield, Glen

1988-01-01

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

Collapse of triangular channels in a soft elastomer

Science.gov (United States)

Tepáyotl-Ramírez, Daniel; Lu, Tong; Park, Yong-Lae; Majidi, Carmel

2013-01-01

We extend classical solutions in contact mechanics to examine the collapse of channels in a soft elastomer. These channels have triangular cross-section and collapse when pressure is applied to the surrounding elastomer. Treating the walls of the channel as indenters that penetrate the channel base, we derive an algebraic mapping between pressure and cross-sectional area. These theoretical predictions are in strong agreement with results that we obtain through finite element analysis and experimental measurements. This is accomplished without data fitting and suggests that the theoretical approach may be generalized to a broad range of cross-sectional geometries in soft microfluidics.

Introduction to finite and spectral element methods using Matlab

CERN Document Server

Pozrikidis, Constantine

2014-01-01

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

Finite Element Methods and Their Applications

CERN Document Server

Chen, Zhangxin

2005-01-01

This book serves as a text for one- or two-semester courses for upper-level undergraduates and beginning graduate students and as a professional reference for people who want to solve partial differential equations (PDEs) using finite element methods. The author has attempted to introduce every concept in the simplest possible setting and maintain a level of treatment that is as rigorous as possible without being unnecessarily abstract. Quite a lot of attention is given to discontinuous finite elements, characteristic finite elements, and to the applications in fluid and solid mechanics including applications to porous media flow, and applications to semiconductor modeling. An extensive set of exercises and references in each chapter are provided.

Programming the finite element method

CERN Document Server

Smith, I M; Margetts, L

2013-01-01

Many students, engineers, scientists and researchers have benefited from the practical, programming-oriented style of the previous editions of Programming the Finite Element Method, learning how to develop computer programs to solve specific engineering problems using the finite element method. This new fifth edition offers timely revisions that include programs and subroutine libraries fully updated to Fortran 2003, which are freely available online, and provides updated material on advances in parallel computing, thermal stress analysis, plasticity return algorithms, convection boundary c

Triangular spiral tilings

International Nuclear Information System (INIS)

Sushida, Takamichi; Hizume, Akio; Yamagishi, Yoshikazu

2012-01-01

The topology of spiral tilings is intimately related to phyllotaxis theory and continued fractions. A quadrilateral spiral tiling is determined by a suitable chosen triple (ζ, m, n), where ζ element of D/R, and m and n are relatively prime integers. We give a simple characterization when (ζ, m, n) produce a triangular spiral tiling. When m and n are fixed, the admissible generators ζ form a curve in the unit disk. The family of triangular spiral tilings with opposed parastichy pairs (m, n) is parameterized by the divergence angle arg (ζ), while triangular spiral tilings with non-opposed parastichy pairs are parameterized by the plastochrone ratio 1/|ζ|. The generators for triangular spiral tilings with opposed parastichy pairs are not dense in the complex parameter space, while those with non-opposed parastichy pairs are dense. The proofs will be given in a general setting of spiral multiple tilings. We present paper-folding (origami) sheets that build spiral towers whose top-down views are triangular tilings. (paper)

Mixed Element Formulation for the Finite Element-Boundary Integral Method

National Research Council Canada - National Science Library

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

2006-01-01

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

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.

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...

Using Finite Element Method

Directory of Open Access Journals (Sweden)

M.H.R. Ghoreishy

2008-02-01

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

Precise magnetostatic field using the finite element method

International Nuclear Information System (INIS)

Nascimento, Francisco Rogerio Teixeira do

2013-01-01

The main objective of this work is to simulate electromagnetic fields using the Finite Element Method. Even in the easiest case of electrostatic and magnetostatic numerical simulation some problems appear when the nodal finite element is used. It is difficult to model vector fields with scalar functions mainly in non-homogeneous materials. With the aim to solve these problems two types of techniques are tried: the adaptive remeshing using nodal elements and the edge finite element that ensure the continuity of tangential components. Some numerical analysis of simple electromagnetic problems with homogeneous and non-homogeneous materials are performed using first, the adaptive remeshing based in various error indicators and second, the numerical solution of waveguides using edge finite element. (author)

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

Science.gov (United States)

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

2017-12-01

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

ANSYS mechanical APDL for finite element analysis

CERN Document Server

Thompson, Mary Kathryn

2017-01-01

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

Finite elements of nonlinear continua

CERN Document Server

Oden, John Tinsley

1972-01-01

Geared toward undergraduate and graduate students, this text extends applications of the finite element method from linear problems in elastic structures to a broad class of practical, nonlinear problems in continuum mechanics. It treats both theory and applications from a general and unifying point of view.The text reviews the thermomechanical principles of continuous media and the properties of the finite element method, and then brings them together to produce discrete physical models of nonlinear continua. The mathematical properties of these models are analyzed, along with the numerical s

The finite element method in engineering, 2nd edition

International Nuclear Information System (INIS)

Rao, S.S.

1986-01-01

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

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

Energy Technology Data Exchange (ETDEWEB)

Lee, Sang Jin; Seo, Jeong Moon

2000-08-01

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

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

International Nuclear Information System (INIS)

Lee, Sang Jin; Seo, Jeong Moon

2000-08-01

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

High accuracy electromagnetic field solvers for cylindrical waveguides and axisymmetric structures using the finite element method

International Nuclear Information System (INIS)

Nelson, E.M.

1993-12-01

Some two-dimensional finite element electromagnetic field solvers are described and tested. For TE and TM modes in homogeneous cylindrical waveguides and monopole modes in homogeneous axisymmetric structures, the solvers find approximate solutions to a weak formulation of the wave equation. Second-order isoparametric lagrangian triangular elements represent the field. For multipole modes in axisymmetric structures, the solver finds approximate solutions to a weak form of the curl-curl formulation of Maxwell's equations. Second-order triangular edge elements represent the radial (ρ) and axial (z) components of the field, while a second-order lagrangian basis represents the azimuthal (φ) component of the field weighted by the radius ρ. A reduced set of basis functions is employed for elements touching the axis. With this basis the spurious modes of the curl-curl formulation have zero frequency, so spurious modes are easily distinguished from non-static physical modes. Tests on an annular ring, a pillbox and a sphere indicate the solutions converge rapidly as the mesh is refined. Computed eigenvalues with relative errors of less than a few parts per million are obtained. Boundary conditions for symmetric, periodic and symmetric-periodic structures are discussed and included in the field solver. Boundary conditions for structures with inversion symmetry are also discussed. Special corner elements are described and employed to improve the accuracy of cylindrical waveguide and monopole modes with singular fields at sharp corners. The field solver is applied to three problems: (1) cross-field amplifier slow-wave circuits, (2) a detuned disk-loaded waveguide linear accelerator structure and (3) a 90 degrees overmoded waveguide bend. The detuned accelerator structure is a critical application of this high accuracy field solver. To maintain low long-range wakefields, tight design and manufacturing tolerances are required

Finite Element Analysis of Pipe T-Joint

OpenAIRE

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

2012-01-01

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

Localized spin-wave modes in a triangular magnetic element studied by micro-focused Brillouin light scattering

Energy Technology Data Exchange (ETDEWEB)

Hwang, S.; Kwon, J.-H. [School of Materials Science and Engineering, Gwangju Institute of Science and Technology (GIST), Gwangju 61005 (Korea, Republic of); Grünberg, P. [Grünberg Center for Magnetic Nanomaterials, Gwangju Institute of Science and Technology (GIST), Gwangju 61005 (Korea, Republic of); Cho, B.K., E-mail: chobk@gist.ac.kr [School of Materials Science and Engineering, Gwangju Institute of Science and Technology (GIST), Gwangju 61005 (Korea, Republic of)

2017-09-01

Highlights: • Direct evidence of localized mode in a triangular nano-magnet using μ-BLS. • Localized regions are identified by the internal field distribution. • The spatially resolved measurement was performed to obtain 2-D intensity map. • Spin modes in same positions can be distinguish comparing with simulated spectrum. • Localized modes were identified by comparing with the simulated spatial profiles. - Abstract: Localized spin-wave modes, which were thermally excited at a specific position in a triangular magnetic element, were investigated using micro-focused Brillouin light scattering in two saturated states, the buckle and Y-states, with an applied magnetic field of 0.24 T parallel and perpendicular to the basal edge, respectively. The measured frequency spectrum at a specific beam spot position, rather than an integrated spectrum, was analyzed by comparing it with the simulation data at a precisely selected position within the beam spot area. The analyzed results were used to plot a two-dimensional intensity map and simulation spatial profile to verify the validity of the analysis. From the analysis process, two localized spin-wave modes in a triangular magnetic element were successfully identified near the apex region in the buckle state and near the basal edge region in the Y-state.

Introduction to finite element analysis using MATLAB and Abaqus

CERN Document Server

Khennane, Amar

2013-01-01

There are some books that target the theory of the finite element, while others focus on the programming side of things. Introduction to Finite Element Analysis Using MATLAB(R) and Abaqus accomplishes both. This book teaches the first principles of the finite element method. It presents the theory of the finite element method while maintaining a balance between its mathematical formulation, programming implementation, and application using commercial software. The computer implementation is carried out using MATLAB, while the practical applications are carried out in both MATLAB and Abaqus. MA

SMPBS: Web server for computing biomolecular electrostatics using finite element solvers of size modified Poisson-Boltzmann equation.

Science.gov (United States)

Xie, Yang; Ying, Jinyong; Xie, Dexuan

2017-03-30

SMPBS (Size Modified Poisson-Boltzmann Solvers) is a web server for computing biomolecular electrostatics using finite element solvers of the size modified Poisson-Boltzmann equation (SMPBE). SMPBE not only reflects ionic size effects but also includes the classic Poisson-Boltzmann equation (PBE) as a special case. Thus, its web server is expected to have a broader range of applications than a PBE web server. SMPBS is designed with a dynamic, mobile-friendly user interface, and features easily accessible help text, asynchronous data submission, and an interactive, hardware-accelerated molecular visualization viewer based on the 3Dmol.js library. In particular, the viewer allows computed electrostatics to be directly mapped onto an irregular triangular mesh of a molecular surface. Due to this functionality and the fast SMPBE finite element solvers, the web server is very efficient in the calculation and visualization of electrostatics. In addition, SMPBE is reconstructed using a new objective electrostatic free energy, clearly showing that the electrostatics and ionic concentrations predicted by SMPBE are optimal in the sense of minimizing the objective electrostatic free energy. SMPBS is available at the URL: smpbs.math.uwm.edu © 2017 Wiley Periodicals, Inc. © 2017 Wiley Periodicals, Inc.

Nonlinear vibrations of thin arbitrarily laminated composite plates subjected to harmonic excitations using DKT elements

Science.gov (United States)

Chiang, C. K.; Xue, David Y.; Mei, Chuh

1993-04-01

A finite element formulation is presented for determining the large-amplitude free and steady-state forced vibration response of arbitrarily laminated anisotropic composite thin plates using the Discrete Kirchhoff Theory (DKT) triangular elements. The nonlinear stiffness and harmonic force matrices of an arbitrarily laminated composite triangular plate element are developed for nonlinear free and forced vibration analyses. The linearized updated-mode method with nonlinear time function approximation is employed for the solution of the system nonlinear eigenvalue equations. The amplitude-frequency relations for convergence with gridwork refinement, triangular plates, different boundary conditions, lamination angles, number of plies, and uniform versus concentrated loads are presented.

Nonlinear finite element modeling of corrugated board

Science.gov (United States)

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

1999-01-01

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

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

Bibliography for finite elements. [2200 references

Energy Technology Data Exchange (ETDEWEB)

Whiteman, J R [comp.

1975-01-01

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

Complex finite element sensitivity method for creep analysis

International Nuclear Information System (INIS)

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

2015-01-01

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

Electro-osmotic flows inside triangular microchannels

International Nuclear Information System (INIS)

Vocale, P; Spiga, M; Geri, M; Morini, G L

2014-01-01

This work presents a numerical investigation of both pure electro-osmotic and combined electro-osmotic/pressure-driven flows inside triangular microchannels. A finite element analysis has been adopted to solve the governing equations for the electric potential and the velocity field, accounting for a finite thickness of the electric double layer. The influence of non-dimensional parameters such as the aspect ratio of the cross-section, the electrokinetic diameter and the ratio of the pressure force to the electric force on the flow behavior has been investigated. Numerical results point out that the velocity field is significantly influenced by the aspect ratio of the cross section and the electrokinetic diameter. More specifically, the aspect ratio plays an important role in determining the maximum volumetric flow rate, while the electrokinetic diameter is crucial to establishing the range of pressures that may be sustained by the electro-osmotic flow. Numerical results are also compared with two correlations available in the literature which enable to assess the volumetric flow rate and the pressure head for microchannels featuring a rectangular, a trapezoidal or an elliptical cross-section.

A finite element analysis of the effects of geometrical shape on the elastic properties of chemical vapor deposited diamond nanowire

Directory of Open Access Journals (Sweden)

Garuma Abdisa Denu

2017-01-01

Full Text Available We report the effect of geometrical shape of diamond nanowire on its mechanical properties. Finite element modeling using COMSOL Multiphysics software is used to simulate various diamond nanowire with circular, square, rectangular, hexagonal and triangular cross-sections. A bending test under concentrated load applied at one of the free ends is simulated using FEM. The force response of the nanowire under different loading is studied for the various cross-sections. The dimensions of each cross-section is chosen so that material properties such as Young’s modulus can be kept constant for comparison in all the cross-sections. It is found out that the bending capability of a triangular nanowire is higher compared to other cross-sections due to its lowest second moment. Circular and hexagonal cross-section show highest stiffness. The study of mechanical property of diamond nanowires is useful for optimal nanomechanical designs where the effect of cross-section has to be taken into account.

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.

Application of Mass Lumped Higher Order Finite Elements

International Nuclear Information System (INIS)

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

2005-01-01

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

The finite element method its basis and fundamentals

CERN Document Server

Zienkiewicz, Olek C; Zhu, JZ

2013-01-01

The Finite Element Method: Its Basis and Fundamentals offers a complete introduction to the basis of the finite element method, covering fundamental theory and worked examples in the detail required for readers to apply the knowledge to their own engineering problems and understand more advanced applications. This edition sees a significant rearrangement of the book's content to enable clearer development of the finite element method, with major new chapters and sections added to cover: Weak forms Variational forms Multi-dimensional field prob

Finite-element formulations for the thermal stress analysis of two- and three-dimensional thin ractor structures

International Nuclear Information System (INIS)

Kulak, R.F.; Kennedy, J.M.; Belytschko, T.B.; Schoeberle, D.F.

1977-01-01

This paper describes finite-element formulations for the thermal stress analysis of LMFBR structures. The first formulation is applicable to large displacement rotation problems in which the strains are small. For this formulation, a general temperature-dependent constituent relationship is derived from a Gibbs potential function and a temperature dependent yield surface. The temperature dependency of the yield surface is based upon a temperature-dependent, material-hardening model. The model uses a temperature-equivalent stress-plastic strain diagram which is generated from isothermal uniaxial stress-strain data. A second formulation is presented for problems characterized by both large displacement-rotations and large strains. Here a set of large strain hypoelastic-plastic relationships are developed to linearly relate the rate of stress to the rate of deformation. The temperature field is described through time-dependent values at mesh node points; the temperature fields in each element are then obtained by interpolation formulas. Hence, problems with both spatial and temporal dependent temperature fields can easily be treated. The above developments were incorporated into two ANL developed finite-element computer codes: the implicit version of STRAW and the 3D Implicit Structural Analysis Code. STRAW is a two-dimensional code with a plane stress/plane strain beam element. The 3D Implicit code has a triangular flat plate element which is capable of sustaining both membrane and bending loads. To insure numerical stability both codes are based on an iterative-incremental solution procedure with equilibrium checks based on an error in energy

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

International Nuclear Information System (INIS)

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

1998-03-01

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

The problem 7 forming triangular geometric line field

Directory of Open Access Journals (Sweden)

Travush Vladimir Iljich

2016-01-01

Full Text Available Investigated a method of formation of triangular networks in the field. Delivered conditions the problem of locating a triangular network in the area. The criterion for assessing the effectiveness of the solution of the problem is the minimum number of sizes of the dome elements, the possibility of pre-assembly and pre-stressing. The solution of the problem of one embodiment of a triangular network of accommodation in a compatible spherical triangle and, accordingly, on the sphere. Optimization of triangular geometric network on a sphere on the criterion of minimum sizes of elements can be solved by placing the system in an irregular hexagon inscribed in a circle of minimal size, maximum regular hexagons.

Finite element formulation for a digital image correlation method

International Nuclear Information System (INIS)

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

2005-01-01

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

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....

Analysis of elastic-plastic problems using edge-based smoothed finite element method

International Nuclear Information System (INIS)

Cui, X.Y.; Liu, G.R.; Li, G.Y.; Zhang, G.Y.; Sun, G.Y.

2009-01-01

In this paper, an edge-based smoothed finite element method (ES-FEM) is formulated for stress field determination of elastic-plastic problems using triangular meshes, in which smoothing domains associated with the edges of the triangles are used for smoothing operations to improve the accuracy and the convergence rate of the method. The smoothed Galerkin weak form is adopted to obtain the discretized system equations, and the numerical integration becomes a simple summation over the edge-based smoothing domains. The pseudo-elastic method is employed for the determination of stress field and Hencky's total deformation theory is used to define effective elastic material parameters, which are treated as field variables and considered as functions of the final state of stress fields. The effective elastic material parameters are then obtained in an iterative manner based on the strain controlled projection method from the uniaxial material curve. Some numerical examples are investigated and excellent results have been obtained demonstrating the effectivity of the present method.

Advances in 3D electromagnetic finite element modeling

International Nuclear Information System (INIS)

Nelson, E.M.

1997-01-01

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

On symmetric pyramidal finite elements

Czech Academy of Sciences Publication Activity Database

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

2004-01-01

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

Finite-element analysis of dynamic fracture

Science.gov (United States)

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

1976-01-01

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

The finite element method in electromagnetics

CERN Document Server

Jin, Jianming

2014-01-01

A new edition of the leading textbook on the finite element method, incorporating major advancements and further applications in the field of electromagnetics The finite element method (FEM) is a powerful simulation technique used to solve boundary-value problems in a variety of engineering circumstances. It has been widely used for analysis of electromagnetic fields in antennas, radar scattering, RF and microwave engineering, high-speed/high-frequency circuits, wireless communication, electromagnetic compatibility, photonics, remote sensing, biomedical engineering, and space exploration. The

Finite elements for analysis and design

CERN Document Server

Akin, J E; Davenport, J H

1994-01-01

The finite element method (FEM) is an analysis tool for problem-solving used throughout applied mathematics, engineering, and scientific computing. Finite Elements for Analysis and Design provides a thoroughlyrevised and up-to-date account of this important tool and its numerous applications, with added emphasis on basic theory. Numerous worked examples are included to illustrate the material.Key Features* Akin clearly explains the FEM, a numerical analysis tool for problem-solving throughout applied mathematics, engineering and scientific computing* Basic theory has bee

A finite element formulation of the Darwin electromagnetic PIC model for unstructured meshes of triangles

International Nuclear Information System (INIS)

Sonnendrucker, E.; Ambrosiano, J.; Brandon, S.

1993-01-01

The Darwin model for electromagnetic simulation is a reduced form of the Maxwell-Vlasov system that retains all essential physical processes except the propagation of light waves. It is useful in modeling systems for which the light-transit timescales are less important than Alfven wave propagation, or quasistatic effects. The Darwin model is elliptic rather than hyperbolic as are the full set of Maxwell's equations. Appropriate boundary conditions must be chosen for the problems to be well-posed. Using finite element techniques to apply this method for unstructured triangular meshes, a mesh made up of unstructured triangles allows realistic device geometries to be modeled without the necessity of using a large number of mesh points. Analyzing the dispersion relation allows us to validate the code as well as the Darwin approximation

The finite element response matrix method

International Nuclear Information System (INIS)

Nakata, H.; Martin, W.R.

1983-02-01

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

Finite Element Method in Machining Processes

CERN Document Server

Markopoulos, Angelos P

2013-01-01

Finite Element Method in Machining Processes provides a concise study on the way the Finite Element Method (FEM) is used in the case of manufacturing processes, primarily in machining. The basics of this kind of modeling are detailed to create a reference that will provide guidelines for those who start to study this method now, but also for scientists already involved in FEM and want to expand their research. A discussion on FEM, formulations and techniques currently in use is followed up by machining case studies. Orthogonal cutting, oblique cutting, 3D simulations for turning and milling, grinding, and state-of-the-art topics such as high speed machining and micromachining are explained with relevant examples. This is all supported by a literature review and a reference list for further study. As FEM is a key method for researchers in the manufacturing and especially in the machining sector, Finite Element Method in Machining Processes is a key reference for students studying manufacturing processes but al...

Inside finite elements

CERN Document Server

Weiser, Martin

2016-01-01

All relevant implementation aspects of finite element methods are discussed in this book. The focus is on algorithms and data structures as well as on their concrete implementation. Theory is covered as far as it gives insight into the construction of algorithms. Throughout the exercises a complete FE-solver for scalar 2D problems will be implemented in Matlab/Octave.

Finite Element Modelling of Seismic Liquefaction in Soils

NARCIS (Netherlands)

Galavi, V.; Petalas, A.; Brinkgreve, R.B.J.

2013-01-01

Numerical aspects of seismic liquefaction in soils as implemented in the finite element code, PLAXIS, is described in this paper. After description of finite element equations of dynamic problems, three practical dynamic boundary conditions, namely viscous boundary tractions, tied degrees of freedom

Laser cutting of triangular geometry into 2024 aluminum alloy: Influence of triangle size on thermal stress field

Energy Technology Data Exchange (ETDEWEB)

Yilbas, Bekir Sami; Akhtar, Syed Sohail [King Fahd University of Petroleum and Minerals, Dhahran (Saudi Arabia); Keles, Omer; Boran, Kurtulus [Gazi University, Ankara (Turkmenistan)

2015-08-15

Laser cutting of a triangular geometry into aluminum 2024 alloy is carried out. Thermal stress field in the cutting section is predicted using the finite element code ABAQUS. Surface temperature predictions are validated through the thermocouple data. Morphological changes in the cut section are examined incorporating optical and electron scanning microscopes. The effects of the size of the triangular geometry on thermal stress field are also examined. It is found that surface temperature predictions agree well with thermocouple data. von Mises stress remains high in the region close to the corners of the triangular geometry, which is more pronounced for the small size triangle. This behavior is associated with the occurrence of the high cooling rates in this region. Laser cut edges are free from large scale sideways burning and large size burr attachments. However, some locally scattered dross attachments are observed at the kerf exit.

