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.
Interpolation theory of anisotropic finite elements and applications
Institute of Scientific and Technical Information of China (English)
CHEN ShaoChun; XIAO LiuChao
2008-01-01
Interpolation theory is the foundation of finite element methods. In this paper, after reviewing some existed interpolation theorems of anisotropic finite element methods, we present a new way to analyse the interpolation error of anisotropic elements based on Newton's formula of polynomial interpolation as well as its applications.
Interpolation theory of anisotropic finite elements and applications
Institute of Scientific and Technical Information of China (English)
2008-01-01
Interpolation theory is the foundation of finite element methods.In this paper,after reviewing some existed interpolation theorems of anisotropic finite element methods,we present a new way to analyse the interpolation error of anisotropic elements based on Newton’s formula of polynomial interpolation as well as its applications.
Finite element analysis theory and application with ANSYS
Moaveni, Saeed
2015-01-01
For courses in Finite Element Analysis, offered in departments of Mechanical or Civil and Environmental Engineering. While many good textbooks cover the theory of finite element modeling, Finite Element Analysis: Theory and Application with ANSYS is the only text available that incorporates ANSYS as an integral part of its content. Moaveni presents the theory of finite element analysis, explores its application as a design/modeling tool, and explains in detail how to use ANSYS intelligently and effectively. Teaching and Learning Experience This program will provide a better teaching and learning experience-for you and your students. It will help: *Present the Theory of Finite Element Analysis: The presentation of theoretical aspects of finite element analysis is carefully designed not to overwhelm students. *Explain How to Use ANSYS Effectively: ANSYS is incorporated as an integral part of the content throughout the book. *Explore How to Use FEA as a Design/Modeling Tool: Open-ended design problems help stude...
Hands on applied finite element analysis application with ANSYS
Arslan, Mehmet Ali
2015-01-01
Hands on Applied Finite Element Analysis Application with Ansys is truly an extraordinary book that offers practical ways of tackling FEA problems in machine design and analysis. In this book, 35 good selection of example problems have been presented, offering students the opportunity to apply their knowledge to real engineering FEA problem solutions by guiding them with real life hands on experience.
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....
Hybrid Fundamental Solution Based Finite Element Method: Theory and Applications
Changyong Cao; Qing-Hua Qin
2015-01-01
An overview on the development of hybrid fundamental solution based finite element method (HFS-FEM) and its application in engineering problems is presented in this paper. The framework and formulations of HFS-FEM for potential problem, plane elasticity, three-dimensional elasticity, thermoelasticity, anisotropic elasticity, and plane piezoelectricity are presented. In this method, two independent assumed fields (intraelement filed and auxiliary frame field) are employed. The formulations for...
Finite Element Program Generator and Its Application in Engineering
Institute of Scientific and Technical Information of China (English)
WANShui; HUHong; CHENJian-pin
2004-01-01
A completely new finite element software, Finite ElementProgram Generator (FEPG), is introduced and its designing thought and organizing structure is presented.FEPG uses the method of components and the technique of artificial intelligence to generate finite element program automatically by a computer according to the general principles of mathematic and internal rules of finite element method,as is similar to the deduction of mathematics.FEPG breaks through the limitation of present finite element software,which only applies to special discipline,while FEPG is suitable for all kinds of differential equations solved by finite element method.Now FEPG has been applied to superconductor research,electromagnetic field study,petroleum exploration,transportation,structure engineering,water conservancy,ship mechanics, solid-liquid coupling problems and liquid dynamics,etc.in China.
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
Thornton, E. A.
1979-01-01
Three practical problems in conduction/forced convection heat transfer are analyzed using a simplified engineering formulation of convective finite elements. Upwind and conventional finite element solutions are compared for steady-state and transient applications.
Hybrid Fundamental Solution Based Finite Element Method: Theory and Applications
Directory of Open Access Journals (Sweden)
Changyong Cao
2015-01-01
Full Text Available An overview on the development of hybrid fundamental solution based finite element method (HFS-FEM and its application in engineering problems is presented in this paper. The framework and formulations of HFS-FEM for potential problem, plane elasticity, three-dimensional elasticity, thermoelasticity, anisotropic elasticity, and plane piezoelectricity are presented. In this method, two independent assumed fields (intraelement filed and auxiliary frame field are employed. The formulations for all cases are derived from the modified variational functionals and the fundamental solutions to a given problem. Generation of elemental stiffness equations from the modified variational principle is also described. Typical numerical examples are given to demonstrate the validity and performance of the HFS-FEM. Finally, a brief summary of the approach is provided and future trends in this field are identified.
Applications of finite element simulation in orthopedic and trauma surgery.
Herrera, Antonio; Ibarz, Elena; Cegoñino, José; Lobo-Escolar, Antonio; Puértolas, Sergio; López, Enrique; Mateo, Jesús; Gracia, Luis
2012-04-18
Research in different areas of orthopedic and trauma surgery requires a methodology that allows both a more economic approach and the ability to reproduce different situations in an easy way. Simulation models have been introduced recently in bioengineering and could become an essential tool in the study of any physiological unity, regardless of its complexity. The main problem in modeling with finite elements simulation is to achieve an accurate reproduction of the anatomy and a perfect correlation of the different structures, in any region of the human body. Authors have developed a mixed technique, joining the use of a three-dimensional laser scanner Roland Picza captured together with computed tomography (CT) and 3D CT images, to achieve a perfect reproduction of the anatomy. Finite element (FE) simulation lets us know the biomechanical changes that take place after hip prostheses or osteosynthesis implantation and biological responses of bone to biomechanical changes. The simulation models are able to predict changes in bone stress distribution around the implant, so allowing preventing future pathologies. The development of a FE model of lumbar spine is another interesting application of the simulation. The model allows research on the lumbar spine, not only in physiological conditions but also simulating different load conditions, to assess the impact on biomechanics. Different degrees of disc degeneration can also be simulated to determine the impact on adjacent anatomical elements. Finally, FE models may be useful to test different fixation systems, i.e., pedicular screws, interbody devices or rigid fixations compared with the dynamic ones. We have also developed models of lumbar spine and hip joint to predict the occurrence of osteoporotic fractures, based on densitometric determinations and specific biomechanical models, including approaches from damage and fracture mechanics. FE simulations also allow us to predict the behavior of orthopedic splints
Finite elements in fracture mechanics theory, numerics, applications
Kuna, Meinhard
2013-01-01
Fracture mechanics has established itself as an important discipline of growing interest to those working to assess the safety, reliability and service life of engineering structures and materials. In order to calculate the loading situation at cracks and defects, nowadays numerical techniques like finite element method (FEM) have become indispensable tools for a broad range of applications. The present monograph provides an introduction to the essential concepts of fracture mechanics, its main goal being to procure the special techniques for FEM analysis of crack problems, which have to date only been mastered by experts. All kinds of static, dynamic and fatigue fracture problems are treated in two- and three-dimensional elastic and plastic structural components. The usage of the various solution techniques is demonstrated by means of sample problems selected from practical engineering case studies. The primary target group includes graduate students, researchers in academia and engineers in practice.
An Application of Finite Element Modelling to Pneumatic Artificial Muscle
Directory of Open Access Journals (Sweden)
R. Ramasamy
2005-01-01
Full Text Available The purpose of this article was to introduce and to give an overview of the Pneumatic Artificial Muscles (PAMs as a whole and to discuss its numerical modelling, using the Finite Element (FE Method. Thus, more information to understand on its behaviour in generating force for actuation was obtained. The construction of PAMs was mainly consists of flexible, inflatable membranes which having orthotropic material behaviour. The main properties influencing the PAMs will be explained in terms of their load-carrying capacity and low weight in assembly. Discussion on their designs and capacity to function as locomotion device in robotics applications will be laid out, followed by FE modelling to represent PAMs overall structural behaviour under any potential operational conditions.
[Application of finite element analysis in Chinese cervical manipulation biomechanics].
Wang, Huihao; Chen, Bo; Zhan, Hongsheng; Wang, Huihao; Chen, Bo; Zhan, Hongsheng
2013-10-01
Clinical advantages of Chinese spinal manipulation therapy (CSMT) were recognized for spinal chronic lesions of soft tissues and bones, such as cervical spondylosis, etc. However, the security of CSMT and the hypotheses of practice mechanisms were questioned for lacking of the relevant basic researches. Researches have proved that these methods could be used to observe the dynamic effects of spine with application of finite element analysis (FEA) computer technology. Combining with other biomechanical experimental methods and applying advanced FEA technology for mechanical problems of CSMT, we may not only find the mechanisms of action and provide theoretical supports for the traditional Chinese therapy, but also standardize the key techniques and optimize the treatment options improving clinical outcomes, and even promote spreading of CSMT. Computer models are ideally suited for studying phenomena that cannot be satisfactorily investigated with other models. However, computer models of CSMT practice remain to be further refined. The results which had been acquired so far not only verified some of the traditional points of view, but also revised and specified some perspectives of the past. This paper intends to review FEA studies with Chinese cervical manipulation therapy (CCMT) for cervical spinal chronic lesions of soft tissues and bones, involving different effects for cervical spine joints (pulling/traction and thrusting) with practice techniques and cervical spine soft tissues (including vessels and its hemodynamics, muscles and fasciae, etc).
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...
Finite element mesh generation
Lo, Daniel SH
2014-01-01
Highlights the Progression of Meshing Technologies and Their ApplicationsFinite Element Mesh Generation provides a concise and comprehensive guide to the application of finite element mesh generation over 2D domains, curved surfaces, and 3D space. Organised according to the geometry and dimension of the problem domains, it develops from the basic meshing algorithms to the most advanced schemes to deal with problems with specific requirements such as boundary conformity, adaptive and anisotropic elements, shape qualities, and mesh optimization. It sets out the fundamentals of popular techniques
Practical Application of Finite Element Analysis to Aircraft Structural Design
1986-08-01
analysis and mechanical properties, including the equivalent inclusion method, elastic constants and internal friction in composites, finite element...intensity factors are not available. The inclusion of fracture constraints in the automated design process is a logical extension of present structural...September 30-Dctober 3, 1975, Proceedings. Volume 1. (A78-19026 06-01) Turin, Libreria Editrice Universitaria Levrotto e Bella, 1975, p. 291-300. In
Stochastic finite element applications in rigid pavement performance
Attoh-Okine, Nii O.
1999-05-01
Rigid pavement structures have uncertainties and variability in their structural layers and components. These variations and uncertainties are seldomly included in performance assessment and evaluation in pavement systems. This paper proposes to use Stochastic Finite Element Method (SFEM) in rigid pavement faulting and load transfer efficiency. The SFEM uses random parameters, as stochastic process namely random fields. These random fields are characterized, quantitatively by spatial functions of statistical moment like the mean, variance and covariance.
Footbridge between finite volumes and finite elements with applications to CFD
Pascal, Frédéric; Ghidaglia, Jean-Michel
2001-12-01
The aim of this paper is to introduce a new algorithm for the discretization of second-order elliptic operators in the context of finite volume schemes on unstructured meshes. We are strongly motivated by partial differential equations (PDEs) arising in computational fluid dynamics (CFD), like the compressible Navier-Stokes equations. Our technique consists of matching up a finite volume discretization based on a given mesh with a finite element representation on the same mesh. An inverse operator is also built, which has the desirable property that in the absence of diffusion, one recovers exactly the finite volume solution. Numerical results are also provided. Copyright
Advanced finite element technologies
Wriggers, Peter
2016-01-01
The book presents an overview of the state of research of advanced finite element technologies. Besides the mathematical analysis, the finite element development and their engineering applications are shown to the reader. The authors give a survey of the methods and technologies concerning efficiency, robustness and performance aspects. The book covers the topics of mathematical foundations for variational approaches and the mathematical understanding of the analytical requirements of modern finite element methods. Special attention is paid to finite deformations, adaptive strategies, incompressible, isotropic or anisotropic material behavior and the mathematical and numerical treatment of the well-known locking phenomenon. Beyond that new results for the introduced approaches are presented especially for challenging nonlinear problems.
Dual Formulations of Mixed Finite Element Methods with Applications.
Gillette, Andrew; Bajaj, Chandrajit
2011-10-01
Mixed finite element methods solve a PDE using two or more variables. The theory of Discrete Exterior Calculus explains why the degrees of freedom associated to the different variables should be stored on both primal and dual domain meshes with a discrete Hodge star used to transfer information between the meshes. We show through analysis and examples that the choice of discrete Hodge star is essential to the numerical stability of the method. Additionally, we define interpolation functions and discrete Hodge stars on dual meshes which can be used to create previously unconsidered mixed methods. Examples from magnetostatics and Darcy flow are examined in detail.
Institute of Scientific and Technical Information of China (English)
Xin-Gao Gong; Lihua Shen; Dier Zhang; Aihui Zhou
2008-01-01
In this paper, both the standard finite element discretization and a two-scale finite element discretization for SchrSdinger equations are studied. The numerical analysis is based on the regularity that is also obtained in this paper for the Schrodinger equations. Very satisfying applications to electronic structure computations are provided, too.
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.
The application of finite element analysis on polydimethylsiloxane
Halim, Siti Aisyah Abdul; Yahud, Shuhaida; Muhamad, Wan Zuki Azman Wan; Daud, Ruslizam; Zain, Noor Alia Md
2015-05-01
An artificial skin should have the similarities of the human skin in term of biomechanical properties. In this paper, Polydimethysiloxane (PDMS) have been chosen as artificial skin material. PDMS specimens were prepared and the hardness of the material will be altered by adding different percentages of diluents to the mixture of the base and a cross-linker component. It indicated that the physiological elastic modulus depends strongly on the definition of the stress-strain curve, mixing ratio and strain rate. Tensile and compression test are conducted to find out the Hyperelastic (HE) coefficient and Young's modulus. These material coefficients will be used to define the constitutive model of PDMS for finite element analysis study. In this paper, three dimensional (3D) finite element (FE) stress and displacement analysis were used. Three types of models with different values of height were simulated in COMSOL MULTIPHYSICS. The analysis of the von Mises stress and surface deflection values revealed that maximum stress and maximum deflection concentration were located in the region near line load. PDMS polymer 10:1 is the softer product and can be commercialized as artificial skin material.
Finite element analysis of (SA) mechanoreceptors in tactile sensing application
N, Syamimi; Yahud, S.
2015-05-01
This paper addresses the structural design of a fingertip model in order to analyse the sensory function of slow adapting (SA) mechanoreceptors by using the finite element analysis (FEA) method. A biologically inspired tactile sensor was designed to mimic a similar response of the human mechanoreceptors in the human glabrous skin. The simulation work was done by using COMSOL Multiphysics. The artificial skin was modelled as a solid square block of silicone elastomer with a semi cylinder protrusion on top. It was modelled as a nearly incompressible and linear hyperelastic material defined by Neo Hookean constitutive law. The sensing element on the other hand was modelled by using constantan alloy mimicking the SA1 receptor. Boundary loads of 1 N/m² to 4 N/m² with the increment of 1 N/m² were applied to the top surface of the protrusion in z and x-direction for normal and shear stress, respectively. The epidermal model base was constrained to maintain the same boundary conditions throughout all simulations. The changes of length experienced by the sensing element were calculated. The simulations result in terms of strain was identified. The simulated result was plotted in terms of sensing element strain against the boundary load and the graph should produce a linear response.
Model order reduction techniques with applications in finite element analysis
Qu, Zu-Qing
2004-01-01
Despite the continued rapid advance in computing speed and memory the increase in the complexity of models used by engineers persists in outpacing them. Even where there is access to the latest hardware, simulations are often extremely computationally intensive and time-consuming when full-blown models are under consideration. The need to reduce the computational cost involved when dealing with high-order/many-degree-of-freedom models can be offset by adroit computation. In this light, model-reduction methods have become a major goal of simulation and modeling research. Model reduction can also ameliorate problems in the correlation of widely used finite-element analyses and test analysis models produced by excessive system complexity. Model Order Reduction Techniques explains and compares such methods focusing mainly on recent work in dynamic condensation techniques: - Compares the effectiveness of static, exact, dynamic, SEREP and iterative-dynamic condensation techniques in producing valid reduced-order mo...
Thornton, E. A.; Decahaumphai, P.; Wieting, A. R.
1980-01-01
An integrated thermal-structural finite element approach for efficient coupling of thermal and structural analysis is presented. An integrated thermal-structural rod element is developed and used in four thermal-structural applications; the accuracy of this integrated approach is illustrated by comparisons with the customary approach of finite difference thermal-finite element structural analyses. Results show that integrated thermal-structural analysis of structures modeled with rod elements is more accurate than conventional analysis, and that its further development promises significant results.
Hashemi-Kia, M.; Toossi, M.
1990-01-01
As a result of this work, a reduction procedure has been developed which can be applied to large finite element model of airframe type structures. This procedure, which is tailored to be used with MSC/NASTRAN finite element code, is applied to the full airframe dynamic finite element model of AH-64A Attack Helicopter. The applicability of the resulting reduced model to parametric and optimization studies is examined. Through application of the design sensitivity analysis, the viability and efficiency of this reduction technique has been demonstrated in a vibration reduction study.
