The blade element momentum (BEM) method
DEFF Research Database (Denmark)
Branlard, Emmanuel Simon Pierre
2017-01-01
. The dynamic effects discussed are the dynamic wake/inflow model, the yaw and tilt model, the dynamic stall model, and models for the interference of the tower and nacelle. Some examples of steady and unsteady BEM simulations are given in a last section. The source code of a steady and unsteady BEM algorithm...
OpenBEM - An open source Boundary Element Method software in Acoustics
DEFF Research Database (Denmark)
Cutanda Henriquez, Vicente; Juhl, Peter Møller
2010-01-01
OpenBEM is a collection of open source programs for solving the Helmholtz Equation using the Boundary Element Method. The collection is written in Matlab by the authors and contains codes for dealing with exterior and interior problems in two or three dimensions as well as implementation of axi......-symmetric and half-space problems. It also contains a number of improvements such a dealing with thin objects and close surfaces, meshing for 2D and axisymmetrical problems, analytical solutions for verification, and a number of additional functions. This paper gives an overview of the capabilities of the program...... with examples of its use. Previous research results where OpenBEM was employed will be mentioned....
Maerten, F.; Maerten, L.; Pollard, D. D.
2014-11-01
Most analytical solutions to engineering or geological problems are limited to simple geometries. For example, analytical solutions have been found to solve for stresses around a circular hole in a plate. To solve more complex problems, mathematicians and engineers have developed powerful computer-aided numerical methods, which can be categorized into two main types: differential methods and integral methods. The finite element method (FEM) is a differential method that was developed in the 1950s and is one of the most commonly used numerical methods today. Since its development, other differential methods, including the boundary element method (BEM), have been developed to solve different types of problems. The purpose of this paper is to describe iBem3D, formally called Poly3D, a C++ and modular 3D boundary element computer program based on the theory of angular dislocations for modeling three-dimensional (3D) discontinuities in an elastic, heterogeneous, isotropic whole- or half-space. After 20 years and more than 150 scientific publications, we present in detail the formulation behind this method, its enhancements over the years as well as some important applications in several domains of the geosciences. The main advantage of using this formulation, for describing geological objects such as faults, resides in the possibility of modeling complex geometries without gaps and overlaps between adjacent triangular dislocation elements, which is a significant shortcoming for models using rectangular dislocation elements. Reliability, speed, simplicity, and accuracy are enhanced in the latest version of the computer code. Industrial applications include subseismic fault modeling, fractured reservoir modeling, interpretation and validation of fault connectivity and reservoir compartmentalization, depleted area and fault reactivation, and pressurized wellbore stability. Academic applications include earthquake and volcano monitoring, hazard mitigation, and slope
Energy Technology Data Exchange (ETDEWEB)
Snel, H. [Netherlands Energy Research Foundation ECN, Renewable Energy, Wind Energy (Netherlands)
1997-08-01
Recently the Blade Element Momentum (BEM) method has been made more versatile. Inclusion of rotational effects on time averaged profile coefficients have improved its achievements for performance calculations in stalled flow. Time dependence as a result of turbulent inflow, pitching actions and yawed operation is now treated more correctly (although more improvement is needed) than before. It is of interest to note that adaptations in modelling of unsteady or periodic induction stem from qualitative and quantitative insights obtained from free vortex models. Free vortex methods and further into the future Navier Stokes (NS) calculations, together with wind tunnel and field experiments, can be very useful in enhancing the potential of BEM for aero-elastic response calculations. It must be kept in mind however that extreme caution must be used with free vortex methods, as will be discussed in the following chapters. A discussion of the shortcomings and the strength of BEM and of vortex wake models is given. Some ideas are presented on how BEM might be improved without too much loss of efficiency. (EG)
Higher Order, Hybrid BEM/FEM Methods Applied to Antenna Modeling
Fink, P. W.; Wilton, D. R.; Dobbins, J. A.
2002-01-01
In this presentation, the authors address topics relevant to higher order modeling using hybrid BEM/FEM formulations. The first of these is the limitation on convergence rates imposed by geometric modeling errors in the analysis of scattering by a dielectric sphere. The second topic is the application of an Incomplete LU Threshold (ILUT) preconditioner to solve the linear system resulting from the BEM/FEM formulation. The final tOpic is the application of the higher order BEM/FEM formulation to antenna modeling problems. The authors have previously presented work on the benefits of higher order modeling. To achieve these benefits, special attention is required in the integration of singular and near-singular terms arising in the surface integral equation. Several methods for handling these terms have been presented. It is also well known that achieving he high rates of convergence afforded by higher order bases may als'o require the employment of higher order geometry models. A number of publications have described the use of quadratic elements to model curved surfaces. The authors have shown in an EFIE formulation, applied to scattering by a PEC .sphere, that quadratic order elements may be insufficient to prevent the domination of modeling errors. In fact, on a PEC sphere with radius r = 0.58 Lambda(sub 0), a quartic order geometry representation was required to obtain a convergence benefi.t from quadratic bases when compared to the convergence rate achieved with linear bases. Initial trials indicate that, for a dielectric sphere of the same radius, - requirements on the geometry model are not as severe as for the PEC sphere. The authors will present convergence results for higher order bases as a function of the geometry model order in the hybrid BEM/FEM formulation applied to dielectric spheres. It is well known that the system matrix resulting from the hybrid BEM/FEM formulation is ill -conditioned. For many real applications, a good preconditioner is required
Stress Wave Propagation in Soils Modelled by the Boundary Element Method
DEFF Research Database (Denmark)
Rasmussen, K. M.
This thesis deals with different aspects of the boundary element method (BEM) applied to stress wave propagation problems in soils. Among other things BEM formulations for coupled FEM and BEM, moving loads, direct BEM and indirect BEM are presented. For all the formulations both analytical...
Fink, P. W.; Khayat, M. A.; Wilton, D. R.
2005-01-01
It is known that higher order modeling of the sources and the geometry in Boundary Element Modeling (BEM) formulations is essential to highly efficient computational electromagnetics. However, in order to achieve the benefits of hIgher order basis and geometry modeling, the singular and near-singular terms arising in BEM formulations must be integrated accurately. In particular, the accurate integration of near-singular terms, which occur when observation points are near but not on source regions of the scattering object, has been considered one of the remaining limitations on the computational efficiency of integral equation methods. The method of singularity subtraction has been used extensively for the evaluation of singular and near-singular terms. Piecewise integration of the source terms in this manner, while manageable for bases of constant and linear orders, becomes unwieldy and prone to error for bases of higher order. Furthermore, we find that the singularity subtraction method is not conducive to object-oriented programming practices, particularly in the context of multiple operators. To extend the capabilities, accuracy, and maintainability of general-purpose codes, the subtraction method is being replaced in favor of the purely numerical quadrature schemes. These schemes employ singularity cancellation methods in which a change of variables is chosen such that the Jacobian of the transformation cancels the singularity. An example of the sin,oularity cancellation approach is the Duffy method, which has two major drawbacks: 1) In the resulting integrand, it produces an angular variation about the singular point that becomes nearly-singular for observation points close to an edge of the parent element, and 2) it appears not to work well when applied to nearly-singular integrals. Recently, the authors have introduced the transformation u(x(prime))= sinh (exp -1) x(prime)/Square root of ((y prime (exp 2))+ z(exp 2) for integrating functions of the form I
The FMM-BEM Method for the 3D Particulate Stokes Flow
Directory of Open Access Journals (Sweden)
Hassib Selmi
2014-01-01
Full Text Available This work introduces new functions based on the spherical harmonics and the solid harmonics which have been used to construct a multipole development for the 3D Stokes problem in order to reduce the operations costs in the BEM method. We show that the major properties of those functions are inherited from the solid harmonics. The contribution of this paper is the introduction of new formulas that serve to calculate the multipole moments and the transfer functions that are necessary for the schemes of order O(NlogN. Moreover, new translation formulas are introduced to obtain an O(N scheme. The error truncation of the resulting scheme is discussed. In comparison to the BEM that attains a limit storage at O(104, we present here a method based on FMM-BEM that attains a storage at a limit of O(106. The implementation of the method achieves a high accuracy level at a reasonable cost.
Investigation of the Unsteady Flow Behaviour on a Wind Turbine Using a BEM and a RANSE Method
Directory of Open Access Journals (Sweden)
Israa Alesbe
2016-01-01
Full Text Available Analyses of the unsteady flow behaviour of a 5 MW horizontal-axis wind turbine (HAWT rotor (Case I and a rotor with tower (Case II are carried out using a panel method and a RANSE method. The panel method calculations are obtained by applying the in-house boundary element method (BEM panMARE code, which is based on the potential flow theory. The BEM is a three-dimensional first-order panel method which can be used for investigating various steady and unsteady flow problems. Viscous flow simulations are carried out by using the RANSE solver ANSYS CFX 14.5. The results of Case I allow for the calculation of the global integral values of the torque and the thrust and include detailed information on the local flow field, such as the pressure distribution on the blade sections and the streamlines. The calculated pressure distribution by the BEM is compared with the corresponding values obtained by the RANSE solver. The tower geometry is considered in the simulation in Case II, so the unsteady forces due to the interaction between the tower and the rotor blades can be calculated. The application of viscous and inviscid flow methods to predict the forces on the HAWT allows for the evaluation of the viscous effects on the calculated HAWT flows.
Boundary element methods for electrical engineers
POLJAK, D
2005-01-01
In the last couple of decades the Boundary Element Method (BEM) has become a well-established technique that is widely used for solving various problems in electrical engineering and electromagnetics. Although there are many excellent research papers published in the relevant literature that describe various BEM applications in electrical engineering and electromagnetics, there has been a lack of suitable textbooks and monographs on the subject. This book presents BEM in a simple fashion in order to help the beginner to understand the very basic principles of the method. It initially derives B
Recent advances in boundary element methods
Manolis, GD
2009-01-01
Addresses the needs of the computational mechanics research community in terms of information on boundary integral equation-based methods and techniques applied to a variety of fields. This book collects both original and review articles on contemporary Boundary Element Methods (BEM) as well as on the Mesh Reduction Methods (MRM).
DEFF Research Database (Denmark)
Mohamed, Nader; Lazarova-Molnar, Sanja; Al-Jaroodi, Jameela
2016-01-01
and costs savings in smart buildings significantly depend on the monitoring and control methods used in the installed BEMS. This paper proposes a Cloud-Enabled BEMS (CE-BEMS) for Smart Buildings. This system can utilize cloud computing to provide enhanced management mechanisms and features for energy...... savings in smart buildings. This system is connected to the cloud to have access to a number of advanced cloud-based services to enhance energy management in smart buildings. In this paper, we discuss the current limitations of BEMS, the conceptual design of the proposed system, and the advantages...
Determining the performance of a Diffuser Augmented Wind Turbine using a combined CFD/BEM method
Directory of Open Access Journals (Sweden)
Kesby Joss E.
2017-01-01
Full Text Available Traditionally, the optimisation of a Diffuser Augmented Wind Turbine has focused on maximising power output. However, due to the often less than ideal location of small-scale turbines, cut-in speed and starting time are of equal importance in maximising Annual Energy Production, which is the ultimate goal of any wind turbine design. This paper proposes a method of determining power output, cut-in speed and starting time using a combination of Computational Fluid Dynamics and Blade Element Momentum theory. The proposed method has been validated against published experimental data.
Application of the boundary element method to transient heat conduction
Dargush, G. F.; Banerjee, P. K.
1991-01-01
An advanced boundary element method (BEM) is presented for the transient heat conduction analysis of engineering components. The numerical implementation necessarily includes higher-order conforming elements, self-adaptive integration and a multiregion capability. Planar, three-dimensional and axisymmetric analyses are all addressed with a consistent time-domain convolution approach, which completely eliminates the need for volume discretization for most practical analyses. The resulting general purpose algorithm establishes BEM as an attractive alternative to the more familiar finite difference and finite element methods for this class of problems. Several detailed numerical examples are included to emphasize the accuracy, stability and generality of the present BEM. Furthermore, a new efficient treatment is introduced for bodies with embedded holes. This development provides a powerful analytical tool for transient solutions of components, such as casting moulds and turbine blades, which are cumbersome to model when employing the conventional domain-based methods.
The nonconforming virtual element method
de Dios, B. Ayuso; Lipnikov, K.; Manzini, G
2014-01-01
We introduce the nonconforming Virtual Element Method (VEM) for the approximation of second order elliptic problems. We present the construction of the new element in two and three dimensions, highlighting the main differences with the conforming VEM and the classical nonconforming finite element methods. We provide the error analysis and establish the equivalence with a family of mimetic finite difference methods.
International Symposium on Boundary Element Methods : Advances in Solid and Fluid Mechanics
Tseng, Kadin
1990-01-01
The Boundary Element Method (BEM) has become established as an effective tool for the solutions of problems in engineering science. The salient features of the BEM have been well documented in the open literature and therefore will not be elaborated here. The BEM research has progressed rapidly, especially in the past decade and continues to evolve worldwide. This Symposium was organized to provide an international forum for presentation of current research in BEM for linear and nonlinear problems in solid and fluid mechanics and related areas. To this end, papers on the following topics were included: rotary wing aerodynamics, unsteady aerodynamics, design and optimization, elasticity, elasto dynamics and elastoplasticity, fracture mechanics, acoustics, diffusion and wave motion, thermal analysis, mathematical aspects and boundary/finite element coupled methods. A special session was devoted to parallel/vector supercomputing with emphasis on mas sive parallelism. This Symposium was sponsored by United ...
DEFF Research Database (Denmark)
Cutanda Henríquez, Vicente; Juhl, Peter Møller
2008-01-01
It is well known that the Boundary Element Method (BEM) in its standard version cannot readily handle situations where the calculation point is very close to a surface. These problems are found: i) when two boundary surfaces are very close together, such as in narrow gaps and thin bodies, and ii)...
quadratic spline finite element method
Directory of Open Access Journals (Sweden)
A. R. Bahadir
2002-01-01
Full Text Available The problem of heat transfer in a Positive Temperature Coefficient (PTC thermistor, which may form one element of an electric circuit, is solved numerically by a finite element method. The approach used is based on Galerkin finite element using quadratic splines as shape functions. The resulting system of ordinary differential equations is solved by the finite difference method. Comparison is made with numerical and analytical solutions and the accuracy of the computed solutions indicates that the method is well suited for the solution of the PTC thermistor problem.
Stochastic finite element method with simple random elements
Starkloff, Hans-Jörg
2008-01-01
We propose a variant of the stochastic finite element method, where the random elements occuring in the problem formulation are approximated by simple random elements, i.e. random elements with only a finite number of possible values.
Programming the finite element method
Smith, I M; Margetts, L
2013-01-01
Many students, engineers, scientists and researchers have benefited from the practical, programming-oriented style of the previous editions of Programming the Finite Element Method, learning how to develop computer programs to solve specific engineering problems using the finite element method. This new fifth edition offers timely revisions that include programs and subroutine libraries fully updated to Fortran 2003, which are freely available online, and provides updated material on advances in parallel computing, thermal stress analysis, plasticity return algorithms, convection boundary c
Wang, Qiao; Zhou, Wei; Cheng, Yonggang; Ma, Gang; Chang, Xiaolin
2017-04-01
A line integration method (LIM) is proposed to calculate the domain integrals for 3D problems. In the proposed method, the domain integrals are transformed into boundary integrals and only line integrals on straight lines are needed to be computed. A background cell structure is applied to further simplify the line integrals and improve the accuracy. The method creates elements only on the boundary, and the integral lines are created from the boundary elements. The procedure is quite suitable for the boundary element method, and we have applied it to 3D situations. Directly applying the method is time-consuming since the complexity of the computational time is O( NM), where N and M are the numbers of nodes and lines, respectively. To overcome this problem, the fast multipole method is used with the LIM for large-scale computation. The numerical results show that the proposed method is efficient and accurate.
Boundary element method applied to a gas-fired pin-fin-enhanced heat pipe
Energy Technology Data Exchange (ETDEWEB)
Andraka, C.E.; Knorovsky, G.A.; Drewien, C.A.
1998-02-01
The thermal conduction of a portion of an enhanced surface heat exchanger for a gas fired heat pipe solar receiver was modeled using the boundary element and finite element methods (BEM and FEM) to determine the effect of weld fillet size on performance of a stud welded pin fin. A process that could be utilized by others for designing the surface mesh on an object of interest, performing a conversion from the mesh into the input format utilized by the BEM code, obtaining output on the surface of the object, and displaying visual results was developed. It was determined that the weld fillet on the pin fin significantly enhanced the heat performance, improving the operating margin of the heat exchanger. The performance of the BEM program on the pin fin was measured (as computational time) and used as a performance comparison with the FEM model. Given similar surface element densities, the BEM method took longer to get a solution than the FEM method. The FEM method creates a sparse matrix that scales in storage and computation as the number of nodes (N), whereas the BEM method scales as N{sup 2} in storage and N{sup 3} in computation.
DEFF Research Database (Denmark)
Døssing, Mads; Aagaard Madsen, Helge; Bak, Christian
2012-01-01
by the positive effect of wake rotation, which locally causes the efficiency to exceed the Betz limit. Wake expansion has a negative effect, which is most important at high tip speed ratios. It was further found that by using , it is possible to obtain a 5% reduction in flap bending moment when compared with BEM...... out using BEM as well. Validation of shows good agreement with the flow calculated using an advanced actuator disk method. The maximum power was found at a tip speed ratio of 7 using , and this is lower than the optimum tip speed ratio of 8 found for BEM. The difference is primarily caused......The blade element momentum (BEM) method is widely used for calculating the quasi-steady aerodynamics of horizontal axis wind turbines. Recently, the BEM method has been expanded to include corrections for wake expansion and the pressure due to wake rotation (), and more accurate solutions can now...
Finite element methods for engineers
Fenner, Roger T
2013-01-01
This book is intended as a textbook providing a deliberately simple introduction to finite element methods in a way that should be readily understandable to engineers, both students and practising professionals. Only the very simplest elements are considered, mainly two dimensional three-noded “constant strain triangles”, with simple linear variation of the relevant variables. Chapters of the book deal with structural problems (beams), classification of a broad range of engineering into harmonic and biharmonic types, finite element analysis of harmonic problems, and finite element analysis of biharmonic problems (plane stress and plane strain). Full Fortran programs are listed and explained in detail, and a range of practical problems solved in the text. Despite being somewhat unfashionable for general programming purposes, the Fortran language remains very widely used in engineering. The programs listed, which were originally developed for use on mainframe computers, have been thoroughly updated for use ...
DEFF Research Database (Denmark)
Cutanda Henriquez, Vicente; Andersen, Peter Risby; Jensen, Jakob Søndergaard
2016-01-01
In recent years, boundary element method (BEM) and finite element method (FEM) implementations of acoustics in fluids with viscous and thermal losses have been developed. They are based on the linearized Navier–Stokes equations with no flow. In this paper, such models with acoustic losses...
DEFF Research Database (Denmark)
Cutanda Henriquez, Vicente; Andersen, Peter Risby; Jensen, Jakob Søndergaard
2016-01-01
In recent years, boundary element method (BEM) and finite element method (FEM) implementations of acoustics in fluids with viscous and thermal losses have been developed. They are based on the linearized Navier–Stokes equations with no flow. In this paper, such models with acoustic losses are app...
Finite elements methods in mechanics
Eslami, M Reza
2014-01-01
This book covers all basic areas of mechanical engineering, such as fluid mechanics, heat conduction, beams, and elasticity with detailed derivations for the mass, stiffness, and force matrices. It is especially designed to give physical feeling to the reader for finite element approximation by the introduction of finite elements to the elevation of elastic membrane. A detailed treatment of computer methods with numerical examples are provided. In the fluid mechanics chapter, the conventional and vorticity transport formulations for viscous incompressible fluid flow with discussion on the method of solution are presented. The variational and Galerkin formulations of the heat conduction, beams, and elasticity problems are also discussed in detail. Three computer codes are provided to solve the elastic membrane problem. One of them solves the Poisson’s equation. The second computer program handles the two dimensional elasticity problems, and the third one presents the three dimensional transient heat conducti...
Boundary element method solution for large scale cathodic protection problems
Rodopoulos, D. C.; Gortsas, T. V.; Tsinopoulos, S. V.; Polyzos, D.
2017-12-01
Cathodic protection techniques are widely used for avoiding corrosion sequences in offshore structures. The Boundary Element Method (BEM) is an ideal method for solving such problems because requires only the meshing of the boundary and not the whole domain of the electrolyte as the Finite Element Method does. This advantage becomes more pronounced in cathodic protection systems since electrochemical reactions occur mainly on the surface of the metallic structure. The present work aims to solve numerically a sacrificial cathodic protection problem for a large offshore platform. The solution of that large-scale problem is accomplished by means of “PITHIA Software” a BEM package enhanced by Hierarchical Matrices (HM) and Adaptive Cross Approximation (ACA) techniques that accelerate drastically the computations and reduce memory requirements. The nonlinear polarization curves for steel and aluminium in seawater are employed as boundary condition for the under protection metallic surfaces and aluminium anodes, respectively. The potential as well as the current density at all the surface of the platform are effectively evaluated and presented.
Directory of Open Access Journals (Sweden)
Dina V. Lazareva
2015-06-01
Full Text Available A new mathematical model of asymmetric support structure frame type is built on the basis of numerical-analytical boundary elements method (BEM. To describe the design scheme used is the graph theory. Building the model taken into account is the effect of frame members restrained torsion, which presence is due to the fact that these elements are thin-walled. The built model represents a real object as a two-axle semi-trailer platform. To implement the BEM algorithm obtained are analytical expressions of the fundamental functions and vector load components. The effected calculations are based on the semi-trailer two different models, using finite elements and boundary elements methods. The analysis showed that the error between the results obtained on the basis of two numerical methods and experimental data is about 4%, that indicates the adequacy of the proposed mathematical model.
Peridynamic Multiscale Finite Element Methods
Energy Technology Data Exchange (ETDEWEB)
Costa, Timothy [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States); Bond, Stephen D. [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States); Littlewood, David John [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States); Moore, Stan Gerald [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)
2015-12-01
The problem of computing quantum-accurate design-scale solutions to mechanics problems is rich with applications and serves as the background to modern multiscale science research. The prob- lem can be broken into component problems comprised of communicating across adjacent scales, which when strung together create a pipeline for information to travel from quantum scales to design scales. Traditionally, this involves connections between a) quantum electronic structure calculations and molecular dynamics and between b) molecular dynamics and local partial differ- ential equation models at the design scale. The second step, b), is particularly challenging since the appropriate scales of molecular dynamic and local partial differential equation models do not overlap. The peridynamic model for continuum mechanics provides an advantage in this endeavor, as the basic equations of peridynamics are valid at a wide range of scales limiting from the classical partial differential equation models valid at the design scale to the scale of molecular dynamics. In this work we focus on the development of multiscale finite element methods for the peridynamic model, in an effort to create a mathematically consistent channel for microscale information to travel from the upper limits of the molecular dynamics scale to the design scale. In particular, we first develop a Nonlocal Multiscale Finite Element Method which solves the peridynamic model at multiple scales to include microscale information at the coarse-scale. We then consider a method that solves a fine-scale peridynamic model to build element-support basis functions for a coarse- scale local partial differential equation model, called the Mixed Locality Multiscale Finite Element Method. Given decades of research and development into finite element codes for the local partial differential equation models of continuum mechanics there is a strong desire to couple local and nonlocal models to leverage the speed and state of the
A Galleria Boundary Element Method for two-dimensional nonlinear magnetostatics
Brovont, Aaron D.
The Boundary Element Method (BEM) is a numerical technique for solving partial differential equations that is used broadly among the engineering disciplines. The main advantage of this method is that one needs only to mesh the boundary of a solution domain. A key drawback is the myriad of integrals that must be evaluated to populate the full system matrix. To this day these integrals have been evaluated using numerical quadrature. In this research, a Galerkin formulation of the BEM is derived and implemented to solve two-dimensional magnetostatic problems with a focus on accurate, rapid computation. To this end, exact, closed-form solutions have been derived for all the integrals comprising the system matrix as well as those required to compute fields in post-processing; the need for numerical integration has been eliminated. It is shown that calculation of the system matrix elements using analytical solutions is 15-20 times faster than with numerical integration of similar accuracy. Furthermore, through the example analysis of a c-core inductor, it is demonstrated that the present BEM formulation is a competitive alternative to the Finite Element Method (FEM) for linear magnetostatic analysis. Finally, the BEM formulation is extended to analyze nonlinear magnetostatic problems via the Dual Reciprocity Method (DRBEM). It is shown that a coarse, meshless analysis using the DRBEM is able to achieve RMS error of 3-6% compared to a commercial FEM package in lightly saturated conditions.
Transmission Loss Assessment for a Muffler by Boundary Element Method Approach
Directory of Open Access Journals (Sweden)
Ovidiu Vasile
2010-01-01
Full Text Available This paper investigates the acoustic performance of two cases for reac-tive mufflers using Boundary Element Method (BEM analysis. Modeling procedures for accurate performance prediction had led to the devel-opment of new methods for practical muffler components in design. The transmission loss (TL is the more widely can be easily computed with a BEM analysis. The author presents an overview of the principles and theoretical formulation of BEM for predicting the transmission loss of a muffler, the pressure and velocity distribution on surfaces of muf-fler. At the end of the paper is presented a comparison of two cases of mufflers for transmission loss. The predicted results agreed in some limits with the experimental data published in literature.
Fast iterative boundary element methods for high-frequency scattering problems in 3D elastodynamics
Chaillat, Stéphanie; Darbas, Marion; Le Louër, Frédérique
2017-07-01
The fast multipole method is an efficient technique to accelerate the solution of large scale 3D scattering problems with boundary integral equations. However, the fast multipole accelerated boundary element method (FM-BEM) is intrinsically based on an iterative solver. It has been shown that the number of iterations can significantly hinder the overall efficiency of the FM-BEM. The derivation of robust preconditioners for FM-BEM is now inevitable to increase the size of the problems that can be considered. The main constraint in the context of the FM-BEM is that the complete system is not assembled to reduce computational times and memory requirements. Analytic preconditioners offer a very interesting strategy by improving the spectral properties of the boundary integral equations ahead from the discretization. The main contribution of this paper is to combine an approximate adjoint Dirichlet to Neumann (DtN) map as an analytic preconditioner with a FM-BEM solver to treat Dirichlet exterior scattering problems in 3D elasticity. The approximations of the adjoint DtN map are derived using tools proposed in [40]. The resulting boundary integral equations are preconditioned Combined Field Integral Equations (CFIEs). We provide various numerical illustrations of the efficiency of the method for different smooth and non-smooth geometries. In particular, the number of iterations is shown to be completely independent of the number of degrees of freedom and of the frequency for convex obstacles.
Spectral BEM for the Analysis of Wave Propagation and Fracture Mechanics
Li, Jun; Khodaei, Zahra Sharif; Aliabadi, M. H.
This paper presents a spectral boundary element formulation for analysis of structures subjected to dynamic loading. Two types of spectral elements based on Lobatto polynomials and Legendre polynomials are used. Two-dimensional analyses of elastic wave propagation in solids with and without cracks are carried out in the Laplace frequency domain with both conventional BEM and the spectral BEM. By imposing the requirement of the same level of accuracy, it was found that the use of spectral elements, compared with conventional quadratic elements, reduced the total number of nodes required for modeling high-frequency wave propagation. Benchmark examples included a simple one-dimensional bar for which analytical solution is available and a more complex crack problem where stress intensity factors were evaluated. Special crack tip elements are developed for the first time for the spectral elements to accurately model the crack tip fields. Although more integration points were used for the integrals associated with spectral elements than the conventional quadratic elements, shorter computation times were achieved through the application of the spectral BEM. This indicates that the spectral BEM is a more efficient method for the numerical modeling of structural health monitoring (SHM) processes, in which high-frequency waves are commonly used to detect damage, such as cracks, in structures.
Directory of Open Access Journals (Sweden)
Syarizal Fonna
2016-01-01
Full Text Available Many studies have suggested that the corrosion detection of reinforced concrete (RC based on electrical potential on concrete surface was an ill-posed problem, and thus it may present an inaccurate interpretation of corrosion. However, it is difficult to prove the ill-posed problem of the RC corrosion detection by experiment. One promising technique is using a numerical method. The objective of this study is to simulate the ill-posed problem of RC corrosion detection based on electrical potential on a concrete surface using the Boundary Element Method (BEM. BEM simulates electrical potential within a concrete domain. In order to simulate the electrical potential, the domain is assumed to be governed by Laplace’s equation. The boundary conditions for the corrosion area and the noncorrosion area of rebar were selected from its polarization curve. A rectangular reinforced concrete model with a single rebar was chosen to be simulated using BEM. The numerical simulation results using BEM showed that the same electrical potential distribution on the concrete surface could be generated from different combinations of parameters. Corresponding to such a phenomenon, this problem can be categorized as an ill-posed problem since it has many solutions. Therefore, BEM successfully simulates the ill-posed problem of reinforced concrete corrosion detection.
Simulations of micron-scale fracture using atomistic-based boundary element method
Wu, Xiaojie; Li, Xiantao
2017-12-01
A new formulation of a boundary element method (BEM) is proposed in this paper to simulate cracks at the micron scale. The main departure from the traditional BEMs is that the current model is derived from the underlying atomistic model, which involves the interactions of atoms at the scale of Angstroms. By using the lattice Green’s function, the new BEM formulation eliminates the excessive atomic degrees of freedom away from crack tips, and directly couples the process zones with the physical boundary conditions. We show that with such a drastic reduction, one can simulate brittle fracture process on the scale of microns, for which the entire system consists of a few billion atoms. We discuss several numerical issues to make the implementation more efficient. Examples will be presented for cracks in the bcc iron system.
Cojocaru, E.
2009-01-01
The finite element method has become a preeminent simulation technique in electromagnetics. For problems involving anisotropic media and metamaterials, proper algorithms should be developed. It has been proved that discretizing in quadratic triangular elements may lead to an improved accuracy. Here we present a collection of elemental matrices evaluated analytically for quadratic triangular elements. They could be useful for the finite element method in advanced electromagnetics.
Automation of finite element methods
Korelc, Jože
2016-01-01
New finite elements are needed as well in research as in industry environments for the development of virtual prediction techniques. The design and implementation of novel finite elements for specific purposes is a tedious and time consuming task, especially for nonlinear formulations. The automation of this process can help to speed up this process considerably since the generation of the final computer code can be accelerated by order of several magnitudes. This book provides the reader with the required knowledge needed to employ modern automatic tools like AceGen within solid mechanics in a successful way. It covers the range from the theoretical background, algorithmic treatments to many different applications. The book is written for advanced students in the engineering field and for researchers in educational and industrial environments.
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.
Galerkin finite element methods for wave problems
Indian Academy of Sciences (India)
Galerkin ﬁnite element methods for wave problems ... hp-Finite element method; continuous Galerkin methods; wave solutions; Gibbs' phenomenon. ... Department of Aerospace Engineering, Indian Institute of Technology, Kanpur 208 016, India; Institute of High Performance Computing, 1, Science Park Road, Singapore ...
Directory of Open Access Journals (Sweden)
Guilherme Borges Bond
2012-07-01
Full Text Available O bem-estar de animais de produção tem sido discutido nos âmbitos comercial, social e acadêmico, sendo que tal discussão pode ser enriquecida pela elaboração de protocolos de diagnóstico de bem-estar animal bem definidos, favorecendo a regulamentação de uma legislação específica. O objetivo desta revisão é discutir os métodos de diagnóstico de bem-estar animal e apontar os principais pontos críticos que afetam o bem-estar dos bovinos leiteiros. O diagnóstico de bem-estar compreende a observação do comportamento animal e de indicadores fisiológicos e sanitários, como análise hematológica e dosagem de hormônios, análise do escore de locomoção, a observação de lesões corporais e o estado geral de saúde dos animais. Tais ferramentas permitem verificar quais são os principais pontos críticos que afetam o bem-estar dos animais e construir estratégias de melhoria. As vacas em lactação podem sofrer restrições ambientais, nutricionais e sanitárias. Os bezerros passam pelo distresse do desmame precoce e do isolamento social. Alguns pontos críticos de bem-estar de gado leiteiro reconhecidos internacionalmente parecem prováveis no cenário brasileiro. Entretanto, é possível a existência de diferenças importantes em relação aos sistemas de produção praticados no Brasil e no exterior, uma vez que o acesso ao pasto é um fator comum na produção brasileira e pode estar associado a um maior grau de bem-estar animal. Dessa forma, é importante a condução de trabalhos de diagnóstico de bem-estar específico para os animais envolvidos com a produção de leite no Brasil.The welfare of farm animals is under broad discussion within the commercial, social and academic environments, and discussion may be enriched by specific guidelines and legislation based on well-defined assessment protocols. The objective of this review is to discuss the methods for assessing animal welfare and to point out the main critical
Hybrid fully nonlinear BEM-LBM numerical wave tank with applications in naval hydrodynamics
Mivehchi, Amin; Grilli, Stephan T.; Dahl, Jason M.; O'Reilly, Chris M.; Harris, Jeffrey C.; Kuznetsov, Konstantin; Janssen, Christian F.
2017-11-01
simulation of the complex dynamics response of ships in waves is typically modeled by nonlinear potential flow theory, usually solved with a higher order BEM. In some cases, the viscous/turbulent effects around a structure and in its wake need to be accurately modeled to capture the salient physics of the problem. Here, we present a fully 3D model based on a hybrid perturbation method. In this method, the velocity and pressure are decomposed as the sum of an inviscid flow and viscous perturbation. The inviscid part is solved over the whole domain using a BEM based on cubic spline element. These inviscid results are then used to force a near-field perturbation solution on a smaller domain size, which is solved with a NS model based on LBM-LES, and implemented on GPUs. The BEM solution for large grids is greatly accelerated by using a parallelized FMM, which is efficiently implemented on large and small clusters, yielding an almost linear scaling with the number of unknowns. A new representation of corners and edges is implemented, which improves the global accuracy of the BEM solver, particularly for moving boundaries. We present model results and the recent improvements of the BEM, alongside results of the hybrid model, for applications to problems. Office of Naval Research Grants N000141310687 and N000141612970.
Stability analysis of shallow tunnels subjected to eccentric loads by a boundary element method
Directory of Open Access Journals (Sweden)
Mehdi Panji
2016-08-01
Full Text Available In this paper, stress behavior of shallow tunnels under simultaneous non-uniform surface traction and symmetric gravity loading was studied using a direct boundary element method (BEM. The existing full-plane elastostatic fundamental solutions to displacement and stress fields were used and implemented in a developed algorithm. The cross-section of the tunnel was considered in circular, square, and horseshoe shapes and the lateral coefficient of the domain was assumed as unit quantity. Double-node procedure of the BEM was applied at the corners to improve the model including sudden traction changes. The results showed that the method used was a powerful tool for modeling underground openings under various external as well as internal loads. Eccentric loads significantly influenced the stress pattern of the surrounding tunnel. The achievements can be practically used in completing and modifying regulations for stability investigation of shallow tunnels.
Quantum algorithms and the finite element method
Montanaro, Ashley; Pallister, Sam
2015-01-01
The finite element method is used to approximately solve boundary value problems for differential equations. The method discretises the parameter space and finds an approximate solution by solving a large system of linear equations. Here we investigate the extent to which the finite element method can be accelerated using an efficient quantum algorithm for solving linear equations. We consider the representative general question of approximately computing a linear functional of the solution t...
DIFFERENT ELEMENT METHODS IN ENGINEERING PRACTICE
African Journals Online (AJOL)
2012-11-03
Nov 3, 2012 ... (or system) in the sense that the behavior at discrete number of ... squares method can be used in deriving the element equation. Whichever formulation approach is used, the result- ing element equation are solved using appropriate ma- trix solvers .... symmetric stiffness matrix, but also the non-essential.
On the modeling of narrow gaps using the standard BEM
DEFF Research Database (Denmark)
Henriquez, Vicente Cutanda; Juhl, P.M.; Jacobsen, Finn
2001-01-01
Numerical methods based on the Helmholtz integral equation are well suited for solving acoustic scattering and diffraction problems at relatively low frequencies. However, it is well known that the standard method becomes degenerate if the objects that disturb the sound field are very thin....... This paper makes use of a standard axisymmetric Helmholtz integral equation formulation and its boundary element method (BEM) implementation to study the behavior of the method on two test cases: a thin rigid disk of variable thickness and two rigid cylinders separated by a gap of variable width. Both...... with in the literature. A simple integration technique that can extend the range of thicknesses/widths tractable by the otherwise unmodified standard formulation is presented and tested. This technique is valid for both cases. The modeling of acoustic transducers Like sound intensity probes and condenser microphones has...
Spectral analysis method for detecting an element
Blackwood, Larry G [Idaho Falls, ID; Edwards, Andrew J [Idaho Falls, ID; Jewell, James K [Idaho Falls, ID; Reber, Edward L [Idaho Falls, ID; Seabury, Edward H [Idaho Falls, ID
2008-02-12
A method for detecting an element is described and which includes the steps of providing a gamma-ray spectrum which has a region of interest which corresponds with a small amount of an element to be detected; providing nonparametric assumptions about a shape of the gamma-ray spectrum in the region of interest, and which would indicate the presence of the element to be detected; and applying a statistical test to the shape of the gamma-ray spectrum based upon the nonparametric assumptions to detect the small amount of the element to be detected.
Directory of Open Access Journals (Sweden)
David A. Johnson
2016-01-01
Full Text Available Predictions of the performance of operating wind turbines are challenging for many reasons including the unsteadiness of the wind and uncertainties in blade aerodynamic behaviour. In the current study an extended blade element momentum (BEM program was developed to compute the rotor power of an existing 4.3 m diameter turbine and compare predictions with reported controlled experimental measurements. Beginning with basic blade geometry and the iterative computation of aerodynamic properties, the method integrated the BEM analysis into the program workflow ensuring that the power production by a blade element agreed with its lift and drag data at the same Reynolds number. The parametric study using the extended BEM algorithm revealed the close association of the power curve behaviour with the aerodynamic characteristics of the blade elements, the discretization of the aerodynamic span, and the dependence on Reynolds number when the blades were stalled. Transition prediction also affected overall performance, albeit to a lesser degree. Finally, to capture blade finite area effects, the tip loss model was adjusted depending on stall conditions. The experimental power curve for the HAWT of the current study was closely matched by the extended BEM simulation.
DEFF Research Database (Denmark)
Jung, Jaesoon; Kook, Junghwan; Goo, Seongyeol
2017-01-01
In this paper, an accurate and efficient numerical method for sound transmission analysis is presented. As an alternative to conventional numerical methods, such as the Finite Element Method (FEM), Boundary Element Method (BEM) and Statistical Energy Analysis (SEA), the FE-ERA method, which...... and efficiency of the FE-ERA method, a novel criterion for the optimal number of elementary radiators is proposed. The criterion is based on the radiator error index that is derived to estimate the accuracy of the computation with used number of radiators. Using the proposed criterion a radiator selection method...
Advanced finite element method in structural engineering
Long, Yu-Qiu; Long, Zhi-Fei
2009-01-01
This book systematically introduces the research work on the Finite Element Method completed over the past 25 years. Original theoretical achievements and their applications in the fields of structural engineering and computational mechanics are discussed.
The finite element method in electromagnetics
Jin, Jianming
2014-01-01
A new edition of the leading textbook on the finite element method, incorporating major advancements and further applications in the field of electromagnetics The finite element method (FEM) is a powerful simulation technique used to solve boundary-value problems in a variety of engineering circumstances. It has been widely used for analysis of electromagnetic fields in antennas, radar scattering, RF and microwave engineering, high-speed/high-frequency circuits, wireless communication, electromagnetic compatibility, photonics, remote sensing, biomedical engineering, and space exploration. The
Implementation aspects of the Boundary Element Method including viscous and thermal losses
DEFF Research Database (Denmark)
Cutanda Henriquez, Vicente; Juhl, Peter Møller
2014-01-01
The implementation of viscous and thermal losses using the Boundary Element Method (BEM) is based on the Kirchhoff’s dispersion relation and has been tested in previous work using analytical test cases and comparison with measurements. Numerical methods that can simulate sound fields in fluids...... including losses are particularly interesting whenever small cavities and narrow passages are present, as is the case with many acoustic devices such as transducers and small audio appliances. The present paper describes current work aimed at improving the method by addressing some specific issues related...
Introducing the Boundary Element Method with MATLAB
Ang, Keng-Cheng
2008-01-01
The boundary element method provides an excellent platform for learning and teaching a computational method for solving problems in physical and engineering science. However, it is often left out in many undergraduate courses as its implementation is deemed to be difficult. This is partly due to the perception that coding the method requires…
Finite element methods a practical guide
Whiteley, Jonathan
2017-01-01
This book presents practical applications of the finite element method to general differential equations. The underlying strategy of deriving the finite element solution is introduced using linear ordinary differential equations, thus allowing the basic concepts of the finite element solution to be introduced without being obscured by the additional mathematical detail required when applying this technique to partial differential equations. The author generalizes the presented approach to partial differential equations which include nonlinearities. The book also includes variations of the finite element method such as different classes of meshes and basic functions. Practical application of the theory is emphasised, with development of all concepts leading ultimately to a description of their computational implementation illustrated using Matlab functions. The target audience primarily comprises applied researchers and practitioners in engineering, but the book may also be beneficial for graduate students.
Multi-domain boundary element method for axi-symmetric layered linear acoustic systems
Reiter, Paul; Ziegelwanger, Harald
2017-12-01
Homogeneous porous materials like rock wool or synthetic foam are the main tool for acoustic absorption. The conventional absorbing structure for sound-proofing consists of one or multiple absorbers placed in front of a rigid wall, with or without air-gaps in between. Various models exist to describe these so called multi-layered acoustic systems mathematically for incoming plane waves. However, there is no efficient method to calculate the sound field in a half space above a multi layered acoustic system for an incoming spherical wave. In this work, an axi-symmetric multi-domain boundary element method (BEM) for absorbing multi layered acoustic systems and incoming spherical waves is introduced. In the proposed BEM formulation, a complex wave number is used to model absorbing materials as a fluid and a coordinate transformation is introduced which simplifies singular integrals of the conventional BEM to non-singular radial and angular integrals. The radial and angular part are integrated analytically and numerically, respectively. The output of the method can be interpreted as a numerical half space Green's function for grounds consisting of layered materials.
Spectral/hp element methods for CFD
Karniadakis, George Em
1999-01-01
Traditionally spectral methods in fluid dynamics were used in direct and large eddy simulations of turbulent flow in simply connected computational domains. The methods are now being applied to more complex geometries, and the spectral/hp element method, which incorporates both multi-domain spectral methods and high-order finite element methods, has been particularly successful. This book provides a comprehensive introduction to these methods. Written by leaders in the field, the book begins with a full explanation of fundamental concepts and implementation issues. It then illustrates how these methods can be applied to advection-diffusion and to incompressible and compressible Navier-Stokes equations. Drawing on both published and unpublished material, the book is an important resource for experienced researchers and for those new to the field.
Galerkin finite element methods for wave problems
Indian Academy of Sciences (India)
One-dimensional wave equation. First, we briefly discuss the Galerkin method that employs piecewise quadratic polynomials for the basis or interpolating functions. We will call this as G2FEM for ease of reference. Here, one would have three quadratic functions for each element (see Reddy 2001, for details). In figure 1, we ...
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...
Solving the ECG forward problem by means of a meshless finite element method
Energy Technology Data Exchange (ETDEWEB)
Li, Z S [College of Electrical Engineering, Zhejiang University, Hangzhou (China); Zhu, S A [College of Electrical Engineering, Zhejiang University, Hangzhou (China); He Bin [Department of Biomedical Engineering, University of Minnesota, 7-105 NHH, Church Street, SE, Minneapolis, MN 55455 (United States)
2007-07-07
The conventional numerical computational techniques such as the finite element method (FEM) and the boundary element method (BEM) require laborious and time-consuming model meshing. The new meshless FEM only uses the boundary description and the node distribution and no meshing of the model is required. This paper presents the fundamentals and implementation of meshless FEM and the meshless FEM method is adapted to solve the electrocardiography (ECG) forward problem. The method is evaluated on a single-layer torso model, in which the analytical solution exists, and tested in a realistic geometry homogeneous torso model, with satisfactory results being obtained. The present results suggest that the meshless FEM may provide an alternative for ECG forward solutions. (note)
Finite Element Methods and Their Applications
Chen, Zhangxin
2005-01-01
This book serves as a text for one- or two-semester courses for upper-level undergraduates and beginning graduate students and as a professional reference for people who want to solve partial differential equations (PDEs) using finite element methods. The author has attempted to introduce every concept in the simplest possible setting and maintain a level of treatment that is as rigorous as possible without being unnecessarily abstract. Quite a lot of attention is given to discontinuous finite elements, characteristic finite elements, and to the applications in fluid and solid mechanics including applications to porous media flow, and applications to semiconductor modeling. An extensive set of exercises and references in each chapter are provided.
Mixed FEM for Second Order Elliptic Problems on Polygonal Meshes with BEM-Based Spaces
Efendiev, Yalchin
2014-01-01
We present a Boundary Element Method (BEM)-based FEM for mixed formulations of second order elliptic problems in two dimensions. The challenge, we would like to address, is a proper construction of H(div)-conforming vector valued trial functions on arbitrary polygonal partitions of the domain. The proposed construction generates trial functions on polygonal elements which inherit some of the properties of the unknown solution. In the numerical realization, the relevant local problems are treated by means of boundary integral formulations. We test the accuracy of the method on two model problems. © 2014 Springer-Verlag.
Introduction to finite and spectral element methods using Matlab
Pozrikidis, Constantine
2014-01-01
The Finite Element Method in One Dimension. Further Applications in One Dimension. High-Order and Spectral Elements in One Dimension. The Finite Element Method in Two Dimensions. Quadratic and Spectral Elements in Two Dimensions. Applications in Mechanics. Viscous Flow. Finite and Spectral Element Methods in Three Dimensions. Appendices. References. Index.
Mixed Finite Element Method for Melt Migration
Taicher, A. L.; Hesse, M. A.; Arbogast, T.
2012-12-01
Multi-phase flow arises during partial melting in the earth mantle, where the porosity is small and material has the characteristics of a compacting porous medium. The equations governing multi-phase flow have been specialized to partially molten materials by McKenzie and Fowler. Their model, also called a Darcy-Stokes system, is highly coupled and non-linear. Melt flow is governed by Darcy's Law while the high temperature, ductile creep of the solid matrix is modeled using viscous non-Newtonian Stokes rheology. In addition, the melt and solid pressures are related through a compaction relation. This nearly elliptic mechanical problem is then coupled with both solute transport and thermal evolution according to the enthalpy method developed by Katz. A suitable numerical method must solve the Darcy-Stokes problem in a manner compatible with the transport problem. Moreover, unlike most porous media problems, partially molten materials transition dynamically from non-porous solid to porous medium. Therefore, a numerical method must also carefully account for the limit of zero porosity. The Darcy-Stokes system for modeling partial melting in the mantle is a novel problem. As far as we know, there currently does not exist a finite element solution in the literature solving these coupled equations. The finite element framework provides support for additional analysis of error and convergence. Moreover, both mesh refinement and anisotropy are naturally incorporated into finite elements. In particular, the mixed finite element method presents a good candidate because it works in both limiting cases: Darcy and incompressible Stokes flow. Mixed methods also produce discretely conservative fluxes that are required for the transport problem to remains stable without violating conservation of mass. Based preliminary investigations in 1D and derived energy estimates, we present a mixed formulation for the Darcy-Stokes system. Next, using novel elements of lowest order and
Boundary element method for internal axisymmetric flow
Directory of Open Access Journals (Sweden)
Gokhman Alexander
1999-01-01
Full Text Available We present an accurate fast method for the computation of potential internal axisymmetric flow based on the boundary element technique. We prove that the computed velocity field asymptotically satisfies reasonable boundary conditions at infinity for various types of inlet/exit. Computation of internal axisymmetric potential flow is an essential ingredient in the three-dimensional problem of computation of velocity fields in turbomachines. We include the results of a practical application of the method to the computation of flow in turbomachines of Kaplan and Francis types.