Performance of an anisotropic Allman/DKT 3-node thin triangular flat shell element

Science.gov (United States)

Ertas, A.; Krafcik, J. T.; Ekwaro-Osire, S.

1992-05-01

A simple, explicit formulation of the stiffness matrix for an anisotropic, 3-node, thin triangular flat shell element in global coordinates is presented. An Allman triangle (AT) is used for membrane stiffness. The membrane stiffness matrix is explicitly derived by applying an Allman transformation to a Felippa 6-node linear strain triangle (LST). Bending stiffness is incorporated by the use of a discrete Kirchhoff triangle (DKT) bending element. Stiffness terms resulting from anisotropic membrane-bending coupling are included by integrating, in area coordinates, the membrane and bending strain-displacement matrices. Using the aforementioned approach, the objective of this study is to develop and test the performance of a practical 3-node flat shell element that could be used in plate problems with unsymmetrically stacked composite laminates. The performance of the latter element is tested on plates of varying aspect ratios. The developed 3-node shell element should simplify the programming task and have the potential of reducing the computational time.

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

International Nuclear Information System (INIS)

Baker, A.R.

1982-07-01

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

A geometric toolbox for tetrahedral finite element partitions

NARCIS (Netherlands)

Brandts, J.; Korotov, S.; Křížek, M.; Axelsson, O.; Karátson, J.

2011-01-01

In this work we present a survey of some geometric results on tetrahedral partitions and their refinements in a unified manner. They can be used for mesh generation and adaptivity in practical calculations by the finite element method (FEM), and also in theoretical finite element (FE) analysis.

Mixed finite element simulations in two-dimensional groundwater flow problems

International Nuclear Information System (INIS)

Kimura, Hideo

1989-01-01

A computer code of groundwater flow in two-dimensional porous media based on the mixed finite element method was developed for accurate approximations of Darcy velocities in safety evaluation of radioactive waste disposal. The mixed finite element procedure solves for both the Darcy velocities and pressure heads simultaneously in the Darcy equation and continuity equation. Numerical results of a single well pumping at a constant rate in a uniform flow field showed that the mixed finite element method gives more accurate Darcy velocities nearly 50 % on average error than standard finite element method. (author)

Finite element analysis of rotating beams physics based interpolation

CERN Document Server

Ganguli, Ranjan

2017-01-01

This book addresses the solution of rotating beam free-vibration problems using the finite element method. It provides an introduction to the governing equation of a rotating beam, before outlining the solution procedures using Rayleigh-Ritz, Galerkin and finite element methods. The possibility of improving the convergence of finite element methods through a judicious selection of interpolation functions, which are closer to the problem physics, is also addressed. The book offers a valuable guide for students and researchers working on rotating beam problems – important engineering structures used in helicopter rotors, wind turbines, gas turbines, steam turbines and propellers – and their applications. It can also be used as a textbook for specialized graduate and professional courses on advanced applications of finite element analysis.

Impact of new computing systems on finite element computations

International Nuclear Information System (INIS)

Noor, A.K.; Fulton, R.E.; Storaasi, O.O.

1983-01-01

Recent advances in computer technology that are likely to impact finite element computations are reviewed. The characteristics of supersystems, highly parallel systems, and small systems (mini and microcomputers) are summarized. The interrelations of numerical algorithms and software with parallel architectures are discussed. A scenario is presented for future hardware/software environment and finite element systems. A number of research areas which have high potential for improving the effectiveness of finite element analysis in the new environment are identified

Finite size effects of a pion matrix element

International Nuclear Information System (INIS)

Guagnelli, M.; Jansen, K.; Palombi, F.; Petronzio, R.; Shindler, A.; Wetzorke, I.

2004-01-01

We investigate finite size effects of the pion matrix element of the non-singlet, twist-2 operator corresponding to the average momentum of non-singlet quark densities. Using the quenched approximation, they come out to be surprisingly large when compared to the finite size effects of the pion mass. As a consequence, simulations of corresponding nucleon matrix elements could be affected by finite size effects even stronger which could lead to serious systematic uncertainties in their evaluation

Variational approach to probabilistic finite elements

Science.gov (United States)

Belytschko, T.; Liu, W. K.; Mani, A.; Besterfield, G.

1991-08-01

Probabilistic finite element methods (PFEM), synthesizing the power of finite element methods with second-moment techniques, are formulated for various classes of problems in structural and solid mechanics. Time-invariant random materials, geometric properties and loads are incorporated in terms of their fundamental statistics viz. second-moments. Analogous to the discretization of the displacement field in finite element methods, the random fields are also discretized. Preserving the conceptual simplicity, the response moments are calculated with minimal computations. By incorporating certain computational techniques, these methods are shown to be capable of handling large systems with many sources of uncertainties. By construction, these methods are applicable when the scale of randomness is not very large and when the probabilistic density functions have decaying tails. The accuracy and efficiency of these methods, along with their limitations, are demonstrated by various applications. Results obtained are compared with those of Monte Carlo simulation and it is shown that good accuracy can be obtained for both linear and nonlinear problems. The methods are amenable to implementation in deterministic FEM based computer codes.

Verification of Orthogrid Finite Element Modeling Techniques

Science.gov (United States)

Steeve, B. E.

1996-01-01

The stress analysis of orthogrid structures, specifically with I-beam sections, is regularly performed using finite elements. Various modeling techniques are often used to simplify the modeling process but still adequately capture the actual hardware behavior. The accuracy of such 'Oshort cutso' is sometimes in question. This report compares three modeling techniques to actual test results from a loaded orthogrid panel. The finite element models include a beam, shell, and mixed beam and shell element model. Results show that the shell element model performs the best, but that the simpler beam and beam and shell element models provide reasonable to conservative results for a stress analysis. When deflection and stiffness is critical, it is important to capture the effect of the orthogrid nodes in the model.

Review of Tomographic Imaging using Finite Element Method

Directory of Open Access Journals (Sweden)

Mohd Fua’ad RAHMAT

2011-12-01

Full Text Available Many types of techniques for process tomography were proposed and developed during the past 20 years. This paper review the techniques and the current state of knowledge and experience on the subject, aimed at highlighting the problems associated with the non finite element methods, such as the ill posed, ill conditioned which relates to the accuracy and sensitivity of measurements. In this paper, considerations for choice of sensors and its applications were outlined and descriptions of non finite element tomography systems were presented. The finite element method tomography system as obtained from recent works, suitable for process control and measurement were also presented.

Magnetic materials and 3D finite element modeling

CERN Document Server

Bastos, Joao Pedro A

2014-01-01

Magnetic Materials and 3D Finite Element Modeling explores material characterization and finite element modeling (FEM) applications. This book relates to electromagnetic analysis based on Maxwell’s equations and application of the finite element (FE) method to low frequency devices. A great source for senior undergraduate and graduate students in electromagnetics, it also supports industry professionals working in magnetics, electromagnetics, ferromagnetic materials science and electrical engineering. The authors present current concepts on ferromagnetic material characterizations and losses. They provide introductory material; highlight basic electromagnetics, present experimental and numerical modeling related to losses and focus on FEM applied to 3D applications. They also explain various formulations, and discuss numerical codes.

New mixed finite-element methods

International Nuclear Information System (INIS)

Franca, L.P.

1987-01-01

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

On higher order pyramidal finite elements

Czech Academy of Sciences Publication Activity Database

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

2011-01-01

Roč. 3, č. 2 (2011), s. 131-140 ISSN 2070-0733 R&D Projects: GA AV ČR(CZ) IAA100190803 Institutional research plan: CEZ:AV0Z10190503 Keywords : pyramidal polynomial basis functions * finite element method * composite elements * three-dimensional mortar elements Subject RIV: BA - General Mathematics Impact factor: 0.750, year: 2011

TSAAS: finite-element thermal and stress analysis of plane and axisymmetric solids with orthotropic temperature-dependent material properties

Energy Technology Data Exchange (ETDEWEB)

Browning, R.V.; Anderson, C.A.

1982-02-01

The finite element method is used to determine the temperatures, displacements, stresses, and strains in axisymmetric solids with orthotropic, temperature-dependent material properties under axisymmetric thermal and mechanical loads. The mechanical loads can be surface pressures, surface shears, and nodal point forces as well as an axial or centripetal acceleration. The continuous solid is replaced by a system of ring elements with triangular or quadrilateral cross sections. Accordingly, the method is valid for solids that are composed of many different materials and that have complex geometry. Nonlinear mechanical behavior as typified by plastic, locking, or creeping materials can be approximated. Two dimensional mesh generation, plotting, and editing features allow the computer program to be readily used. In addition to a stress analysis program that is based on a modified version of the SAAS code, TSAAS can carry out a transient thermal analysis with the finite element mesh used in stress analysis. An implicit time differencing scheme allows the use of arbitrary time steps with consequent fast running times. At specified times, the program will return to SAAS for thermal stress analysis. Nonlinear thermal properties and Arrhenius reaction kinetics are also incorporated into TSAAS. Several versions of TSAAS are in use at Los Alamos, running on CDC-7600, CRAY-1 and VAX 11/780 computers. This report describes the nominal TSAAS; other versions may have some unique features.

Validation of High Displacement Piezoelectric Actuator Finite Element Models

Science.gov (United States)

Taleghani, B. K.

2000-01-01

The paper presents the results obtained by using NASTRAN(Registered Trademark) and ANSYS(Regitered Trademark) finite element codes to predict doming of the THUNDER piezoelectric actuators during the manufacturing process and subsequent straining due to an applied input voltage. To effectively use such devices in engineering applications, modeling and characterization are essential. Length, width, dome height, and thickness are important parameters for users of such devices. Therefore, finite element models were used to assess the effects of these parameters. NASTRAN(Registered Trademark) and ANSYS(Registered Trademark) used different methods for modeling piezoelectric effects. In NASTRAN(Registered Trademark), a thermal analogy was used to represent voltage at nodes as equivalent temperatures, while ANSYS(Registered Trademark) processed the voltage directly using piezoelectric finite elements. The results of finite element models were validated by using the experimental results.

The finite-difference and finite-element modeling of seismic wave propagation and earthquake motion

International Nuclear Information System (INIS)

Moszo, P.; Kristek, J.; Galis, M.; Pazak, P.; Balazovijech, M.

2006-01-01

Numerical modeling of seismic wave propagation and earthquake motion is an irreplaceable tool in investigation of the Earth's structure, processes in the Earth, and particularly earthquake phenomena. Among various numerical methods, the finite-difference method is the dominant method in the modeling of earthquake motion. Moreover, it is becoming more important in the seismic exploration and structural modeling. At the same time we are convinced that the best time of the finite-difference method in seismology is in the future. This monograph provides tutorial and detailed introduction to the application of the finite-difference, finite-element, and hybrid finite-difference-finite-element methods to the modeling of seismic wave propagation and earthquake motion. The text does not cover all topics and aspects of the methods. We focus on those to which we have contributed. (Author)

A set of pathological tests to validate new finite elements

Indian Academy of Sciences (India)

M. Senthilkumar (Newgen Imaging) 1461 1996 Oct 15 13:05:22

The finite element method entails several approximations. Hence it ... researchers have designed several pathological tests to validate any new finite element. The .... Three dimensional thick shell elements using a hybrid/mixed formu- lation.

Crack Propagation by Finite Element Method

Directory of Open Access Journals (Sweden)

Luiz Carlos H. Ricardo

2018-01-01

Full Text Available Crack propagation simulation began with the development of the finite element method; the analyses were conducted to obtain a basic understanding of the crack growth. Today structural and materials engineers develop structures and materials properties using this technique. The aim of this paper is to verify the effect of different crack propagation rates in determination of crack opening and closing stress of an ASTM specimen under a standard suspension spectrum loading from FDandE SAE Keyhole Specimen Test Load Histories by finite element analysis. To understand the crack propagation processes under variable amplitude loading, retardation effects are observed

Finite element analysis of plastic recycling machine designed for ...

African Journals Online (AJOL)

... design was evaluated using finite element analysis (FEA) tool in Solid Works Computer ... Also, a minimum factor of safety value of 5.3 was obtained for shredder shaft ... Machine; Design; Recycling; Sustainability; Finite Element; Simulation ...

An introduction to the UNCLE finite element scheme

International Nuclear Information System (INIS)

Enderby, J.A.

1983-01-01

UNCLE is a completely general finite element scheme which provides common input, output, equation-solving and other facilities for a family of finite element codes for linear and non-linear stress analysis, heat transfer etc. This report describes the concepts on which UNCLE is based and gives a general account of the facilities provided. (author)

An introduction to the UNCLE finite element scheme

Energy Technology Data Exchange (ETDEWEB)

Enderby, J A [UK Atomic Energy Authority, Northern Division, Risley Nuclear Power Development Establishment, Risley, Warrington (United Kingdom)

1983-05-01

UNCLE is a completely general finite element scheme which provides common input, output, equation-solving and other facilities for a family of finite element codes for linear and non-linear stress analysis, heat transfer etc. This report describes the concepts on which UNCLE is based and gives a general account of the facilities provided. (author)

The problem 4 of placement triangular geometric line field

Directory of Open Access Journals (Sweden)

Travush Vladimir Iljich

2016-01-01

Full Text Available One of the a method of formation of triangular networks in the field is investigated. Conditions the problem of locating a triangular network in the area are delivered. The criterion for assessing the effectiveness of the solution of the problem is the minimum number of sizes of the dome elements, the possibility of pre-assembly and pre-stressing. The solution of the problem of one embodiment of a triangular network of accommodation in a compatible spherical triangle and, accordingly, on the sphere. Optimization of triangular geometric network on a sphere on the criterion of minimum sizes of elements can be solved by placing the system in an irregular hexagon inscribed in a circle of minimal size, maximum regular hexagons.

A particle finite element method for machining simulations

Science.gov (United States)

Sabel, Matthias; Sator, Christian; Müller, Ralf

2014-07-01

The particle finite element method (PFEM) appears to be a convenient technique for machining simulations, since the geometry and topology of the problem can undergo severe changes. In this work, a short outline of the PFEM-algorithm is given, which is followed by a detailed description of the involved operations. The -shape method, which is used to track the topology, is explained and tested by a simple example. Also the kinematics and a suitable finite element formulation are introduced. To validate the method simple settings without topological changes are considered and compared to the standard finite element method for large deformations. To examine the performance of the method, when dealing with separating material, a tensile loading is applied to a notched plate. This investigation includes a numerical analysis of the different meshing parameters, and the numerical convergence is studied. With regard to the cutting simulation it is found that only a sufficiently large number of particles (and thus a rather fine finite element discretisation) leads to converged results of process parameters, such as the cutting force.

A finite element primer for beginners the basics

CERN Document Server

Zohdi, Tarek I

2014-01-01

The purpose of this primer is to provide the basics of the Finite Element Method, primarily illustrated through a classical model problem, linearized elasticity. The topics covered are:(1) Weighted residual methods and Galerkin approximations,(2) A model problem for one-dimensional?linear elastostatics,(3) Weak formulations in one dimension,(4) Minimum principles in one dimension,(5) Error estimation in one dimension,(5) Construction of Finite Element basis functions in one dimension,(6) Gaussian Quadrature,(7) Iterative solvers and element by element data structures,(8) A model problem for th

On the reliability of finite element solutions

International Nuclear Information System (INIS)

Prasad, K.S.R.K.

1975-01-01

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

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

International Nuclear Information System (INIS)

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

2011-01-01

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

Automation of finite element methods

CERN Document Server

Korelc, Jože

2016-01-01

New finite elements are needed as well in research as in industry environments for the development of virtual prediction techniques. The design and implementation of novel finite elements for specific purposes is a tedious and time consuming task, especially for nonlinear formulations. The automation of this process can help to speed up this process considerably since the generation of the final computer code can be accelerated by order of several magnitudes. This book provides the reader with the required knowledge needed to employ modern automatic tools like AceGen within solid mechanics in a successful way. It covers the range from the theoretical background, algorithmic treatments to many different applications. The book is written for advanced students in the engineering field and for researchers in educational and industrial environments.

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...

A New Accurate yet Simple Shear Flexible Triangular Plate Element with Linear Bending Strains

DEFF Research Database (Denmark)

Damkilde, Lars; Pedersen, Ronnie

2010-01-01

The paper describes a new shear flexible triangular element. The formulation is based on displacement interpolation of the transverse displacement of the midsurface and the rotations of the cross-sections, and the element is fully compatible. The basic principle is to use a so-called balanced...... interpolation so that the part of the shear strains that relates to the transverse displacement has the same polynomial variation as the part of the shear strains that relates to the rotations of the cross-section. This balanced interpolation in combination with complete polynomial interpolations prevents shear...... are virtually the same. The slightly incompatible formulation can be implemented directly into commercial codes....

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.

High accuracy 3D electromagnetic finite element analysis

International Nuclear Information System (INIS)

Nelson, Eric M.

1997-01-01

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

High accuracy 3D electromagnetic finite element analysis

International Nuclear Information System (INIS)

Nelson, E.M.

1996-01-01

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

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

Directory of Open Access Journals (Sweden)

Pavel A. Akimov

2017-12-01

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

Finite element simulation and testing of ISW CFRP anchorage

DEFF Research Database (Denmark)

Schmidt, Jacob Wittrup; Goltermann, Per; Hertz, Kristian Dahl

2013-01-01

is modelled in the 3D finite Element program ABAQUS, just as digital image correlation (DIC) testing was performed to verify the finite element simulation. Also a new optimized design was produced to ensure that the finite element simulation and anchorage behaviour correlated well. It is seen....... This paper presents a novel mechanical integrated sleeve wedge anchorage which seem very promising when perusing the scope of ultimate utilization of CFRP 8mm rods (with a tension capacity of approximately 140kN). Compression transverse to the CFRP is evaluated to prevent premature failure. The anchorage...

Hydrothermal analysis in engineering using control volume finite element method

CERN Document Server

Sheikholeslami, Mohsen

2015-01-01

Control volume finite element methods (CVFEM) bridge the gap between finite difference and finite element methods, using the advantages of both methods for simulation of multi-physics problems in complex geometries. In Hydrothermal Analysis in Engineering Using Control Volume Finite Element Method, CVFEM is covered in detail and applied to key areas of thermal engineering. Examples, exercises, and extensive references are used to show the use of the technique to model key engineering problems such as heat transfer in nanofluids (to enhance performance and compactness of energy systems),

A multiscale mortar multipoint flux mixed finite element method

KAUST Repository

Wheeler, Mary Fanett; Xue, Guangri; Yotov, Ivan

2012-01-01

In this paper, we develop a multiscale mortar multipoint flux mixed finite element method for second order elliptic problems. The equations in the coarse elements (or subdomains) are discretized on a fine grid scale by a multipoint flux mixed finite

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

Energy Technology Data Exchange (ETDEWEB)

Kim, S. [Purdue Univ., West Lafayette, IN (United States)

1994-12-31

Parallel iterative procedures based on domain decomposition techniques are defined and analyzed for the numerical solution of wave propagation by finite element and finite difference methods. For finite element methods, in a Lagrangian framework, an efficient way for choosing the algorithm parameter as well as the algorithm convergence are indicated. Some heuristic arguments for finding the algorithm parameter for finite difference schemes are addressed. Numerical results are presented to indicate the effectiveness of the methods.

Global-Local Finite Element Analysis of Bonded Single-Lap Joints

Science.gov (United States)

Kilic, Bahattin; Madenci, Erdogan; Ambur, Damodar R.

2004-01-01

Adhesively bonded lap joints involve dissimilar material junctions and sharp changes in geometry, possibly leading to premature failure. Although the finite element method is well suited to model the bonded lap joints, traditional finite elements are incapable of correctly resolving the stress state at junctions of dissimilar materials because of the unbounded nature of the stresses. In order to facilitate the use of bonded lap joints in future structures, this study presents a finite element technique utilizing a global (special) element coupled with traditional elements. The global element includes the singular behavior at the junction of dissimilar materials with or without traction-free surfaces.

FEWA: a Finite Element model of Water flow through Aquifers

International Nuclear Information System (INIS)

Yeh, G.T.; Huff, D.D.

1983-11-01

This report documents the implementation and demonstration of a Finite Element model of Water flow through Aquifers (FEWA). The particular features of FEWA are its versatility and flexibility to deal with as many real-world problems as possible. Point as well as distributed sources/sinks are included to represent recharges/pumpings and rainfall infiltrations. All sources/sinks can be transient or steady state. Prescribed hydraulic head on the Dirichlet boundaries and fluxes on Neumann or Cauchy boundaries can be time-dependent or constant. Source/sink strength over each element and node, hydraulic head at each Dirichlet boundary node, and flux at each boundary segment can vary independently of each other. Either completely confined or completely unconfined aquifers, or partially confined and partially unconfined aquifers can be dealt with effectively. Discretization of a compound region with very irregular curved boundaries is made easy by including both quadrilateral and triangular elements in the formulation. Large-field problems can be solved efficiently by including a pointwise iterative solution strategy as an optional alternative to the direct elimination solution method for the matrix equation approximating the partial differential equation of groundwater flow. FEWA also includes transient flow through confining leaky aquifers lying above and/or below the aquifer of interest. The model is verified against three simple cases to which analytical solutions are available. It is then demonstrated by two examples of how the model can be applied to heterogeneous and anisotropic aquifers with transient boundary conditions, time-dependent sources/sinks, and confining aquitards for a confined aquifer of variable thickness and for a free surface problem in an unconfined aquifer, respectively. 20 references, 25 figures, 8 tables

FEWA: a Finite Element model of Water flow through Aquifers

Energy Technology Data Exchange (ETDEWEB)

Yeh, G.T.; Huff, D.D.

1983-11-01

This report documents the implementation and demonstration of a Finite Element model of Water flow through Aquifers (FEWA). The particular features of FEWA are its versatility and flexibility to deal with as many real-world problems as possible. Point as well as distributed sources/sinks are included to represent recharges/pumpings and rainfall infiltrations. All sources/sinks can be transient or steady state. Prescribed hydraulic head on the Dirichlet boundaries and fluxes on Neumann or Cauchy boundaries can be time-dependent or constant. Source/sink strength over each element and node, hydraulic head at each Dirichlet boundary node, and flux at each boundary segment can vary independently of each other. Either completely confined or completely unconfined aquifers, or partially confined and partially unconfined aquifers can be dealt with effectively. Discretization of a compound region with very irregular curved boundaries is made easy by including both quadrilateral and triangular elements in the formulation. Large-field problems can be solved efficiently by including a pointwise iterative solution strategy as an optional alternative to the direct elimination solution method for the matrix equation approximating the partial differential equation of groundwater flow. FEWA also includes transient flow through confining leaky aquifers lying above and/or below the aquifer of interest. The model is verified against three simple cases to which analytical solutions are available. It is then demonstrated by two examples of how the model can be applied to heterogeneous and anisotropic aquifers with transient boundary conditions, time-dependent sources/sinks, and confining aquitards for a confined aquifer of variable thickness and for a free surface problem in an unconfined aquifer, respectively. 20 references, 25 figures, 8 tables.