Finite Element Analysis of Wrinkled Membrane Structures for Sunshield Applications
Johnston, John D.; Brodeur, Stephen J. (Technical Monitor)
2002-01-01
The deployable sunshield is an example of a gossamer structure envisioned for use on future space telescopes. The basic structure consists of multiple layers of pretensioned, thin-film membranes supported by deployable booms. The prediction and verification of sunshield dynamics has been identified as an area in need of technology development due to the difficulties inherent in predicting nonlinear structural behavior of the membranes and because of the challenges involved. in ground testing of the full-scale structure. This paper describes a finite element analysis of a subscale sunshield that has been subjected to ground testing in support of the Next Generation Space Telescope (NGST) program. The analysis utilizes a nonlinear material model that accounts for wrinkling of the membranes. Results are presented from a nonlinear static preloading analysis and subsequent dynamics analyses to illustrate baseline sunshield structural characteristics. Studies are then described which provide further insight into the effect of membrane. preload on sunshield dynamics and the performance of different membrane modeling techniques. Lastly, a comparison of analytical predictions and ground test results is presented.
Nakamura, Keiko; Tajima, Kiyoshi; Chen, Ker-Kong; Nagamatsu, Yuki; Kakigawa, Hiroshi; Masumi, Shin-ich
2013-12-01
This study focused on the application of novel finite-element analysis software for constructing a finite-element model from the computed tomography data of a human dentulous mandible. The finite-element model is necessary for evaluating the mechanical response of the alveolar part of the mandible, resulting from occlusal force applied to the teeth during biting. Commercially available patient-specific general computed tomography-based finite-element analysis software was solely applied to the finite-element analysis for the extraction of computed tomography data. The mandibular bone with teeth was extracted from the original images. Both the enamel and the dentin were extracted after image processing, and the periodontal ligament was created from the segmented dentin. The constructed finite-element model was reasonably accurate using a total of 234,644 nodes and 1,268,784 tetrahedral and 40,665 shell elements. The elastic moduli of the heterogeneous mandibular bone were determined from the bone density data of the computed tomography images. The results suggested that the software applied in this study is both useful and powerful for creating a more accurate three-dimensional finite-element model of a dentulous mandible from the computed tomography data without the need for any other software.
Rational bases and generalized barycentrics applications to finite elements and graphics
Wachspress, Eugene
2016-01-01
This three-part volume explores theory for construction of rational interpolation functions for continuous patchwork approximation. Authored by the namesake of the Wachspress Coordinates, the book develops construction of basis functions for a broad class of elements which have widespread graphics and finite element application. Part one is the 1975 book A Rational Finite Element Basis (with minor updates and corrections) written by Dr. Wachspress. Part two describes theoretical advances since 1975 and includes analysis of elements not considered previously. Part three consists of annotated MATLAB programs implementing theory presented in parts one and two.
APPLICATION OF PENALTY FUNCTION METHOD IN ISOPARAMETRIC HYBRID FINITE ELEMENT ANALYSIS
Institute of Scientific and Technical Information of China (English)
CHEN Dao-zheng; JIAO Zhao-ping
2005-01-01
By the aid of the penalty function method, the equilibrium restriction conditions were introduced to the isoparametric hybrid finite element analysis, and the concrete application course of the penalty function method in three-dimensional isoparametric hybrid finite element was discussed. The separated penalty parameters method and the optimal hybrid element model with penalty balance were also presented.The penalty balance method can effectively refrain the parasitical stress on the premise of no additional degrees of freedom. The numeric experiment shows that the presented element not only is effective in improving greatly the numeric calculation precision of distorted grids but also has the universality.
Solution of Finite Element Equations
DEFF Research Database (Denmark)
Krenk, Steen
An important step in solving any problem by the finite element method is the solution of the global equations. Numerical solution of linear equations is a subject covered in most courses in numerical analysis. However, the equations encountered in most finite element applications have some special...
Arya, V. K.; Kaufman, A.
1989-01-01
A description of the finite element implementation of Robinson's unified viscoplastic model into the General Purpose Finite Element Program (MARC) is presented. To demonstrate its application, the implementation is applied to some uniaxial and multiaxial problems. A comparison of the results for the multiaxial problem of a thick internally pressurized cylinder, obtained using the finite element implementation and an analytical solution, is also presented. The excellent agreement obtained confirms the correct finite element implementation of Robinson's model.
Bathe, Klaus-Jürgen
2015-01-01
Finite element procedures are now an important and frequently indispensable part of engineering analyses and scientific investigations. This book focuses on finite element procedures that are very useful and are widely employed. Formulations for the linear and nonlinear analyses of solids and structures, fluids, and multiphysics problems are presented, appropriate finite elements are discussed, and solution techniques for the governing finite element equations are given. The book presents general, reliable, and effective procedures that are fundamental and can be expected to be in use for a long time. The given procedures form also the foundations of recent developments in the field.
Parallel performance of a preconditioned CG solver for unstructured finite element applications
Energy Technology Data Exchange (ETDEWEB)
Shadid, J.N.; Hutchinson, S.A.; Moffat, H.K. [Sandia National Labs., Albuquerque, NM (United States)
1994-12-31
A parallel unstructured finite element (FE) implementation designed for message passing MIMD machines is described. This implementation employs automated problem partitioning algorithms for load balancing unstructured grids, a distributed sparse matrix representation of the global finite element equations and a parallel conjugate gradient (CG) solver. In this paper a number of issues related to the efficient implementation of parallel unstructured mesh applications are presented. These include the differences between structured and unstructured mesh parallel applications, major communication kernels for unstructured CG solvers, automatic mesh partitioning algorithms, and the influence of mesh partitioning metrics on parallel performance. Initial results are presented for example finite element (FE) heat transfer analysis applications on a 1024 processor nCUBE 2 hypercube. Results indicate over 95% scaled efficiencies are obtained for some large problems despite the required unstructured data communication.
A variational method for finite element stress recovery: Applications in one-dimension
Riggs, H. Ronald
1992-09-01
It is well-known that stresses (and strains) calculated by a displacement-based finite element analysis are generally not as accurate as the displacements. In addition, the calculated stress field is typically discontinuous at element interfaces. Because the stresses are typically of more interest than the displacements, several procedures have been proposed to obtain a smooth stress field, given the finite element stresses, and to improve the accuracy. Hinton and Irons introduced global least squares smoothing of discrete data defined on a plane using a finite element formulation. Tessler and co-workers recently developed a conceptually similar formulation for smoothing of two-dimensional data based on a discrete least square approximation with a penalty constraint. The penalty constraint results in a stress field which is C(exp 1)-continuous, a result not previously obtained. The approach requires additional, 'smoothing' finite element analysis and for their two-dimensional application, they used a conforming C(exp 0)-continuous triangular finite element based on a conforming plate element. This paper presents the results of a detailed investigation into the application of Tessler's smoothing procedure to the smoothing of finite element stresses from one-dimensional problems. Although the one-dimensional formulation has some practical applicability, such as in truss, beam, axisymmetric mechanics, and one-dimensional heat conduction, the primary motivation for developing the one-dimensional smoothing case is to explore the characteristics of the general smoothing strategy. In particular, it is used to describe the behavior of the method and to explore the suitability of criteria proposed for the smoothing analysis. Prior to presenting numerical results, the variational formulation of the smoothing strategy is presented and a criterion for the smoothing analysis is described.
Application of a data base management system to a finite element model
Rogers, J. L., Jr.
1980-01-01
In today's software market, much effort is being expended on the development of data base management systems (DBMS). Most commercially available DBMS were designed for business use. However, the need for such systems within the engineering and scientific communities is becoming apparent. A potential DBMS application that appears attractive is the handling of data for finite element engineering models. The applications of a commercially available, business-oriented DBMS to a structural engineering, finite element model is explored. The model, DBMS, an approach to using the DBMS, advantages and disadvantages are described. Plans for research on a scientific and engineering DBMS are discussed.
Chi, Heng; Lopez-Pamies, Oscar; Paulino, Glaucio H.
2016-02-01
This paper presents a new variational principle in finite elastostatics applicable to arbitrary elastic solids that may contain constitutively rigid spatial domains (e.g., rigid inclusions). The basic idea consists in describing the constitutive rigid behavior of a given spatial domain as a set of kinematic constraints over the boundary of the domain. From a computational perspective, the proposed formulation is shown to reduce to a set of algebraic constraints that can be implemented efficiently in terms of both single-field and mixed finite elements of arbitrary order. For demonstration purposes, applications of the proposed rigid-body-constraint formulation are illustrated within the context of elastomers, reinforced with periodic and random distributions of rigid filler particles, undergoing finite deformations.
Abdelal, Gasser F; Gad, Ahmed H
2013-01-01
Designing satellite structures poses an ongoing challenge as the interaction between analysis, experimental testing, and manufacturing phases is underdeveloped. Finite Element Analysis for Satellite Structures: Applications to Their Design, Manufacture and Testing explains the theoretical and practical knowledge needed to perform design of satellite structures. By layering detailed practical discussions with fully developed examples, Finite Element Analysis for Satellite Structures: Applications to Their Design, Manufacture and Testing provides the missing link between theory and implementation. Computational examples cover all the major aspects of advanced analysis; including modal analysis, harmonic analysis, mechanical and thermal fatigue analysis using finite element method. Test cases are included to support explanations an a range of different manufacturing simulation techniques are described from riveting to shot peening to material cutting. Mechanical design of a satellites structures are covered...
Finite element computational fluid mechanics
Baker, A. J.
1983-01-01
Finite element analysis as applied to the broad spectrum of computational fluid mechanics is analyzed. The finite element solution methodology is derived, developed, and applied directly to the differential equation systems governing classes of problems in fluid mechanics. The heat conduction equation is used to reveal the essence and elegance of finite element theory, including higher order accuracy and convergence. The algorithm is extended to the pervasive nonlinearity of the Navier-Stokes equations. A specific fluid mechanics problem class is analyzed with an even mix of theory and applications, including turbulence closure and the solution of turbulent flows.
Finite elements and approximation
Zienkiewicz, O C
2006-01-01
A powerful tool for the approximate solution of differential equations, the finite element is extensively used in industry and research. This book offers students of engineering and physics a comprehensive view of the principles involved, with numerous illustrative examples and exercises.Starting with continuum boundary value problems and the need for numerical discretization, the text examines finite difference methods, weighted residual methods in the context of continuous trial functions, and piecewise defined trial functions and the finite element method. Additional topics include higher o
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. Superconve
Asgharpour, Z; Baumgartner, D; Willinger, R; Graw, M; Peldschus, S
2014-05-01
Traumatic head injuries can result from vehicular accidents, sports, falls or assaults. The current advances in computational methods and the detailed finite element models of the human head provide a significant opportunity for biomechanical study of human head injuries. The biomechanical characteristics of the human head through head impact scenarios can be studied in detail by using the finite element models. Skull fracture is one of the most frequent occurring types of head injuries. The purpose of this study is to analyse the experimental head impacts on cadavers by means of the Strasbourg University Finite Element Head Model (SUFEHM). The results of the numerical model and experimental data are compared for validation purpose. The finite element model has also been applied to predict the skull bone fracture in frontal impacts. The head model includes the scalp, the facial bone, the skull, the cerebral spinal fluid, the meninges, the cerebrum and the cerebellum. The model is used to simulate the experimental frontal head impact tests using a cylindrical padded impactor. Results of the computational simulation shows that the model correlated well with a number of experimental data and a global fracture pattern has been predicted well by the model. Therefore the presented numerical model could be used for reconstruction of head impacts in different impact conditions also the forensic application of the head model would provide a tool for investigation of the causes and mechanism of head injuries.
Some shell formulations, in view of their applicability to finite elements
Debongnie, Jean-François
1986-01-01
Surface geometry and shell geometry, in the frame of general tensor calculus. Fundamentals of the theory of thin shells. Expressing strains from curvilinear components of the displacements. Applicability of the preceeding theory to finite elements. Expressing strains from the cartesian components of the displacements. Moderate rotation theory (curvilinear components). Moderate rotation theory (cartesian components). Quasi-plane and almost-plane shells. Shells with shearing strains (cartesian ...
van de Walle, Axel; Rouleau, Lucie; Deckers, Elke; Desmet, Wim
2015-01-01
In many engineering applications, viscoelastic treatments are used to suppress vibrations of lightly damped structures. Computational methods provide powerful tools for the design and analysis of these structures. The most commonly used method to model the dynamics of complex structures is the finite element method. Its use, however, often results in very large and computationally demanding models, especially when viscoelastic material behaviour has to be taken into account. To alleviate this...
Finite Element Modeling of Dynamic Properties of Power Supply for an Industrial Application
2014-01-01
In this thesis, the dynamic properties of the mechanic structure of Power Supply for an Industrial Application, an Alstom company product, are considered. A finite element model of the Power Supply mechanic structure have been generated with the aid of the MSC Marc software. Based on the FE model; modal analysis have been carried out and the eigenfrequencies and eigenmodes for the FE model have been calculated in a suitable frequency range. Relevant frequency response functions for the FE mod...
Finite element modelling of the foot for clinical application: A systematic review.
Behforootan, Sara; Chatzistergos, Panagiotis; Naemi, Roozbeh; Chockalingam, Nachiappan
2017-01-01
Over the last two decades finite element modelling has been widely used to give new insight on foot and footwear biomechanics. However its actual contribution for the improvement of the therapeutic outcome of different pathological conditions of the foot, such as the diabetic foot, remains relatively limited. This is mainly because finite element modelling has only been used within the research domain. Clinically applicable finite element modelling can open the way for novel diagnostic techniques and novel methods for treatment planning/optimisation which would significantly enhance clinical practice. In this context this review aims to provide an overview of modelling techniques in the field of foot and footwear biomechanics and to investigate their applicability in a clinical setting. Even though no integrated modelling system exists that could be directly used in the clinic and considerable progress is still required, current literature includes a comprehensive toolbox for future work towards clinically applicable finite element modelling. The key challenges include collecting the information that is needed for geometry design, the assignment of material properties and loading on a patient-specific basis and in a cost-effective and non-invasive way. The ultimate challenge for the implementation of any computational system into clinical practice is to ensure that it can produce reliable results for any person that belongs in the population for which it was developed. Consequently this highlights the need for thorough and extensive validation of each individual step of the modelling process as well as for the overall validation of the final integrated system. Copyright © 2016 IPEM. Published by Elsevier Ltd. All rights reserved.
2010-01-01
Finite element analysis is an engineering method for the numerical analysis of complex structures. This book provides a bird's eye view on this very broad matter through 27 original and innovative research studies exhibiting various investigation directions. Through its chapters the reader will have access to works related to Biomedical Engineering, Materials Engineering, Process Analysis and Civil Engineering. The text is addressed not only to researchers, but also to professional engineers, engineering lecturers and students seeking to gain a better understanding of where Finite Element Analysis stands today.
Finite elements of nonlinear continua
Oden, J T
2000-01-01
Geared toward undergraduate and graduate students, this text extends applications of the finite element method from linear problems in elastic structures to a broad class of practical, nonlinear problems in continuum mechanics. It treats both theory and applications from a general and unifying point of view.The text reviews the thermomechanical principles of continuous media and the properties of the finite element method, and then brings them together to produce discrete physical models of nonlinear continua. The mathematical properties of these models are analyzed, along with the numerical s
FINITE ELEMENT ANALYSIS OF STRUCTURES
Directory of Open Access Journals (Sweden)
PECINGINA OLIMPIA-MIOARA
2015-05-01
Full Text Available The application of finite element method is analytical when solutions can not be applied for deeper study analyzes static, dynamic or other types of requirements in different points of the structures .In practice it is necessary to know the behavior of the structure or certain parts components of the machine under the influence of certain factors static and dynamic . The application of finite element in the optimization of components leads to economic growth , to increase reliability and durability organs studied, thus the machine itself.
Application of Bond-Slip in the Finite Element Analyses of Reinforced Concrete Shear Walls
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İlker Kazaz
2012-03-01
Full Text Available Transfer of tensile forces from reinforcing steel into the surrounding concrete affects the behavior of reinforced concrete members. This transfer relies on the bond action between the steel and the concrete. Under monotonic loading the part of bond strength due to chemical adhesion is easily exhausted and bearing against the lugs is the primary load-transfer mechanism at loads near the ultimate. These stresses cause internal cracking of concrete at the steel-concrete interface. This paper deals with the finite element modeling of the bond-slip and its application due to internal cracking of the first layer of concrete surrounding the bar and the bending and/ or cracking of the small concrete teeth near the bar lugs. A previously proposed constitutive steel stress-bond slip relation by Mirza and Houde (1979 was used in finite element analysis of reinforced concrete shear wall specimens and the results were presented.
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...
Real-Time Nonlinear Finite Element Computations on GPU - Application to Neurosurgical Simulation.
Joldes, Grand Roman; Wittek, Adam; Miller, Karol
2010-12-15
Application of biomechanical modeling techniques in the area of medical image analysis and surgical simulation implies two conflicting requirements: accurate results and high solution speeds. Accurate results can be obtained only by using appropriate models and solution algorithms. In our previous papers we have presented algorithms and solution methods for performing accurate nonlinear finite element analysis of brain shift (which includes mixed mesh, different non-linear material models, finite deformations and brain-skull contacts) in less than a minute on a personal computer for models having up to 50.000 degrees of freedom. In this paper we present an implementation of our algorithms on a Graphics Processing Unit (GPU) using the new NVIDIA Compute Unified Device Architecture (CUDA) which leads to more than 20 times increase in the computation speed. This makes possible the use of meshes with more elements, which better represent the geometry, are easier to generate, and provide more accurate results.