Wave interaction with Very Large Floating Structure (VLFS using BEM approach – Revisited
Directory of Open Access Journals (Sweden)
Anoop I. Shirkol
2016-09-01
Full Text Available In the present study, a brief discussion on the hydroelastic analysis of VLFS using Boundary Element Method (BEM with basic assumptions, boundary conditions and support conditions required are presented. An overview of present scenario about development of VLFS using BEM and also future prospects are presented. The study on existing VLFS systems floated in the sea around world could be considered as indicative of the present state of affairs. Further, various numerical methods adopted by the researchers is reviewed in particular, on the hydroelastic analysis of VLFS, dynamic, static and structural response of the system is discussed. The study presented herein will be helpful to naval architects, ocean and structural engineers for suitable design and analysis of VLFS subjected to wave force.
Generalized multiscale finite element methods: Oversampling strategies
Efendiev, Yalchin R.
2014-01-01
In this paper, we propose oversampling strategies in the generalized multiscale finite element method (GMsFEM) framework. The GMsFEM, which has been recently introduced in Efendiev et al. (2013b) [Generalized Multiscale Finite Element Methods, J. Comput. Phys., vol. 251, pp. 116-135, 2013], allows solving multiscale parameter-dependent problems at a reduced computational cost by constructing a reduced-order representation of the solution on a coarse grid. The main idea of the method consists of (1) the construction of snapshot space, (2) the construction of the offline space, and (3) construction of the online space (the latter for parameter-dependent problems). In Efendiev et al. (2013b) [Generalized Multiscale Finite Element Methods, J. Comput. Phys., vol. 251, pp. 116-135, 2013], it was shown that the GMsFEM provides a flexible tool to solve multiscale problems with a complex input space by generating appropriate snapshot, offline, and online spaces. In this paper, we develop oversampling techniques to be used in this context (see Hou and Wu (1997) where oversampling is introduced for multiscale finite element methods). It is known (see Hou and Wu (1997)) that the oversampling can improve the accuracy of multiscale methods. In particular, the oversampling technique uses larger regions (larger than the target coarse block) in constructing local basis functions. Our motivation stems from the analysis presented in this paper, which shows that when using oversampling techniques in the construction of the snapshot space and offline space, GMsFEM will converge independent of small scales and high contrast under certain assumptions. We consider the use of a multiple eigenvalue problems to improve the convergence and discuss their relation to single spectral problems that use oversampled regions. The oversampling procedures proposed in this paper differ from those in Hou and Wu (1997). In particular, the oversampling domains are partially used in constructing local
Adaptive finite element methods for differential equations
Bangerth, Wolfgang
2003-01-01
These Lecture Notes discuss concepts of `self-adaptivity' in the numerical solution of differential equations, with emphasis on Galerkin finite element methods. The key issues are a posteriori error estimation and it automatic mesh adaptation. Besides the traditional approach of energy-norm error control, a new duality-based technique, the Dual Weighted Residual method for goal-oriented error estimation, is discussed in detail. This method aims at economical computation of arbitrary quantities of physical interest by properly adapting the computational mesh. This is typically required in the design cycles of technical applications. For example, the drag coefficient of a body immersed in a viscous flow is computed, then it is minimized by varying certain control parameters, and finally the stability of the resulting flow is investigated by solving an eigenvalue problem. `Goal-oriented' adaptivity is designed to achieve these tasks with minimal cost. At the end of each chapter some exercises are posed in order ...
Mixed Finite Element Methods for Melt Migration
Taicher, A. L.
2013-12-01
Multi-phase flow arises during partial melting in the earth mantle, where the porosity is small and material has the characteristics of a compacting porous medium. The equations governing multi-phase flow have been specialized to partially molten materials by McKenzie and Fowler. Their model, also called a Darcy-Stokes system, is highly coupled and non-linear. Melt flow is governed by Darcy's Law while the high temperature, ductile creep of the solid matrix is modeled using viscous non-Newtonian Stokes rheology. In addition, the melt and solid pressures are related through a compaction relation. This nearly elliptic mechanical problem is then coupled with both solute transport and thermal evolution according to the enthalpy method developed by Katz. A suitable numerical method must solve the Darcy-Stokes problem in a manner compatible with the transport problem. Moreover, unlike most porous media problems, partially molten materials transition dynamically from non-porous solid to porous medium so must carefully account for the limit of zero porosity. The Darcy-Stokes system for modeling partial melting in the mantle is a novel problem. As far as we know, there currently does not exist a finite element solution in the literature solving these coupled equations. In particular, the mixed finite element method presents a good candidate because it works in both limiting cases: Darcy and incompressible Stokes flow. We present a mixed formulation for the Darcy-Stokes system. Next, we present novel elements of lowest order and compatible with both Darcy and Stokes flow Finally, we present our 2D mixed FEM code result for solving Stokes and Darcy flow as well as the coupled Darcy-Stokes system the mid-ocean ridge or corner flow problem.
Directory of Open Access Journals (Sweden)
Marco Gonzalez
Full Text Available Abstract The analysis of cracked brittle mechanical components considering linear elastic fracture mechanics is usually reduced to the evaluation of stress intensity factors (SIFs. The SIF calculation can be carried out experimentally, theoretically or numerically. Each methodology has its own advantages but the use of numerical methods has become very popular. Several schemes for numerical SIF calculations have been developed, the J-integral method being one of the most widely used because of its energy-like formulation. Additionally, some variations of the J-integral method, such as displacement-based methods, are also becoming popular due to their simplicity. In this work, a simple displacement-based scheme is proposed to calculate SIFs, and its performance is compared with contour integrals. These schemes are all implemented with the Boundary Element Method (BEM in order to exploit its advantages in crack growth modelling. Some simple examples are solved with the BEM and the calculated SIF values are compared against available solutions, showing good agreement between the different schemes.
Finite element modeling methods for photonics
Rahman, B M Azizur
2013-01-01
The term photonics can be used loosely to refer to a vast array of components, devices, and technologies that in some way involve manipulation of light. One of the most powerful numerical approaches available to engineers developing photonic components and devices is the Finite Element Method (FEM), which can be used to model and simulate such components/devices and analyze how they will behave in response to various outside influences. This resource provides a comprehensive description of the formulation and applications of FEM in photonics applications ranging from telecommunications, astron
Final Report of the Project "From the finite element method to the virtual element method"
Energy Technology Data Exchange (ETDEWEB)
Manzini, Gianmarco [Los Alamos National Lab. (LANL), Los Alamos, NM (United States); Gyrya, Vitaliy [Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
2017-12-20
The Finite Element Method (FEM) is a powerful numerical tool that is being used in a large number of engineering applications. The FEM is constructed on triangular/tetrahedral and quadrilateral/hexahedral meshes. Extending the FEM to general polygonal/polyhedral meshes in straightforward way turns out to be extremely difficult and leads to very complex and computationally expensive schemes. The reason for this failure is that the construction of the basis functions on elements with a very general shape is a non-trivial and complex task. In this project we developed a new family of numerical methods, dubbed the Virtual Element Method (VEM) for the numerical approximation of partial differential equations (PDE) of elliptic type suitable to polygonal and polyhedral unstructured meshes. We successfully formulated, implemented and tested these methods and studied both theoretically and numerically their stability, robustness and accuracy for diffusion problems, convection-reaction-diffusion problems, the Stokes equations and the biharmonic equations.
Energy Technology Data Exchange (ETDEWEB)
Manzini, Gianmarco [Los Alamos National Laboratory
2012-07-13
We develop and analyze a new family of virtual element methods on unstructured polygonal meshes for the diffusion problem in primal form, that use arbitrarily regular discrete spaces V{sub h} {contained_in} C{sup {alpha}} {element_of} N. The degrees of freedom are (a) solution and derivative values of various degree at suitable nodes and (b) solution moments inside polygons. The convergence of the method is proven theoretically and an optimal error estimate is derived. The connection with the Mimetic Finite Difference method is also discussed. Numerical experiments confirm the convergence rate that is expected from the theory.
Unsteady three-dimensional thermal field prediction in turbine blades using nonlinear BEM
Martin, Thomas J.; Dulikravich, George S.
1993-01-01
A time-and-space accurate and computationally efficient fully three dimensional unsteady temperature field analysis computer code has been developed for truly arbitrary configurations. It uses boundary element method (BEM) formulation based on an unsteady Green's function approach, multi-point Gaussian quadrature spatial integration on each panel, and a highly clustered time-step integration. The code accepts either temperatures or heat fluxes as boundary conditions that can vary in time on a point-by-point basis. Comparisons of the BEM numerical results and known analytical unsteady results for simple shapes demonstrate very high accuracy and reliability of the algorithm. An example of computed three dimensional temperature and heat flux fields in a realistically shaped internally cooled turbine blade is also discussed.
Adaptive finite element method for shape optimization
Morin, Pedro
2012-01-16
We examine shape optimization problems in the context of inexact sequential quadratic programming. Inexactness is a consequence of using adaptive finite element methods (AFEM) to approximate the state and adjoint equations (via the dual weighted residual method), update the boundary, and compute the geometric functional. We present a novel algorithm that equidistributes the errors due to shape optimization and discretization, thereby leading to coarse resolution in the early stages and fine resolution upon convergence, and thus optimizing the computational effort. We discuss the ability of the algorithm to detect whether or not geometric singularities such as corners are genuine to the problem or simply due to lack of resolution - a new paradigm in adaptivity. © EDP Sciences, SMAI, 2012.
Immersed molecular electrokinetic finite element method
Kopacz, Adrian M.; Liu, Wing K.
2013-07-01
A unique simulation technique has been developed capable of modeling electric field induced detection of biomolecules such as viruses, at room temperatures where thermal fluctuations must be considered. The proposed immersed molecular electrokinetic finite element method couples electrokinetics with fluctuating hydrodynamics to study the motion and deformation of flexible objects immersed in a suspending medium under an applied electric field. The force induced on an arbitrary object due to an electric field is calculated based on the continuum electromechanics and the Maxwell stress tensor. The thermal fluctuations are included in the Navier-Stokes fluid equations via the stochastic stress tensor. Dielectrophoretic and fluctuating forces acting on the particle are coupled through the fluid-structure interaction force calculated within the surrounding environment. This method was used to perform concentration and retention efficacy analysis of nanoscale biosensors using gold particles of various sizes. The analysis was also applied to a human papillomavirus.
Computation of Aerodynamic Noise Radiated from Ducted Tail Rotor Using Boundary Element Method
Directory of Open Access Journals (Sweden)
Yunpeng Ma
2017-01-01
Full Text Available A detailed aerodynamic performance of a ducted tail rotor in hover has been numerically studied using CFD technique. The general governing equations of turbulent flow around ducted tail rotor are given and directly solved by using finite volume discretization and Runge-Kutta time integration. The calculations of the lift characteristics of the ducted tail rotor can be obtained. In order to predict the aerodynamic noise, a hybrid method combining computational aeroacoustic with boundary element method (BEM has been proposed. The computational steps include the following: firstly, the unsteady flow around rotor is calculated using the CFD method to get the noise source information; secondly, the radiate sound pressure is calculated using the acoustic analogy Curle equation in the frequency domain; lastly, the scattering effect of the duct wall on the propagation of the sound wave is presented using an acoustic thin-body BEM. The aerodynamic results and the calculated sound pressure levels are compared with the known technique for validation. The sound pressure directivity and scattering effect are shown to demonstrate the validity and applicability of the method.
On the modeling of narrow gaps using the standard boundary element method
DEFF Research Database (Denmark)
Cutanda Henríquez, Vicente; Juhl, Peter Møller; Jacobsen, Finn
2001-01-01
Numerical methods based on the Helmholtz integral equation are well suited for solving acoustic scattering and diffraction problems at relatively low frequencies. However, it is well known that the standard method becomes degenerate if the objects that disturb the sound field are very thin....... This paper makes use of a standard axisymmetric Helmholtz integral equation formulation and its boundary element method (BEM) implementation to study the behavior of the method on two test cases: a thin rigid disk of variable thickness and two rigid cylinders separated by a gap of variable width. Both...... with in the literature. A simple integration technique that can extend the range of thicknesses/widths tractable by the otherwise unmodified standard formulation is presented and tested. This technique is valid for both cases. The modeling of acoustic transducers Like sound intensity probes and condenser microphones has...
A coupled boundary element-finite difference solution of the elliptic modified mild slope equation
DEFF Research Database (Denmark)
Naserizadeh, R.; Bingham, Harry B.; Noorzad, A.
2011-01-01
The modified mild slope equation of [5] is solved using a combination of the boundary element method (BEM) and the finite difference method (FDM). The exterior domain of constant depth and infinite horizontal extent is solved by a BEM using linear or quadratic elements. The interior domain...
New formulation of the discrete element method
Rojek, Jerzy; Zubelewicz, Aleksander; Madan, Nikhil; Nosewicz, Szymon
2018-01-01
A new original formulation of the discrete element method based on the soft contact approach is presented in this work. The standard DEM has heen enhanced by the introduction of the additional (global) deformation mode caused by the stresses in the particles induced by the contact forces. Uniform stresses and strains are assumed for each particle. The stresses are calculated from the contact forces. The strains are obtained using an inverse constitutive relationship. The strains allow us to obtain deformed particle shapes. The deformed shapes (ellipses) are taken into account in contact detection and evaluation of the contact forces. A simple example of a uniaxial compression of a rectangular specimen, discreti.zed with equal sized particles is simulated to verify the DDEM algorithm. The numerical example shows that a particle deformation changes the particle interaction and the distribution of forces in the discrete element assembly. A quantitative study of micro-macro elastic properties proves the enhanced capabilities of the DDEM as compared to standard DEM.
Vitório, Paulo Cezar; Leonel, Edson Denner
2017-10-01
The structural design must ensure suitable working conditions by attending for safe and economic criteria. However, the optimal solution is not easily available, because these conditions depend on the bodies' dimensions, materials strength and structural system configuration. In this regard, topology optimization aims for achieving the optimal structural geometry, i.e. the shape that leads to the minimum requirement of material, respecting constraints related to the stress state at each material point. The present study applies an evolutionary approach for determining the optimal geometry of 2D structures using the coupling of the boundary element method (BEM) and the level set method (LSM). The proposed algorithm consists of mechanical modelling, topology optimization approach and structural reconstruction. The mechanical model is composed of singular and hyper-singular BEM algebraic equations. The topology optimization is performed through the LSM. Internal and external geometries are evolved by the LS function evaluated at its zero level. The reconstruction process concerns the remeshing. Because the structural boundary moves at each iteration, the body's geometry change and, consequently, a new mesh has to be defined. The proposed algorithm, which is based on the direct coupling of such approaches, introduces internal cavities automatically during the optimization process, according to the intensity of Von Mises stress. The developed optimization model was applied in two benchmarks available in the literature. Good agreement was observed among the results, which demonstrates its efficiency and accuracy.
Dynamic Stationary Response of Reinforced Plates by the Boundary Element Method
Directory of Open Access Journals (Sweden)
Luiz Carlos Facundo Sanches
2007-01-01
Full Text Available A direct version of the boundary element method (BEM is developed to model the stationary dynamic response of reinforced plate structures, such as reinforced panels in buildings, automobiles, and airplanes. The dynamic stationary fundamental solutions of thin plates and plane stress state are used to transform the governing partial differential equations into boundary integral equations (BIEs. Two sets of uncoupled BIEs are formulated, respectively, for the in-plane state (membrane and for the out-of-plane state (bending. These uncoupled systems are joined to form a macro-element, in which membrane and bending effects are present. The association of these macro-elements is able to simulate thin-walled structures, including reinforced plate structures. In the present formulation, the BIE is discretized by continuous and/or discontinuous linear elements. Four displacement integral equations are written for every boundary node. Modal data, that is, natural frequencies and the corresponding mode shapes of reinforced plates, are obtained from information contained in the frequency response functions (FRFs. A specific example is presented to illustrate the versatility of the proposed methodology. Different configurations of the reinforcements are used to simulate simply supported and clamped boundary conditions for the plate structures. The procedure is validated by comparison with results determined by the finite element method (FEM.
Element-by-element parallel spectral-element methods for 3-D teleseismic wave modeling
Liu, Shaolin
2017-09-28
The development of an efficient algorithm for teleseismic wave field modeling is valuable for calculating the gradients of the misfit function (termed misfit gradients) or Fréchet derivatives when the teleseismic waveform is used for adjoint tomography. Here, we introduce an element-by-element parallel spectral-element method (EBE-SEM) for the efficient modeling of teleseismic wave field propagation in a reduced geology model. Under the plane-wave assumption, the frequency-wavenumber (FK) technique is implemented to compute the boundary wave field used to construct the boundary condition of the teleseismic wave incidence. To reduce the memory required for the storage of the boundary wave field for the incidence boundary condition, a strategy is introduced to efficiently store the boundary wave field on the model boundary. The perfectly matched layers absorbing boundary condition (PML ABC) is formulated using the EBE-SEM to absorb the scattered wave field from the model interior. The misfit gradient can easily be constructed in each time step during the calculation of the adjoint wave field. Three synthetic examples demonstrate the validity of the EBE-SEM for use in teleseismic wave field modeling and the misfit gradient calculation.
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....
Nonconforming finite element methods on quadrilateral meshes
Hu, Jun; Zhang, ShangYou
2013-12-01
It is well-known that it is comparatively difficult to design nonconforming finite elements on quadrilateral meshes by using Gauss-Legendre points on each edge of triangulations. One reason lies in that these degrees of freedom associated to these Gauss-Legendre points are not all linearly independent for usual expected polynomial spaces, which explains why only several lower order nonconforming quadrilateral finite elements can be found in literature. The present paper proposes two families of nonconforming finite elements of any odd order and one family of nonconforming finite elements of any even order on quadrilateral meshes. Degrees of freedom are given for these elements, which are proved to be well-defined for their corresponding shape function spaces in a unifying way. These elements generalize three lower order nonconforming finite elements on quadrilaterals to any order. In addition, these nonconforming finite element spaces are shown to be full spaces which is somehow not discussed for nonconforming finite elements in literature before.
DEFF Research Database (Denmark)
Sørensen, Jens Nørkær
2016-01-01
Although there exists a large variety of methods for predicting performance and loadings of wind turbines, the only approach used today by wind turbine manufacturers is based on the blade-element/momentum (BEM) theory by Glauert (Aerodynamic theory. Springer, Berlin, pp. 169-360, 1935). A basic...... assumption in the BEM theory is that the flow takes place in independent stream tubes and that the loading is determined from two-dimensional sectional airfoil characteristics....
Glenn-ht/bem Conjugate Heat Transfer Solver for Large-scale Turbomachinery Models
Divo, E.; Steinthorsson, E.; Rodriquez, F.; Kassab, A. J.; Kapat, J. S.; Heidmann, James D. (Technical Monitor)
2003-01-01
A coupled Boundary Element/Finite Volume Method temperature-forward/flux-hack algorithm is developed for conjugate heat transfer (CHT) applications. A loosely coupled strategy is adopted with each field solution providing boundary conditions for the other in an iteration seeking continuity of temperature and heat flux at the fluid-solid interface. The NASA Glenn Navier-Stokes code Glenn-HT is coupled to a 3-D BEM steady state heat conduction code developed at the University of Central Florida. Results from CHT simulation of a 3-D film-cooled blade section are presented and compared with those computed by a two-temperature approach. Also presented are current developments of an iterative domain decomposition strategy accommodating large numbers of unknowns in the BEM. The blade is artificially sub-sectioned in the span-wise direction, 3-D BEM solutions are obtained in the subdomains, and interface temperatures are averaged symmetrically when the flux is updated while the fluxes are averaged anti-symmetrically to maintain continuity of heat flux when the temperatures are updated. An initial guess for interface temperatures uses a physically-based 1-D conduction argument to provide an effective starting point and significantly reduce iteration. 2-D and 3-D results show the process converges efficiently and offers substantial computational and storage savings. Future developments include a parallel multi-grid implementation of the approach under MPI for computation on PC clusters.
Functional Element Test Tool and Method
2001-07-03
functional element 6 involved in the run test case step 8 6 of a test. SAFE test tool 7 10 preferably operates in several selectable modes of...options 9 (e.g., data initiation buttons) are displayed as dictated by 10 each test case. The run test case step 86 is then performed 11 under...19 object functional element being tested during run test case step 20 8 6 would be maintained via SAFE test tool 10 for later 21 comparison or
A stabilised nonconforming finite element method for steady incompressible flows
Huang, Pengzhan; Feng, Xinlong; Liu, Demin
2012-02-01
A stabilised nonconforming finite element method for the steady incompressible flow problem with damping based on local Gauss integration is considered in this article. The method combines the nonconforming finite element method with the stabilised strategy. Moreover, the stability and error estimates are analysed. Finally, numerical results are shown to support the developed theory analysis. Compared with some classical, closely related mixed finite element methods, the results of the present method show its better performance than others.
The Matrix Element Method and Vector-Like Quark Searches
Morrison, Benjamin
2016-01-01
In my time at the CERN summer student program, I worked on applying the matrix element method to vector-like quark identification. I worked in the ATLAS University of Geneva group under Dr. Olaf Nackenhorst. I developed automated plotting tools with ROOT, a script for implementing and optimizing generated matrix element calculation code, and kinematic transforms for the matrix element method.
Multidirectional random wave diffraction in a real harbor by using 3-D boundary element method
Kumar, Prashant; Gulshan, Rajni
2017-10-01
The mathematical model is constructed based on 3-D Boundary Element Method (BEM) with the consideration of diffraction, reflection and refraction of multidirectional incident waves utilizing the Laplace equation in a complex geometry harbors. The geometry of the harbor is divided into bounded and open sea region. The partial reflection boundary with variable bathymetry is also considered to analyze the wave spectrum. A Mitsuyasu's wave spectrum is applied to estimate the wave spectrum with multidirectional incident waves. The current numerical approach is practically applied on realistic Pohang New Harbor (PNH), Pohang South Korea. The validation of numerical scheme is done by comparison of measurement data with simulation results at different port stations. Therefore, the current numerical approach is provide the efficient numerical tool to foster the prediction of wave-induced oscillation in a harbor with irregular geometry.
Hydraulic fracturing with distinct element method
Pruiksma, J.P.; Bezuijen, A.
2002-01-01
In this report, hydraulic fracturing is investigated using the distinct element code PFC2D from Itasca. Special routines were written to be able to model hydraulic fracturing. These include adding fluid flow to PFC2D and updating the fluid flow domains when fractures appear. A brief description of
da psicopatologia ao bem-estar
Ferreira, Cristiana
2015-01-01
Dissertação apresentada à Universidade Fernando Pessoa como parte dos requisitos para a obtenção do grau de Mestre em Psicologia, ramo de Psicologia Clínica e da Saúde A saúde mental é conceptualizada como um “estado completo” em que os indivíduos estão livres de psicopatologia e em flourishing, e com níveis elevados de bem-estar emocional, psicológico e social (Keyes, 2002). Este constructo indica que quando um indivíduo se sente bem, é mais produtivo, sociável, criativo, tem perspetivas ...
Calculation of marine propeller static strength based on coupled BEM/FEM
Directory of Open Access Journals (Sweden)
YE Liyu
2017-10-01
Full Text Available [Objectives] The reliability of propeller stress has a great influence on the safe navigation of a ship. To predict propeller stress quickly and accurately,[Methods] a new numerical prediction model is developed by coupling the Boundary Element Method(BEMwith the Finite Element Method (FEM. The low order BEM is used to calculate the hydrodynamic load on the blades, and the Prandtl-Schlichting plate friction resistance formula is used to calculate the viscous load. Next, the calculated hydrodynamic load and viscous correction load are transmitted to the calculation of the Finite Element as surface loads. Considering the particularity of propeller geometry, a continuous contact detection algorithm is developed; an automatic method for generating the finite element mesh is developed for the propeller blade; a code based on the FEM is compiled for predicting blade stress and deformation; the DTRC 4119 propeller model is applied to validate the reliability of the method; and mesh independence is confirmed by comparing the calculated results with different sizes and types of mesh.[Results] The results show that the calculated blade stress and displacement distribution are reliable. This method avoids the process of artificial modeling and finite element mesh generation, and has the advantages of simple program implementation and high calculation efficiency.[Conclusions] The code can be embedded into the code of theoretical and optimized propeller designs, thereby helping to ensure the strength of designed propellers and improve the efficiency of propeller design.
The finite element method its basis and fundamentals
Zienkiewicz, Olek C; Zhu, JZ
2013-01-01
The Finite Element Method: Its Basis and Fundamentals offers a complete introduction to the basis of the finite element method, covering fundamental theory and worked examples in the detail required for readers to apply the knowledge to their own engineering problems and understand more advanced applications. This edition sees a significant rearrangement of the book's content to enable clearer development of the finite element method, with major new chapters and sections added to cover: Weak forms Variational forms Multi-dimensional field prob
An optimal adaptive finite element method for the Stokes problem
Kondratyuk, Y.; Stevenson, R.
2008-01-01
A new adaptive finite element method for solving the Stokes equations is developed, which is shown to converge with the best possible rate. The method consists of 3 nested loops. The outermost loop consists of an adaptive finite element method for solving the pressure from the (elliptic) Schur
Discrete element analysis methods of generic differential quadratures
Chen, Chang-New
2008-01-01
Presents generic differential quadrature, the extended differential quadrature and the related discrete element analysis methods. This book demonstrated their ability for solving generic scientific and engineering problems.
h-p Spectral element methods for three dimensional elliptic ...
Indian Academy of Sciences (India)
Keywords. Spectral element method; non-smooth domains; geometric mesh; vertex singularity; edge singularity; vertex-edge singularity; differentiability estimates; stability estimates; exponential accuracy.
Spectral/hp element methods: Recent developments, applications, and perspectives
DEFF Research Database (Denmark)
Xu, Hui; Cantwell, Chris; Monteserin, Carlos
2018-01-01
The spectral/hp element method combines the geometric flexibility of the classical h-type finite element technique with the desirable numerical properties of spectral methods, employing high-degree piecewise polynomial basis functions on coarse finite element-type meshes. The spatial approximation...... regularity assumptions an exponential reduction in approximation error between numerical and exact solutions can be achieved. This method has now been applied in many simulation studies of both fundamental and practical engineering flows. This paper briefly describes the formulation of the spectral/hp...... element method and provides an overview of its application to computational fluid dynamics. In particular, it focuses on the use of the spectral/hp element method in transitional flows and ocean engineering. Finally, some of the major challenges to be overcome in order to use the spectral/hp element...
Wave Scattering in Heterogeneous Media using the Finite Element Method
2016-10-21
AFRL-AFOSR-JP-TR-2016-0086 Wave Scattering in Heterogeneous Media using the Finite Element Method Chiruvai Vendhan INDIAN INSTITUTE OF TECHNOLOGY...Scattering in Heterogeneous Media using the Finite Element Method 5a. CONTRACT NUMBER 5b. GRANT NUMBER FA2386-12-1-4026 5c. PROGRAM ELEMENT NUMBER 61102F 6...heterogeneous ocean acoustic waveguide. 15. SUBJECT TERMS Acoustics, Finite Element Methods , Wave propagation 16. SECURITY CLASSIFICATION OF: 17
Ablative Thermal Response Analysis Using the Finite Element Method
Dec John A.; Braun, Robert D.
2009-01-01
A review of the classic techniques used to solve ablative thermal response problems is presented. The advantages and disadvantages of both the finite element and finite difference methods are described. As a first step in developing a three dimensional finite element based ablative thermal response capability, a one dimensional computer tool has been developed. The finite element method is used to discretize the governing differential equations and Galerkin's method of weighted residuals is used to derive the element equations. A code to code comparison between the current 1-D tool and the 1-D Fully Implicit Ablation and Thermal Response Program (FIAT) has been performed.
A coupling procedure for modeling acoustic problems using finite elements and boundary elements
Coyette, J.; Vanderborck, G.; Steichen, W.
1994-01-01
Finite element (FEM) and boundary element (BEM) methods have been used for a long time for the numerical simulation of acoustic problems. The development presented in this paper deals with a general procedure for coupling acoustic finite elements with acoustic boundary elements in order to solve efficiently acoustic problems involving non homogeneous fluids. Emphasis is made on problems where finite elements are used for a confined (bounded) fluid while boundary elements are selected for an e...
A simplified two-dimensional boundary element method with arbitrary uniform mean flow
Directory of Open Access Journals (Sweden)
Bassem Barhoumi
2017-07-01
Full Text Available To reduce computational costs, an improved form of the frequency domain boundary element method (BEM is proposed for two-dimensional radiation and propagation acoustic problems in a subsonic uniform flow with arbitrary orientation. The boundary integral equation (BIE representation solves the two-dimensional convected Helmholtz equation (CHE and its fundamental solution, which must satisfy a new Sommerfeld radiation condition (SRC in the physical space. In order to facilitate conventional formulations, the variables of the advanced form are expressed only in terms of the acoustic pressure as well as its normal and tangential derivatives, and their multiplication operators are based on the convected Greenâs kernel and its modified derivative. The proposed approach significantly reduces the CPU times of classical computational codes for modeling acoustic domains with arbitrary mean flow. It is validated by a comparison with the analytical solutions for the sound radiation problems of monopole, dipole and quadrupole sources in the presence of a subsonic uniform flow with arbitrary orientation. Keywords: Two-dimensional convected Helmholtz equation, Two-dimensional convected Greenâs function, Two-dimensional convected boundary element method, Arbitrary uniform mean flow, Two-dimensional acoustic sources
Leapfrog/finite element method for fractional diffusion equation.
Zhao, Zhengang; Zheng, Yunying
2014-01-01
We analyze a fully discrete leapfrog/Galerkin finite element method for the numerical solution of the space fractional order (fractional for simplicity) diffusion equation. The generalized fractional derivative spaces are defined in a bounded interval. And some related properties are further discussed for the following finite element analysis. Then the fractional diffusion equation is discretized in space by the finite element method and in time by the explicit leapfrog scheme. For the resulting fully discrete, conditionally stable scheme, we prove an L (2)-error bound of finite element accuracy and of second order in time. Numerical examples are included to confirm our theoretical analysis.
Review on Finite Element Method * ERHUNMWUN, ID ...
African Journals Online (AJOL)
ADOWIE PERE
Again, 3D printing is a complex process that involves phase changes, thermal interactions etc. It's again a coupled problem. There have been many alternative methods proposed in the recent decades. But their commercial applicability is yet to be proved. A recent trend has also been application of cloud-computing for FEM.
Equivariant preconditioners for boundary element methods
Energy Technology Data Exchange (ETDEWEB)
Tausch, J. [Colorado State Univ., Fort Collins, CO (United States)
1994-12-31
In this paper the author proposes and discusses two preconditioners for boundary integral equations on domains which are nearly symmetric. The preconditioners under consideration are equivariant, that is, they commute with a group of permutation matrices. Numerical experiments demonstrate their efficiency for the GMRES method.
Hydrothermal analysis in engineering using control volume finite element method
Sheikholeslami, Mohsen
2015-01-01
Control volume finite element methods (CVFEM) bridge the gap between finite difference and finite element methods, using the advantages of both methods for simulation of multi-physics problems in complex geometries. In Hydrothermal Analysis in Engineering Using Control Volume Finite Element Method, CVFEM is covered in detail and applied to key areas of thermal engineering. Examples, exercises, and extensive references are used to show the use of the technique to model key engineering problems such as heat transfer in nanofluids (to enhance performance and compactness of energy systems),
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.
Transforming Mean and Osculating Elements Using Numerical Methods
Ely, Todd A.
2010-01-01
Mean element propagation of perturbed two body orbits has as its mathematical basis averaging theory of nonlinear dynamical systems. Averaged mean elements define the long-term evolution characteristics of an orbit. Using averaging theory, a near identity transformation can be found that transforms the mean elements back to the osculating elements that contain short period terms in addition to the secular and long period mean elements. The ability to perform the conversion is necessary so that orbit design conducted in mean elements can be converted back into osculating results. In the present work, this near identity transformation is found using the Fast Fourier Transform. An efficient method is found that is capable of recovering the osculating elements to first order
Element Free Lattice Boltzmann Method for Fluid-Flow Problems
Energy Technology Data Exchange (ETDEWEB)
Jo, Jong Chull; Roh, Kyung Wan; Yune, Young Gill; Kim, Hho Jhung [Korea Institute of Nuclear Safety, Daejeon (Korea, Republic of); Kwon, Young Kwon [US Naval Postgraduate School, New York (United States)
2007-10-15
The Lattice Boltzmann Method (LBM) has been developed for application to thermal-fluid problems. Most of the those studies considered a regular shape of lattice or mesh like square and cubic grids. In order to apply the LBM to more practical cases, it is necessary to be able to solve complex or irregular shapes of problem domains. Some techniques were based on the finite element method. Generally, the finite element method is very powerful for solving two or three-dimensional complex or irregular shapes of domains using the iso-parametric element formulation which is based on a mathematical mapping from a regular shape of element in an imaginary domain to a more general and irregular shape of element in the physical domain. In addition, the element free technique is also quite useful to analyze a complex shape of domain because there is no need to divide a domain by a compatible finite element mesh. This paper presents a new finite element and element free formulations for the lattice Boltzmann equation using the general weighted residual technique. Then, a series of validation examples are presented.
A Method of Assembling Wall or Floor Elements
DEFF Research Database (Denmark)
2002-01-01
The invention relates to a method of constructing, at the site of use, a building wall (1) or a building floor (1) using a plurality of prefabricated concrete or lightweight concrete plate-shaped wall of floor elements (10), in particular cast elements, which have a front side and a rear side...
Nonconforming hp spectral element methods for elliptic problems
Indian Academy of Sciences (India)
In this paper we show that we can use a modified version of the ℎ- spectral element method proposed in [6,7,13,14] to solve elliptic problems with general boundary conditions to exponential accuracy on polygonal domains using nonconforming spectral element functions. A geometrical mesh is used in a neighbourhood ...
Stability estimates for hp spectral element methods for general ...
Indian Academy of Sciences (India)
Home; Journals; Proceedings – Mathematical Sciences; Volume 113; Issue 4. Stability Estimates for ℎ- Spectral ... We establish basic stability estimates for a non-conforming ℎ- spectral element method which allows for simultaneous mesh refinement and variable polynomial degree. The spectral element functions are ...
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.
About the Finite Element Method Applied to Thick Plates
Directory of Open Access Journals (Sweden)
Mihaela Ibănescu
2006-01-01
Full Text Available The present paper approaches of plates subjected to transverse loads, when the shear force and the actual boundary conditions are considered, by using the Finite Element Method. The isoparametric finite elements create real facilities in formulating the problems and great possibilities in creating adequate computer programs.
Methods to prevent turbogenerators design elements defects
Directory of Open Access Journals (Sweden)
Валентина Володимирівна Шевченко
2016-11-01
Full Text Available The paper shows that the determination of a failure probability due to the design, technological and operational drawbacks, as well as due to the turbogenerators working time exceeding from statistics data is inaccurate. Machine park of turbogenerators being rather limited in number, the classification and the distribution of generators into groups is random. It can not be used in practice to identify the pre-emergency state of turbogenerators and their timely stop. Analysis and classification of most frequent defects of turbogenerators has been performed. Methods for assessing such defects and reduction of their development have been offered. The article notes that expenses should be taken into account when setting up a monitoring system to assess the state and to identify defects. Reduction of expenditures on both operating and new turbogenerators must be justified. Rapid return of investments must be ensured. The list of additional tests has been proposed: measurement of infrared radiation outside the body of the turbogenerator for the estimation of the thermal field distribution and the defects of gas coolers identification; vibroacoustic inspection of the stator core and casing to find out the defects in the suspension of the core in the stator casing; analysis of the impurities in the cooling gas and in the dry remains of the drainage products to detect the products of the steel core and the winding insulation wear; value measurement and establishment of the partial discharges formation position; research of vibrations to reveal the cracks in the shaft, circuiting in the rotor windings and defects in the bearings. The paper notes that at upgrading as power grows overall and mounting dimensions must be preserved so that the existing foundation could be used as well as the existing security systems. Therefore, when designing or upgrading turbogenerators with an increase in power it is necessary to introduce new design decisions
Finite-element method for above-core structures. [LMFBR
Energy Technology Data Exchange (ETDEWEB)
Kennedy, J.M.; Belytschko, T.B.
1979-12-01
Three-dimensional finite-element models for the treatment of the nonlinear, transient response of a fast breeder reactor's above-core structures are described. For purposes of treating arbitrarily large rotations, node orientations are described by unit vectors and the deformable elements are treated by a corotational formulation in which the coordinate system is embedded in the elements. Deformable elements may be connected either to nodes directly or through rigid bodies. The time integration is carried out by the Newmark ..beta.. method. These features have been incorporated to form the finite-element program SAFE/RAS (Safety Analysis by Finite Elements/Reactor Analysis and Safety Division). Computations are presented for semianalytical comparisons, simple scoping studies, and Stanford Research Institute (SRI) test comparisons.
Modelling of fabric draping: Finite elements versus a geometrical method
Lamers, E.A.D.; Wijskamp, Sebastiaan; Akkerman, Remko
2001-01-01
Thermoplastic composite materials can be processed by Rubber Press Forming at elevated temperatures. Process specific boundary conditions are difficult to incorporate in the classical geometric drape simulation methods. Therefore, a fabric reinforced fluid model was implemented in the Finite Element
Generalized multiscale finite element method. Symmetric interior penalty coupling
Efendiev, Yalchin R.
2013-12-01
Motivated by applications to numerical simulations of flows in highly heterogeneous porous media, we develop multiscale finite element methods for second order elliptic equations. We discuss a multiscale model reduction technique in the framework of the discontinuous Galerkin finite element method. We propose two different finite element spaces on the coarse mesh. The first space is based on a local eigenvalue problem that uses an interior weighted L2-norm and a boundary weighted L2-norm for computing the "mass" matrix. The second choice is based on generation of a snapshot space and subsequent selection of a subspace of a reduced dimension. The approximation with these multiscale spaces is based on the discontinuous Galerkin finite element method framework. We investigate the stability and derive error estimates for the methods and further experimentally study their performance on a representative number of numerical examples. © 2013 Elsevier Inc.
Comparison of different precondtioners for nonsymmtric finite volume element methods
Energy Technology Data Exchange (ETDEWEB)
Mishev, I.D.
1996-12-31
We consider a few different preconditioners for the linear systems arising from the discretization of 3-D convection-diffusion problems with the finite volume element method. Their theoretical and computational convergence rates are compared and discussed.
Methods and devices for fabricating and assembling printable semiconductor elements
Energy Technology Data Exchange (ETDEWEB)
Nuzzo, Ralph G.; Rogers, John A.; Menard, Etienne; Lee, Keon Jae; Khang, Dahl-Young; Sun, Yugang; Meitl, Matthew; Zhu, Zhengtao
2017-09-19
The invention provides methods and devices for fabricating printable semiconductor elements and assembling printable semiconductor elements onto substrate surfaces. Methods, devices and device components of the present invention are capable of generating a wide range of flexible electronic and optoelectronic devices and arrays of devices on substrates comprising polymeric materials. The present invention also provides stretchable semiconductor structures and stretchable electronic devices capable of good performance in stretched configurations.
Methods and devices for fabricating and assembling printable semiconductor elements
Nuzzo, Ralph G; Rogers, John A; Menard, Etienne; Lee, Keon Jae; Khang, Dahl-Young; Sun, Yugang; Meitl, Matthew; Zhu, Zhengtao
2013-05-14
The invention provides methods and devices for fabricating printable semiconductor elements and assembling printable semiconductor elements onto substrate surfaces. Methods, devices and device components of the present invention are capable of generating a wide range of flexible electronic and optoelectronic devices and arrays of devices on substrates comprising polymeric materials. The present invention also provides stretchable semiconductor structures and stretchable electronic devices capable of good performance in stretched configurations.
Analysis of Finite Element Methods for Vector Laplacians on Surfaces
Hansbo, Peter; Larson, Mats G.; Larsson, Karl
2016-01-01
We develop a finite element method for the vector Laplacian based on the covariant derivative of tangential vector fields on surfaces embedded in $\\mathbb{R}^3$. Closely related operators arise in models of flow on surfaces as well as elastic membranes and shells. The method is based on standard continuous parametric Lagrange elements with one order higher polynomial degree for the mapping. The tangent condition is weakly enforced using a penalization term. We derive error estimates that take...
Methods and devices for fabricating and assembling printable semiconductor elements
Energy Technology Data Exchange (ETDEWEB)
Nuzzo, Ralph G.; Rogers, John A.; Menard, Etienne; Lee, Keon Jae; Khang, Dahl-Young; Sun, Yugang; Meitl, Matthew; Zhu, Zhengtao
2017-09-12
The invention provides methods and devices for fabricating printable semiconductor elements and assembling printable semiconductor elements onto substrate surfaces. Methods, devices and device components of the present invention are capable of generating a wide range of flexible electronic and optoelectronic devices and arrays of devices on substrates comprising polymeric materials. The present invention also provides stretchable semiconductor structures and stretchable electronic devices capable of good performance in stretched configurations.
Souza, Luciana Karine de; Duarte, Mônica Grace
2013-01-01
A amizade contribui para o bem-estar subjetivo (BES), e este estudo buscou analisar a relação entre essas variáveis. Participaram 116 universitários de Belo Horizonte e 116 de Porto Alegre, que responderam aos Questionários McGill de Amizade, escalas PANAS e Escala de Satisfação de Vida. As mulheres apontaram mais satisfação e mais sentimentos positivos com a melhor amizade; a amostra mineira indicou mais sentimentos negativos; a satisfação com a amizade correlacionou positivamente com satisf...
Optimization of thin noise barrier designs using Evolutionary Algorithms and a Dual BEM Formulation
Toledo, R.; Aznárez, J. J.; Maeso, O.; Greiner, D.
2015-01-01
This work aims at assessing the acoustic efficiency of different thin noise barrier models. These designs frequently feature complex profiles and their implementation in shape optimization processes may not always be easy in terms of determining their topological feasibility. A methodology to conduct both overall shape and top edge optimizations of thin cross section acoustic barriers by idealizing them as profiles with null boundary thickness is proposed. This procedure is based on the maximization of the insertion loss of candidate profiles proposed by an evolutionary algorithm. The special nature of these sorts of barriers makes necessary the implementation of a complementary formulation to the classical Boundary Element Method (BEM). Numerical simulations of the barriers' performance are conducted by using a 2D Dual BEM code in eight different barrier configurations (covering overall shaped and top edge configurations; spline curved and polynomial shaped based designs; rigid and noise absorbing boundaries materials). While results are achieved by using a specific receivers' scheme, the influence of the receivers' location on the acoustic performance is previously addressed. With the purpose of testing the methodology here presented, a numerical model validation on the basis of experimental results from a scale model test [34] is conducted. Results obtained show the usefulness of representing complex thin barrier configurations as null boundary thickness-like models.
The Matrix Element Method at Next-to-Leading Order
Campbell, John M.; Giele, Walter T.; Williams, Ciaran
2012-01-01
This paper presents an extension of the matrix element method to next-to-leading order in perturbation theory. To accomplish this we have developed a method to calculate next-to-leading order weights on an event-by-event basis. This allows for the definition of next-to-leading order likelihoods in exactly the same fashion as at leading order, thus extending the matrix element method to next-to-leading order. A welcome by-product of the method is the straightforward and efficient generation of...
Ground water modeling applications using the analytic element method.
Hunt, Randall J
2006-01-01
Though powerful and easy to use, applications of the analytic element method are not as widespread as finite-difference or finite-element models due in part to their relative youth. Although reviews that focus primarily on the mathematical development of the method have appeared in the literature, a systematic review of applications of the method is not available. An overview of the general types of applications of analytic elements in ground water modeling is provided in this paper. While not fully encompassing, the applications described here cover areas where the method has been historically applied (regional, two-dimensional steady-state models, analyses of ground water-surface water interaction, quick analyses and screening models, wellhead protection studies) as well as more recent applications (grid sensitivity analyses, estimating effective conductivity and dispersion in highly heterogeneous systems). The review of applications also illustrates areas where more method development is needed (three-dimensional and transient simulations).
Nonconforming mortar element methods: Application to spectral discretizations
Maday, Yvon; Mavriplis, Cathy; Patera, Anthony
1988-01-01
Spectral element methods are p-type weighted residual techniques for partial differential equations that combine the generality of finite element methods with the accuracy of spectral methods. Presented here is a new nonconforming discretization which greatly improves the flexibility of the spectral element approach as regards automatic mesh generation and non-propagating local mesh refinement. The method is based on the introduction of an auxiliary mortar trace space, and constitutes a new approach to discretization-driven domain decomposition characterized by a clean decoupling of the local, structure-preserving residual evaluations and the transmission of boundary and continuity conditions. The flexibility of the mortar method is illustrated by several nonconforming adaptive Navier-Stokes calculations in complex geometry.
The matrix element method at next-to-leading order
Campbell, John M.; Giele, Walter T.; Williams, Ciaran
2012-11-01
This paper presents an extension of the matrix element method to next-to-leading order in perturbation theory, for electro-weak final states. To accomplish this we have developed a method to calculate next-to-leading order weights on an event-by-event basis. This allows for the definition of next-to-leading order likelihoods in exactly the same fashion as at leading order, thus extending the matrix element method to next-to-leading order. A welcome by-product of the method is the straightforward and efficient generation of unweighted next-to-leading order events. As examples of the application of our next-to-leading order matrix element method we consider the measurement of the mass of the Z boson and also the search for the Higgs boson in the four lepton channel.
Multibody Finite Element Method and Application in Hydraulic Structure Analysis
Directory of Open Access Journals (Sweden)
Chao Su
2015-01-01
Full Text Available Multibody finite element method is proposed for analysis of contact problems in hydraulic structure. This method is based on the block theory of discontinuous deformation analysis (DDA method and combines advantages of finite element method (FEM and the displacement compatibility equation in classical elastic mechanics. Each single block is analyzed using FEM in corresponding local coordinate system and all contacting blocks need to satisfy the displacement compatibility requirement between any two blocks in a blocky system. It is proved that this method is very efficient and practical to overcome the limitations in DDA method when tackling contact problems, such as the overlap problem and the equal strain assumption. In this paper, detailed theoretical basis and formulations are given. Two numerical examples are performed to verify the proposed method successfully. Furthermore, this method is adopted to study the stability issues of underground houses of a large hydropower station.
Structural analysis with the finite element method linear statics
Oñate, Eugenio
2013-01-01
STRUCTURAL ANALYSIS WITH THE FINITE ELEMENT METHOD Linear Statics Volume 1 : The Basis and Solids Eugenio Oñate The two volumes of this book cover most of the theoretical and computational aspects of the linear static analysis of structures with the Finite Element Method (FEM). The content of the book is based on the lecture notes of a basic course on Structural Analysis with the FEM taught by the author at the Technical University of Catalonia (UPC) in Barcelona, Spain for the last 30 years. Volume1 presents the basis of the FEM for structural analysis and a detailed description of the finite element formulation for axially loaded bars, plane elasticity problems, axisymmetric solids and general three dimensional solids. Each chapter describes the background theory for each structural model considered, details of the finite element formulation and guidelines for the application to structural engineering problems. The book includes a chapter on miscellaneous topics such as treatment of inclined supports, elas...