Finite element simulation of laser transmission welding of dissimilar ...

African Journals Online (AJOL)

user

materials between polyvinylidene fluoride and titanium ... finite element (FE) thermal model is developed to simulate the laser ... Keywords: Laser transmission welding, Temperature field, Weld dimension, Finite element analysis, Thermal modeling. 1. .... 4) The heating phenomena due to the phase changes are neglected.

Finite element analysis of tibial fractures

DEFF Research Database (Denmark)

Wong, Christian Nai En; Mikkelsen, Mikkel Peter W; Hansen, Leif Berner

2010-01-01

Project. The data consisted of 21,219 3D elements with a cortical shell and a trabecular core. Three types of load of torsion, a direct lateral load and axial compression were applied. RESULTS: The finite element linear static analysis resulted in relevant fracture localizations and indicated relevant...

Generalized multiscale finite element method. Symmetric interior penalty coupling

KAUST Repository

Efendiev, Yalchin R.; Galvis, Juan; Lazarov, Raytcho D.; Moon, M.; Sarkis, Marcus V.

2013-01-01

Motivated by applications to numerical simulations of flows in highly heterogeneous porous media, we develop multiscale finite element methods for second order elliptic equations. We discuss a multiscale model reduction technique in the framework of the discontinuous Galerkin finite element method. We propose two different finite element spaces on the coarse mesh. The first space is based on a local eigenvalue problem that uses an interior weighted L2-norm and a boundary weighted L2-norm for computing the "mass" matrix. The second choice is based on generation of a snapshot space and subsequent selection of a subspace of a reduced dimension. The approximation with these multiscale spaces is based on the discontinuous Galerkin finite element method framework. We investigate the stability and derive error estimates for the methods and further experimentally study their performance on a representative number of numerical examples. © 2013 Elsevier Inc.

Generalized multiscale finite element method. Symmetric interior penalty coupling

KAUST Repository

Efendiev, Yalchin R.

2013-12-01

Motivated by applications to numerical simulations of flows in highly heterogeneous porous media, we develop multiscale finite element methods for second order elliptic equations. We discuss a multiscale model reduction technique in the framework of the discontinuous Galerkin finite element method. We propose two different finite element spaces on the coarse mesh. The first space is based on a local eigenvalue problem that uses an interior weighted L2-norm and a boundary weighted L2-norm for computing the "mass" matrix. The second choice is based on generation of a snapshot space and subsequent selection of a subspace of a reduced dimension. The approximation with these multiscale spaces is based on the discontinuous Galerkin finite element method framework. We investigate the stability and derive error estimates for the methods and further experimentally study their performance on a representative number of numerical examples. © 2013 Elsevier Inc.

Finite Element Analysis of Circular Plate using SolidWorks

International Nuclear Information System (INIS)

Kang, Yeo Jin; Jhung, Myung Jo

2011-01-01

Circular plates are used extensively in mechanical engineering for nuclear reactor internal components. The examples in the reactor vessel internals are upper guide structure support plate, fuel alignment plate, lower support plate etc. To verify the structural integrity of these plates, the finite element analyses are performed, which require the development of the finite element model. Sometimes it is very costly and time consuming to make the model especially for the beginners who start their engineering job for the structural analysis, necessitating a simple method to develop the finite element model for the pursuing structural analysis. Therefore in this study, the input decks are generated for the finite element analysis of a circular plate as shown in Fig. 1, which can be used for the structural analysis such as modal analysis, response spectrum analysis, stress analysis, etc using the commercial program Solid Works. The example problems are solved and the results are included for analysts to perform easily the finite element analysis of the mechanical plate components due to various loadings. The various results presented in this study would be helpful not only for the benchmark calculations and results comparisons but also as a part of the knowledge management for the future generation of young designers, scientists and computer analysts

A multiscale mortar multipoint flux mixed finite element method

KAUST Repository

Wheeler, Mary Fanett

2012-02-03

In this paper, we develop a multiscale mortar multipoint flux mixed finite element method for second order elliptic problems. The equations in the coarse elements (or subdomains) are discretized on a fine grid scale by a multipoint flux mixed finite element method that reduces to cell-centered finite differences on irregular grids. The subdomain grids do not have to match across the interfaces. Continuity of flux between coarse elements is imposed via a mortar finite element space on a coarse grid scale. With an appropriate choice of polynomial degree of the mortar space, we derive optimal order convergence on the fine scale for both the multiscale pressure and velocity, as well as the coarse scale mortar pressure. Some superconvergence results are also derived. The algebraic system is reduced via a non-overlapping domain decomposition to a coarse scale mortar interface problem that is solved using a multiscale flux basis. Numerical experiments are presented to confirm the theory and illustrate the efficiency and flexibility of the method. © EDP Sciences, SMAI, 2012.

High accuracy 3D electromagnetic finite element analysis

International Nuclear Information System (INIS)

Nelson, E.M.

1997-01-01

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

finite element model for predicting residual stresses in shielded

African Journals Online (AJOL)

eobe

This paper investigates the prediction of residual stresses developed ... steel plates through Finite Element Model simulation and experiments. ... The experimental values as measured by the X-Ray diffractometer were of ... Based on this, it can be concluded that Finite Element .... Comparison of Residual Stresses from X.

Simultaneous triangularization

CERN Document Server

Radjavi, Heydar

2000-01-01

A collection of matrices is said to be triangularizable if there is an invertible matrix S such that S1 AS is upper triangular for every A in the collection. This generalization of commutativity is the subject of many classical theorems due to Engel, Kolchin, Kaplansky, McCoy and others. The concept has been extended to collections of bounded linear operators on Banach spaces: such a collection is defined to be triangularizable if there is a maximal chain of subspaces of the Banach space, each of which is invariant under every member of the collection. Most of the classical results have been generalized to compact operators, and there are also recent theorems in the finite-dimensional case. This book is the first comprehensive treatment of triangularizability in both the finite and infinite-dimensional cases. It contains numerous very recent results and new proofs of many of the classical theorems. It provides a thorough background for research in both the linear-algebraic and operator-theoretic aspects of tr...

Finite-Element Modeling of Timber Joints with Punched Metal Plate Fasteners

DEFF Research Database (Denmark)

Ellegaard, Peter

2006-01-01

The focus of this paper is to describe the idea and the theory behind a finite-element model developed for analysis of timber trusses with punched metal plate fasteners (nail plates). The finite-element model includes the semirigid and nonlinear behavior of the joints (nonlinear nail and plate...... elements) and contact between timber beams, if any (bilinear contact elements). The timber beams have linear-elastic properties. The section forces needed for design of the joints are given directly by the finite-element model, since special elements are used to model the nail groups and the nail plate...... the behavior of the joints very well at lower load levels. At higher load levels the stiffness is overestimated due to development of cracks in the timber and the linear-elastic timber properties in the finite-element model....

Finite element analysis of inelastic structural behavior

International Nuclear Information System (INIS)

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

1977-01-01

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

Numerical experiment on finite element method for matching data

International Nuclear Information System (INIS)

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

1993-03-01

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

Analytical and finite element modeling of grounding systems

Energy Technology Data Exchange (ETDEWEB)

Luz, Mauricio Valencia Ferreira da [University of Santa Catarina (UFSC), Florianopolis, SC (Brazil)], E-mail: mauricio@grucad.ufsc.br; Dular, Patrick [University of Liege (Belgium). Institut Montefiore], E-mail: Patrick.Dular@ulg.ac.be

2007-07-01

Grounding is the art of making an electrical connection to the earth. This paper deals with the analytical and finite element modeling of grounding systems. An electrokinetic formulation using a scalar potential can benefit from floating potentials to define global quantities such as electric voltages and currents. The application concerns a single vertical grounding with one, two and three-layer soil, where the superior extremity stays in the surface of the soil. This problem has been modeled using a 2D axi-symmetric electrokinetic formulation. The grounding resistance obtained by finite element method is compared with the analytical one for one-layer soil. With the results of this paper it is possible to show that finite element method is a powerful tool in the analysis of the grounding systems in low frequencies. (author)

Robust mixed finite element methods to deal with incompressibility in finite strain in an industrial framework

International Nuclear Information System (INIS)

Al-Akhrass, Dina

2014-01-01

Simulations in solid mechanics exhibit several difficulties, as dealing with incompressibility, with nonlinearities due to finite strains, contact laws, or constitutive laws. The basic motivation of our work is to propose efficient finite element methods capable of dealing with incompressibility in finite strain context, and using elements of low order. During the three last decades, many approaches have been proposed in the literature to overcome the incompressibility problem. Among them, mixed formulations offer an interesting theoretical framework. In this work, a three-field mixed formulation (displacement, pressure, volumetric strain) is investigated. In some cases, this formulation can be condensed in a two-field (displacement - pressure) mixed formulation. However, it is well-known that the discrete problem given by the Galerkin finite element technique, does not inherit the 'inf-sup' stability condition from the continuous problem. Hence, the interpolation orders in displacement and pressure have to be chosen in a way to satisfy the Brezzi-Babuska stability conditions when using Galerkin approaches. Interpolation orders must be chosen so as to satisfy this condition. Two possibilities are considered: to use stable finite element satisfying this requirement, or to use finite element that does not satisfy this condition, and to add terms stabilizing the FE Galerkin formulation. The latter approach allows the use of equal order interpolation. In this work, stable finite element P2/P1 and P2/P1/P1 are used as reference, and compared to P1/P1 and P1/P1/P1 formulations stabilized with a bubble function or with a VMS method (Variational Multi-Scale) based on a sub-grid-space orthogonal to the FE space. A finite strain model based on logarithmic strain is selected. This approach is extended to three and two field mixed formulations with stable or stabilized elements. These approaches are validated on academic cases and used on industrial cases. (author)

Non-Linear Three Dimensional Finite Elements for Composite Concrete Structures

Directory of Open Access Journals (Sweden)

O. Kohnehpooshi

Full Text Available Abstract The current investigation focused on the development of effective and suitable modelling of reinforced concrete component with and without strengthening. The modelling includes physical and constitutive models. New interface elements have been developed, while modified constitutive law have been applied and new computational algorithm is utilised. The new elements are the Truss-link element to model the interaction between concrete and reinforcement bars, the interface element between two plate bending elements and the interface element to represent the interfacial behaviour between FRP, steel plates and concrete. Nonlinear finite-element (FE codes were developed with pre-processing. The programme was written using FORTRAN language. The accuracy and efficiency of the finite element programme were achieved by analyzing several examples from the literature. The application of the 3D FE code was further enhanced by carrying out the numerical analysis of the three dimensional finite element analysis of FRP strengthened RC beams, as well as the 3D non-linear finite element analysis of girder bridge. Acceptable distributions of slip, deflection, stresses in the concrete and FRP plate have also been found. These results show that the new elements are effective and appropriate to be used for structural component modelling.

Finite elements methods in mechanics

CERN Document Server

Eslami, M Reza

2014-01-01

This book covers all basic areas of mechanical engineering, such as fluid mechanics, heat conduction, beams, and elasticity with detailed derivations for the mass, stiffness, and force matrices. It is especially designed to give physical feeling to the reader for finite element approximation by the introduction of finite elements to the elevation of elastic membrane. A detailed treatment of computer methods with numerical examples are provided. In the fluid mechanics chapter, the conventional and vorticity transport formulations for viscous incompressible fluid flow with discussion on the method of solution are presented. The variational and Galerkin formulations of the heat conduction, beams, and elasticity problems are also discussed in detail. Three computer codes are provided to solve the elastic membrane problem. One of them solves the Poisson’s equation. The second computer program handles the two dimensional elasticity problems, and the third one presents the three dimensional transient heat conducti...

A finite element conjugate gradient FFT method for scattering

Science.gov (United States)

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

1991-01-01

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

SEACAS Theory Manuals: Part III. Finite Element Analysis in Nonlinear Solid Mechanics

Energy Technology Data Exchange (ETDEWEB)

Laursen, T.A.; Attaway, S.W.; Zadoks, R.I.

1999-03-01

This report outlines the application of finite element methodology to large deformation solid mechanics problems, detailing also some of the key technological issues that effective finite element formulations must address. The presentation is organized into three major portions: first, a discussion of finite element discretization from the global point of view, emphasizing the relationship between a virtual work principle and the associated fully discrete system, second, a discussion of finite element technology, emphasizing the important theoretical and practical features associated with an individual finite element; and third, detailed description of specific elements that enjoy widespread use, providing some examples of the theoretical ideas already described. Descriptions of problem formulation in nonlinear solid mechanics, nonlinear continuum mechanics, and constitutive modeling are given in three companion reports.

Finite element approximation to the even-parity transport equation

International Nuclear Information System (INIS)

Lewis, E.E.

1981-01-01

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

Linear finite element method for one-dimensional diffusion problems

Energy Technology Data Exchange (ETDEWEB)

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

2011-07-01

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

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...

Development of a partitioned finite volume-finite element fluid-structure interaction scheme for strongly-coupled problems

CSIR Research Space (South Africa)

Suliman, Ridhwaan

2012-07-01

Full Text Available -linear deformations are accounted for. As will be demonstrated, the finite volume approach exhibits similar disad- vantages to the linear Q4 finite element formulation when undergoing bending. An enhanced finite volume approach is discussed and compared with finite...

The finite element analysis program MSC Marc/Mentat a first introduction

CERN Document Server

Öchsner, Andreas

2016-01-01

Based on simple examples, this book offers a short introduction to the general-purpose finite element program MSC Marc, a specialized program for non-linear problems (implicit solver) distributed by the MSC Software Corporation, which is commonly used in academia and industry. Today the documentation of all finite element programs includes a variety of step-by-step examples of differing complexity, and in addition, all software companies offer professional workshops on different topics. As such, rather than competing with these, the book focuses on providing simple examples, often single-element problems, which can easily be related to the theory that is discussed in finite element lectures. This makes it an ideal companion book to classical introductory courses on the finite element method.

Torque calculation in the induction motor with the finite element method; Calculo del par en el motor de induccion con el metodo del elemento finito

Energy Technology Data Exchange (ETDEWEB)

Castillo Diaz, Ramon

2002-06-15

In this work the method of the finite element is applied to the bi-dimensional analysis of the induction motor in operation in steady state, excited by sine sources of laminar currents and sine sources of voltage. The analysis is focused mainly in the calculation of the electromagnetic torque. The topics of electromagnetic theory are covered and in an idealized model of the induction motor, analytically and numerically with the method of the finite element, in the variant method of Galerkin, the vectorial potential and the torque are calculated. The results obtained with the analytical and numerical methods are compared. Three formulations are developed to calculate the torque with the method of the finite element, using triangular elements of first order, based in the equation of force of Lorentz, the Maxwell tensor and the principle of the virtual work. Finally, a motor of induction of real characteristics is simulated, assuming it is connected to a three-phase voltage source. In this motor it is analyzed the convergence and the evolution in the results obtained of the torque with different discretions, and the torque-velocity performance curve is calculated. [Spanish] En este trabajo se aplica el metodo del elemento finito al analisis bidimensional del motor de induccion en operacion en estado estable, excitado por fuentes de corriente laminar senoidales y fuentes de voltaje senoidales. El analisis se enfoca principalmente en el calculo del par electromagnetico. Se tratan los topicos de teoria electromagnetica involucrados y en un modelo idealizado del motor de induccion, se calculan analitica y numericamente con el metodo del elemento finito, en la variante metodo de Galerkin, el potencial vectorial y el par. Se comparan resultados obtenidos con los metodos analiticos y numericos. Se desarrollan tres formulaciones para calcular el par con el metodo del elemento finito, utilizando elementos triangulares de primer orden, basadas en la ecuacion de fuerza de

A finite element thermohydrodynamic analyis of profile bore bearing

International Nuclear Information System (INIS)

Shah Nor bin Basri

1994-01-01

A finite element-based method is presented for analysing the thermohydrodynamic (THD) behaviour of profile bore bearing. A variational statement for the governing equation is derived and used to formulate a non-linear quadrilateral finite element of serendipity family. The predicted behaviour is compared with experimental evidence where possible and favorable correlation is obtained

Hualien forced vibration calculation with a finite element model

International Nuclear Information System (INIS)

Wang, F.; Gantenbein, F.; Nedelec, M.; Duretz, Ch.

1995-01-01

The forced vibration tests of the Hualien mock-up were useful to validate finite element models developed for soil-structure interaction. In this paper the two sets of tests with and without backfill were analysed. the methods used are based on finite element modeling for the soil. Two approaches were considered: calculation of soil impedance followed by the calculation of the transfer functions with a model taking into account the superstructure and the impedance; direct calculation of the soil-structure transfer functions, with the soil and the structure being represented in the same model by finite elements. Blind predictions and post-test calculations are presented and compared with the test results. (author). 4 refs., 8 figs., 2 tabs

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.

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

Directory of Open Access Journals (Sweden)

Rajeev Kumar

2008-01-01

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

Finite element model updating of concrete structures based on imprecise probability

Science.gov (United States)

Biswal, S.; Ramaswamy, A.

2017-09-01

Imprecise probability based methods are developed in this study for the parameter estimation, in finite element model updating for concrete structures, when the measurements are imprecisely defined. Bayesian analysis using Metropolis Hastings algorithm for parameter estimation is generalized to incorporate the imprecision present in the prior distribution, in the likelihood function, and in the measured responses. Three different cases are considered (i) imprecision is present in the prior distribution and in the measurements only, (ii) imprecision is present in the parameters of the finite element model and in the measurement only, and (iii) imprecision is present in the prior distribution, in the parameters of the finite element model, and in the measurements. Procedures are also developed for integrating the imprecision in the parameters of the finite element model, in the finite element software Abaqus. The proposed methods are then verified against reinforced concrete beams and prestressed concrete beams tested in our laboratory as part of this study.

A three-dimensional cell-based smoothed finite element method for elasto-plasticity

International Nuclear Information System (INIS)

Lee, Kye Hyung; Im, Se Yong; Lim, Jae Hyuk; Sohn, Dong Woo

2015-01-01

This work is concerned with a three-dimensional cell-based smoothed finite element method for application to elastic-plastic analysis. The formulation of smoothed finite elements is extended to cover elastic-plastic deformations beyond the classical linear theory of elasticity, which has been the major application domain of smoothed finite elements. The finite strain deformations are treated with the aid of the formulation based on the hyperelastic constitutive equation. The volumetric locking originating from the nearly incompressible behavior of elastic-plastic deformations is remedied by relaxing the volumetric strain through the mean value. The comparison with the conventional finite elements demonstrates the effectiveness and accuracy of the present approach.

A three-dimensional cell-based smoothed finite element method for elasto-plasticity

Energy Technology Data Exchange (ETDEWEB)

Lee, Kye Hyung; Im, Se Yong [KAIST, Daejeon (Korea, Republic of); Lim, Jae Hyuk [KARI, Daejeon (Korea, Republic of); Sohn, Dong Woo [Korea Maritime and Ocean University, Busan (Korea, Republic of)

2015-02-15

This work is concerned with a three-dimensional cell-based smoothed finite element method for application to elastic-plastic analysis. The formulation of smoothed finite elements is extended to cover elastic-plastic deformations beyond the classical linear theory of elasticity, which has been the major application domain of smoothed finite elements. The finite strain deformations are treated with the aid of the formulation based on the hyperelastic constitutive equation. The volumetric locking originating from the nearly incompressible behavior of elastic-plastic deformations is remedied by relaxing the volumetric strain through the mean value. The comparison with the conventional finite elements demonstrates the effectiveness and accuracy of the present approach.

Critical thickness for Nb nanofilm on sapphire substrate: a critical analysis using finite element method

International Nuclear Information System (INIS)

Kumar, Arun; Subramaniam, Anandh

2009-01-01

Full text: On growth beyond critical thickness, interfacial misfit dislocations partially relax the misfit strains, in epitaxially grown nanofilms. In this study the stress state and growth of nanofilms is simulated using Finite Element Method (FEM); by imposing stress-free strains, corresponding to the lattice mismatch between Nb nanofilm and Sapphire substrate. On growth of the Nb nanofilm, a triangular network of edge misfit dislocations nucleates at the (0001) Al2ο3 || (111) Nb , interface. Using a combined simulation of a coherently strained nanofilm and an edge dislocation, the equilibrium criterion for the nucleation of an edge dislocation is determined. Theoretical analyses in literature use only the component of the Burger's vector parallel to the interface, which is an erroneous description of the stress state and energetics of the system. In this investigation the full interfacial edge dislocation is simulated using standard commercially available software and comparisons are made with results available in literature to bring out the utility of the methodology

On Using Particle Finite Element for Hydrodynamics Problems Solving

Directory of Open Access Journals (Sweden)

E. V. Davidova

2015-01-01

Full Text Available The aim of the present research is to develop software for the Particle Finite Element Method (PFEM and its verification on the model problem of viscous incompressible flow simulation in a square cavity. The Lagrangian description of the medium motion is used: the nodes of the finite element mesh move together with the fluid that allows to consider them as particles of the medium. Mesh cells deform when in time-stepping procedure, so it is necessary to reconstruct the mesh to provide stability of the finite element numerical procedure.Meshing algorithm allows us to obtain the mesh, which satisfies the Delaunay criteria: it is called \\the possible triangles method". This algorithm is based on the well-known Fortune method of Voronoi diagram constructing for a certain set of points in the plane. The graphical representation of the possible triangles method is shown. It is suitable to use generalization of Delaunay triangulation in order to construct meshes with polygonal cells in case of multiple nodes close to be lying on the same circle.The viscous incompressible fluid flow is described by the Navier | Stokes equations and the mass conservation equation with certain initial and boundary conditions. A fractional steps method, which allows us to avoid non-physical oscillations of the pressure, provides the timestepping procedure. Using the finite element discretization and the Bubnov | Galerkin method allows us to carry out spatial discretization.For form functions calculation of finite element mesh with polygonal cells, \

FINITE ELEMENT ANALYSIS OF ELEMENT ANALYSIS OF A FREE ...

African Journals Online (AJOL)

eobe

the stairs and to compare the finite element ana ... tual three dimensional behavior of the stair slab system. ..... due to its close relation of output with the propo .... flights. It is best not to consider any open well when .... thermodynamics of solids.