Jara-Almonte, J.; Mitchell, L. D.
1988-01-01
The paper covers two distinct parts: theory and application. The goal of this work was the reduction of model size with an increase in eigenvalue/vector accuracy. This method is ideal for the condensation of large truss- or beam-type structures. The theoretical approach involves the conversion of a continuum transfer matrix beam element into an 'Exact' dynamic stiffness element. This formulation is implemented in a finite element environment. This results in the need to solve a transcendental eigenvalue problem. Once the eigenvalue is determined the eigenvectors can be reconstructed with any desired spatial precision. No discretization limitations are imposed on the reconstruction. The results of such a combined finite element and transfer matrix formulation is a much smaller FEM eigenvalue problem. This formulation has the ability to extract higher eigenvalues as easily and as accurately as lower eigenvalues. Moreover, one can extract many more eigenvalues/vectors from the model than the number of degrees of freedom in the FEM formulation. Typically, the number of eigenvalues accurately extractable via the 'Exact' element method are at least 8 times the number of degrees of freedom. In contrast, the FEM usually extracts one accurate (within 5 percent) eigenvalue for each 3-4 degrees of freedom. The 'Exact' element results in a 20-30 improvement in the number of accurately extractable eigenvalues and eigenvectors.
Jara-Almonte, J.; Mitchell, L. D.
1988-01-01
The paper covers two distinct parts: theory and application. The goal of this work was the reduction of model size with an increase in eigenvalue/vector accuracy. This method is ideal for the condensation of large truss- or beam-type structures. The theoretical approach involves the conversion of a continuum transfer matrix beam element into an 'Exact' dynamic stiffness element. This formulation is implemented in a finite element environment. This results in the need to solve a transcendental eigenvalue problem. Once the eigenvalue is determined the eigenvectors can be reconstructed with any desired spatial precision. No discretization limitations are imposed on the reconstruction. The results of such a combined finite element and transfer matrix formulation is a much smaller FEM eigenvalue problem. This formulation has the ability to extract higher eigenvalues as easily and as accurately as lower eigenvalues. Moreover, one can extract many more eigenvalues/vectors from the model than the number of degrees of freedom in the FEM formulation. Typically, the number of eigenvalues accurately extractable via the 'Exact' element method are at least 8 times the number of degrees of freedom. In contrast, the FEM usually extracts one accurate (within 5 percent) eigenvalue for each 3-4 degrees of freedom. The 'Exact' element results in a 20-30 improvement in the number of accurately extractable eigenvalues and eigenvectors.
Weiser, Martin
2016-01-01
All relevant implementation aspects of finite element methods are discussed in this book. The focus is on algorithms and data structures as well as on their concrete implementation. Theory is covered as far as it gives insight into the construction of algorithms. Throughout the exercises a complete FE-solver for scalar 2D problems will be implemented in Matlab/Octave.
Bíró, Oszkár; Koczka, Gergely; Preis, Kurt
2014-05-01
An efficient finite element method to take account of the nonlinearity of the magnetic materials when analyzing three-dimensional eddy current problems is presented in this paper. The problem is formulated in terms of vector and scalar potentials approximated by edge and node based finite element basis functions. The application of Galerkin techniques leads to a large, nonlinear system of ordinary differential equations in the time domain. The excitations are assumed to be time-periodic and the steady-state periodic solution is of interest only. This is represented either in the frequency domain as a finite Fourier series or in the time domain as a set of discrete time values within one period for each finite element degree of freedom. The former approach is the (continuous) harmonic balance method and, in the latter one, discrete Fourier transformation will be shown to lead to a discrete harmonic balance method. Due to the nonlinearity, all harmonics, both continuous and discrete, are coupled to each other. The harmonics would be decoupled if the problem were linear, therefore, a special nonlinear iteration technique, the fixed-point method is used to linearize the equations by selecting a time-independent permeability distribution, the so-called fixed-point permeability in each nonlinear iteration step. This leads to uncoupled harmonics within these steps. As industrial applications, analyses of large power transformers are presented. The first example is the computation of the electromagnetic field of a single-phase transformer in the time domain with the results compared to those obtained by traditional time-stepping techniques. In the second application, an advanced model of the same transformer is analyzed in the frequency domain by the harmonic balance method with the effect of the presence of higher harmonics on the losses investigated. Finally a third example tackles the case of direct current (DC) bias in the coils of a single-phase transformer.
An Object-Oriented Smartphone Application for Structural Finite Element Analysis
Directory of Open Access Journals (Sweden)
B.J. Mac Donald
2014-08-01
Full Text Available Smartphones are becoming increasingly ubiquitous both in general society and the workplace. Recent increases in mobile processing power have shown the current generation of smartphones has equivalent processing power to a supercomputer from the early 1990s. Many industries have abandoned desktop computing and are now entirely reliant on mobile devices. Given these facts it is logical that smartphones are considered as the next platform for finite element analysis (FEA. This paper presents an architecture for a smartphone FEA application using object-oriented programming. A MVC design pattern is adopted and a demonstration FEA application for the Android smartphone platform is presented.
Finite Element Modeling of Five Phase Permanent Magnet BLDC Motor for High Power Density Application
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Kiran George
2013-12-01
Full Text Available Fault-tolerant capability of electrical motor drives is an essential feature in applications such as automotive, aeronautic, and many others. A multi-phase permanent-magnet BLDC motor exhibits a high fault tolerant capability hence increasing the reliability, as it can be designed to reduce the fault occurrence as well as to operate indefinitely in the presence of fault. With multi independent phases, in the event of failure of one or more, the remaining healthy phases let the motor to operate properly. This paper presents finite element modeling and results of a five-phase permanent magnet brushless motor designed for high power density application .
Kumar, Anuruddh; Sharma, Anshul; Kumar, Rajeev; Vaish, Rahul; Chauhan, Vishal S.; Bowen, C. R.
2015-03-01
This paper examines the selection and performance evaluation of a variety of piezoelectric materials for cantilever-based sensor applications. The finite element analysis method is implemented to evaluate the relative importance of materials properties such as Young's Modulus (E), piezoelectric stress constants (e31), dielectric constant (ɛ) and Poisson's ratio (υ) for cantilever-based sensor applications. An analytic hierarchy process (AHP) is used to assign weights to the properties that are studied for the sensor structure under study. A technique for order preference by similarity to ideal solution (TOPSIS) is used to rank the performance of the piezoelectric materials in the context of sensor voltage outputs. The ranking achieved by the TOPSIS analysis is in good agreement with the results obtained from finite element method simulation. The numerical simulations show that K0.5Na0.5NbO3-LiSbO3 (KNN-LS) materials family is important for sensor application. Young's modulus (E) is most influencing material's property followed by piezoelectric constant (e31), dielectric constant (ɛ) and Poisson's ratio (υ) for cantilever-based piezoelectric sensor applications.
Solving the transport equation with quadratic finite elements: Theory and applications
Energy Technology Data Exchange (ETDEWEB)
Ferguson, J.M. [Lawrence Livermore National Lab., CA (United States)
1997-12-31
At the 4th Joint Conference on Computational Mathematics, the author presented a paper introducing a new quadratic finite element scheme (QFEM) for solving the transport equation. In the ensuing year the author has obtained considerable experience in the application of this method, including solution of eigenvalue problems, transmission problems, and solution of the adjoint form of the equation as well as the usual forward solution. He will present detailed results, and will also discuss other refinements of his transport codes, particularly for 3-dimensional problems on rectilinear and non-rectilinear grids.
Adaptive finite element simulation of flow and transport applications on parallel computers
Kirk, Benjamin Shelton
The subject of this work is the adaptive finite element simulation of problems arising in flow and transport applications on parallel computers. Of particular interest are new contributions to adaptive mesh refinement (AMR) in this parallel high-performance context, including novel work on data structures, treatment of constraints in a parallel setting, generality and extensibility via object-oriented programming, and the design/implementation of a flexible software framework. This technology and software capability then enables more robust, reliable treatment of multiscale--multiphysics problems and specific studies of fine scale interaction such as those in biological chemotaxis (Chapter 4) and high-speed shock physics for compressible flows (Chapter 5). The work begins by presenting an overview of key concepts and data structures employed in AMR simulations. Of particular interest is how these concepts are applied in the physics-independent software framework which is developed here and is the basis for all the numerical simulations performed in this work. This open-source software framework has been adopted by a number of researchers in the U.S. and abroad for use in a wide range of applications. The dynamic nature of adaptive simulations pose particular issues for efficient implementation on distributed-memory parallel architectures. Communication cost, computational load balance, and memory requirements must all be considered when developing adaptive software for this class of machines. Specific extensions to the adaptive data structures to enable implementation on parallel computers is therefore considered in detail. The libMesh framework for performing adaptive finite element simulations on parallel computers is developed to provide a concrete implementation of the above ideas. This physics-independent framework is applied to two distinct flow and transport applications classes in the subsequent application studies to illustrate the flexibility of the
The application of finite element analysis in the skull biomechanics and dentistry.
Prado, Felippe Bevilacqua; Rossi, Ana Cláudia; Freire, Alexandre Rodrigues; Ferreira Caria, Paulo Henrique
2014-01-01
Empirical concepts describe the direction of the masticatory stress dissipation in the skull. The scientific evidence of the trajectories and the magnitude of stress dissipation can help in the diagnosis of the masticatory alterations and the planning of oral rehabilitation in the different areas of Dentistry. The Finite Element Analysis (FEA) is a tool that may reproduce complex structures with irregular geometries of natural and artificial tissues of the human body because it uses mathematical functions that enable the understanding of the craniofacial biomechanics. The aim of this study was to review the literature on the advantages and limitations of FEA in the skull biomechanics and Dentistry study. The keywords of the selected original research articles were: Finite element analysis, biomechanics, skull, Dentistry, teeth, and implant. The literature review was performed in the databases, PUBMED, MEDLINE and SCOPUS. The selected books and articles were between the years 1928 and 2010. The FEA is an assessment tool whose application in different areas of the Dentistry has gradually increased over the past 10 years, but its application in the analysis of the skull biomechanics is scarce. The main advantages of the FEA are the realistic mode of approach and the possibility of results being based on analysis of only one model. On the other hand, the main limitation of the FEA studies is the lack of anatomical details in the modeling phase of the craniofacial structures and the lack of information about the material properties.
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.
Finite-Element Software for Conceptual Design
DEFF Research Database (Denmark)
Lindemann, J.; Sandberg, G.; Damkilde, Lars
2010-01-01
and research. Forcepad is an effort to provide a conceptual design and teaching tool in a finite-element software package. Forcepad is a two-dimensional finite-element application based on the same conceptual model as image editing applications such as Adobe Photoshop or Microsoft Paint. Instead of using...
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
The application of finite element method to forward and inverse seismic problems in frequency domain
Energy Technology Data Exchange (ETDEWEB)
Shaoyou, J.; Xiangheng, J.; Shizhe, X.
1987-04-01
Unstable result is obtained when the boundary problem of wave equation is solved using finite element method in time domain. However, when the boundary problem of wave equation is solved by finite element method in frequency domain, not only the unstablity can be avoided but also computation is speeded up because of using FFT. The procedure for solving the boundary problem using finite element method in frequency domain is as follows: 1. the wave equation is transformed into Helmholtz equation by making one-dimensional Fourier transform with respect to time; 2. Helmholtz equation is solved using finite element method in frequency domain; 3. the obtained result is returned to time domain by making inverse Fourier transform. Both forward and inverse seismic problems can be solved by this method.
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.
Directory of Open Access Journals (Sweden)
Jesús López
2015-02-01
Full Text Available In this work, a methodology to create parameterized finite element models is presented, particularly focusing on the development of suitable algorithms in order to generate models and meshes with high computational efficiency. The methodology is applied to the modeling of two common mechanical devices: an optical linear encoder and a gear transmission. This practical application constitutes a tough test to the methodology proposed, given the complexity and the large number of components that set up this high-precision measurement device and the singularity of the internal gears. The geometrical and mechanical particularities of the components lead to multidimensional modeling, seeking to ensure proper interaction between the different types of finite elements. Besides, modeling criteria to create components such as compression and torsion springs, sheet springs, bearings, or adhesive joints are also presented in the article. The last part of the work aims to validate the simulation results obtained with the methodology proposed with those derived from experimental tests through white noise base-driven vibration and hammer impact excitation modal analysis.
Hillerich, B; Nagler, O
2001-11-01
Thermal finite element method (FEM) calculations and SPICE-based dynamic thermal models are used to simulate and optimize the static and dynamic performance of miniaturized oven-controlled crystal oscillators (OCXOs). FEM can be used to generate the values of the SPICE circuit elements. Good agreement is achieved between simulation and measurement. Several application examples, including directly heated OCXOs, are discussed.
Zhao, Bin
2015-02-01
Temperature-pressure coupled field analysis of liquefied petroleum gas (LPG) tank under jet fire can offer theoretical guidance for preventing the fire accidents of LPG tank, the application of super wavelet finite element on it is studied in depth. First, review of related researches on heat transfer analysis of LPG tank under fire and super wavelet are carried out. Second, basic theory of super wavelet transform is studied. Third, the temperature-pressure coupled model of gas phase and liquid LPG under jet fire is established based on the equation of state, the VOF model and the RNG k-ɛ model. Then the super wavelet finite element formulation is constructed using the super wavelet scale function as interpolating function. Finally, the simulation is carried out, and results show that the super wavelet finite element method has higher computing precision than wavelet finite element method.
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.
A globally well-posed finite element algorithm for aerodynamics applications
Iannelli, G. S.; Baker, A. J.
1991-01-01
A finite element CFD algorithm is developed for Euler and Navier-Stokes aerodynamic applications. For the linear basis, the resultant approximation is at least second-order-accurate in time and space for synergistic use of three procedures: (1) a Taylor weak statement, which provides for derivation of companion conservation law systems with embedded dispersion-error control mechanisms; (2) a stiffly stable second-order-accurate implicit Rosenbrock-Runge-Kutta temporal algorithm; and (3) a matrix tensor product factorization that permits efficient numerical linear algebra handling of the terminal large-matrix statement. Thorough analyses are presented regarding well-posed boundary conditions for inviscid and viscous flow specifications. Numerical solutions are generated and compared for critical evaluation of quasi-one- and two-dimensional Euler and Navier-Stokes benchmark test problems.
A simple introduction to the mixed finite element method theory and applications
Gatica, Gabriel N
2014-01-01
The main purpose of this book is to provide a simple and accessible introduction to the mixed finite element method as a fundamental tool to numerically solve a wide class of boundary value problems arising in physics and engineering sciences. The book is based on material that was taught in corresponding undergraduate and graduate courses at the Universidad de Concepcion, Concepcion, Chile, during the last 7 years. As compared with several other classical books in the subject, the main features of the present one have to do, on one hand, with an attempt of presenting and explaining most of the details in the proofs and in the different applications. In particular several results and aspects of the corresponding analysis that are usually available only in papers or proceedings are included here.
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.
DOLFIN: Automated Finite Element Computing
Logg, Anders; 10.1145/1731022.1731030
2011-01-01
We describe here a library aimed at automating the solution of partial differential equations using the finite element method. By employing novel techniques for automated code generation, the library combines a high level of expressiveness with efficient computation. Finite element variational forms may be expressed in near mathematical notation, from which low-level code is automatically generated, compiled and seamlessly integrated with efficient implementations of computational meshes and high-performance linear algebra. Easy-to-use object-oriented interfaces to the library are provided in the form of a C++ library and a Python module. This paper discusses the mathematical abstractions and methods used in the design of the library and its implementation. A number of examples are presented to demonstrate the use of the library in application code.
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.
Element-topology-independent preconditioners for parallel finite element computations
Park, K. C.; Alexander, Scott
1992-01-01
A family of preconditioners for the solution of finite element equations are presented, which are element-topology independent and thus can be applicable to element order-free parallel computations. A key feature of the present preconditioners is the repeated use of element connectivity matrices and their left and right inverses. The properties and performance of the present preconditioners are demonstrated via beam and two-dimensional finite element matrices for implicit time integration computations.
Element-topology-independent preconditioners for parallel finite element computations
Park, K. C.; Alexander, Scott
1992-01-01
A family of preconditioners for the solution of finite element equations are presented, which are element-topology independent and thus can be applicable to element order-free parallel computations. A key feature of the present preconditioners is the repeated use of element connectivity matrices and their left and right inverses. The properties and performance of the present preconditioners are demonstrated via beam and two-dimensional finite element matrices for implicit time integration computations.
Application of the Single Hardening Model in the Finite Element Program ABAQUS
DEFF Research Database (Denmark)
Jakobsen, Kim Parsberg
that several conceptual models, describing the non-linear and irreversible behaviour of soil, have been developed over the last three decades few of them are accessible in commercial finite element programs. In the present study the Single Hardening Model, that is a time independent elastoplastic constitutive...... or in combined deformation and flow problems. Today, many of these problems are solved using various finite element computer softwares, capable of handling both geometric and material non-linearities. The latter is especially important in soil mechanics and soil-structure interaction problems. Despite the feat...... model, developed by Lade and Kim (Kim & Lade 1988, Lade & Kim 1988a, Lade & Kim 1988b) is implemented as a user defined material module, UMAT, in the commercial finite element program, ABAQUS. The advantages of the Single Hardening Model Iie in its ability to predict elastic and plastic displacements...