A finite element conjugate gradient FFT method for scattering
Collins, Jeffery D.; Ross, Dan; Jin, J.-M.; Chatterjee, A.; Volakis, John L.
1991-01-01
Validated results are presented for the new 3D body of revolution finite element boundary integral code. A Fourier series expansion of the vector electric and mangnetic fields is employed to reduce the dimensionality of the system, and the exact boundary condition is employed to terminate the finite element mesh. The mesh termination boundary is chosen such that is leads to convolutional boundary operatores of low O(n) memory demand. Improvements of this code are discussed along with the proposed formulation for a full 3D implementation of the finite element boundary integral method in conjunction with a conjugate gradiant fast Fourier transformation (CGFFT) solution.
Finite element and discontinuous Galerkin methods for transient wave equations
Cohen, Gary
2017-01-01
This monograph presents numerical methods for solving transient wave equations (i.e. in time domain). More precisely, it provides an overview of continuous and discontinuous finite element methods for these equations, including their implementation in physical models, an extensive description of 2D and 3D elements with different shapes, such as prisms or pyramids, an analysis of the accuracy of the methods and the study of the Maxwell’s system and the important problem of its spurious free approximations. After recalling the classical models, i.e. acoustics, linear elastodynamics and electromagnetism and their variational formulations, the authors present a wide variety of finite elements of different shapes useful for the numerical resolution of wave equations. Then, they focus on the construction of efficient continuous and discontinuous Galerkin methods and study their accuracy by plane wave techniques and a priori error estimates. A chapter is devoted to the Maxwell’s system and the important problem ...
Symmetric Matrix Fields in the Finite Element Method
Directory of Open Access Journals (Sweden)
Gerard Awanou
2010-07-01
Full Text Available The theory of elasticity is used to predict the response of a material body subject to applied forces. In the linear theory, where the displacement is small, the stress tensor which measures the internal forces is the variable of primal importance. However the symmetry of the stress tensor which expresses the conservation of angular momentum had been a challenge for finite element computations. We review in this paper approaches based on mixed finite element methods.
Accurate load prediction by BEM with airfoil data from 3D RANS simulations
Schneider, Marc S.; Nitzsche, Jens; Hennings, Holger
2016-09-01
In this paper, two methods for the extraction of airfoil coefficients from 3D CFD simulations of a wind turbine rotor are investigated, and these coefficients are used to improve the load prediction of a BEM code. The coefficients are extracted from a number of steady RANS simulations, using either averaging of velocities in annular sections, or an inverse BEM approach for determination of the induction factors in the rotor plane. It is shown that these 3D rotor polars are able to capture the rotational augmentation at the inner part of the blade as well as the load reduction by 3D effects close to the blade tip. They are used as input to a simple BEM code and the results of this BEM with 3D rotor polars are compared to the predictions of BEM with 2D airfoil coefficients plus common empirical corrections for stall delay and tip loss. While BEM with 2D airfoil coefficients produces a very different radial distribution of loads than the RANS simulation, the BEM with 3D rotor polars manages to reproduce the loads from RANS very accurately for a variety of load cases, as long as the blade pitch angle is not too different from the cases from which the polars were extracted.
On angle conditions in the finite element method
Brandts, J.; Hannukainen, A.; Korotov, S.; Krizek, M.
2011-01-01
Abstract Angle conditions play an important role in the analysis of the finite element method. They enable us to derive the optimal interpolation order and prove convergence of this method, to derive various a posteriori error estimates, to perform regular mesh refinements, etc. In 1968, Miloˇs
Different Element Methods in Engineering Practice | Onah | Nigerian ...
African Journals Online (AJOL)
Nigerian Journal of Technology ... general manner so that engineers and scientists who are increasingly, called upon to use element methods to support and check their analyses and/or designs can appreciate the essential dierences and similarities in the various methods and their possible advantages and disadvantages.
The future of the finite element method in geotechnics
Brinkgreve, R.B.J.
2012-01-01
In this presentation a vision is given on tlie fiiture of the finite element method (FEM) for geotechnical engineering and design. In the past 20 years the FEM has proven to be a powerful method for estimating deformation, stability and groundwater flow in geoteclmical stmctures. Much has been
Supervised learning method for predicting chromatin boundary associated insulator elements.
Bednarz, Paweł; Wilczyński, Bartek
2014-12-01
In eukaryotic cells, the DNA material is densely packed inside the nucleus in the form of a DNA-protein complex structure called chromatin. Since the actual conformation of the chromatin fiber defines the possible regulatory interactions between genes and their regulatory elements, it is very important to understand the mechanisms governing folding of chromatin. In this paper, we show that supervised methods for predicting chromatin boundary elements are much more effective than the currently popular unsupervised methods. Using boundary locations from published Hi-C experiments and modEncode tracks as features, we can tell the insulator elements from randomly selected background sequences with great accuracy. In addition to accurate predictions of the training boundary elements, our classifiers make new predictions. Many of them correspond to the locations of known insulator elements. The key features used for predicting boundary elements do not depend on the prediction method. Because of its miniscule size, chromatin state cannot be measured directly, we need to rely on indirect measurements, such as ChIP-Seq and fill in the gaps with computational models. Our results show that currently, at least in the model organisms, where we have many measurements including ChIP-Seq and Hi-C, we can make accurate predictions of insulator positions.
Convergence of multigrid method for edge-based finite-element method
Watanabe, K.; Igarashi, H.; Honma, T.
2003-01-01
This paper discusses robustness of the multigrid (MG) method against distortion of finite elements. The convergence of MG method becomes considerably worse as the finite elements become flat. It is shown that the smoother used in the MG method cannot effectively eliminate the high-frequency component of the residue for flat elements, and this gives rise to deterioration in the convergence. Moreover, the multigrid method with conjugate gradient (CG) smoother is shown to be more robust against ...
da psicopatologia ao bem-estar
Monte, Kelly Pavão
2014-01-01
Dissertação apresentada à Universidade Fernando Pessoa como parte dos requisitos para a obtenção do grau de Mestre em Psicologia, ramo de Psicologia Clínica e da Saúde Em termos históricos, a investigação da saúde mental alicerçou-se nos pressupostos teóricos do modelo médico, que a define como a ausência de doença mental ou psicopatologia. Recentemente, a Organização Mundial de Saúde (WHO, 2005) definiu a saúde mental como “um estado de bem-estar no qual o indivíduo realiza as suas própri...
From GPlates to BEM-Earth: Tectonic Reconstruction Data Mining and Geodynamic Simulations
Quevedo, L. E.; Morra, G.; Butterworth, N.; Matthews, K. J.; Müller, D.
2010-12-01
The present day status of high resolution global geological and geophysical datasets poses a unique oportunity to build fine-scale dynamic models of the Earth's evolution. Using the power of the GPlates software, tectonic reconstructions of the last 200 million years of Earth's history are easily built, organized and queried. We present a framework that uses data mining techniques currently under development to extend GPlates capabilities to build and test geodynamic models adapted to our best knowledge of the kinematic, topographic and material features of the post-Triassic Earth. Numerical simulation of global plate-mantle interaction which in the past could not be coupled to small scale dynamics due to computational limitations is achieved by using the BEM-Earth software. The novel approach of BEM-Earth departs from the classical Finite Element methods by solving viscous flow with the Fast Multipole Boundary Element Method and using Multigrid Finite Differences to include advection-diffusion and non linear rheology effects. It uses 3D analytical solutions defined only in the surface of the regions of interest, thus reducing the dimensionality of the problem; and adaptive surface meshes that allows treating multi-scale systems taking full advantage of state of the art observational constraints. This framework opens the door to self-consistent study of geodynamic models and provides a way to gauge the unknown driving forces of tectonics including slab pull, ridge push or mantle drag in a dynamic fashion. Global lithospheric model from GPlates data (above) and forward numerical model of Nazca subduction (below)
Scalable fast multipole methods for vortex element methods
Hu, Qi
2012-11-01
We use a particle-based method to simulate incompressible flows, where the Fast Multipole Method (FMM) is used to accelerate the calculation of particle interactions. The most time-consuming kernelsâ\\'the Biot-Savart equation and stretching term of the vorticity equationâ\\'are mathematically reformulated so that only two Laplace scalar potentials are used instead of six, while automatically ensuring divergence-free far-field computation. Based on this formulation, and on our previous work for a scalar heterogeneous FMM algorithm, we develop a new FMM-based vortex method capable of simulating general flows including turbulence on heterogeneous architectures, which distributes the work between multi-core CPUs and GPUs to best utilize the hardware resources and achieve excellent scalability. The algorithm also uses new data structures which can dynamically manage inter-node communication and load balance efficiently but with only a small parallel construction overhead. This algorithm can scale to large-sized clusters showing both strong and weak scalability. Careful error and timing trade-off analysis are also performed for the cutoff functions induced by the vortex particle method. Our implementation can perform one time step of the velocity+stretching for one billion particles on 32 nodes in 55.9 seconds, which yields 49.12 Tflop/s. © 2012 IEEE.
[Application of finite element method in spinal biomechanics].
Liu, Qiang; Zhang, Jun; Sun, Shu-Chun; Wang, Fei
2017-02-25
The finite element model is one of the most important methods in study of modern spinal biomechanics, according to the needs to simulate the various states of the spine, calculate the stress force and strain distribution of the different groups in the state, and explore its principle of mechanics, mechanism of injury, and treatment effectiveness. In addition, in the study of the pathological state of the spine, the finite element is mainly used in the understanding the mechanism of lesion location, evaluating the effects of different therapeutic tool, assisting and completing the selection and improvement of therapeutic tool, in order to provide a theoretical basis for the rehabilitation of spinal lesions. Finite element method can be more provide the service for the patients suffering from spinal correction, operation and individual implant design. Among the design and performance evaluation of the implant need to pay attention to the individual difference and perfect the evaluation system. At present, how to establish a model which is more close to the real situation has been the focus and difficulty of the study of human body's finite element.Although finite element method can better simulate complex working condition, it is necessary to improve the authenticity of the model and the sharing of the group by using many kinds of methods, such as image science, statistics, kinematics and so on. Copyright© 2017 by the China Journal of Orthopaedics and Traumatology Press.
Finite element method for eigenvalue problems in electromagnetics
Reddy, C. J.; Deshpande, Manohar D.; Cockrell, C. R.; Beck, Fred B.
1994-01-01
Finite element method (FEM) has been a very powerful tool to solve many complex problems in electromagnetics. The goal of the current research at the Langley Research Center is to develop a combined FEM/method of moments approach to three-dimensional scattering/radiation problem for objects with arbitrary shape and filled with complex materials. As a first step toward that goal, an exercise is taken to establish the power of FEM, through closed boundary problems. This paper demonstrates the developed of FEM tools for two- and three-dimensional eigenvalue problems in electromagnetics. In section 2, both the scalar and vector finite elements have been used for various waveguide problems to demonstrate the flexibility of FEM. In section 3, vector finite element method has been extended to three-dimensional eigenvalue problems.
Finite Element Method for Capturing Ultra-relativistic Shocks
Richardson, G. A.; Chung, T. J.
2003-01-01
While finite element methods are used extensively by researchers solving computational fluid dynamics in fields other than astrophysics, their use in astrophysical fluid simulations has been predominantly overlooked. Current simulations using other methods such as finite difference and finite volume (based on finite difference) have shown remarkable results, but these methods are limited by their fundamental properties in aspects that are important for simulations with complex geometries and widely varying spatial and temporal scale differences. We have explored the use of finite element methods for astrophysical fluids in order to establish the validity of using such methods in astrophysical environments. We present our numerical technique applied to solving ultra-relativistic (Lorentz Factor Gamma >> 1) shocks which are prevalent in astrophysical studies including relativistic jets and gamma-ray burst studies. We show our finite element formulation applied to simulations where the Lorentz factor ranges up to 2236 and demonstrate its stability in solving ultra-relativistic flows. Our numerical method is based on the Flowfield Dependent Variation (FDV) Method, unique in that numerical diffusion is derived from physical parameters rather than traditional artificial viscosity methods. Numerical instabilities account for most of the difficulties when capturing shocks in this regime. Our method results in stable solutions and accurate results as compared with other methods.
Spectral element method implementation on GPU for Lamb wave simulation
Kudela, Pawel; Wandowski, Tomasz; Radzienski, Maciej; Ostachowicz, Wieslaw
2017-04-01
Parallel implementation of the time domain spectral element method on GPU (Graphics Processing Unit) is presented. The proposed spectral element method implementation is based on sparse matrix storage of local shape function derivatives calculated at Gauss-Lobatto-Legendre points. The algorithm utilizes two basic operations: multiplication of sparse matrix by vector and element-by-element vectors multiplication. Parallel processing is performed on the degree of freedom level. The assembly of resultant force is done by the aid of a mesh coloring algorithm. The implementation enables considerable computation speedup as well as a simulation of complex structural health monitoring systems based on anomalies of propagating Lamb waves. Hence, the complexity of various models can be tested and compared in order to be as close to reality as possible by using modern computers. A comparative example of a composite laminate modeling by using homogenization of material properties in one layer of 3D brick spectral elements with composite in which each ply is simulated by separate layer of 3D brick spectral elements is described. Consequences of application of each technique are explained. Further analysis is performed for composite laminate with delamination. In each case piezoelectric transducer as well as glue layer between actuator and host structure is modeled.
Tissue-fluid interface analysis using biphasic finite element method.
Unnikrishnan, G U; Unnikrishnan, V U; Reddy, J N
2009-04-01
Numerical studies on fluid-structure interaction have primarily relied on decoupling the solid and fluid sub-domains with the interactions treated as external boundary conditions on the individual sub-domains. The finite element applications for the fluid-structure interactions can be divided into iterative algorithms and sequential algorithms. In this paper, a new computational methodology for the analysis of tissue-fluid interaction problems is presented. The whole computational domain is treated as a single biphasic continuum, and the same space and time discretisation is carried out for the sub-domains using a penalty-based finite element model. This procedure does not require the explicit modelling of additional boundary conditions or interface elements. The developed biphasic interface finite element model is used in analysing blood flow through normal and stenotic arteries. The increase in fluid flow velocity when passing through a stenosed artery and the drop in pressure at the region are captured using this method.
The spectral-element method, Beowulf computing, and global seismology.
Komatitsch, Dimitri; Ritsema, Jeroen; Tromp, Jeroen
2002-11-29
The propagation of seismic waves through Earth can now be modeled accurately with the recently developed spectral-element method. This method takes into account heterogeneity in Earth models, such as three-dimensional variations of seismic wave velocity, density, and crustal thickness. The method is implemented on relatively inexpensive clusters of personal computers, so-called Beowulf machines. This combination of hardware and software enables us to simulate broadband seismograms without intrinsic restrictions on the level of heterogeneity or the frequency content.
Automated discrete element method calibration using genetic and optimization algorithms
Do, Huy Q.; Aragón, Alejandro M.; Schott, Dingena L.
2017-06-01
This research aims at developing a universal methodology for automated calibration of microscopic properties of modelled granular materials. The proposed calibrator can be applied for different experimental set-ups. Two optimization approaches: (1) a genetic algorithm and (2) DIRECT optimization, are used to identify discrete element method input model parameters, e.g., coefficients of sliding and rolling friction. The algorithms are used to minimize the objective function characterized by the discrepancy between the experimental macroscopic properties and the associated numerical results. Two test cases highlight the robustness, stability, and reliability of the two algorithms used for automated discrete element method calibration with different set-ups.
Fast Stiffness Matrix Calculation for Nonlinear Finite Element Method
Directory of Open Access Journals (Sweden)
Emir Gülümser
2014-01-01
Full Text Available We propose a fast stiffness matrix calculation technique for nonlinear finite element method (FEM. Nonlinear stiffness matrices are constructed using Green-Lagrange strains, which are derived from infinitesimal strains by adding the nonlinear terms discarded from small deformations. We implemented a linear and a nonlinear finite element method with the same material properties to examine the differences between them. We verified our nonlinear formulation with different applications and achieved considerable speedups in solving the system of equations using our nonlinear FEM compared to a state-of-the-art nonlinear FEM.
Meshless element-free Galerkin method in NDT applications
Xuan, L.; Zeng, Z.; Shanker, B.; Udpa, L.
2002-05-01
Finite element methods (FEM) are widely used for modeling a variety of problems in Nondestructive Evaluation (NDE). For example, in the modeling of multilayer aircraft geometry with third layer cracks under fasteners, the reliance of FEM on a mesh leads to several problems, particularly when tight cracks have to be introduced into the sample. Furthermore remeshing is often required in handling probe motion can be time consuming. This paper presents a meshless element-free Galerkin method (EFG), where the approximation is entirely constructed in terms of a set of nodes. The model is validated and applied to two dimensional magneto-static and eddy current NDT problems.
Parallel computing for the finite element method in MATLAB
Directory of Open Access Journals (Sweden)
Aurimas Šimkus
2013-09-01
Full Text Available In this research, parallel computing capabilities of MATLAB and the capabilities for the finite element method were analyzed. A program for solving a heat transfer problem by the finite element method was implemented. Three different parallel algorithms using CPU and GPU for solving steady state and transient heat transfer problems were proposed and implemented. A maximal speedup of around 2.3 times for steady state and 2 times for transient problem solving time was achieved by using a quad-core CPU.
Efficient partial element calculation and the extension to cylindrical elements for the PEEC method
Energy Technology Data Exchange (ETDEWEB)
Muesing, A.; Kolar, J. W.
2008-07-01
For various electrical interconnect and electromagnetic compatibility (EMC) problems, the Partial Element Equivalent Circuit (PEEC) method has proven to be a valid and fast solution method of the electrical field integral equation in the time as well as the frequency domain. Therefore, PEEC has become a multipurpose full-wave simulation method, especially suited for the solution of combined circuit and EM problems, as found on printed circuit board layouts, power electronics devices or EMC filters. Recent research introduced various extensions to the basic PEEC approach, for example a non-orthogonal cell geometry formulation. This work presents a fast, flexible and accurate computational method for determining the matrix entries of partial inductances and the coefficients of potential for general non-orthogonal PEEC cell geometries. The presented computation method utilizes analytical filament formulas to reduce the integration order and therefore to reduce computation time. The validity, accuracy and speed of the proposed method is compared with a standard integration routine on example cell geometries where the numeric results of the new method show improved accuracy, coming along with reduced computation time. Furthermore, this work shows an extension to cylindrical elements which is consistent with classical PEEC models, using the proposed integration routines for the partial element calculations. (author)
A multiscale mortar multipoint flux mixed finite element method
Wheeler, Mary Fanett
2012-02-03
In this paper, we develop a multiscale mortar multipoint flux mixed finite element method for second order elliptic problems. The equations in the coarse elements (or subdomains) are discretized on a fine grid scale by a multipoint flux mixed finite element method that reduces to cell-centered finite differences on irregular grids. The subdomain grids do not have to match across the interfaces. Continuity of flux between coarse elements is imposed via a mortar finite element space on a coarse grid scale. With an appropriate choice of polynomial degree of the mortar space, we derive optimal order convergence on the fine scale for both the multiscale pressure and velocity, as well as the coarse scale mortar pressure. Some superconvergence results are also derived. The algebraic system is reduced via a non-overlapping domain decomposition to a coarse scale mortar interface problem that is solved using a multiscale flux basis. Numerical experiments are presented to confirm the theory and illustrate the efficiency and flexibility of the method. © EDP Sciences, SMAI, 2012.
Ultrasonic Method for Deployment Mechanism Bolt Element Preload Verification
Johnson, Eric C.; Kim, Yong M.; Morris, Fred A.; Mitchell, Joel; Pan, Robert B.
2014-01-01
Deployment mechanisms play a pivotal role in mission success. These mechanisms often incorporate bolt elements for which a preload within a specified range is essential for proper operation. A common practice is to torque these bolt elements to a specified value during installation. The resulting preload, however, can vary significantly with applied torque for a number of reasons. The goal of this effort was to investigate ultrasonic methods as an alternative for bolt preload verification in such deployment mechanisms. A family of non-explosive release mechanisms widely used by satellite manufacturers was chosen for the work. A willing contractor permitted measurements on a sampling of bolt elements for these release mechanisms that were installed by a technician following a standard practice. A variation of approximately 50% (+/- 25%) in the resultant preloads was observed. An alternative ultrasonic method to set the preloads was then developed and calibration data was accumulated. The method was demonstrated on bolt elements installed in a fixture instrumented with a calibrated load cell and designed to mimic production practice. The ultrasonic method yielded results within +/- 3% of the load cell reading. The contractor has since adopted the alternative method for its future production. Introduction
A quantitative method for clustering size distributions of elements
Dillner, Ann M.; Schauer, James J.; Christensen, William F.; Cass, Glen R.
A quantitative method was developed to group similarly shaped size distributions of particle-phase elements in order to ascertain sources of the elements. This method was developed and applied using data from two sites in Houston, TX; one site surrounded by refineries, chemical plants and vehicular and commercial shipping traffic, and the other site, 25 miles inland surrounded by residences, light industrial facilities and vehicular traffic. Twenty-four hour size-segregated (0.056fluid catalytic cracking unit catalysts, fuel oil burning, a coal-fired power plant, and high-temperature metal working. The clustered elements were generally attributed to different sources at the two sites during each sampling day indicating the diversity of local sources that impact heavy metals concentrations in the region.
Engineering computation of structures the finite element method
Neto, Maria Augusta; Roseiro, Luis; Cirne, José; Leal, Rogério
2015-01-01
This book presents theories and the main useful techniques of the Finite Element Method (FEM), with an introduction to FEM and many case studies of its use in engineering practice. It supports engineers and students to solve primarily linear problems in mechanical engineering, with a main focus on static and dynamic structural problems. Readers of this text are encouraged to discover the proper relationship between theory and practice, within the finite element method: Practice without theory is blind, but theory without practice is sterile. Beginning with elasticity basic concepts and the classical theories of stressed materials, the work goes on to apply the relationship between forces, displacements, stresses and strains on the process of modeling, simulating and designing engineered technical systems. Chapters discuss the finite element equations for static, eigenvalue analysis, as well as transient analyses. Students and practitioners using commercial FEM software will find this book very helpful. It us...
Development of Efficient Trace Element Quantification Methods in Carbonate Rocks
Kehoe, K. W.; Lonero, A.; Liddell, D.
2016-12-01
This study evaluates the feasibility of using a faster handheld x-ray fluorescence (XRF) method with little to no sample preparation to facilitate the analysis of several important trace elements in carbonate rocks when dealing with large sample quantities. The use of handheld energy-dispersive x-ray fluorescence (ED-XRF) has become popular because it offers nondestructive quantifiable elemental analyses of samples. ED-XRF has been used by geologists in rock core analyses, and has been shown to be capable of producing robust quantifiable results when compared with wavelength-dispersive x-ray fluorescence (WD-XRF) for many elements in pelitic rocks. However, there has been little to no published studies on the use of XRF on carbonate rocks, which may be partly due to the scarcity of internationally accepted trace element reference standards. Trace element abundances of several marine carbonate and carbonatite rocks are presented which have been determined in this study by multiple XRF and inductively coupled plasma mass spectrometry (ICP-MS) methods. Four carbonate standards in development, provided by the USGS, have been characterized with the use of ICP-MS and WD-XRF. Analyses of all samples were performed using different methods by two independent labs at Utah State University and Washington State University. These standards offer the wide elemental ranges necessary to properly quantify geochemical data within the unique matrix of carbonate rocks. A comparison of pressed powder pellets was made between ED-XRF and WD-XRF on carbonate rock samples from the Ordovician Garden City Formation and Pogonip Group of northern and west-central Utah respectively, to determine differences in results between the two methods. Additionally, slabbed hand samples as well as loose powdered samples prepared from the same rock samples were also analyzed and compared with the pressed powder pellets with ED-XRF, to determine if sample preparation had significant effects on sample
A Monte Carlo adapted finite element method for dislocation ...
Indian Academy of Sciences (India)
Home; Journals; Journal of Earth System Science; Volume 126; Issue 7. A Monte Carlo adapted finite element method for dislocation ... However, geological features of a fault cannot be measured exactly, and therefore these features and data involve uncertainties. This paper presents a Monte Carlo based random model of ...
hp Spectral element methods for three dimensional elliptic problems ...
Indian Academy of Sciences (India)
Abstract. This is the first of a series of papers devoted to the study of h-p spec- tral element methods for solving three dimensional elliptic boundary value problems on non-smooth domains using parallel computers. In three dimensions there are three different types of singularities namely; the vertex, the edge and the ...
Piezoelectric Accelerometers Modification Based on the Finite Element Method
DEFF Research Database (Denmark)
Liu, Bin; Kriegbaum, B.
2000-01-01
The paper describes the modification of piezoelectric accelerometers using a Finite Element (FE) method. Brüel & Kjær Accelerometer Type 8325 is chosen as an example to illustrate the advanced accelerometer development procedure. The deviation between the measurement and FE simulation results...
h-p Spectral element methods for three dimensional elliptic ...
Indian Academy of Sciences (India)
The h-p version of the finite element method for solving three dimensional elliptic problems on non-smooth domains with exponential accuracy was proposed by Guo in [9,. 12]. To overcome the singularities which arise along vertices and edges they used geo- metric meshes which are defined in neighbourhoods of vertices, ...
Review on finite element method | Erhunmwun | Journal of Applied ...
African Journals Online (AJOL)
In this work, we have discussed what Finite Element Method (FEM) is, its historical development, advantages and its future. The eventual intension of using FEM is to determine the nodal solution of a particular problem under study. The power of FEM is its ability to discretize complex problems and analyse it part by part.
Reliable finite element methods for self-adjoint singular perturbation ...
African Journals Online (AJOL)
It is well known that the standard finite element method based on the space Vh of continuous piecewise linear functions is not reliable in solving singular perturbation problems. It is also known that the solution of a two-point boundaryvalue singular perturbation problem admits a decomposition into a regular part and a finite ...
Modelling of Granular Materials Using the Discrete Element Method
DEFF Research Database (Denmark)
Ullidtz, Per
1997-01-01
With the Discrete Element Method it is possible to model materials that consists of individual particles where a particle may role or slide on other particles. This is interesting because most of the deformation in granular materials is due to rolling or sliding rather that compression of the gra...
Surface processing methods for point sets using finite elements
Clarenz, Ulrich; Rumpf, Martin; Telea, Alexandru
2004-01-01
We present a framework for processing point-based surfaces via partial differential equations (PDEs). Our framework efficiently and effectively brings well-known PDE-based processing techniques to the field of point-based surfaces. At the core of our method is a finite element discretization of PDEs
Nonconforming h-p spectral element methods for elliptic problems
Indian Academy of Sciences (India)
of the corners, modified polar coordinates are used and a global coordinate system elsewhere. ... applies to elliptic systems too. A method ... Schur complement. Let M denote the number of corner layers and W denote the number of degrees of freedom in each independent variable of the spectral element functions, which.
A Finite Element Removal Method for 3D Topology Optimization
Directory of Open Access Journals (Sweden)
M. Akif Kütük
2013-01-01
Full Text Available Topology optimization provides great convenience to designers during the designing stage in many industrial applications. With this method, designers can obtain a rough model of any part at the beginning of a designing stage by defining loading and boundary conditions. At the same time the optimization can be used for the modification of a product which is being used. Lengthy solution time is a disadvantage of this method. Therefore, the method cannot be widespread. In order to eliminate this disadvantage, an element removal algorithm has been developed for topology optimization. In this study, the element removal algorithm is applied on 3-dimensional parts, and the results are compared with the ones available in the related literature. In addition, the effects of the method on solution times are investigated.
Method for recovering elemental silicon from cutting remains.
Ulset, Torgeir; Julrud, Stein; Cassayre, Laurent; Chamelot, Pierre; Massot, Laurent; Taxil, Pierre
2008-01-01
This invention relates to a method for recovering elemental silicon cutting remains containing silicon particles, wherein the method comprises manufacturing solid anodes from the cutting remains, arranging one or more manufactured anode (s) in an electrolytic cell with a molten salt electrolyte and one or more cathode (s), and applying a potential difference between the one or more anode (s) and cathode (s) to obtain an oxidation of metallic silicon in the one or more anode (s), tran...
Discontinuous Galerkin Finite Element Method for Parabolic Problems
Kaneko, Hideaki; Bey, Kim S.; Hou, Gene J. W.
2004-01-01
In this paper, we develop a time and its corresponding spatial discretization scheme, based upon the assumption of a certain weak singularity of parallel ut(t) parallel Lz(omega) = parallel ut parallel2, for the discontinuous Galerkin finite element method for one-dimensional parabolic problems. Optimal convergence rates in both time and spatial variables are obtained. A discussion of automatic time-step control method is also included.
Convergence of a residual based artificial viscosity finite element method
Nazarov, Murtazo
2013-02-01
We present a residual based artificial viscosity finite element method to solve conservation laws. The Galerkin approximation is stabilized by only residual based artificial viscosity, without any least-squares, SUPG, or streamline diffusion terms. We prove convergence of the method, applied to a scalar conservation law in two space dimensions, toward an unique entropy solution for implicit time stepping schemes. © 2012 Elsevier B.V. All rights reserved.
Nonlinear nonuniform torsional vibrations of bars by the boundary element method
Sapountzakis, E. J.; Tsipiras, V. J.
2010-05-01
In this paper a boundary element method is developed for the nonuniform torsional vibration problem of bars of arbitrary doubly symmetric constant cross-section taking into account the effect of geometrical nonlinearity. The bar is subjected to arbitrarily distributed or concentrated conservative dynamic twisting and warping moments along its length, while its edges are supported by the most general torsional boundary conditions. The transverse displacement components are expressed so as to be valid for large twisting rotations (finite displacement-small strain theory), thus the arising governing differential equations and boundary conditions are in general nonlinear. The resulting coupling effect between twisting and axial displacement components is considered and torsional vibration analysis is performed in both the torsional pre- or post-buckled state. A distributed mass model system is employed, taking into account the warping, rotatory and axial inertia, leading to the formulation of a coupled nonlinear initial boundary value problem with respect to the variable along the bar angle of twist and to an "average" axial displacement of the cross-section of the bar. The numerical solution of the aforementioned initial boundary value problem is performed using the analog equation method, a BEM based method, leading to a system of nonlinear differential-algebraic equations (DAE), which is solved using an efficient time discretization scheme. Additionally, for the free vibrations case, a nonlinear generalized eigenvalue problem is formulated with respect to the fundamental mode shape at the points of reversal of motion after ignoring the axial inertia to verify the accuracy of the proposed method. The problem is solved using the direct iteration technique (DIT), with a geometrically linear fundamental mode shape as a starting vector. The validity of negligible axial inertia assumption is examined for the problem at hand.
Extended Finite Element Method for Fracture Analysis of Structures
Mohammadi, Soheil
2008-01-01
This important textbook provides an introduction to the concepts of the newly developed extended finite element method (XFEM) for fracture analysis of structures, as well as for other related engineering applications.One of the main advantages of the method is that it avoids any need for remeshing or geometric crack modelling in numerical simulation, while generating discontinuous fields along a crack and around its tip. The second major advantage of the method is that by a small increase in number of degrees of freedom, far more accurate solutions can be obtained. The method has recently been
Unconstrained paving and plastering method for generating finite element meshes
Staten, Matthew L.; Owen, Steven J.; Blacker, Teddy D.; Kerr, Robert
2010-03-02
Computer software for and a method of generating a conformal all quadrilateral or hexahedral mesh comprising selecting an object with unmeshed boundaries and performing the following while unmeshed voids are larger than twice a desired element size and unrecognizable as either a midpoint subdividable or pave-and-sweepable polyhedra: selecting a front to advance; based on sizes of fronts and angles with adjacent fronts, determining which adjacent fronts should be advanced with the selected front; advancing the fronts; detecting proximities with other nearby fronts; resolving any found proximities; forming quadrilaterals or unconstrained columns of hexahedra where two layers cross; and establishing hexahedral elements where three layers cross.
Discontinuous Galerkin finite element methods for gradient plasticity.
Energy Technology Data Exchange (ETDEWEB)
Garikipati, Krishna. (University of Michigan, Ann Arbor, MI); Ostien, Jakob T.
2010-10-01
In this report we apply discontinuous Galerkin finite element methods to the equations of an incompatibility based formulation of gradient plasticity. The presentation is motivated with a brief overview of the description of dislocations within a crystal lattice. A tensor representing a measure of the incompatibility with the lattice is used in the formulation of a gradient plasticity model. This model is cast in a variational formulation, and discontinuous Galerkin machinery is employed to implement the formulation into a finite element code. Finally numerical examples of the model are shown.
Hybrid finite element and Brownian dynamics method for charged particles
Energy Technology Data Exchange (ETDEWEB)
Huber, Gary A., E-mail: ghuber@ucsd.edu; Miao, Yinglong [Howard Hughes Medical Institute, University of California San Diego, La Jolla, California 92093-0365 (United States); Zhou, Shenggao [Department of Mathematics and Mathematical Center for Interdiscipline Research, Soochow University, 1 Shizi Street, Suzhou, 215006 Jiangsu (China); Li, Bo [Department of Mathematics and Quantitative Biology Graduate Program, University of California, San Diego, 9500 Gilman Drive, La Jolla, California 92093-0112 (United States); McCammon, J. Andrew [Howard Hughes Medical Institute, University of California San Diego, La Jolla, California 92093 (United States); Department of Chemistry and Biochemistry, University of California San Diego, La Jolla, California 92093-0365 (United States); Department of Pharmacology, University of California San Diego, La Jolla, California 92093-0636 (United States)
2016-04-28
Diffusion is often the rate-determining step in many biological processes. Currently, the two main computational methods for studying diffusion are stochastic methods, such as Brownian dynamics, and continuum methods, such as the finite element method. A previous study introduced a new hybrid diffusion method that couples the strengths of each of these two methods, but was limited by the lack of interactions among the particles; the force on each particle had to be from an external field. This study further develops the method to allow charged particles. The method is derived for a general multidimensional system and is presented using a basic test case for a one-dimensional linear system with one charged species and a radially symmetric system with three charged species.
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.
High-order finite element methods for cardiac monodomain simulations
Directory of Open Access Journals (Sweden)
Kevin P Vincent
2015-08-01
Full Text Available Computational modeling of tissue-scale cardiac electrophysiology requires numerically converged solutions to avoid spurious artifacts. The steep gradients inherent to cardiac action potential propagation necessitate fine spatial scales and therefore a substantial computational burden. The use of high-order interpolation methods has previously been proposed for these simulations due to their theoretical convergence advantage. In this study, we compare the convergence behavior of linear Lagrange, cubic Hermite, and the newly proposed cubic Hermite-style serendipity interpolation methods for finite element simulations of the cardiac monodomain equation. The high-order methods reach converged solutions with fewer degrees of freedom and longer element edge lengths than traditional linear elements. Additionally, we propose a dimensionless number, the cell Thiele modulus, as a more useful metric for determining solution convergence than element size alone. Finally, we use the cell Thiele modulus to examine convergence criteria for obtaining clinically useful activation patterns for applications such as patient-specific modeling where the total activation time is known a priori.
High-order finite element methods for cardiac monodomain simulations
Vincent, Kevin P.; Gonzales, Matthew J.; Gillette, Andrew K.; Villongco, Christopher T.; Pezzuto, Simone; Omens, Jeffrey H.; Holst, Michael J.; McCulloch, Andrew D.
2015-01-01
Computational modeling of tissue-scale cardiac electrophysiology requires numerically converged solutions to avoid spurious artifacts. The steep gradients inherent to cardiac action potential propagation necessitate fine spatial scales and therefore a substantial computational burden. The use of high-order interpolation methods has previously been proposed for these simulations due to their theoretical convergence advantage. In this study, we compare the convergence behavior of linear Lagrange, cubic Hermite, and the newly proposed cubic Hermite-style serendipity interpolation methods for finite element simulations of the cardiac monodomain equation. The high-order methods reach converged solutions with fewer degrees of freedom and longer element edge lengths than traditional linear elements. Additionally, we propose a dimensionless number, the cell Thiele modulus, as a more useful metric for determining solution convergence than element size alone. Finally, we use the cell Thiele modulus to examine convergence criteria for obtaining clinically useful activation patterns for applications such as patient-specific modeling where the total activation time is known a priori. PMID:26300783
Interpolation functions in control volume finite element method
Abbassi, H.; Turki, S.; Nasrallah, S. Ben
The main contribution of this paper is the study of interpolation functions in control volume finite element method used in equal order and applied to an incompressible two-dimensional fluid flow. Especially, the exponential interpolation function expressed in the elemental local coordinate system is compared to the classic linear interpolation function expressed in the global coordinate system. A quantitative comparison is achieved by the application of these two schemes to four flows that we know the analytical solutions. These flows are classified in two groups: flows with privileged direction and flows without. The two interpolation functions are applied to a triangular element of the domain then; a direct comparison of the results given by each interpolation function to the exact value is easily realized. The two functions are also compared when used to solve the discretized equations over the entire domain. Stability of the numerical process and accuracy of solutions are compared.
Flow Applications of the Least Squares Finite Element Method
Jiang, Bo-Nan
1998-01-01
The main thrust of the effort has been towards the development, analysis and implementation of the least-squares finite element method (LSFEM) for fluid dynamics and electromagnetics applications. In the past year, there were four major accomplishments: 1) special treatments in computational fluid dynamics and computational electromagnetics, such as upwinding, numerical dissipation, staggered grid, non-equal order elements, operator splitting and preconditioning, edge elements, and vector potential are unnecessary; 2) the analysis of the LSFEM for most partial differential equations can be based on the bounded inverse theorem; 3) the finite difference and finite volume algorithms solve only two Maxwell equations and ignore the divergence equations; and 4) the first numerical simulation of three-dimensional Marangoni-Benard convection was performed using the LSFEM.
Problems and methods for determining reserves of renewable elements
Energy Technology Data Exchange (ETDEWEB)
Dalkowski, T.; Dabrowska, I.
1983-01-01
The effects of spare parts on reliability of mining equipment used in coal surface mining are discussed. The optimum number of spare parts and elements used in equipment repair depends on reliability and service life of each element and on failure rates, which are influenced by local conditions. A method for determining the optimum number of spare parts for mining equipment which treats a machine failure as an event of random character is analyzed. Problems associated with replacing elements removed due to wear or failures as well as problems of repair are investigated. A model of spare part management and repair shop management in a coal surface mine is evaluated. Spare part management in the Belchatow brown coal surface mine is discussed with the example of maintenance and repair of belt conveyors. 10 references.
Foundations of the complex variable boundary element method
Hromadka, Theodore
2014-01-01
This book explains and examines the theoretical underpinnings of the Complex Variable Boundary Element Method (CVBEM) as applied to higher dimensions, providing the reader with the tools for extending and using the CVBEM in various applications. Relevant mathematics and principles are assembled and the reader is guided through the key topics necessary for an understanding of the development of the CVBEM in both the usual two- as well as three- or higher dimensions. In addition to this, problems are provided that build upon the material presented. The Complex Variable Boundary Element Method (CVBEM) is an approximation method useful for solving problems involving the Laplace equation in two dimensions. It has been shown to be a useful modelling technique for solving two-dimensional problems involving the Laplace or Poisson equations on arbitrary domains. The CVBEM has recently been extended to 3 or higher spatial dimensions, which enables the precision of the CVBEM in solving the Laplace equation to be now ava...
Sapountzakis, E. J.; Tsipiras, V. J.; Argyridi, A. K.
2015-10-01
In this paper a boundary element method (BEM) is developed for the torsional vibration problem of bars of arbitrary doubly symmetric constant cross section, taking into account the nonuniform warping and secondary torsional shear deformation effects (STSDE). The bar is subjected to arbitrarily distributed or concentrated dynamic torsional loading along its length, while its edges are subjected to the most general torsional and warping boundary conditions. Apart from the angle of twist, the primary angle of twist per unit length is considered as an additional 1-D degree of freedom in order to account for the STSDE in the equations of motion of the bar. The warping shear stress distribution and the pertinent secondary torsional rigidity are computed by satisfying local equilibrium considerations under dynamic conditions without adhering to assumptions of Thin Tube Theory (TTT). By employing a distributed mass model system accounting for rotatory and warping inertia, an initial boundary value and two boundary value problems with respect to the variable along the bar time-dependent 1-D kinematical components, to the primary and secondary warping functions, respectively, are formulated. The latter are solved employing a pure BE method, requiring exclusively boundary discretization of the bar's cross section. The numerical solution of the aforementioned initial boundary value problem is performed through a BE method leading to a system of differential equations with displacement only unknowns, which is solved using an efficient direct time integration technique. Additionally, for the free vibrations case, a generalized eigenvalue problem is formulated through a similar BE technique. The accuracy and reliability of the results is assessed by FEM solutions employing solid or shell modelling. Both open- and closed-shaped cross section bars are examined and the necessity to include nonuniform torsional and STSD effects in the dynamic analysis of bars is demonstrated.
Implicit extrapolation methods for multilevel finite element computations
Energy Technology Data Exchange (ETDEWEB)
Jung, M.; Ruede, U. [Technische Universitaet Chemnitz-Zwickau (Germany)
1994-12-31
The finite element package FEMGP has been developed to solve elliptic and parabolic problems arising in the computation of magnetic and thermomechanical fields. FEMGP implements various methods for the construction of hierarchical finite element meshes, a variety of efficient multilevel solvers, including multigrid and preconditioned conjugate gradient iterations, as well as pre- and post-processing software. Within FEMGP, multigrid {tau}-extrapolation can be employed to improve the finite element solution iteratively to higher order. This algorithm is based on an implicit extrapolation, so that the algorithm differs from a regular multigrid algorithm only by a slightly modified computation of the residuals on the finest mesh. Another advantage of this technique is, that in contrast to explicit extrapolation methods, it does not rely on the existence of global error expansions, and therefore neither requires uniform meshes nor global regularity assumptions. In the paper the authors will analyse the {tau}-extrapolation algorithm and present experimental results in the context of the FEMGP package. Furthermore, the {tau}-extrapolation results will be compared to higher order finite element solutions.
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
The Iris biometric feature segmentation using finite element method
Directory of Open Access Journals (Sweden)
David Ibitayo LANLEGE
2015-05-01
Full Text Available This manuscript presents a method for segmentation of iris images based on a deformable contour (active contour paradigm. The deformable contour is a novel approach in image segmentation. A type of active contour is the Snake. Snake is a parametric curve defined within the domain of the image. Snake properties are specified through a function called energy functional. This means they consist of packets of energy which expressed as partial Differential Equations. The partial Differential Equation is the controlling engine of the active contour since this project, the Finite Element Method (Standard Galerkin Method implementation for deformable model is presented.
Finite element method for time-space-fractional Schrodinger equation
Directory of Open Access Journals (Sweden)
Xiaogang Zhu
2017-07-01
Full Text Available In this article, we develop a fully discrete finite element method for the nonlinear Schrodinger equation (NLS with time- and space-fractional derivatives. The time-fractional derivative is described in Caputo's sense and the space-fractional derivative in Riesz's sense. Its stability is well derived; the convergent estimate is discussed by an orthogonal operator. We also extend the method to the two-dimensional time-space-fractional NLS and to avoid the iterative solvers at each time step, a linearized scheme is further conducted. Several numerical examples are implemented finally, which confirm the theoretical results as well as illustrate the accuracy of our methods.
Analysis of Waveguide Junction Discontinuities Using Finite Element Method
Deshpande, Manohar D.
1997-01-01
A Finite Element Method (FEM) is presented to determine reflection and transmission coefficients of rectangular waveguide junction discontinuities. An H-plane discontinuity, an E-plane ridge discontinuity, and a step discontinuity in a concentric rectangular waveguide junction are analyzed using the FEM procedure. Also, reflection and transmission coefficients due to presence of a gap between two sections of a rectangular waveguide are determined using the FEM. The numerical results obtained by the present method are in excellent agreement with the earlier published results. The numerical results obtained by the FEM are compared with the numerical results obtained using the Mode Matching Method (MMM) and also with the measured data.
The Matrix Element Method in the LHC era
Wertz, Sébastien
2017-03-01
The Matrix Element Method (MEM) is a powerful multivariate method allowing to maximally exploit the experimental and theoretical information available to an analysis. The method is reviewed in depth, and several recent applications of the MEM at LHC experiments are discussed, such as searches for rare processes and measurements of Standard Model observables in Higgs and Top physics. Finally, a new implementation of the MEM is presented. This project builds on established phase-space parametrisations known to greatly improve the speed of the calculations, and aims at a much improved modularity and maintainability compared to previous software, easing the use of the MEM for high-statistics data analyses.
Stochastic Finite Element Method in Geotechnical Engineering. Spectral Approach
Directory of Open Access Journals (Sweden)
Auvinet-Guichard G.
2013-01-01
Full Text Available This paper presents the mathematical tools in which the formulation of Spectral Stochastic Finite Element Method is based. The usefulness of this method to model the spatial variability of heterogeneous materials, and in particular of soils, is illustrated by a practical example in which the propagation of the uncertainty on the deformation modulus to the computed displacement field is assessed. The influence of the correlation length on the distribution of uncertainty is set forth. Finally, the advantages of the method in geotechnical engineering are evaluated and some conclusions are presented.
Free vibration analysis of dragonfly wings using finite element method
Directory of Open Access Journals (Sweden)
M Darvizeh
2016-04-01
Full Text Available In the present work, investigations on the microstructure and mechanicalproperties of the dragonfly wing are carried out and numerical modelingbased on Finite Element Method (FEM is developed to predict Flightcharacteristics of dragonfly wings. Vibrational behavior of wings typestructures is immensely important in analysis, design and manufacturing ofsimilar engineering structures. For this purpose natural frequencies andmode shapes are calculated. In addition, the kind of deformation in eachmode shape evaluated and the ratio between numerical natural frequencyand experimental natural frequency presented as damping ratio. Theresults obtain from present method are in good agreement with sameexperimental methods.
Unstructured spectral element methods of simulation of turbulent flows
Energy Technology Data Exchange (ETDEWEB)
Henderson, R.D. [California Inst. of Technology, Pasadena, CA (United States); Karniadakis, G.E. [Brown Univ., Providence, RI (United States)
1995-12-01
In this paper we present a spectral element-Fourier algorithm for simulating incompressible turbulent flows in complex geometries using unstructured quadrilateral meshes. To this end, we compare two different interface formulations for extending the conforming spectral element method in order to allow for surgical mesh refinement and still retain spectral accuracy: the Zanolli iterative procedure and variational patching based on auxiliary {open_quotes}mortar{close_quotes} functions. We present an interpretation of the original mortar element method as a patching scheme and develop direct and iterative solution techniques that make the method efficient for simulations of turbulent flows. The properties of the new method are analyzed in detail by studying the eigenspectra of the advection and diffusion operators. We then present numerical results that illustrate the flexibility as well as the exponential convergence of the new algorithm for nonconforming discretizations. We conclude with simulation studies of the turbulent cylinder wake at Re = 1000 (external flow) and turbulent flow over riblets at Re = 3280 (internal flow). 36 refs., 29 figs., 7 tabs.