Nonlinear Legendre Spectral Finite Elements for Wind Turbine Blade Dynamics: Preprint

Energy Technology Data Exchange (ETDEWEB)

Wang, Q.; Sprague, M. A.; Jonkman, J.; Johnson, N.

2014-01-01

This paper presents a numerical implementation and examination of new wind turbine blade finite element model based on Geometrically Exact Beam Theory (GEBT) and a high-order spectral finite element method. The displacement-based GEBT is presented, which includes the coupling effects that exist in composite structures and geometric nonlinearity. Legendre spectral finite elements (LSFEs) are high-order finite elements with nodes located at the Gauss-Legendre-Lobatto points. LSFEs can be an order of magnitude more efficient that low-order finite elements for a given accuracy level. Interpolation of the three-dimensional rotation, a major technical barrier in large-deformation simulation, is discussed in the context of LSFEs. It is shown, by numerical example, that the high-order LSFEs, where weak forms are evaluated with nodal quadrature, do not suffer from a drawback that exists in low-order finite elements where the tangent-stiffness matrix is calculated at the Gauss points. Finally, the new LSFE code is implemented in the new FAST Modularization Framework for dynamic simulation of highly flexible composite-material wind turbine blades. The framework allows for fully interactive simulations of turbine blades in operating conditions. Numerical examples showing validation and LSFE performance will be provided in the final paper.

Finite element simulations of two rock mechanics tests

International Nuclear Information System (INIS)

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

1986-04-01

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

Explicit formulation of an anisotropic Allman/DKT 3-node thin triangular flat shell elements

Science.gov (United States)

Ertas, A.; Krafcik, J. T.; Ekwaro-Osire, S.

A simple, explicit formulation of the stiffness matrix for an anisotropic, 3-node, thin triangular, flat shell element in global coordinates is presented. An Allman triangle is used for membrane stiffness. The membrane stiffness matrix is explicitly derived by applying an Allman transformation to a Felippa 6-node linear strain triangle (LST). Bending stiffness is incorporated by the use of a discrete Kirchhoff triangle (DKT) bending triangle. Stiffness terms resulting from anisotropic membrane-bending coupling are included by integrating, in area coordinates, membrane and bending strain-displacement matrices.

A simple finite element method for linear hyperbolic problems

International Nuclear Information System (INIS)

Mu, Lin; Ye, Xiu

2017-01-01

Here, we introduce a simple finite element method for solving first order hyperbolic equations with easy implementation and analysis. Our new method, with a symmetric, positive definite system, is designed to use discontinuous approximations on finite element partitions consisting of arbitrary shape of polygons/polyhedra. Error estimate is established. Extensive numerical examples are tested that demonstrate the robustness and flexibility of the method.

Finite element computation of plasma equilibria

International Nuclear Information System (INIS)

Rivier, M.

1977-01-01

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

Flow Applications of the Least Squares Finite Element Method

Science.gov (United States)

Jiang, Bo-Nan

1998-01-01

The main thrust of the effort has been towards the development, analysis and implementation of the least-squares finite element method (LSFEM) for fluid dynamics and electromagnetics applications. In the past year, there were four major accomplishments: 1) special treatments in computational fluid dynamics and computational electromagnetics, such as upwinding, numerical dissipation, staggered grid, non-equal order elements, operator splitting and preconditioning, edge elements, and vector potential are unnecessary; 2) the analysis of the LSFEM for most partial differential equations can be based on the bounded inverse theorem; 3) the finite difference and finite volume algorithms solve only two Maxwell equations and ignore the divergence equations; and 4) the first numerical simulation of three-dimensional Marangoni-Benard convection was performed using the LSFEM.

Investigation of Shear Stud Performance in Flat Plate Using Finite Element Analysis

Directory of Open Access Journals (Sweden)

T.S. Viswanathan

2014-09-01

Full Text Available Three types of shear stud arrangement, respectively featuring an orthogonal, a radial and a critical perimeter pattern, were evaluated numerically. A numerical investigation was conducted using the finite element software ABAQUS to evaluate their ability to resist punching shear in a flat plate. The finite element analysis here is an application of the nonlinear analysis of reinforced concrete structures using three-dimensional solid finite elements. The nonlinear characteristics of concrete were achieved by employing the concrete damaged plasticity model in the finite element program. Transverse shear stress was evaluated using finite element analysis in terms of shear stress distribution for flat plate with and without shear stud reinforcement. The model predicted that shear studs placed along the critical perimeter are more effective compared to orthogonal and radial patterns.

Sacroiliac joint stability: Finite element analysis of implant number, orientation, and superior implant length.

Science.gov (United States)

Lindsey, Derek P; Kiapour, Ali; Yerby, Scott A; Goel, Vijay K

2018-03-18

To analyze how various implants placement variables affect sacroiliac (SI) joint range of motion. An experimentally validated finite element model of the lumbar spine and pelvis was used to simulate a fusion of the SI joint using various placement configurations of triangular implants (iFuse Implant System ® ). Placement configurations were varied by changing implant orientation, superior implant length, and number of implants. The range of motion of the SI joint was calculated using a constant moment of 10 N-m with a follower load of 400 N. The changes in motion were compared between the treatment groups to assess how the different variables affected the overall motion of the SI joint. Transarticular placement of 3 implants with superior implants that end in the middle of the sacrum resulted in the greatest reduction in range of motion (flexion/extension = 73%, lateral bending = 42%, axial rotation = 72%). The range of motions of the SI joints were reduced with use of transarticular orientation (9%-18%) when compared with an inline orientation. The use of a superior implant that ended mid-sacrum resulted in median reductions of (8%-14%) when compared with a superior implant that ended in the middle of the ala. Reducing the number of implants, resulted in increased SI joint range of motions for the 1 and 2 implant models of 29%-133% and 2%-39%, respectively, when compared with the 3 implant model. Using a validated finite element model we demonstrated that placement of 3 implants across the SI joint using a transarticular orientation with superior implant reaching the sacral midline resulted in the most stable construct. Additional clinical studies may be required to confirm these results.

Aspects of Finite Element Simulation of Axi-Symmetric Hydromechanical Deep Drawing

DEFF Research Database (Denmark)

Jensen, Morten Rikard; Olovsson, Lars; Danckert, Joachim

1999-01-01

A new approach for the Finite Element modelling of the hydromechanical deep drawing process is evaluated. In the model a Finite Difference approximation of Reynold’s equation is solved for the fluid flow between the blank and the draw die in the flange region. The approach is implemented...... as a contact algorithm in an explicit Finite Element code, Exhale2D. The developed model is verified against experiments and good agreement is obtained. It is concluded that the developed model is a promising approach for simulating the hydromechanical deep drawing process using the Finite Element Method....

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...

A General Finite Element Scheme for Limit State Analysis and Optimization

DEFF Research Database (Denmark)

Damkilde, Lars

1999-01-01

Limit State analysis which is based on a perfect material behaviour is used in many different applications primarily within Structural Engineering and Geotechnics. The calculation methods have not reached the same level of automation such as Finite Element Analysis for elastic structures....... The computer based systems are more ad hoc based and are typically not well-integrated with pre- and postprocessors well-known from commercial Finite Element codes.A finite element based formulation of limit state analysis is presented which allows an easy integration with standard Finite Element codes...... for elastic analysis. In this way the user is able to perform a limit state analysis on the same model used for elastic analysis only adding data for the yield surface.The method is based on the lower-bound theorem and uses stress-based elements with a linearized yield surface. The mathematical problem...

Finite element modeling of piezoelectric elements with complex electrode configuration

International Nuclear Information System (INIS)

Paradies, R; Schläpfer, B

2009-01-01

It is well known that the material properties of piezoelectric materials strongly depend on the state of polarization of the individual element. While an unpolarized material exhibits mechanically isotropic material properties in the absence of global piezoelectric capabilities, the piezoelectric material properties become transversally isotropic with respect to the polarization direction after polarization. Therefore, for evaluating piezoelectric elements the material properties, including the coupling between the mechanical and the electromechanical behavior, should be addressed correctly. This is of special importance for the micromechanical description of piezoelectric elements with interdigitated electrodes (IDEs). The best known representatives of this group are active fiber composites (AFCs), macro fiber composites (MFCs) and the radial field diaphragm (RFD), respectively. While the material properties are available for a piezoelectric wafer with a homogeneous polarization perpendicular to its plane as postulated in the so-called uniform field model (UFM), the same information is missing for piezoelectric elements with more complex electrode configurations like the above-mentioned ones with IDEs. This is due to the inhomogeneous field distribution which does not automatically allow for the correct assignment of the material, i.e. orientation and property. A variation of the material orientation as well as the material properties can be accomplished by including the polarization process of the piezoelectric transducer in the finite element (FE) simulation prior to the actual load case to be investigated. A corresponding procedure is presented which automatically assigns the piezoelectric material properties, e.g. elasticity matrix, permittivity, and charge vector, for finite element models (FEMs) describing piezoelectric transducers according to the electric field distribution (field orientation and strength) in the structure. A corresponding code has been

Engineering computation of structures the finite element method

CERN Document Server

Neto, Maria Augusta; Roseiro, Luis; Cirne, José; Leal, Rogério

2015-01-01

This book presents theories and the main useful techniques of the Finite Element Method (FEM), with an introduction to FEM and many case studies of its use in engineering practice. It supports engineers and students to solve primarily linear problems in mechanical engineering, with a main focus on static and dynamic structural problems. Readers of this text are encouraged to discover the proper relationship between theory and practice, within the finite element method: Practice without theory is blind, but theory without practice is sterile. Beginning with elasticity basic concepts and the classical theories of stressed materials, the work goes on to apply the relationship between forces, displacements, stresses and strains on the process of modeling, simulating and designing engineered technical systems. Chapters discuss the finite element equations for static, eigenvalue analysis, as well as transient analyses. Students and practitioners using commercial FEM software will find this book very helpful. It us...

On the interference rejection capabilities of triangular antenna array for cellular base stations

KAUST Repository

Atat, Rachad; Shakir, Muhammad; Alouini, Mohamed-Slim

2012-01-01

In this paper, we present the performance analysis of the triangular antenna arrays in terms of the interference rejection capability. In this context, we derive an expression to calculate the spatial interference suppression coefficient for the triangular antenna array with variable number of antenna elements. The performance of the triangular antenna array has been compared with the circular antenna array with respect to interference suppression performance, steering beam pattern, beamwidth and directivity. Simulation results show that the triangular array with large number of elements produces a sharper beamwidth and better interference suppression performance than the circular antenna array. © 2012 IEEE.

On the interference rejection capabilities of triangular antenna array for cellular base stations

KAUST Repository

Atat, Rachad

2012-03-01

In this paper, we present the performance analysis of the triangular antenna arrays in terms of the interference rejection capability. In this context, we derive an expression to calculate the spatial interference suppression coefficient for the triangular antenna array with variable number of antenna elements. The performance of the triangular antenna array has been compared with the circular antenna array with respect to interference suppression performance, steering beam pattern, beamwidth and directivity. Simulation results show that the triangular array with large number of elements produces a sharper beamwidth and better interference suppression performance than the circular antenna array. © 2012 IEEE.

Modelling drawbeads with finite elements and verification

NARCIS (Netherlands)

Carleer, B.D.; Carleer, B.D.; Vreede, P.T.; Vreede, P.T.; Louwes, M.F.M.; Louwes, M.F.M.; Huetink, Han

1994-01-01

Drawbeads are commonly used in deep drawing processes to control the flow of the blank during the forming operation. In finite element simulations of deep drawing the drawbead geometries are seldom included because of the small radii; because of these small radii a very large number of elements is

Essentials of the finite element method for mechanical and structural engineers

CERN Document Server

Pavlou, Dimitrios G

2015-01-01

Fundamental coverage, analytic mathematics, and up-to-date software applications are hard to find in a single text on the finite element method (FEM). Dimitrios Pavlou's Essentials of the Finite Element Method: For Structural and Mechanical Engineers makes the search easier by providing a comprehensive but concise text for those new to FEM, or just in need of a refresher on the essentials. Essentials of the Finite Element Method explains the basics of FEM, then relates these basics to a number of practical engineering applications. Specific topics covered include linear spring elements, bar elements, trusses, beams and frames, heat transfer, and structural dynamics. Throughout the text, readers are shown step-by-step detailed analyses for finite element equations development. The text also demonstrates how FEM is programmed, with examples in MATLAB, CALFEM, and ANSYS allowing readers to learn how to develop their own computer code. Suitable for everyone from first-time BSc/MSc students to practicing mechanic...

A partly and fully cracked triangular XFEM element for modeling cohesive fracture

DEFF Research Database (Denmark)

Mougaard, Jens Falkenskov; Poulsen, Peter Noe; Nielsen, Leif Otto

2011-01-01

This paper discusses the build‐up of a partly cracked cohesive crack tip element. The crack tip element is based on the principles of the eXtended Finite Element Method (XFEM) and is of Linear Strain Triangle (LST) type. The composition of the enrichment has been in focus to achieve as complete...... as a fully cracked element with a few restrictions in the displacement field. The performance of the developed element has been tested in three examples. One example is an infinite sheet with an initial flaw in pure tension, where a semianalytical solution exists. The two other examples are the two benchmark...

A finite element solution method for quadrics parallel computer

International Nuclear Information System (INIS)

Zucchini, A.

1996-08-01

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

Evaluation of Concrete Cylinder Tests Using Finite Elements

DEFF Research Database (Denmark)

Saabye Ottosen, Niels

1984-01-01

Nonlinear axisymmetric finite element analyses are performed on the uniaxial compressive test of concrete cylinders. The models include thick steel loading plates, and cylinders with height‐to‐diameter ratios (h/d) ranging from 1‐3 are treated. A simple constitutive model of the concrete is emplo......Nonlinear axisymmetric finite element analyses are performed on the uniaxial compressive test of concrete cylinders. The models include thick steel loading plates, and cylinders with height‐to‐diameter ratios (h/d) ranging from 1‐3 are treated. A simple constitutive model of the concrete...... uniaxial strength the use of geometrically matched loading plates seems to be advantageous. Finally, it is observed that for variations of the element size within limits otherwise required to obtain a realistic analysis, the results are insensitive to the element size....

A semi-analytical finite element process for nonlinear elastoplastic analysis of arbitrarily loaded shells of revolution

International Nuclear Information System (INIS)

Rensch, H.J.; Wunderlich, W.

1981-01-01

The governing partial differential equations used are valid for small strains and moderate rotations. Plasticity relations are based on J 2 -flow theory. In order to eliminate the circumferential coordinate, the loading as well as the unkown quantities are expanded in Fourier series in the circumferential direction. The nonlinear terms due to moderate rotations and plastic deformations are treated as pseudo load quantities. In this way, the governing equations can be reduced to uncoupled systems of first-order ordinary differential equations in the meridional direction. They are then integrated over a shell segment via a matrix series expansion. The resulting element transfer matrices are transformed into stiffness matrices, and for the analysis of the total structure the finite element method is employed. Thus, arbitrary branching of the shell geometry is possible. Compared to two-dimensional approximations, the major advantage of the semi-analytical procedure is that the structural stiffness matrix usually has a small handwidth, resulting in shorter computer run times. Moreover, its assemblage and triangularization has to be carried out only once bacause all nonlinear effects are treated as initial loads. (orig./HP)

Finite element analysis of structures through unified formulation

CERN Document Server

Carrera, Erasmo; Petrolo, Marco; Zappino, Enrico

2014-01-01

The finite element method (FEM) is a computational tool widely used to design and analyse  complex structures. Currently, there are a number of different approaches to analysis using the FEM that vary according to the type of structure being analysed: beams and plates may use 1D or 2D approaches, shells and solids 2D or 3D approaches, and methods that work for one structure are typically not optimized to work for another. Finite Element Analysis of Structures Through Unified Formulation deals with the FEM used for the analysis of the mechanics of structures in the case of linear elasticity. The novelty of this book is that the finite elements (FEs) are formulated on the basis of a class of theories of structures known as the Carrera Unified Formulation (CUF). It formulates 1D, 2D and 3D FEs on the basis of the same ''fundamental nucleus'' that comes from geometrical relations and Hooke''s law, and presents both 1D and 2D refined FEs that only have displacement variables as in 3D elements. It also covers 1D...

Exponentially-convergent Monte Carlo via finite-element trial spaces

International Nuclear Information System (INIS)

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

2011-01-01

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

Finite element simulation of ironing process under warm conditions

Directory of Open Access Journals (Sweden)

Swadesh Kumar Singh

2014-01-01

Full Text Available Metal forming is one of the most important steps in manufacturing of a large variety of products. Ironing in deep drawing is done by adjusting the clearance between the punch and the die and allow the material flow over the punch. In the present investigation effect of extent of ironing behavior on the characteristics of the product like thickness distribution with respect to temperature was studied. With the help of finite element simulation using explicit finite element code LS-DYNA the stress in the drawn cup were predicted in the drawn cup. To increase the accuracy in the simulation process, numbers of integration points were increased in the thickness direction and it was found that there is very close prediction of finite element results to that of experimental ones.

Finite element method analysis of band gap and transmission of two-dimensional metallic photonic crystals at terahertz frequencies.

Science.gov (United States)

Degirmenci, Elif; Landais, Pascal

2013-10-20

Photonic band gap and transmission characteristics of 2D metallic photonic crystals at THz frequencies have been investigated using finite element method (FEM). Photonic crystals composed of metallic rods in air, in square and triangular lattice arrangements, are considered for transverse electric and transverse magnetic polarizations. The modes and band gap characteristics of metallic photonic crystal structure are investigated by solving the eigenvalue problem over a unit cell of the lattice using periodic boundary conditions. A photonic band gap diagram of dielectric photonic crystal in square lattice array is also considered and compared with well-known plane wave expansion results verifying our FEM approach. The photonic band gap designs for both dielectric and metallic photonic crystals are consistent with previous studies obtained by different methods. Perfect match is obtained between photonic band gap diagrams and transmission spectra of corresponding lattice structure.

Analysis of Tube Drawing Process – A Finite Element Approach ...

African Journals Online (AJOL)

In this paper the effect of die semi angle on drawing load in cold tube drawing has been investigated numerically using the finite element method. The equation governing the stress distribution was derived and solved using Galerkin finite element method. An isoparametric formulation for the governing equation was utilized ...

COMPUTER EXPERIMENTS WITH FINITE ELEMENTS OF HIGHER ORDER

Directory of Open Access Journals (Sweden)

Khomchenko A.

2017-12-01

Full Text Available The paper deals with the problem of constructing the basic functions of a quadrilateral finite element of the fifth order by the means of the computer algebra system Maple. The Lagrangian approximation of such a finite element contains 36 nodes: 20 nodes perimeter and 16 internal nodes. Alternative models with reduced number of internal nodes are considered. Graphs of basic functions and cognitive portraits of lines of zero level are presented. The work is aimed at studying the possibilities of using modern information technologies in the teaching of individual mathematical disciplines.

Fourier analysis of finite element preconditioned collocation schemes

Science.gov (United States)

Deville, Michel O.; Mund, Ernest H.

1990-01-01

The spectrum of the iteration operator of some finite element preconditioned Fourier collocation schemes is investigated. The first part of the paper analyses one-dimensional elliptic and hyperbolic model problems and the advection-diffusion equation. Analytical expressions of the eigenvalues are obtained with use of symbolic computation. The second part of the paper considers the set of one-dimensional differential equations resulting from Fourier analysis (in the tranverse direction) of the 2-D Stokes problem. All results agree with previous conclusions on the numerical efficiency of finite element preconditioning schemes.

Stochastic Finite Elements in Reliability-Based Structural Optimization

DEFF Research Database (Denmark)

Sørensen, John Dalsgaard; Engelund, S.

Application of stochastic finite elements in structural optimization is considered. It is shown how stochastic fields modelling e.g. the modulus of elasticity can be discretized in stochastic variables and how a sensitivity analysis of the reliability of a structural system with respect to optimi......Application of stochastic finite elements in structural optimization is considered. It is shown how stochastic fields modelling e.g. the modulus of elasticity can be discretized in stochastic variables and how a sensitivity analysis of the reliability of a structural system with respect...

Modelling bucket excavation by finite element

Science.gov (United States)

Pecingina, O. M.

2015-11-01

Changes in geological components of the layers from lignite pits have an impact on the sustainability of the cup path elements and under the action of excavation force appear efforts leading to deformation of the entire assembly. Application of finite element method in the optimization of components leads to economic growth, to increase the reliability and durability of the studied machine parts thus the machine. It is obvious usefulness of knowledge the state of mechanical tensions that the designed piece or the assembly not to break under the action of tensions that must cope during operation. In the course of excavation work on all bucket cutting force components, the first coming into contact with the material being excavated cutting edge. Therefore in the study with finite element analysis is retained only cutting edge. To study the field of stress and strain on the cutting edge will be created geometric patterns for each type of cup this will be subject to static analysis. The geometric design retains the cutting edge shape and on this on the tooth cassette location will apply an areal force on the abutment tooth. The cutting edge real pattern is subjected to finite element study for the worst case of rock cutting by symmetrical and asymmetrical cups whose profile is different. The purpose of this paper is to determine the displacement and tensions field for both profiles considering the maximum force applied on the cutting edge and the depth of the cutting is equal with the width of the cutting edge of the tooth. It will consider the worst case when on the structure will act both the tangential force and radial force on the bucket profile. For determination of stress and strain field on the form design of cutting edge profile will apply maximum force assuming uniform distribution and on the edge surface force will apply a radial force. After geometric patterns discretization on the cutting knives and determining stress field, can be seen that at the

Introduction to the Explicit Finite Element Method for Nonlinear Transient Dynamics

CERN Document Server

Wu, Shen R

2012-01-01

A systematic introduction to the theories and formulations of the explicit finite element method As numerical technology continues to grow and evolve with industrial applications, understanding the explicit finite element method has become increasingly important, particularly in the areas of crashworthiness, metal forming, and impact engineering. Introduction to the Explicit FiniteElement Method for Nonlinear Transient Dynamics is the first book to address specifically what is now accepted as the most successful numerical tool for nonlinear transient dynamics. The book aids readers in master

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

International Nuclear Information System (INIS)

Sung, Jin Il; Yoo, Jeong Hoon

2002-01-01

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

Finite element analysis of car hood for impact test by using ...

African Journals Online (AJOL)

Finite element analysis of car hood for impact test by using solidworks software ... high safety and at the same time can be built according to market demands. ... Keywords: finite element analysis; impact test; Solidworks; automation, car hood.

Coupling of smooth particle hydrodynamics with the finite element method

International Nuclear Information System (INIS)

Attaway, S.W.; Heinstein, M.W.; Swegle, J.W.