Application of the Finite Element Method in the Glass Fiber Bushing Research
Institute of Scientific and Technical Information of China (English)
CHEN Song; LU Jiansheng; GUAN Weiming; ZHANG Kunhua; PAN Yong; TAN Zhilong; XIA Lu
2012-01-01
Design and optimization of bushing at present mainly use the traditional experience method.The relevant research that adopts computer simulation to carry on the operation behavior of the bushing has appeared in recent years.How to use the finite element method to research bushing was introduced in the article.Physics fields and many relevant parameters of one real bushing were calculated.Through the results of calculation,it indicate that the finite element method is very useful in bushing research of designing and optimizing.
Robinson, J. C.
1982-01-01
A systematic finite-element model modification technique has been applied to two small problems and a model of the main wing box of a research drone aircraft. The procedure determines the sensitivity of the eigenvalues and eigenvector components to specific structural changes, calculates the required changes and modifies the finite-element model. Good results were obtained where large stiffness modifications were required to satisfy large eigenvalue changes. Sensitivity matrix conditioning problems required the development of techniques to insure existence of a solution and accelerate its convergence. A method is proposed to assist the analyst in selecting stiffness parameters for modification.
Institute of Scientific and Technical Information of China (English)
Tie Zhang; Yan-ping Lin; Robert J.Tait
2002-01-01
In this paper, we present a general error analysis framework for the finite volume element (FVE) approximation to the Ritz-Volterra projection, the Sobolev equations and parabolic integro-differential equations. The main idea in our paper is to consider the FVE methods as perturbations of standard finite element methods which enables us to derive the optimal L2 and H1 norm error estimates, and the L∞ and W1∞ norm error estimates by means of the time dependent Green functions. Our disc ussions also include elliptic and parabolic problems as the special cases.
Numerical computation of transonic flows by finite-element and finite-difference methods
Hafez, M. M.; Wellford, L. C.; Merkle, C. L.; Murman, E. M.
1978-01-01
Studies on applications of the finite element approach to transonic flow calculations are reported. Different discretization techniques of the differential equations and boundary conditions are compared. Finite element analogs of Murman's mixed type finite difference operators for small disturbance formulations were constructed and the time dependent approach (using finite differences in time and finite elements in space) was examined.
Directory of Open Access Journals (Sweden)
Marek Krynke
2013-03-01
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. The methods of modelling the rolling elements in the slewing bearing, in which balls have been 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.
DEFF Research Database (Denmark)
Frederiksson, Per; Gudmundson, Peter; Mikkelsen, Lars Pilgaard
2009-01-01
A framework of finite element equations for strain gradient plasticity is presented. The theoretical framework requires plastic strain degrees of freedom in addition to displacements and a plane strain version is implemented into a commercial finite element code. A couple of different elements...... of quadrilateral type are examined and a few numerical issues are addressed related to these elements as well as to strain gradient plasticity theories in general. Numerical results are presented for an idealized cell model of a metal matrix composite under shear loading. It is shown that strengthening due...... to fiber size is captured but strengthening due to fiber shape is not. A few modelling aspects of this problem are discussed as well. An analytic solution is also presented which illustrates similarities to other theories....
Validation of the 3D finite element transport theory code EVENT for shielding applications
Energy Technology Data Exchange (ETDEWEB)
Warner, Paul [Rolls Royce Power Engineering Plc., Derby (United Kingdom); Oliveira, R.E. de [T. H. Huxley School of Environment, Earth Science and Engineering, Imperial College of Science Technology and Medicine, London (United Kingdom)
2000-03-01
This paper is concerned with the validation of the 3D deterministic neutral-particle transport theory code EVENT for shielding applications. The code is based on the finite element-spherical harmonics (FE-P{sub N}) method which has been extensively developed over the last decade. A general multi-group, anisotropic scattering formalism enables the code to address realistic steady state and time dependent, multi-dimensional coupled neutron/gamma radiation transport problems involving high scattering and deep penetration alike. The powerful geometrical flexibility and competitive computational effort makes the code an attractive tool for shielding applications. In recognition of this, EVENT is currently in the process of being adopted by the UK nuclear industry. The theory behind EVENT is described and its numerical implementation is outlined. Numerical results obtained by the code are compared with predictions of the Monte Carlo code MCBEND and also with the results from benchmark shielding experiments. In particular, results are presented for the ASPIS experimental configuration for both neutron and gamma ray calculations using the BUGLE 96 nuclear data library. (author)
Zain-Ul-Abdein, Muhammad; Ijaz, Hassan; Saleem, Waqas; Raza, Kabeer; Mahfouz, Abdullah Salmeen Bin; Mabrouki, Tarek
2017-07-02
Copper/diamond (Cu/D) composites are famous in thermal management applications for their high thermal conductivity values. They, however, offer some interface related problems like high thermal boundary resistance and excessive debonding. This paper investigates interfacial debonding in Cu/D composites subjected to steady-state and transient thermal cyclic loading. A micro-scale finite element (FE) model was developed from a SEM image of the Cu/20 vol % D composite sample. Several test cases were assumed with respect to the direction of heat flow and the boundary interactions between Cu/uncoated diamonds and Cu/Cr-coated diamonds. It was observed that the debonding behavior varied as a result of the differences in the coefficients of thermal expansions (CTEs) among Cu, diamond, and Cr. Moreover, the separation of interfaces had a direct influence upon the equivalent stress state of the Cu-matrix, since diamond particles only deformed elastically. It was revealed through a fully coupled thermo-mechanical FE analysis that repeated heating and cooling cycles resulted in an extremely high stress state within the Cu-matrix along the diamond interface. Since these stresses lead to interfacial debonding, their computation through numerical means may help in determining the service life of heat sinks for a given application beforehand.
Applications of Taylor-Galerkin finite element method to compressible internal flow problems
Sohn, Jeong L.; Kim, Yongmo; Chung, T. J.
1989-01-01
A two-step Taylor-Galerkin finite element method with Lapidus' artificial viscosity scheme is applied to several test cases for internal compressible inviscid flow problems. Investigations for the effect of supersonic/subsonic inlet and outlet boundary conditions on computational results are particularly emphasized.
Massively Parallel Finite Element Programming
Heister, Timo
2010-01-01
Today\\'s large finite element simulations require parallel algorithms to scale on clusters with thousands or tens of thousands of processor cores. We present data structures and algorithms to take advantage of the power of high performance computers in generic finite element codes. Existing generic finite element libraries often restrict the parallelization to parallel linear algebra routines. This is a limiting factor when solving on more than a few hundreds of cores. We describe routines for distributed storage of all major components coupled with efficient, scalable algorithms. We give an overview of our effort to enable the modern and generic finite element library deal.II to take advantage of the power of large clusters. In particular, we describe the construction of a distributed mesh and develop algorithms to fully parallelize the finite element calculation. Numerical results demonstrate good scalability. © 2010 Springer-Verlag.
Electrical machine analysis using finite elements
Bianchi, Nicola
2005-01-01
OUTLINE OF ELECTROMAGNETIC FIELDSVector AnalysisElectromagnetic FieldsFundamental Equations SummaryReferencesBASIC PRINCIPLES OF FINITE ELEMENT METHODSIntroductionField Problems with Boundary ConditionsClassical Method for the Field Problem SolutionThe Classical Residual Method (Galerkin's Method)The Classical Variational Method (Rayleigh-Ritz's Method)The Finite Element MethodReferencesAPPLICATIONS OF THE FINITE ELEMENT METHOD TO TWO-DIMENSIONAL FIELDSIntroductionLinear Interpolation of the Function fApplication of the Variational MethodSimple Descriptions of Electromagnetic FieldsAppendix: I
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.
Advanced finite element simulation with MSC Marc application of user subroutines
Javanbakht, Zia
2017-01-01
This book offers an in-depth insight into the general-purpose finite element program MSC Marc, which is distributed by MSC Software Corporation. It is a specialized program for nonlinear problems (implicit solver) which is common in academia and industry. The primary goal of this book is to provide a comprehensive introduction to a special feature of this software: the user can write user-subroutines in the programming language Fortran, which is the language of all classical finite element packages. This subroutine feature allows the user to replace certain modules of the core code and to implement new features such as constitutive laws or new elements. Thus, the functionality of commercial codes (‘black box’) can easily be extended by linking user written code to the main core of the program. This feature allows to take advantage of a commercial software package with the flexibility of a ‘semi-open’ code. .
Interval finite element method and its application on anti-slide stability analysis
Institute of Scientific and Technical Information of China (English)
SHAO Guo-jian; SU Jing-bo
2007-01-01
The problem of interval correlation results in interval extension is discussed by the relationship of interval-valued functions and real-valued functions. The methods of reducing interval extension are given. Based on the ideas of the paper, the formulas of sub-interval perturbed finite element method based on the elements are given. The sub-interval amount is discussed and the approximate computation formula is given. At the same time, the computational precision is discussed and some measures of improving computational efficiency are given. Finally, based on sub-interval perturbed finite element method and anti-slide stability analysis method, the formula for computing the bounds of stability factor is given. It provides a basis for estimating and evaluating reasonably anti-slide stability of structures.
Energy Technology Data Exchange (ETDEWEB)
Cwik, T.; Jamnejad, V.; Zuffada, C. [California Institute of Technology, Pasadena, CA (United States)
1994-12-31
The usefulness of finite element modeling follows from the ability to accurately simulate the geometry and three-dimensional fields on the scale of a fraction of a wavelength. To make this modeling practical for engineering design, it is necessary to integrate the stages of geometry modeling and mesh generation, numerical solution of the fields-a stage heavily dependent on the efficient use of a sparse matrix equation solver, and display of field information. The stages of geometry modeling, mesh generation, and field display are commonly completed using commercially available software packages. Algorithms for the numerical solution of the fields need to be written for the specific class of problems considered. Interior problems, i.e. simulating fields in waveguides and cavities, have been successfully solved using finite element methods. Exterior problems, i.e. simulating fields scattered or radiated from structures, are more difficult to model because of the need to numerically truncate the finite element mesh. To practically compute a solution to exterior problems, the domain must be truncated at some finite surface where the Sommerfeld radiation condition is enforced, either approximately or exactly. Approximate methods attempt to truncate the mesh using only local field information at each grid point, whereas exact methods are global, needing information from the entire mesh boundary. In this work, a method that couples three-dimensional finite element (FE) solutions interior to the bounding surface, with an efficient integral equation (IE) solution that exactly enforces the Sommerfeld radiation condition is developed. The bounding surface is taken to be a surface of revolution (SOR) to greatly reduce computational expense in the IE portion of the modeling.
A new cortical thickness mapping method with application to an in vivo finite element model.
Kim, Young Ho; Kim, Jong-Eun; Eberhardt, Alan W
2014-01-01
Finite element modelling of musculoskeletal systems, with geometrical structures constructed from computed tomography (CT) scans, is a useful and powerful tool for biomechanical studies. The use of CT scans from living human subjects, however, is still limited. Accurate reconstruction of thin cortical bone structures from CT scans of living human subjects is especially problematic, due to low CT resolution that results from mandatory low radiation doses and/or involuntary movements of the subject. In this study, a new method for mapping cortical thickness is described. Using the method, cortical thickness measurements of a coxal (pelvis) bone obtained from CT scans of a cadaver were mapped to the coxal geometry as obtained through CT scans of a live human subject, resulting in accurate cortical thickness while maintaining geometric fidelity of the live subject. The mapping procedure includes shape-preserving parameterisation, mesh movement and interpolation of thickness using a search algorithm. The methodology is applicable to modelling of other bones where accurate cortical thickness is needed and for which such data exist.
Application of scaled boundary finite element method in static and dynamic fracture problems
Institute of Scientific and Technical Information of China (English)
Zhenjun Yang
2006-01-01
The scaled boundary finite element method (SBFEM) is a recently developed numerical method combining advantages of both finite element methods (FEM)and boundary element methods (BEM) and with its own special features as well. One of the most prominent advantages is its capability of calculating stress intensity factors (SIFs) directly from the stress solutions whose singularities at crack tips are analytically represented. This advantage is taken in this study to model static and dynamic fracture problems. For static problems, a remeshing algorithm as simple as used in the BEM is developed while retaining the generality and flexibility of the FEM. Fully-automatic modelling of the mixed-mode crack propagation is then realised by combining the remeshing algorithm with a propagation criterion.F0r dynamic fracture problems, a newly developed series-increasing solution to the SBFEM governing equations in the frequency domain is applied to calculate dynamic SIFs. Three plane problems are modelled. The numerical results show that the SBFEM can accurately predict static and dynamic SIFs, cracking paths and load-displacement curves, using only a fraction of degrees of freedom generally needed by the traditional finite element methods.
Finite element simulations with ANSYS workbench 15 theory, applications, case studies
Lee, Huei-Huang
2014-01-01
Finite Element Simulations with ANSYS Workbench 15 is a comprehensive and easy to understand workbook. It utilizes step-by-step instructions to help guide you to learn finite element simulations. Twenty seven real world case studies are used throughout the book. Many of these cases are industrial or research projects you build from scratch. An accompanying DVD contains all the files you may need if you have trouble. Relevant background knowledge is reviewed whenever necessary. To be efficient, the review is conceptual rather than mathematical, short, yet comprehensive. Key concepts are inserted whenever appropriate and summarized at the end of each chapter. Additional exercises or extension research problems are provided as homework at the end of each chapter. A learning approach emphasizing hands-on experiences spreads through this entire book. A typical chapter consists of 6 sections. The first two provide two step-by-step examples. The third section tries to complement the exercises by providing a more sy...
A Finite Element Cable Model and Its Applications Based on the Cubic Spline Curve
Institute of Scientific and Technical Information of China (English)
方子帆; 贺青松; 向兵飞; 肖化攀; 何孔德; 杜义贤
2013-01-01
For accurate prediction of the deformation of cable in the towed system, a new finite element model is presented that provides a representation of both the bending and torsional effects. In this paper, the cubic spline interpolation function is applied as the trial solution. By using a weighted residual approach, the discretized motion equations for the new finite element model are developed. The model is calculated with the computation program complier by Matlab. Several numerical examples are presented to illustrate the numerical schemes. The results of numerical simulation are stable and valid, and consistent with the mechanical properties of the cable. The model can be applied to kinematics analysis and the design of ocean cable, such as mooring lines, towing, and ROV umbilical cables.
Mitchell, Lawrence
2016-01-01
The implementation of efficient multigrid preconditioners for elliptic partial differential equations (PDEs) is a challenge due to the complexity of the resulting algorithms and corresponding computer code. For sophisticated finite element discretisations on unstructured grids an efficient implementation can be very time consuming and requires the programmer to have in-depth knowledge of the mathematical theory, parallel computing and optimisation techniques on manycore CPUs. In this paper we show how the development of bespoke multigrid preconditioners can be simplified significantly by using a framework which allows the expression of the each component of the algorithm at the correct abstraction level. Our approach (1) allows the expression of the finite element problem in a language which is close to the mathematical formulation of the problem, (2) guarantees the automatic generation and efficient execution of parallel optimised low-level computer code and (3) is flexible enough to support different abstra...
Marwala, Tshilidzi
2010-01-01
Finite element models (FEMs) are widely used to understand the dynamic behaviour of various systems. FEM updating allows FEMs to be tuned better to reflect measured data and may be conducted using two different statistical frameworks: the maximum likelihood approach and Bayesian approaches. Finite Element Model Updating Using Computational Intelligence Techniques applies both strategies to the field of structural mechanics, an area vital for aerospace, civil and mechanical engineering. Vibration data is used for the updating process. Following an introduction a number of computational intelligence techniques to facilitate the updating process are proposed; they include: • multi-layer perceptron neural networks for real-time FEM updating; • particle swarm and genetic-algorithm-based optimization methods to accommodate the demands of global versus local optimization models; • simulated annealing to put the methodologies into a sound statistical basis; and • response surface methods and expectation m...
Finite element simulations with ANSYS workbench 17 theory, applications, case studies
Lee, Huei-Huang
2017-01-01
Finite Element Simulations with ANSYS Workbench 17 is a comprehensive and easy to understand workbook. Printed in full color, it utilizes rich graphics and step-by-step instructions to guide you through learning how to perform finite element simulations using ANSYS Workbench. Twenty seven real world case studies are used throughout the book. Many of these case studies are industrial or research projects that you build from scratch. Prebuilt project files are available for download should you run into any problems. Companion videos, that demonstrate exactly how to perform each tutorial, are also available. Relevant background knowledge is reviewed whenever necessary. To be efficient, the review is conceptual rather than mathematical. Key concepts are inserted whenever appropriate and summarized at the end of each chapter. Additional exercises or extension research problems are provided as homework at the end of each chapter. A learning approach emphasizing hands-on experiences spreads though this entire boo...
Institute of Scientific and Technical Information of China (English)
SHEN Xiao-wen; YU Hang-ping; ZOU Wei
2008-01-01
.The incidence rate of cervical spondylosis is high,and due to the complicacy of cervical vertebra structure, irregularity of shapes and non-uniformity of components, sometimes it's difficult to achieve planned objectives by experiments in vitro through stress and strain analysis. Besides, the biomechanical factors are of vital significance in the cause of spinal disorders. In this paper the author makes a summary of the present modeling of human cervical vertebra and describes the major methods of establishing the finite element model of human cervical vertebra through several self-constructed models. With the advance of computer technology, the finite element methods have been rapidly developed in cervical vertebra biomechanical researches and have became a major approach for biomechanical researches to simulate more and more clinical conditions.