Practical Aspects of Finite Element Method Applications in Dentistry
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Grbović Aleksandar
2017-07-01
Full Text Available The use of numerical methods, such as finite element method (FEM, has been widely adopted in solving structural problems with complex geometry under external loads when analytical solutions are unachievable. Basic idea behind FEM is to divide the complex body geometry into smaller and simpler domains, called finite elements, and then to formulate solution for each element instead of seeking a solution for the entire domain. After finding the solutions for all elements they can be combined to obtain a solution for the whole domain. This numerical method is mostly used in engineering, but it is also useful for studying the biomechanical properties of materials used in medicine and the influence of mechanical forces on the biological systems. Since its introduction in dentistry four decades ago, FEM became powerful tool for the predictions of stress and strain distribution on teeth, dentures, implants and surrounding bone. FEM can indicate aspects of biomaterials and human tissues that can hardly be measured in vivo and can predict the stress distribution in the contact areas which are not accessible, such as areas between the implant and cortical bone, denture and gingiva, or around the apex of the implant in trabecular bone. Aim of this paper is to present - using results of several successful FEM studies - the usefulness of this method in solving dentistry problems, as well as discussing practical aspects of FEM applications in dentistry. Some of the method limitations, such as impossibility of complete replication of clinical conditions and need for simplified assumptions regarding loads and materials modeling, are also presented. However, the emphasis is on FE modelling of teeth, bone, dentures and implants and their modifications according to the requirements. All presented studies have been carried out in commercial software for FE analysis ANSYS Workbench.
Directory of Open Access Journals (Sweden)
Letícia Machado Spinelli
2012-08-01
Full Text Available http://dx.doi.org/10.5007/1677-2954.2012v11n1p37 O que aqui nos propomos fazer é explicitar o conceito de sumo bem enquanto bem comunitário, em que se evidencia um desdobramento da formulação do conceito de sumo bem sob a perspectiva de um bem coletivo. Esse conceito foi apresentado por Kant na terceira parte de A religião nos limites da simples razão, contexto no qual se dedicou a tratar da noção de um progresso moral nos termos de uma comunidade ética.
Multiscale finite-element method for linear elastic geomechanics
Castelletto, Nicola; Hajibeygi, Hadi; Tchelepi, Hamdi A.
2017-02-01
The demand for accurate and efficient simulation of geomechanical effects is widely increasing in the geoscience community. High resolution characterizations of the mechanical properties of subsurface formations are essential for improving modeling predictions. Such detailed descriptions impose severe computational challenges and motivate the development of multiscale solution strategies. We propose a multiscale solution framework for the geomechanical equilibrium problem of heterogeneous porous media based on the finite-element method. After imposing a coarse-scale grid on the given fine-scale problem, the coarse-scale basis functions are obtained by solving local equilibrium problems within coarse elements. These basis functions form the restriction and prolongation operators used to obtain the coarse-scale system for the displacement-vector. Then, a two-stage preconditioner that couples the multiscale system with a smoother is derived for the iterative solution of the fine-scale linear system. Various numerical experiments are presented to demonstrate accuracy and robustness of the method.
Introduction to assembly of finite element methods on graphics processors
Cecka, Cristopher; Lew, Adrian; Darve, Eric
2010-06-01
Recently, graphics processing units (GPUs) have had great success in accelerating numerical computations. We present their application to computations on unstructured meshes such as those in finite element methods. Multiple approaches in assembling and solving sparse linear systems with NVIDIA GPUs and the Compute Unified Device Architecture (CUDA) are presented and discussed. Multiple strategies for efficient use of global, shared, and local memory, methods to achieve memory coalescing, and optimal choice of parameters are introduced. We find that with appropriate preprocessing and arrangement of support data, the GPU coprocessor achieves speedups of 30x or more in comparison to a well optimized serial implementation on the CPU. We also find that the optimal assembly strategy depends on the order of polynomials used in the finite-element discretization.
Assembly of finite element methods on graphics processors
Cecka, Cris
2010-08-23
Recently, graphics processing units (GPUs) have had great success in accelerating many numerical computations. We present their application to computations on unstructured meshes such as those in finite element methods. Multiple approaches in assembling and solving sparse linear systems with NVIDIA GPUs and the Compute Unified Device Architecture (CUDA) are created and analyzed. Multiple strategies for efficient use of global, shared, and local memory, methods to achieve memory coalescing, and optimal choice of parameters are introduced. We find that with appropriate preprocessing and arrangement of support data, the GPU coprocessor using single-precision arithmetic achieves speedups of 30 or more in comparison to a well optimized double-precision single core implementation. We also find that the optimal assembly strategy depends on the order of polynomials used in the finite element discretization. © 2010 John Wiley & Sons, Ltd.
The finite element method and applications in engineering using ANSYS
Madenci, Erdogan
2015-01-01
This textbook offers theoretical and practical knowledge of the finite element method. The book equips readers with the skills required to analyze engineering problems using ANSYS®, a commercially available FEA program. Revised and updated, this new edition presents the most current ANSYS® commands and ANSYS® screen shots, as well as modeling steps for each example problem. This self-contained, introductory text minimizes the need for additional reference material by covering both the fundamental topics in finite element methods and advanced topics concerning modeling and analysis. It focuses on the use of ANSYS® through both the Graphics User Interface (GUI) and the ANSYS® Parametric Design Language (APDL). Extensive examples from a range of engineering disciplines are presented in a straightforward, step-by-step fashion. Key topics include: • An introduction to FEM • Fundamentals and analysis capabilities of ANSYS® • Fundamentals of discretization and approximation functions • Modeling techniq...
Least-squares finite element method for fluid dynamics
Jiang, Bo-Nan; Povinelli, Louis A.
1989-01-01
An overview is given of new developments of the least squares finite element method (LSFEM) in fluid dynamics. Special emphasis is placed on the universality of LSFEM; the symmetry and positiveness of the algebraic systems obtained from LSFEM; the accommodation of LSFEM to equal order interpolations for incompressible viscous flows; and the natural numerical dissipation of LSFEM for convective transport problems and high speed compressible flows. The performance of LSFEM is illustrated by numerical examples.
Application of Finite Element Method to Analyze Inflatable Waveguide Structures
Deshpande, M. D.
1998-01-01
A Finite Element Method (FEM) is presented to determine propagation characteristics of deformed inflatable rectangular waveguide. Various deformations that might be present in an inflatable waveguide are analyzed using the FEM. The FEM procedure and the code developed here are so general that they can be used for any other deformations that are not considered in this report. The code is validated by applying the present code to rectangular waveguide without any deformations and comparing the numerical results with earlier published results.
Method for detection of antibodies for metallic elements
Barrick, Charles W.; Clarke, Sara M.; Nordin, Carl W.
1993-11-30
An apparatus and method for detecting antibodies specific to non-protein antigens. The apparatus is an immunological plate containing a plurality of plastic projections coated with a non-protein material. Assays utilizing the plate are capable of stabilizing the non-protein antigens with detection levels for antibodies specific to the antigens on a nanogram level. A screening assay with the apparatus allows for early detection of exposure to non-protein materials. Specifically metallic elements are detected.
Free vibration analysis of dragonfly wings using finite element method
M Darvizeh; A Darvizeh; H Rajabi; A Rezaei
2016-01-01
In the present work, investigations on the microstructure and mechanicalproperties of the dragonfly wing are carried out and numerical modelingbased on Finite Element Method (FEM) is developed to predict Flightcharacteristics of dragonfly wings. Vibrational behavior of wings typestructures is immensely important in analysis, design and manufacturing ofsimilar engineering structures. For this purpose natural frequencies andmode shapes are calculated. In addition, the kind of deformation in eac...
Hydro-elastic analysis of marine propellers based on a BEM-FEM coupled FSI algorithm
Directory of Open Access Journals (Sweden)
Lee Hyoungsuk
2014-09-01
Full Text Available A reliable steady/transient hydro-elastic analysis is developed for flexible (composite marine propeller blade design which deforms according to its environmental load (ship speed, revolution speed, wake distribution, etc. Hydro-elastic analysis based on CFD and FEM has been widely used in the engineering field because of its accurate results however it takes large computation time to apply early propeller design stage. Therefore the analysis based on a boundary element method-Finite Element Method (BEM-FEM Fluid-Structure Interaction (FSI is introduced for computational efficiency and accuracy. The steady FSI analysis, and its application to reverse engineering, is designed for use regarding optimum geometry and ply stack design. A time domain two-way coupled transient FSI analysis is developed by considering the hydrodynamic damping ffects of added mass due to fluid around the propeller blade. The analysis makes possible to evaluate blade strength and also enable to do risk assessment by estimating the change in performance and the deformation depending on blade position in the ship’s wake. To validate this hydro-elastic analysis methodology, published model test results of P5479 and P5475 are applied to verify the steady and the transient FSI analysis, respectively. As the results, the proposed steady and unsteady analysis methodology gives sufficient accuracy to apply flexible marine propeller design
Hydro-elastic analysis of marine propellers based on a BEM-FEM coupled FSI algorithm
Directory of Open Access Journals (Sweden)
Hyoungsuk Lee
2014-09-01
Full Text Available A reliable steady/transient hydro-elastic analysis is developed for flexible (composite marine propeller blade design which deforms according to its environmental load (ship speed, revolution speed, wake distribution, etc. Hydro-elastic analysis based on CFD and FEM has been widely used in the engineering field because of its accurate results however it takes large computation time to apply early propeller design stage. Therefore the analysis based on a boundary element method-Finite Element Method (BEM-FEM Fluid-Structure Interaction (FSI is introduced for computational efficiency and accuracy. The steady FSI analysis, and its application to reverse engineering, is designed for use regarding optimum geometry and ply stack design. A time domain two-way coupled transient FSI analysis is developed by considering the hydrodynamic damping ffects of added mass due to fluid around the propeller blade. The analysis makes possible to evaluate blade strength and also enable to do risk assessment by estimating the change in performance and the deformation depending on blade position in the ship's wake. To validate this hydro-elastic analysis methodology, published model test results of P5479 and P5475 are applied to verify the steady and the transient FSI analysis, respectively. As the results, the proposed steady and unsteady analysis methodology gives sufficient accuracy to apply flexible marine propeller design.
A tephrochronologic method based on apatite trace-element chemistry
Sell, Bryan Keith; Samson, Scott Douglas
Geochemical correlation of ash-fall beds with conventional tephrochronologic methods is not feasible when original glass composition is altered. Thus, alternative correlation methods may be required. Initial studies of heavily altered Paleozoic tephra (K-bentonites) have suggested the potential for employing trace-element concentrations in apatite as ash-fall bed discriminators. To further test the utility of apatite trace-element tephrochronology, we analyzed apatite phenocrysts from unaltered volcanic rocks with an electron microprobe: nine samples from rocks erupted during the Quaternary and one sample from a rock erupted during the Paleogene. The resulting apatite trace-element data provide unique bed discriminators despite within-crystal variability. Each of the volcanic rocks studied possesses unique trends in Mg, Cl, Mn, Fe, Ce and Y concentrations in apatite. The results from this study establish an important tephrochronologic method that can be applied to nearly all portions of the Phanerozoic stratigraphic record and greatly assist development of an advanced timescale. In addition to establishing a fingerprint for a particular eruption, apatite chemistry provides useful information about the source magma.
Parallel 3D Mortar Element Method for Adaptive Nonconforming Meshes
Feng, Huiyu; Mavriplis, Catherine; VanderWijngaart, Rob; Biswas, Rupak
2004-01-01
High order methods are frequently used in computational simulation for their high accuracy. An efficient way to avoid unnecessary computation in smooth regions of the solution is to use adaptive meshes which employ fine grids only in areas where they are needed. Nonconforming spectral elements allow the grid to be flexibly adjusted to satisfy the computational accuracy requirements. The method is suitable for computational simulations of unsteady problems with very disparate length scales or unsteady moving features, such as heat transfer, fluid dynamics or flame combustion. In this work, we select the Mark Element Method (MEM) to handle the non-conforming interfaces between elements. A new technique is introduced to efficiently implement MEM in 3-D nonconforming meshes. By introducing an "intermediate mortar", the proposed method decomposes the projection between 3-D elements and mortars into two steps. In each step, projection matrices derived in 2-D are used. The two-step method avoids explicitly forming/deriving large projection matrices for 3-D meshes, and also helps to simplify the implementation. This new technique can be used for both h- and p-type adaptation. This method is applied to an unsteady 3-D moving heat source problem. With our new MEM implementation, mesh adaptation is able to efficiently refine the grid near the heat source and coarsen the grid once the heat source passes. The savings in computational work resulting from the dynamic mesh adaptation is demonstrated by the reduction of the the number of elements used and CPU time spent. MEM and mesh adaptation, respectively, bring irregularity and dynamics to the computer memory access pattern. Hence, they provide a good way to gauge the performance of computer systems when running scientific applications whose memory access patterns are irregular and unpredictable. We select a 3-D moving heat source problem as the Unstructured Adaptive (UA) grid benchmark, a new component of the NAS Parallel
Simulating Space Capsule Water Landing with Explicit Finite Element Method
Wang, John T.; Lyle, Karen H.
2007-01-01
A study of using an explicit nonlinear dynamic finite element code for simulating the water landing of a space capsule was performed. The finite element model contains Lagrangian shell elements for the space capsule and Eulerian solid elements for the water and air. An Arbitrary Lagrangian Eulerian (ALE) solver and a penalty coupling method were used for predicting the fluid and structure interaction forces. The space capsule was first assumed to be rigid, so the numerical results could be correlated with closed form solutions. The water and air meshes were continuously refined until the solution was converged. The converged maximum deceleration predicted is bounded by the classical von Karman and Wagner solutions and is considered to be an adequate solution. The refined water and air meshes were then used in the models for simulating the water landing of a capsule model that has a flexible bottom. For small pitch angle cases, the maximum deceleration from the flexible capsule model was found to be significantly greater than the maximum deceleration obtained from the corresponding rigid model. For large pitch angle cases, the difference between the maximum deceleration of the flexible model and that of its corresponding rigid model is smaller. Test data of Apollo space capsules with a flexible heat shield qualitatively support the findings presented in this paper.
Application of least-squares spectral element solver methods to incompressible flow problems
M.M.J. Proot; M.I. Gerritsma; M. Nool (Margreet)
2003-01-01
textabstractLeast-squares spectral element methods are based on two important and successful numerical methods: spectral /hp element methods and least-squares finite element methods. In this respect, least-squares spectral element methods are very powerfull since they combine the generality of
Computational methods for the analysis of primate mobile elements
Cordaux, Richard; Sen, Shurjo K.; Konkel, Miriam K.; Batzer, Mark A.
2010-01-01
Transposable elements (TE), defined as discrete pieces of DNA that can move from site to another site in genomes, represent significant components of eukaryotic genomes, including primates. Comparative genome-wide analyses have revealed the considerable structural and functional impact of TE families on primate genomes. Insights into these questions have come in part from the development of computational methods that allow detailed and reliable identification, annotation and evolutionary analyses of the many TE families that populate primate genomes. Here, we present an overview of these computational methods, and describe efficient data mining strategies for providing a comprehensive picture of TE biology in newly available genome sequences. PMID:20238080
Bases teóricas de bem-estar subjetivo, bem-estar psicológico e bem-estar no trabalho
Directory of Open Access Journals (Sweden)
Mirlene Maria Matias Siqueira
Full Text Available A concepção de saúde inclui bem-estar como um conceito chave. Em decorrência, encontram-se na literatura diferentes proposições teóricas para bem-estar. Este artigo tem como objetivo apresentar duas visões tradicionais e uma concepção nova sobre bem-estar. Inicialmente, são revisadas as bases teóricas que sustentam o bem-estar subjetivo. As concepções sobre bem-estar psicológico, ancoradas nas teorias que desenharam os primórdios da psicologia positiva, são apresentadas na segunda seção. Na seqüência, o conceito de bem-estar no trabalho é formulado apontando-se seus componentes assentados em vínculos positivos com o trabalho e com a organização. Na seção que encerra o artigo, sugere-se uma articulação, com base nas proposições da psicologia positiva, no intuito de ampliar a compreensão de fatores que contribuem para promover uma existência mais saudável.
Scientific use of the finite element method in Orthodontics
Knop, Luegya; Gandini, Luiz Gonzaga; Shintcovsk, Ricardo Lima; Gandini, Marcia Regina Elisa Aparecida Schiavon
2015-01-01
INTRODUCTION: The finite element method (FEM) is an engineering resource applied to calculate the stress and deformation of complex structures, and has been widely used in orthodontic research. With the advantage of being a non-invasive and accurate method that provides quantitative and detailed data on the physiological reactions possible to occur in tissues, applying the FEM can anticipate the visualization of these tissue responses through the observation of areas of stress created from applied orthodontic mechanics. OBJECTIVE: This article aims at reviewing and discussing the stages of the finite element method application and its applicability in Orthodontics. RESULTS: FEM is able to evaluate the stress distribution at the interface between periodontal ligament and alveolar bone, and the shifting trend in various types of tooth movement when using different types of orthodontic devices. Therefore, it is necessary to know specific software for this purpose. CONCLUSIONS: FEM is an important experimental method to answer questions about tooth movement, overcoming the disadvantages of other experimental methods. PMID:25992996
8th International Conference on Boundary Element Methods
Brebbia, C
1986-01-01
The International Conference on Boundary Element Methods in Engineering was started in 1978 with the following objectives: i) To act as a focus for BE research at a time when the technique wasjust emerging as a powerful tool for engineering analysis. ii) To attract new as weIl as established researchers on Boundary Elements, in order to maintain its vitality and originality. iii) To try to relate the Boundary Element Method to other engineering techniques in an effort to help unify the field of engineering analysis, rather than to contribute to its fragmentation. These objectives were achieved during the last 7 conferences and this meeting - the eighth - has continued to be as innovative and dynamic as any ofthe previous conferences. Another important aim ofthe conference is to encourage the participation of researchers from as many different countries as possible and in this regard it is a policy of the organizers to hold the conference in different locations. It is easy to forget when working on scientific ...
Envelhecimento bem-sucedido: uma meta no curso da vida
Directory of Open Access Journals (Sweden)
Ilka Nicéia D'Aquino Oliveira Teixeira
2008-03-01
Full Text Available Não há definição consensual de envelhecimento bem-sucedido. Os termos envelhecimento ativo, robusto e bem-sucedido são usados de maneira indiscriminada para explicar o processo de envelhecer bem. O objetivo deste artigo é discutir o significado de envelhecimento bem-sucedido, enfatizando que a subjetividade do conceito está relacionada à individualidade e às diferenças socioculturais. A longevidade não deve ser o único componente para avaliar o envelhecimento bem-sucedido. Envelhecer bem envolve múltiplos fatores, incluindo individuais, psicológicos, biológicos e sociais. A conclusão é que o bem-estar subjetivo é o componente mais importante para avaliar o “sucesso”. O envelhecimento bem-sucedido assemelha-se a um princípio organizacional que pode ser alcançado estabelecendo-se metas pessoais realistas no curso de vida.
Reliability-Based Shape Optimization using Stochastic Finite Element Methods
DEFF Research Database (Denmark)
Enevoldsen, Ib; Sørensen, John Dalsgaard; Sigurdsson, G.
1991-01-01
(7). In this paper a reliability-based shape optimization problem is formulated with the total expected cost as objective function and some requirements for the reliability measures (element or systems reliability measures) as constraints, see section 2. As design variables sizing variables......Application of first-order reliability methods FORM (see Madsen, Krenk & Lind [8)) in structural design problems has attracted growing interest in recent years, see e.g. Frangopol [4), Murotsu, Kishi, Okada, Yonezawa & Taguchi [9) and Sørensen [14). In probabilistically based optimal design...... stochastic fields (e.g. loads and material parameters such as Young's modulus and the Poisson ratio). In this case stochastic finite element techniques combined with FORM analysis can be used to obtain measures of the reliability of the structural systems, see Der Kiureghian & Ke (6) and Liu & Der Kiureghian...
The nonconforming virtual element method for eigenvalue problems
Energy Technology Data Exchange (ETDEWEB)
Gardini, Francesca [Univ. of Pavia (Italy). Dept. of Mathematics; Manzini, Gianmarco [Los Alamos National Lab. (LANL), Los Alamos, NM (United States); Vacca, Giuseppe [Univ. of Milano-Bicocca, Milan (Italy). Dept. of Mathematics and Applications
2018-02-05
We analyse the nonconforming Virtual Element Method (VEM) for the approximation of elliptic eigenvalue problems. The nonconforming VEM allow to treat in the same formulation the two- and three-dimensional case.We present two possible formulations of the discrete problem, derived respectively by the nonstabilized and stabilized approximation of the L^{2}-inner product, and we study the convergence properties of the corresponding discrete eigenvalue problems. The proposed schemes provide a correct approximation of the spectrum and we prove optimal-order error estimates for the eigenfunctions and the usual double order of convergence of the eigenvalues. Finally we show a large set of numerical tests supporting the theoretical results, including a comparison with the conforming Virtual Element choice.
The mixed finite element multigrid method for stokes equations.
Muzhinji, K; Shateyi, S; Motsa, S S
2015-01-01
The stable finite element discretization of the Stokes problem produces a symmetric indefinite system of linear algebraic equations. A variety of iterative solvers have been proposed for such systems in an attempt to construct efficient, fast, and robust solution techniques. This paper investigates one of such iterative solvers, the geometric multigrid solver, to find the approximate solution of the indefinite systems. The main ingredient of the multigrid method is the choice of an appropriate smoothing strategy. This study considers the application of different smoothers and compares their effects in the overall performance of the multigrid solver. We study the multigrid method with the following smoothers: distributed Gauss Seidel, inexact Uzawa, preconditioned MINRES, and Braess-Sarazin type smoothers. A comparative study of the smoothers shows that the Braess-Sarazin smoothers enhance good performance of the multigrid method. We study the problem in a two-dimensional domain using stable Hood-Taylor Q2-Q1 pair of finite rectangular elements. We also give the main theoretical convergence results. We present the numerical results to demonstrate the efficiency and robustness of the multigrid method and confirm the theoretical results.
Architecting the Finite Element Method Pipeline for the GPU.
Fu, Zhisong; Lewis, T James; Kirby, Robert M; Whitaker, Ross T
2014-02-01
The finite element method (FEM) is a widely employed numerical technique for approximating the solution of partial differential equations (PDEs) in various science and engineering applications. Many of these applications benefit from fast execution of the FEM pipeline. One way to accelerate the FEM pipeline is by exploiting advances in modern computational hardware, such as the many-core streaming processors like the graphical processing unit (GPU). In this paper, we present the algorithms and data-structures necessary to move the entire FEM pipeline to the GPU. First we propose an efficient GPU-based algorithm to generate local element information and to assemble the global linear system associated with the FEM discretization of an elliptic PDE. To solve the corresponding linear system efficiently on the GPU, we implement a conjugate gradient method preconditioned with a geometry-informed algebraic multi-grid (AMG) method preconditioner. We propose a new fine-grained parallelism strategy, a corresponding multigrid cycling stage and efficient data mapping to the many-core architecture of GPU. Comparison of our on-GPU assembly versus a traditional serial implementation on the CPU achieves up to an 87 × speedup. Focusing on the linear system solver alone, we achieve a speedup of up to 51 × versus use of a comparable state-of-the-art serial CPU linear system solver. Furthermore, the method compares favorably with other GPU-based, sparse, linear solvers.
Methods and framework for visualizing higher-order finite elements.
Schroeder, William J; Bertel, François; Malaterre, Mathieu; Thompson, David; Pébay, Philippe P; O'Bara, Robert; Tendulkar, Saurabh
2006-01-01
The finite element method is an important, widely used numerical technique for solving partial differential equations. This technique utilizes basis functions for approximating the geometry and the variation of the solution field over finite regions, or elements, of the domain. These basis functions are generally formed by combinations of polynomials. In the past, the polynomial order of the basis has been low-typically of linear and quadratic order. However, in recent years so-called p and hp methods have been developed, which may elevate the order of the basis to arbitrary levels with the aim of accelerating the convergence of the numerical solution. The increasing complexity of numerical basis functions poses a significant challenge to visualization systems. In the past, such systems have been loosely coupled to simulation packages, exchanging data via file transfer, and internally reimplementing the basis functions in order to perform interpolation and implement visualization algorithms. However, as the basis functions become more complex and, in some cases, proprietary in nature, it becomes increasingly difficult if not impossible to reimplement them within the visualization system. Further, most visualization systems typically process linear primitives, in part to take advantage of graphics hardware and, in part, due to the inherent simplicity of the resulting algorithms. Thus, visualization of higher-order finite elements requires tessellating the basis to produce data compatible with existing visualization systems. In this paper, we describe adaptive methods that automatically tessellate complex finite element basis functions using a flexible and extensible software framework. These methods employ a recursive, edge-based subdivision algorithm driven by a set of error metrics including geometric error, solution error, and error in image space. Further, we describe advanced pretessellation techniques that guarantees capture of the critical points of the
Generalized multiscale finite element methods. nonlinear elliptic equations
Efendiev, Yalchin R.
2013-01-01
In this paper we use the Generalized Multiscale Finite Element Method (GMsFEM) framework, introduced in [26], in order to solve nonlinear elliptic equations with high-contrast coefficients. The proposed solution method involves linearizing the equation so that coarse-grid quantities of previous solution iterates can be regarded as auxiliary parameters within the problem formulation. With this convention, we systematically construct respective coarse solution spaces that lend themselves to either continuous Galerkin (CG) or discontinuous Galerkin (DG) global formulations. Here, we use Symmetric Interior Penalty Discontinuous Galerkin approach. Both methods yield a predictable error decline that depends on the respective coarse space dimension, and we illustrate the effectiveness of the CG and DG formulations by offering a variety of numerical examples. © 2014 Global-Science Press.
7th International Conference on Discrete Element Methods
Feng, Yuntian; Mustoe, Graham
2017-01-01
This book presents the latest advances in Discrete Element Methods (DEM) and technology. It is the proceeding of 7th International Conference on DEM which was held at Dalian University of Technology on August 1 - 4, 2016. The subject of this book are the DEM and related computational techniques such as DDA, FEM/DEM, molecular dynamics, SPH, Meshless methods, etc., which are the main computational methods for modeling discontinua. In comparison to continua which have been already studied for a long time, the research of discontinua is relatively new, but increases dramatically in recent years and has already become an important field. This book will benefit researchers and scientists from the academic fields of physics, engineering and applied mathematics, as well as from industry and national laboratories who are interested in the DEM. .
Lamichhane, Bishnu P.
2014-01-01
We present a finite element method for Stokes equations using the Crouzeix-Raviart element for the velocity and the continuous linear element for the pressure. We show that the inf-sup condition is satisfied for this pair. Two numerical experiments are presented to support the theoretical results.
Flexural Modeling of the Andean System Using Finite Element Method
Sacek, V.; Ussami, N.
2007-05-01
The general equation of flexure of the lithosphere in cartesian coordinates is solved using a numerical Finite Element Method (FEM) with triangular elements in non-structured meshes. This alternative way to model bending of thin elastic plates lying over an inviscid fluid allows taking into account lateral variation of rigidity, plate discontinuities and full 3-D representation of loads. The numerical solution was initially compared with the analytical solution of bending of an elastic plate loaded by an uniformally distributed load. The method was applied to model flexure of a plate due to curved orogenic belts and the results were compared with solutions obtained if a 2-D approximation of plates and loads was considered. The proposed numerical method was applied to study flexural deformation of the western edge of the South American lithospheric plate due to the loads of the Andean mountains, using Te =75 km for both continuous and broken plates. The predicted forebulges agree with the observed distribution of positive gravity anomalies paralleling the negative gravity anomalies associated with the high topography of the Andes. Maximum amplitudes of forebulges correlate with Purus Arch in Solimões basin (W Brazil) and the Chaco Pampeana plain (Argentina), and between these two regions, a saddle point occurs over the Pantanal wetland (SW Brazil).
The Distinct Element Method - Application to Structures in Jointed Rock
Energy Technology Data Exchange (ETDEWEB)
Morris, J.P.; Glen, L.; Blair, S.; Heuze, F.
2001-11-30
The Distinct Element Method (DEM) is a meshfree method with applications to rock mechanics, mining sciences, simulations of nuclear repositories, and the stability of underground structures. Continuum mesh-based methods have been applied successfully to many problems in geophysics. Even if the geology includes fractures and faults, when sufficiently large length scales are considered a continuum approximation may be sufficient. However, a large class of problems exist where individual rock joints must be taken into account. This includes problems where the structures of interest have sizes comparable with the block size. In addition, it is possible that while the structure may experience loads which do no measurable damage to individual blocks, some joints may fail. This may launch smaller blocks as dangerous projectiles or even cause total failure of a tunnel. Traditional grid-based continuum approaches are wholly unsuited to this class of problem. It is possible to introduce discontinuities or slide lines into existing grid-based methods, however, such limited approaches can break down when new contacts form between blocks. The distinct element method (DEM) is an alternative, meshfree approach. The DEM can directly approximate the block structure of the jointed rock using arbitrary polyhedra. Using this approach, preexisting joints are readily incorporated into the DEM model. In addition, the method detects all new contacts between blocks resulting from relative block motion. We will describe the background of the DEM and review previous application of the DEM to geophysical problems. Finally we present preliminary results from a investigation into the stability of underground structures subjected to dynamic loading.
Modeling of coal stockpiles using a finite elements method
Energy Technology Data Exchange (ETDEWEB)
Ozdeniz, A.H.; Sensogut, C. [Dumlupinar University, Kutahya (Turkey)
2008-07-01
In the case of coal stockpiles finding suitable environmental conditions, spontaneous combustion phenomenon will be unavoidable. In this study, an industrial-sized stockpile having a shape of triangle prism was constituted in a coal stockyard of Western Lignite Corporation (WLC), Turkey. The parameters of time, humidity and temperature of air, atmospheric pressure, velocity and direction of wind values that are effective on coal stockpile were measured in a continuous manner. These experimental works were transferred into a computer media in order to obtain similar outcomes by carrying out 2-dimensional analysis of the stockpile with Finite Elements Method (FEM). The performed experimental studies and obtained results were then compared.
Piezoelectric Analysis of Saw Sensor Using Finite Element Method
Directory of Open Access Journals (Sweden)
Vladimír KUTIŠ
2013-06-01
Full Text Available In this contribution modeling and simulation of surface acoustic waves (SAW sensor using finite element method will be presented. SAW sensor is made from piezoelectric GaN layer and SiC substrate. Two different analysis types are investigated - modal and transient. Both analyses are only 2D. The goal of modal analysis, is to determine the eigenfrequency of SAW, which is used in following transient analysis. In transient analysis, wave propagation in SAW sensor is investigated. Both analyses were performed using FEM code ANSYS.
Stress Reduction of Pickup Truck Chassis Using Finite Element Method
Kurdi, O.; Yob, M. S.; Dasson, S. R.; Barrathi, S.; Altayeb, A. A.; Yulianti, I.
2017-04-01
This paper performed stress reduction of the chassis of single cab pick truck using Finite Element Method (FEM). The first step was to evaluate and identify the critical area or maximum values of the static stress and its locations. The second stage of this project was dealing with designing a new chassis based on the Tata model, and then the final stage was a validation of numerical results with both experiments and analytical calculation to get the desired chassis that have strong and high-quality design.
Simulation of dry granular flows using discrete element methods
Martin, Hugo; Lefebvre, Aline; Maday, Yvon; Mangeney, Anne; Maury, Bertrand; Sainte-Marie, Jacques
2017-04-01
Granular flows are composed of interacting particles (for instance sand grains). While natural flow simulations at the field scale are generally based on continuum models, discrete element methods are very useful to get insight into the detailed contact interactions between the particles involved. We shall consider here both well known molecular dynamics (MD) and contact dynamics (CD) methods to simulate granular particle interaction. The difference between these methods is the linearisation of contact forces in MD. We are interested to compare these methods, and especially the effects of the linearisation in simulations. In the present work, we introduce a new rigid bodies model at the scale of the particles and its resolution by contact dynamics. The interesting aspect of our CD method is to treat the contacts in all the material system in one step without any iterative process required when the contacts are dealt with one after the other. All contacts are calculated here at the same time in just one iteration and the normal and tangential constraints are treated simultaneously. The present model follows from a convex optimization problem presented in [1] by B. Maury in which we add a frictional behaviour to the contact law between the particles. To analyse the behaviour of this model, we compare our results to analytical solutions when we can compute them and otherwise to simulations with molecular dynamics method. [1] A time-stepping scheme for inelastic collisions. Numerical handling of the nonoverlapping constraint, B. Maury, Numerische Mathematik, 17 january 2006.
Mixed Generalized Multiscale Finite Element Methods and Applications
Chung, Eric T.
2015-03-03
In this paper, we present a mixed generalized multiscale finite element method (GMsFEM) for solving flow in heterogeneous media. Our approach constructs multiscale basis functions following a GMsFEM framework and couples these basis functions using a mixed finite element method, which allows us to obtain a mass conservative velocity field. To construct multiscale basis functions for each coarse edge, we design a snapshot space that consists of fine-scale velocity fields supported in a union of two coarse regions that share the common interface. The snapshot vectors have zero Neumann boundary conditions on the outer boundaries, and we prescribe their values on the common interface. We describe several spectral decompositions in the snapshot space motivated by the analysis. In the paper, we also study oversampling approaches that enhance the accuracy of mixed GMsFEM. A main idea of oversampling techniques is to introduce a small dimensional snapshot space. We present numerical results for two-phase flow and transport, without updating basis functions in time. Our numerical results show that one can achieve good accuracy with a few basis functions per coarse edge if one selects appropriate offline spaces. © 2015 Society for Industrial and Applied Mathematics.
Adaptive Finite Element Methods for Elliptic Problems with Discontinuous Coefficients
Bonito, Andrea
2013-01-01
Elliptic PDEs with discontinuous diffusion coefficients occur in application domains such as diffusions through porous media, electromagnetic field propagation on heterogeneous media, and diffusion processes on rough surfaces. The standard approach to numerically treating such problems using finite element methods is to assume that the discontinuities lie on the boundaries of the cells in the initial triangulation. However, this does not match applications where discontinuities occur on curves, surfaces, or manifolds, and could even be unknown beforehand. One of the obstacles to treating such discontinuity problems is that the usual perturbation theory for elliptic PDEs assumes bounds for the distortion of the coefficients in the L∞ norm and this in turn requires that the discontinuities are matched exactly when the coefficients are approximated. We present a new approach based on distortion of the coefficients in an Lq norm with q < ∞ which therefore does not require the exact matching of the discontinuities. We then use this new distortion theory to formulate new adaptive finite element methods (AFEMs) for such discontinuity problems. We show that such AFEMs are optimal in the sense of distortion versus number of computations, and report insightful numerical results supporting our analysis. © 2013 Societ y for Industrial and Applied Mathematics.
Boundary element method for surface nonlinear optics of nanoparticles.
Mäkitalo, Jouni; Suuriniemi, Saku; Kauranen, Martti
2011-11-07
We present the frequency-domain boundary element formulation for solving surface second-harmonic generation from nanoparticles of virtually arbitrary shape and material. We use the Rao-Wilton-Glisson basis functions and Galerkin's testing, which leads to very accurate solutions for both near and far fields. This is verified by a comparison to a solution obtained via multipole expansion for the case of a spherical particle. The frequency-domain formulation allows the use of experimentally measured linear and nonlinear material parameters or the use of parameters obtained using ab-initio principles. As an example, the method is applied to a non-centrosymmetric L-shaped gold nanoparticle to illustrate the formation of surface nonlinear polarization and the second-harmonic radiation properties of the particle. This method provides a theoretically well-founded approach for modelling nonlinear optical phenomena in nanoparticles.
O bem-estar subjectivo de adolescentes institucionalizados
Silva, Maria João Marques Xavier da
2011-01-01
Tese de mestrado, Psicologia (Secção de Psicologia Clínica e da Saúde - Núcleo de Psicoterapia Cognitivo-Comportamental e Integrativa), Universidade de Lisboa, Faculdade de Psicologia, 2011 A população de adolescentes institucionalizados, a adolescência em si e o bem-estar continuam a ser alvo de diversas investigações, dada a importância de identificar os factores que promovem o bem-estar nesta faixa etária. No entanto, escassas são as investigações que relacionam o bem-estar com o proces...
System and Method for Finite Element Simulation of Helicopter Turbulence
McFarland, R. E. (Inventor); Dulsenberg, Ken (Inventor)
1999-01-01
The present invention provides a turbulence model that has been developed for blade-element helicopter simulation. This model uses an innovative temporal and geometrical distribution algorithm that preserves the statistical characteristics of the turbulence spectra over the rotor disc, while providing velocity components in real time to each of five blade-element stations along each of four blades. for a total of twenty blade-element stations. The simulator system includes a software implementation of flight dynamics that adheres to the guidelines for turbulence set forth in military specifications. One of the features of the present simulator system is that it applies simulated turbulence to the rotor blades of the helicopter, rather than to its center of gravity. The simulator system accurately models the rotor penetration into a gust field. It includes time correlation between the front and rear of the main rotor, as well as between the side forces felt at the center of gravity and at the tail rotor. It also includes features for added realism, such as patchy turbulence and vertical gusts in to which the rotor disc penetrates. These features are realized by a unique real time implementation of the turbulence filters. The new simulator system uses two arrays one on either side of the main rotor to record the turbulence field and to produce time-correlation from the front to the rear of the rotor disc. The use of Gaussian Interpolation between the two arrays maintains the statistical properties of the turbulence across the rotor disc. The present simulator system and method may be used in future and existing real-time helicopter simulations with minimal increase in computational workload.
Multiscale Finite Element Methods for Flows on Rough Surfaces
Efendiev, Yalchin
2013-01-01
In this paper, we present the Multiscale Finite Element Method (MsFEM) for problems on rough heterogeneous surfaces. We consider the diffusion equation on oscillatory surfaces. Our objective is to represent small-scale features of the solution via multiscale basis functions described on a coarse grid. This problem arises in many applications where processes occur on surfaces or thin layers. We present a unified multiscale finite element framework that entails the use of transformations that map the reference surface to the deformed surface. The main ingredients of MsFEM are (1) the construction of multiscale basis functions and (2) a global coupling of these basis functions. For the construction of multiscale basis functions, our approach uses the transformation of the reference surface to a deformed surface. On the deformed surface, multiscale basis functions are defined where reduced (1D) problems are solved along the edges of coarse-grid blocks to calculate nodalmultiscale basis functions. Furthermore, these basis functions are transformed back to the reference configuration. We discuss the use of appropriate transformation operators that improve the accuracy of the method. The method has an optimal convergence if the transformed surface is smooth and the image of the coarse partition in the reference configuration forms a quasiuniform partition. In this paper, we consider such transformations based on harmonic coordinates (following H. Owhadi and L. Zhang [Comm. Pure and Applied Math., LX(2007), pp. 675-723]) and discuss gridding issues in the reference configuration. Numerical results are presented where we compare the MsFEM when two types of deformations are used formultiscale basis construction. The first deformation employs local information and the second deformation employs a global information. Our numerical results showthat one can improve the accuracy of the simulations when a global information is used. © 2013 Global-Science Press.
Generalized multiscale finite element methods (GMsFEM)
Efendiev, Yalchin R.
2013-10-01
In this paper, we propose a general approach called Generalized Multiscale Finite Element Method (GMsFEM) for performing multiscale simulations for problems without scale separation over a complex input space. As in multiscale finite element methods (MsFEMs), the main idea of the proposed approach is to construct a small dimensional local solution space that can be used to generate an efficient and accurate approximation to the multiscale solution with a potentially high dimensional input parameter space. In the proposed approach, we present a general procedure to construct the offline space that is used for a systematic enrichment of the coarse solution space in the online stage. The enrichment in the online stage is performed based on a spectral decomposition of the offline space. In the online stage, for any input parameter, a multiscale space is constructed to solve the global problem on a coarse grid. The online space is constructed via a spectral decomposition of the offline space and by choosing the eigenvectors corresponding to the largest eigenvalues. The computational saving is due to the fact that the construction of the online multiscale space for any input parameter is fast and this space can be re-used for solving the forward problem with any forcing and boundary condition. Compared with the other approaches where global snapshots are used, the local approach that we present in this paper allows us to eliminate unnecessary degrees of freedom on a coarse-grid level. We present various examples in the paper and some numerical results to demonstrate the effectiveness of our method. © 2013 Elsevier Inc.
Kruyt, Nicolaas P.; Cuvelier, C.; Segal, A.; van der Zanden, J.
1988-01-01
In this paper a total linearization method is derived for solving steady viscous free boundary flow problems (including capillary effects) by the finite element method. It is shown that the influence of the geometrical unknown in the totally linearized weak formulation can be expressed in terms of
Hybrid finite difference/finite element immersed boundary method.
E Griffith, Boyce; Luo, Xiaoyu
2017-12-01
The immersed boundary method is an approach to fluid-structure interaction that uses a Lagrangian description of the structural deformations, stresses, and forces along with an Eulerian description of the momentum, viscosity, and incompressibility of the fluid-structure system. The original immersed boundary methods described immersed elastic structures using systems of flexible fibers, and even now, most immersed boundary methods still require Lagrangian meshes that are finer than the Eulerian grid. This work introduces a coupling scheme for the immersed boundary method to link the Lagrangian and Eulerian variables that facilitates independent spatial discretizations for the structure and background grid. This approach uses a finite element discretization of the structure while retaining a finite difference scheme for the Eulerian variables. We apply this method to benchmark problems involving elastic, rigid, and actively contracting structures, including an idealized model of the left ventricle of the heart. Our tests include cases in which, for a fixed Eulerian grid spacing, coarser Lagrangian structural meshes yield discretization errors that are as much as several orders of magnitude smaller than errors obtained using finer structural meshes. The Lagrangian-Eulerian coupling approach developed in this work enables the effective use of these coarse structural meshes with the immersed boundary method. This work also contrasts two different weak forms of the equations, one of which is demonstrated to be more effective for the coarse structural discretizations facilitated by our coupling approach. © 2017 The Authors International Journal for Numerical Methods in Biomedical Engineering Published by John Wiley & Sons Ltd.
Assessment of Carrying Capacity of Timber Element Using SBRA Method
Kraus, Michal
2017-10-01
Wood as a building material has a significant perspective in the context of nonrenewable energy sources and production of greenhouse gas emissions. The subject of this paper is to verify the carrying capacity of the timber element using the probabilistic method Simulation Based Reliability Assessment (SBRA). The simulation is performed for one million cycles. Key factors decreasing the strength of wooden material at the time include the duration of the loads, and combinations thereof. Inconsiderable factor affecting the strength of wood is also the humidity. Continuous beam with three fields (length 15 m, glued laminated timber, and strength class GL 36 according to the DIN EN 1194) is placed in an environment with a thermal-humidity regime of the 2nd class according to the EC 5. Average life of carrying timber structure is estimated to be 50 years. The simulation results show that there is no risk of failure of wood during the first year. The probability of failure is common in the 10 years of its life. Then, wooden element already meets only a reduced level of reliability.
Finite element method application for turbulent and transitional flow
Directory of Open Access Journals (Sweden)
Sváček Petr
2016-01-01
Full Text Available This paper is interested in numerical simulations of the interaction of the fluid flow with an airfoil. Particularly, the problem of the turbulent flow around the airfoil with elastic support is considered. The main attention is paid to the numerical approximation of the flow problem using the finite element approximations. The laminar - turbulence transition of the flow on the surface airfoil is considered. The chois of the transition model is discussed. The transition model based on the two equation k−ω turbulence model is used. The structure motion is described with the aid of two degrees of freedom. The motion of the computational domain is treated with the aid of the arbitrary Lagrangian-Eulerian method. Numerical results are shown.
A mixed finite element method for nonlinear diffusion equations
Burger, Martin
2010-01-01
We propose a mixed finite element method for a class of nonlinear diffusion equations, which is based on their interpretation as gradient flows in optimal transportation metrics. We introduce an appropriate linearization of the optimal transport problem, which leads to a mixed symmetric formulation. This formulation preserves the maximum principle in case of the semi-discrete scheme as well as the fully discrete scheme for a certain class of problems. In addition solutions of the mixed formulation maintain exponential convergence in the relative entropy towards the steady state in case of a nonlinear Fokker-Planck equation with uniformly convex potential. We demonstrate the behavior of the proposed scheme with 2D simulations of the porous medium equations and blow-up questions in the Patlak-Keller-Segel model. © American Institute of Mathematical Sciences.
Spectral Analysis of Large Finite Element Problems by Optimization Methods
Directory of Open Access Journals (Sweden)
Luca Bergamaschi
1994-01-01
Full Text Available Recently an efficient method for the solution of the partial symmetric eigenproblem (DACG, deflated-accelerated conjugate gradient was developed, based on the conjugate gradient (CG minimization of successive Rayleigh quotients over deflated subspaces of decreasing size. In this article four different choices of the coefficient βk required at each DACG iteration for the computation of the new search direction Pk are discussed. The “optimal” choice is the one that yields the same asymptotic convergence rate as the CG scheme applied to the solution of linear systems. Numerical results point out that the optimal βk leads to a very cost effective algorithm in terms of CPU time in all the sample problems presented. Various preconditioners are also analyzed. It is found that DACG using the optimal βk and (LLT−1 as a preconditioner, L being the incomplete Cholesky factor of A, proves a very promising method for the partial eigensolution. It appears to be superior to the Lanczos method in the evaluation of the 40 leftmost eigenpairs of five finite element problems, and particularly for the largest problem, with size equal to 4560, for which the speed gain turns out to fall between 2.5 and 6.0, depending on the eigenpair level.
Finite Element Method for Analysis of Material Properties
DEFF Research Database (Denmark)
Rauhe, Jens Christian
The use of cellular and composite materials have in recent years become more and more common in all kinds of structural components and accurate knowledge of the effective properties is therefore essential. In this wok the effective properties are determined using the real material microstructure...... theoretical models. Besides the determination of the effective properties, viscoelastic and damage analysis have been performed on a number of material microstructures....... description of the material microstructure the finite element models must contain a large number of elements and this problem is solved by using the preconditioned conjugated gradient solver with an Element-By-Element preconditioner. Finite element analysis provides the volume averaged stresses and strains...
Energy Technology Data Exchange (ETDEWEB)
Dohrmann, C.R.; Heinstein, M.W.; Jung, J.; Key, S.W.
1999-01-01
This report documents a collection of papers on a family of uniform strain tetrahedral finite elements and their connection to different element types. Also included in the report are two papers which address the general problem of connecting dissimilar meshes in two and three dimensions. Much of the work presented here was motivated by the development of the tetrahedral element described in the report "A Suitable Low-Order, Eight-Node Tetrahedral Finite Element For Solids," by S. W. Key {ital et al.}, SAND98-0756, March 1998. Two basic issues addressed by the papers are: (1) the performance of alternative tetrahedral elements with uniform strain and enhanced uniform strain formulations, and (2) the proper connection of tetrahedral and other element types when two meshes are "tied" together to represent a single continuous domain.
Deng, Yongbo; Korvink, Jan G
2016-05-01
This paper develops a topology optimization procedure for three-dimensional electromagnetic waves with an edge element-based finite-element method. In contrast to the two-dimensional case, three-dimensional electromagnetic waves must include an additional divergence-free condition for the field variables. The edge element-based finite-element method is used to both discretize the wave equations and enforce the divergence-free condition. For wave propagation described in terms of the magnetic field in the widely used class of non-magnetic materials, the divergence-free condition is imposed on the magnetic field. This naturally leads to a nodal topology optimization method. When wave propagation is described using the electric field, the divergence-free condition must be imposed on the electric displacement. In this case, the material in the design domain is assumed to be piecewise homogeneous to impose the divergence-free condition on the electric field. This results in an element-wise topology optimization algorithm. The topology optimization problems are regularized using a Helmholtz filter and a threshold projection method and are analysed using a continuous adjoint method. In order to ensure the applicability of the filter in the element-wise topology optimization version, a regularization method is presented to project the nodal into an element-wise physical density variable.
Korvink, Jan G.