1994-01-01

A gridless technique called smooth particle hydrodynamics (SPH) has been coupled with the transient dynamics finite element code ppercase[pronto]. In this paper, a new weighted residual derivation for the SPH method will be presented, and the methods used to embed SPH within ppercase[pronto] will be outlined. Example SPH ppercase[pronto] calculations will also be presented. One major difficulty associated with the Lagrangian finite element method is modeling materials with no shear strength; for example, gases, fluids and explosive biproducts. Typically, these materials can be modeled for only a short time with a Lagrangian finite element code. Large distortions cause tangling of the mesh, which will eventually lead to numerical difficulties, such as negative element area or ''bow tie'' elements. Remeshing will allow the problem to continue for a short while, but the large distortions can prevent a complete analysis. SPH is a gridless Lagrangian technique. Requiring no mesh, SPH has the potential to model material fracture, large shear flows and penetration. SPH computes the strain rate and the stress divergence based on the nearest neighbors of a particle, which are determined using an efficient particle-sorting technique. Embedding the SPH method within ppercase[pronto] allows part of the problem to be modeled with quadrilateral finite elements, while other parts are modeled with the gridless SPH method. SPH elements are coupled to the quadrilateral elements through a contact-like algorithm. ((orig.))

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

International Nuclear Information System (INIS)

Liu Zhuyong; Hong Jiazhen; Liu Jinyang

2009-01-01

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

Finite element analysis of the neutron transport equation in spherical geometry

International Nuclear Information System (INIS)

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

1992-01-01

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

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

International Nuclear Information System (INIS)

Cambon, S.; Lacoste, P.

2011-01-01

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

Isogeometric finite element analysis of poroelasticity

NARCIS (Netherlands)

Irzal, F.; Remmers, J.J.C.; Verhoosel, C.V.; Borst, de R.

2013-01-01

We present an alternative numerical approach for predicting the behaviour of a deformable fluid-saturated porous medium. The conventional finite element technology is replaced by isogeometric analysis that uses non-uniform rational B-splines. The ability of these functions to provide higher-order

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...

Simplicial Finite Elements in Higher Dimensions

Czech Academy of Sciences Publication Activity Database

Brandts, J.; Korotov, S.; Křížek, Michal

2007-01-01

Roč. 52, č. 3 (2007), s. 251-265 ISSN 0862-7940 R&D Projects: GA ČR GA201/04/1503 Institutional research plan: CEZ:AV0Z10190503 Keywords : n-simplex * finite element method * superconvergence Subject RIV: BA - General Mathematics

Finite element analysis of human joints

Energy Technology Data Exchange (ETDEWEB)

Bossart, P.L.; Hollerbach, K.

1996-09-01

Our work focuses on the development of finite element models (FEMs) that describe the biomechanics of human joints. Finite element modeling is becoming a standard tool in industrial applications. In highly complex problems such as those found in biomechanics research, however, the full potential of FEMs is just beginning to be explored, due to the absence of precise, high resolution medical data and the difficulties encountered in converting these enormous datasets into a form that is usable in FEMs. With increasing computing speed and memory available, it is now feasible to address these challenges. We address the first by acquiring data with a high resolution C-ray CT scanner and the latter by developing semi-automated method for generating the volumetric meshes used in the FEM. Issues related to tomographic reconstruction, volume segmentation, the use of extracted surfaces to generate volumetric hexahedral meshes, and applications of the FEM are described.

Finite element analysis of human joints

International Nuclear Information System (INIS)

Bossart, P.L.; Hollerbach, K.

1996-09-01

Our work focuses on the development of finite element models (FEMs) that describe the biomechanics of human joints. Finite element modeling is becoming a standard tool in industrial applications. In highly complex problems such as those found in biomechanics research, however, the full potential of FEMs is just beginning to be explored, due to the absence of precise, high resolution medical data and the difficulties encountered in converting these enormous datasets into a form that is usable in FEMs. With increasing computing speed and memory available, it is now feasible to address these challenges. We address the first by acquiring data with a high resolution C-ray CT scanner and the latter by developing semi-automated method for generating the volumetric meshes used in the FEM. Issues related to tomographic reconstruction, volume segmentation, the use of extracted surfaces to generate volumetric hexahedral meshes, and applications of the FEM are described

Finite element simulation of piezoelectric transformers.

Science.gov (United States)

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

2001-07-01

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

A Note on Symplectic, Multisymplectic Scheme in Finite Element Method

Institute of Scientific and Technical Information of China (English)

GUO Han-Ying; JI Xiao-Mei; LI Yu-Qi; WU Ke

2001-01-01

We find that with uniform mesh, the numerical schemes derived from finite element method can keep a preserved symplectic structure in one-dimensional case and a preserved multisymplectic structure in two-dimensional case respectively. These results are in fact the intrinsic reason why the numerical experiments show that such finite element algorithms are accurate in practice.``

Comparison of 3-D finite elements for incompressible fluid flow

International Nuclear Information System (INIS)

Robichaud, M.; Tanguy, P.A.

1985-01-01

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

Finite element analysis of an inflatable torus considering air mass structural element

Science.gov (United States)

Gajbhiye, S. C.; Upadhyay, S. H.; Harsha, S. P.

2014-01-01

Inflatable structures, also known as gossamer structures, are at high boom in the current space technology due to their low mass and compact size comparing to the traditional spacecraft designing. Internal pressure becomes the major source of strength and rigidity, essentially stiffen the structure. However, inflatable space based membrane structure are at high risk to the vibration disturbance due to their low structural stiffness and material damping. Hence, the vibration modes of the structure should be known to a high degree of accuracy in order to provide better control authority. In the past, most of the studies conducted on the vibration analysis of gossamer structures used inaccurate or approximate theories in modeling the internal pressure. The toroidal shaped structure is one of the important key element in space application, helps to support the reflector in space application. This paper discusses the finite-element analysis of an inflated torus. The eigen-frequencies are obtained via three-dimensional small-strain elasticity theory, based on extremum energy principle. The two finite-element model (model-1 and model-2) have cases have been generated using a commercial finite-element package. The structure model-1 with shell element and model-2 with the combination of the mass of enclosed fluid (air) added to the shell elements have been taken for the study. The model-1 is computed with present analytical approach to understand the convergence rate and the accuracy. The convergence study is made available for the symmetric modes and anti-symmetric modes about the centroidal-axis plane, meeting the eigen-frequencies of an inflatable torus with the circular cross section. The structural model-2 is introduced with air mass element and analyzed its eigen-frequency with different aspect ratio and mode shape response using in-plane and out-plane loading condition are studied.

Error-controlled adaptive finite elements in solid mechanics

National Research Council Canada - National Science Library

Stein, Erwin; Ramm, E

2003-01-01

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

Stress analysis of heated concrete using finite elements

International Nuclear Information System (INIS)

Majumdar, P.; Gupta, A.; Marchertas, A.

1994-01-01

Described is a finite element analysis of concrete, which is subjected to rapid heating. Using thermal mass transport calculation, the moisture content, temperature and pore pressure distribution over space and time is obtained first. From these effects, stress at various points of the concrete are computed using the finite element method. Contribution to the stress formulation comes from three components, namely the thermal expansion, pore pressure, and the shrinkage of concrete due to moisture loss (from dehydration). The material properties of concrete are assumed to be homogeneous, elastic, and cracking is not taken into consideration. (orig.)

Finite element simulation of internal flows with heat transfer using a ...

Indian Academy of Sciences (India)

Unknown

Velocity correction method; finite element simulation; turbulent .... CFD, developments in turbulence modeling have been only evolutionary and ...... variables are made dimensionless using appropriate combinations of Uav, H, ...... Srinivas M 1994 Finite element analysis of internal flows with heat transfer Ph D thesis, Indian.

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

Science.gov (United States)

Bartels, Robert E.

2005-01-01

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

Integral finite element analysis of turntable bearing with flexible rings

Science.gov (United States)

Deng, Biao; Liu, Yunfei; Guo, Yuan; Tang, Shengjin; Su, Wenbin; Lei, Zhufeng; Wang, Pengcheng

2018-03-01

This paper suggests a method to calculate the internal load distribution and contact stress of the thrust angular contact ball turntable bearing by FEA. The influence of the stiffness of the bearing structure and the plastic deformation of contact area on the internal load distribution and contact stress of the bearing is considered. In this method, the load-deformation relationship of the rolling elements is determined by the finite element contact analysis of a single rolling element and the raceway. Based on this, the nonlinear contact between the rolling elements and the inner and outer ring raceways is same as a nonlinear compression spring and bearing integral finite element analysis model including support structure was established. The effects of structural deformation and plastic deformation on the built-in stress distribution of slewing bearing are investigated on basis of comparing the consequences of load distribution, inner and outer ring stress, contact stress and other finite element analysis results with the traditional bearing theory, which has guiding function for improving the design of slewing bearing.

Finite Element Simulation of Fracture Toughness Test

International Nuclear Information System (INIS)

Chu, Seok Jae; Liu, Cong Hao

2013-01-01

Finite element simulations of tensile tests were performed to determine the equivalent stress - equivalent plastic strain curves, critical equivalent stresses, and critical equivalent plastic strains. Then, the curves were used as inputs to finite element simulations of fracture toughness tests to determine the plane strain fracture toughness. The critical COD was taken as the COD when the equivalent plastic strain at the crack tip reached a critical value, and it was used as a crack growth criterion. The relationship between the critical COD and the critical equivalent plastic strain or the reduction of area was found. The relationship between the plane strain fracture toughness and the product of the critical equivalent stress and the critical equivalent plastic strain was also found

Semianalytic Design Sensitivity Analysis of Nonlinear Structures With a Commercial Finite Element Package

International Nuclear Information System (INIS)

Lee, Tae Hee; Yoo, Jung Hun; Choi, Hyeong Cheol

2002-01-01

A finite element package is often used as a daily design tool for engineering designers in order to analyze and improve the design. The finite element analysis can provide the responses of a system for given design variables. Although finite element analysis can quite well provide the structural behaviors for given design variables, it cannot provide enough information to improve the design such as design sensitivity coefficients. Design sensitivity analysis is an essential step to predict the change in responses due to a change in design variables and to optimize a system with the aid of the gradient-based optimization techniques. To develop a numerical method of design sensitivity analysis, analytical derivatives that are based on analytical differentiation of the continuous or discrete finite element equations are effective but analytical derivatives are difficult because of the lack of internal information of the commercial finite element package such as shape functions. Therefore, design sensitivity analysis outside of the finite element package is necessary for practical application in an industrial setting. In this paper, the semi-analytic method for design sensitivity analysis is used for the development of the design sensitivity module outside of a commercial finite element package of ANSYS. The direct differentiation method is employed to compute the design derivatives of the response and the pseudo-load for design sensitivity analysis is effectively evaluated by using the design variation of the related internal nodal forces. Especially, we suggest an effective method for stress and nonlinear design sensitivity analyses that is independent of the commercial finite element package is also discussed. Numerical examples are illustrated to show the accuracy and efficiency of the developed method and to provide insights for implementation of the suggested method into other commercial finite element packages

Implementation of advanced finite element technology in structural analysis computer codes

International Nuclear Information System (INIS)

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

1975-01-01

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

Probabilistic finite elements for transient analysis in nonlinear continua

Science.gov (United States)

Liu, W. K.; Belytschko, T.; Mani, A.

1985-01-01

The probabilistic finite element method (PFEM), which is a combination of finite element methods and second-moment analysis, is formulated for linear and nonlinear continua with inhomogeneous random fields. Analogous to the discretization of the displacement field in finite element methods, the random field is also discretized. The formulation is simplified by transforming the correlated variables to a set of uncorrelated variables through an eigenvalue orthogonalization. Furthermore, it is shown that a reduced set of the uncorrelated variables is sufficient for the second-moment analysis. Based on the linear formulation of the PFEM, the method is then extended to transient analysis in nonlinear continua. The accuracy and efficiency of the method is demonstrated by application to a one-dimensional, elastic/plastic wave propagation problem. The moments calculated compare favorably with those obtained by Monte Carlo simulation. Also, the procedure is amenable to implementation in deterministic FEM based computer programs.

Adaptive finite-element ballooning analysis of bipolar ionized fields

International Nuclear Information System (INIS)

Al-Hamouz, Z.M.

1995-01-01

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

Straightened cervical lordosis causes stress concentration: a finite element model study

Energy Technology Data Exchange (ETDEWEB)

Wei, Wei; Shi, Shiyuan; Fei, Jun; Wang, Yifan; Chen, Chunyue [Hangzhou Red Cross Hospital, Hangzhou, Zhejiang, (China); Liao, Shenhui [School of Information Science and Engineering, Central South University, Changsha, Hunan (China)

2013-03-15

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.

Straightened cervical lordosis causes stress concentration: a finite element model study

International Nuclear Information System (INIS)

Wei, Wei; Shi, Shiyuan; Fei, Jun; Wang, Yifan; Chen, Chunyue; Liao, Shenhui

2013-01-01

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.

Finite element model for heat conduction in jointed rock masses

International Nuclear Information System (INIS)

Gartling, D.K.; Thomas, R.K.

1981-01-01

A computatonal procedure for simulating heat conduction in a fractured rock mass is proposed and illustrated in the present paper. The method makes use of a simple local model for conduction in the vicinity of a single open fracture. The distributions of fractures and fracture properties within the finite element model are based on a statistical representation of geologic field data. Fracture behavior is included in the finite element computation by locating local, discrete fractures at the element integration points

Mixed finite element - discontinuous finite volume element discretization of a general class of multicontinuum models

Science.gov (United States)

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

hpGEM -- A software framework for discontinuous Galerkin finite element methods

NARCIS (Netherlands)

Pesch, L.; Bell, A.; Sollie, W.E.H.; Ambati, V.R.; Bokhove, Onno; van der Vegt, Jacobus J.W.

2006-01-01

hpGEM, a novel framework for the implementation of discontinuous Galerkin finite element methods, is described. We present structures and methods that are common for many (discontinuous) finite element methods and show how we have implemented the components as an object-oriented framework. This

Orthodontic treatment: Introducing finite element analysis

NARCIS (Netherlands)

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

A finite element modeling method for predicting long term corrosion rates

International Nuclear Information System (INIS)

Fu, J.W.; Chan, S.

1984-01-01

For the analyses of galvanic corrosion, pitting and crevice corrosion, which have been identified as possible corrosion processes for nuclear waste isolation, a finite element method has been developed for the prediction of corrosion rates. The method uses a finite element mesh to model the corrosive environment and the polarization curves of metals are assigned as the boundary conditions to calculate the corrosion cell current distribution. A subroutine is used to calculate the chemical change with time in the crevice or the pit environments. In this paper, the finite element method is described along with experimental confirmation

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.

Introduction to nonlinear finite element analysis

CERN Document Server

Kim, Nam-Ho

2015-01-01

This book introduces the key concepts of nonlinear finite element analysis procedures. The book explains the fundamental theories of the field and provides instructions on how to apply the concepts to solving practical engineering problems. Instead of covering many nonlinear problems, the book focuses on three representative problems: nonlinear elasticity, elastoplasticity, and contact problems. The book is written independent of any particular software, but tutorials and examples using four commercial programs are included as appendices: ANSYS, NASTRAN, ABAQUS, and MATLAB. In particular, the MATLAB program includes all source codes so that students can develop their own material models, or different algorithms. This book also: ·         Presents clear explanations of nonlinear finite element analysis for elasticity, elastoplasticity, and contact problems ·         Includes many informative examples of nonlinear analyses so that students can clearly understand the nonlinear theory ·    ...

Finite element analysis of multilayer coextrusion.

Energy Technology Data Exchange (ETDEWEB)

Hopkins, Matthew Morgan; Schunk, Peter Randall; Baer, Thomas A. (Proctor & Gamble Company, West Chester, OH); Mrozek, Randy A. (Army Research Laboratory, Adelphi, MD); Lenhart, Joseph Ludlow (Army Research Laboratory, Adelphi, MD); Rao, Rekha Ranjana; Collins, Robert (Oak Ridge National Laboratory); Mondy, Lisa Ann

2011-09-01

Multilayer coextrusion has become a popular commercial process for producing complex polymeric products from soda bottles to reflective coatings. A numerical model of a multilayer coextrusion process is developed based on a finite element discretization and two different free-surface methods, an arbitrary-Lagrangian-Eulerian (ALE) moving mesh implementation and an Eulerian level set method, to understand the moving boundary problem associated with the polymer-polymer interface. The goal of this work is to have a numerical capability suitable for optimizing and troubleshooting the coextrusion process, circumventing flow instabilities such as ribbing and barring, and reducing variability in layer thickness. Though these instabilities can be both viscous and elastic in nature, for this work a generalized Newtonian description of the fluid is used. Models of varying degrees of complexity are investigated including stability analysis and direct three-dimensional finite element free surface approaches. The results of this work show how critical modeling can be to reduce build test cycles, improve material choices, and guide mold design.

Finite element analysis of ARPS structures

International Nuclear Information System (INIS)

Ruhkamp, J.D.; McDougal, J.R.; Kramer, D.P.

1998-01-01

Algor finite element software was used to determine the stresses and deflections in the metallic walls of Advanced Radioisotope Power Systems (ARPS) designs. The preliminary design review of these systems often neglects the structural integrity of the design which can effect fabrication and the end use of the design. Before finite element analysis (FEA) was run on the canister walls of the thermophotovoltaic (TPV) generator, hand calculations were used to approximate the stresses and deflections in a flat plate. These results compared favorably to the FEA results of a similar size flat plate. The AMTEC (Alkali Metal Thermal-to-Electric Conversion) cells were analyzed by FEA and the results compared to two cells that were mechanically tested. The mechanically tested cells buckled in the thin sections, one at the top and one in the lower section. The FEA predicted similar stress and shape results but the critical buckling load was found to be very shape dependent

A short summary on finite element modelling of fatigue crack closure

Energy Technology Data Exchange (ETDEWEB)

Singh, Konjengbam Darunkumar [Indian Institute of Technology, Guwahati (India); Parry, Matthew Roger [Airbus Operations Ltd, Bristol(United Kingdom); Sinclair, Ian [University of Southampton, Southampton (United Kingdom)

2011-12-15

This paper presents a short summary pertaining to the finite element modelling of fatigue crack closure. Several key issues related to finite element modelling of fatigue crack closure are highlighted: element type, mesh refinement, stabilization of crack closure, crack-tip node release scheme, constitutive model, specimen geometry, stress-states (i.e., plane stress, plane strain), crack closure monitoring. Reviews are presented for both straight and deflected cracks.

Overlapping Schwarz for Nonlinear Problems. An Element Agglomeration Nonlinear Additive Schwarz Preconditioned Newton Method for Unstructured Finite Element Problems

Energy Technology Data Exchange (ETDEWEB)

Cai, X C; Marcinkowski, L; Vassilevski, P S

2005-02-10

This paper extends previous results on nonlinear Schwarz preconditioning ([4]) to unstructured finite element elliptic problems exploiting now nonlocal (but small) subspaces. The non-local finite element subspaces are associated with subdomains obtained from a non-overlapping element partitioning of the original set of elements and are coarse outside the prescribed element subdomain. The coarsening is based on a modification of the agglomeration based AMGe method proposed in [8]. Then, the algebraic construction from [9] of the corresponding non-linear finite element subproblems is applied to generate the subspace based nonlinear preconditioner. The overall nonlinearly preconditioned problem is solved by an inexact Newton method. Numerical illustration is also provided.

Generalized multiscale finite element methods: Oversampling strategies

KAUST Repository

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

2014-01-01

In this paper, we propose oversampling strategies in the generalized multiscale finite element method (GMsFEM) framework. The GMsFEM, which has been recently introduced in Efendiev et al. (2013b) [Generalized Multiscale Finite Element Methods, J. Comput. Phys., vol. 251, pp. 116-135, 2013], allows solving multiscale parameter-dependent problems at a reduced computational cost by constructing a reduced-order representation of the solution on a coarse grid. The main idea of the method consists of (1) the construction of snapshot space, (2) the construction of the offline space, and (3) construction of the online space (the latter for parameter-dependent problems). In Efendiev et al. (2013b) [Generalized Multiscale Finite Element Methods, J. Comput. Phys., vol. 251, pp. 116-135, 2013], it was shown that the GMsFEM provides a flexible tool to solve multiscale problems with a complex input space by generating appropriate snapshot, offline, and online spaces. In this paper, we develop oversampling techniques to be used in this context (see Hou and Wu (1997) where oversampling is introduced for multiscale finite element methods). It is known (see Hou and Wu (1997)) that the oversampling can improve the accuracy of multiscale methods. In particular, the oversampling technique uses larger regions (larger than the target coarse block) in constructing local basis functions. Our motivation stems from the analysis presented in this paper, which shows that when using oversampling techniques in the construction of the snapshot space and offline space, GMsFEM will converge independent of small scales and high contrast under certain assumptions. We consider the use of a multiple eigenvalue problems to improve the convergence and discuss their relation to single spectral problems that use oversampled regions. The oversampling procedures proposed in this paper differ from those in Hou and Wu (1997). In particular, the oversampling domains are partially used in constructing local

Groundwater flow analysis using mixed hybrid finite element method for radioactive waste disposal facilities

International Nuclear Information System (INIS)

Aoki, Hiroomi; Shimomura, Masanori; Kawakami, Hiroto; Suzuki, Shunichi

2011-01-01

In safety assessments of radioactive waste disposal facilities, ground water flow analysis are used for calculating the radionuclide transport pathway and the infiltration flow rate of groundwater into the disposal facilities. For this type of calculations, the mixed hybrid finite element method has been used and discussed about the accuracy of ones in Europe. This paper puts great emphasis on the infiltration flow rate of groundwater into the disposal facilities, and describes the accuracy of results obtained from mixed hybrid finite element method by comparing of local water mass conservation and the reliability of the element breakdown numbers among the mixed hybrid finite element method, finite volume method and nondegenerated finite element method. (author)

Finite element elastic-plastic analysis of LMFBR components

International Nuclear Information System (INIS)

Levy, A.; Pifko, A.; Armen, H. Jr.

1978-01-01

The present effort involves the development of computationally efficient finite element methods for accurately predicting the isothermal elastic-plastic three-dimensional response of thick and thin shell structures subjected to mechanical and thermal loads. This work will be used as the basis for further development of analytical tools to be used to verify the structural integrity of liquid metal fast breeder reactor (LMFBR) components. The methods presented here have been implemented into the three-dimensional solid element module (HEX) of the Grumman PLANS finite element program. These methods include the use of optimal stress points as well as a variable number of stress points within an element. This allows monitoring the stress history at many points within an element and hence provides an accurate representation of the elastic-plastic boundary using a minimum number of degrees of freedom. Also included is an improved thermal stress analysis capability in which the temperature variation and corresponding thermal strain variation are represented by the same functional form as the displacement variation. Various problems are used to demonstrate these improved capabilities. (Auth.)