Tamma, Kumar K.; Namburu, Raju R.
1990-01-01
The present paper describes recent advances and trends in finite element developments and applications for solidification problems. In particular, in comparison to traditional methods of approach, new enthalpy-based architectures based on a generalized trapezoidal family of representations are presented which provide different perspectives, physical interpretation and solution architectures for effective numerical simulation of phase change processes encountered in solidification problems. Various numerical test models are presented and the results support the proposition for employing such formulations for general phase change applications.
Villanueva Perez, Carlos Hernan
Computational design optimization provides designers with automated techniques to develop novel and non-intuitive optimal designs. Topology optimization is a design optimization technique that allows for the evolution of a broad variety of geometries in the optimization process. Traditional density-based topology optimization methods often lack a sufficient resolution of the geometry and physical response, which prevents direct use of the optimized design in manufacturing and the accurate modeling of the physical response of boundary conditions. The goal of this thesis is to introduce a unified topology optimization framework that uses the Level Set Method (LSM) to describe the design geometry and the eXtended Finite Element Method (XFEM) to solve the governing equations and measure the performance of the design. The methodology is presented as an alternative to density-based optimization approaches, and is able to accommodate a broad range of engineering design problems. The framework presents state-of-the-art methods for immersed boundary techniques to stabilize the systems of equations and enforce the boundary conditions, and is studied with applications in 2D and 3D linear elastic structures, incompressible flow, and energy and species transport problems to test the robustness and the characteristics of the method. A comparison of the framework against density-based topology optimization approaches is studied with regards to convergence, performance, and the capability to manufacture the designs. Furthermore, the ability to control the shape of the design to operate within manufacturing constraints is developed and studied. The analysis capability of the framework is validated quantitatively through comparison against previous benchmark studies, and qualitatively through its application to topology optimization problems. The design optimization problems converge to intuitive designs and resembled well the results from previous 2D or density-based studies.
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.
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
Indian Academy of Sciences (India)
K Mallick; K K Sharma
2001-03-01
A new space-domain operator based on the shape function concept of finite element analysis has been developed to derive the residual maps of the Gorda Plate of western United States. The technique does not require explicit assumptions on isostatic models. Besides delineating the Gorda Plate boundary, the residual maps exhibit a close match both in their anomaly patterns and magnitudes with previously computed residual maps based on the theory of isostasy.
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
Application of a floating point systems AP190L array processor to finite element analysis
Energy Technology Data Exchange (ETDEWEB)
Young, R.C.
1982-04-01
This report discusses the implementation of a finite element program on a Floating Point Systems AP190L array processor attached to a Univac 1182 host computer. The array processor was used to perform all calculations on the global system of linear equations including matrix assembly, matrix factoring and vector solution. A large scratch disk was attached directly to the array processor for storing the factored matrix. The remaining calculations, including data preparation, element matrix formation, stress integration and output display were performed by the host computer.
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.
Institute of Scientific and Technical Information of China (English)
Jun Liu; Zheng Nan; Ping Yi
2012-01-01
In the last decade,three dimensional discontinuous deformation analyses (3D DDA) has attracted more and more attention of researchers and geotechnical engineers worldwide.The original DDA formulation utilizes a linear displacement function to describe the block movement and deformation,which would cause block expansion under rigid body rotation and thus limit its capability to model block deformation.In this paper,3D DDA is coupled with tetrahedron finite elements to tackle these two problems.Tetrahedron is the simplest in the 3D domain and makes it easy to implement automatic discretization,even for complex topology shape.Furthermore,element faces will remain planar and element edges will remain straight after deformation for tetrahedron finite elements and polyhedral contact detection schemes can be used directly.The matrices of equilibrium equations for this coupled method are given in detail and an effective contact searching algorithm is suggested.Validation is conducted by comparing the results of the proposed coupled method with that of physical model tests using one of the most common failure modes,i.e.,wedge failure.Most of the failure modes predicted by the coupled method agree with the physical model results except for 4 cases out of the total 65 cases.Finally,a complex rockslide example demonstrates the robustness and versatility of the coupled method.
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
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
Bucki, Marek; Payan, Yohan; 10.1016/j.media.2010.02.003
2010-01-01
Finite Element mesh generation remains an important issue for patient specific biomechanical modeling. While some techniques make automatic mesh generation possible, in most cases, manual mesh generation is preferred for better control over the sub-domain representation, element type, layout and refinement that it provides. Yet, this option is time consuming and not suited for intraoperative situations where model generation and computation time is critical. To overcome this problem we propose a fast and automatic mesh generation technique based on the elastic registration of a generic mesh to the specific target organ in conjunction with element regularity and quality correction. This Mesh-Match-and-Repair (MMRep) approach combines control over the mesh structure along with fast and robust meshing capabilities, even in situations where only partial organ geometry is available. The technique was successfully tested on a database of 5 pre-operatively acquired complete femora CT scans, 5 femoral heads partially...
Application of Wavelet Finite Element Method to Simulation of the Temperature Field of Copier Paper
Institute of Scientific and Technical Information of China (English)
无
2002-01-01
Simulation of the temperature field of copier paper in copier fusing is very important for improving the fusing property of reprography. The temperature field of copier paper varies with a high gradient when the copier paper is moving through the fusing rollers. By means of conventional shaft elements, the high gradient temperature variety causes the oscillation of the numerical solution. Based on the Daubechies scaling functions, a kind of wavelet-based element is constructed for the above problem. The temperature field of the copier paper moving through the fusing rollers is simulated using the two methods. Comparison of the results shows the advantages of the wavelet finite element method,which provides a new method for improving the copier properties.
Second order tensor finite element
Oden, J. Tinsley; Fly, J.; Berry, C.; Tworzydlo, W.; Vadaketh, S.; Bass, J.
1990-01-01
The results of a research and software development effort are presented for the finite element modeling of the static and dynamic behavior of anisotropic materials, with emphasis on single crystal alloys. Various versions of two dimensional and three dimensional hybrid finite elements were implemented and compared with displacement-based elements. Both static and dynamic cases are considered. The hybrid elements developed in the project were incorporated into the SPAR finite element code. In an extension of the first phase of the project, optimization of experimental tests for anisotropic materials was addressed. In particular, the problem of calculating material properties from tensile tests and of calculating stresses from strain measurements were considered. For both cases, numerical procedures and software for the optimization of strain gauge and material axes orientation were developed.
Institute of Scientific and Technical Information of China (English)
Yi-rang Yuan
2007-01-01
For a coupled system of multiplayer dynamics of fluids in porous media,the characteristic finite element domain decomposition procedures applicable to parallel arithmetic are put forward.Techniques such as calculus of variations,domain decomposition,characteristic method,negative norm estimate,energy method and the theory of prior estimates are adopted.Optimal order estimates in L2 norm are derived for the error in the approximate solution.
Infinite to finite: An overview of finite element analysis
Directory of Open Access Journals (Sweden)
Srirekha A
2010-01-01
Full Text Available The method of finite elements was developed at perfectly right times; growing computer capacities, growing human skills and industry demands for ever faster and cost effective product development providing unlimited possibilities for the researching community. This paper reviews the basic concept, current status, advances, advantages, limitations and applications of finite element method (FEM in restorative dentistry and endodontics. Finite element method is able to reveal the otherwise inaccessible stress distribution within the tooth-restoration complex and it has proven to be a useful tool in the thinking process for the understanding of tooth biomechanics and the biomimetic approach in restorative dentistry. Further improvement of the non-linear FEM solutions should be encouraged to widen the range of applications in dental and oral health science.
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 ...
Kingan, Michael J.; Yang, Yi; Mace, Brian R.
2016-09-01
This paper concerns the prediction of sound transmission through a cylindrical structure. The problem considered is that of sound generated by a line source located exterior to a two-dimensional circular cylinder which produces sound waves which transmit through the cylinder to an internal medium. An analytical solution is presented for the case of sound transmission through a thin cylindrical shell, by modelling the shell response using the Flugge- Byrne-Lur'ye equations. This solution is then compared to calculations where the response of the cylinder is calculated using the Wave and Finite Element (WFE) method. The WFE method involves modelling a small segment of a structure using traditional finite element (FE) methods. The mass and stiffness matrices of the segment are then used to calculate the response of the structure to excitation by an acoustic field. The WFE approach for calculating sound transmission is validated by comparison with the analytic solution. Formulating analytic solutions for more complicated structures can be cumbersome whereas using a numerical technique, such as the WFE method, is relatively straightforward.
A high-accuracy optical linear algebra processor for finite element applications
Casasent, D.; Taylor, B. K.
1984-01-01
Optical linear processors are computationally efficient computers for solving matrix-matrix and matrix-vector oriented problems. Optical system errors limit their dynamic range to 30-40 dB, which limits their accuray to 9-12 bits. Large problems, such as the finite element problem in structural mechanics (with tens or hundreds of thousands of variables) which can exploit the speed of optical processors, require the 32 bit accuracy obtainable from digital machines. To obtain this required 32 bit accuracy with an optical processor, the data can be digitally encoded, thereby reducing the dynamic range requirements of the optical system (i.e., decreasing the effect of optical errors on the data) while providing increased accuracy. This report describes a new digitally encoded optical linear algebra processor architecture for solving finite element and banded matrix-vector problems. A linear static plate bending case study is described which quantities the processor requirements. Multiplication by digital convolution is explained, and the digitally encoded optical processor architecture is advanced.
Expanded Mixed Multiscale Finite Element Methods and Their Applications for Flows in Porous Media
Jiang, L.
2012-01-01
We develop a family of expanded mixed multiscale finite element methods (MsFEMs) and their hybridizations for second-order elliptic equations. This formulation expands the standard mixed multiscale finite element formulation in the sense that four unknowns (hybrid formulation) are solved simultaneously: pressure, gradient of pressure, velocity, and Lagrange multipliers. We use multiscale basis functions for both the velocity and the gradient of pressure. In the expanded mixed MsFEM framework, we consider both separable and nonseparable spatial scales. Specifically, we analyze the methods in three categories: periodic separable scales, G-convergent separable scales, and a continuum of scales. When there is no scale separation, using some global information can significantly improve the accuracy of the expanded mixed MsFEMs. We present a rigorous convergence analysis of these methods that includes both conforming and nonconforming formulations. Numerical results are presented for various multiscale models of flow in porous media with shale barriers that illustrate the efficacy of the proposed family of expanded mixed MsFEMs. © 2012 Society for Industrial and Applied Mathematics.
A stabilized finite element formulation for liquid shells and its application to lipid bilayers
Sauer, Roger A.; Duong, Thang X.; Mandadapu, Kranthi K.; Steigmann, David J.
2017-02-01
This paper presents a new finite element (FE) formulation for liquid shells that is based on an explicit, 3D surface discretization using C1-continuous finite elements constructed from NURBS interpolation. Both displacement-based and mixed displacement/pressure FE formulations are proposed. The latter is needed for area-incompressible material behavior, where penalty-type regularizations can lead to misleading results. In order to obtain quasi-static solutions for liquid shells devoid of shear stiffness, several numerical stabilization schemes are proposed based on adding stiffness, adding viscosity or using projection. Several numerical examples are considered in order to illustrate the accuracy and the capabilities of the proposed formulation, and to compare the different stabilization schemes. The presented formulation is capable of simulating non-trivial surface shapes associated with tube formation and protein-induced budding of lipid bilayers. In the latter case, the presented formulation yields non-axisymmetric solutions, which have not been observed in previous simulations. It is shown that those non-axisymmetric shapes are preferred over axisymmetric ones.
Directory of Open Access Journals (Sweden)
Reem Yassine
2016-12-01
Full Text Available The frequency response function is a quantitative measure used in structural analysis and engineering design; hence, it is targeted for accuracy. For a large structure, a high number of substructures, also called cells, must be considered, which will lead to a high amount of computational time. In this paper, the recursive method, a finite element method, is used for computing the frequency response function, independent of the number of cells with much lesser time costs. The fundamental principle is eliminating the internal degrees of freedom that are at the interface between a cell and its succeeding one. The method is applied solely for free (no load nodes. Based on the boundary and interior degrees of freedom, the global dynamic stiffness matrix is computed by means of products and inverses resulting with a dimension the same as that for one cell. The recursive method is demonstrated on periodic structures (cranes and buildings under harmonic vibrations. The method yielded a satisfying time decrease with a maximum time ratio of 1 18 and a percentage difference of 19%, in comparison with the conventional finite element method. Close values were attained at low and very high frequencies; the analysis is supported for two types of materials (steel and plastic. The method maintained its efficiency with a high number of forces, excluding the case when all of the nodes are under loads.
Zhong, Jianghong; Tian, Jie; Yang, Xin; Qin, Chenghu
2010-01-01
Only a planar bioluminescence image acquired from an ordinary cooled charge-coupled device (CCD) array every time, how to re-establish the three-dimensional small animal shape and light intensity distribution on the surface has become urgent to be solved as a bottleneck of bioluminescence tomography (BLT) reconstruction. In this paper, a finite element algorithm to solve the Dirichlet type problem for the first order Hamilton-Jacobi equation related to the shape-fromshading model is adopted. The algorithm outputting the globally maximal solution of the above problem avoids cumbersome boundary conditions on the interfaces between light and shadows and the use of additional information on the surface. The results of the optimization method are satisfied. It demonstrates the feasibility and potential of the finite element shape-fromshading (FE-SFS) model for reconstructing the small animal surface that lays one of key foundations for a fast low-cost application of the BLT in the next future.
Applications of 3D finite element modeling to the study of ventricular physiology
Moulton, Michael J.; Creswell, Lawrence L.; Hu, Ning S.; Actis, Ricardo L.; Myers, Kent W.; Szabo, Barna A.; Pasque, Michael K.
1995-05-01
A 3D, nonlinear finite element (FE) model of the diastolic canine heart was constructed from multislice magnetic resonance images (MRI). The model was solved using the p-version of the FE method to predict stress and deformation in diastole. Finite element models were employed in an 'inverse' problem to estimate the nonlinear material properties of intact diastolic myocardium. Additionally, FE models were employed to examine the effects of RV pressure overload on LV pressure-volume (P- V) relationships in the pathologic heart. A 3D, nonlinear FE model had 1,704 degrees of freedom and 8 elements, it had a maximum principal stress value of 429,127 dynes/cm2 and a minimum principal stress of -344,599 dynes/cm2 at p equals 6. Average nonlinear material parameters estimated for 6 dogs were E equals 28,722 +/- 15,984 dynes/cm2 and c equals 0.00182 +/- 0.00232 cm2/dyne. Examination of the effects of RV pressure increase on LV P-V relationships indicated substantially different effects of RV pressure overload on the different pathologic conditions (p < 0.005 by ANOVA) with increasing RV pressure having a more pronounced effect on the dilated heart than the hypertrophied heart. When the mechanical effects of the pericardium were included in the model, at higher RV pressures, all of the pressure-volume (P-V) curves became similar indicating that at higher RV pressures, the P-V curves were independent of ventricular shape and material properties and depended only on the RV pressure. In conclusion, FE models of the heart were constructed from MRI images of the heart and were employed to study diastolic ventricular function in the normal and pathologic heart.
Lagache, Jean-Marie; Assaf, Samir; Schulte, Christian
2008-02-01
The present study addresses the modal synthesis of dynamic responses or receptances, which can be considered as a major issue in vibratory or acoustic design. A new method termed "method of orthocomplement" offers to increase the accuracy of modal superposition. Two apparently independent domains are considered: first, the numerical control of round-off errors in finite-dimensional models; second, the regularization of modal boundary discontinuities in infinite-dimensional formulations. Concerning the finite-dimensional systems, using the proposed method in conjunction with pseudo-inversion theorems, proves that "inertia relief corrections" remedy modal truncation problems in singular floating systems, just as static corrections do for simply supported systems. The proof is based on hitherto unpublished expressions of inertial contributions in terms of orthogonal projectors. It is worth noting that such expressions present by themselves some technical interest. Modal formulae being delivered in closed form, a thorough analysis of errors becomes possible. Special "spectrograms" are introduced to appraise the convergence of ordinary or modified modal sums. When applied to infinite-dimensional modal boundary discontinuities, the method of orthocomplement eliminates the Gibbs oscillations that affect the ordinary spectral sums, and produces the same corrected formulae as it did for finite-dimensional examples. Effective solutions for the computation of vibratory or acoustic boundary receptances, are developed in that way. The paper once again illustrates how orthogonal projectors can contribute to the determination of static corrections. Future applications to coupling problems, model reduction and modal synthesis are briefly presented at the end of the text.
Finite Element Computational Dynamics of Rotating Systems
Directory of Open Access Journals (Sweden)
Jaroslav Mackerle
1999-01-01
Full Text Available This bibliography lists references to papers, conference proceedings and theses/dissertations dealing with finite element analysis of rotor dynamics problems that were published in 1994–1998. It contains 319 citations. Also included, as separate subsections, are finite element analyses of rotor elements – discs, shafts, spindles, and blades. Topics dealing with fracture mechanics, contact and stability problems of rotating machinery are also considered in specific sections. The last part of the bibliography presents papers dealing with specific industrial applications.