2016-01-01
This paper develops a topology optimization procedure for three-dimensional electromagnetic waves with an edge element-based finite-element method. In contrast to the two-dimensional case, three-dimensional electromagnetic waves must include an additional divergence-free condition for the field variables. The edge element-based finite-element method is used to both discretize the wave equations and enforce the divergence-free condition. For wave propagation described in terms of the magnetic field in the widely used class of non-magnetic materials, the divergence-free condition is imposed on the magnetic field. This naturally leads to a nodal topology optimization method. When wave propagation is described using the electric field, the divergence-free condition must be imposed on the electric displacement. In this case, the material in the design domain is assumed to be piecewise homogeneous to impose the divergence-free condition on the electric field. This results in an element-wise topology optimization algorithm. The topology optimization problems are regularized using a Helmholtz filter and a threshold projection method and are analysed using a continuous adjoint method. In order to ensure the applicability of the filter in the element-wise topology optimization version, a regularization method is presented to project the nodal into an element-wise physical density variable. PMID:27279766
Randomized Oversampling for Generalized Multiscale Finite Element Methods
Calo, Victor M.
2016-03-23
In this paper, we develop efficient multiscale methods for flows in heterogeneous media. We use the generalized multiscale finite element (GMsFEM) framework. GMsFEM approximates the solution space locally using a few multiscale basis functions. This approximation selects an appropriate snapshot space and a local spectral decomposition, e.g., the use of oversampled regions, in order to achieve an efficient model reduction. However, the successful construction of snapshot spaces may be costly if too many local problems need to be solved in order to obtain these spaces. We use a moderate quantity of local solutions (or snapshot vectors) with random boundary conditions on oversampled regions with zero forcing to deliver an efficient methodology. Motivated by the randomized algorithm presented in [P. G. Martinsson, V. Rokhlin, and M. Tygert, A Randomized Algorithm for the approximation of Matrices, YALEU/DCS/TR-1361, Yale University, 2006], we consider a snapshot space which consists of harmonic extensions of random boundary conditions defined in a domain larger than the target region. Furthermore, we perform an eigenvalue decomposition in this small space. We study the application of randomized sampling for GMsFEM in conjunction with adaptivity, where local multiscale spaces are adaptively enriched. Convergence analysis is provided. We present representative numerical results to validate the method proposed.
Numerical simulation for cracks detection using the finite elements method
Directory of Open Access Journals (Sweden)
S Bennoud
2016-09-01
Full Text Available The means of detection must ensure controls either during initial construction, or at the time of exploitation of all parts. The Non destructive testing (NDT gathers the most widespread methods for detecting defects of a part or review the integrity of a structure. In the areas of advanced industry (aeronautics, aerospace, nuclear …, assessing the damage of materials is a key point to control durability and reliability of parts and materials in service. In this context, it is necessary to quantify the damage and identify the different mechanisms responsible for the progress of this damage. It is therefore essential to characterize materials and identify the most sensitive indicators attached to damage to prevent their destruction and use them optimally. In this work, simulation by finite elements method is realized with aim to calculate the electromagnetic energy of interaction: probe and piece (with/without defect. From calculated energy, we deduce the real and imaginary components of the impedance which enables to determine the characteristic parameters of a crack in various metallic parts.
Generalized multiscale finite element method for elasticity equations
Chung, Eric T.
2014-10-05
In this paper, we discuss the application of generalized multiscale finite element method (GMsFEM) to elasticity equation in heterogeneous media. We consider steady state elasticity equations though some of our applications are motivated by elastic wave propagation in subsurface where the subsurface properties can be highly heterogeneous and have high contrast. We present the construction of main ingredients for GMsFEM such as the snapshot space and offline spaces. The latter is constructed using local spectral decomposition in the snapshot space. The spectral decomposition is based on the analysis which is provided in the paper. We consider both continuous Galerkin and discontinuous Galerkin coupling of basis functions. Both approaches have their cons and pros. Continuous Galerkin methods allow avoiding penalty parameters though they involve partition of unity functions which can alter the properties of multiscale basis functions. On the other hand, discontinuous Galerkin techniques allow gluing multiscale basis functions without any modifications. Because basis functions are constructed independently from each other, this approach provides an advantage. We discuss the use of oversampling techniques that use snapshots in larger regions to construct the offline space. We provide numerical results to show that one can accurately approximate the solution using reduced number of degrees of freedom.
Matrix element method for high performance computing platforms
Grasseau, G.; Chamont, D.; Beaudette, F.; Bianchini, L.; Davignon, O.; Mastrolorenzo, L.; Ochando, C.; Paganini, P.; Strebler, T.
2015-12-01
Lot of efforts have been devoted by ATLAS and CMS teams to improve the quality of LHC events analysis with the Matrix Element Method (MEM). Up to now, very few implementations try to face up the huge computing resources required by this method. We propose here a highly parallel version, combining MPI and OpenCL, which makes the MEM exploitation reachable for the whole CMS datasets with a moderate cost. In the article, we describe the status of two software projects under development, one focused on physics and one focused on computing. We also showcase their preliminary performance obtained with classical multi-core processors, CUDA accelerators and MIC co-processors. This let us extrapolate that with the help of 6 high-end accelerators, we should be able to reprocess the whole LHC run 1 within 10 days, and that we have a satisfying metric for the upcoming run 2. The future work will consist in finalizing a single merged system including all the physics and all the parallelism infrastructure, thus optimizing implementation for best hardware platforms.
Hybrid BEM/empirical approach for scattering of correlated sources in rocket noise prediction
Barbarino, Mattia; Adamo, Francesco P.; Bianco, Davide; Bartoccini, Daniele
2017-09-01
Empirical models such as the Eldred standard model are commonly used for rocket noise prediction. Such models directly provide a definition of the Sound Pressure Level through the quadratic pressure term by uncorrelated sources. In this paper, an improvement of the Eldred Standard model has been formulated. This new formulation contains an explicit expression for the acoustic pressure of each noise source, in terms of amplitude and phase, in order to investigate the sources correlation effects and to propagate them through a wave equation. In particular, the correlation effects between adjacent and not-adjacent sources have been modeled and analyzed. The noise prediction obtained with the revised Eldred-based model has then been used for formulating an empirical/BEM (Boundary Element Method) hybrid approach that allows an evaluation of the scattering effects. In the framework of the European Space Agency funded program VECEP (VEga Consolidation and Evolution Programme), these models have been applied for the prediction of the aeroacoustics loads of the VEGA (Vettore Europeo di Generazione Avanzata - Advanced Generation European Carrier Rocket) launch vehicle at lift-off and the results have been compared with experimental data.
An improved BEM model for the power curve prediction of stall-regulated wind turbines
Energy Technology Data Exchange (ETDEWEB)
Martinez, J.; Bernabini, L. [Instituto Tecnologico y de Estudios Superiores de Monterrey (Mexico). Physics Dept.; Probst, O. [Instituto Tecnologico y de Estudios Superiores de Monterrey (Mexico). Center for Energy Studies; Rodriguez, C. [Instituto Tecnologico y de Estudios Superiores de Monterrey (Mexico). Center for Integrated Manufacturing Systems
2005-10-15
Blade element momentum (BEM) theory is the standard computational technique for the prediction of power curves of wind turbines; it is based on the two-dimensional aerodynamic properties of aerofoil blade elements and some corrections accounting for three-dimensional wing aerodynamics. Although most BEM models yield acceptable results for low-wind and pitch-controlled regimes where the local angles of attack are small, no generally accepted model exists up to date that consistently predicts the power curve in the stall regime for a variety of blade properties and operating conditions. In this article we present a modified BEM model which satisfactorily reproduces the power curves of four experimental wind turbines reported in the literature, using no free fit parameters. Since these four experimental cases comprehend a great variety of conditions (wind tunnel vs field experiments, different air densities) and blade parameters (no twist and no taper, no taper but twist, both twist and taper, different aerofoil families), it is believed that our model represents a useful working tool for the aerodynamic design of stall-regulated wind turbines. (author)
Perucchio, R.; Ingraffea, A. R.
1984-01-01
The establishment of the boundary element method (BEM) as a valid tool for solving problems in structural mechanics and in other fields of applied physics is discussed. The development of an integrated interactive computer graphic system for the application of the BEM to three dimensional problems in elastostatics is described. The integration of interactive computer graphic techniques and the BEM takes place at the preprocessing and postprocessing stages of the analysis process, when, respectively, the data base is generated and the results are interpreted. The interactive computer graphic modeling techniques used for generating and discretizing the boundary surfaces of a solid domain are outlined.
Hermitian Mindlin Plate Wavelet Finite Element Method for Load Identification
Xiaofeng Xue; Xuefeng Chen; Xingwu Zhang; Baijie Qiao; Jia Geng
2016-01-01
A new Hermitian Mindlin plate wavelet element is proposed. The two-dimensional Hermitian cubic spline interpolation wavelet is substituted into finite element functions to construct frequency response function (FRF). It uses a system’s FRF and response spectrums to calculate load spectrums and then derives loads in the time domain via the inverse fast Fourier transform. By simulating different excitation cases, Hermitian cubic spline wavelets on the interval (HCSWI) finite elements are used t...
Efficiency of High Order Spectral Element Methods on Petascale Architectures
Hutchinson, Maxwell
2016-06-14
High order methods for the solution of PDEs expose a tradeoff between computational cost and accuracy on a per degree of freedom basis. In many cases, the cost increases due to higher arithmetic intensity while affecting data movement minimally. As architectures tend towards wider vector instructions and expect higher arithmetic intensities, the best order for a particular simulation may change. This study highlights preferred orders by identifying the high order efficiency frontier of the spectral element method implemented in Nek5000 and NekBox: the set of orders and meshes that minimize computational cost at fixed accuracy. First, we extract Nek’s order-dependent computational kernels and demonstrate exceptional hardware utilization by hardware-aware implementations. Then, we perform productionscale calculations of the nonlinear single mode Rayleigh-Taylor instability on BlueGene/Q and Cray XC40-based supercomputers to highlight the influence of the architecture. Accuracy is defined with respect to physical observables, and computational costs are measured by the corehour charge of the entire application. The total number of grid points needed to achieve a given accuracy is reduced by increasing the polynomial order. On the XC40 and BlueGene/Q, polynomial orders as high as 31 and 15 come at no marginal cost per timestep, respectively. Taken together, these observations lead to a strong preference for high order discretizations that use fewer degrees of freedom. From a performance point of view, we demonstrate up to 60% full application bandwidth utilization at scale and achieve ≈1PFlop/s of compute performance in Nek’s most flop-intense methods.
The Blended Finite Element Method for Multi-fluid Plasma Modeling
2016-07-01
Briefing Charts 3. DATES COVERED (From - To) 07 June 2016 - 01 July 2016 4. TITLE AND SUBTITLE The Blended Finite Element Method for Multi-fluid Plasma...BLENDED FINITE ELEMENT METHOD FOR MULTI-FLUID PLASMA MODELING Éder M. Sousa1, Uri Shumlak2 1ERC INC., IN-SPACE PROPULSION BRANCH (RQRS) AIR FORCE RESEARCH...MULTI-FLUID PLASMA MODEL 2 BLENDED FINITE ELEMENT METHOD Blended Finite Element Method Nodal Continuous Galerkin Modal Discontinuous Galerkin Model
Analysis of a non-standard mixed finite element method with applications to superconvergence
Brandts, J.H.
2009-01-01
We show that a non-standard mixed finite element method proposed by Barrios and Gatica in 2007, is a higher order perturbation of the least-squares mixed finite element method. Therefore, it is also superconvergent whenever the least-squares mixed finite element method is superconvergent.
Finite element analysis of CFRP reinforced silo structure design method
Yuan, Long; Xu, Xinsheng
2017-11-01
Because of poor construction, there is a serious problem of concrete quality in the silo project, which seriously affects the safe use of the structure. Concrete quality problems are mainly seen in three aspects: concrete strength cannot meet the design requirements, concrete cracking phenomenon is serious, and the unreasonable concrete vibration leads to a lot of honeycombs and surface voids. Silos are usually reinforced by carbon fiber cloth in order to ensure the safe use of silos. By the example of an alumina silo in a fly ash plant in Binzhou, Shandong Province, the alumina silo project was tested and examined on site. According to filed test results, the actual concrete strength was determined, and the damage causes of the silo was analysed. Then, a finite element analysis model of this silo was established, the CFRP cloth reinforcement method was adopted to strengthen the silo, and other technology like additional reinforcement, rebar planting, carbon fiber bonding technology was also expounded. The research of this paper is of great significance to the design and construction of silo structure.
A top quark mass measurement using a matrix element method
Energy Technology Data Exchange (ETDEWEB)
Linacre, Jacob Thomas [St. John' s College, Annapolis, MD (United States)
2009-01-01
A measurement of the mass of the top quark is presented, using top-antitop pair (t$\\bar{t}$) candidate events for the lepton+jets decay channel. The measurement makes use of Tevatron p$\\bar{p}$ collision data at centre-of-mass energy √s = 1.96 TeV, collected at the CDF detector. The top quark mass is measured by employing an unbinned maximum likelihood method where the event probability density functions are calculated using signal (t$\\bar{t}$) and background (W+jets) matrix elements, as well as a set of parameterised jet-to-parton mapping functions. The likelihood function is maximised with respect to the top quark mass, the fraction of signal events, and a correction to the jet energy scale (JES) of the calorimeter jets. The simultaneous measurement of the JES correction (Δ_{JES}) provides an in situ jet energy calibration based on the known mass of the hadronically decaying W boson. Using 578 lepton+jets candidate events corresponding to 3.2 fb ^{-1} of integrated luminosity, the top quark mass is measured to be m_{t} = 172.4± 1.4 (stat+Δ_{JES}) ±1.3 (syst) GeV=c^{2}, one of the most precise single measurements to date.
Finite element analysis of chip formation usingale method
Jayaprakash, V.
2017-05-01
In recent times, many studies made in FEM on plain isotropic metal plate formulation. The stress analysis plays the significant role in the stability of structural safety and system. The stress and distortion estimation is very helpful for designing and manufacturing product well. Usually the residual stress and plastic strain determine the fatigue life of structure, it also plays the significant role in designing and choosing material. When the load magnitude increases the crack starts to form, decreasing the work load and the residual stress reduces the damage of the metal. The manufacturing process is a key parameter in process and forming the part of any system. However, machining operation involves complex thing like hot development, material property and other estimates based on transition of the plastic strain and residual stress. The reduction of residual stress plays the complexity role in the finite element study. This paper deals with the manufacturing process with less residual stress and strain. The results shows that, by applying the ALE method in machining we can reduce the load on the work piece hence the life type of the work piece can be increased. We also investigate the cutting tool wear and there efficiency since it is a essential machine member in fabrication technology. ABAQUS platform used to solve the machining operation
Mechanics of binary crushable granular assembly through discrete element method
Directory of Open Access Journals (Sweden)
Raghuram Karthik Desu
2016-12-01
Full Text Available The mechanical response of a granular system is not only influenced by the bulk material properties but also on various factors due to it’s discrete nature. The factors like topology, packing fraction, friction between particles, particle size distribution etc. influence the behavior of granular systems. For a reliable design of such systems like fusion breeder units comprising of pebble beds, it is essential to understand the various factors influencing the response of the system. Mechanical response of a binary assembly consisting of crushable spherical pebbles is studied using Discrete Element Method (DEM which is based on particle–particle interactions. The influence of above mentioned factors on the macroscopic stress–strain response is investigated using an in-house DEM code. Furthermore, the effect of these factors on the damage in the assembly is investigated. This present investigation helps in understanding the macroscopic response and damage in terms of microscopic factors paving way to develop a unified prediction tool for a binary crushable granular assembly.
Thermal analysis of disc brakes using finite element method
Jaenudin, Jamari, J.; Tauviqirrahman, M.
2017-01-01
Disc brakes are components of a vehicle that serve to slow or stop the rotation of the wheel. This paper discusses the phenomenon of heat distribution on the brake disc during braking. Heat distribution on the brake disc is caused by kinetic energy changing into mechanical energy. Energy changes occur during the braking process due to friction between the surface of the disc and a disc pad. The temperature resulting from this friction rises high. This thermal analysis on brake discs is aimed to evaluate the performance of an electric car in the braking process. The aim of this study is to analyze the thermal behavior of the brake discs using the Finite Element Method (FEM) through examining the heat distribution on the brake disc using 3-D modeling. Results obtained from the FEM reflect the effects of high heat due to the friction between the disc pad with the disc rotor. Results of the simulation study are used to identify the effect of the heat distribution that occurred during the braking process.
A local level set method based on a finite element method for unstructured meshes
Energy Technology Data Exchange (ETDEWEB)
Ngo, Long Cu; Choi, Hyoung Gwon [School of Mechanical Engineering, Seoul National University of Science and Technology, Seoul (Korea, Republic of)
2016-12-15
A local level set method for unstructured meshes has been implemented by using a finite element method. A least-square weighted residual method was employed for implicit discretization to solve the level set advection equation. By contrast, a direct re-initialization method, which is directly applicable to the local level set method for unstructured meshes, was adopted to re-correct the level set function to become a signed distance function after advection. The proposed algorithm was constructed such that the advection and direct reinitialization steps were conducted only for nodes inside the narrow band around the interface. Therefore, in the advection step, the Gauss–Seidel method was used to update the level set function using a node-by-node solution method. Some benchmark problems were solved by using the present local level set method. Numerical results have shown that the proposed algorithm is accurate and efficient in terms of computational time.
Wang, Wansheng; Chen, Long; Zhou, Jie
2015-01-01
A postprocessing technique for mixed finite element methods for the Cahn-Hilliard equation is developed and analyzed. Once the mixed finite element approximations have been computed at a fixed time on the coarser mesh, the approximations are postprocessed by solving two decoupled Poisson equations in an enriched finite element space (either on a finer grid or a higher-order space) for which many fast Poisson solvers can be applied. The nonlinear iteration is only applied to a much smaller size problem and the computational cost using Newton and direct solvers is negligible compared with the cost of the linear problem. The analysis presented here shows that this technique remains the optimal rate of convergence for both the concentration and the chemical potential approximations. The corresponding error estimate obtained in our paper, especially the negative norm error estimates, are non-trivial and different with the existing results in the literatures. PMID:27110063
Energy Technology Data Exchange (ETDEWEB)
Salinas, F S; Lancaster, J L; Fox, P T [Research Imaging Center, University of Texas Health Science Center at San Antonio, San Antonio, TX 78229 (United States)
2009-06-21
Transcranial magnetic stimulation (TMS) delivers highly localized brain stimulations via non-invasive externally applied magnetic fields. This non-invasive, painless technique provides researchers and clinicians with a unique tool capable of stimulating both the central and peripheral nervous systems. However, a complete analysis of the macroscopic electric fields produced by TMS has not yet been performed. In this paper, we addressed the importance of the secondary E-field created by surface charge accumulation during TMS using the boundary element method (BEM). 3D models were developed using simple head geometries in order to test the model and compare it with measured values. The effects of tissue geometry, size and conductivity were also investigated. Finally, a realistically shaped head model was used to assess the effect of multiple surfaces on the total E-field. Secondary E-fields have the greatest impact at areas in close proximity to each tissue layer. Throughout the head, the secondary E-field magnitudes typically range from 20% to 35% of the primary E-field's magnitude. The direction of the secondary E-field was generally in opposition to the primary E-field; however, for some locations, this was not the case (i.e. going from high to low conductivity tissues). These findings show that realistically shaped head geometries are important for accurate modeling of the total E-field.
Salinas, F S; Lancaster, J L; Fox, P T
2009-06-21
Transcranial magnetic stimulation (TMS) delivers highly localized brain stimulations via non-invasive externally applied magnetic fields. This non-invasive, painless technique provides researchers and clinicians with a unique tool capable of stimulating both the central and peripheral nervous systems. However, a complete analysis of the macroscopic electric fields produced by TMS has not yet been performed. In this paper, we addressed the importance of the secondary E-field created by surface charge accumulation during TMS using the boundary element method (BEM). 3D models were developed using simple head geometries in order to test the model and compare it with measured values. The effects of tissue geometry, size and conductivity were also investigated. Finally, a realistically shaped head model was used to assess the effect of multiple surfaces on the total E-field. Secondary E-fields have the greatest impact at areas in close proximity to each tissue layer. Throughout the head, the secondary E-field magnitudes typically range from 20% to 35% of the primary E-field's magnitude. The direction of the secondary E-field was generally in opposition to the primary E-field; however, for some locations, this was not the case (i.e. going from high to low conductivity tissues). These findings show that realistically shaped head geometries are important for accurate modeling of the total E-field.
Residual-driven online generalized multiscale finite element methods
Chung, Eric T.
2015-09-08
The construction of local reduced-order models via multiscale basis functions has been an area of active research. In this paper, we propose online multiscale basis functions which are constructed using the offline space and the current residual. Online multiscale basis functions are constructed adaptively in some selected regions based on our error indicators. We derive an error estimator which shows that one needs to have an offline space with certain properties to guarantee that additional online multiscale basis function will decrease the error. This error decrease is independent of physical parameters, such as the contrast and multiple scales in the problem. The offline spaces are constructed using Generalized Multiscale Finite Element Methods (GMsFEM). We show that if one chooses a sufficient number of offline basis functions, one can guarantee that additional online multiscale basis functions will reduce the error independent of contrast. We note that the construction of online basis functions is motivated by the fact that the offline space construction does not take into account distant effects. Using the residual information, we can incorporate the distant information provided the offline approximation satisfies certain properties. In the paper, theoretical and numerical results are presented. Our numerical results show that if the offline space is sufficiently large (in terms of the dimension) such that the coarse space contains all multiscale spectral basis functions that correspond to small eigenvalues, then the error reduction by adding online multiscale basis function is independent of the contrast. We discuss various ways computing online multiscale basis functions which include a use of small dimensional offline spaces.
Modeling 3D PCMI using the Extended Finite Element Method with higher order elements
Energy Technology Data Exchange (ETDEWEB)
Jiang, W. [Idaho National Lab. (INL), Idaho Falls, ID (United States); Spencer, Benjamin W. [Idaho National Lab. (INL), Idaho Falls, ID (United States)
2017-03-31
This report documents the recent development to enable XFEM to work with higher order elements. It also demonstrates the application of higher order (quadratic) elements to both 2D and 3D models of PCMI problems, where discrete fractures in the fuel are represented using XFEM. The modeling results demonstrate the ability of the higher order XFEM to accurately capture the effects of a crack on the response in the vicinity of the intersecting surfaces of cracked fuel and cladding, as well as represent smooth responses in the regions away from the crack.
Comparison between OpenFOAM CFD & BEM theory for variable speed – variable pitch HAWT
Directory of Open Access Journals (Sweden)
ElQatary Islam
2014-01-01
Full Text Available OpenFoam is used to compare computational fluid dynamics (CFD with blade element momentum theory (BEM for a variable speed - variable pitch HAWT (Horizontal Axis Wind Turbine. The wind turbine is first designed using the BEM to determine the blade chord, twist and operating conditions. The wind turbine blade has an outer diameter of 14 m, uses a NACA 63–415 profile for the entire blade and root to tip twist distribution of 15deg (Figure 3. The RPM varies from 20–75 for freestream velocities varying between 3–10.5 m/s (variable speed and a constant RPM of 78.78 for velocities ranging between 11–25 m/s (variable pitch. OpenFOAM is used to investigate the wind turbine performance at several operating points including cut-in wind speed (3 m/s, rated wind speed (10.5 m/s and in the variable pitch zone. Simulation results show that in the variable-speed operating range, both CFD and BEM compare reasonably well. This agreement can be attributed to the fact that the complex three-dimensional flow around the turbine blades can be split into two radial segments. For radii less than the mid-span, the flow is three-dimensional, whereas for radii greater than the mid-span, the flow is approximately two-dimensional. Since the majority of the power is produced from sections beyond the mid-span, the agreement between CFD and BEM is reasonable. For the variable-pitch operating range the CFD results and BEM deviate considerably. In this case the majority of the power is produced from the inner sections in which the flow is three-dimensional and can no longer be predicted by the BEM. The results show that differences in pitch angles up to 10deg can result to regulate the power for high wind speeds in the variable-pitch operation zone.
A cut finite element method for the Bernoulli free boundary value problem
National Research Council Canada - National Science Library
Burman, Erik; Elfverson, Daniel; Hansbo, Peter; Larson, Mats G; Larsson, Karl
2017-01-01
We develop a cut finite element method for the Bernoulli free boundary problem. The free boundary, represented by an approximate signed distance function on a fixed background mesh, is allowed to intersect elements in an arbitrary fashion...
O direito dos povos: uma proposta de sociedade bem ordenada
Directory of Open Access Journals (Sweden)
Jéssica de Farias Mesquita
2017-02-01
Full Text Available O presente texto tem como objetivo examinar a visão de John Rawls acerca das sociedades bem ordenadas na obra O Direito dos Povos, bem como o significado destas para o desenvolvimento da proposta de sociedade democrática liberal. Rawls, na primeira parte da obra, que trata sobre a teoria ideal, refere-se à ideia geral de contrato social nas Sociedades dos Povos democráticos liberais. O autor prossegue com a mesma ideia, na segunda parte da obra quando trata da teoria não-ideal, referindo-se aos povos decentes. Uma sociedade dos povos decentes, segundo Rawls, é uma sociedade cujas características são aceitáveis como membro de uma Sociedade dos Povos razoável, embora não seja uma sociedade democrática liberal. Ambas as sociedades, seja ela democrática liberal ou decente, fazem parte de uma sociedade bem ordenada por obedecerem aos critérios estabelecidos pela Sociedade dos Povos. Para a garantia de uma sociedade bem ordenada, Rawls expõe uma série de condições para que esse tipo de sociedade seja possível, uma dessas condições é o modo como essas sociedades se encontram reguladas.
E. Yari; H. Ghassemi
2016-01-01
The main objective of this paper is to provide an applied algorithm for analyzing propeller-shaft vibrations in marine vessels. Firstly an underwater marine vehicle has been analyzed at different speed in unsteady condition using the finite volume method. Based on the results of this analysis, flow field of marine vehicle (wake of stern) and velocity inlet to the marine propeller is extracted at different times. Propeller inlet flow field is applied in the boundary element code and usin...
Hong, C. P.; Umeda, T.; Kimura, Y.
1984-01-01
A new numerical model, which is based on the boundary element method, was proposed for the simulation of solidification problems, and its application was demonstrated for solidification of metals in metal and sand molds. Comparisons were made between results from this model and those from the explicit finite difference method. Temperature recovery method was successfully adopted to estimate the liberation of latent heat of freezing in the boundary element method. A coupling method was proposed for problems in which the boundary condition of the interface consisting of inhomogeneous bodies is governed by Newton’s law of cooling in the boundary element method. It was concluded that the boundary element method which has several advantages, such as the wide variety of element shapes, simplicity of data preparation, and small CPU times, will find wide application as an alternative for finite difference or finite element methods, in the fields of solidification problems, especially for complex, three-dimensional geometries.
Wing Rib Stress Analysis and Design Optimization Using Constrained Natural Element Method
Amine Bennaceur, Mohamed; Xu, Yuan-ming; Layachi, Hemza
2017-09-01
This paper demonstrates the applicability of a novel meshless method in solving problems related to aeronautical engineering, the constraint-natural element method is used to optimize a wing rib where it present several shape of cut-outs deals with the results findings we select the optimum design, we focus on the description and analysis of the constraint-natural element method and its application for simulating mechanical problems, the constraint natural element method is the alternative method for the finite element method where the shape functions is constructed on an extension of Voronoi diagram dual of Delaunay tessellation for non-convex domains.
Finite element and finite difference methods in electromagnetic scattering
Morgan, MA
2013-01-01
This second volume in the Progress in Electromagnetic Research series examines recent advances in computational electromagnetics, with emphasis on scattering, as brought about by new formulations and algorithms which use finite element or finite difference techniques. Containing contributions by some of the world's leading experts, the papers thoroughly review and analyze this rapidly evolving area of computational electromagnetics. Covering topics ranging from the new finite-element based formulation for representing time-harmonic vector fields in 3-D inhomogeneous media using two coupled sca
Membrane finite element method for simulating fluid flow in porous medium
Directory of Open Access Journals (Sweden)
Mei-li Zhan
2009-06-01
Full Text Available A new membrane finite element method for modeling fluid flow in a porous medium is presented in order to quickly and accurately simulate the geo-membrane fabric used in civil engineering. It is based on discontinuous finite element theory, and can be easily coupled with the normal Galerkin finite element method. Based on the saturated seepage equation, the element coefficient matrix of the membrane element method is derived, and a geometric transform relation for the membrane element between a global coordinate system and a local coordinate system is obtained. A method for the determination of the fluid flux conductivity of the membrane element is presented. This method provides a basis for determining discontinuous parameters in discontinuous finite element theory. An anti-seepage problem regarding the foundation of a building is analyzed by coupling the membrane finite element method with the normal Galerkin finite element method. The analysis results demonstrate the utility and superiority of the membrane finite element method in fluid flow analysis of a porous medium.
Superconvergence for tetrahedral quadratic finite element methods for elliptic equations
Brandts, J.H.; Krizek, M.
2005-01-01
For a model elliptic boundary value problem we will prove that on strongly regular families of uniform tetrahedral partitions of the domain, the gradient of the quadratic finite element approximation is superclose to the gradient of the quadratic Lagrange interpolant of the exact solution. This
The finite element method in computational fluid mechanics
Baker, A. J.
1977-01-01
A finite element solution algorithm is established for a general statement of the time-averaged Navier-Stokes equations governing multi-dimensional turbulent flows. Numerical results are presented which evaluate factors affecting solution accuracy for a broad spectrum of linear and non-linear problem classes.
A BEM approach to validate a model for predicting sound propagation over non-flat terrain
DEFF Research Database (Denmark)
Quirós Alpera, Susana; Jacobsen, Finn; Juhl, Peter Møller
2003-01-01
A two-dimensional boundary element model for sound propagation in a homogeneous atmosphere above non-flat terrain has been constructed. An infinite impedance plane is taken into account in the Green's function in the underlying integral equation, so that only the nonflat parts of the terrain need....... Sound Vibrat. 223 (1999) 355]. The resulting BEM model, which can handle arbitrary combinations of barriers and hollows, has been used for validating a ray model for various difficult configurations, including combinations of valleys and barriers. (C) 2003 Elsevier Science Ltd. All rights reserved....
A BEM approach to validate a model for predicting sound propagation over non-flat terrain
DEFF Research Database (Denmark)
Quirósy Alpera, S.; Jacobsen, Finn; Juhl, P.M.
2003-01-01
A two-dimensional boundary element model for sound propagation in a homogeneous atmosphere above non-flat terrain has been constructed. An infinite impedance plane is taken into account in the Green's function in the underlying integral equation, so that only the nonflat parts of the terrain need....... Sound Vibrat. 223 (1999) 355]. The resulting BEM model, which can handle arbitrary combinations of barriers and hollows, has been used for validating a ray model for various difficult configurations, including combinations of valleys and barriers....
Structured Extended Finite Element Methods of Solids Defined by Implicit Surfaces
Energy Technology Data Exchange (ETDEWEB)
Belytschko, T; Mish, K; Moes, N; Parimi, C
2002-11-17
A paradigm is developed for generating structured finite element models from solid models by means of implicit surface definitions. The implicit surfaces are defined by radial basis functions. Internal features, such as material interfaces, sliding interfaces and cracks are treated by enrichment techniques developed in the extended finite element method (X-FEM). Methods for integrating the weak form for such models are proposed. These methods simplify the generation of finite element models. Results presented for several examples show that the accuracy of this method is comparable to standard unstructured finite element methods.
Self-supporting method; an alternative method for steel truss bridge element replacement
Arsyad, Muhammad; Sangadji, Senot; As’ad, Sholihin
2017-11-01
Steel truss bridge often requires replacement of its element due to serious damage caused by traffic accidents. This replacement is carried out using temporary supporting structure. It would be difficult when the available space for the temporary structure is quite limited and or the position of work is at a high elevation. The self-supporting method is proposed instead of temporary supporting structure. This paper will discuss an innovative method of bridge rehabilitation by utilizing the existing bridge structure. It requires such temporary connecting structure that installed on the existing bridge element, therefore, the forces during replacement process could be transferred to the bridge foundation directly. By taking the case on a steel truss bridge Jetis Salatiga which requires element replacement due to its damages on two main diagonals, a modeling is carried out to get a proper repair method. Structural analysis is conducted for three temporary connecting structure models: “I,” “V,” and triangular model. Stresses and translations that occur in the structure are used as constraints. Bridge bearings are modeled in two different modes: fixed-fixed system and fixed-free one. Temperature load is given in each condition to obtain the appropriate time for execution. The triangular model is chosen as the best one. In the fixed-fixed mode, this method can be carried out in a temperature range 27-28.8° C, while in fixed-free one, the temperature it is allowed between 27-43.4 °C. The D4 is dismantled first by cutting the D4 leaving an area of 1140.2 mm2 or 127 mm web length to enable plastic condition until the D4 collapses. At the beginning of elongation occurs, immediately performed a slowly jacking on a temporary connecting structure so that the force on D4 is gradually transferred to the temporary connecting structure then the D4 and D5 are set in their place.
Simulation of a soil loosening process by means of the modified distinct element method
Momuzu, M.; Oida, A.; Yamazaki, M.; Koolen, A.J.
2002-01-01
We apply the Distinct Element Method (DEM) to analyze the dynamic behavior of soil. However, the conventional DEM model for calculation of contact forces between elements has some problems; for example, the movement of elements is too discrete to simulate real soil particle movement. Therefore, we
Stability estimates for h-p spectral element methods for general ...
Indian Academy of Sciences (India)
R. Narasimhan (Krishtel eMaging) 1461 1996 Oct 15 13:05:22
be noted that the method is assymptotically faster then the h-p finite element method. For problems with mixed boundary conditions we cannot use this stability theorem to parallelize our method since the factor in the stability estimate can grow as M4. To get around this problem we make the spectral element functions ...
A system and a method comprising an array of bending elements for determining a condition
DEFF Research Database (Denmark)
2014-01-01
A system comprising a sensor element and a sensing system, a method of operating it, a sensor element and a method of providing it, where the sensor element has a substrate from which a plurality of elongate, bendable elements extend. The elongated elements are configured to bend, in the same...... direction, when exposed to a condition, which may be a temperature, a pressure, a pH, a humidity or a presence of a predetermined molecule. The elongated elements may have a first surface and a second surface having different degrees of contraction/extension when exposed to the condition, where the first...... surfaces all point in the same direction. The sensing system may relate on a large number of elongate elements positioned within a given area on the sensor element....
Directory of Open Access Journals (Sweden)
Marek Krynke
2013-02-01
Full Text Available In slewing bearings, a great number of contact pairs are present on the contact surfaces between the rolling elements and raceways of the bearing. Computations to determine the load of the individual rolling elements, taking into account the flexibility of the bearing ring, are most often carried out using the finite element method. Construction of a FEM full model of the bearing, taking into account the shape of the rolling elements and the determination of the contact problem for every rolling element, leads to a singularity of stiffness matrix, which in turn makes the problem impossible to solve. In FEM models the rolling elements are replaced by one-dimensional finite elements (linear elements to simplify the computation procedure and to obtain an optimal time for computations. replaced by truss elements with a material non-linear characteristic located between the raceway centres of the curvatures in their axial section, are presented in the paper
Method for recovering catalytic elements from fuel cell membrane electrode assemblies
Shore, Lawrence [Edison, NJ; Matlin, Ramail [Berkeley Heights, NJ; Heinz, Robert [Ludwigshafen, DE
2012-06-26
A method for recovering catalytic elements from a fuel cell membrane electrode assembly is provided. The method includes converting the membrane electrode assembly into a particulate material, wetting the particulate material, forming a slurry comprising the wetted particulate material and an acid leachate adapted to dissolve at least one of the catalytic elements into a soluble catalytic element salt, separating the slurry into a depleted particulate material and a supernatant containing the catalytic element salt, and washing the depleted particulate material to remove any catalytic element salt retained within pores in the depleted particulate material.
Bem-estar de animais de laboratório
Deguchi, Bernardo Graça Fatori
2013-01-01
Resumo: Com pesquisas e legislação incipientes acerca do bem-estar animal (BEA) em animais de laboratório, a expansão de sua discussão no Brasil tende a promover avanços metodológicos e éticos na sociedade. Para que mudanças sejam realizadas é necessário conhecer e discutir as características atuais relativas às condições de BEA nos laboratórios. O objetivo deste trabalho foi identificar e diagnosticar em diferentes âmbitos fatores que podem definir o grau de bem-estar dos animais de laborató...
1984-07-01
Ackroyd , R. T. "A Finite Element Technique for the Even Parity Neutron Transport Equation," The Mathematics of Finite Elements and...state transport equation. In 1972 a more detailed examination of the use of finite elements to solve neutron diffusion problems was provided by Kaper...79, 269-277 (1981). Ukai, S., "Solution of the Multi-dimensional Neutron Transport Equation by Finite Element Methods,"
On modelling three-dimensional piezoelectric smart structures with boundary spectral element method
Zou, Fangxin; Aliabadi, M. H.
2017-05-01
The computational efficiency of the boundary element method in elastodynamic analysis can be significantly improved by employing high-order spectral elements for boundary discretisation. In this work, for the first time, the so-called boundary spectral element method is utilised to formulate the piezoelectric smart structures that are widely used in structural health monitoring (SHM) applications. The resultant boundary spectral element formulation has been validated by the finite element method (FEM) and physical experiments. The new formulation has demonstrated a lower demand on computational resources and a higher numerical stability than commercial FEM packages. Comparing to the conventional boundary element formulation, a significant reduction in computational expenses has been achieved. In summary, the boundary spectral element formulation presented in this paper provides a highly efficient and stable mathematical tool for the development of SHM applications.
A Bayes factor meta-analysis of Bem's ESP claim.
Rouder, Jeffrey N; Morey, Richard D
2011-08-01
In recent years, statisticians and psychologists have provided the critique that p-values do not capture the evidence afforded by data and are, consequently, ill suited for analysis in scientific endeavors. The issue is particular salient in the assessment of the recent evidence provided for ESP by Bem (2011) in the mainstream Journal of Personality and Social Psychology. Wagenmakers, Wetzels, Borsboom, and van der Maas (Journal of Personality and Social Psychology, 100, 426-432, 2011) have provided an alternative Bayes factor assessment of Bem's data, but their assessment was limited to examining each experiment in isolation. We show here that the variant of the Bayes factor employed by Wagenmakers et al. is inappropriate for making assessments across multiple experiments, and cannot be used to gain an accurate assessment of the total evidence in Bem's data. We develop a meta-analytic Bayes factor that describes how researchers should update their prior beliefs about the odds of hypotheses in light of data across several experiments. We find that the evidence that people can feel the future with neutral and erotic stimuli to be slight, with Bayes factors of 3.23 and 1.57, respectively. There is some evidence, however, for the hypothesis that people can feel the future with emotionally valenced nonerotic stimuli, with a Bayes factor of about 40. Although this value is certainly noteworthy, we believe it is orders of magnitude lower than what is required to overcome appropriate skepticism of ESP.
A Discontinuous Galerkin Finite Element Method for Hamilton-Jacobi Equations
Hu, Changqing; Shu, Chi-Wang
1998-01-01
In this paper, we present a discontinuous Galerkin finite element method for solving the nonlinear Hamilton-Jacobi equations. This method is based on the Runge-Kutta discontinuous Galerkin finite element method for solving conservation laws. The method has the flexibility of treating complicated geometry by using arbitrary triangulation, can achieve high order accuracy with a local, compact stencil, and are suited for efficient parallel implementation. One and two dimensional numerical examples are given to illustrate the capability of the method.
Directory of Open Access Journals (Sweden)
Pengzhan Huang
2011-01-01
Full Text Available Several stabilized finite element methods for the Stokes eigenvalue problem based on the lowest equal-order finite element pair are numerically investigated. They are penalty, regular, multiscale enrichment, and local Gauss integration method. Comparisons between them are carried out, which show that the local Gauss integration method has good stability, efficiency, and accuracy properties, and it is a favorite method among these methods for the Stokes eigenvalue problem.
On Round-off Error for Adaptive Finite Element Methods
Alvarez-Aramberri, J.
2012-06-02
Round-off error analysis has been historically studied by analyzing the condition number of the associated matrix. By controlling the size of the condition number, it is possible to guarantee a prescribed round-off error tolerance. However, the opposite is not true, since it is possible to have a system of linear equations with an arbitrarily large condition number that still delivers a small round-off error. In this paper, we perform a round-off error analysis in context of 1D and 2D hp-adaptive Finite Element simulations for the case of Poisson equation. We conclude that boundary conditions play a fundamental role on the round-off error analysis, specially for the so-called ‘radical meshes’. Moreover, we illustrate the importance of the right-hand side when analyzing the round-off error, which is independent of the condition number of the matrix.
Strong Superconvergence of Finite Element Methods for Linear Parabolic Problems
Directory of Open Access Journals (Sweden)
Kening Wang
2009-01-01
Full Text Available We study the strong superconvergence of a semidiscrete finite element scheme for linear parabolic problems on =Ω×(0,], where Ω is a bounded domain in ℛ(≤4 with piecewise smooth boundary. We establish the global two order superconvergence results for the error between the approximate solution and the Ritz projection of the exact solution of our model problem in 1,(Ω and ( with 2≤<∞ and the almost two order superconvergence in 1,∞(Ω and ∞(. Results of the =∞ case are also included in two space dimensions (=1 or 2. By applying the interpolated postprocessing technique, similar results are also obtained on the error between the interpolation of the approximate solution and the exact solution.
Studying apple bruise using a finite element method analysis
Pascoal-Faria, P.; Alves, N.
2017-07-01
Apple bruise damage from harvesting, handling, transporting and sorting is considered to be the major source of reduced fruit quality, resulting in a loss of profits for the entire fruit industry. Bruising is defined as damage and discoloration of fruit flesh, usually with no breach of the skin. The three factors which can physically cause fruit bruising are vibration, compression load and impact. The last one is the main source of bruise damage. Therefore, prediction of the level of damage, stress distribution and deformation of the fruits under external force has become a very important task. To address these problems a finite element analysis has been developed for studying Portuguese Royal Gala apple bruise. The results obtained will be suitable to apple distributors and sellers and will allow a reduction of the impact caused by bruise damage in apple annual production.
Energy Technology Data Exchange (ETDEWEB)
Feng, Xiaobing [Univ. of Tennessee, Knoxville, TN (United States)
1996-12-31
A non-overlapping domain decomposition iterative method is proposed and analyzed for mixed finite element methods for a sequence of noncoercive elliptic systems with radiation boundary conditions. These differential systems describe the motion of a nearly elastic solid in the frequency domain. The convergence of the iterative procedure is demonstrated and the rate of convergence is derived for the case when the domain is decomposed into subdomains in which each subdomain consists of an individual element associated with the mixed finite elements. The hybridization of mixed finite element methods plays a important role in the construction of the discrete procedure.
Directory of Open Access Journals (Sweden)
Jeong-Hoon Song
2013-01-01
Full Text Available A simplified implementation of the conventional extended finite element method (XFEM for dynamic fracture in thin shells is presented. Though this implementation uses the same linear combination of the conventional XFEM, it allows for considerable simplifications of the discontinuous displacement and velocity fields in shell finite elements. The proposed method is implemented for the discrete Kirchhoff triangular (DKT shell element, which is one of the most popular shell elements in engineering analysis. Numerical examples for dynamic failure of shells under impulsive loads including implosion and explosion are presented to demonstrate the effectiveness and robustness of the method.
Vibration Analysis of Collecting Electrodes by means of the Hybrid Finite Element Method
Directory of Open Access Journals (Sweden)
I. Adamiec-Wójcik
2014-01-01
Full Text Available The paper presents a hybrid finite element method of shell modeling in order to model collecting electrodes of electrostatic precipitators. The method uses the finite element method to reflect elastic features and the rigid finite element method in order to model mass features of the body. A model of dust removal systems of an electrostatic precipitator is presented. The system consists of two beams which are modeled by means of the rigid finite element method and a system of collecting shells modeled by means of the hybrid finite element method. The paper discusses both the procedure of deriving the equations of motion and the results of numerical simulations carried out in order to analyze vibrations of the whole system. Experimental verification of the model is also presented.
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 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....
Gallello, Gianni; Ramacciotti, Mirco; Lezzerini, Marco; Hernandez, Emilia; Calvo, Matias; Morales, Angel; Pastor, Agustin; de la Guardia, Miguel
2017-01-01
A novel indirect chronology method has been developed to identify Sagunto Castle construction periods. The method is based on the use of inductively coupled plasma mass spectrometry (ICP-MS) to determine rare earth elements (REE) and other trace elements in mortars. Additionally, a no destructive geochemical analysis based on X-ray fluorescence (XRF) was employed for major elements determination. Collected chemical data were processed through Principal Component Analysis (PCA) to highlight an...
Vibration analysis of composite pipes using the finite element method with B-spline wavelets
Energy Technology Data Exchange (ETDEWEB)
Oke, Wasiu A.; Khulief, Yehia A. [King Fahd University of Petroleum and Minerals, Dhahran (Saudi Arabia)
2016-02-15
A finite element formulation using the B-spline wavelets on the interval is developed for modeling the free vibrations of composite pipes. The composite FRP pipe element is treated as a beam element. The finite pipe element is constructed in the wavelet space and then transformed to the physical space. Detailed expressions of the mass and stiffness matrices are derived for the composite pipe using the Bspline scaling and wavelet functions. Both Euler-Bernoulli and Timoshenko beam theories are considered. The generalized eigenvalue problem is formulated and solved to obtain the modal characteristics of the composite pipe. The developed wavelet-based finite element discretization scheme utilizes significantly less elements compared to the conventional finite element method for modeling composite pipes. Numerical solutions are obtained to demonstrate the accuracy of the developed element, which is verified by comparisons with some available results in the literature.
Free vibration analysis by BEM using particular integrals
Ahmad, S.; Banerjee, P. K.
1986-01-01
A new method for the free-vibration analysis using the boundary element technique is presented. The method utilizes a fictitious vector function to approximate the inertia forces and then uses the well-known concept of complementary functions and particular integrals to solve the resulting governing differential equations. The necessary particular integrals are defined for the two and three-dimensional analyses, and the present formulation is applied to a number of two-dimensional problems to show its accuracy and efficiency in the solution of realistic engineering problems.
A novel hybrid stress-function finite element method immune to severe mesh distortion
Cen, Song; Fu, Xiang-Rong; Zhou, Ming-Jue
2010-06-01
This paper introduces a hybrid stress-function finite element method proposed recently for developing 2D finite element models immune to element shapes. Deferent from the first version of the hybrid-stress element constructed by Pian, the stress function phi of 2D elastic or fracture problem is regarded as the functional variable of the complementary energy functional. Then, the basic analytical solutions of phi are taken as the trial functions for finite element models, and meanwhile, the corresponding unknown stress-function constants are introduced. By using the principle of minimum complementary energy, these unknown stress-function constants can be expressed in terms of the displacements along element edges. Finally, the complementary energy functional can be rewritten in terms of element nodal displacement vector, and thus, the element stiffness matrix of such hybrid-function element can be obtained. As examples, two (8- and 12-node) quadrilateral plane elements and an arbitrary polygonal crack element are constructed by employing different basic analytical solutions of different stress functions. Numerical results show that, the 8- and 12-node plane models can produce the exact solutions for pure bending and linear bending problems, respectively, even the element shape degenerates into triangle and concave quadrangle; and the crack element can also predict accurate results with very low computational cost in analysis of stress-singularity problems.
Application of the Tangent-Stiffness Method in the Finite Element ...
African Journals Online (AJOL)
To simulate the behaviour of an interface formed between two contacting bodies using the finite element method, a review of previous approaches employed by other authors who worked with the same finite element method is carried out; their models and experimental data evaluated. A third-degree polynomial ...