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.

Marginally Stable Triangular Recurrent Neural Network Architecture for Time Series Prediction.

Science.gov (United States)

Sivakumar, Seshadri; Sivakumar, Shyamala

2017-09-25

This paper introduces a discrete-time recurrent neural network architecture using triangular feedback weight matrices that allows a simplified approach to ensuring network and training stability. The triangular structure of the weight matrices is exploited to readily ensure that the eigenvalues of the feedback weight matrix represented by the block diagonal elements lie on the unit circle in the complex z-plane by updating these weights based on the differential of the angular error variable. Such placement of the eigenvalues together with the extended close interaction between state variables facilitated by the nondiagonal triangular elements, enhances the learning ability of the proposed architecture. Simulation results show that the proposed architecture is highly effective in time-series prediction tasks associated with nonlinear and chaotic dynamic systems with underlying oscillatory modes. This modular architecture with dual upper and lower triangular feedback weight matrices mimics fully recurrent network architectures, while maintaining learning stability with a simplified training process. While training, the block-diagonal weights (hence the eigenvalues) of the dual triangular matrices are constrained to the same values during weight updates aimed at minimizing the possibility of overfitting. The dual triangular architecture also exploits the benefit of parsing the input and selectively applying the parsed inputs to the two subnetworks to facilitate enhanced learning performance.

Finite element modeling of the filament winding process using ABAQUS

OpenAIRE

Miltenberger, Louis C.

1992-01-01

A comprehensive stress model of the filament winding fabrication process, previously implemented in the finite element program, WACSAFE, was implemented using the ABAQUS finite element software package. This new implementation, referred to as the ABWACSAFE procedure, consists of the ABAQUS software and a pre/postprocessing routine that was developed to prepare necessary ABAQUS input files and process ABAQUS displacement results for stress and strain computation. The ABWACSAF...

Finite element reliability analysis of fatigue life

International Nuclear Information System (INIS)

Harkness, H.H.; Belytschko, T.; Liu, W.K.

1992-01-01

Fatigue reliability is addressed by the first-order reliability method combined with a finite element method. Two-dimensional finite element models of components with cracks in mode I are considered with crack growth treated by the Paris law. Probability density functions of the variables affecting fatigue are proposed to reflect a setting where nondestructive evaluation is used, and the Rosenblatt transformation is employed to treat non-Gaussian random variables. Comparisons of the first-order reliability results and Monte Carlo simulations suggest that the accuracy of the first-order reliability method is quite good in this setting. Results show that the upper portion of the initial crack length probability density function is crucial to reliability, which suggests that if nondestructive evaluation is used, the probability of detection curve plays a key role in reliability. (orig.)

Stochastic Finite Elements in Reliability-Based Structural Optimization

DEFF Research Database (Denmark)

Sørensen, John Dalsgaard; Engelund, S.

1995-01-01

Application of stochastic finite elements in structural optimization is considered. It is shown how stochastic fields modelling e.g. the modulus of elasticity can be discretized in stochastic variables and how a sensitivity analysis of the reliability of a structural system with respect to optimi......Application of stochastic finite elements in structural optimization is considered. It is shown how stochastic fields modelling e.g. the modulus of elasticity can be discretized in stochastic variables and how a sensitivity analysis of the reliability of a structural system with respect...... to optimization variables can be performed. A computer implementation is described and an illustrative example is given....

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

International Nuclear Information System (INIS)

Ratnajeevan, S.; Hoole, H.

1990-01-01

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

Finite element model updating of natural fibre reinforced composite structure in structural dynamics

Directory of Open Access Journals (Sweden)

Sani M.S.M.

2016-01-01

Full Text Available Model updating is a process of making adjustment of certain parameters of finite element model in order to reduce discrepancy between analytical predictions of finite element (FE and experimental results. Finite element model updating is considered as an important field of study as practical application of finite element method often shows discrepancy to the test result. The aim of this research is to perform model updating procedure on a composite structure as well as trying improving the presumed geometrical and material properties of tested composite structure in finite element prediction. The composite structure concerned in this study is a plate of reinforced kenaf fiber with epoxy. Modal properties (natural frequency, mode shapes, and damping ratio of the kenaf fiber structure will be determined using both experimental modal analysis (EMA and finite element analysis (FEA. In EMA, modal testing will be carried out using impact hammer test while normal mode analysis using FEA will be carried out using MSC. Nastran/Patran software. Correlation of the data will be carried out before optimizing the data from FEA. Several parameters will be considered and selected for the model updating procedure.

Synthesis of hydrocode and finite element technology for large deformation Lagrangian computation

International Nuclear Information System (INIS)

Goudreau, G.L.; Hallquist, J.O.

1979-08-01

Large deformation engineering analysis at Lawrence Livermore Laboratory has benefited from a synthesis of computational technology from the finite difference hydrocodes of the scientific weapons community and the structural finite element methodology of engineering. Two- and three-dimensional explicit and implicit Lagrangian continuum codes have been developed exploiting the strengths of each. The explicit methodology primarily exploits the primitive constant stress (or one point integration) brick element. Similarity and differences with the integral finite difference method are discussed. Choice of stress and finite strain measures, and selection of hour glass viscosity are also considered. The implicit codes also employ a Cauchy formulation, with Newton iteration and a symmetric tangent matrix. A library of finite strain material routines includes hypoelastic/plastic, hyperelastic, viscoelastic, as well as hydrodynamic behavior. Arbitrary finite element topology and a general slide-line treatment significantly extends Lagrangian hydrocode application. Computational experience spans weapons and non-weapons applications

Advanced finite element method in structural engineering

CERN Document Server

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.

Optical Finite Element Processor

Science.gov (United States)

Casasent, David; Taylor, Bradley K.

1986-01-01

A new high-accuracy optical linear algebra processor (OLAP) with many advantageous features is described. It achieves floating point accuracy, handles bipolar data by sign-magnitude representation, performs LU decomposition using only one channel, easily partitions and considers data flow. A new application (finite element (FE) structural analysis) for OLAPs is introduced and the results of a case study presented. Error sources in encoded OLAPs are addressed for the first time. Their modeling and simulation are discussed and quantitative data are presented. Dominant error sources and the effects of composite error sources are analyzed.

Investigation of the Behavior of Steel Shear Walls Using Finite Elements Analysis

Directory of Open Access Journals (Sweden)

K. Abubakri

2016-10-01

Full Text Available Currently, steel shear walls are considered by engineers as an economic method against lateral loads imposed by wind and earthquake in tall structures. Accordingly, there is a growing need to develop accurate methods alongside approximation methods to estimate the behavior of these structural elements. The finite element technique is one of the strongest numerical methods in analysis of solid mechanics problems. Finite element analysis however requires high technical knowledge of the behavioral models of materials. Therefore, it is less used by designers for certain structural elements such as steel shear walls. This study examines the failure mechanism of steel shear walls using finite elements analysis and validates this modeling by comparing the results with experimental studies.

Matlab and C programming for Trefftz finite element methods

CERN Document Server

Qin, Qing-Hua

2008-01-01

Although the Trefftz finite element method (FEM) has become a powerful computational tool in the analysis of plane elasticity, thin and thick plate bending, Poisson's equation, heat conduction, and piezoelectric materials, there are few books that offer a comprehensive computer programming treatment of the subject. Collecting results scattered in the literature, MATLAB® and C Programming for Trefftz Finite Element Methods provides the detailed MATLAB® and C programming processes in applications of the Trefftz FEM to potential and elastic problems. The book begins with an introduction to th

Preconditioning for Mixed Finite Element Formulations of Elliptic Problems

KAUST Repository

Wildey, Tim; Xue, Guangri

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.

A Kohn–Sham equation solver based on hexahedral finite elements

International Nuclear Information System (INIS)

Fang Jun; Gao Xingyu; Zhou Aihui

2012-01-01

We design a Kohn–Sham equation solver based on hexahedral finite element discretizations. The solver integrates three schemes proposed in this paper. The first scheme arranges one a priori locally-refined hexahedral mesh with appropriate multiresolution. The second one is a modified mass-lumping procedure which accelerates the diagonalization in the self-consistent field iteration. The third one is a finite element recovery method which enhances the eigenpair approximations with small extra work. We carry out numerical tests on each scheme to investigate the validity and efficiency, and then apply them to calculate the ground state total energies of nanosystems C 60 , C 120 , and C 275 H 172 . It is shown that our solver appears to be computationally attractive for finite element applications in electronic structure study.

Investigation of faulted tunnel models by combined photoelasticity and finite element analysis

International Nuclear Information System (INIS)

Ladkany, S.G.; Huang, Yuping

1994-01-01

Models of square and circular tunnels with short faults cutting through their surfaces are investigated by photoelasticity. These models, when duplicated by finite element analysis can predict the stress states of square or circular faulted tunnels adequately. Finite element analysis, using gap elements, may be used to investigate full size faulted tunnel system

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

International Nuclear Information System (INIS)

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

1978-01-01

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

Review on Finite Element Method * ERHUNMWUN, ID ...

African Journals Online (AJOL)

ADOWIE PERE

ABSTRACT: In this work, we have discussed what Finite Element Method (FEM) is, its historical development, advantages and ... residual procedures, are examples of the direct approach ... The paper centred on the "stiffness and deflection of ...

Finite element evaluation of erosion/corrosion affected reducing elbow

International Nuclear Information System (INIS)

Basavaraju, C.

1996-01-01

Erosion/corrosion is a primary source for wall thinning or degradation of carbon steel piping systems in service. A number of piping failures in the power industry have been attributed to erosion/corrosion. Piping elbow is one of such susceptible components for erosion/corrosion because of increased flow turbulence due to its geometry. In this paper, the acceptability of a 12 in. x 8 in. reducing elbow in RHR service water pump discharge piping, which experienced significant degradation due to wall thinning in localized areas, was evaluated using finite element analysis methodology. Since the simplified methods showed very small margin and recommended replacement of the elbow, a detailed 3-D finite element model was built using shell elements and analyzed for internal pressure and moment loadings. The finite element analysis incorporated the U.T. measured wall thickness data at various spots that experienced wall thinning. The results showed that the elbow is acceptable as-is until the next fuel cycle. FEA, though cumbersome, and time consuming is a valuable analytical tool in making critical decisions with regard to component replacement of border line situation cases, eliminating some conservatism while not compromising the safety

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

International Nuclear Information System (INIS)

Du Chengbin; Jiang Shouyan; Ying Zongquan

2010-01-01

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

On the performance of piezoelectric harvesters loaded by finite width impulses

Science.gov (United States)

Doria, A.; Medè, C.; Desideri, D.; Maschio, A.; Codecasa, L.; Moro, F.

2018-02-01

The response of cantilevered piezoelectric harvesters loaded by finite width impulses of base acceleration is studied analytically in the frequency domain in order to identify the parameters that influence the generated voltage. Experimental tests are then performed on harvesters loaded by hammer impacts. The latter are used to confirm analytical results and to validate a linear finite element (FE) model of a unimorph harvester. The FE model is, in turn, used to extend analytical results to more general harvesters (tapered, inverse tapered, triangular) and to more general impulses (heel strike in human gait). From analytical and numerical results design criteria for improving harvester performance are obtained.

A fully coupled finite element framework for thermal fracturing simulation in subsurface cold CO2 injection

Directory of Open Access Journals (Sweden)

Shunde Yin

2018-03-01

Simulation of thermal fracturing during cold CO2 injection involves the coupled processes of heat transfer, mass transport, rock deforming as well as fracture propagation. To model such a complex coupled system, a fully coupled finite element framework for thermal fracturing simulation is presented. This framework is based on the theory of non-isothermal multiphase flow in fracturing porous media. It takes advantage of recent advances in stabilized finite element and extended finite element methods. The stabilized finite element method overcomes the numerical instability encountered when the traditional finite element method is used to solve the convection dominated heat transfer equation, while the extended finite element method overcomes the limitation with traditional finite element method that a model has to be remeshed when a fracture is initiated or propagating and fracturing paths have to be aligned with element boundaries.

Finite element modelling of solidification phenomena

Indian Academy of Sciences (India)

Unknown

Abstract. 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 ...

Surface-Enhanced Raman Spectroscopy of Dye and Thiol Molecules Adsorbed on Triangular Silver Nanostructures: A Study of Near-Field Enhancement, Localization of Hot-Spots, and Passivation of Adsorbed Carbonaceous Species

Directory of Open Access Journals (Sweden)

Manuel R. Gonçalves

2012-01-01

Full Text Available Surface-enhanced Raman spectroscopy (SERS of thiols and dye molecules adsorbed on triangular silver nanostructures was investigated. The SERS hot-spots are localized at the edges and corners of the silver triangular particles. AFM and SEM measurements permit to observe many small clusters formed at the edges of triangular particles fabricated by nanosphere lithography. Finite-element calculations show that near-field enhancements can reach values of more than 200 at visible wavelengths, in the gaps between small spherical particles and large triangular particles, although for the later no plasmon resonance was found at the wavelengths investigated. The regions near the particles showing strong near-field enhancement are well correlated with spatial localization of SERS hot-spots done by confocal microscopy. Silver nanostructures fabricated by thermal evaporation present strong and fast fluctuating SERS activity, due to amorphous carbon contamination. Thiols and dye molecules seem to be able to passivate the undesired SERS activity on fresh evaporated silver.

Energy flow in plate assembles by hierarchical version of finite element method

DEFF Research Database (Denmark)

Wachulec, Marcin; Kirkegaard, Poul Henning

method has been proposed. In this paper a modified hierarchical version of finite element method is used for modelling of energy flow in plate assembles. The formulation includes description of in-plane forces so that planes lying in different planes can be modelled. Two examples considered are: L......The dynamic analysis of structures in medium and high frequencies are usually focused on frequency and spatial averages of energy of components, and not the displacement/velocity fields. This is especially true for structure-borne noise modelling. For the analysis of complicated structures...... the finite element method has been used to study the energy flow. The finite element method proved its usefulness despite the computational expense. Therefore studies have been conducted in order to simplify and reduce the computations required. Among others, the use of hierarchical version of finite element...

Finite element bending behaviour of discretely delaminated ...

African Journals Online (AJOL)

user

due to their light weight, high specific strength and stiffness properties. ... cylindrical shell roofs respectively using finite element method with centrally located .... where { }ε and { }γ are the direct and shear strains in midplane and { }κ denotes ...

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.

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

Science.gov (United States)

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

2015-05-01

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

Recent uses of the finite element method in design/analysis of CANDU fuel

International Nuclear Information System (INIS)

Tayal, M.; Lim, D.

1985-06-01

Finite element codes FEAST and ELESTRES have been used to show: that initial pellet density can have a significant effect on the probability of fuel defect near end cap welds; that sheath stresses/strains are highly multiaxial near circumferential ridges; and that the multiaxiality affects sheath integrity significantly. The finite element thermal code FEAT was used to redesign bearing pads to obtain lower temperture; this eliminated crevice corrosion. FEAT was also used to assess the influences of braze voids and of end flux peaking. These analyses involved complex geometries. By using finite elements, we could obtain accurate assessments economically and rapidly. Finite element codes are also being developed for bowing, diffusion, flow patterns, and stress corrosion cracking

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

Energy Technology Data Exchange (ETDEWEB)

Pepper, D W; Cooper, R E

1980-01-01

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

Fluid-structure finite-element vibrational analysis

Science.gov (United States)

Feng, G. C.; Kiefling, L.

1974-01-01

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

Finite element analysis of degraded concrete structures - Workshop proceedings

International Nuclear Information System (INIS)

1999-09-01

This workshop is related to the finite element analysis of degraded concrete structures. It is composed of three sessions. The first session (which title is: the use of finite element analysis in safety assessments) comprises six papers which titles are: Historical Development of Concrete Finite Element Modeling for Safety Evaluation of Accident-Challenged and Aging Concrete Structures; Experience with Finite Element Methods for Safety Assessments in Switzerland; Stress State Analysis of the Ignalina NPP Confinement System; Prestressed Containment: Behaviour when Concrete Cracking is Modelled; Application of FEA for Design and Support of NPP Containment in Russia; Verification Problems of Nuclear Installations Safety Software of Strength Analysis (NISS SA). The second session (title: concrete containment structures under accident loads) comprises seven papers which titles are: Two Application Examples of Concrete Containment Structures under Accident Load Conditions Using Finite Element Analysis; What Kind of Prediction for Leak rates for Nuclear Power Plant Containments in Accidental Conditions; Influence of Different Hypotheses Used in Numerical Models for Concrete At Elevated Temperatures on the Predicted Behaviour of NPP Core Catchers Under Severe Accident Conditions; Observations on the Constitutive Modeling of Concrete Under Multi-Axial States at Elevated Temperatures; Analyses of a Reinforced Concrete Containment with Liner Corrosion Damage; Program of Containment Concrete Control During Operation for the Temelin Nuclear Power Plant; Static Limit Load of a Deteriorated Hyperbolic Cooling Tower. The third session (concrete structures under extreme environmental load) comprised five papers which titles are: Shear Transfer Mechanism of RC Plates After Cracking; Seismic Back Calculation of an Auxiliary Building of the Nuclear Power Plant Muehleberg, Switzerland; Seismic Behaviour of Slightly Reinforced Shear Wall Structures; FE Analysis of Degraded Concrete

Finite element analysis of adanced composite structures containing mechanically fastened joints

International Nuclear Information System (INIS)

Baumann, E.

1982-01-01

Although the usual engineering practice is to ignore joint effects in finite element models of overall structures, there are times when the inclusion of fastener effects in a model is necessary for accurate analysis. This paper describes some simple but accurate methods for accommodating this modeling requirement. The approach involves correlation of test results from a few composite mechanically fastened joints with finite element analyses of joints. It is assumed that if the fastener actions in the test articles can be properly predicted by simple finite element techniques, then these same techniques can be applied to large overall structure models. During the course of this test-analysis effort it was determined that it is possible to obtain correct results for overall structure-joint analyses by using simple modeling concepts provided special care is employed. Also, some emphasis is given in this paper to the importance of properly reducing test data in order to obtain meaningful correlations with finite element analysis. Finally, for those interested, the appendix contains brief descriptions of the test results and failure modes explored in the test program. (orig.)

Multisymplectic Structure－Preserving in Simple Finite Element Method in High Dimensional Case

Institute of Scientific and Technical Information of China (English)

BAIYong-Qiang; LIUZhen; PEIMing; ZHENGZhu-Jun

2003-01-01

In this paper, we study a finite element scheme of some semi-linear elliptic boundary value problems in high-dhnensjonal space. With uniform mesh, we find that, the numerical scheme derived from finite element method can keep a preserved multisymplectic structure.

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 ...

Performance and scalability of finite-difference and finite-element wave-propagation modeling on Intel's Xeon Phi

NARCIS (Netherlands)

Zhebel, E.; Minisini, S.; Kononov, A.; Mulder, W.A.

2013-01-01

With the rapid developments in parallel compute architectures, algorithms for seismic modeling and imaging need to be reconsidered in terms of parallelization. The aim of this paper is to compare scalability of seismic modeling algorithms: finite differences, continuous mass-lumped finite elements

Thermal stresses in rectangular plates: variational and finite element solutions

International Nuclear Information System (INIS)

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

1978-01-01

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

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

Science.gov (United States)

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

2011-04-01

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

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

DEFF Research Database (Denmark)

Lucht, Tore

2009-01-01

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

Finite element modeling of TFTR poloidal field coils

International Nuclear Information System (INIS)

Baumgartner, J.A.; O'Toole, J.A.

1986-01-01

The Tokamak Fusion Test Reactor (TFTR) Poloidal Field (PF) coils were originally analyzed to TFTR design conditions. The coils have been reanalyzed by PPPL and Grumman to determine operating limits under as-built conditions. Critical stress levels, based upon data obtained from the reanalysis of each PF coil, are needed for input to the TFTR simulation code algorithms. The primary objective regarding structural integrity has been to ascertain the magnitude and location of critical internal stresses in each PF coil due to various combinations of electromagnetic and thermally induced loads. For each PF coil, a global finite element model (FEM) of a coil sector is being analyzed to obtain the basic coil internal loads and displacements. Subsequent fine mesh local models of the coil lead stem and lead spur regions produce the magnitudes and locations of peak stresses. Each copper turn and its surrounding insulation are modeled using solid finite elements. The corresponding electromagnetic and thermal analyses are similarly modeled. A series of test beams were developed to determine the best combination of MSC/NASTRAN-type finite elements for use in PF coil analysis. The results of this analysis compare favorably with those obtained by the earlier analysis which was limited in scope

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

International Nuclear Information System (INIS)

Touze, F.; Le Meur, G.

1990-06-01

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

European column buckling curves and finite element modelling including high strength steels

DEFF Research Database (Denmark)

Jönsson, Jeppe; Stan, Tudor-Cristian

2017-01-01

Eurocode allows for finite element modelling of plated steel structures, however the information in the code on how to perform the analysis or what assumptions to make is quite sparse. The present paper investigates the deterministic modelling of flexural column buckling using plane shell elements...... imperfections may be very conservative if considered by finite element analysis as described in the current Eurocode code. A suggestion is given for a slightly modified imperfection formula within the Ayrton-Perry formulation leading to adequate inclusion of modern high grade steels within the original four...... bucking curves. It is also suggested that finite element or frame analysis may be performed with equivalent column bow imperfections extracted directly from the Ayrton-Perry formulation....

Finite element method - theory and applications

International Nuclear Information System (INIS)

Baset, S.

1992-01-01

This paper summarizes the mathematical basis of the finite element method. Attention is drawn to the natural development of the method from an engineering analysis tool into a general numerical analysis tool. A particular application to the stress analysis of rubber materials is presented. Special advantages and issues associated with the method are mentioned. (author). 4 refs., 3 figs

Finite groups with three conjugacy class sizes of some elements

Indian Academy of Sciences (India)

Conjugacy class sizes; p-nilpotent groups; finite groups. 1. Introduction. All groups ... group G has exactly two conjugacy class sizes of elements of prime power order. .... [5] Huppert B, Character Theory of Finite Groups, de Gruyter Exp. Math.

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

International Nuclear Information System (INIS)

Ackroyd, R.T.