Babuska, Ivo
2010-01-01
The paper addresses a numerical method for solving second order elliptic partial differential equations that describe fields inside heterogeneous media. The scope is general and treats the case of rough coefficients, i.e. coefficients with values in $L^\\infty(\\Omega)$. This class of coefficients includes as examples media with micro-structure as well as media with multiple non-separated length scales. The approach taken here is based on the the generalized finite element method (GFEM) introduced in \\cite{107}, and elaborated in \\cite{102}, \\cite{103} and \\cite{104}. The GFEM is constructed by partitioning the computational domain $\\Omega$ into to a collection of preselected subsets $\\omega_{i},i=1,2,..m$ and constructing finite dimensional approximation spaces $\\Psi_{i}$ over each subset using local information. The notion of the Kolmogorov $n$-width is used to identify the optimal local approximation spaces. These spaces deliver local approximations with errors that decay almost exponentially with the degree...
Hidalgo, Homero, Jr.
2000-01-01
An innovative methodology for determining structural target mode selection and mode selection based on a specific criterion is presented. An effective approach to single out modes which interact with specific locations on a structure has been developed for the X-33 Launch Vehicle Finite Element Model (FEM). We presented Root-Sum-Square (RSS) displacement method computes resultant modal displacement for each mode at selected degrees of freedom (DOF) and sorts to locate modes with highest values. This method was used to determine modes, which most influenced specific locations/points on the X-33 flight vehicle such as avionics control components, aero-surface control actuators, propellant valve and engine points for use in flight control stability analysis and for flight POGO stability analysis. Additionally, the modal RSS method allows for primary or global target vehicle modes to also be identified in an accurate and efficient manner.
Energy Technology Data Exchange (ETDEWEB)
Jeong, Hyun Jo; Kim, Tae Ho [Wonkwang University, Iksan (Korea, Republic of); Lee, Seung Seok; Kim, Young Kil [KRISS, Daejeon (Korea, Republic of)
2008-04-15
The generation of axisymmetric Lamb waves and interaction with wall thinning (corrosion) defects in hollow cylinders are simulated using the finite element method. Guided wave interaction with defects in cylinders is challenged by the multi-mode dispersion and the mode conversion. In this paper, two longitudinal, axisymmetric modes are generated using the concept of a time-delay periodic ring arrays (TDPRA), which makes use of the constructive/destructive interference concept to achieve the unidirectional emission and reception of guided waves. The axisymmetric scattering by the wall thinning extending in full circumference of a cylinder is studied with a two-dimensional FE simulation. The effect of wall thinning depth, axial extension, and the edge shape on the reflections of guided waves is discussed.
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ROMERO,VICENTE J.; SWILER,LAURA PAINTON; GIUNTA,ANTHONY A.
2000-04-25
This paper examines the modeling accuracy of finite element interpolation, kriging, and polynomial regression used in conjunction with the Progressive Lattice Sampling (PLS) incremental design-of-experiments approach. PLS is a paradigm for sampling a deterministic hypercubic parameter space by placing and incrementally adding samples in a manner intended to maximally reduce lack of knowledge in the parameter space. When combined with suitable interpolation methods, PLS is a formulation for progressive construction of response surface approximations (RSA) in which the RSA are efficiently upgradable, and upon upgrading, offer convergence information essential in estimating error introduced by the use of RSA in the problem. The three interpolation methods tried here are examined for performance in replicating an analytic test function as measured by several different indicators. The process described here provides a framework for future studies using other interpolation schemes, test functions, and measures of approximation quality.
Bedingham, W; Neavin, T D
1991-01-01
A commercial finite element modeling program (FIDAP) was adapted to compute the fluid dynamics of laminar blood flow around an intra-arterial catheter and/or sensor probe. The model provided an accurate transient solution to the Navier-Stokes equations under pulsatile blood flow conditions. To simulate the compliance in the catheter tubing set, a second order convolution integral was incorporated into the boundary conditions. The saline drip rate and catheter compliance could be specified, and the bulk blood flow, blood pressure, and heart rate were varied to simulate specific patient conditions. Analysis of the transient solution was used to assess probable sites for thrombus activation and deposition. The transient velocity and pressure fields identified regions of separated flow and recirculation. The computed shear rates and stresses were used to predict hemolysis, platelet activation, and thrombus formation. Analysis of particle paths provided an estimate of residence times and thrombus deposition sites.
Development and application of a three-dimensional finite element vapor intrusion model.
Pennell, Kelly G; Bozkurt, Ozgur; Suuberg, Eric M
2009-04-01
Details of a three-dimensional finite element model of soil vapor intrusion, including the overall modeling process and the stepwise approach, are provided. The model is a quantitative modeling tool that can help guide vapor intrusion characterization efforts. It solves the soil gas continuity equation coupled with the chemical transport equation, allowing for both advective and diffusive transport. Three-dimensional pressure, velocity, and chemical concentration fields are produced from the model. Results from simulations involving common site features, such as impervious surfaces, porous foundation sub-base material, and adjacent structures are summarized herein. The results suggest that site-specific features are important to consider when characterizing vapor intrusion risks. More importantly, the results suggest that soil gas or subslab gas samples taken without proper regard for particular site features may not be suitable for evaluating vapor intrusion risks; rather, careful attention needs to be given to the many factors that affect chemical transport into and around buildings.
Institute of Scientific and Technical Information of China (English)
LI Yifeng; LIN Zhiqi; LI Guofeng; WANG Yun
2012-01-01
A method was presented to extend the Convolution Perfectly Matched Layer （CPML）, which bases on the complex coordinates transformation and complex frequency shifted stretched- coordinate metrics, to the 2D acoustic equation calculated with the method of Finite Element Method （FEM）. This non-physical layer is used at the computational edge of a FEM as an Ab- sorbing Boundary Condition （ABC） to truncate unbounded media. In this paper, the CPML equations have been presented in frequency domain and in time domain, respectively, and the calculations have been realized in the FEM software of COMSOL. The main advantage of CPML over the classical PML layer is that it is based on the unsplit components of the wave field leading to a more stable, highly effective absorption and a more facility to realize. The results of numerical simulation demonstrate that CPML has better absorbability than PML and it absorbs the out~oin~ energy more effectivelv.
DEFF Research Database (Denmark)
Martínez Pañeda, Emilio; Niordson, Christian Frithiof; Bardella, Lorenzo
2016-01-01
A novel general purpose Finite Element framework is presented to study small-scale metal plasticity. A distinct feature of the adopted distortion gradient plasticity formulation, with respect to strain gradient plasticity theories, is the constitutive inclusion of the plastic spin, as proposed...... by Gurtin (2004) through the prescription of a free energy dependent on Nye’s dislocation density tensor. The proposed numerical scheme is developed by following and extending the mathematical principles established by Fleck and Willis (2009). The modeling of thin metallic foils under bending reveals......, if either viscoplasticity or isotropic hardening are included in the model. In order to study the effect of dissipative higher-order stresses, the mechanical response under non-proportional loading is also investigated....
Abdul-Aziz, Ali; Baaklini, George Y.; Bhatt, Ramakrishna T.
2001-01-01
Two- and three-dimensional finite element analyses were performed on uncoated and thermal barrier coated (TBC) silicon nitride plates with and without internal cooling by air. Steady-state heat-transfer analyses were done to optimize the size and the geometry of the cooling channels to reduce thermal stresses, and to evaluate the thermal environment experienced by the plate during burner rig testing. The limited experimental data available were used to model the thermal profile exerted by the flame on the plate. Thermal stress analyses were performed to assess the stress response due to thermal loading. Contours for the temperature and the representative stresses for the plates were generated and presented for different cooling hole sizes and shapes. Analysis indicates that the TBC experienced higher stresses, and the temperature gradient was much reduced when the plate was internally cooled by air. The advantages and disadvantages of several cooling channel layouts were evaluated.
Mitchell, Lawrence; Müller, Eike Hermann
2016-12-01
The implementation of efficient multigrid preconditioners for elliptic partial differential equations (PDEs) is a challenge due to the complexity of the resulting algorithms and corresponding computer code. For sophisticated (mixed) finite element discretisations on unstructured grids an efficient implementation can be very time consuming and requires the programmer to have in-depth knowledge of the mathematical theory, parallel computing and optimisation techniques on manycore CPUs. In this paper we show how the development of bespoke multigrid preconditioners can be simplified significantly by using a framework which allows the expression of the each component of the algorithm at the correct abstraction level. Our approach (1) allows the expression of the finite element problem in a language which is close to the mathematical formulation of the problem, (2) guarantees the automatic generation and efficient execution of parallel optimised low-level computer code and (3) is flexible enough to support different abstraction levels and give the programmer control over details of the preconditioner. We use the composable abstractions of the Firedrake/PyOP2 package to demonstrate the efficiency of this approach for the solution of strongly anisotropic PDEs in atmospheric modelling. The weak formulation of the PDE is expressed in Unified Form Language (UFL) and the lower PyOP2 abstraction layer allows the manual design of computational kernels for a bespoke geometric multigrid preconditioner. We compare the performance of this preconditioner to a single-level method and hypre's BoomerAMG algorithm. The Firedrake/PyOP2 code is inherently parallel and we present a detailed performance analysis for a single node (24 cores) on the ARCHER supercomputer. Our implementation utilises a significant fraction of the available memory bandwidth and shows very good weak scaling on up to 6,144 compute cores.
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Johannesson, G; Glaser, R E; Lee, C L; Nitao, J J; Hanley, W G
2005-02-07
Estimating unknown system configurations/parameters by combining system knowledge gained from a computer simulation model on one hand and from observed data on the other hand is challenging. An example of such inverse problem is detecting and localizing potential flaws or changes in a structure by using a finite-element model and measured vibration/displacement data. We propose a probabilistic approach based on Bayesian methodology. This approach does not only yield a single best-guess solution, but a posterior probability distribution over the parameter space. In addition, the Bayesian approach provides a natural framework to accommodate prior knowledge. A Markov chain Monte Carlo (MCMC) procedure is proposed to generate samples from the posterior distribution (an ensemble of likely system configurations given the data). The MCMC procedure proposed explores the parameter space at different resolutions (scales), resulting in a more robust and efficient procedure. The large-scale exploration steps are carried out using coarser-resolution finite-element models, yielding a considerable decrease in computational time, which can be a crucial for large finite-element models. An application is given using synthetic displacement data from a simple cantilever beam with MCMC exploration carried out at three different resolutions.
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Rieben, R; White, D; Rodrigue, G
2004-01-13
In this paper we motivate the use of a novel high order time domain vector finite element method that is of arbitrary order accuracy in space and up to 5th order accurate in time; and in particular, we apply it to the case of photonic band-gap (PBG) structures. Such structures have been extensively studied in the literature with several practical applications; in particular, for the low loss transmission of electromagnetic energy around sharp 90 degree bends [1]. Typically, such structures are simulated via a numerical solution of Maxwell's equations either in the frequency domain or directly in the time domain over a computational grid. The majority of numerical simulations performed for such structures make use of the widely popular finite difference time domain (FDTD) method [2], where the time dependent electric and magnetic fields are discretized over a ''dual'' grid to second order accuracy in space and time. However, such methods do not generalize to unstructured, non-orthogonal grids or to higher order spatial discretization schemes. To simulate more complicated structures with curved boundaries, such as the structure of [3], a cell based finite element method with curvilinear elements is preferred over standard stair-stepped Cartesian meshes; and to more efficiently reduce the effects of numerical dispersion, a higher order method is highly desirable. In this paper, the high order basis functions of [5] are used in conjunction with the high order energy conserving symplectic time integration algorithms of [6] resulting in a high order, fully mimetic, mixed vector finite element method.
Latest Trends in Finite Element Analysis
Directory of Open Access Journals (Sweden)
L. S. Madhav
1996-01-01
Full Text Available This paper highlights the advances in computer graphics and the computational power of the processors which have promoted a method of analysis, applicable to almost all the fields of engineering. The advantages of the computers have been judiciously used in the design of algorithms, based on the principles of finite difference, finite element, boundary element, etc., intended for the analysis of engineering components. The concept of finite element method which has been generalised with the availability of commercial software, is also reviewed with a special emphasis on the future trends. The modelling and visualisation techniques have also been discussed with an inner perspective on future of visual display of multidimensional complex information. The application of these techniques in some fields is also indicated.
The Relation of Finite Element and Finite Difference Methods
Vinokur, M.
1976-01-01
Finite element and finite difference methods are examined in order to bring out their relationship. It is shown that both methods use two types of discrete representations of continuous functions. They differ in that finite difference methods emphasize the discretization of independent variable, while finite element methods emphasize the discretization of dependent variable (referred to as functional approximations). An important point is that finite element methods use global piecewise functional approximations, while finite difference methods normally use local functional approximations. A general conclusion is that finite element methods are best designed to handle complex boundaries, while finite difference methods are superior for complex equations. It is also shown that finite volume difference methods possess many of the advantages attributed to finite element methods.
Institute of Scientific and Technical Information of China (English)
Feng Zhang; Yonglin Xiong; Sheng Zhang; Bin Ye
2014-01-01
In this paper, a finite element method (FEM)-based multi-phase problem based on a newly proposed thermal elastoplastic constitutive model for saturated/unsaturated geomaterial is discussed. A program of FEM named as SOFT, adopting unified field equations for thermo-hydro-mechanical-air (THMA) behavior of geomaterial and using finite element-finite difference (FE-FD) scheme for soilewatereair three-phase coupling problem, is used in the numerical simulation. As an application of the newly proposed numerical method, two engineering problems, one for slope failure in unsaturated model ground and another for in situ heating test related to deep geological repository of high-level radioactive waste (HLRW), are simulated. The model tests on slope failure in unsaturated Shirasu ground, carried out by Kitamura et al. (2007), is simulated in the framework of soilewatereair three-phase coupling under the condition of constant temperature. While the in situ heating test reported by Munoz (2006) is simulated in the same framework under the conditions of variable temperature but constant air pressure. © 2014 Institute of Rock and Soil Mechanics, Chinese Academy of Sciences. Production and hosting by Elsevier B.V. All rights reserved.
Finite Element Analysis of System-Level Electronic Packages for Space Applications
Directory of Open Access Journals (Sweden)
Adrien Lambert
2015-01-01
Full Text Available Thermal analysis was required in order to aid in the design and testing of a radiation tolerant computing (RTC system using a radiation sensor. During development of the system, different test beds were employed in order to characterize the radiation sensor and its supporting electronic systems. The most common preliminary tests are high altitude balloon tests which allow the sensor to experience cosmic radiation at high altitudes, consistent with space flight operations. In this study, finite element analysis (FEA was used to evaluate primary system architecture, system support structures, and the flight payload in order to determine if the system would survive preliminary and future testing. ANSYS FEA software was used to create thermal models which accurately simulated convective cooling, system heat generation, and solar radiation loading on the exterior of the payload. The results of the models were then used to optimize payload PC board (PCB design to ensure that the internal electronic systems would be within acceptable operating temperatures.
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Gelinas, R.J.; Doss, S.K.; Miller, K.
1981-03-01
The moving finite element (MFE) method has been reduced to practice in the automatic solution program DYLA for general systems of transient partial differential equations (PDEs) in 1-D. Several test examples are presented which illustrate the unique node movement and systematic control features which are intrinsic in the MFE method. Computational dilemmas of numerical diffusion, Gibbs overshooting and undershooting, zone tangling, and grid remap (or re-connection) aliasing, which occur frequently in conventional PDE methods, are essentially eliminated in the MFE mehtod. Arbitrarily large gradients (or shocks) can be solved with extremely high resolution and accuracy for non-coincident, or even counterdirected, propagating wavefronts. Boundary layers of arbitrarily small dimensions are solved with high accuracy simultaneously with the large-scale structures in reactive and non-reactive fluid calculations. The MFE method requires a small fraction of the grid nodes which are used in conventional PDE solution methods because the nodes migrate continuously and systematically to those positions where they are most needed in order to yield accurate PDE solutions on entire problem domains. Courant--Friedrichs--Lewy time-step limits are exceeded by wide margins (by factors of two to several thousand). Finally, the extension of the MFE method to 2-D is briefly discussed.
Application of finite-element sensitivities to power cable thermal field analysis
Energy Technology Data Exchange (ETDEWEB)
Al-Saud, M.S.; El-Kady, M.A.; Findlay, R.D. [McMaster Univ., Hamilton, ON (Canada). Dept. of Electrical and Computer Engineering
2006-07-01
A new approach for calculating the thermal field and ampacity of electrical cables was presented. The proposed perturbed finite-element analysis technique provides sensitivity information of the cable ampacity with respect to fluctuations in the cable thermal circuit parameters. As such, it can assess the effects on the permissible cable loading caused by these fluctuations without repeating the entire thermal analysis when parameters of the thermal circuit of power cables change according to geographical and seasonal variations. The technique can be applied to the design phase and the operational aspects of power cables buried in complex media of soil, heat sources and sinks or other variable boundary conditions. The sensitivity information is useful in determining the important and non-important parameter variations in terms of their relative effect on the cable temperature and ampacity. This paper described the analytical and computational aspects of the sensitivity methodology and demonstrated the usefulness of the developed methodology in 6 directly buried cable systems under different loading, soil and atmospheric conditions. The sensitivity results showed that the variations of the thermal conductivity of the soil affects the cable temperatures more than variations of other parameters. 8 refs., 5 tabs., 5 figs.