Improved blade element momentum theory for wind turbine aerodynamic computations
DEFF Research Database (Denmark)
Sun, Zhenye; Chen, Jin; Shen, Wen Zhong
2016-01-01
Blade element momentum (BEM) theory is widely used in aerodynamic performance predictions and design applications for wind turbines. However, the classic BEM method is not quite accurate which often tends to under-predict the aerodynamic forces near root and over-predict its performance near tip....... The reliability of the aerodynamic calculations and design optimizations is greatly reduced due to this problem. To improve the momentum theory, in this paper the influence of pressure drop due to wake rotation and the effect of radial velocity at the rotor disc in the momentum theory are considered. Thus...
Improved fixed point iterative method for blade element momentum computations
DEFF Research Database (Denmark)
Sun, Zhenye; Shen, Wen Zhong; Chen, Jin
2017-01-01
, the convergence ability of the iterative method will be greatly enhanced. Numerical tests have been performed under different combinations of local tip speed ratio, local solidity, local twist and airfoil aerodynamic data. Results show that the simple iterative methods have a good convergence ability which...... to the physical solution, especially for the locations near the blade tip and root where the failure rate of the iterative method is high. The stability and accuracy of aerodynamic calculations and optimizations are greatly reduced due to this problem. The intrinsic mechanisms leading to convergence problems...
Energy Technology Data Exchange (ETDEWEB)
Peterson, Kara J. [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States); Bochev, Pavel Blagoveston [Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)
2011-08-01
In [3] we proposed a new Control Volume Finite Element Method with multi-dimensional, edge- based Scharfetter-Gummel upwinding (CVFEM-MDEU). This report follows up with a detailed computational study of the method. The study compares the CVFEM-MDEU method with other CVFEM and FEM formulations for a set of standard scalar advection-diffusion test problems in two dimensions. The first two CVFEM formulations are derived from the CVFEM-MDEU by simplifying the computation of the flux integrals on the sides of the control volumes, the third is the nodal CVFEM [2] without upwinding, and the fourth is the streamline upwind version of CVFEM [10]. The finite elements in our study are the standard Galerkin, SUPG and artificial diffusion methods. All studies employ logically Cartesian partitions of the unit square into quadrilateral elements. Both uniform and non-uniform grids are considered. Our results demonstrate that CVFEM-MDEU and its simplified versions perform equally well on rectangular or nearly rectangular grids. However, performance of the simplified versions significantly degrades on non-affine grids, whereas the CVFEM-MDEU remains stable and accurate over a wide range of mesh Peclet numbers and non-affine grids. Compared to FEM formulations the CVFEM-MDEU appears to be slightly more dissipative than the SUPG, but has much less local overshoots and undershoots.
Apparatus comprising trace element dosage and method for treating raw water in biofilter
DEFF Research Database (Denmark)
2015-01-01
elements such as certain metals (Cu, Co, Cr, Mo, Ni, W, Zn or a mixture thereof). The apparatus comprising - a volume provided with an inlet (2) for raw water and an outlet (3) for water having been subjected to microbial activity, a filter and a trace element dosage device (13) are placed in this volume...... the inlet (2) to the outlet (3) or in the reverse direction, - the trace element dosage device (13) is positioned upstream of the porous filter material and microbial biomass and is configured to dose trace element(s) to the water flowing through the filter. A method for treating raw water by microbial...
Bluff Body Flow Simulation Using a Vortex Element Method
Energy Technology Data Exchange (ETDEWEB)
Anthony Leonard; Phillippe Chatelain; Michael Rebel
2004-09-30
Heavy ground vehicles, especially those involved in long-haul freight transportation, consume a significant part of our nation's energy supply. it is therefore of utmost importance to improve their efficiency, both to reduce emissions and to decrease reliance on imported oil. At highway speeds, more than half of the power consumed by a typical semi truck goes into overcoming aerodynamic drag, a fraction which increases with speed and crosswind. Thanks to better tools and increased awareness, recent years have seen substantial aerodynamic improvements by the truck industry, such as tractor/trailer height matching, radiator area reduction, and swept fairings. However, there remains substantial room for improvement as understanding of turbulent fluid dynamics grows. The group's research effort focused on vortex particle methods, a novel approach for computational fluid dynamics (CFD). Where common CFD methods solve or model the Navier-Stokes equations on a grid which stretches from the truck surface outward, vortex particle methods solve the vorticity equation on a Lagrangian basis of smooth particles and do not require a grid. They worked to advance the state of the art in vortex particle methods, improving their ability to handle the complicated, high Reynolds number flow around heavy vehicles. Specific challenges that they have addressed include finding strategies to accurate capture vorticity generation and resultant forces at the truck wall, handling the aerodynamics of spinning bodies such as tires, application of the method to the GTS model, computation time reduction through improved integration methods, a closest point transform for particle method in complex geometrics, and work on large eddy simulation (LES) turbulence modeling.
Mahya, M. J.; Sanny, T. A.
2017-04-01
Lembang and Cimandiri fault are active faults in West Java that thread people near the faults with earthquake and surface deformation risk. To determine the deformation, GPS measurements around Lembang and Cimandiri fault was conducted then the data was processed to get the horizontal velocity at each GPS stations by Graduate Research of Earthquake and Active Tectonics (GREAT) Department of Geodesy and Geomatics Engineering Study Program, ITB. The purpose of this study is to model the displacement distribution as deformation parameter in the area along Lembang and Cimandiri fault using 2-dimensional boundary element method (BEM) using the horizontal velocity that has been corrected by the effect of Sunda plate horizontal movement as the input. The assumptions that used at the modeling stage are the deformation occurs in homogeneous and isotropic medium, and the stresses that acted on faults are in elastostatic condition. The results of modeling show that Lembang fault had left-lateral slip component and divided into two segments. A lineament oriented in southwest-northeast direction is observed near Tangkuban Perahu Mountain separating the eastern and the western segments of Lembang fault. The displacement pattern of Cimandiri fault shows that Cimandiri fault is divided into the eastern segment with right-lateral slip component and the western segment with left-lateral slip component separated by a northwest-southeast oriented lineament at the western part of Gede Pangrango Mountain. The displacement value between Lembang and Cimandiri fault is nearly zero indicating that Lembang and Cimandiri fault are not connected each other and this area is relatively safe for infrastructure development.
Finite Element Analysis of Nondestructive Testing by Leakage Flux Method Using Remanent Magnetism
坪井, 始; 瀬島, 紀夫; 田中, 始男; ツボイ, ハジメ; セシマ, ノリオ; タナカ, モトオ; Hajime, TSUBOI; Norio, SESHIMA; Motoo, TANAKA
2003-01-01
Magnetic field analysis of nondestructive testing using remanent magnetism was performed by using two-dimensional finite element method. A leakage flux method using remanent magnetism is applied to magnetic material as nondestructive testing method. The remanent magnetism is approximated by equivalent magnetizing electric current. And we assumed that the remanent magnetization is in proportion to the magnetization in the magnetizing process. Formulation of the finite element method using magn...
Relić, Dubravka; Héberger, Károly; Sakan, Sanja; Škrbić, Biljana; Popović, Aleksandar; Đorđević, Dragana
2018-01-03
This study aims to compare three extraction techniques of four sequential element extraction steps from soil and sediment samples that were taken from the location of the Pančevo petrochemical industry (Serbia). Elements were extracted using three different techniques: conventional, microwave and ultrasound extraction. A novel procedure - sum of the ranking differences (SRD) - was able to rank the techniques and elements, to see whether this method is a suitable tool to reveal the similarities and dissimilarities in element extraction techniques, provided that a proper ranking reference is available. The concentrations of the following elements Al, Ba, Ca, Cd, Co, Cr, Cu, Fe, K, Mg, Mn, Na, Ni, Pb, Si, Sn, Sr, V and Zn were determined through ICP OES. The different efficiencies and recovery values of element concentrations using each of the three extraction techniques were examined by the CRM BCR-701. By using SRD, we obtained a better separation between the different extraction techniques and steps when we rank their differences among the samples while lower separation was obtained according to analysed elements. Appling this method for ordering the elements could be useful for three purposes: (i) to find possible associations among the elements; (ii) to find possible elements that have outlier concentrations or (iii) detect differences in geochemical origin or behaviour of elements. Cross-validation of the SRD values in combination with cluster and principal component analysis revealed the same groups of extraction steps and techniques. Copyright © 2018 Elsevier Ltd. All rights reserved.
Vibration analysis of structural elements using differential quadrature method
Directory of Open Access Journals (Sweden)
Mohamed Nassar
2013-01-01
Full Text Available The method of differential quadrature is employed to analyze the free vibration of a cracked cantilever beam resting on elastic foundation. The beam is made of a functionally graded material and rests on a Winkler–Pasternak foundation. The crack action is simulated by a line spring model. Also, the differential quadrature method with a geometric mapping are applied to study the free vibration of irregular plates. The obtained results agreed with the previous studies in the literature. Further, a parametric study is introduced to investigate the effects of geometric and elastic characteristics of the problem on the natural frequencies.
An adaptive finite element method for high speed flows
Peraire, J.; Morgan, K.; Peiro, J.; Zienkiewicz, O. C.
1987-01-01
The solution of the equations of compressible high speed flow, on unstructured triangular grids in 2D and tetrahedral grids in 3D, is considered. Solution methods based upon both Taylor-Galerkin and Runge-Kutta time-stepping techniques are presented and the incorporation of the ideas of flux corrected transport (FCT) is discussed. These methods are combined with an adaptive mesh regeneration procedure and are employed in the solution of several examples, consisting of Euler flows in both 2D and 3D and Navier-Stokes flows in 2D.
General advancing front packing algorithm for the discrete element method
Morfa, Carlos A. Recarey; Pérez Morales, Irvin Pablo; de Farias, Márcio Muniz; de Navarra, Eugenio Oñate Ibañez; Valera, Roberto Roselló; Casañas, Harold Díaz-Guzmán
2018-01-01
A generic formulation of a new method for packing particles is presented. It is based on a constructive advancing front method, and uses Monte Carlo techniques for the generation of particle dimensions. The method can be used to obtain virtual dense packings of particles with several geometrical shapes. It employs continuous, discrete, and empirical statistical distributions in order to generate the dimensions of particles. The packing algorithm is very flexible and allows alternatives for: 1—the direction of the advancing front (inwards or outwards), 2—the selection of the local advancing front, 3—the method for placing a mobile particle in contact with others, and 4—the overlap checks. The algorithm also allows obtaining highly porous media when it is slightly modified. The use of the algorithm to generate real particle packings from grain size distribution curves, in order to carry out engineering applications, is illustrated. Finally, basic applications of the algorithm, which prove its effectiveness in the generation of a large number of particles, are carried out.
Adaptive Vector Finite Element Methods for the Maxwell Equations
Harutyunyan, D.
2007-01-01
The increasing demand to understand the behaviour of electromagnetic waves in many real life problems requires solution of the Maxwell equations. In most cases the exact solution of the Maxwell equations is not available, hence numerical methods are indispensable tool to solve them numerically using
THERM3D -- A boundary element computer program for transient heat conduction problems
Energy Technology Data Exchange (ETDEWEB)
Ingber, M.S. [New Mexico Univ., Albuquerque, NM (United States). Dept. of Mechanical Engineering
1994-02-01
The computer code THERM3D implements the direct boundary element method (BEM) to solve transient heat conduction problems in arbitrary three-dimensional domains. This particular implementation of the BEM avoids performing time-consuming domain integrations by approximating a ``generalized forcing function`` in the interior of the domain with the use of radial basis functions. An approximate particular solution is then constructed, and the original problem is transformed into a sequence of Laplace problems. The code is capable of handling a large variety of boundary conditions including isothermal, specified flux, convection, radiation, and combined convection and radiation conditions. The computer code is benchmarked by comparisons with analytic and finite element results.
Energy flow in plate assembles by hierarchical version of finite element method
DEFF Research Database (Denmark)
Wachulec, Marcin; Kirkegaard, Poul Henning
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...... 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......-corner of two rectangular plates an a I-shaped plate girder made of five plates. Energy distribution among plates due to harmonic load is studied and the comparison of performance between the hierarchical and standard finite element formulation is presented....
The simulation of Lamb waves in a cracked plate using the scaled boundary finite element method.
Gravenkamp, Hauke; Prager, Jens; Saputra, Albert A; Song, Chongmin
2012-09-01
The scaled boundary finite element method is applied to the simulation of Lamb waves for ultrasonic testing applications. With this method, the general elastodynamic problem is solved, while only the boundary of the domain under consideration has to be discretized. The reflection of the fundamental Lamb wave modes from cracks of different geometry in a steel plate is modeled. A test problem is compared with commercial finite element software, showing the efficiency and convergence of the scaled boundary finite element method. A special formulation of this method is utilized to calculate dispersion relations for plate structures. For the discretization of the boundary, higher-order elements are employed to improve the efficiency of the simulations. The simplicity of mesh generation of a cracked plate for a scaled boundary finite element analysis is illustrated.
Energy Technology Data Exchange (ETDEWEB)
Carpenter, D.C.
1998-01-01
This bibliography provides a list of references on finite element and related methods analysis in reactor physics computations. These references have been published in scientific journals, conference proceedings, technical reports, thesis/dissertations and as chapters in reference books from 1971 to the present. Both English and non-English references are included. All references contained in the bibliography are sorted alphabetically by the first author`s name and a subsort by date of publication. The majority of the references relate to reactor physics analysis using the finite element method. Related topics include the boundary element method, the boundary integral method, and the global element method. All aspects of reactor physics computations relating to these methods are included: diffusion theory, deterministic radiation and neutron transport theory, kinetics, fusion research, particle tracking in finite element grids, and applications. For user convenience, many of the listed references have been categorized. The list of references is not all inclusive. In general, nodal methods were purposely excluded, although a few references do demonstrate characteristics of finite element methodology using nodal methods (usually as a non-conforming element basis). This area could be expanded. The author is aware of several other references (conferences, thesis/dissertations, etc.) that were not able to be independently tracked using available resources and thus were not included in this listing.
Rapid method to estimate temperature changes in electronics elements
Directory of Open Access Journals (Sweden)
Oborskii G. A., Savel’eva O. S., Shikhireva Yu. V.
2014-06-01
Full Text Available Thermal behavior of electronic equipment is the determining factor for performing rapid assessment of the effectiveness of design and operation of the equipment. The assessment method proposed in this article consists in fixation of an infrared video stream from the surface of the device and converting it into a visible flow by means of a thermal imager, splitting it into component colors and their further processing using parabolic transformation. The result of the transformation is the number used as a rapid criterion for estimation of distribution stability of heat in the equipment.
Computational Aspects of the h, p and h-p Versions of the Finite Element Method.
1987-03-01
Analisi Numerics del CNR, 27100 Pavia, Italy 1. Introduction very complex, hence we will consider only some aspects of finite element method for linear...analysis pf plates in bending, in Proceeding of the Conference tional comparisons of the finite element methods, on Matrix Methods in Structural Mechanics...426) 1962 6- We did not address here the question of the rela- [16] Morley, L.S.D.: Skew plates and structures , Pergamon tion of the quality results
The Lower Bounds for Eigenvalues of Elliptic Operators --By Nonconforming Finite Element Methods
Hu, Jun; Huang, Yunqing; Lin, Qun
2011-01-01
The aim of the paper is to introduce a new systematic method that can produce lower bounds for eigenvalues. The main idea is to use nonconforming finite element methods. The general conclusion herein is that if local approximation properties of nonconforming finite element spaces $V_h$ are better than global continuity properties of $V_h$, corresponding methods will produce lower bounds for eigenvalues. More precisely, under three conditions on continuity and approximation properties of nonco...
Previdência social e bem estar no Brasil
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Ellery Junior Roberto de Goes
2003-01-01
Full Text Available Este artigo busca avaliar os impactos do Regime Geral de Previdência Social (RGPS sobre o bem-estar da sociedade. A análise será feita por meio da simulação numérica de um modelo de gerações superpostas, calibrado para reproduzir fatos da economia brasileira, contemplando o fato de que o período de vida dos agentes é incerto e incorporando tanto a hipótese de restrição ao crédito quanto a existência de incerteza sobre a renda dos indivíduos. Dentre as conclusões obtidas destaca-se a de que um sistema de previdência do tipo repartição pode apresentar ganhos de bem-estar em relação a um sistema onde a previdência seja financiada pela poupança dos indivíduos. Porém, este resultado depende do valor atribuído para o fator de desconto intertemporal.
Envolvimento religioso e bem-estar subjetivo em idosos
Directory of Open Access Journals (Sweden)
Myrian Cristina da Silva Cardoso
Full Text Available As inter-relações do envolvimento religioso com o bem-estar subjetivo em idosos foram investigadas neste trabalho. Participaram da pesquisa 256 indivíduos de ambos os sexos, com idades variando de 60 a 90 anos, que responderam a três instrumentos destinados a mensurar sua satisfação com a vida, seus afetos positivos e negativos e seu envolvimento religioso bem como a perguntas de natureza sociodemográfica. Os resultados evidenciaram que, dentre as dimensões do envolvimento religioso, apenas a religiosidade subjetiva se correlacionou positiva e significativamente com a satisfação com a vida, que não foram observadas correlações entre o envolvimento religioso e os afetos positivos e negativos, e que os idosos protestantes apresentaram níveis mais elevados de afetos positivos que os católicos. Tais resultados são discutidos à luz dos estudos empíricos e dos modelos conceituais que deram suporte à pesquisa.
van der Stelt, A.A.; Bor, Teunis Cornelis; Geijselaers, Hubertus J.M.; Quak, W.; Akkerman, Remko; Huetink, Han; Menary, G
2011-01-01
In this paper, the material flow around the pin during friction stir welding (FSW) is simulated using a 2D plane strain model. A pin rotates without translation in a disc with elasto-viscoplastic material properties and the outer boundary of the disc is clamped. Two numerical methods are used to
Application of the control volume mixed finite element method to a triangular discretization
Naff, R.L.
2012-01-01
A two-dimensional control volume mixed finite element method is applied to the elliptic equation. Discretization of the computational domain is based in triangular elements. Shape functions and test functions are formulated on the basis of an equilateral reference triangle with unit edges. A pressure support based on the linear interpolation of elemental edge pressures is used in this formulation. Comparisons are made between results from the standard mixed finite element method and this control volume mixed finite element method. Published 2011. This article is a US Government work and is in the public domain in the USA. ?? 2012 John Wiley & Sons, Ltd. This article is a US Government work and is in the public domain in the USA.
Zhang, Xiaotian; Liu, Tao; Qiu, Xinming
2017-11-01
This paper reports a finite element modeling approach to simulate the hypervelocity impact (HVI) response of composite laminate. Node-separation finite element (NSFE) method based on scalar-element-fracture technique for isotropic material in HVI simulation has been presented in the previous study. To extend NSFE to composite materials, an orthotropic node-separation finite element (ONSFE) method is developed. This approach employs an orthotropic continuum material model and a corresponding orthotropic-element-fracture technique to represent the HVI behavior/damage of composite laminate. A series of HVI simulations are conducted and the developed ONSFE method is validated by comparing with the experimental data. The simulation results show that ONSFE can successfully capture the HVI phenomena of composite laminate, such as the orthotropic property, nonlinear shock response, perforation, fiber breakage and delamination. Finally, a HVI event of Whipple shield is simulated and the computational capability of ONSFE for predicting the damage state of the composite bumper is further evaluated.
Steady-state solution of the PTC thermistor problem using a quadratic spline finite element method
Directory of Open Access Journals (Sweden)
Bahadir A. R.
2002-01-01
Full Text Available The problem of heat transfer in a Positive Temperature Coefficient (PTC thermistor, which may form one element of an electric circuit, is solved numerically by a finite element method. The approach used is based on Galerkin finite element using quadratic splines as shape functions. The resulting system of ordinary differential equations is solved by the finite difference method. Comparison is made with numerical and analytical solutions and the accuracy of the computed solutions indicates that the method is well suited for the solution of the PTC thermistor problem.
Introduction to the Explicit Finite Element Method for Nonlinear Transient Dynamics
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
Chen, Jiefu; Zeng, Shubin; Dong, Qiuzhao; Huang, Yueqin
2017-02-01
An axisymmetric semianalytical finite element method is proposed and employed for rapid simulations of electromagnetic telemetry in layered underground formation. In this method, the layered media is decomposed into several subdomains and the interfaces between subdomains are discretized by conventional finite elements. Then a Riccati equation based high precision integration scheme is applied to exploit the homogeneity along the vertical direction in each layer. This semianalytical finite element scheme is very efficient in modeling electromagnetic telemetry in layered formation. Numerical examples as well as a field case with water based mud as drilling fluid are given to demonstrate the validity and effectiveness of this method.
A Generalized Finite Element Method for polycrystals with discontinuous grain boundaries
Simone, A.; Duarte, C. A.; Van der Giessen, E.
2006-01-01
We present a Generalized Finite Element Method for the analysis of polycrystals with explicit treatment of grain boundaries. Grain boundaries and junctions, understood as loci of possible displacement discontinuity, are inserted into finite elements by exploiting the partition of unity property of
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.
A parallel implementation of an EBE solver for the finite element method
Energy Technology Data Exchange (ETDEWEB)
Silva, R.P.; Las Casas, E.B.; Carvalho, M.L.B. [Federal Univ. of Minas Gerais, Belo Horizonte (Brazil)
1994-12-31
A parallel implementation using PVM on a cluster of workstations of an Element By Element (EBE) solver using the Preconditioned Conjugate Gradient (PCG) method is described, along with an application in the solution of the linear systems generated from finite element analysis of a problem in three dimensional linear elasticity. The PVM (Parallel Virtual Machine) system, developed at the Oak Ridge Laboratory, allows the construction of a parallel MIMD machine by connecting heterogeneous computers linked through a network. In this implementation, version 3.1 of PVM is used, and 11 SLC Sun workstations and a Sun SPARC-2 model are connected through Ethernet. The finite element program is based on SDP, System for Finite Element Based Software Development, developed at the Brazilian National Laboratory for Scientific Computation (LNCC). SDP provides the basic routines for a finite element application program, as well as a standard for programming and documentation, intended to allow exchanges between research groups in different centers.
High-precision solution to the moving load problem using an improved spectral element method
Wen, Shu-Rui; Wu, Zhi-Jing; Lu, Nian-Li
2017-06-01
In this paper, the spectral element method (SEM) is improved to solve the moving load problem. In this method, a structure with uniform geometry and material properties is considered as a spectral element, which means that the element number and the degree of freedom can be reduced significantly. Based on the variational method and the Laplace transform theory, the spectral stiffness matrix and the equivalent nodal force of the beam-column element are established. The static Green function is employed to deduce the improved function. The proposed method is applied to two typical engineering practices—the one-span bridge and the horizontal jib of the tower crane. The results have revealed the following. First, the new method can yield extremely high-precision results of the dynamic deflection, the bending moment and the shear force in the moving load problem. In most cases, the relative errors are smaller than 1%. Second, by comparing with the finite element method, one can obtain the highly accurate results using the improved SEM with smaller element numbers. Moreover, the method can be widely used for statically determinate as well as statically indeterminate structures. Third, the dynamic deflection of the twin-lift jib decreases with the increase in the moving load speed, whereas the curvature of the deflection increases. Finally, the dynamic deflection, the bending moment and the shear force of the jib will all increase as the magnitude of the moving load increases.
A multilevel correction adaptive finite element method for Kohn-Sham equation
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.
The Innovative Bike Conceptual Design by Using Modified Functional Element Design Method
Directory of Open Access Journals (Sweden)
Nien-Te Liu
2016-11-01
Full Text Available The purpose of the study is to propose a new design process by modifying functional element design approach which can commence a large amount of innovative concepts within a short period of time. Firstly, the original creative functional elements design method is analyzed and the drawbacks are discussed. Then, the modified is proposed and is divided into 6 steps. The creative functional element representations, generalization, specialization, and particularization are used in this method. Every step is described clearly, and users could design by following the process easily. In this paper, a clear and accurate design process is proposed based on the creative functional element design method. By following this method, a lot of innovative bicycles will be created quickly.
A stabilised nodal spectral element method for fully nonlinear water waves
DEFF Research Database (Denmark)
Engsig-Karup, Allan Peter; Eskilsson, C.; Bigoni, Daniele
2016-01-01
the numerical implementation differs greatly. Features of the proposed spectral element method include: nodal Lagrange basis functions, a general quadrature-free approach and gradient recovery using global L2 projections. The quartic nonlinear terms present in the Zakharov form of the free surface conditions......We present an arbitrary-order spectral element method for general-purpose simulation of non-overturning water waves, described by fully nonlinear potential theory. The method can be viewed as a high-order extension of the classical finite element method proposed by Cai et al. (1998) [5], although...... can cause severe aliasing problems and consequently numerical instability for marginally resolved or very steep waves. We show how the scheme can be stabilised through a combination of over-integration of the Galerkin projections and a mild spectral filtering on a per element basis. This effectively...
Directory of Open Access Journals (Sweden)
V. E. Strizhius
2015-01-01
Full Text Available Methods of the approximate estimations of fatigue durability of composite airframe component typical elements which can be recommended for application at the stage of outline designing of the airplane are generated and presented.
A finite element method for netting application to fish cages and fishing gear
Priour, Daniel
2014-01-01
This book describes a finite element method for netting that describes the relation between forces and deformation of the netting and takes into account forces due to the twine elasticity, the hydrodynamic forces, the catch effect, the mesh opening stiffness.
h-p adaptive finite element methods in computational fluid dynamics
Oden, J. T.; Demkowicz, L.
1991-01-01
The principal ideas of h-p adaptive finite element methods for fluid dynamics problems are discussed. Applications include acoustics, compressible Euler and both compressible and incompressible Navier-Stokes equations. Several numerical examples illustrate the presented concepts.
Abedi, Reza; Mudaliar, Saba
2017-12-01
We present an asynchronous spacetime discontinuous Galerkin (aSDG) method for time domain electromagnetics in which space and time are directly discretized. By using differential forms we express Maxwell's equations and consequently their discontinuous Galerkin discretization for arbitrary domains in spacetime. The elements are discretized with electric and magnetic basis functions that are discontinuous across all inter-element boundaries and can have arbitrary high and per element spacetime orders. When restricted to unstructured grids that satisfy a specific causality constraint, the method has a local and asynchronous solution procedure with linear solution complexity in terms of the number of elements. We numerically investigate the convergence properties of the method for 1D to 3D uniform grids for energy dissipation, an error relative to the exact solution, and von Neumann dissipation and dispersion errors. Two dimensional simulations demonstrate the effectiveness of the method in resolving sharp wave fronts.
The Spectral/hp-Finite Element Method for Partial Differential Equations
DEFF Research Database (Denmark)
Engsig-Karup, Allan Peter
2009-01-01
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...... independently. The original set of course notes has been modified and updated and additional chapters describing the high-order extensions to form the Spectral/$hp$-Finite Element Method have been included. Thus the significant contributions of Chapters 1, 2 and 5 covering the classical Finite Element Method...... are in large parts due to V. A. Barker and J. Reffstrup. With this set of lecture notes it should be possible for the reader to make a Spectral/$hp$-FEM toolbox in successive steps with the support given in the text. Emphasis is on the practical details supported with basic and sufficient theory to build...
A Stabilised Nodal Spectral Element Method for Fully Nonlinear Water Waves
Engsig-Karup, Allan Peter; Bigoni, Daniele
2015-01-01
We present an arbitrary-order spectral element method for general-purpose simulation of non-overturning water waves, described by fully nonlinear potential theory. The method can be viewed as a high-order extension of the classical finite element method proposed by Cai et al (1998) \\cite{CaiEtAl1998}, although the numerical implementation differs greatly. Features of the proposed spectral element method include: nodal Lagrange basis functions, a general quadrature-free approach and gradient recovery using global $L^2$ projections. The quartic nonlinear terms present in the Zakharov form of the free surface conditions can cause severe aliasing problems and consequently numerical instability for marginally resolved or very steep waves. We show how the scheme can be stabilised through a combination of over-integration of the Galerkin projections and a mild spectral filtering on a per element basis. This effectively removes any aliasing driven instabilities while retaining the high-order accuracy of the numerical...
Description of selected structural elements of composite foams using statistical methods
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K. Gawdzińska
2011-04-01
Full Text Available This article makes use of images from a computer tomograph for the description of selected structure elements of metal and compositefoams by means of statistical methods. Besides, compression stress of the tested materials has been determined.
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
A Consistent Immersed Finite Element Method for the Interface Elasticity Problems
Directory of Open Access Journals (Sweden)
Sangwon Jin
2016-01-01
Full Text Available We propose a new scheme for elasticity problems having discontinuity in the coefficients. In the previous work (Kwak et al., 2014, the authors suggested a method for solving such problems by finite element method using nonfitted grids. The proposed method is based on the P1-nonconforming finite element methods with stabilizing terms. In this work, we modify the method by adding the consistency terms, so that the estimates of consistency terms are not necessary. We show optimal error estimates in H1 and divergence norms under minimal assumptions. Various numerical experiments also show optimal rates of convergence.
A stable cutting method for finite elements based virtual surgery simulation.
Jerábková, Lenka; Jerábek, Jakub; Chudoba, Rostislav; Kuhlen, Torsten
2007-01-01
In this paper we present a novel approach for stable interactive cutting of deformable objects in virtual environments. Our method is based on the extended finite elements method, allowing for a modeling of discontinuities without remeshing. As no new elements are created, the impact on simulation performance is minimized. We also propose an appropriate mass lumping technique to guarantee for the stability of the simulation regardless of the position of the cut.
Determination of rare-earth elements in Luna 16 regolith sample by chemical spectral method
Stroganova, N. S.; Ryabukhin, V. A.; Laktinova, N. V.; Ageyeva, L. V.; Galkina, I. P.; Gatinskaya, N. G.; Yermakov, A. N.; Karyakin, A. V.
1974-01-01
An analysis was made of regolith from layer A of the Luna 16 sample for rare earth elements, by a chemical spectral method. Chemical and ion exchange concentrations were used to determine the content of 12 elements and Y at the level 0.001 to 0.0001 percent with 10 to 15 percent reproducibility of the emission determination. Results within the limits of reproducibility agree with data obtained by mass spectra, activation, and X-ray fluorescent methods.
Comparison of finite elements and discrete ordinate methods for one-dimensional multigroup problems
Energy Technology Data Exchange (ETDEWEB)
Quah, C.S. (Imperial Coll. of Science and Technology, London (UK). Dept. of Mechanical Engineering)
1981-01-01
The finite element formulation for the multigroup neutron transport equation is utilized to solve both shielding and eigenvalue problems in one dimension. In particular the variational formulated by Ackroyd are used. Results obtained for a three-group constant source and a five-group eigenvalue problem show the accuracy and efficiency of the finite element method in comparison with the discrete ordinates finite difference method.
Simulation of 3D tumor cell growth using nonlinear finite element method.
Dong, Shoubing; Yan, Yannan; Tang, Liqun; Meng, Junping; Jiang, Yi
2016-01-01
We propose a novel parallel computing framework for a nonlinear finite element method (FEM)-based cell model and apply it to simulate avascular tumor growth. We derive computation formulas to simplify the simulation and design the basic algorithms. With the increment of the proliferation generations of tumor cells, the FEM elements may become larger and more distorted. Then, we describe a remesh and refinement processing of the distorted or over large finite elements and the parallel implementation based on Message Passing Interface to improve the accuracy and efficiency of the simulation. We demonstrate the feasibility and effectiveness of the FEM model and the parallelization methods in simulations of early tumor growth.
An Automated Method for Landmark Identification and Finite-Element Modeling of the Lumbar Spine.
Campbell, Julius Quinn; Petrella, Anthony J
2015-11-01
The purpose of this study was to develop a method for the automated creation of finite-element models of the lumbar spine. Custom scripts were written to extract bone landmarks of lumbar vertebrae and assemble L1-L5 finite-element models. End-plate borders, ligament attachment points, and facet surfaces were identified. Landmarks were identified to maintain mesh correspondence between meshes for later use in statistical shape modeling. 90 lumbar vertebrae were processed creating 18 subject-specific finite-element models. Finite-element model surfaces and ligament attachment points were reproduced within 1e-5 mm of the bone surface, including the critical contact surfaces of the facets. Element quality exceeded specifications in 97% of elements for the 18 models created. The current method is capable of producing subject-specific finite-element models of the lumbar spine with good accuracy, quality, and robustness. The automated methods developed represent advancement in the state of the art of subject-specific lumbar spine modeling to a scale not possible with prior manual and semiautomated methods.
DEFF Research Database (Denmark)
Cutanda Henriquez, Vicente; Juhl, Peter Møller
2013-01-01
The formulation presented in this paper is based on the Boundary Element Method (BEM) and implements Kirchhoff’s decomposition into viscous, thermal and acoustic components, which can be treated independently everywhere in the domain except on the boundaries. The acoustic variables with losses ar...
Experimental validation of a boundary element solver for exterior acoustic radiation problems
Visser, Rene; Nilsson, A.; Boden, H.
2003-01-01
The relation between harmonic structural vibrations and the corresponding acoustic radiation is given by the Helmholtz integral equation (HIE). To solve this integral equation a new solver (BEMSYS) based on the boundary element method (BEM) has been implemented. This numerical tool can be used for
A level-set based topology optimization using the element connectivity parameterization method
Van Dijk, N.P.; Yoon, G.H.; Van Keulen, F.; Langelaar, M.
2010-01-01
This contribution presents a novel and versatile approach to geometrically nonlinear topology optimization by combining the level-set method with the element connectivity parameterization method or ECP. The combined advantages of both methods open up the possibility to treat a wide range of
Rigid Finite Element Method in Analysis of Dynamics of Offshore Structures
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...
Synthetic Study of 2.5-D ATEM Based on Finite Element Method
DEFF Research Database (Denmark)
Qiang, Jianke; Zhou, Junjie; Cai, Hongzhu
2013-01-01
Based on the regular triangular dissection for finite element method, we implemented the forward modeling of 2.5-D airborne transient electromagnetic method. The 3-D EM field was firstly transformed into Laplace domain and after that we will apply Fourier transform to reduce the dimension from 3-D...... study shows that our numerical solution fits well with the analytical solution for homogeneous and layered earth model. The study also demonstrated the effectiveness of our numerical method....... to 2.5-D. We can obtain the EM field solution in Laplace domain by applying finite element method. The inverse Laplace transform is applied to our solution which finally leads to the airborne EM response in time domain. In compared to the traditional method, we apply our finite element method...
Modelling measurement microphones using BEM with visco-thermal losses
DEFF Research Database (Denmark)
Cutanda Henriquez, Vicente; Juhl, Peter Møller
2012-01-01
visco-thermal losses is used to model measurement condenser microphones. The models presented are fully coupled and include a FEM model of the diaphragm. The behaviour of the acoustic variables in the gap and the effect of the pressure equalization vent are discussed, as well as the practical difficulty......For many decades, models that can explain the behaviour of measurement condenser microphones have been proposed in the literature. These devices have an apparently simple working principle, a charged capacitor whose charge varies when one of its electrodes, the diaphragm, moves as a result of sound...... these subsystems form a strongly coupled device that cannot be modelled properly as a superposition of submodels, but rather as a whole. For this reason, the challenge of microphone modelling is still an ongoing area of research. In this work, a newly developed Boundary Element Method implementation that includes...
Kaljevic, Igor; Patnaik, Surya N.; Hopkins, Dale A.
1996-01-01
The Integrated Force Method has been developed in recent years for the analysis of structural mechanics problems. This method treats all independent internal forces as unknown variables that can be calculated by simultaneously imposing equations of equilibrium and compatibility conditions. In this paper a finite element library for analyzing two-dimensional problems by the Integrated Force Method is presented. Triangular- and quadrilateral-shaped elements capable of modeling arbitrary domain configurations are presented. The element equilibrium and flexibility matrices are derived by discretizing the expressions for potential and complementary energies, respectively. The displacement and stress fields within the finite elements are independently approximated. The displacement field is interpolated as it is in the standard displacement method, and the stress field is approximated by using complete polynomials of the correct order. A procedure that uses the definitions of stress components in terms of an Airy stress function is developed to derive the stress interpolation polynomials. Such derived stress fields identically satisfy the equations of equilibrium. Moreover, the resulting element matrices are insensitive to the orientation of local coordinate systems. A method is devised to calculate the number of rigid body modes, and the present elements are shown to be free of spurious zero-energy modes. A number of example problems are solved by using the present library, and the results are compared with corresponding analytical solutions and with results from the standard displacement finite element method. The Integrated Force Method not only gives results that agree well with analytical and displacement method results but also outperforms the displacement method in stress calculations.
A Novel Assessment Method of Charging Station Planning Based on Fuzzy Matter Element Theory
Directory of Open Access Journals (Sweden)
Zhao Junyi
2017-01-01
Full Text Available Scientific and rational planning of urban electric vehicles (EVs charging station is an important prerequisite for large scale EVs interact with smart grid friendly. This article realizes the planning assessment of EV charging station based on fuzzy matter element theory. The features of urban EV charging station are analyzed, and the evaluation index system of alternative charging station is established. The paper applies fuzzy matter element analysis method to obtain the optimal fuzzy matter element sequence with alternative points, and as a reference sequence. The weights of alternative points corresponding evaluation index are obtained by entropy method. Then, the paper applies the gray correlation analysis to calculate the gray relational weighing degree of fuzzy matter element sequence of alternative points, and determine the EV charging station plan based on the size of gray relational weighing degree. Finally, the simulation results show that the proposed method is effective and feasible for EV charging station planning.
An enriched finite element method to fractional advection-diffusion equation
Luan, Shengzhi; Lian, Yanping; Ying, Yuping; Tang, Shaoqiang; Wagner, Gregory J.; Liu, Wing Kam
2017-08-01
In this paper, an enriched finite element method with fractional basis [ 1,x^{α }] for spatial fractional partial differential equations is proposed to obtain more stable and accurate numerical solutions. For pure fractional diffusion equation without advection, the enriched Galerkin finite element method formulation is demonstrated to simulate the exact solution successfully without any numerical oscillation, which is advantageous compared to the traditional Galerkin finite element method with integer basis [ 1,x] . For fractional advection-diffusion equation, the oscillatory behavior becomes complex due to the introduction of the advection term which can be characterized by a fractional element Peclet number. For the purpose of addressing the more complex numerical oscillation, an enriched Petrov-Galerkin finite element method is developed by using a dimensionless fractional stabilization parameter, which is formulated through a minimization of the residual of the nodal solution. The effectiveness and accuracy of the enriched finite element method are demonstrated by a series of numerical examples of fractional diffusion equation and fractional advection-diffusion equation, including both one-dimensional and two-dimensional, steady-state and time-dependent cases.
Directory of Open Access Journals (Sweden)
Jilian Wu
2013-01-01
Full Text Available We discuss several stabilized finite element methods, which are penalty, regular, multiscale enrichment, and local Gauss integration method, for the steady incompressible flow problem with damping based on the lowest equal-order finite element space pair. Then we give the numerical comparisons between them in three numerical examples which show that the local Gauss integration method has good stability, efficiency, and accuracy properties and it is better than the others for the steady incompressible flow problem with damping on the whole. However, to our surprise, the regular method spends less CPU-time and has better accuracy properties by using Crout solver.
A parallel finite element method for the analysis of crystalline solids
DEFF Research Database (Denmark)
Sørensen, N.J.; Andersen, B.S.
1996-01-01
A parallel finite element method suitable for the analysis of 3D quasi-static crystal plasticity problems has been developed. The method is based on substructuring of the original mesh into a number of substructures which are treated as isolated finite element models related via the interface...... conditions. The resulting interface equations are solved using a direct solution method. The method shows a good speedup when increasing the number of processors from 1 to 8 and the effective solution of 3D crystal plasticity problems whose size is much too large for a single work station becomes possible....
Energy Technology Data Exchange (ETDEWEB)
Ackroyd, R.T. (UKAEA Risley Nuclear Power Development Establishment. Technical Services and Planning Directorate); Splawski, B.A. (Queen Mary Coll., London (UK). Dept. of Nuclear Engineering)
1982-01-01
It is shown that the finite element method also shares with Monte Carlo the capability to bracket local characteristics of a solution, such as the reaction rate for a small locality. The bracketing bounds for the Monte Carlo method have a statistical error, whereas these bounds are rigorous for the finite element method. The latter bounds for a locality of a system are obtained by a bi-variational method with the aid of an associated system. For cell problems very tight bounds can be computed, but in deep-penetration problems for shields there are some difficulties to be overcome. Reasons are advanced for the difficulties.
DEFF Research Database (Denmark)
Yoon, Gil Ho; Joung, Young Soo; Kim, Yoon Young
2005-01-01
of freedom of the element-connectivity parameterizing links are eliminated in element level before the total system matrix is assembled. In terms of implementation, however, the E-ECP is easier to use because the sensitivity analysis in E-ECP does not require the explicit expression of the (tangent......The topology design optimization of “three-dimensional geometrically-nonlinear” continuum structures is still a difficult problem not only because of its problem size but also the occurrence of unstable continuum finite elements during the design optimization. To overcome this difficulty......) stiffness matrix of continuum finite elements. Therefore, any finite element code, including commercial codes, can be readily used for the ECP implementation. The key ideas and characteristics of these methods will be presented in this paper....
Directory of Open Access Journals (Sweden)
Shouyan Jiang
2017-01-01
Full Text Available We model the fluid flow within the crack as one-dimensional flow and assume that the flow is laminar; the fluid is incompressible and accounts for the time-dependent rate of crack opening. Here, we discretise the flow equation by finite volume methods. The extended finite element methods are used for solving solid medium with crack under dynamic loads. Having constructed the approximation of dynamic extended finite element methods, the derivation of governing equation for dynamic extended finite element methods is presented. The implicit time algorithm is elaborated for the time descritisation of dominant equation. In addition, the interaction integral method is given for evaluating stress intensity factors. Then, the coupling model for modelling hydraulic fracture can be established by the extended finite element methods and the finite volume methods. We compare our present numerical results with our experimental results for verifying the proposed model. Finally, we investigate the water pressure distribution along crack surface and the effect of water pressure distribution on the fracture property.
Directory of Open Access Journals (Sweden)
Jinhua Xie
2012-01-01
Full Text Available Based on the transmission and equilibrium relationship of vibration energy in beam-like structures, the Galerkin weighted residual method was applied to equation discretization. An equivalent transformation of feedback element was suggested to develop the Energy Finite Element model of a composite piezoelectric cantilever beam driven by harmonic excitation on lateral direction, with both systems with and without time delay being studied and the power input estimation of harmonic excitation was discussed for the resolution of Energy Finite Element function. Then the energy density solutions of the piezoelectric coupling beam through Energy Finite Element Method (EFEM and classical wave theory were compared to verify the EFEM model, which presented a good accordance. Further investigation was undertaken about the influence of control parameters including the feedback gain and arrangement of piezoelectric patches on characteristics of system energy density distribution.
A Floating Node Method for the Modelling of Discontinuities Within a Finite Element
Pinho, Silvestre T.; Chen, B. Y.; DeCarvalho, Nelson V.; Baiz, P. M.; Tay, T. E.
2013-01-01
This paper focuses on the accurate numerical representation of complex networks of evolving discontinuities in solids, with particular emphasis on cracks. The limitation of the standard finite element method (FEM) in approximating discontinuous solutions has motivated the development of re-meshing, smeared crack models, the eXtended Finite Element Method (XFEM) and the Phantom Node Method (PNM). We propose a new method which has some similarities to the PNM, but crucially: (i) does not introduce an error on the crack geometry when mapping to natural coordinates; (ii) does not require numerical integration over only part of a domain; (iii) can incorporate weak discontinuities and cohesive cracks more readily; (iv) is ideally suited for the representation of multiple and complex networks of (weak, strong and cohesive) discontinuities; (v) leads to the same solution as a finite element mesh where the discontinuity is represented explicitly; and (vi) is conceptually simpler than the PNM.
A new method for true quantitative elemental imaging using PIXE and the proton microprobe
Energy Technology Data Exchange (ETDEWEB)
Ryan, C.G. [Commonwealth Scientific and Industrial Research Organisation (CSIRO), North Ryde, NSW (Australia). Div. of Exploration Geoscience; Jamieson, D.N. [Melbourne Univ., Parkville, VIC (Australia). School of Physics; Churms, C.L.; Pilcher, J.V. [National Accelerator Centre, Faure (South Africa)
1993-12-31
Traditional methods for X-ray imaging using PIXE and the Proton Microprobe have used a simple gate set on an X-ray peak in a spectrum from a Si(Li) detector to provide an image of the distribution of an element. This method can produce artefacts in images, due to overlapping X-ray lines from interfering elements, charge collection tails on peaks, background variation, Si escape peaks and pileup, all of which can render images misleading or qualitative at best. To address this problem, a matrix transform method has been developed at the CSIRO which not only eliminates most artefacts, but can be implemented on-line. The method has been applied to study trace gold distribution in a complex gold bearing ore from Fiji , and more recently has been installed for direct on-line elemental imaging at the NAC in South Africa. 4 refs., 2 figs.
Quick Method for Aeroelastic and Finite Element Modeling of Wind Turbine Blades
DEFF Research Database (Denmark)
Bennett, Jeffrey; Bitsche, Robert; Branner, Kim
2014-01-01
In this paper a quick method for modeling composite wind turbine blades is developed for aeroelastic simulations and finite element analyses. The method reduces the time to model a wind turbine blade by automating the creation of a shell finite element model and running it through a cross...... the user has two models of the same blade, one for performing a structural finite element model analysis and one for aeroelastic simulations. Here, the method is implemented and applied to reverse engineer a structural layup for the NREL 5MW reference blade. The model is verified by comparing natural......-sectional analysis tool in order to obtain cross-sectional properties for the aeroelastic simulations. The method utilizes detailed user inputs of the structural layup and aerodynamic profile including ply thickness, orientation, material properties and airfoils to create the models. After the process is complete...
Janssen, Bärbel
2011-01-01
A multilevel method on adaptive meshes with hanging nodes is presented, and the additional matrices appearing in the implementation are derived. Smoothers of overlapping Schwarz type are discussed; smoothing is restricted to the interior of the subdomains refined to the current level; thus it has optimal computational complexity. When applied to conforming finite element discretizations of elliptic problems and Maxwell equations, the method\\'s convergence rates are very close to those for the nonadaptive version. Furthermore, the smoothers remain efficient for high order finite elements. We discuss the implementation in a general finite element code using the example of the deal.II library. © 2011 Societ y for Industrial and Applied Mathematics.
A new mixed element method for a class of time-fractional partial differential equations.
Liu, Yang; Li, Hong; Gao, Wei; He, Siriguleng; Fang, Zhichao
2014-01-01
A kind of new mixed element method for time-fractional partial differential equations is studied. The Caputo-fractional derivative of time direction is approximated by two-step difference method and the spatial direction is discretized by a new mixed element method, whose gradient belongs to the simple (L (2)(Ω)(2)) space replacing the complex H(div; Ω) space. Some a priori error estimates in L (2)-norm for the scalar unknown u and in (L (2))(2)-norm for its gradient σ. Moreover, we also discuss a priori error estimates in H (1)-norm for the scalar unknown u.
Kou, Jisheng
2014-01-01
The gradient theory for the surface tension of simple fluids and mixtures is rigorously analyzed based on mathematical theory. The finite element approximation of surface tension is developed and analyzed, and moreover, an adaptive finite element method based on a physical-based estimator is proposed and it can be coupled efficiently with Newton\\'s method as well. The numerical tests are carried out both to verify the proposed theory and to demonstrate the efficiency of the proposed method. © 2013 Elsevier B.V. All rights reserved.
Level set discrete element method for three-dimensional computations with triaxial case study
Kawamoto, Reid; Andò, Edward; Viggiani, Gioacchino; Andrade, José E.