1987-01-01

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

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

Science.gov (United States)

Romero, Ignacio; Segurado, Javier; LLorca, Javier

2008-04-01

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

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

International Nuclear Information System (INIS)

Romero, Ignacio; Segurado, Javier; LLorca, Javier

2008-01-01

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

Material model for non-linear finite element analyses of large concrete structures

NARCIS (Netherlands)

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

2016-01-01

A fully triaxial material model for concrete was implemented in a commercial finite element code. The only required input parameter was the cylinder compressive strength. The material model was suitable for non-linear finite element analyses of large concrete structures. The importance of including

Mathematical aspects of finite element methods for incompressible viscous flows

Science.gov (United States)

Gunzburger, M. D.

1986-01-01

Mathematical aspects of finite element methods are surveyed for incompressible viscous flows, concentrating on the steady primitive variable formulation. The discretization of a weak formulation of the Navier-Stokes equations are addressed, then the stability condition is considered, the satisfaction of which insures the stability of the approximation. Specific choices of finite element spaces for the velocity and pressure are then discussed. Finally, the connection between different weak formulations and a variety of boundary conditions is explored.

Extension to linear dynamics for hybrid stress finite element formulation based on additional displacements

Science.gov (United States)

Sumihara, K.

Based upon legitimate variational principles, one microscopic-macroscopic finite element formulation for linear dynamics is presented by Hybrid Stress Finite Element Method. The microscopic application of Geometric Perturbation introduced by Pian and the introduction of infinitesimal limit core element (Baby Element) have been consistently combined according to the flexible and inherent interpretation of the legitimate variational principles initially originated by Pian and Tong. The conceptual development based upon Hybrid Finite Element Method is extended to linear dynamics with the introduction of physically meaningful higher modes.

Finite element modelling of aluminum alloy 2024-T3 under transverse impact loading

Science.gov (United States)

Abdullah, Ahmad Sufian; Kuntjoro, Wahyu; Yamin, A. F. M.

2017-12-01

Fiber metal laminate named GLARE is a new aerospace material which has great potential to be widely used in future lightweight aircraft. It consists of aluminum alloy 2024-T3 and glass-fiber reinforced laminate. In order to produce reliable finite element model of impact response or crashworthiness of structure made of GLARE, one can initially model and validate the finite element model of the impact response of its constituents separately. The objective of this study was to develop a reliable finite element model of aluminum alloy 2024-T3 under low velocity transverse impact loading using commercial software ABAQUS. Johnson-Cook plasticity and damage models were used to predict the alloy's material properties and impact behavior. The results of the finite element analysis were compared to the experiment that has similar material and impact conditions. Results showed good correlations in terms of impact forces, deformation and failure progressions which concluded that the finite element model of 2024-T3 aluminum alloy under low velocity transverse impact condition using Johnson-Cook plastic and damage models was reliable.

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

International Nuclear Information System (INIS)

Lee Hae Sung.

1991-01-01

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

A finite element method for neutron transport

International Nuclear Information System (INIS)

Ackroyd, R.T.

1983-01-01

A completely boundary-free maximum principle for the first-order Boltzmann equation is derived from the completely boundary-free maximum principle for the mixed-parity Boltzmann equation. When continuity is imposed on the trial function for directions crossing interfaces the completely boundary-free principle for the first-order Boltzmann equation reduces to a maximum principle previously established directly from first principles and indirectly by the Euler-Lagrange method. Present finite element methods for the first-order Boltzmann equation are based on a weighted-residual method which permits the use of discontinuous trial functions. The new principle for the first-order equation can be used as a basis for finite-element methods with the same freedom from boundary conditions as those based on the weighted-residual method. The extremum principle as the parent of the variationally-derived weighted-residual equations ensures their good behaviour. (author)

Isogeometric finite element data structures based on Bézier extraction of T-splines

NARCIS (Netherlands)

Scott, M.A.; Borden, M.J.; Verhoosel, C.V.; Sederberg, T.W.; Hughes, T.J.R.

2011-01-01

We develop finite element data structures for T-splines based on Bézier extraction generalizing our previous work for NURBS. As in traditional finite element analysis, the extracted Bézier elements are defined in terms of a fixed set of polynomial basis functions, the so-called Bernstein basis. The

Rational bases and generalized barycentrics applications to finite elements and graphics

CERN Document Server

Wachspress, Eugene

2016-01-01

This three-part volume explores theory for construction of rational interpolation functions for continuous patchwork approximation.  Authored by the namesake of the Wachspress Coordinates, the book develops construction of basis functions for a broad class of elements which have widespread graphics and finite element application. Part one is the 1975 book A Rational Finite Element Basis (with minor updates and corrections) written by Dr. Wachspress.  Part two describes theoretical advances since 1975 and includes analysis of elements not considered previously.  Part three consists of annotated MATLAB programs implementing theory presented in parts one and two.

Finite element modelling of transport and drift effects in tokamak divertor and SOL

International Nuclear Information System (INIS)

Simard, M.; Marchand, R.; Boucher, C.; Gunn, J.P.

1996-01-01

A finite element code is used to simulate transport of a single-species plasma in the edge and divertor of a tokamak. The physical model is based on Braginskii's fluid equations for the conservation of particles, parallel momentum, ion and electron energy. In modelling recycling, transport of neutral density and energy is treated in the diffusion approximation. The electrostatic potential is obtained from the generalized Ohm's law. It is used to compute the electric field and the associated E x B drift. In a first approximation, transport is assumed to be ambipolar. The system of equations is discretized on an unstructured triangular mesh, thus permitting good spatial resolution near the X-point and an accurate description of divertor plates of arbitrary shape. Special care must be taken to prevent numerical corruption of the highly anisotropic thermal diffusion. Comparisons will be made between simulations and experimental results from TdeV. This will focus, in particular, on density and temperature profiles at the divertor plates, and on the plasma parallel velocity in the SOL. The asymmetry in the power deposited to the inner and outer divertors and the effect of magnetic field reversal will be considered. Comparisons with B2-Eirene simulation results will also be presented

Stochastic Finite Element Analysis of Non-Linear Structures Modelled by Plasticity Theory

DEFF Research Database (Denmark)

Frier, Christian; Sørensen, John Dalsgaard

2003-01-01

A Finite Element Reliability Method (FERM) is introduced to perform reliability analyses on two-dimensional structures in plane stress, modeled by non-linear plasticity theory. FERM is a coupling between the First Order Reliability Method (FORM) and the Finite Element Method (FEM). FERM can be us...

Multilayer Finite-Element Model Application to Define the Bearing Structure Element Stress State of Launch Complexes

Directory of Open Access Journals (Sweden)

V. A. Zverev

2016-01-01

Full Text Available The article objective is to justify the rationale for selecting the multilayer finite element model parameters of the bearing structure of a general-purpose launch complex unit.A typical design element of the launch complex unit, i.e. a mount of the hydraulic or pneumatic cylinder, block, etc. is under consideration. The mount represents a set of the cantilevered axis and external structural cage. The most loaded element of the cage is disk to which a moment is transferred from the cantilevered axis due to actuator effort acting on it.To calculate the stress-strain state of disk was used a finite element method. Five models of disk mount were created. The only difference in models was the number of layers of the finite elements through the thickness of disk. There were models, which had one, three, five, eight, and fourteen layers of finite elements through the thickness of disk. For each model, we calculated the equivalent stresses arising from the action of the test load. Disk models were formed and calculated using the MSC Nastran complex software.The article presents results in the table to show data of equivalent stresses in each of the multi-layered models and graphically to illustrate the changing equivalent stresses through the thickness of disk.Based on these results we have given advice on selecting the proper number of layers in the model allowing a desirable accuracy of results with the lowest run time. In addition, it is concluded that there is a need to use the multi-layer models in assessing the performance of structural elements in case the stress exceeds the allowable one in their surface layers.

OpenSeesPy: Python library for the OpenSees finite element framework

Science.gov (United States)

Zhu, Minjie; McKenna, Frank; Scott, Michael H.

2018-01-01

OpenSees, an open source finite element software framework, has been used broadly in the earthquake engineering community for simulating the seismic response of structural and geotechnical systems. The framework allows users to perform finite element analysis with a scripting language and for developers to create both serial and parallel finite element computer applications as interpreters. For the last 15 years, Tcl has been the primary scripting language to which the model building and analysis modules of OpenSees are linked. To provide users with different scripting language options, particularly Python, the OpenSees interpreter interface was refactored to provide multi-interpreter capabilities. This refactoring, resulting in the creation of OpenSeesPy as a Python module, is accomplished through an abstract interface for interpreter calls with concrete implementations for different scripting languages. Through this approach, users are able to develop applications that utilize the unique features of several scripting languages while taking advantage of advanced finite element analysis models and algorithms.

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

International Nuclear Information System (INIS)

Yeh, G.T.

1980-07-01

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

Numerical simulation of mechatronic sensors and actuators finite elements for computational multiphysics

CERN Document Server

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...

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

Energy Technology Data Exchange (ETDEWEB)

Yeh, G.T.

1980-07-01

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

[Research Progress and Prospect of Applications of Finite Element Method in Lumbar Spine Biomechanics].

Science.gov (United States)

Zhang, Zhenjun; Li, Yang; Liao, Zhenhua; Liu, Weiqiang

2016-12-01

Based on the application of finite element analysis in spine biomechanics,the research progress of finite element method applied in lumbar spine mechanics is reviewed and the prospect is forecasted.The related works,including lumbar ontology modeling,clinical application research,and occupational injury and protection,are summarized.The main research areas of finite element method are as follows:new accurate modeling process,the optimized simulation method,diversified clinical effect evaluation,and the clinical application of artificial lumbar disc.According to the recent research progress,the application prospects of finite element method,such as automation and individuation of modeling process,evaluation and analysis of new operation methods and simulation of mechanical damage and dynamic response,are discussed.The purpose of this paper is to provide the theoretical reference and practical guidance for the clinical lumbar problems by reviewing the application of finite element method in the field of the lumbar spine biomechanics.

Finite element analyses for RF photoinjector gun cavities

International Nuclear Information System (INIS)

Marhauser, F.

2006-01-01

This paper details electromagnetical, thermal and structural 3D Finite Element Analyses (FEA) for normal conducting RF photoinjector gun cavities. The simulation methods are described extensively. Achieved results are presented. (orig.)

Finite element analyses for RF photoinjector gun cavities

Energy Technology Data Exchange (ETDEWEB)

Marhauser, F. [Berliner Elektronenspeicherring-Gesellschaft fuer Synchrotronstrahlung mbH (BESSY), Berlin (Germany)

2006-07-01

This paper details electromagnetical, thermal and structural 3D Finite Element Analyses (FEA) for normal conducting RF photoinjector gun cavities. The simulation methods are described extensively. Achieved results are presented. (orig.)

Validation Assessment of a Glass-to-Metal Seal Finite-Element Model

Energy Technology Data Exchange (ETDEWEB)

Jamison, Ryan Dale [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States); Buchheit, Thomas E. [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States); Emery, John M [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States); Romero, Vicente J. [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States); Stavig, Mark E. [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States); Newton, Clay S. [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States); Brown, Arthur [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)

2017-10-01

Sealing glasses are ubiquitous in high pressure and temperature engineering applications, such as hermetic feed-through electrical connectors. A common connector technology are glass-to-metal seals where a metal shell compresses a sealing glass to create a hermetic seal. Though finite-element analysis has been used to understand and design glass-to-metal seals for many years, there has been little validation of these models. An indentation technique was employed to measure the residual stress on the surface of a simple glass-to-metal seal. Recently developed rate- dependent material models of both Schott 8061 and 304L VAR stainless steel have been applied to a finite-element model of the simple glass-to-metal seal. Model predictions of residual stress based on the evolution of material models are shown. These model predictions are compared to measured data. Validity of the finite- element predictions is discussed. It will be shown that the finite-element model of the glass-to-metal seal accurately predicts the mean residual stress in the glass near the glass-to-metal interface and is valid for this quantity of interest.

A cohesive finite element formulation for modelling fracture and ...

Indian Academy of Sciences (India)

cohesive elements experience material softening and lose their stress carrying capacity. A few simple ..... In the present work, a Lagrangian finite element procedure is employed. In this formu clation ...... o, is related to 'c o by,. 't o='c o ¼ 1 ہ. 1.

Some aspects of the quality assurance of personnel carrying out finite element analysis

International Nuclear Information System (INIS)

Dickenson, P.W.

1990-01-01

In this paper, the need to assess the competence of personnel carrying out finite element analysis is emphasised. In carrying out its regulatory role on behalf of the Health and Safety Executive, the Nuclear Installations Inspectorate (NII) must be satisfied that appropriate standards are developed and maintained by the licensee. Since finite element methods have an important bearing on the acceptance of a safety case, it follows that relevant codes should be adequately validated and the personnel applying the code should be competent. Attention is drawn to the work of the Quality Assurance Working Group of the National Agency for Finite Element Methods and Standards (NAFEMS) who are active in this area. The paper also considers the methods that are available to assess the competence of personnel engaged in finite element methods. (author)

Advances in dynamic relaxation techniques for nonlinear finite element analysis

International Nuclear Information System (INIS)

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

1995-01-01

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

Modelling of Conveyor Belt Passage by Driving Drum Using Finite Element Methods

Directory of Open Access Journals (Sweden)

Nikoleta Mikušová

2017-12-01

Full Text Available The finite element methods are used in many disciplines by the development of products, typically in mechanical engineering (for example in automotive industry, biomechanics, etc.. Some modern programs of the finite element's methods have specific tools (electromagnetic, fluid and structural simulations. The finite elements methods allow detailed presentation of structures by bending or torsion, complete design, testing and optimization before the prototype production. The aims of this paper were to the model of conveyor belt passage by driving drum. The model was created by the program Abaqus CAE. The created model presented data about forces, pressures, and deformation of the belt conveyor.

Finite-element pre-analysis for pressurized thermoshock tests

International Nuclear Information System (INIS)

Keinaenen, H.; Talja, H.; Lehtonen, M.; Rintamaa, R.; Bljumin, A.; Timofeev, B.

1992-05-01

The behaviour of a model pressure vessel is studied in a pressurized thermal shock loading. The tests were performed at the Prometey Institute in St. Petersburg. The calculations were performed at the Technical Research Centre of Finland. The report describes the preliminary finite-element analyses for the fourth, fifth and sixth thermoshock tests with the first model pressure vessel. Seven pressurized thermoshock tests were made with the same model using five different flaw geometries. In the first three tests the flaw was actually a blunt notch. In the two following tests (tests 4 and 5) a sharp pre-crack was produced before the test. In the last two test (tests 6 and 7) the old crack was used. According to the measurements and post-test ultrasonic examination of the crack front, the sixth test led to significant crack extension. Both temperatures and stresses were calculated using the finite-element method. The calculations were made using the idealized initial flaw geometry and preliminary material data. Both two-and three-dimensional models were used in the calculations. J-integral values were calculated from the elastic-plastic finite-element results. The stress intensity factor values were evaluated on the basis of the calculated J-integrals and compared with the preliminary material fracture toughness data obtained from the Prometey Institute

Finite element analysis of FRP-strengthened RC beams

Directory of Open Access Journals (Sweden)

Teeraphot Supaviriyakit

2004-05-01

Full Text Available This paper presents a non-linear finite element analysis of reinforced concrete beam strengthened with externally bonded FRP plates. The finite element modeling of FRP-strengthened beams is demonstrated. Concrete and reinforcing bars are modeled together as 8-node isoparametric 2D RC element. The FRP plate is modeled as 8-node isoparametric 2D elastic element. The glue is modeled as perfect compatibility by directly connecting the nodes of FRP with those of concrete since there is no failure at the glue layer. The key to the analysis is the correct material models of concrete, steel and FRP. Cracks and steel bars are modeled as smeared over the entire element. Stress-strain properties of cracked concrete consist of tensile stress model normal to crack, compressive stress model parallel to crack and shear stress model tangential to crack. Stressstrain property of reinforcement is assumed to be elastic-hardening to account for the bond between concrete and steel bars. FRP is modeled as elastic-brittle material. From the analysis, it is found that FEM can predict the load-displacement relation, ultimate load and failure mode of the beam correctly. It can also capture the cracking process for both shear-flexural peeling and end peeling modes similar to the experiment.

Finite Element Method Based Modeling of Resistance Spot-Welded Mild Steel

Directory of Open Access Journals (Sweden)

Miloud Zaoui

Full Text Available Abstract This paper deals with Finite Element refined and simplified models of a mild steel spot-welded specimen, developed and validated based on quasi-static cross-tensile experimental tests. The first model was constructed with a fine discretization of the metal sheet and the spot weld was defined as a special geometric zone of the specimen. This model provided, in combination with experimental tests, the input data for the development of the second model, which was constructed with respect to the mesh size used in the complete car finite element model. This simplified model was developed with coarse shell elements and a spring-type beam element was used to model the spot weld behavior. The global accuracy of the two models was checked by comparing simulated and experimental load-displacement curves and by studying the specimen deformed shapes and the plastic deformation growth in the metal sheets. The obtained results show that both fine and coarse finite element models permit a good prediction of the experimental tests.

Image segmentation with a finite element method

DEFF Research Database (Denmark)

Bourdin, Blaise

1999-01-01

regularization results, make possible to imagine a finite element resolution method.In a first time, the Mumford-Shah functional is introduced and some existing results are quoted. Then, a discrete formulation for the Mumford-Shah problem is proposed and its $\\Gamma$-convergence is proved. Finally, some...

Investigations on Actuator Dynamics through Theoretical and Finite Element Approach

Directory of Open Access Journals (Sweden)

Somashekhar S. Hiremath

2010-01-01

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

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

Science.gov (United States)

Hu, Guanghui; Xie, Hehu; Xu, Fei

2018-02-01

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

Finite element modeling of trolling-mode AFM.

Science.gov (United States)

Sajjadi, Mohammadreza; Pishkenari, Hossein Nejat; Vossoughi, Gholamreza

2018-06-01

Trolling mode atomic force microscopy (TR-AFM) has overcome many imaging problems in liquid environments by considerably reducing the liquid-resonator interaction forces. The finite element model of the TR-AFM resonator considering the effects of fluid and nanoneedle flexibility is presented in this research, for the first time. The model is verified by ABAQUS software. The effect of installation angle of the microbeam relative to the horizon and the effect of fluid on the system behavior are investigated. Using the finite element model, frequency response curve of the system is obtained and validated around the frequency of the operating mode by the available experimental results, in air and liquid. The changes in the natural frequencies in the presence of liquid are studied. The effects of tip-sample interaction on the excitation of higher order modes of the system are also investigated in air and liquid environments. Copyright © 2018 Elsevier B.V. All rights reserved.

Finite element simulations with ANSYS workbench 16

CERN Document Server

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...

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

KAUST Repository

Bangerth, Wolfgang

2011-12-01

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

Rigid body formulation in a finite element context with contact interaction

Science.gov (United States)

Refachinho de Campos, Paulo R.; Gay Neto, Alfredo

2018-03-01

The present work proposes a formulation to employ rigid bodies together with flexible bodies in the context of a nonlinear finite element solver, with contact interactions. Inertial contributions due to distribution of mass of a rigid body are fully developed, considering a general pole position associated with a single node, representing a rigid body element. Additionally, a mechanical constraint is proposed to connect a rigid region composed by several nodes, which is useful for linking rigid/flexible bodies in a finite element environment. Rodrigues rotation parameters are used to describe finite rotations, by an updated Lagrangian description. In addition, the contact formulation entitled master-surface to master-surface is employed in conjunction with the rigid body element and flexible bodies, aiming to consider their interaction in a rigid-flexible multibody environment. New surface parameterizations are presented to establish contact pairs, permitting pointwise interaction in a frictional scenario. Numerical examples are provided to show robustness and applicability of the methods.

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

Science.gov (United States)

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

2018-06-01

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

The Spectral/hp-Finite Element Method for Partial Differential Equations

DEFF Research Database (Denmark)

Engsig-Karup, Allan Peter

2009-01-01

dimensions. In the course the chosen programming environment is Matlab, however, this is by no means a necessary requirement. The mathematical level needed to grasp the details of this set of notes requires an elementary background in mathematical analysis and linear algebra. Each chapter is supplemented......This set of lecture notes provides an elementary introduction to both the classical Finite Element Method (FEM) and the extended Spectral/$hp$-Finite Element Method for solving Partial Differential Equations (PDEs). Many problems in science and engineering can be formulated mathematically...

Application of the finite element method to the neutron transport equation

International Nuclear Information System (INIS)

Martin, W.R.

1976-01-01

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

Stability Analysis of Anchored Soil Slope Based on Finite Element Limit Equilibrium Method

Directory of Open Access Journals (Sweden)

Rui Zhang

2016-01-01

Full Text Available Under the condition of the plane strain, finite element limit equilibrium method is used to study some key problems of stability analysis for anchored slope. The definition of safe factor in slices method is generalized into FEM. The “true” stress field in the whole structure can be obtained by elastic-plastic finite element analysis. Then, the optimal search for the most dangerous sliding surface with Hooke-Jeeves optimized searching method is introduced. Three cases of stability analysis of natural slope, anchored slope with seepage, and excavation anchored slope are conducted. The differences in safety factor quantity, shape and location of slip surface, anchoring effect among slices method, finite element strength reduction method (SRM, and finite element limit equilibrium method are comparatively analyzed. The results show that the safety factor given by the FEM is greater and the unfavorable slip surface is deeper than that by the slice method. The finite element limit equilibrium method has high calculation accuracy, and to some extent the slice method underestimates the effect of anchor, and the effect of anchor is overrated in the SRM.

FINITE ELEMENT MODELING OF THIN CIRCULAR SANDWICH PLATES DEFLECTION

Directory of Open Access Journals (Sweden)

K. S. Kurachka

2014-01-01

Full Text Available A mathematical model of a thin circular sandwich plate being under the vertical load is proposed. The model employs the finite element method and takes advantage of an axisymmetric finite element that leads to the small dimension of the resulting stiffness matrix and sufficient accuracy for practical calculations. The analytical expressions for computing local stiffness matrices are found, which can significantly speed up the process of forming the global stiffness matrix and increase the accuracy of calculations. A software is under development and verification. The discrepancy between the results of the mathematical model and those of analytical formulas for homogeneous thin circularsandwich plates does not exceed 7%.

Domain Decomposition Solvers for Frequency-Domain Finite Element Equations

KAUST Repository

Copeland, Dylan

2010-10-05

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

Domain Decomposition Solvers for Frequency-Domain Finite Element Equations

KAUST Repository

Copeland, Dylan; Kolmbauer, Michael; Langer, Ulrich

2010-01-01

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

A finite element model of ferroelectric/ferroelastic polycrystals

Energy Technology Data Exchange (ETDEWEB)

HWANG,STEPHEN C.; MCMEEKING,ROBERT M.