Valero, C.; Javierre, E.; García-Aznar, J. M.; Gómez-Benito, M. J.
2015-01-01
SUMMARY Wound healing is a process driven by biochemical and mechanical variables in which new tissue is synthesised to recover original tissue functionality. Wound morphology plays a crucial role in this process, as the skin behaviour is not uniform along different directions. In this work we simulate the contraction of surgical wounds, which can be characterised as elongated and deep wounds. Due to the regularity of this morphology, we approximate the evolution of the wound through its cross-section, adopting a plane strain hypothesis. This simplification reduces the complexity of the computational problem while maintaining allows for a thorough analysis of the role of wound depth in the healing process, an aspect of medical and computational relevance that has not yet been addressed. To reproduce wound contraction we consider the role of fibroblasts, myofibroblasts, collagen and a generic growth factor. The contraction phenomenon is driven by cell-generated forces. We postulate that these forces are adjusted to the mechanical environment of the tissue where cells are embedded through a mechanosensing and mechanotransduction mechanism. To solve the non-linear problem we use the Finite Element Method and an updated Lagrangian approach to represent the change in the geometry. To elucidate the role of wound depth and width on the contraction pattern and evolution of the involved species, we analyse different wound geometries with the same wound area. We find that deeper wounds contract less and reach a maximum contraction rate earlier than superficial wounds. PMID:24443355
Valero, C; Javierre, E; García-Aznar, J M; Gómez-Benito, M J
2014-06-01
Wound healing is a process driven by biochemical and mechanical variables in which a new tissue is synthesised to recover original tissue functionality. Wound morphology plays a crucial role in this process, as the skin behaviour is not uniform along different directions. In this work, we simulate the contraction of surgical wounds, which can be characterised as elongated and deep wounds. Because of the regularity of this morphology, we approximate the evolution of the wound through its cross section, adopting a plane strain hypothesis. This simplification reduces the complexity of the computational problem; while allows for a thorough analysis of the role of wound depth in the healing process, an aspect of medical and computational relevance that has not yet been addressed. To reproduce wound contraction, we consider the role of fibroblasts, myofibroblasts, collagen and a generic growth factor. The contraction phenomenon is driven by cell-generated forces. We postulate that these forces are adjusted to the mechanical environment of the tissue where cells are embedded through a mechanosensing and mechanotransduction mechanism. To solve the nonlinear problem, we use the finite element method (FEM) and an updated Lagrangian approach to represent the change in the geometry. To elucidate the role of wound depth and width on the contraction pattern and evolution of the involved species, we analyse different wound geometries with the same wound area. We find that deeper wounds contract less and reach a maximum contraction rate earlier than superficial wounds. Copyright © 2014 John Wiley & Sons, Ltd.
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Quinones, Armando, Sr. (Arquin Corporation, La Luz, NM); Bibeau, Tiffany A.; Ho, Clifford Kuofei
2008-08-01
Finite-element analyses were performed to simulate the response of a hypothetical vertical masonry wall subject to different lateral loads with and without continuous horizontal filament ties laid between rows of concrete blocks. A static loading analysis and cost comparison were also performed to evaluate optimal materials and designs for the spacers affixed to the filaments. Results showed that polypropylene, ABS, and polyethylene (high density) were suitable materials for the spacers based on performance and cost, and the short T-spacer design was optimal based on its performance and functionality. Simulations of vertical walls subject to static loads representing 100 mph winds (0.2 psi) and a seismic event (0.66 psi) showed that the simulated walls performed similarly and adequately when subject to these loads with and without the ties. Additional simulations and tests are required to assess the performance of actual walls with and without the ties under greater loads and more realistic conditions (e.g., cracks, non-linear response).
Application of the wave finite element method to reinforced concrete structures with damage
El Masri, Evelyne; Ferguson, Neil; Waters, Timothy
2016-09-01
Vibration based methods are commonly deployed to detect structural damage using sensors placed remotely from potential damage sites. Whilst many such techniques are modal based there are advantages to adopting a wave approach, in which case it is essential to characterise wave propagation in the structure. The Wave Finite Element method (WFE) is an efficient approach to predicting the response of a composite waveguide using a conventional FE model of a just a short segment. The method has previously been applied to different structures such as laminated plates, thinwalled structures and fluid-filled pipes. In this paper, the WFE method is applied to a steel reinforced concrete beam. Dispersion curves and wave mode shapes are first presented from free wave solutions, and these are found to be insensitive to loss of thickness in a single reinforcing bar. A reinforced beam with localised damage is then considered by coupling an FE model of a short damaged segment into the WFE model of the undamaged beam. The fundamental bending, torsion and axial waves are unaffected by the damage but some higher order waves of the cross section are significantly reflected close to their cut-on frequencies. The potential of this approach for detecting corrosion and delamination in reinforced concrete beams will be investigated in future work.
Finite elements for analysis and design
Akin, J E; Davenport, J H
1994-01-01
The finite element method (FEM) is an analysis tool for problem-solving used throughout applied mathematics, engineering, and scientific computing. Finite Elements for Analysis and Design provides a thoroughlyrevised and up-to-date account of this important tool and its numerous applications, with added emphasis on basic theory. Numerous worked examples are included to illustrate the material.Key Features* Akin clearly explains the FEM, a numerical analysis tool for problem-solving throughout applied mathematics, engineering and scientific computing* Basic theory has bee
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...
Selective Smoothed Finite Element Method
Institute of Scientific and Technical Information of China (English)
无
2007-01-01
The paper examines three selective schemes for the smoothed finite element method (SFEM) which was formulated by incorporating a cell-wise strain smoothing operation into the standard compatible finite element method (FEM). These selective SFEM schemes were formulated based on three selective integration FEM schemes with similar properties found between the number of smoothing cells in the SFEM and the number of Gaussian integration points in the FEM. Both scheme 1 and scheme 2 are free of nearly incompressible locking, but scheme 2 is more general and gives better results than scheme 1. In addition, scheme 2 can be applied to anisotropic and nonlinear situations, while scheme 1 can only be applied to isotropic and linear situations. Scheme 3 is free of shear locking. This scheme can be applied to plate and shell problems. Results of the numerical study show that the selective SFEM schemes give more accurate results than the FEM schemes.
A finite element model of the foot and ankle for automotive impact applications.
Shin, Jaeho; Yue, Neng; Untaroiu, Costin D
2012-12-01
A finite element (FE) model of the foot and leg was developed to improve understanding of injury mechanisms of the ankle and subtalar joints during vehicle collisions and to aid in the design of injury countermeasures. The FE model was developed based on the reconstructed geometry of a male volunteer close to the anthropometry of a 50th percentile male and a commercial anatomical database. While the forefoot bones were defined as rigid bodies connected by ligament models, the surrounding bones of the ankle and subtalar joints and the leg bones were modeled as deformable structures. The material and structural properties were selected based on a synthesis of current knowledge of the constitutive models for each tissue. The whole foot and leg model was validated in different loading conditions including forefoot impact, axial rotation, dorsiflexion, and combined loadings. Overall results obtained in the model validation indicated improved biofidelity relative to previous FE models. The developed model was used to investigate the injury tolerance of the ankle joint under brake pedal loading for internally and externally rotated feet. Ligament failures were predicted as the main source of injury in this loading condition. A 12% variation of failure moment was observed in the range of axial foot rotations (±15°). The most vulnerable position was the internally rotated (15°) posture among three different foot positions. Furthermore, the present foot and ankle model will be coupled together with other body region FE models into the state-of-art human FE model to be used in the field of automotive safety.
Fwu, Peter Tramyeon
The medical image is very complex by its nature. Modeling built upon the medical image is challenging due to the lack of analytical solution. Finite element method (FEM) is a numerical technique which can be used to solve the partial differential equations. It utilized the transformation from a continuous domain into solvable discrete sub-domains. In three-dimensional space, FEM has the capability dealing with complicated structure and heterogeneous interior. That makes FEM an ideal tool to approach the medical-image based modeling problems. In this study, I will address the three modeling in (1) photon transport inside the human breast by implanting the radiative transfer equation to simulate the diffuse optical spectroscopy imaging (DOSI) in order to measurement the percent density (PD), which has been proven as a cancer risk factor in mammography. Our goal is to use MRI as the ground truth to optimize the DOSI scanning protocol to get a consistent measurement of PD. Our result shows DOSI measurement is position and depth dependent and proper scanning scheme and body configuration are needed; (2) heat flow in the prostate by implementing the Penne's bioheat equation to evaluate the cooling performance of regional hypothermia during the robot assisted radical prostatectomy for the individual patient in order to achieve the optimal cooling setting. Four factors are taken into account during the simulation: blood abundance, artery perfusion, cooling balloon temperature, and the anatomical distance. The result shows that blood abundance, prostate size, and anatomical distance are significant factors to the equilibrium temperature of neurovascular bundle; (3) shape analysis in hippocampus by using the radial distance mapping, and two registration methods to find the correlation between sub-regional change to the age and cognition performance, which might not reveal in the volumetric analysis. The result gives a fundamental knowledge of normal distribution in young
Chen, Si; Xu, Tian-min; Lou, Hang-di; Rong, Qi-guo
2012-12-01
To get individualized facial three-dimensional finite element (FE) model from transformation of a generic one to assist orthodontic analysis and prediction of treatment-related morphological change of facial soft tissue. A generic three-dimensional FE model of craniofacial soft and hard tissue was constructed based on a volunteer's spiral CT data. Seven pairs of main peri-oral muscles were constructed based on a combination of CT image and anatomical method. Individualized model could be obtained through transformation of the generic model based on selection of corresponding anatomical landmarks and radial basis functions (RBF) method. Validation was analyzed through superimposition of the transformed model and cone-beam CT (CBCT) reconstruction data. Pre- and post-treatment CBCT data of two patients were collected, which were superimposed to gain the amount of anterior teeth retraction and anterior alveolar surface remodeling that could be used as boundary condition. Different values of Poisson ratio ν and Young's modulus E were tested during simulation. Average deviation was 0.47 mm and 0.75 mm in the soft and hard tissue respectively. It could be decreased to a range of +0.29 mm and -0.21 mm after a second transformation at the lip-mouth region. The best correspondence between simulation and post-treatment result was found with elastic properties of soft tissues defined as follows. Poisson ratio ν for skin, muscle and fat being set as 0.45 while Young's modulus being set as 90.0 kPa, 6.2 kPa and 2.0 kPa respectively. Individualized three-dimensional facial FE model could be obtained through mathematical model transformation. With boundary condition defined according to treatment plan such FE model could be used to analyze the effect of orthodontic treatment on facial soft tissue.
Directory of Open Access Journals (Sweden)
Tie Ming
2012-02-01
Full Text Available Recent trends of structural mechanics applications in finite element analysis demonstrate an increasing demand for efficient analysis tools. This paper presents a probabilistic analysis approach applied in finite element analysis for modeling prestressed inverted T-beams with web openings structure used in building service system (mechanical, electrical, communications, and plumbing. The experimental program reported in this paper tested four prestressed inverted T-beams with circular web openings to failure to evaluate the openings' effect on various beam behaviors. Using ANSYS, finite element models were developed to simulate beam deflection behavior. Comparison of analytical results with the available experimental results for loaddeflection relationships showed good agreement between both results. Probabilistic analysis methodology could predict the response (i.e., deflection, stress, strain etc due to various combination of input variables (i.e., Poisson`s ratio, modulus of elasticity, etc. In reality, uncertainties exist in a system and environment that may make the application of deterministic design unreliable which causes the values of the variables that are acting on the system cannot be predicted with certainty. As such, probabilistic approach was applied to the model after deterministic analysis. In this study, the probabilistic analysis approach was applied to account for the variability in fabrication. Probabilistic methodology applied in finite element modeling provides another alternative ways of structural analysis of preststressed inverted T-beams with web openings to achieve a robust and reliable design in a more efficient way. In this study, Monte Carlo simulation was used to analyze the effect of parameter uncertainty for the prestressed inverted T-beams with web openings. From the analysis results, it was observed that the changes in prestressing force, elastic modulus of prestressing steel, ultimate tensile strength of
Infinite Possibilities for the Finite Element.
Finlayson, Bruce A.
1981-01-01
Describes the uses of finite element methods in solving problems of heat transfer, fluid flow, etc. Suggests that engineers should know the general concepts and be able to apply the principles of finite element methods. (Author/WB)
Institute of Scientific and Technical Information of China (English)
Yang Liu; DeJun Wang; Jun Ma; Yang Li
2014-01-01
To investigate the application of meta-model for finite element ( FE) model updating of structures, the performance of two popular meta-model, i.e., Kriging model and response surface model (RSM), were compared in detail. Firstly, above two kinds of meta-model were introduced briefly. Secondly, some key issues of the application of meta-model to FE model updating of structures were proposed and discussed, and then some advices were presented in order to select a reasonable meta-model for the purpose of updating the FE model of structures. Finally, the procedure of FE model updating based on meta-model was implemented by updating the FE model of a truss bridge model with the measured modal parameters. The results showed that the Kriging model was more proper for FE model updating of complex structures.
Institute of Scientific and Technical Information of China (English)
B L Ooi; J M Gilbert; A Rashid A Aziz
2016-01-01
Owing to the increasing demand for harvesting energy from environmental vibration for use in self-powered electronic applications, cantilever-based vibration energy harvesting has attracted considerable interest from various parties and has become one of the most common approaches to converting redundant mechanical energy into electrical energy. As the output voltage produced from a piezoelec-tric material depends largely on the geometric shape and the size of the beam, there is a need to model and compare the performance of cantilever beams of differing geometries. This paper presents the study of strain distribution in various shapes of cantilever beams, including a convex and concave edge profile elliptical beam that have not yet been discussed in any prior literature. Both analytical and finite-element models are derived and the resultant strain distributions in the beam are computed based on a MATLAB solver and ANSYS finite-element analysis tools. An optimum geome-try for a vibration-based energy harvesting system is verified. Finally, experimental results comparing the power density for triangular and rectangular piezoelectric beams are also pre-sented to validate the findings of the study, and the claim, as suggested in the literature, is verified.
Ooi, B. L.; Gilbert, J. M.; Aziz, A. Rashid A.
2016-08-01
Owing to the increasing demand for harvesting energy from environmental vibration for use in self-powered electronic applications, cantilever-based vibration energy harvesting has attracted considerable interest from various parties and has become one of the most common approaches to converting redundant mechanical energy into electrical energy. As the output voltage produced from a piezoelectric material depends largely on the geometric shape and the size of the beam, there is a need to model and compare the performance of cantilever beams of differing geometries. This paper presents the study of strain distribution in various shapes of cantilever beams, including a convex and concave edge profile elliptical beam that have not yet been discussed in any prior literature. Both analytical and finite-element models are derived and the resultant strain distributions in the beam are computed based on a MATLAB solver and ANSYS finite-element analysis tools. An optimum geometry for a vibration-based energy harvesting system is verified. Finally, experimental results comparing the power density for triangular and rectangular piezoelectric beams are also presented to validate the findings of the study, and the claim, as suggested in the literature, is verified.
Solomon, S. C.
1980-01-01
The measurability of changes in plate driving or resistive forces associated with plate boundary earthquakes by laser rangefinding or VLBI is considered with emphasis on those aspects of plate forces that can be characterized by such measurements. Topics covered include: (1) analytic solutions for two dimensional stress diffusion in a plate following earthquake faulting on a finite fault; (2) two dimensional finite-element solutions for the global state of stress at the Earth's surface for possible plate driving forces; and (3) finite-element solutions for three dimensional stress diffusion in a viscoelastic Earth following earthquake faulting.
Introduction to finite element analysis using MATLAB and Abaqus
Khennane, Amar
2013-01-01
There are some books that target the theory of the finite element, while others focus on the programming side of things. Introduction to Finite Element Analysis Using MATLAB(R) and Abaqus accomplishes both. This book teaches the first principles of the finite element method. It presents the theory of the finite element method while maintaining a balance between its mathematical formulation, programming implementation, and application using commercial software. The computer implementation is carried out using MATLAB, while the practical applications are carried out in both MATLAB and Abaqus. MA
Energy Technology Data Exchange (ETDEWEB)
Herrmann, K.P. [Paderborn Univ. (Gesamthochschule) (Germany). Lab. fuer Technische Mechanik; Mueller, W.H. [Heriot-Watt Univ., Edinburgh (United Kingdom). Dept. of Mechanical and Chemical Engineering; Neumann, S. [Paderborn Univ. (Gesamthochschule) (Germany). Lab. fuer Technische Mechanik
2001-07-01
The objective of our contribution is to present the discrete Fouriertransformation (DFT) as a serious alternative for the numerical computation of local stresses and strains in a two dimensional representative volume element (RVE) containing heterogeneities of complex shape and high volume fractions. The methodology is based on the application of the so-called ''equivalent inclusion method'' (Mura 1987). This method is used to devolve the original problem onto the determination of an auxiliary strain field which is related to the stresses by virtue of a spatially constant auxiliary stiffness tensor. The resulting partial differential equations (PDE) are firstly approximated by difference schemes leading to a linear system of equations (LSE) to solve. Two different types of difference schemes for an approximation are presented, a 9-pixelstar which is well-known in this context and a new one which uses 21 pixel for the numerical approach in order to increase the quality of the numerical solution. In a second step the DFT has been used which allows to solve the LSE analytically, obtaining a functional relation for the auxiliary strain field. Finally the solution of this equation is determined approximately by virtue of a Neumann iteration procedure. Different heterogeneity problems are considered where the accuracy of both difference stars is checked by existing analytical solutions. (orig.)