2016-06-01
In this paper, we outline the level set discrete element method (LS-DEM) which is a discrete element method variant able to simulate systems of particles with arbitrary shape using level set functions as a geometric basis. This unique formulation allows seamless interfacing with level set-based characterization methods as well as computational ease in contact calculations. We then apply LS-DEM to simulate two virtual triaxial specimens generated from XRCT images of experiments and demonstrate LS-DEM's ability to quantitatively capture and predict stress-strain and volume-strain behavior observed in the experiments.
Wheeler, Mary
2013-11-16
We study the numerical approximation on irregular domains with general grids of the system of poroelasticity, which describes fluid flow in deformable porous media. The flow equation is discretized by a multipoint flux mixed finite element method and the displacements are approximated by a continuous Galerkin finite element method. First-order convergence in space and time is established in appropriate norms for the pressure, velocity, and displacement. Numerical results are presented that illustrate the behavior of the method. © Springer Science+Business Media Dordrecht 2013.
An Ellipsoidal Particle-Finite Element Method for Hypervelocity Impact Simulation. Chapter 1
Shivarama, Ravishankar; Fahrenthold, Eric P.
2004-01-01
A number of coupled particle-element and hybrid particle-element methods have been developed for the simulation of hypervelocity impact problems, to avoid certain disadvantages associated with the use of pure continuum based or pure particle based methods. To date these methods have employed spherical particles. In recent work a hybrid formulation has been extended to the ellipsoidal particle case. A model formulation approach based on Lagrange's equations, with particles entropies serving as generalized coordinates, avoids the angular momentum conservation problems which have been reported with ellipsoidal smooth particle hydrodynamics models.
Application of a boundary element method to the study of dynamical torsion of beams
Czekajski, C.; Laroze, S.; Gay, D.
1982-01-01
During dynamic torsion of beam elements, consideration of nonuniform warping effects involves a more general technical formulation then that of Saint-Venant. Nonclassical torsion constants appear in addition to the well known torsional rigidity. The adaptation of the boundary integral element method to the calculation of these constants for general section shapes is described. The suitability of the formulation is investigated with some examples of thick as well as thin walled cross sections.
Directory of Open Access Journals (Sweden)
Yang Liu
2012-01-01
Full Text Available A new positive definite expanded mixed finite element method is proposed for parabolic partial integrodifferential equations. Compared to expanded mixed scheme, the new expanded mixed element system is symmetric positive definite and both the gradient equation and the flux equation are separated from its scalar unknown equation. The existence and uniqueness for semidiscrete scheme are proved and error estimates are derived for both semidiscrete and fully discrete schemes. Finally, some numerical results are provided to confirm our theoretical analysis.
Optimal error estimates of the penalty finite element method for micropolar fluids equations
Ortega Torres, Elva Eliana; Rojas Medar, Marko Antonio
2007-01-01
An optimal error estimate of the numerical velocity, pressure and angular velocity, is proved for the fully discrete penalty finite element method of the micropolar equations, when the parameters ², ∆t and h are sufficiently small. In order to obtain above we present the time discretization of the penalty micropolar equation which is based on the backward Euler scheme; the spatial discretization of the time discretized penalty Micropolar equation is based on a finite elements space pair (Hh, ...
Trace and minor elements in coal and methods of their investigation
Páchová, Helena
2016-01-01
The aim of the bachelor thesis is to provide an overview of the minor and trace elements in coal matter and to characterize their origin, distribution and effect on quality of coal in term of its industrial utilization, including potential environmental impacts. The thesis describes main methods currently used when investigating coal geochemistry and mineralogy. The thesis includes overview of the distribution of these elements in the major coal deposits of the Czech Republic.
A goal-oriented adaptive finite element method with convergence rates
Mommer, M.S.; Stevenson, R.
2009-01-01
An adaptive finite element method is analyzed for approximating functionals of the solution of symmetric elliptic second order boundary value problems. We show that the method converges and derive a favorable upper bound for its convergence rate and computational complexity. We illustrate our
Space-time discontinuous Galerkin finite element method for inviscid gas dynamics
van der Ven, H.; van der Vegt, Jacobus J.W.; Bouwman, E.G.; Bathe, K.J.
2003-01-01
In this paper an overview is given of the space-time discontinuous Galerkin finite element method for the solution of the Euler equations of gas dynamics. This technique is well suited for problems which require moving meshes to deal with changes in the domain boundary. The method is demonstrated
C1-continuous Virtual Element Method for Poisson-Kirchhoff plate problem
Energy Technology Data Exchange (ETDEWEB)
Gyrya, Vitaliy [Los Alamos National Lab. (LANL), Los Alamos, NM (United States); Mourad, Hashem Mohamed [Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
2016-09-20
We present a family of C1-continuous high-order Virtual Element Methods for Poisson-Kirchho plate bending problem. The convergence of the methods is tested on a variety of meshes including rectangular, quadrilateral, and meshes obtained by edge removal (i.e. highly irregular meshes). The convergence rates are presented for all of these tests.
Korobanov, Yurii M.; Lishchuk, Ohnieslav M.; Lishchuk, Ivan M.
2014-01-01
The generalization of theoretical bases for engineering calculations of ship structures in the Ukrainian computer-aided design systems is performed. The mathematical base of the boundary elements method is set out; the boundary integral equation is presented. The method of fictitious loads is considered as the basis of ship structures calculation realization.
Research on a special scarifier mechanism with Finite Element Analysis method.
Jiandong Jian,; Hoogmoed, W.B.; GuoXing Tao,; Jie Gao,; Xian Zhang,
2012-01-01
A scarifier mechanism with rotary tillage and anti-rotary grubbing is proposed for inducing the power of tillage in hardens soil. MAT147 material modal is amended by experimental method and soil high-speed cutting finite element modal is build through SPH method, further, the tools parameter of
Research on a special scarifier mechanism with finite element analysis method
Jiang, J.D.; Hoogmoed, W.B.; Tao, G.X.; Gao, Jie; Zhang, X.
2010-01-01
Abstract—A scarifier mechanism with rotary tillage and antirotary grubbing is proposed for inducing the power of tillage in hardens soil. MAT147 material modal is amended by experimental method and soil high-speed cutting finite element modal is build through SPH method, further, the tools parameter
Variational finite element method to study the absorption rate of drug ...
African Journals Online (AJOL)
Methods: The finite element method has been used to obtain the solution of the mass diffusion equation with appropriate boundary conditions. The tissue absorption rate of drug has been taken as the decreasing function of drug concentration from the skin surface towards the target site. The concentration at nodal points ...
Analysis of eigenfrequencies in piezoelectric transducers using the finite element method
DEFF Research Database (Denmark)
Jensen, Henrik
1988-01-01
It is noted that the finite-element method is a valuable supplement to the traditional methods for design of novel transducer types because it can determine the vibrational pattern of piezoelectric transducers and is applicable to any geometry. Computer programs for analysis of axisymmetric...
Direct Determination of Asymptotic Structural Postbuckling Behaviour by the finite element method
DEFF Research Database (Denmark)
Poulsen, Peter Noe; Damkilde, Lars
1998-01-01
Application of the finite element method to Koiter's asymptotic postbuckling theory often leads to numerical problems. Generally it is believed that these problems are due to locking of non-linear terms of different orders. A general method is given here that explains the reason for the numerical...... convergence of the postbuckling coefficients. (C) 1998 John Wiley & Sons, Ltd....
Rahman, T.; Jansen, E.L.; Tiso, P.
2011-01-01
In this paper, a finite element-based approach for nonlinear vibration analysis of shell structures is presented. The approach makes use of a perturbation method that gives an approximation for the amplitude-frequency relation of the structure. The method is formulated using a functional notation
1990-01-01
by the method of moments [1,3, 5,16,17). A plane wave is tapered to avoid edge effects from a finite surface using a Gaussian taper function which...Finite Element Methods in CAD: Electrical and Magnectic Fields, Springer-Verlag New York Inc., New York, 1987. [13] Shen, J. and A.A. Maradudin
Automated finite element grid break-up method, a verification of the six node averaging approach
Barten, H. J.
1975-01-01
The verification of the nodal averaging method for generating automated finite triangular element grids was demonstrated. This was accomplished with a six node averaging program (SNAP) which was placed on an IBM 2250 vector graphics scope terminal. The advantage of this method is that it is unnecessary to program time consuming geometric division and transition algorithms.
Application of the pulsed fast/thermal neutron method for soil elemental analysis
Soil science is a research field where physic concepts and experimental methods are widely used, particularly in agro-chemistry and soil elemental analysis. Different methods of analysis are currently available. The evolution of nuclear physics (methodology and instrumentation) combined with the ava...
DEFF Research Database (Denmark)
For solving partial differential equations (or distributed dynamic systems), the method of lines (MOL) and the space-time conservation element and solution element (CE/SE) method are compared in terms of computational efficiency, solution accuracy and stability. Several representative examples....... It is concluded that the CE/SE method is adequate to capturing shocks in PDEs but for diffusion-dominated stiff PDEs, the MOL with an ODE time integrator is complementary to the CE/SE method....
A simple gamma spectrometry method for evaluating the burnup of MTR-type HEU fuel elements
Energy Technology Data Exchange (ETDEWEB)
Makmal, T. [The Unit of Nuclear Engineering, Ben-Gurion University of The Negev, Beer-Sheva 84105 (Israel); Nuclear Physics and Engineering Division, Soreq Nuclear Research Center, Yavne 81800 (Israel); Aviv, O. [Radiation Safety Division, Soreq Nuclear Research Center, Yavne 81800 (Israel); Gilad, E., E-mail: gilade@bgu.ac.il [The Unit of Nuclear Engineering, Ben-Gurion University of The Negev, Beer-Sheva 84105 (Israel)
2016-10-21
A simple method for the evaluation of the burnup of a materials testing reactor (MTR) fuel element by gamma spectrometry is presented. The method was applied to a highly enriched uranium MTR nuclear fuel element that was irradiated in a 5 MW pool-type research reactor for a total period of 34 years. The experimental approach is based on in-situ measurements of the MTR fuel element in the reactor pool by a portable high-purity germanium detector located in a gamma cell. To corroborate the method, analytical calculations (based on the irradiation history of the fuel element) and computer simulations using a dedicated fuel cycle burnup code ORIGEN2 were performed. The burnup of the MTR fuel element was found to be 52.4±8.8%, which is in good agreement with the analytical calculations and the computer simulations. The method presented here is suitable for research reactors with either a regular or an irregular irradiation regime and for reactors with limited infrastructure and/or resources. In addition, its simplicity and the enhanced safety it confers may render this method suitable for IAEA inspectors in fuel element burnup assessments during on-site inspections. - Highlights: • Simple, inexpensive, safe and flexible experimental setup that can be quickly deployed. • Experimental results are thoroughly corroborated against ORIGEN2 burnup code. • Experimental uncertainty of 9% and 5% deviation between measurements and simulations. • Very high burnup MTR fuel element is examined, with 60% depletion of {sup 235}U. • Impact of highly irregular irradiation regime on burnup evaluation is studied.
The finite element method in making up meshes in ANSYS Meshing for CFD models
Directory of Open Access Journals (Sweden)
Віктор Іванович Троханяк
2015-11-01
Full Text Available Method of finite elements (FEM is used in calculating tasks of hydrodynamics and heat transfer tasks. The essence of the method consists in the approximate solution of a variational task. To formulate this task a functional concept is used. The type of a functional is different for different tasks and is selected through a special choice. Currently FEM is widely used in calculating the strength and in solving tasks of heat transfer in solids. However, it can be applied in calculating the flow of liquids and gases. There are also methods that combine elements of the finite volumes and finite elements methods. The combination of these methods make it possible to use a wide range of computational meshes ( tetragonal meshes, pyramidal meshes, prismatic meshes, polyhedral meshes what is necessary for solving tasks with complex geometry. This approach is used by CFD packages Ansys CFX, Ansys Fluent, Star-CD, Star-CCM +, Comsol and others. The method and the analysis of 2D mesh were carried out, using a method of final elements in ANSYS Meshing for heat exchangers with an inline arrangement of tubes in banks and with their curvilinear arrangement in compact banks of tubes of a new design. Particular features were considered and the algorithm of making up a mesh was developed for tasks of hydraulic and gas dynamics and thermal mass transfer. The most optimum and qualitative meshes for CFD models were chosen
Stochastic BEM for the Vibroacoustic Analysis of Three-Dimensional Structures
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R. D'Amico
2011-01-01
Full Text Available Nowadays, extending the NVH prediction reliability to the whole frequency range is an attractive goal of vibroacoustics. Deterministic methodologies are well established for the low-frequency range, but, decreasing the wavelength, energy-based methods are necessary. In such a range, a crucial role is played by small perturbations which highly influence the response sensitivity. Moreover, taking into account these variations allows to make the product design more robust and even quicker. Introducing geometrical uncertainties within the classic BEM formulation allows to obtain the so-called stochastic BEM. As a result, the solution shows deterministic behaviour at low frequencies; decreasing the wavelength, the effect of the uncertainties smooths the response. Consequently, it is possible to obtain an averaged trend over the whole frequency range which asymptotically tends to the deterministic one. In this paper, we deal with three-dimensional acoustic SBEM. First, the formulation and its basic assumptions are presented. Secondly, they are applied to academic cases to show its potentialities in predicting vibroacoustic behaviour over a wide frequency range.
Fault diagnosis of rolling element bearing using a new optimal scale morphology analysis method.
Yan, Xiaoan; Jia, Minping; Zhang, Wan; Zhu, Lin
2018-02-01
Periodic transient impulses are key indicators of rolling element bearing defects. Efficient acquisition of impact impulses concerned with the defects is of much concern to the precise detection of bearing defects. However, transient features of rolling element bearing are generally immersed in stochastic noise and harmonic interference. Therefore, in this paper, a new optimal scale morphology analysis method, named adaptive multiscale combination morphological filter-hat transform (AMCMFH), is proposed for rolling element bearing fault diagnosis, which can both reduce stochastic noise and reserve signal details. In this method, firstly, an adaptive selection strategy based on the feature energy factor (FEF) is introduced to determine the optimal structuring element (SE) scale of multiscale combination morphological filter-hat transform (MCMFH). Subsequently, MCMFH containing the optimal SE scale is applied to obtain the impulse components from the bearing vibration signal. Finally, fault types of bearing are confirmed by extracting the defective frequency from envelope spectrum of the impulse components. The validity of the proposed method is verified through the simulated analysis and bearing vibration data derived from the laboratory bench. Results indicate that the proposed method has a good capability to recognize localized faults appeared on rolling element bearing from vibration signal. The study supplies a novel technique for the detection of faulty bearing. Copyright © 2018. Published by Elsevier Ltd.
Rudimentary overview of the capabilities and problems concerning the finite-element method
Energy Technology Data Exchange (ETDEWEB)
Klaasen, J.J.
1991-02-01
The finite element method is very powerful and flexible to model complex geometries with computers, because the region of interest can be subdivided into finite elements accurately. The advantages and drawbacks of the finite-element method will be the focus of the rudimentary investigation presented in this report. Especially, the requirements in terms of computational effort and computer memory storage will be investigated with respect to Nuclear ElectroMagnetic Pulse (NEMP) research requirements, i.e., with configurations frequently found in NEMP research such as coupling and interaction studies, simulator design and sensor design. Such configurations are often three dimensional and of intricate geometry. It is found that with present day computer capability it is not yet possible to solve real-life three dimensional geometries with the finite-element method, because of the memory requirements needed to store the resulting system of equations. Two dimensional geometries can at present be solved with the finite-element method, but the usefulness of two dimensional geometries for NEMP research purposes is questionable.
A partially penalty immersed Crouzeix-Raviart finite element method for interface problems
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Na An
2017-08-01
Full Text Available Abstract The elliptic equations with discontinuous coefficients are often used to describe the problems of the multiple materials or fluids with different densities or conductivities or diffusivities. In this paper we develop a partially penalty immersed finite element (PIFE method on triangular grids for anisotropic flow models, in which the diffusion coefficient is a piecewise definite-positive matrix. The standard linear Crouzeix-Raviart type finite element space is used on non-interface elements and the piecewise linear Crouzeix-Raviart type immersed finite element (IFE space is constructed on interface elements. The piecewise linear functions satisfying the interface jump conditions are uniquely determined by the integral averages on the edges as degrees of freedom. The PIFE scheme is given based on the symmetric, nonsymmetric or incomplete interior penalty discontinuous Galerkin formulation. The solvability of the method is proved and the optimal error estimates in the energy norm are obtained. Numerical experiments are presented to confirm our theoretical analysis and show that the newly developed PIFE method has optimal-order convergence in the L 2 $L^{2}$ norm as well. In addition, numerical examples also indicate that this method is valid for both the isotropic and the anisotropic elliptic interface problems.
Scattering Cross Section of Sound Waves by the Modal Element Method
Baumeister, Kenneth J.; Kreider, Kevin L.
1994-01-01
#he modal element method has been employed to determine the scattered field from a plane acoustic wave impinging on a two dimensional body. In the modal element method, the scattering body is represented by finite elements, which are coupled to an eigenfunction expansion representing the acoustic pressure in the infinite computational domain surrounding the body. The present paper extends the previous work by developing the algorithm necessary to calculate the acoustics scattering cross section by the modal element method. The scattering cross section is the acoustical equivalent to the Radar Cross Section (RCS) in electromagnetic theory. Since the scattering cross section is evaluated at infinite distance from the body, an asymptotic approximation is used in conjunction with the standard modal element method. For validation, the scattering cross section of the rigid circular cylinder is computed for the frequency range 0.1 is less than or equal to ka is less than or equal to 100. Results show excellent agreement with the analytic solution.
A partially penalty immersed Crouzeix-Raviart finite element method for interface problems.
An, Na; Yu, Xijun; Chen, Huanzhen; Huang, Chaobao; Liu, Zhongyan
2017-01-01
The elliptic equations with discontinuous coefficients are often used to describe the problems of the multiple materials or fluids with different densities or conductivities or diffusivities. In this paper we develop a partially penalty immersed finite element (PIFE) method on triangular grids for anisotropic flow models, in which the diffusion coefficient is a piecewise definite-positive matrix. The standard linear Crouzeix-Raviart type finite element space is used on non-interface elements and the piecewise linear Crouzeix-Raviart type immersed finite element (IFE) space is constructed on interface elements. The piecewise linear functions satisfying the interface jump conditions are uniquely determined by the integral averages on the edges as degrees of freedom. The PIFE scheme is given based on the symmetric, nonsymmetric or incomplete interior penalty discontinuous Galerkin formulation. The solvability of the method is proved and the optimal error estimates in the energy norm are obtained. Numerical experiments are presented to confirm our theoretical analysis and show that the newly developed PIFE method has optimal-order convergence in the [Formula: see text] norm as well. In addition, numerical examples also indicate that this method is valid for both the isotropic and the anisotropic elliptic interface problems.
Free-Vibration Analysis of Rotating Beams by a Variable-Order Finite-Element Method
Hodges, Dewey H.; Rutkowski, Michael J.
1981-01-01
The free vibration of rotating beams is analyzed by means of a finite-element method of variable order. This method entails displacement functions that are a complete power series of a variable number of terms. The terms are arranged so that the generalized coordinates are composed of displacements and slopes at the element extremities and, additionally, displacements at certain points within the element. The displacement is assumed to be analytic within an element and thus can be approximated to any degree of accuracy desired by a complete power series. Numerical results are presented for uniform beams with zero and nonzero hub radii, tapered beams, and a nonuniform beam with discontinuities. Since the present method reduces to a conventional beam finite-element method for a cubic displacement function, the results are compared and found to be superior to the conventional results in terms of accuracy for a given number of degrees of freedom. Indeed, essentially exact eigenvalues and eigenvectors are obtained with this technique, which is far more rapidly convergent than other approaches in the literature.
Finite element method for one-dimensional rill erosion simulation on a curved slope
Directory of Open Access Journals (Sweden)
Lijuan Yan
2015-03-01
Full Text Available Rill erosion models are important to hillslope soil erosion prediction and to land use planning. The development of rill erosion models and their use has become increasingly of great concern. The purpose of this research was to develop mathematic models with computer simulation procedures to simulate and predict rill erosion. The finite element method is known as an efficient tool in many other applications than in rill soil erosion. In this study, the hydrodynamic and sediment continuity model equations for a rill erosion system were solved by the Galerkin finite element method and Visual C++ procedures. The simulated results are compared with the data for spatially and temporally measured processes for rill erosion under different conditions. The results indicate that the one-dimensional linear finite element method produced excellent predictions of rill erosion processes. Therefore, this study supplies a tool for further development of a dynamic soil erosion prediction model.
Jiang, Lijian
2010-08-01
In this paper, we discuss a numerical multiscale approach for solving wave equations with heterogeneous coefficients. Our interest comes from geophysics applications and we assume that there is no scale separation with respect to spatial variables. To obtain the solution of these multiscale problems on a coarse grid, we compute global fields such that the solution smoothly depends on these fields. We present a Galerkin multiscale finite element method using the global information and provide a convergence analysis when applied to solve the wave equations. We investigate the relation between the smoothness of the global fields and convergence rates of the global Galerkin multiscale finite element method for the wave equations. Numerical examples demonstrate that the use of global information renders better accuracy for wave equations with heterogeneous coefficients than the local multiscale finite element method. © 2010 IMACS.
The use of Galerkin finite-element methods to solve mass-transport equations
Grove, David B.
1977-01-01
The partial differential equation that describes the transport and reaction of chemical solutes in porous media was solved using the Galerkin finite-element technique. These finite elements were superimposed over finite-difference cells used to solve the flow equation. Both convection and flow due to hydraulic dispersion were considered. Linear and Hermite cubic approximations (basis functions) provided satisfactory results: however, the linear functions were computationally more efficient for two-dimensional problems. Successive over relaxation (SOR) and iteration techniques using Tchebyschef polynomials were used to solve the sparce matrices generated using the linear and Hermite cubic functions, respectively. Comparisons of the finite-element methods to the finite-difference methods, and to analytical results, indicated that a high degree of accuracy may be obtained using the method outlined. The technique was applied to a field problem involving an aquifer contaminated with chloride, tritium, and strontium-90. (Woodard-USGS)
Adaptive mixed finite element methods for Darcy flow in fractured porous media
Chen, Huangxin
2016-09-21
In this paper, we propose adaptive mixed finite element methods for simulating the single-phase Darcy flow in two-dimensional fractured porous media. The reduced model that we use for the simulation is a discrete fracture model coupling Darcy flows in the matrix and the fractures, and the fractures are modeled by one-dimensional entities. The Raviart-Thomas mixed finite element methods are utilized for the solution of the coupled Darcy flows in the matrix and the fractures. In order to improve the efficiency of the simulation, we use adaptive mixed finite element methods based on novel residual-based a posteriori error estimators. In addition, we develop an efficient upscaling algorithm to compute the effective permeability of the fractured porous media. Several interesting examples of Darcy flow in the fractured porous media are presented to demonstrate the robustness of the algorithm.
Multigrid Finite Element Method in Calculation of 3D Homogeneous and Composite Solids
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A.D. Matveev
2016-12-01
Full Text Available In the present paper, a method of multigrid finite elements to calculate elastic three-dimensional homogeneous and composite solids under static loading has been suggested. The method has been developed based on the finite element method algorithms using homogeneous and composite three-dimensional multigrid finite elements (MFE. The procedures for construction of MFE of both rectangular parallelepiped and complex shapes have been shown. The advantages of MFE are that they take into account, following the rules of the microapproach, heterogeneous and microhomogeneous structures of the bodies, describe the three-dimensional stress-strain state (without any simplifying hypotheses in homogeneous and composite solids, as well as generate small dimensional discrete models and numerical solutions with a high accuracy.
Directory of Open Access Journals (Sweden)
Zhao Tang
2016-04-01
Full Text Available The crashworthiness of a railway vehicle relates to its passive safety performance. Due to mesh distortion and difficulty in controlling the hourglass energy, conventional finite element methods face great challenges in crashworthiness simulation of large-scale complex railway vehicle models. Meshfree methods such as element-free Galerkin method offer an alternative approach to overcome those limitations but have proved time-consuming. In this article, a coupled finite element/meshfree method is proposed to study the crashworthiness of railway vehicles. A representative scenario, in which the leading vehicle of a high-speed train impacts to a rigid wall, is simulated with the coupled finite element/element-free Galerkin method in LS-DYNA. We have compared the conventional finite element method and the coupled finite element/element-free Galerkin method with the simulation results of different levels of discretization. Our work showed that coupled finite element/element-free Galerkin method is a suitable alternative of finite element method to handle the nonlinear deformation in full-size railway vehicle crashworthiness simulation. The coupled method can reduce the hourglass energy in finite element simulation, to produce robust simulation.
Directory of Open Access Journals (Sweden)
Ping Zhang
2014-01-01
Full Text Available The variational multiscale element free Galerkin method is extended to simulate the Stokes flow problems in a circular cavity as an irregular geometry. The method is combined with Hughes’s variational multiscale formulation and element free Galerkin method; thus it inherits the advantages of variational multiscale and meshless methods. Meanwhile, a simple technique is adopted to impose the essential boundary conditions which makes it easy to solve problems with complex area. Finally, two examples are solved and good results are obtained as compared with solutions of analytical and numerical methods, which demonstrates that the proposed method is an attractive approach for solving incompressible fluid flow problems in terms of accuracy and stability, even for complex irregular boundaries.
The Interpolating Element-Free Galerkin Method for 2D Transient Heat Conduction Problems
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Na Zhao
2014-01-01
Full Text Available An interpolating element-free Galerkin (IEFG method is presented for transient heat conduction problems. The shape function in the moving least-squares (MLS approximation does not satisfy the property of Kronecker delta function, so an interpolating moving least-squares (IMLS method is discussed; then combining the shape function constructed by the IMLS method and Galerkin weak form of the 2D transient heat conduction problems, the interpolating element-free Galerkin (IEFG method for transient heat conduction problems is presented, and the corresponding formulae are obtained. The main advantage of this approach over the conventional meshless method is that essential boundary conditions can be applied directly. Numerical results show that the IEFG method has high computational accuracy.
Meng, Weijuan; Fu, Li-Yun
2017-08-01
The finite element method is a very important tool for modeling seismic wave propagation in complex media, but it usually consumes a large amount of memory which significantly decreases computational efficiency when solving large-scale seismic problems. Here, a modified finite element method (MFEM) is proposed to improve efficiency. Triangular elements are employed to mesh the topography and the discontinuous interface more flexibly. In the two-dimensional case, the Jacobian matrix is obtained by using three controlling points instead of all nodes in each element with MFEM, which separates the Jacobian matrix from the stiffness matrix. The kernel matrices of the stiffness matrix rather than the global matrix are stored, and memory requirements are thus reduced significantly. Meanwhile, the element-by-element scheme is adopted to spare large sparse matrices and make the program easily parallelized. A second-order perfectly matched layer (PML) is also implemented to eliminate artificial reflections. Finally, the accuracy and efficiency of our algorithm are validated by numerical tests.
Alteration of trace element concentrations in plants by adhering particles - Methods of correction.
Pospiech, Solveig; Fahlbusch, Wiebke; Sauer, Benedikt; Pasold, Tino; Ruppert, Hans
2017-09-01
Trace element concentrations in plants may be influenced by airborne dust or adhering soil particles. Neglecting adhering particles in plant tissue leads to misinterpretation of trace element concentrations in research fields such as phytomining, phytoremediation, bio-monitoring, uptake of micronutrients and provenance studies. In case washing or brushing the samples prior to analysis is insufficient or impossible due to fragile or pre-processed samples mathematical correction should be applied. In this study three methods are presented allowing to subtract the influence of adhering particles in order to obtain the element concentrations in plants resulting only from uptake. All mathematical models are based on trace elements with negligible soil to plant transfer. A prerequisite for the correction methods is trace element analytics with good accuracy and high precision, e.g. through complete acid digestion. In a data set of 1040 plant samples grown in open field and pot trials most plants show a small but detectable amount of adhering particles. While concentrations of nutrients are nearly unaffected trace element concentrations such as Al, Cd, Co, Cr, Fe, Mn, Ni, Pb, REEs, Ti and U may be significantly altered. Different sampling techniques like cutting height can also significantly alter the concentrations measured in the samples. Copyright © 2017 Elsevier Ltd. All rights reserved.
Numerical Acoustic Models Including Viscous and Thermal losses: Review of Existing and New Methods
DEFF Research Database (Denmark)
Andersen, Peter Risby; Cutanda Henriquez, Vicente; Aage, Niels
2017-01-01
This work presents an updated overview of numerical methods including acoustic viscous and thermal losses. Numerical modelling of viscothermal losses has gradually become more important due to the general trend of making acoustic devices smaller. Not including viscothermal acoustic losses...... in such numerical computations will therefore lead to inaccurate or even wrong results. Both, Finite Element Method (FEM) and Boundary Element Method (BEM), formulations are available that incorporate these loss mechanisms. Including viscothermal losses in FEM computations can be computationally very demanding, due...... and BEM method including viscothermal dissipation are compared and investigated....
An Automatic Detection Method of Nanocomposite Film Element Based on GLCM and Adaboost M1
Directory of Open Access Journals (Sweden)
Hai Guo
2015-01-01
Full Text Available An automatic detection model adopting pattern recognition technology is proposed in this paper; it can realize the measurement to the element of nanocomposite film. The features of gray level cooccurrence matrix (GLCM can be extracted from different types of surface morphology images of film; after that, the dimension reduction of film can be handled by principal component analysis (PCA. So it is possible to identify the element of film according to the Adaboost M1 algorithm of a strong classifier with ten decision tree classifiers. The experimental result shows that this model is superior to the ones of SVM (support vector machine, NN and BayesNet. The method proposed can be widely applied to the automatic detection of not only nanocomposite film element but also other nanocomposite material elements.
Ghadyani, Hamid R.; Srinivasan, Subhadra; Pogue, Brian W.; Paulsen, Keith D.
2010-01-01
The quantification of total hemoglobin concentration (HbT) obtained from multi-modality image-guided near infrared spectroscopy (IG-NIRS) was characterized using the boundary element method (BEM) for 3D image reconstruction. Multi-modality IG-NIRS systems use a priori information to guide the reconstruction process. While this has been shown to improve resolution, the effect on quantitative accuracy is unclear. Here, through systematic contrast-detail analysis, the fidelity of IG-NIRS in quantifying HbT was examined using 3D simulations. These simulations show that HbT could be recovered for medium sized (20mm in 100mm total diameter) spherical inclusions with an average error of 15%, for the physiologically relevant situation of 2:1 or higher contrast between background and inclusion. Using partial 3D volume meshes to reduce the ill-posed nature of the image reconstruction, inclusions as small as 14mm could be accurately quantified with less than 15% error, for contrasts of 1.5 or higher. This suggests that 3D IG-NIRS provides quantitatively accurate results for sizes seen early in treatment cycle of patients undergoing neoadjuvant chemotherapy when the tumors are larger than 30mm. PMID:20720975
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Uma Devi Kumaravelu
2012-01-01
Full Text Available A method of simulation and modeling outer rotor permanent magnet brushless DC (ORPMBLDC motor under dynamic conditions using finite element method by FEMM 4.2 software package is presented. In the proposed simulation, the torque developed at various positions of the rotor, under a complete cycle of excitation of the stator, is analysed. A novel method of sinusoidal excitation is proposed to enhance the overall torque development of ORPMBLDC motor.
Uma Devi Kumaravelu; Sanavullah Mohamed Yakub
2012-01-01
A method of simulation and modeling outer rotor permanent magnet brushless DC (ORPMBLDC) motor under dynamic conditions using finite element method by FEMM 4.2 software package is presented. In the proposed simulation, the torque developed at various positions of the rotor, under a complete cycle of excitation of the stator, is analysed. A novel method of sinusoidal excitation is proposed to enhance the overall torque development of ORPMBLDC motor.
Pardo D.; Nam M.J.; Torres-Verdín C.; Hoversten M.G.; Garay Iñ.
2011-01-01
We introduce a new numerical method to simulate geophysical marine controlled source electromagnetic (CSEM) measurements for the case of 2D structures and finite 3D sources of electromagnetic (EM) excitation. The method of solution is based on a spatial discretization that combines a 1D Fourier transform with a 2D self-adaptive, goal-oriented, hp-Finite element method. It enables fast and accurate simulations for a variety of important, challenging and practical cases of marine CSEM acquisiti...
Lacour, Catherine; Maday, Yvon
1997-01-01
Travail fait pendant la thèse de Catherine lacour à l'ONERA: Office National d'Etudes et de Recherches Aerospatiales 92322 Chatillon FRANCE; International audience; When using domain decomposition in a finite element framework for the approximation of second order elliptic or parabolic type problems, it has become appealing to tune the mesh of each subdomain to the local behaviour of the solution. The resulting discretization being then nonconforming, different approaches have been advocated ...
Utilization of Advanced Methods in the Control of a Mechatronic System with Flexible Elements
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Juhás Martin
2016-12-01
Full Text Available Analysis of the negative impact of a mechatronic system with the flexible elements parameter error and the possibilities of impact reduction are presented in this contribution. Two advanced methods – the Model Predictive Control method and the inclusion of an LMS filter into the control process are proposed for the reduction of the insufficient effect of a double notch filter, which was initially integrated into the system for elimination of two-mass flexible joint parasitic frequencies. Simulation experiments results – response of system angular velocity and control process quality analysis confirmed the correctness of the proposition for the usage of these progressive control elements.
Annotations on the virtual element method for second-order elliptic problems
Energy Technology Data Exchange (ETDEWEB)
Manzini, Gianmarco [Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
2017-01-03
This document contains working annotations on the Virtual Element Method (VEM) for the approximate solution of diffusion problems with variable coefficients. To read this document you are assumed to have familiarity with concepts from the numerical discretization of Partial Differential Equations (PDEs) and, in particular, the Finite Element Method (FEM). This document is not an introduction to the FEM, for which many textbooks (also free on the internet) are available. Eventually, this document is intended to evolve into a tutorial introduction to the VEM (but this is really a long-term goal).
P1 Nonconforming Finite Element Method for the Solution of Radiation Transport Problems
Kang, Kab S.
2002-01-01
The simulation of radiation transport in the optically thick flux-limited diffusion regime has been identified as one of the most time-consuming tasks within large simulation codes. Due to multimaterial complex geometry, the radiation transport system must often be solved on unstructured grids. In this paper, we investigate the behavior and the benefits of the unstructured P(sub 1) nonconforming finite element method, which has proven to be flexible and effective on related transport problems, in solving unsteady implicit nonlinear radiation diffusion problems using Newton and Picard linearization methods. Key words. nonconforrning finite elements, radiation transport, inexact Newton linearization, multigrid preconditioning
The next step in coastal numerical models: spectral/hp element methods?
DEFF Research Database (Denmark)
Eskilsson, Claes; Engsig-Karup, Allan Peter; Sherwin, Spencer J.
2005-01-01
In this paper we outline the application of spectral/hp element methods for modelling nonlinear and dispersive waves. We present one- and two-dimensional test cases for the shallow water equations and Boussinesqtype equations – including highly dispersive Boussinesq-type equations.......In this paper we outline the application of spectral/hp element methods for modelling nonlinear and dispersive waves. We present one- and two-dimensional test cases for the shallow water equations and Boussinesqtype equations – including highly dispersive Boussinesq-type equations....
Modeling the mechanics of axonal fiber tracts using the embedded finite element method.
Garimella, Harsha T; Kraft, Reuben H
2017-05-01
A subject-specific human head finite element model with embedded axonal fiber tractography obtained from diffusion tensor imaging was developed. The axonal fiber tractography finite element model was coupled with the volumetric elements in the head model using the embedded element method. This technique enables the calculation of axonal strains and real-time tracking of the mechanical response of the axonal fiber tracts. The coupled model was then verified using pressure and relative displacement-based (between skull and brain) experimental studies and was employed to analyze a head impact, demonstrating the applicability of this method in studying axonal injury. Following this, a comparison study of different injury criteria was performed. This model was used to determine the influence of impact direction on the extent of the axonal injury. The results suggested that the lateral impact loading is more dangerous compared to loading in the sagittal plane, a finding in agreement with previous studies. Through this analysis, we demonstrated the viability of the embedded element method as an alternative numerical approach for studying axonal injury in patient-specific human head models. Copyright © 2016 John Wiley & Sons, Ltd.
[Research on Test Method of Metallic Element Contained in Tea Based on EDXRF Technique].
Qin, Xu-lei; Li, Ye; Song, Zhong-hua; Wang, Guo-zheng; Li, Shen; Shan, Gao-feng; Duanmu, Qing-duc
2015-04-01
As it has been certified by experimental testing that when using the energy-dispersive X-ray fluorescence (EDXRF) method to analyze the metallic elements contained in the tea the energy segment of effective X-ray fluorescence photons is located between 3 and 16 keV. Accordingly the spectral correction element is targeted at the copper elements located near the energy center(8 keV). The copper elements are also used as the picketage to be the standard curve. In the energy segment of effective X-ray fluorescence photons contained in the tea 1.25 mg · kg(-1) of the average detection limit was obtained by using the spiked method to analyze four elements of copper, iron, zinc and lead. Compared with the flame atomic absorption spectrum(FAAS), the actual relative error of the tested value by EDXRF is less than 6%, and the relative standard deviation is less than 5%. The result by T test shows that p > 0.05. The conclusions are that there are no statistically significant differences between EDXRF and FAAS. The measured results gained by the two methods agree with each other. And EDXRF can be used thoroughly to test the metal contents contained in the tea. The result shows that it is feasible to test the metallic contents contained in the tea by EDXRF, and its measured result can meet the requirements of field testing and analysis.
Weak Galerkin finite element methods for Darcy flow: Anisotropy and heterogeneity
Lin, Guang; Liu, Jiangguo; Mu, Lin; Ye, Xiu
2014-11-01
This paper presents a family of weak Galerkin finite element methods (WGFEMs) for Darcy flow computation. The WGFEMs are new numerical methods that rely on the novel concept of discrete weak gradients. The WGFEMs solve for pressure unknowns both in element interiors and on the mesh skeleton. The numerical velocity is then obtained from the discrete weak gradient of the numerical pressure. The new methods are quite different than many existing numerical methods in that they are locally conservative by design, the resulting discrete linear systems are symmetric and positive-definite, and there is no need for tuning problem-dependent penalty factors. We test the WGFEMs on benchmark problems to demonstrate the strong potential of these new methods in handling strong anisotropy and heterogeneity in Darcy flow.
Spectral element method for elastic and acoustic waves in frequency domain
Energy Technology Data Exchange (ETDEWEB)
Shi, Linlin; Zhou, Yuanguo; Wang, Jia-Min; Zhuang, Mingwei [Institute of Electromagnetics and Acoustics, and Department of Electronic Science, Xiamen, 361005 (China); Liu, Na, E-mail: liuna@xmu.edu.cn [Institute of Electromagnetics and Acoustics, and Department of Electronic Science, Xiamen, 361005 (China); Liu, Qing Huo, E-mail: qhliu@duke.edu [Department of Electrical and Computer Engineering, Duke University, Durham, NC, 27708 (United States)
2016-12-15
Numerical techniques in time domain are widespread in seismic and acoustic modeling. In some applications, however, frequency-domain techniques can be advantageous over the time-domain approach when narrow band results are desired, especially if multiple sources can be handled more conveniently in the frequency domain. Moreover, the medium attenuation effects can be more accurately and conveniently modeled in the frequency domain. In this paper, we present a spectral-element method (SEM) in frequency domain to simulate elastic and acoustic waves in anisotropic, heterogeneous, and lossy media. The SEM is based upon the finite-element framework and has exponential convergence because of the use of GLL basis functions. The anisotropic perfectly matched layer is employed to truncate the boundary for unbounded problems. Compared with the conventional finite-element method, the number of unknowns in the SEM is significantly reduced, and higher order accuracy is obtained due to its spectral accuracy. To account for the acoustic-solid interaction, the domain decomposition method (DDM) based upon the discontinuous Galerkin spectral-element method is proposed. Numerical experiments show the proposed method can be an efficient alternative for accurate calculation of elastic and acoustic waves in frequency domain.
Spectral element method for elastic and acoustic waves in frequency domain
Shi, Linlin; Zhou, Yuanguo; Wang, Jia-Min; Zhuang, Mingwei; Liu, Na; Liu, Qing Huo
2016-12-01
Numerical techniques in time domain are widespread in seismic and acoustic modeling. In some applications, however, frequency-domain techniques can be advantageous over the time-domain approach when narrow band results are desired, especially if multiple sources can be handled more conveniently in the frequency domain. Moreover, the medium attenuation effects can be more accurately and conveniently modeled in the frequency domain. In this paper, we present a spectral-element method (SEM) in frequency domain to simulate elastic and acoustic waves in anisotropic, heterogeneous, and lossy media. The SEM is based upon the finite-element framework and has exponential convergence because of the use of GLL basis functions. The anisotropic perfectly matched layer is employed to truncate the boundary for unbounded problems. Compared with the conventional finite-element method, the number of unknowns in the SEM is significantly reduced, and higher order accuracy is obtained due to its spectral accuracy. To account for the acoustic-solid interaction, the domain decomposition method (DDM) based upon the discontinuous Galerkin spectral-element method is proposed. Numerical experiments show the proposed method can be an efficient alternative for accurate calculation of elastic and acoustic waves in frequency domain.
Symmetric-Galerkin BEM simulation of fracture with frictional contact
CSIR Research Space (South Africa)
Phan, AV
2003-06-14
Full Text Available A symmetric-Galerkin boundary element framework for fracture analysis with frictional contact (crack friction) on the crack surfaces is presented. The algorithm employs a continuous interpolation on the crack surface (utilizing quadratic boundary...
Xu, M; Nowinski, W L
2001-12-01
In this paper, a novel non-rigid registration method is proposed for registration of the Talairach-Tournoux brain atlas with MRI images and the Schaltenbrand-Wahren brain atlas. A metalforming principle-based finite element method with the large deformation problem is used to find the local deformation, in which finite element equations are governed by constraints in the form of displacements derived from the correspondence relationship between extracted feature points. Some detectable substructures, such as the cortical surface, ventricles and corpus callosum, are first extracted from MRI, forming feature points which are classified into different groups. The softassign method is used to establish the correspondence relationship between feature points within each group and to obtain the global transformation concurrently. The displacement constraints are then derived from the correspondence relationship. A metalforming principle-based finite element method with the large deformation problem is used in which finite element equations are reorganized and simplified by integrating the displacement constraints into the system equations. Our method not only matches the model to the data efficiently, but also decreases the degrees of freedom of the system and consequently reduces the computational cost. The method is illustrated by matching the Talairach-Tournoux brain atlas to MRI normal and pathological data and to the Schaltenbrand-Wahren brain atlas. We compare the results quantitatively between the force assignment-based method and the proposed method. The results show that the proposed method yields more accurate results in a fraction of the time taken by the previous method.
Finite Element Method Application in Areal Rainfall Estimation Case Study; Mashhad Plain Basin
Directory of Open Access Journals (Sweden)
M. Irani
2016-10-01
Full Text Available Introduction: The hydrological models are very important tools for planning and management of water resources. These models can be used for identifying basin and nature problems and choosing various managements. Precipitation is based on these models. Calculations of rainfall would be affected by displacement and region factor such as topography, etc. Estimating areal rainfall is one of the basic needs in meteorological, water resources and others studies. There are various methods for the estimation of rainfall, which can be evaluated by using statistical data and mathematical terms. In hydrological analysis, areal rainfall is so important because of displacement of precipitation. Estimating areal rainfall is divided to three methods: 1- graphical. 2-topographical. 3-numerical. This paper represented calculating mean precipitation (daily, monthly and annual using Galerkin’s method (numerical method and it was compared with other methods such as kriging, IDW, Thiessen and arithmetic mean. In this study, there were 42 actual gauges and thirteen dummies in Mashhad plain basin which is calculated by Galerkin’s method. The method included the use of interpolation functions, allowing an accurate representation of shape and relief of catchment with numerical integration performed by Gaussian quadrature and represented the allocation of weights to stations. Materials and Methods:The estimation of areal rainfall (daily, monthly,… is the basic need for meteorological project. In this field ,there are various methods that one of them is finite element method. Present study aimed to estimate areal rainfall with a 16-year period (1997-2012 by using Galerkin method ( finite element in Mashhad plain basin for 42 station. Therefore, it was compared with other usual methods such as arithmetic mean, Thiessen, Kriging and IDW. The analysis of Thiessen, Kriging and IDW were in ArcGIS10.0 software environment and finite element analysis did by using of Matlab
Bilyeu, David
This dissertation presents an extension of the Conservation Element Solution Element (CESE) method from second- to higher-order accuracy. The new method retains the favorable characteristics of the original second-order CESE scheme, including (i) the use of the space-time integral equation for conservation laws, (ii) a compact mesh stencil, (iii) the scheme will remain stable up to a CFL number of unity, (iv) a fully explicit, time-marching integration scheme, (v) true multidimensionality without using directional splitting, and (vi) the ability to handle two- and three-dimensional geometries by using unstructured meshes. This algorithm has been thoroughly tested in one, two and three spatial dimensions and has been shown to obtain the desired order of accuracy for solving both linear and non-linear hyperbolic partial differential equations. The scheme has also shown its ability to accurately resolve discontinuities in the solutions. Higher order unstructured methods such as the Discontinuous Galerkin (DG) method and the Spectral Volume (SV) methods have been developed for one-, two- and three-dimensional application. Although these schemes have seen extensive development and use, certain drawbacks of these methods have been well documented. For example, the explicit versions of these two methods have very stringent stability criteria. This stability criteria requires that the time step be reduced as the order of the solver increases, for a given simulation on a given mesh. The research presented in this dissertation builds upon the work of Chang, who developed a fourth-order CESE scheme to solve a scalar one-dimensional hyperbolic partial differential equation. The completed research has resulted in two key deliverables. The first is a detailed derivation of a high-order CESE methods on unstructured meshes for solving the conservation laws in two- and three-dimensional spaces. The second is the code implementation of these numerical methods in a computer code. For
Improved Element Erosion Function for Concrete-Like Materials with the SPH Method
Directory of Open Access Journals (Sweden)
Jiří Kala
2016-01-01
Full Text Available The subject of the paper is a description of a simple test from the field of terminal ballistics and the handling of issues arising during its simulation using the numerical techniques of the finite element method. With regard to the possible excessive reshaping of the finite element mesh there is a danger that problems will arise such as the locking of elements or the appearance of negative volumes. It is often necessary to introduce numerical extensions so that the simulations can be carried out at all. When examining local damage to structures, such as the penetration of the outer shell or its perforation, it is almost essential to introduce the numerical erosion of elements into the simulations. However, when using numerical erosion, the dissipation of matter and energy from the computational model occurs in the mathematical background to the calculation. It is a phenomenon which can reveal itself in the final result when a discrepancy appears between the simulations and the experiments. This issue can be solved by transforming the eroded elements into smoothed particle hydrodynamics particles. These newly created particles can then assume the characteristics of the original elements and preserve the matter and energy of the numerical model.
Carvalho Silva, Guilherme; Pereira Cornacchia, Tulimar Machado; Barbosa de Las Casas, Estevam; Silami de Magalhães, Cláudia; Moreira, Allyson Nogueira
2013-06-01
The aim of the study was to present a methodology of development of a virtual 3-dimensional dental implant model for analyses via the finite element method. A set, consisting of a dental implant and abutment, was embedded in acrylic resin for subsequent metallographic grinding and polishing. After the evidentiation of the internal geometry of the implant, the specimen was treated in a sputter for observation using scanning electron microscopy (SEM). The SEM image was transported to computer-aided design software by which all details of the implant were measured. With the measures obtained, the geometry was reproduced with 3-dimensional modeling software. Finally, the model was imported into finite element method analysis software with which it was discretized, generating a mesh. A model with the accurate geometry of the implant was developed. A mesh of 297,600 elements and 490,045 nodes was generated. An aleatory acceleration simulation was performed to test the mesh, and no errors were identified. The developed methodology generated a precise dental implant model, which can be applied in different finite element method simulations.