2000-02-17

A finite element model of polarization switching in a polycrystalline ferroelectric/ferroelastic ceramic is developed. It is assumed that a crystallite switches if the reduction in potential energy of the polycrystal exceeds a critical energy barrier per unit volume of switching material. Each crystallite is represented by a finite element with the possible dipole directions assigned randomly subject to crystallographic constraints. The model accounts for both electric field induced (i.e. ferroelectric) switching and stress induced (i.e. ferroelastic) switching with piezoelectric interactions. Experimentally measured elastic, dielectric, and piezoelectric constants are used consistently, but different effective critical energy barriers are selected phenomenologically. Electric displacement versus electric field, strain versus electric field, stress versus strain, and stress versus electric displacement loops of a ceramic lead lanthanum zirconate titanate (PLZT) are modeled well below the Curie temperature.

Finite Element Method for Analysis of Material Properties

DEFF Research Database (Denmark)

Rauhe, Jens Christian

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......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...

A Finite Element Model for convection-dominatel transport problems

International Nuclear Information System (INIS)

Carmo, E.G.D. do; Galeao, A.C.N.R.

1987-08-01

A new Protev-Galerkin Finite Element Model which automatically incorporates the search for the appropriate upwind direction is presented. It is also shown that modifying the Petrov-Galerkin weightin functions associated with elements adjascent to downwing boudaries effectively eliminates numerical oscillations normally obtained near boundary layers. (Author) [pt

Modelling Convergence of Finite Element Analysis of Cantilever Beam

African Journals Online (AJOL)

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

Finite element modeling of nanotube structures linear and non-linear models

CERN Document Server

Awang, Mokhtar; Muhammad, Ibrahim Dauda

2016-01-01

This book presents a new approach to modeling carbon structures such as graphene and carbon nanotubes using finite element methods, and addresses the latest advances in numerical studies for these materials. Based on the available findings, the book develops an effective finite element approach for modeling the structure and the deformation of grapheme-based materials. Further, modeling processing for single-walled and multi-walled carbon nanotubes is demonstrated in detail.

Investigation of the Behavior of Steel Shear Walls Using Finite Elements Analysis

OpenAIRE

Abubakri, K.; Veladi, H.

2016-01-01

Currently, steel shear walls are considered by engineers as an economic method against lateral loads imposed by wind and earthquake in tall structures. Accordingly, there is a growing need to develop accurate methods alongside approximation methods to estimate the behavior of these structural elements. The finite element technique is one of the strongest numerical methods in analysis of solid mechanics problems. Finite element analysis however requires high technical knowledge of the behavior...

Natural convection in asymmetric triangular enclosures heated from below

Science.gov (United States)

Kamiyo, O. M.; Angeli, D.; Barozzi, G. S.; Collins, M. W.

2014-11-01

Triangular enclosures are typical configurations of attic spaces found in residential as well as industrial pitched-roof buildings. Natural convection in triangular rooftops has received considerable attention over the years, mainly on right-angled and isosceles enclosures. In this paper, a finite volume CFD package is employed to study the laminar air flow and temperature distribution in asymmetric rooftop-shaped triangular enclosures when heated isothermally from the base wall, for aspect ratios (AR) 0.2 <= AR <= 1.0, and Rayleigh number (Ra) values 8 × 105 <= Ra <= 5 × 107. The effects of Rayleigh number and pitch angle on the flow structure and temperature distributions within the enclosure are analysed. Results indicate that, at low pitch angle, the heat transfer between the cold inclined and the hot base walls is very high, resulting in a multi-cellular flow structure. As the pitch angle increases, however, the number of cells reduces, and the total heat transfer rate progressively reduces, even if the Rayleigh number, being based on the enclosure height, rapidly increases. Physical reasons for the above effect are inspected.

Finite element modelling

International Nuclear Information System (INIS)

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

2015-01-01

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

Steam generator tube rupture simulation using extended finite element method

Energy Technology Data Exchange (ETDEWEB)

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

2016-08-15

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

Steam generator tube rupture simulation using extended finite element method

International Nuclear Information System (INIS)

Mohanty, Subhasish; Majumdar, Saurin; Natesan, Ken

2016-01-01

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

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

Science.gov (United States)

Rogers, J M; McCulloch, A D

1994-08-01

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

Finite element stress analysis of brick-mortar masonry under ...

African Journals Online (AJOL)

Stress analysis of a brick-mortar couplet as a substitute for brick wall structure has been performed by finite element method, and algorithm for determining the element stiffness matrix for a plane stress problem using the displacement approach was developed. The nodal displacements were derived for the stress in each ...

Generalization of mixed multiscale finite element methods with applications

Energy Technology Data Exchange (ETDEWEB)

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

2016-08-01

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

A review on application of finite element modelling in bone biomechanics

Directory of Open Access Journals (Sweden)

Sandeep Kumar Parashar

2016-09-01

Full Text Available In the past few decades the finite element modelling has been developed as an effective tool for modelling and simulation of the biomedical engineering system. Finite element modelling (FEM is a computational technique which can be used to solve the biomedical engineering problems based on the theories of continuum mechanics. This paper presents the state of art review on finite element modelling application in the four areas of bone biomechanics, i.e., analysis of stress and strain, determination of mechanical properties, fracture fixation design (implants, and fracture load prediction. The aim of this review is to provide a comprehensive detail about the development in the area of application of FEM in bone biomechanics during the last decades. It will help the researchers and the clinicians alike for the better treatment of patients and future development of new fixation designs.

Three- and four-noded planar elements using absolute nodal coordinate formulation

International Nuclear Information System (INIS)

Olshevskiy, Alexander; Dmitrochenko, Oleg; Kim, Changwan

2013-01-01

This paper investigates two new types of planar finite elements containing three and four nodes. These elements are the reduced forms of the spatial plate elements employing the absolute nodal coordinate approach. Elements of the first type use translations of nodes and global slopes as nodal coordinates and have 18 and 24 degrees of freedom. The slopes facilitate the prevention of the shear locking effect in bending problems. Furthermore, the slopes accurately describe the deformed shape of the elements. Triangular and quadrilateral elements of the second type use translational degrees of freedom only and, therefore, can be utilized successfully in problems without bending. These simple elements with 6 and 8 degrees of freedom are identical to the elements used in conventional formulation of the finite element method from the kinematical point of view. Similarly to the famous problem called “flying spaghetti” which is used often as a benchmark for beam elements, a kind of “flying lasagna” is simulated for the planar elements. Numerical results of simulations are presented.

Heat transfer model and finite element formulation for simulation of selective laser melting

Science.gov (United States)

Roy, Souvik; Juha, Mario; Shephard, Mark S.; Maniatty, Antoinette M.

2017-10-01

A novel approach and finite element formulation for modeling the melting, consolidation, and re-solidification process that occurs in selective laser melting additive manufacturing is presented. Two state variables are introduced to track the phase (melt/solid) and the degree of consolidation (powder/fully dense). The effect of the consolidation on the absorption of the laser energy into the material as it transforms from a porous powder to a dense melt is considered. A Lagrangian finite element formulation, which solves the governing equations on the unconsolidated reference configuration is derived, which naturally considers the effect of the changing geometry as the powder melts without needing to update the simulation domain. The finite element model is implemented into a general-purpose parallel finite element solver. Results are presented comparing to experimental results in the literature for a single laser track with good agreement. Predictions for a spiral laser pattern are also shown.

Biquartic Finite Volume Element Metho d Based on Lobatto-Guass Structure

Institute of Scientific and Technical Information of China (English)

Gao Yan-ni; Chen Yan-li

2015-01-01

In this paper, a biquartic finite volume element method based on Lobatto-Guass structure is presented for variable coefficient elliptic equation on rectangular partition. Not only the optimal H1 and L2 error estimates but also some super-convergent properties are available and could be proved for this method. The numer-ical results obtained by this finite volume element scheme confirm the validity of the theoretical analysis and the effectiveness of this method.

Finite element concept to derive isostatic residual maps ...

Indian Academy of Sciences (India)

A new space-domain operator based on the shape function concept of finite element analysis has been developed to derive the ... not require explicit assumptions on isostatic models. Besides .... This information is implicit in the Bouguer ...

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

International Nuclear Information System (INIS)

Toshimitsu, Fujisawa; Genki, Yagawa

2003-01-01

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

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

Energy Technology Data Exchange (ETDEWEB)

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

2003-07-01

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

Finite-element simulation of blood perfusion in muscle tissue during compression and sustained contraction.

Science.gov (United States)

Vankan, W J; Huyghe, J M; Slaaf, D W; van Donkelaar, C C; Drost, M R; Janssen, J D; Huson, A

1997-09-01

Mechanical interaction between tissue stress and blood perfusion in skeletal muscles plays an important role in blood flow impediment during sustained contraction. The exact mechanism of this interaction is not clear, and experimental investigation of this mechanism is difficult. We developed a finite-element model of the mechanical behavior of blood-perfused muscle tissue, which accounts for mechanical blood-tissue interaction in maximally vasodilated vasculature. Verification of the model was performed by comparing finite-element results of blood pressure and flow with experimental measurements in a muscle that is subject to well-controlled mechanical loading conditions. In addition, we performed simulations of blood perfusion during tetanic, isometric contraction and maximal vasodilation in a simplified, two-dimensional finite-element model of a rat calf muscle. A vascular waterfall in the venous compartment was identified as the main cause for blood flow impediment both in the experiment and in the finite-element simulations. The validated finite-element model offers possibilities for detailed analysis of blood perfusion in three-dimensional muscle models under complicated loading conditions.

Finite Element Crash Simulations and Impact-Induced Injuries

Directory of Open Access Journals (Sweden)

Jaroslav Mackerle

1999-01-01

Full Text Available This bibliography lists references to papers, conference proceedings and theses/dissertations dealing with finite element simulations of crashes, impact-induced injuries and their protection that were published in 1980–1998. 390 citations are listed.

Finite element simulation of thermal, elastic and plastic phenomena in fuel elements

International Nuclear Information System (INIS)

Soba, Alejandro; Denis, Alicia C.

1999-01-01

Taking as starting point an irradiation experiment of the first Argentine MOX fuel prototype, performed at the HFR reactor of Petten, Holland, the deformation suffered by the fuel element materials during burning has been numerically studied. Analysis of the pellet-cladding interaction is made by the finite element method. The code determines the temperature distribution and analyzes elastic and creep deformations, taking into account the dependency of the physical parameters of the problem on temperature. (author)

Hybrid Discrete Element - Finite Element Simulation for Railway Bridge-Track Interaction

Science.gov (United States)

Kaewunruen, S.; Mirza, O.

2017-10-01

At the transition zone or sometimes called ‘bridge end’ or ‘bridge approach’, the stiffness difference between plain track and track over bridge often causes aggravated impact loading due to uneven train movement onto the area. The differential track settlement over the transition has been a classical problem in railway networks, especially for the aging rail infrastructures around the world. This problem is also additionally worsened by the fact that the construction practice over the area is difficult, resulting in a poor compaction of formation and subgrade. This paper presents an advanced hybrid simulation using coupled discrete elements and finite elements to investigate dynamic interaction at the transition zone. The goal is to evaluate the dynamic stresses and to better understand the impact dynamics redistribution at the bridge end. An existing bridge ‘Salt Pan Creek Railway Bridge’, located between Revesby and Kingsgrove, has been chosen for detailed investigation. The Salt Pan Bridge currently demonstrates crushing of the ballast causing significant deformation and damage. Thus, it’s imperative to assess the behaviours of the ballast under dynamic loads. This can be achieved by modelling the nonlinear interactions between the steel rail and sleeper, and sleeper to ballast. The continuum solid elements of track components have been modelled using finite element approach, while the granular media (i.e. ballast) have been simulated by discrete element method. The hybrid DE/FE model demonstrates that ballast experiences significant stresses at the contacts between the sleeper and concrete section. These overburden stress exists in the regions below the outer rails, identify fouling and permanent deformation of the ballast.

Application of finite-element method to three-dimensional nuclear reactor analysis

International Nuclear Information System (INIS)

Cheung, K.Y.

1985-01-01

The application of the finite element method to solve a realistic one-or-two energy group, multiregion, three-dimensional static neutron diffusion problem is studied. Linear, quadratic, and cubic serendipity box-shape elements are used. The resulting sets of simultaneous algebraic equations with thousands of unknowns are solved by the conjugate gradient method, without forming the large coefficient matrix explicitly. This avoids the complicated data management schemes to store such a large coefficient matrix. Three finite-element computer programs: FEM-LINEAR, FEM-QUADRATIC and FEM-CUBIC were developed, using the linear, quadratic, and cubic box-shape elements respectively. They are self-contained, using simple nodal labeling schemes, without the need for separate finite element mesh generating routines. The efficiency and accuracy of these computer programs are then compared among themselves, and with other computer codes. The cubic element model is not recommended for practical usage because it gives almost identical results as the quadratic model, but it requires considerably longer computation time. The linear model is less accurate than the quadratic model, but it requires much shorter computation time. For a large 3-D problem, the linear model is to be preferred since it gives acceptable accuracy. The quadratic model may be used if improved accuracy is desired

Linear and Nonlinear Finite Elements.

Science.gov (United States)

1983-12-01

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

Assembly of finite element methods on graphics processors

KAUST Repository

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.

FINELM: a multigroup finite element diffusion code

International Nuclear Information System (INIS)

Higgs, C.E.; Davierwalla, D.M.

1981-06-01

FINELM is a FORTRAN IV program to solve the Neutron Diffusion Equation in X-Y, R-Z, R-theta, X-Y-Z and R-theta-Z geometries using the method of Finite Elements. Lagrangian elements of linear or higher degree to approximate the spacial flux distribution have been provided. The method of dissections, coarse mesh rebalancing and Chebyshev acceleration techniques are available. Simple user defined input is achieved through extensive input subroutines. The input preparation is described followed by a program structure description. Sample test cases are provided. (Auth.)

Hybrid Finite Element and Volume Integral Methods for Scattering Using Parametric Geometry

DEFF Research Database (Denmark)

Volakis, John L.; Sertel, Kubilay; Jørgensen, Erik

2004-01-01

n this paper we address several topics relating to the development and implementation of volume integral and hybrid finite element methods for electromagnetic modeling. Comparisons of volume integral equation formulations with the finite element-boundary integral method are given in terms of accu...... of vanishing divergence within the element but non-zero curl. In addition, a new domain decomposition is introduced for solving array problems involving several million degrees of freedom. Three orders of magnitude CPU reduction is demonstrated for such applications....

An efficient structural finite element for inextensible flexible risers

Science.gov (United States)

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

2017-12-01

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

Finite-element analysis of elastic sound-proof coupling thermal state

Science.gov (United States)

Tsyss, V. G.; Strokov, I. M.; Sergaeva, M. Yu

2018-01-01

The aim is in calculated determining of the elastic rubber-metal element thermal state of soundproof coupling ship shafting under variable influence during loads in time. Thermal coupling calculation is performed with finite element method using NX Simens software with Nastran solver. As a result of studies, the following results were obtained: - a volumetric picture of the temperature distribution over the array of the deformed coupling body is obtained; - time to reach steady-state thermal coupling mode has been determined; - dependences of maximum temperature and time to reach state on the established operation mode on rotation frequency and ambient temperature are determined. The findings prove the conclusion that usage of finite element analysis modern software can significantly speed up problem solving.

Hermitian Mindlin Plate Wavelet Finite Element Method for Load Identification

Directory of Open Access Journals (Sweden)

Xiaofeng Xue

2016-01-01

Full Text Available A new Hermitian Mindlin plate wavelet element is proposed. The two-dimensional Hermitian cubic spline interpolation wavelet is substituted into finite element functions to construct frequency response function (FRF. It uses a system’s FRF and response spectrums to calculate load spectrums and then derives loads in the time domain via the inverse fast Fourier transform. By simulating different excitation cases, Hermitian cubic spline wavelets on the interval (HCSWI finite elements are used to reverse load identification in the Mindlin plate. The singular value decomposition (SVD method is adopted to solve the ill-posed inverse problem. Compared with ANSYS results, HCSWI Mindlin plate element can accurately identify the applied load. Numerical results show that the algorithm of HCSWI Mindlin plate element is effective. The accuracy of HCSWI can be verified by comparing the FRF of HCSWI and ANSYS elements with the experiment data. The experiment proves that the load identification of HCSWI Mindlin plate is effective and precise by using the FRF and response spectrums to calculate the loads.

Rigid Finite Element Method in Analysis of Dynamics of Offshore Structures

CERN Document Server

Wittbrodt, Edmund; Maczyński, Andrzej; Wojciech, Stanisław

2013-01-01

This book describes new methods developed for modelling dynamics of machines commonly used in the offshore industry. These methods are based both on the rigid finite element method, used for the description of link deformations, and on homogeneous transformations and joint coordinates, which is applied to the modelling of multibody system dynamics. In this monograph, the bases of the rigid finite element method  and homogeneous transformations are introduced. Selected models for modelling dynamics of offshore devices are then verified both by using commercial software, based on the finite element method, as well as by using additional methods. Examples of mathematical models of offshore machines, such as a gantry crane for Blowout-Preventer (BOP) valve block transportation, a pedestal crane with shock absorber, and pipe laying machinery are presented. Selected problems of control in offshore machinery as well as dynamic optimization in device control are also discussed. Additionally, numerical simulations of...

Efficient Finite Element Models for Calculation of the No-load losses of the Transformer

Directory of Open Access Journals (Sweden)

Kamran Dawood

2017-10-01

Full Text Available Different transformer models are examined for the calculation of the no-load losses using finite element analysis. Two-dimensional and three-dimensional finite element analyses are used for the simulation of the transformer. Results of the finite element method are also compared with the experimental results. The Result shows that 3-dimensional provide high accuracy as compared to the 2 dimensional full and half model. However, the 2-dimensional half model is the less time-consuming method as compared to the 3 and 2-dimensional full model. Simulation time duration taken by the different models of the transformer is also compared. The difference between the 3-dimensional finite element method and experimental results are less than 3%. These numerical methods can help transformer designers to minimize the development of the prototype transformers.

The finite element response Matrix method

International Nuclear Information System (INIS)

Nakata, H.; Martin, W.R.

1983-01-01

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

Optimization of forging processes using finite element simulations

NARCIS (Netherlands)

Bonte, M.H.A.; Fourment, Lionel; Do, Tien-tho; van den Boogaard, Antonius H.; Huetink, Han

2010-01-01

During the last decades, simulation software based on the Finite Element Method (FEM) has significantly contributed to the design of feasible forming processes. Coupling FEM to mathematical optimization algorithms offers a promising opportunity to design optimal metal forming processes rather than

Finite element method for radiation heat transfer in multi-dimensional graded index medium

International Nuclear Information System (INIS)

Liu, L.H.; Zhang, L.; Tan, H.P.

2006-01-01

In graded index medium, ray goes along a curved path determined by Fermat principle, and curved ray-tracing is very difficult and complex. To avoid the complicated and time-consuming computation of curved ray trajectories, a finite element method based on discrete ordinate equation is developed to solve the radiative transfer problem in a multi-dimensional semitransparent graded index medium. Two particular test problems of radiative transfer are taken as examples to verify this finite element method. The predicted dimensionless net radiative heat fluxes are determined by the proposed method and compared with the results obtained by finite volume method. The results show that the finite element method presented in this paper has a good accuracy in solving the multi-dimensional radiative transfer problem in semitransparent graded index medium

An isoparametric shell of revolution finite element for harmonic loadings of any order

International Nuclear Information System (INIS)

Johnson, J.J.; Charman, C.M.

1981-01-01

A general isoparametric shell of revolution finite element subjected to any order harmonic loading is presented. Derivation of the element properties, its implementation in a general purpose finite element program, and its application to a sample problem are discussed. The element is isoparametric, that is, the variation of the displacements along the meridian of the shell and the shape of the meridian itself are approximated in an identical manner. The element has been implemented in the computer program MODSAP. A sample problem of a cooling tower subjected to wind loading is presented. (orig./HP)

Surface-Enhanced Raman Spectroscopy of Dye and Thiol Molecules Adsorbed on Triangular Silver Nano structures: A Study of Near-Field Enhancement, Localization of Hot-Spots, and Passivation of Adsorbed Carbonaceous Species

International Nuclear Information System (INIS)

Goncalves, M.R.; Marti, O.; Fabian Enderle, F.

2012-01-01

Surface-enhanced Raman spectroscopy (SERS) of thiols and dye molecules adsorbed on triangular silver nanostructures was investigated. The SERS hot-spots are localized at the edges and corners of the silver triangular particles. AFM and SEM measurements permit to observe many small clusters formed at the edges of triangular particles fabricated by nanosphere lithography. Finite-element calculations show that near-field enhancements can reach values of more than 200 at visible wavelengths, in the gaps between small spherical particles and large triangular particles, although for the later no plasmon resonance was found at the wavelengths investigated. The regions near the particles showing strong near-field enhancement are well correlated with spatial localization of SERS hot-spots done by confocal microscopy. Silver nanostructures fabricated by thermal evaporation present strong and fast fluctuating SERS activity, due to amorphous carbon contamination. Thiols and dye molecules seem to be able to passivate the undesired SERS activity on fresh evaporated silver. excitation: by far-field illumination of metal nanostructures or rough metal Raman scattering cross-section of gold-palladium target Temporal Fluctuation in SERS Temporal and spectral fluctuations.

Finite-element stress and deflection analysis of CDF yike and end plug

International Nuclear Information System (INIS)

Wands, R.; Grimson, J.; Kephart, R.; Theriot, D.

1982-01-01

A large detector is being designed to study anti pp collisions at center-of-mass energies of up to 2000 GeV as part of the Fermilab Collider Detector Facility (CDF). The central detector of this facility consists of a solenoid, calorimeter yoke, and a variety of particle measurement devices. The yoke will be a large steel structure that will provide the magnetic flux return path as well as support structure for calorimetry and other instrumentation. It must resist both electromagnetic and gravitational loads while exhibiting only small elastic deformations. The instrumented endplugs of the yoke are subjected to large electromagnetic loads. Moreover, due to the presence of wire chambers within these plugs, they must also be particularly stiff. The purpose of this paper is to present the results of a finite element stress and deflection analysis of these structures under various anticipated load conditions. The PATRAN-G finite element modeling program, installed on a CDF-VAX 11/780 and operating from a Ramtek 6212 colorgraphics terminal, was used to generate the analysis models. The actual finite element analysis was performed by the ANSYS general purpose finite element program, installed on the Fermilab Cyber 175's

Expanded Mixed Multiscale Finite Element Methods and Their Applications for Flows in Porous Media