Methode des elements finis hybride appliquee aux vibrations des coques spheriques
Menaa, Mohamed
The analysis of spherical shells filled with fluid and subjected to supersonic flow has been the subject of few research. Most of these studies treat the dynamic behaviour of empty shells. Few works have investigated spherical shells filled with fluid or subjected to supersonic flutter. In this thesis, we propose to develop a model to analyse the vibratory behaviour of both empty spherical shells and partially filled with fluid. This model is also applicable to study of the dynamic stability of spherical shells subjected to supersonic flow. The model developed is a combination of finite element method, thin shell theory, potential fluid theory and aerodynamic fluid theory. Different parameters are considered here in this study. In the first part of this study, free vibration analysis of spherical shell is carried out. The structural model is based on a combination of thin shell theory and the classical finite element method. Free vibration equations using the hybrid finite element formulation are derived and solved numerically. The results are validated using numerical and theoretical data available in the literature. The analysis is accomplished for spherical shells of different geometries, boundary conditions and radius to thickness ratios. This proposed hybrid finite element method can be used efficiently for design and analysis of spherical shells employed in high speed aircraft structures. In the second part of the present study, a hybrid finite element method is applied to investigate the free vibration of spherical shell filled with fluid. The structural model is based on a combination of thin shell theory and the classical finite element method. It is assumed that the fluid is incompressible and has no free-surface effect. Fluid is considered as a velocity potential variable at each node of the shell element where its motion is expressed in terms of nodal elastic displacement at the fluid-structure interface. Numerical simulation is done and vibration
Energy Technology Data Exchange (ETDEWEB)
Arnoux-Guisse, F.; Bonnin, O.; Leal de Sousa, L.; Nicolas, G.
1995-05-01
After outlining the space and time discretization methods used in the N3S thermal hydraulic code developed at EDF/NHL, we describe the possibilities of the peripheral version, the Adaptative Mesh, which comprises two separate parts: the error indicator computation and the development of a module subdividing elements usable by the solid dynamics code ASTER and the electromagnetism code TRIFOU also developed by R and DD. The error indicators implemented in N3S are described. They consist of a projection indicator quantifying the space error in laminar or turbulent flow calculations and a Navier-Stokes residue indicator calculated on each element. The method for subdivision of triangles into four sub-triangles and tetrahedra into eight sub-tetrahedra is then presented with its advantages and drawbacks. It is illustrated by examples showing the efficiency of the module. The last concerns the 2 D case of flow behind a backward-facing step. (authors). 9 refs., 5 figs., 1 tab.
Main formulations of the finite element method for the problems of structural mechanics. Part 3
Directory of Open Access Journals (Sweden)
Ignat’ev Aleksandr Vladimirovich
2015-01-01
Full Text Available In this paper the author offers is the classification of the formulae of Finite Element Method. This classification help to orient in a huge number of published articles, as well as those to be published, which are dedicated to the problem of enhancing the efficiency of the most commonly used method. The third part of the article considers the variation formulations of FEM and the energy principles lying in the basis of it. If compared to the direct method, which is applied only to finite elements of a simple geometrical type, the variation formulations of FEM are applicable to the elements of any type. All the variation methods can be conventionally divided into two groups. The methods of the first group are based on the principle of energy functional stationarity - a potential system energy, additional energy or on the basis of these energies, which means the full energy. The methods of the second group are based on the variants of mathematical methods of weighted residuals for solving the differential equations, which in some cases can be handled according to the principle of possible displacements or extreme energy principles. The most widely used and multipurpose is the approach based on the use of energy principles coming from the energy conservation law: principle of possible changes in stress state, principle of possible change in stress-strain state.
SQA of finite element method (FEM) codes used for analyses of pit storage/transport packages
Energy Technology Data Exchange (ETDEWEB)
Russel, E. [Lawrence Livermore National Lab., CA (United States)
1997-11-01
This report contains viewgraphs on the software quality assurance of finite element method codes used for analyses of pit storage and transport projects. This methodology utilizes the ISO 9000-3: Guideline for application of 9001 to the development, supply, and maintenance of software, for establishing well-defined software engineering processes to consistently maintain high quality management approaches.
On the Finite Volume Element Method for Self-Adjoint Parabolic Integrodifferential Equations
Directory of Open Access Journals (Sweden)
Mohamed Bahaj
2013-01-01
Full Text Available Finite volume element schemes for non-self-adjoint parabolic integrodifferential equations are derived and stated. For the spatially discrete scheme, optimal-order error estimates in , , and , norms for are obtained. In this paper, we also study the lumped mass modification. Based on the Crank-Nicolson method, a time discretization scheme is discussed and related error estimates are derived.
An Introduction of Finite Element Method in the Engineering Teaching at the University of Camaguey.
Napoles, Elsa; Blanco, Ramon; Jimenez, Rafael; Mc.Pherson, Yoanka
This paper illuminates experiences related to introducing finite element methods (FEM) in mechanical and civil engineering courses at the University of Camaguey in Cuba and provides discussion on using FEM in postgraduate courses for industry engineers. Background information on the introduction of FEM in engineering teaching is focused on…
Variable Mesh Stiffness of spur gear teeth using finite element method
African Journals Online (AJOL)
The objective of this paper is to determine the variable mesh stiffness of spur gear teeth using the finite element method. There are many factors for the variation of stiffness. In this paper only the numbers of contact tooth pairs and applied load are taken into considerations. For accomplishing the objective, a computer ...
Gradient plasticity crack tip characterization by means of the extended finite element method
DEFF Research Database (Denmark)
Martínez Pañeda, Emilio; Natarajan, S.; Bordas, S.
2017-01-01
, however, the use of a very refined meshwithin microns to the crack. In this work a novel andefficient gradient-enhanced numerical framework is developedby means of the extended finite element method(X-FEM). A mechanism-based gradient plasticity modelis employed and the approximation...
A stable and optimal complexity solution method for mixed finite element discretizations
Brandts, J.; Stevenson, R.
2001-01-01
We outline a solution method for mixed finite element discretizations based on dissecting the problem into three separate steps. The first handles the inho- mogeneous constraint, the second solves the flux variable from the homogeneous problem, whereas the third step, adjoint to the first,
Topological Design for Acoustic-Structure Interaction Problems with a Mixed Finite Element Method
DEFF Research Database (Denmark)
Yoon, Gil Ho; Jensen, Jakob Søndergaard; Sigmund, Ole
2006-01-01
to subdomain interfaces evolving during the optimization process. In this paper, we propose to use a mixed finite element formulation with displacements and pressure as primary variables (u/p formulation) which eliminates the need for explicit boundary representation. In order to describe the Helmholtz...... acoustic-structure interaction problems are optimized to show the validity of the proposed method....
A Stimulating Approach To Teaching, Learning and Assessing Finite Element Methods: A Case Study.
Karadelis, J. N.
1998-01-01
Examines the benefits of introducing finite element methods into the curriculum of undergraduate courses. Analyzes the structure of the computer-assisted-design module and the extent to which it fulfills its main objectives. Discusses the efficiency of modern teaching and learning techniques used to develop skills for solving engineering problems;…
Integrated Stiffness Analysis of Redundant Parallel Manipulator Based on Finite Element Method
Wang, S.; Cheng, G.; Pang, Y.; Lodewijks, G.
2015-01-01
An integrated stiffness model is established for a Planar Parallel Manipulator (PPM) with actuation redundancy based on Finite Element Method (FEM), and the static stiffness, dynamitic stiffness and moving stiffness of the PPM are analyzed according to the integrated stiffness model. Firstly, a
Comments on mapping in the use of finite element method | Ahie ...
African Journals Online (AJOL)
The use of mapping in finite element method is either parametric or non parametric, while the space under mapping could be finite or infinite. Here our claim is that parametric mapping by blending function is cheaper and has this same accuracy with her competitor 'mapping by solving auxillary Equation'. This is because ...
Multiscale Model Reduction with Generalized Multiscale Finite Element Methods in Geomathematics
Efendiev, Yalchin R.
2015-09-02
In this chapter, we discuss multiscale model reduction using Generalized Multiscale Finite Element Methods (GMsFEM) in a number of geomathematical applications. GMsFEM has been recently introduced (Efendiev et al. 2012) and applied to various problems. In the current chapter, we consider some of these applications and outline the basic methodological concepts.
Stability estimates for h-p spectral element methods for elliptic ...
Indian Academy of Sciences (India)
R. Narasimhan (Krishtel eMaging) 1461 1996 Oct 15 13:05:22
Stability estimates for h-p spectral element methods for elliptic problems. PRAVIR DUTT, SATYENDRA TOMAR. ∗ and. B V RATHISH KUMAR. Department of Mathematics, Indian Institute of Technology, Kanpur 208 016, India. ∗. Present address: Post Doctoral Researcher, Department of Mathematical Physics and.
History and future of superconvergence in three-dimensional finite element methods
Brandts, J.; Krizek, M.
2000-01-01
We will give anoverview of superconvergence results for nite element methods applied to problems in three space dimensions. Apart from that, we sketch techniques that could be applied to three dimensional superconvergence questions, and indicate what exactly makes the three-dimensional case so much
Discontinuous Galerkin finite element methods for (non)conservative partial differential equations
Rhebergen, Sander
2010-01-01
The first research topic in this thesis is the development of discontinuous Galerkin (DG) finite element methods for partial differential equations containing nonconservative products, which are present in many two-phase flow models. For this, we combine the theory of Dal Maso, LeFloch and Murat, in
Thompson, D.J.; Vliet, W.J. van; Verheij, J.W.
1998-01-01
The complex stiffness of resilient elements is an important parameter required in order to model vibration isolation for many applications. Measurement methods are being standardized which allow such a stiffness to be measured as a function of excitation frequency for known loading conditions. This
A finite element method for solving the shallow water equations on the sphere
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.
Simulation of incompressible flows with heat and mass transfer using parallel finite element method
Directory of Open Access Journals (Sweden)
Jalal Abedi
2003-02-01
Full Text Available The stabilized finite element formulations based on the SUPG (Stream-line-Upwind/Petrov-Galerkin and PSPG (Pressure-Stabilization/Petrov-Galerkin methods are developed and applied to solve buoyancy-driven incompressible flows with heat and mass transfer. The SUPG stabilization term allows us to solve flow problems at high speeds (advection dominant flows and the PSPG term eliminates instabilities associated with the use of equal order interpolation functions for both pressure and velocity. The finite element formulations are implemented in parallel using MPI. In parallel computations, the finite element mesh is partitioned into contiguous subdomains using METIS, which are then assigned to individual processors. To ensure a balanced load, the number of elements assigned to each processor is approximately equal. To solve nonlinear systems in large-scale applications, we developed a matrix-free GMRES iterative solver. Here we totally eliminate a need to form any matrices, even at the element levels. To measure the accuracy of the method, we solve 2D and 3D example of natural convection flows at moderate to high Rayleigh numbers.
Gherlone, Marco; Cerracchio, Priscilla; Mattone, Massimiliano; Di Sciuva, Marco; Tessler, Alexander
2011-01-01
A robust and efficient computational method for reconstructing the three-dimensional displacement field of truss, beam, and frame structures, using measured surface-strain data, is presented. Known as shape sensing , this inverse problem has important implications for real-time actuation and control of smart structures, and for monitoring of structural integrity. The present formulation, based on the inverse Finite Element Method (iFEM), uses a least-squares variational principle involving strain measures of Timoshenko theory for stretching, torsion, bending, and transverse shear. Two inverse-frame finite elements are derived using interdependent interpolations whose interior degrees-of-freedom are condensed out at the element level. In addition, relationships between the order of kinematic-element interpolations and the number of required strain gauges are established. As an example problem, a thin-walled, circular cross-section cantilevered beam subjected to harmonic excitations in the presence of structural damping is modeled using iFEM; where, to simulate strain-gauge values and to provide reference displacements, a high-fidelity MSC/NASTRAN shell finite element model is used. Examples of low and high-frequency dynamic motion are analyzed and the solution accuracy examined with respect to various levels of discretization and the number of strain gauges.
Testing the Bergerhoff method to determine the bulk deposition loads of 49 elements
Thöni, Lotti; Krieg, Fritz; Siewers, Ulrich
The suitability of the simple and rather cheap Bergerhoff method for the determination of bulk deposition loads of 49 elements was tested. The method is suitable for the following elements: Ag, Al, As, Ba, Be, Bi, Ca, Cd, Ce, Co, Cr, Cs, Cu, Fe, Ga, Ge, In, K, La, Li, Mg, Mn, Mo, Na, Nb, Ni, Pb, Rb, S, Sb, Sc, Se, Sn, Sr, Th, Ti, Tl, V, W, Y and Zn provided that for some of these elements one does not get total recovery with HNO 3-digestion. This, nevertheless, supplies sufficient information for most concerns. Analytical problems were encountered for the following elements: U and Te concentrations in our samples were close to the blanks; P and Ta were highly variable within the sampling areas; B, Hf and Zr leached out of the glass of the digestion vessels; Hg is highly volatile. Field studies at three background sites in Switzerland, two on the northern side of the Alps and one in the southern Alps, showed higher burdens of element emissions in the latter, partly because of higher precipitation, and partly because of higher concentrations in the dust. An anthropogenic influence can be inferred for Ag, Bi, Cd, Cu, Hg, Mo, Pb, Sb, Te, W and Zn and probably also for As, P, S (with associated Se) and Sn.
A Family of Multipoint Flux Mixed Finite Element Methods for Elliptic Problems on General Grids
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.
High-order evolving surface finite element method for parabolic problems on evolving surfaces
Kovács, Balázs
2016-01-01
High-order spatial discretisations and full discretisations of parabolic partial differential equations on evolving surfaces are studied. We prove convergence of the high-order evolving surface finite element method, by showing high-order versions of geometric approximation errors and perturbation error estimates and by the careful error analysis of a modified Ritz map. Furthermore, convergence of full discretisations using backward difference formulae and implicit Runge-Kutta methods are als...
A multiscale finite element method for modeling fully coupled thermomechanical problems in solids
Sengupta, Arkaprabha
2012-05-18
This article proposes a two-scale formulation of fully coupled continuum thermomechanics using the finite element method at both scales. A monolithic approach is adopted in the solution of the momentum and energy equations. An efficient implementation of the resulting algorithm is derived that is suitable for multicore processing. The proposed method is applied with success to a strongly coupled problem involving shape-memory alloys. © 2012 John Wiley & Sons, Ltd.
Liu, Meilin
2011-07-01
A discontinuous Galerkin finite element method (DG-FEM) with a highly-accurate time integration scheme is presented. The scheme achieves its high accuracy using numerically constructed predictor-corrector integration coefficients. Numerical results show that this new time integration scheme uses considerably larger time steps than the fourth-order Runge-Kutta method when combined with a DG-FEM using higher-order spatial discretization/basis functions for high accuracy. © 2011 IEEE.
A p-version finite element method for steady incompressible fluid flow and convective heat transfer
Winterscheidt, Daniel L.
1993-01-01
A new p-version finite element formulation for steady, incompressible fluid flow and convective heat transfer problems is presented. The steady-state residual equations are obtained by considering a limiting case of the least-squares formulation for the transient problem. The method circumvents the Babuska-Brezzi condition, permitting the use of equal-order interpolation for velocity and pressure, without requiring the use of arbitrary parameters. Numerical results are presented to demonstrate the accuracy and generality of the method.
A nonconforming finite element method for the Cahn-Hilliard equation
Zhang, Shuo; Wang, Ming
2010-09-01
This paper reports a fully discretized scheme for the Cahn-Hilliard equation. The method uses a convexity-splitting scheme to discretize in the temporal variable and a nonconforming finite element method to discretize in the spatial variable. And, the scheme can preserve the mass conservation and energy dissipation properties of the original problem. Some typical phase transition phenomena are also observed through the numerical examples.
Directory of Open Access Journals (Sweden)
Mohamed Abdelwahed
2017-01-01
Full Text Available We the solvability of the two-dimensional stream function-vorticity formulation of the Navier-Stokes equations. We use the time discretization and the method of characteristics order one for solving a quasi-Stokes system that we discretize by a piecewise continuous finite element method. A stabilization technique is used to overcome the loss of optimal error estimate. Finally a parallel numerical algorithm is presented and tested.
Application of finite element method in mechanical design of automotive parts
Gu, Suohai
2017-09-01
As an effective numerical analysis method, finite element method (FEM) has been widely used in mechanical design and other fields. In this paper, the development of FEM is introduced firstly, then the specific steps of FEM applications are illustrated and the difficulties of FEM are summarized in detail. Finally, applications of FEM in automobile components such as automobile wheel, steel plate spring, body frame, shaft parts and so on are summarized, compared with related research experiments.
Chung, T. J. (Editor); Karr, Gerald R. (Editor)
1989-01-01
Recent advances in computational fluid dynamics are examined in reviews and reports, with an emphasis on finite-element methods. Sections are devoted to adaptive meshes, atmospheric dynamics, combustion, compressible flows, control-volume finite elements, crystal growth, domain decomposition, EM-field problems, FDM/FEM, and fluid-structure interactions. Consideration is given to free-boundary problems with heat transfer, free surface flow, geophysical flow problems, heat and mass transfer, high-speed flow, incompressible flow, inverse design methods, MHD problems, the mathematics of finite elements, and mesh generation. Also discussed are mixed finite elements, multigrid methods, non-Newtonian fluids, numerical dissipation, parallel vector processing, reservoir simulation, seepage, shallow-water problems, spectral methods, supercomputer architectures, three-dimensional problems, and turbulent flows.
Hybrid of Natural Element Method (NEM with Genetic Algorithm (GA to find critical slip surface
Directory of Open Access Journals (Sweden)
Shahriar Shahrokhabadi
2014-06-01
Full Text Available One of the most important issues in geotechnical engineering is the slope stability analysis for determination of the factor of safety and the probable slip surface. Finite Element Method (FEM is well suited for numerical study of advanced geotechnical problems. However, mesh requirements of FEM creates some difficulties for solution processing in certain problems. Recently, motivated by these limitations, several new Meshfree methods such as Natural Element Method (NEM have been used to analyze engineering problems. This paper presents advantages of using NEM in 2D slope stability analysis and Genetic Algorithm (GA optimization to determine the probable slip surface and the related factor of safety. The stress field is produced under plane strain condition using natural element formulation to simulate material behavior analysis utilized in conjunction with a conventional limit equilibrium method. In order to justify the preciseness and convergence of the proposed method, two kinds of examples, homogenous and non-homogenous, are conducted and results are compared with FEM and conventional limit equilibrium methods. The results show the robustness of the NEM in slope stability analysis.
Directory of Open Access Journals (Sweden)
F. Nicot
2002-01-01
Full Text Available The search of improvement of protective techniques against natural phenomena such as snow avalanches continues to use classic methods for calculating flexible structures. This paper deals with a new method to design avalanche protection nets. This method is based on a coupled analysis of both net structure and snow mantle by using a Discrete Element Method. This has led to the development of computational software so that avalanche nets can be easily designed. This tool gives the evolution of the forces acting in several parts of the work as a function of the snow situation.
A least-squares finite element method for incompressible Navier-Stokes problems
Jiang, Bo-Nan
1989-01-01
A least-squares finite element method, based on the velocity-pressure-vorticity formulation, is developed for solving steady incompressible Navier-Stokes problems. This method leads to a minimization problem rather than to a saddle-point problem by the classic mixed method, and can thus accommodate equal-order interpolations. This method has no parameter to tune. The associated algebraic system is symmetric, and positive definite. Numerical results for the cavity flow at Reynolds number up to 10,000 and the backward-facing step flow at Reynolds number up to 900 are presented.
Kojic, Milos; Filipovic, Nenad; Tsuda, Akira
2012-01-01
A multiscale procedure to couple a mesoscale discrete particle model and a macroscale continuum model of incompressible fluid flow is proposed in this study. We call this procedure the mesoscopic bridging scale (MBS) method since it is developed on the basis of the bridging scale method for coupling molecular dynamics and finite element models [G.J. Wagner, W.K. Liu, Coupling of atomistic and continuum simulations using a bridging scale decomposition, J. Comput. Phys. 190 (2003) 249–274]. We derive the governing equations of the MBS method and show that the differential equations of motion of the mesoscale discrete particle model and finite element (FE) model are only coupled through the force terms. Based on this coupling, we express the finite element equations which rely on the Navier–Stokes and continuity equations, in a way that the internal nodal FE forces are evaluated using viscous stresses from the mesoscale model. The dissipative particle dynamics (DPD) method for the discrete particle mesoscale model is employed. The entire fluid domain is divided into a local domain and a global domain. Fluid flow in the local domain is modeled with both DPD and FE method, while fluid flow in the global domain is modeled by the FE method only. The MBS method is suitable for modeling complex (colloidal) fluid flows, where continuum methods are sufficiently accurate only in the large fluid domain, while small, local regions of particular interest require detailed modeling by mesoscopic discrete particles. Solved examples – simple Poiseuille and driven cavity flows illustrate the applicability of the proposed MBS method. PMID:23814322
Barycentric Interpolation and Exact Integration Formulas for the Finite Volume Element Method
Voitovich, Tatiana V.; Vandewalle, Stefan
2008-09-01
This contribution concerns with the construction of a simple and effective technology for the problem of exact integration of interpolation polynomials arising while discretizing partial differential equations by the finite volume element method on simplicial meshes. It is based on the element-wise representation of the local shape functions through barycentric coordinates (barycentric interpolation) and the introducing of classes of integration formulas for the exact integration of generic monomials of barycentric coordinates over the geometrical shapes defined by a barycentric dual mesh. Numerical examples are presented that illustrate the validity of the technology.
A multi-mesh finite element method for phase-field based photonic band structure optimization
Wu, Shengyang; Hu, Xianliang; Zhu, Shengfeng
2018-03-01
A novel finite element method with multiple meshes is proposed, which is applied to solve the phase-field models for photonic band structures optimization. In our approach, fine meshes are used for the phase field evolution, which allows fine resolution for shape representations. The coarse meshes are adopted for the finite element analysis of the state equation. Such a multi-mesh approach could save a considerable amount of computational costs. Numerical convergence is illustrated through comparisons between our computational results and benchmarks. The efficiency and robustness of the multi-mesh approach are also shown.
An explicit Lagrangian finite element method for free-surface weakly compressible flows
Cremonesi, Massimiliano; Meduri, Simone; Perego, Umberto; Frangi, Attilio
2017-07-01
In the present work, an explicit finite element approach to the solution of the Lagrangian formulation of the Navier-Stokes equations for weakly compressible fluids or fluid-like materials is investigated. The introduction of a small amount of compressibility is shown to allow for the formulation of a fast and robust explicit solver based on a particle finite element method. Newtonian and Non-Newtonian Bingham laws are considered. A barotropic equation of state completes the model relating pressure and density fields. The approach has been validated through comparison with experimental tests and numerical simulations of free surface fluid problems involving water and water-soil mixtures.
Fractal Two-Level Finite Element Method For Free Vibration of Cracked Beams
Directory of Open Access Journals (Sweden)
A.Y.T. Leung
1998-01-01
Full Text Available The fractal two-level finite element method is extended to the free vibration behavior of cracked beams for various end boundary conditions. A cracked beam is separated into its singular and regular regions. Within the singular region, infinite number of finite elements are virturally generated by fractal geometry to model the singular behavior of the crack tip. The corresponding numerous degrees of freedom are reduced to a small set of generalized displacements by fractal transformation technique. The solution time and computer storage can be remarkably reduced without sacrifying accuracy. The resonant frequencies and mode shapes computed compared well with the results from a commercial program.
Stress recovery techniques for natural element method in 2-D solid mechanics
Energy Technology Data Exchange (ETDEWEB)
Cho, Jin Rae [Dept. of Naval Architecture and Ocean Engineering, Hongik University, Sejong (Korea, Republic of)
2016-11-15
This paper is concerned with the stress recovery for the natural element method in which the problem domain is discretized with Delaunay triangles and the structural behavior is approximated with Laplace interpolation functions. Basically, the global and local patch recovery techniques based on the L2-projection method are adopted. For the local patch recovery, the local element patches are defined by the supports of each Laplace interpolation function. For the comparison purpose, the local stress recovery is also performed using Lagrange-type basis functions that are used for 3- and 6-node triangular elements. The stresses that are recovered by the present global and local recovery techniques are compared each other and compared with the available analytic solution, in terms of their spatial distributions and the convergence rates. As well, the dependence of the recovered stress field on the type of test basis functions that are used forbnov-Galerkin (BG) and Petrov-Galerkin (PG) natural element methods is also investigated.
Dynamic analysis of suspension cable based on vector form intrinsic finite element method
Qin, Jian; Qiao, Liang; Wan, Jiancheng; Jiang, Ming; Xia, Yongjun
2017-10-01
A vector finite element method is presented for the dynamic analysis of cable structures based on the vector form intrinsic finite element (VFIFE) and mechanical properties of suspension cable. Firstly, the suspension cable is discretized into different elements by space points, the mass and external forces of suspension cable are transformed into space points. The structural form of cable is described by the space points at different time. The equations of motion for the space points are established according to the Newton’s second law. Then, the element internal forces between the space points are derived from the flexible truss structure. Finally, the motion equations of space points are solved by the central difference method with reasonable time integration step. The tangential tension of the bearing rope in a test ropeway with the moving concentrated loads is calculated and compared with the experimental data. The results show that the tangential tension of suspension cable with moving loads is consistent with the experimental data. This method has high calculated precision and meets the requirements of engineering application.
Study by PIXE method of trace elements transferred from prostheses to soft tissues and organs
Energy Technology Data Exchange (ETDEWEB)
Oudadesse, H. E-mail: hassane.oudadesse@univ-rennes1.froudadess@clermont.in2p3.fr; Guibert, G.; Chassot, E.; Irigaray, J.L.; Terver, S.; Vanneuville, G.; Tessier, Y.; Sauvage, T.; Blondiaux, G
2002-05-01
Some metallic prostheses inserted in human hip undergo physico-chemical modification, a few years after their implantation. Tissues surrounding these prostheses are damaged by metallic element transfer. Surgeons in Clermont-Ferrand Hospital (France) recover tissues of abnormal coloration that were in contact with metallic implants. PIXE technique (particles induced X-ray emission) with a 400 {mu}m proton beam and 3 MeV of energy is an efficient technique to analyze these tissues and to detect elements, which are transferred from prosthesis to tissues. PIXE analyses were carried at the CERI-CNRS Laboratory. We have applied this method to determine qualitatively and quantitatively trace elements migration from metallic implants to surrounding tissues and organs, like kidney, spleen, liver, lymphatic gland and lung.
Local Projection-Based Stabilized Mixed Finite Element Methods for Kirchhoff Plate Bending Problems
Directory of Open Access Journals (Sweden)
Xuehai Huang
2013-01-01
Full Text Available Based on stress-deflection variational formulation, we propose a family of local projection-based stabilized mixed finite element methods for Kirchhoff plate bending problems. According to the error equations, we obtain the error estimates of the approximation to stress tensor in energy norm. And by duality argument, error estimates of the approximation to deflection in H1-norm are achieved. Then we design an a posteriori error estimator which is closely related to the equilibrium equation, constitutive equation, and nonconformity of the finite element spaces. With the help of Zienkiewicz-Guzmán-Neilan element spaces, we prove the reliability of the a posteriori error estimator. And the efficiency of the a posteriori error estimator is proved by standard bubble function argument.
Simulation of the Carton Erection for the Rubber Glove Packing Machine Using Finite Element Method
Directory of Open Access Journals (Sweden)
Jewsuwun Kawin
2017-01-01
Full Text Available The rubber glove packing machine had been designed an important function which worked with folding carton. Each folded paper carton would be pulled to be erected by vacuum cups. Some carton could not completely form because of an unsuitable design of the erector. Cartons were collapsed or buckling while pulled by vacuum cups that cause to sudden stop the packing process and affect to number and cost of rubber glove production. This research aimed to use simulation method to erect the folded carton. Finite element (FE model of the rubber glove carton was created with shell elements. The orthotropic material properties were employed to specify FE model for analysis erection behavior of the folding carton. Vacuum cups number, positions and rotation points were simulated until obtained a good situation of the folding carton erector. Subsequently, finite element analysis results will be used to fabricate erector of the rubber glove packing machine in a further work.
Modal analysis of double-walled carbon nanocones using the finite element method
Rouhi, S.; Ansari, R.; Nickabadi, S.
2017-12-01
The vibrational properties of double-walled carbon nanocones are investigated herein. The double-walled carbon nanocones with different geometries including apex angles and lengths are considered. The simply supported-simply supported, clamped-free and clamped-clamped boundary conditions are applied on the nanocones. A linear elastic beam-based finite element method is employed to obtain the frequencies of the double-walled carbon nanocones. Elastic beam elements are used to model the carbon-carbon bond in the structure of the nanocones. Besides, the spring elements are employed to describe the nonbonding van der Waals interactions between different layers. Natural frequencies and mode shapes of the double-walled carbon nanocones are extracted by solving the eigenvalue problem. It is observed that increasing the disclination angle of nanocones increases their natural frequency. However, increasing the nanocone’s height leads to decreasing the frequency.
SOLUTION OF TRANSIENT HEAT CONDUCTION PROBLEM BY THE FINITE ELEMENT METHOD
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Süleyman TAŞGETİREN
1995-01-01
Full Text Available Determination of temperature distribution is generally the first step in the design of machine elements subjected to ubnormal temperatures in their service life and for selection of materials. During this heat transfer analysis, the boundary and enviromental conditions must be modeled realistically and the geometry must be well represented. A variety of materials deviating from simple constant property isotropic material to composit materials having different properties according to direction of reinforcements are to be analysed. Then, the finite element method finds a large application area due to its use of same notation in heat transfer analysis and mechanical analysis of elements. In this study, the general formulation of two dimensional transient heat conduction is developed and a sample solution is given for arectangular bar subjected to convection baundary condition.
Alrasyid, Harun; Safi, Fahrudin; Iranata, Data; Chen-Ou, Yu
2017-11-01
This research shows the prediction of shear behavior of High-Strength Reinforced Concrete Columns using Finite-Element Method. The experimental data of nine half scale high-strength reinforced concrete were selected. These columns using specified concrete compressive strength of 70 MPa, specified yield strength of longitudinal and transverse reinforcement of 685 and 785 MPa, respectively. The VecTor2 finite element software was used to simulate the shear critical behavior of these columns. The combination axial compression load and monotonic loading were applied at this prediction. It is demonstrated that VecTor2 finite element software provides accurate prediction of load-deflection up to peak at applied load, but provide similar behavior at post peak load. The shear strength prediction provide by VecTor 2 are slightly conservative compare to test result.
Fracture Capabilities in Grizzly with the extended Finite Element Method (X-FEM)
Energy Technology Data Exchange (ETDEWEB)
Dolbow, John [Idaho National Lab. (INL), Idaho Falls, ID (United States); Zhang, Ziyu [Idaho National Lab. (INL), Idaho Falls, ID (United States); Spencer, Benjamin [Idaho National Lab. (INL), Idaho Falls, ID (United States); Jiang, Wen [Idaho National Lab. (INL), Idaho Falls, ID (United States)
2015-09-01
Efforts are underway to develop fracture mechanics capabilities in the Grizzly code to enable it to be used to perform deterministic fracture assessments of degraded reactor pressure vessels (RPVs). A capability was previously developed to calculate three-dimensional interaction- integrals to extract mixed-mode stress-intensity factors. This capability requires the use of a finite element mesh that conforms to the crack geometry. The eXtended Finite Element Method (X-FEM) provides a means to represent a crack geometry without explicitly fitting the finite element mesh to it. This is effected by enhancing the element kinematics to represent jump discontinuities at arbitrary locations inside of the element, as well as the incorporation of asymptotic near-tip fields to better capture crack singularities. In this work, use of only the discontinuous enrichment functions was examined to see how accurate stress intensity factors could still be calculated. This report documents the following work to enhance Grizzly’s engineering fracture capabilities by introducing arbitrary jump discontinuities for prescribed crack geometries; X-FEM Mesh Cutting in 3D: to enhance the kinematics of elements that are intersected by arbitrary crack geometries, a mesh cutting algorithm was implemented in Grizzly. The algorithm introduces new virtual nodes and creates partial elements, and then creates a new mesh connectivity; Interaction Integral Modifications: the existing code for evaluating the interaction integral in Grizzly was based on the assumption of a mesh that was fitted to the crack geometry. Modifications were made to allow for the possibility of a crack front that passes arbitrarily through the mesh; and Benchmarking for 3D Fracture: the new capabilities were benchmarked against mixed-mode three-dimensional fracture problems with known analytical solutions.
Guo, Hongbo; He, Xiaowei; Liu, Muhan; Zhang, Zeyu; Hu, Zhenhua; Tian, Jie
2017-03-01
Cerenkov luminescence tomography (CLT), as a promising optical molecular imaging modality, can be applied to cancer diagnostic and therapeutic. Most researches about CLT reconstruction are based on the finite element method (FEM) framework. However, the quality of FEM mesh grid is still a vital factor to restrict the accuracy of the CLT reconstruction result. In this paper, we proposed a multi-grid finite element method framework, which was able to improve the accuracy of reconstruction. Meanwhile, the multilevel scheme adaptive algebraic reconstruction technique (MLS-AART) based on a modified iterative algorithm was applied to improve the reconstruction accuracy. In numerical simulation experiments, the feasibility of our proposed method were evaluated. Results showed that the multi-grid strategy could obtain 3D spatial information of Cerenkov source more accurately compared with the traditional single-grid FEM.
Error Analysis of a Finite Element Method for the Space-Fractional Parabolic Equation
Jin, Bangti
2014-01-01
© 2014 Society for Industrial and Applied Mathematics We consider an initial boundary value problem for a one-dimensional fractional-order parabolic equation with a space fractional derivative of Riemann-Liouville type and order α ∈ (1, 2). We study a spatial semidiscrete scheme using the standard Galerkin finite element method with piecewise linear finite elements, as well as fully discrete schemes based on the backward Euler method and the Crank-Nicolson method. Error estimates in the L2(D)- and Hα/2 (D)-norm are derived for the semidiscrete scheme and in the L2(D)-norm for the fully discrete schemes. These estimates cover both smooth and nonsmooth initial data and are expressed directly in terms of the smoothness of the initial data. Extensive numerical results are presented to illustrate the theoretical results.
Kawahara, Mutsuto
2016-01-01
This book focuses on the finite element method in fluid flows. It is targeted at researchers, from those just starting out up to practitioners with some experience. Part I is devoted to the beginners who are already familiar with elementary calculus. Precise concepts of the finite element method remitted in the field of analysis of fluid flow are stated, starting with spring structures, which are most suitable to show the concepts of superposition/assembling. Pipeline system and potential flow sections show the linear problem. The advection–diffusion section presents the time-dependent problem; mixed interpolation is explained using creeping flows, and elementary computer programs by FORTRAN are included. Part II provides information on recent computational methods and their applications to practical problems. Theories of Streamline-Upwind/Petrov–Galerkin (SUPG) formulation, characteristic formulation, and Arbitrary Lagrangian–Eulerian (ALE) formulation and others are presented with practical results so...
Complete Tangent Stiffness for eXtended Finite Element Method by including crack growth parameters
DEFF Research Database (Denmark)
Mougaard, J.F.; Poulsen, P.N.; Nielsen, L.O.
2013-01-01
The eXtended Finite Element Method (XFEM) is a useful tool for modeling the growth of discrete cracks in structures made of concrete and other quasi‐brittle and brittle materials. However, in a standard application of XFEM, the tangent stiffness is not complete. This is a result of not including...... within the same standard nonlinear iterations. This new solution strategy is believed to provide the modeling capabilities to deal with simultaneous growth of several cracks. A cohesive crack modeling is used. The method is applied to a partly cracked XFEM element of linear strain triangle type...... the crack geometry parameters, such as the crack length and the crack direction directly in the virtual work formulation. For efficiency, it is essential to obtain a complete tangent stiffness. A new method in this work is presented to include an incremental form the crack growth parameters on equal terms...
Nonlinear tracking in a diffusion process with a Bayesian filter and the finite element method
DEFF Research Database (Denmark)
Pedersen, Martin Wæver; Thygesen, Uffe Høgsbro; Madsen, Henrik
2011-01-01
become complicated using SMC because Monte Carlo randomness is introduced. The finite element (FE) method solves the Kolmogorov equations of the SDE numerically on a triangular unstructured mesh for which boundary conditions to the state-space are simple to incorporate. The FE approach to nonlinear state...... estimation is suited for off-line data analysis because the computed smoothed state densities, maximum a posteriori parameter estimates and state sequence are deterministic conditional on the finite element mesh and the observations. The proposed method is conceptually similar to existing point...... on the state-space do not in general provide analytical solutions. A widely used numerical approach is the sequential Monte Carlo (SMC) method which relies on stochastic simulations to approximate state densities. For offline analysis, however, accurate smoothed state density and parameter estimation can...
OPTIMIZATION OF I-SECTION PROFILE DESIGN BY THE FINITE ELEMENT METHOD
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Patryk Różyło
2016-03-01
Full Text Available This paper discusses the problem of design optimization for an I-section profile. The optimization process was performed using the Abaqus program. The numerical analysis of a strictly static problem was based on the finite element method. The scope of the analysis involved both determination of stresses and displacements in the profile and structure topology optimization. The main focus of the numerical analysis was put on reducing profile volume while maintaining the same load and similar stresses prior to and after optimization. The solution of the optimization problem is just an example of the potential of using this method in combination with the finite element method in the Abaqus environment. Nowadays numerical analysis is the most effective cost-reducing alternative to experimental tests and it enables structure examination by means of a computer.
Cecka, Cris
2012-01-01
This chapter discusses multiple strategies to perform general computations on unstructured grids, with specific application to the assembly of matrices in finite element methods (FEMs). It reviews and applies two methods for assembly of FEMs to produce and accelerate a FEM model for a nonlinear hyperelastic solid where the assembly, solution, update, and visualization stages are performed solely on the GPU, benefiting from speed-ups in each stage and avoiding costly GPUCPU transfers of data. For each method, the chapter discusses the NVIDIA GPU hardware\\'s limiting resources, optimizations, key data structures, and dependence of the performance with respect to problem size, element size, and GPU hardware generation. Furthermore, this chapter informs potential users of the benefits of GPU technology, provides guidelines to help them implement their own FEM solutions, gives potential speed-ups that can be expected, and provides source code for reference. © 2012 Elsevier Inc. All rights reserved.
Local-gauge finite-element method for electron waves in magnetic fields.
Ueta, Tsuyoshi; Miyagawa, Yuu
2012-08-01
The finite-element method (FEM) has already been extended to analyze transport properties of electron waves of two-dimensional electron systems in magnetic fields. Although many researchers have created new formulations or improvements to this method, few have analyzed how this method is applied to realistic systems. The present paper suggests that conventional formulations of the FEM do not give accurate results for large systems or for strong magnetic fields; in addition, it suggests that the selected gauge significantly influences the numerical results. Furthermore, this paper proposes a conceptually different formulation of the FEM that solves the poor convergence problem. This formulation is simple: matrix elements are multiplied by the Peierls phase in the absence of a magnetic field. To show the advantages of this formulation, numerical examples are presented.
Prediction of the wind turbine performance by using BEM with airfoil data extracted from CFD
DEFF Research Database (Denmark)
Yang, Hua; Shen, Wen Zhong; Xu, Haoran
2014-01-01
and the coefficient of lift and drag is determined by the forces on the blade. The extracted airfoil data are put into a BEM code without further corrections, and the calculated axial and tangential forces are compared to both computations using BEM with Shen's tip loss correction model and experimental data...
BEMS: emissie-eisen voor middelgrote stookinstallaties : Informatie voor de VROM-Inspectie
de Groot GM; IMG
2010-01-01
Het RIVM heeft een overzicht gemaakt van de belangrijkste wijzigingen in het nieuwe Besluit emissieeisen middelgrote stookinstallaties (BEMS) en de consequenties daarvan. Dit is gedaan op verzoek van de VROM-Inspectie, die deze informatie gebruikt om het toezicht op de naleving van het BEMS concreet
The Reliability and Validity of Bem and Allen's Measure of Cross-Situational Consistency.
Greaner, Jackie L.; Penner, Louis A.
1982-01-01
Investigated the reliability and validity of Bem and Allen's cross-situational consistency measuring technique. Results showed low reliability for Bem and Allen's test-retest, high reliability for Snyder's Self-Monitoring Scale, and significant correlation between self-reported academic behavior variability and actual grade variability. (WAS)
Chen, T.; Raju, I. S.
2002-01-01
A coupled finite element (FE) method and meshless local Petrov-Galerkin (MLPG) method for analyzing two-dimensional potential problems is presented in this paper. The analysis domain is subdivided into two regions, a finite element (FE) region and a meshless (MM) region. A single weighted residual form is written for the entire domain. Independent trial and test functions are assumed in the FE and MM regions. A transition region is created between the two regions. The transition region blends the trial and test functions of the FE and MM regions. The trial function blending is achieved using a technique similar to the 'Coons patch' method that is widely used in computer-aided geometric design. The test function blending is achieved by using either FE or MM test functions on the nodes in the transition element. The technique was evaluated by applying the coupled method to two potential problems governed by the Poisson equation. The coupled method passed all the patch test problems and gave accurate solutions for the problems studied.
Finite-Element Methods for Real-Time Simulation of Surgery
Basdogan, Cagatay
2003-01-01
Two finite-element methods have been developed for mathematical modeling of the time-dependent behaviors of deformable objects and, more specifically, the mechanical responses of soft tissues and organs in contact with surgical tools. These methods may afford the computational efficiency needed to satisfy the requirement to obtain computational results in real time for simulating surgical procedures as described in Simulation System for Training in Laparoscopic Surgery (NPO-21192) on page 31 in this issue of NASA Tech Briefs. Simulation of the behavior of soft tissue in real time is a challenging problem because of the complexity of soft-tissue mechanics. The responses of soft tissues are characterized by nonlinearities and by spatial inhomogeneities and rate and time dependences of material properties. Finite-element methods seem promising for integrating these characteristics of tissues into computational models of organs, but they demand much central-processing-unit (CPU) time and memory, and the demand increases with the number of nodes and degrees of freedom in a given finite-element model. Hence, as finite-element models become more realistic, it becomes more difficult to compute solutions in real time. In both of the present methods, one uses approximate mathematical models trading some accuracy for computational efficiency and thereby increasing the feasibility of attaining real-time up36 NASA Tech Briefs, October 2003 date rates. The first of these methods is based on modal analysis. In this method, one reduces the number of differential equations by selecting only the most significant vibration modes of an object (typically, a suitable number of the lowest-frequency modes) for computing deformations of the object in response to applied forces.
A Posteriori Error Estimation for Finite Element Methods and Iterative Linear Solvers
Energy Technology Data Exchange (ETDEWEB)
Melboe, Hallgeir
2001-10-01
This thesis addresses a posteriori error estimation for finite element methods and iterative linear solvers. Adaptive finite element methods have gained a lot of popularity over the last decades due to their ability to produce accurate results with limited computer power. In these methods a posteriori error estimates play an essential role. Not only do they give information about how large the total error is, they also indicate which parts of the computational domain should be given a more sophisticated treatment in order to reduce the error. A posteriori error estimates are traditionally aimed at estimating the global error, but more recently so called goal oriented error estimators have been shown a lot of interest. The name reflects the fact that they estimate the error in user-defined local quantities. In this thesis the main focus is on global error estimators for highly stretched grids and goal oriented error estimators for flow problems on regular grids. Numerical methods for partial differential equations, such as finite element methods and other similar techniques, typically result in a linear system of equations that needs to be solved. Usually such systems are solved using some iterative procedure which due to a finite number of iterations introduces an additional error. Most such algorithms apply the residual in the stopping criterion, whereas the control of the actual error may be rather poor. A secondary focus in this thesis is on estimating the errors that are introduced during this last part of the solution procedure. The thesis contains new theoretical results regarding the behaviour of some well known, and a few new, a posteriori error estimators for finite element methods on anisotropic grids. Further, a goal oriented strategy for the computation of forces in flow problems is devised and investigated. Finally, an approach for estimating the actual errors associated with the iterative solution of linear systems of equations is suggested. (author)
Energy Technology Data Exchange (ETDEWEB)
Kumar, Abhishek; Kollath-Leiß, Krisztina; Kempken, Frank, E-mail: fkempken@bot.uni-kiel.de
2013-08-30
Highlights: •All eukaryotes have at least a single copy of a bem46 ortholog. •The catalytic triad of BEM46 is illustrated using sequence and structural analysis. •We identified indels in the conserved domain of BEM46 protein. •Localization studies of BEM46 protein were carried out using GFP-fusion tagging. -- Abstract: The bud emergence 46 (BEM46) protein from Neurospora crassa belongs to the α/β-hydrolase superfamily. Recently, we have reported that the BEM46 protein is localized in the perinuclear ER and also forms spots close by the plasma membrane. The protein appears to be required for cell type-specific polarity formation in N. crassa. Furthermore, initial studies suggested that the BEM46 amino acid sequence is conserved in eukaryotes and is considered to be one of the widespread conserved “known unknown” eukaryotic genes. This warrants for a comprehensive phylogenetic analysis of this superfamily to unravel origin and molecular evolution of these genes in different eukaryotes. Herein, we observe that all eukaryotes have at least a single copy of a bem46 ortholog. Upon scanning of these proteins in various genomes, we find that there are expansions leading into several paralogs in vertebrates. Usingcomparative genomic analyses, we identified insertion/deletions (indels) in the conserved domain of BEM46 protein, which allow to differentiate fungal classes such as ascomycetes from basidiomycetes. We also find that exonic indels are able to differentiate BEM46 homologs of different eukaryotic lineage. Furthermore, we unravel that BEM46 protein from N. crassa possess a novel endoplasmic-retention signal (PEKK) using GFP-fusion tagging experiments. We propose that three residues namely a serine 188S, a histidine 292H and an aspartic acid 262D are most critical residues, forming a catalytic triad in BEM46 protein from N. crassa. We carried out a comprehensive study on bem46 genes from a molecular evolution perspective with combination of functional
Energy Technology Data Exchange (ETDEWEB)
Neki, I.; Tada, T. [Ishikawajima-Harima Heavy Industries Co. Ltd., Tokyo (Japan)
1996-12-31
This paper reports a method to develop a new finite element by source (FES) for a two-dimensional plane problem and a three-dimensional solid problem as a method to analyze ship body structures. The paper describes development of a plate bending element by using a similar method, and the fundamental principle thereof. The present method can prepare a finite element of an arbitrary shape by simply providing a contact point only on a boundary. It can also derive good calculation accuracy with less number of contact points and elements. These facts are shown by examples of analyses on a square plate, a triangle plate and a semi-circular plate. Particularly, since a plate bending problem has a large order of differential calculus in a governing equation, this method being a semi-analytical method derives a result with very good accuracy even with less number of contact points. A hypothetical boundary method or a hypothetical electric charge method presents not a very high accuracy even if a large number of contact points are provided. This is because the method hypothesizes only a bending moment vertical to the boundary, but does not consider a source of the moment relative to the boundary. In contrast, the present method hypothesizes both of bending and twisting as the sources, hence its accuracy is better than with the above two methods. 5 refs., 11 figs., 7 tabs.