Revolution in Orthodontics: Finite element analysis
Singh, Johar Rajvinder; Kambalyal, Prabhuraj; Jain, Megha; Khandelwal, Piyush
2016-01-01
Engineering has not only developed in the field of medicine but has also become quite established in the field of dentistry, especially Orthodontics. Finite element analysis (FEA) is a computational procedure to calculate the stress in an element, which performs a model solution. This structural analysis allows the determination of stress resulting from external force, pressure, thermal change, and other factors. This method is extremely useful for indicating mechanical aspects of biomaterials and human tissues that can hardly be measured in vivo. The results obtained can then be studied using visualization software within the finite element method (FEM) to view a variety of parameters, and to fully identify implications of the analysis. This is a review to show the applications of FEM in Orthodontics. It is extremely important to verify what the purpose of the study is in order to correctly apply FEM. PMID:27114948
Directory of Open Access Journals (Sweden)
Vuksanović Đorđe
2015-01-01
Full Text Available Laminar composites are modern engineering materials widely used in the mechanical and civil engineering. In the paper, some recent advances in a numerical analysis of laminated composite and sandwich plates and shells of different shapes, with existing zones of partial delamination, are presented. The layered finite elements, based on the extended version of the Generalized Laminated Plate Theory of Reddy, are applied for the numerical solution of several structural problems. After the verification of the proposed model for intact structures using the existing data from the literature, the effects of the size and the position of embedded delamination zones on the structural response of laminated structures are investigated numerically by means of a variety of numerical applications.
Finite element analysis of human joints
Energy Technology Data Exchange (ETDEWEB)
Bossart, P.L.; Hollerbach, K.
1996-09-01
Our work focuses on the development of finite element models (FEMs) that describe the biomechanics of human joints. Finite element modeling is becoming a standard tool in industrial applications. In highly complex problems such as those found in biomechanics research, however, the full potential of FEMs is just beginning to be explored, due to the absence of precise, high resolution medical data and the difficulties encountered in converting these enormous datasets into a form that is usable in FEMs. With increasing computing speed and memory available, it is now feasible to address these challenges. We address the first by acquiring data with a high resolution C-ray CT scanner and the latter by developing semi-automated method for generating the volumetric meshes used in the FEM. Issues related to tomographic reconstruction, volume segmentation, the use of extracted surfaces to generate volumetric hexahedral meshes, and applications of the FEM are described.
The 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
Quick finite elements for electromagnetic waves
Pelosi, Giuseppe; Selleri, Stefano
2009-01-01
This practical book and accompanying software enables you to quickly and easily work out challenging microwave engineering and high-frequency electromagnetic problems using the finite element method (FEM) Using clear, concise text and dozens of real-world application examples, the book provides a detailed description of FEM implementation, while the software provides the code and tools needed to solve the three major types of EM problems: guided propagation, scattering, and radiation.
EXODUS II: A finite element data model
Energy Technology Data Exchange (ETDEWEB)
Schoof, L.A.; Yarberry, V.R.
1994-09-01
EXODUS II is a model developed to store and retrieve data for finite element analyses. It is used for preprocessing (problem definition), postprocessing (results visualization), as well as code to code data transfer. An EXODUS II data file is a random access, machine independent, binary file that is written and read via C, C++, or Fortran library routines which comprise the Application Programming Interface (API).
Finite element differential forms on cubical meshes
Arnold, Douglas N
2012-01-01
We develop a family of finite element spaces of differential forms defined on cubical meshes in any number of dimensions. The family contains elements of all polynomial degrees and all form degrees. In two dimensions, these include the serendipity finite elements and the rectangular BDM elements. In three dimensions they include a recent generalization of the serendipity spaces, and new H(curl) and H(div) finite element spaces. Spaces in the family can be combined to give finite element subcomplexes of the de Rham complex which satisfy the basic hypotheses of the finite element exterior calculus, and hence can be used for stable discretization of a variety of problems. The construction and properties of the spaces are established in a uniform manner using finite element exterior calculus.
Directory of Open Access Journals (Sweden)
Elena Ibarz
2013-01-01
Full Text Available The knowledge of the lumbar spine biomechanics is essential for clinical applications. Due to the difficulties to experiment on living people and the irregular results published, simulation based on finite elements (FE has been developed, making it possible to adequately reproduce the biomechanics of the lumbar spine. A 3D FE model of the complete lumbar spine (vertebrae, discs, and ligaments has been developed. To verify the model, radiological images (X-rays were taken over a group of 25 healthy, male individuals with average age of 27.4 and average weight of 78.6 kg with the corresponding informed consent. A maximum angle of 34.40° is achieved in flexion and of 35.58° in extension with a flexion-extension angle of 69.98°. The radiological measurements were 33.94 ± 4.91°, 38.73 ± 4.29°, and 72.67°, respectively. In lateral bending, the maximum angles were 19.33° and 23.40 ± 2.39, respectively. In rotation a maximum angle of 9.96° was obtained. The model incorporates a precise geometrical characterization of several elements (vertebrae, discs, and ligaments, respecting anatomical features and being capable of reproducing a wide range of physiological movements. Application to disc degeneration (L5-S1 allows predicting the affection in the mobility of the different lumbar segments, by means of parametric studies for different ranges of degeneration.
User's Manual for the FEHM Application-A Finite-Element Heat- and Mass-Transfer Code
Energy Technology Data Exchange (ETDEWEB)
George A. Zyvoloski; Bruce A. Robinson; Zora V. Dash; Lynn L. Trease
1997-07-07
This document is a manual for the use of the FEHM application, a finite-element heat- and mass-transfer computer code that can simulate nonisothermal multiphase multicomponent flow in porous media. The use of this code is applicable to natural-state studies of geothermal systems and groundwater flow. A primary use of the FEHM application will be to assist in the understanding of flow fields and mass transport in the saturated and unsaturated zones below the proposed Yucca Mountain nuclear waste repository in Nevada. The equations of heat and mass transfer for multiphase flow in porous and permeable media are solved in the FEHM application by using the finite-element method. The permeability and porosity of the medium are allowed to depend on pressure and temperature. The code also has provisions for movable air and water phases and noncoupled tracers; that is, tracer solutions that do not affect the heat- and mass-transfer solutions. The tracers can be passive or reactive. The code can simulate two-dimensional, two-dimensional radial, or three-dimensional geometries. In fact, FEHM is capable of describing flow that is dominated in many areas by fracture and fault flow, including the inherently three-dimensional flow that results from permeation to and from faults and fractures. The code can handle coupled heat and mass-transfer effects, such as boiling, dryout, and condensation that can occur in the near-field region surrounding the potential repository and the natural convection that occurs through Yucca Mountain due to seasonal temperature changes. The code is also capable of incorporating the various adsorption mechanisms, ranging from simple linear relations to nonlinear isotherms, needed to describe the very complex transport processes at Yucca Mountain. This report outlines the uses and capabilities of the FEHM application, initialization of code variables, restart procedures, and error processing. The report describes all the data files, the input data
Finite-Element 2D and 3D PIC Modeling of RF Devices with Applications to Multipacting
De Ford, John F; Petillo, John
2005-01-01
Multipacting currently limits the performance of many high power radio-frequency (RF) devices, particularly couplers and windows. Models have helped researchers understand and mitigate this problem in 2D structures, but useful multipacting models for complicated 3D structures are still a challenge. A combination of three recent technologies that have been developed in the Analyst and MICHELLE codes begin to address this challenge: high-order adaptive finite-element RF field calculations, advanced particle tracking on unstructured grids, and comprehensive secondary emission models. Analyst employs high-order adaptive finite-element methods to accurately compute driven RF fields and eigenmodes in complex geometries, particularly near edges, corners, and curved surfaces. To perform a multipacting analysis, we use the mesh and fields from Analyst in a modified version of the self-consistent, finite-element gun code MICHELLE. MICHELLE has both a fast, accurate, and reliable particle tracker for unstructured grids ...
Sethuraman, V.; Hunt, P. M.
1988-06-01
The adaptive multigrid technique in the finite element method of the solution of partial differential equations is examined in the context of model problems in atom-atom and collinear atom-diatom collisions. For the problem leading to scattering along an L-shaped region, the technique yields accurate results for regions of energy far from the threshold for excitation of a new channel without inclusion of virtual states. Close to the threshold, the cusplike structure of the transition probability (vs. energy) and the time delay associated with the onset of a resonance are recovered only by inclusion of the new (closed) channel in the finite element solution. For atom-diatom collinear collisions, use of an orthogonal coordinate system facilitates dicretization and adds no extra labor in the finite element method, compared to the usual mass-weighted system.
Elements with Square Roots in Finite Groups
Institute of Scientific and Technical Information of China (English)
M.S. Lucido; M.R. Pournaki
2005-01-01
In this paper, we study the probability that a randomly chosen element in a finite group has a square root, in particular the simple groups of Lie type of rank 1, the sporadic finite simple groups and the alternating groups.
Conforming finite elements with embedded strong discontinuities
Dias-da-Costa, D.; Alfaiate, J.; Sluys, L.J.; Areias, P.; Fernandes, C.; Julio, E.
2012-01-01
The possibility of embedding strong discontinuities into finite elements allowed the simulation of different problems, namely, brickwork masonry fracture, dynamic fracture, failure in finite strain problems and simulation of reinforcement concrete members. However, despite the significant contributi
Quantum Finite Elements for Lattice Field Theory
Brower, Richard C; Gasbarro, Andrew; Raben, Timothy; Tan, Chung-I; Weinberg, Evan
2016-01-01
Viable non-perturbative methods for lattice quantum field theories on curved manifolds are difficult. By adapting features from the traditional finite element methods (FEM) and Regge Calculus, a new simplicial lattice Quantum Finite Element (QFE) Lagrangian is constructed for fields on a smooth Riemann manifold. To reach the continuum limit additional counter terms must be constructed to cancel the ultraviolet distortions. This is tested by the comparison of phi 4-th theory at the Wilson-Fisher fixed point with the exact Ising (c =1/2) CFT on a 2D Riemann sphere. The Dirac equation is also constructed on a simplicial lattice approximation to a Riemann manifold by introducing a lattice vierbein and spin connection on each link. Convergence of the QFE Dirac equation is tested against the exact solution for the 2D Riemann sphere. Future directions and applications to Conformal Field Theories are suggested.
Kang, Gyeong Pil; Lee, Kyounghoon; Kim, Yong Hwan; Park, Sang Jun; Shin, Kwang Seon
2017-09-01
A methodology on the multiscale simulation of metal forming processes is presented, which fully integrates the visco-plastic self-consistent (VPSC) polycrystal model into rigid plastic finite element method (FEM). To accurately predict the material behavior of a magnesium alloy from the microstructural level, the VPSC crystal plasticity model was used as a constitutive equation in this methodology. An optimization program VPSC-GA was developed in order to calculate the hardening parameters for each slip and twin mode of a single crystal from a couple of simple tension/compression tests. The existing constitutive equation for rigid plastic FEM is modified using the deviatoric stress components and the derivatives of them with respect to strain rate components. The stiffness matrix and the load vector were derived based on a new approach and implemented into DEFORMTM-3D via a user subroutine which handles stiffness matrix in elemental level. An application to the Erichsen tests of magnesium alloys was done and the stretch formability of two different Mg alloy sheets was analyzed using the results of both experiment and simulation.
Finite Element Analysis of Reverberation Chambers
Bunting, Charles F.; Nguyen, Duc T.
2000-01-01
The primary motivating factor behind the initiation of this work was to provide a deterministic means of establishing the validity of the statistical methods that are recommended for the determination of fields that interact in -an avionics system. The application of finite element analysis to reverberation chambers is the initial step required to establish a reasonable course of inquiry in this particularly data-intensive study. The use of computational electromagnetics provides a high degree of control of the "experimental" parameters that can be utilized in a simulation of reverberating structures. As the work evolved there were four primary focus areas they are: 1. The eigenvalue problem for the source free problem. 2. The development of a complex efficient eigensolver. 3. The application of a source for the TE and TM fields for statistical characterization. 4. The examination of shielding effectiveness in a reverberating environment. One early purpose of this work was to establish the utility of finite element techniques in the development of an extended low frequency statistical model for reverberation phenomena. By employing finite element techniques, structures of arbitrary complexity can be analyzed due to the use of triangular shape functions in the spatial discretization. The effects of both frequency stirring and mechanical stirring are presented. It is suggested that for the low frequency operation the typical tuner size is inadequate to provide a sufficiently random field and that frequency stirring should be used. The results of the finite element analysis of the reverberation chamber illustrate io-W the potential utility of a 2D representation for enhancing the basic statistical characteristics of the chamber when operating in a low frequency regime. The basic field statistics are verified for frequency stirring over a wide range of frequencies. Mechanical stirring is shown to provide an effective frequency deviation.
Application of the p-version of the finite-element method to global-local problems
Szabo, Barna A.
1989-01-01
A brief survey is given of some recent developments in finite-element analysis technology which bear upon the three main research areas under consideration in this workshop: (1) analysis methods; (2) software testing and quality assurance; and (3) parallel processing. The variational principle incorporated in a finite-element computer program, together with a particular set of input data, determines the exact solution corresponding to that input data. Most finite-element analysis computer programs are based on the principle of virtual work. In the following, researchers consider only programs based on the principle of virtual work and denote the exact displacement vector field corresponding to some specific set of input data by vector u(EX). The exact solution vector u(EX) is independent of the design of the mesh or the choice of elements. Except for very simple problems, or specially constructed test problems, vector u(EX) is not known. Researchers perform a finite-element analysis (or any other numerical analysis) because they wish to make conclusions concerning the response of a physical system to certain imposed conditions, as if vector u(EX) were known.
Finite Element Analysis of Deformed Legs of Offshore Platform Structures
Institute of Scientific and Technical Information of China (English)
柳春图; 秦太验; 段梦兰
2002-01-01
The element stiffness matrix of the equivalent beam or pipe element of the deformed leg of the platform is derived bythe finite element method. The stresses and displacements of some damaged components are calculated, and the numeri-cal solutions agree well with those obtained by the fine mesh finite element method. Finally, as an application of thismethod, the stresses of some platform structures are calculated and analyzed.
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.
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
Iterative methods for mixed finite element equations
Nakazawa, S.; Nagtegaal, J. C.; Zienkiewicz, O. C.
1985-01-01
Iterative strategies for the solution of indefinite system of equations arising from the mixed finite element method are investigated in this paper with application to linear and nonlinear problems in solid and structural mechanics. The augmented Hu-Washizu form is derived, which is then utilized to construct a family of iterative algorithms using the displacement method as the preconditioner. Two types of iterative algorithms are implemented. Those are: constant metric iterations which does not involve the update of preconditioner; variable metric iterations, in which the inverse of the preconditioning matrix is updated. A series of numerical experiments is conducted to evaluate the numerical performance with application to linear and nonlinear model problems.
Unified Framework for Finite Element Assembly
Alnæs, Martin Sandve; Mardal, Kent-Andre; Skavhaug, Ola; Langtangen, Hans Petter; 10.1504/IJCSE.2009.029160
2012-01-01
At the heart of any finite element simulation is the assembly of matrices and vectors from discrete variational forms. We propose a general interface between problem-specific and general-purpose components of finite element programs. This interface is called Unified Form-assembly Code (UFC). A wide range of finite element problems is covered, including mixed finite elements and discontinuous Galerkin methods. We discuss how the UFC interface enables implementations of variational form evaluation to be independent of mesh and linear algebra components. UFC does not depend on any external libraries, and is released into the public domain.
Gélat, P.; Yang, J.; Thomas, P. J.; Hutchins, D. A.; Akanji, O.; Davis, L. A. J.; Freear, S.; Harput, S.; Saffari, N.
2016-01-01
There has been recent interest in the transmission of acoustic signals along granular chains of spherical beads to produce waveforms of relevance to biomedical ultrasound applications. Hertzian contact between adjacent beads can introduce different harmonic content into the signal as it propagates. This transduction mechanism has the potential to be of use in both diagnostic and therapeutic ultrasound applications, and is the object of the study presented here. Although discrete dynamics models of this behaviour exist, a more comprehensive solution must be sought if changes in shape and deformation of individual beads are to be considered. Thus, the finite element method was used to investigate the dynamics of a granular chain of six, 1 mm diameter chrome steel spherical beads excited at one end using a sinusoidal displacement signal at 73 kHz. Output from this model was compared with the solution provided by the discrete dynamics model, and good overall agreement obtained. In addition, it was able to resolve the complex dynamics of the granular chain, including the multiple collisions which occur. It was demonstrated that under dynamic excitation conditions, the inability of discrete mechanics models to account for elastic deformation of the beads when these lose contact, could lead to discrepancies with experimental observations.
Guo, Guifang; Long, Bo; Cheng, Bo; Zhou, Shiqiong; Xu, Peng; Cao, Binggang
In order to better understand the thermal abuse behavior of high capacities and large power lithium-ion batteries for electric vehicle application, a three-dimensional thermal model has been developed for analyzing the temperature distribution under abuse conditions. The model takes into account the effects of heat generation, internal conduction and convection, and external heat dissipation to predict the temperature distribution in a battery. Three-dimensional model also considers the geometrical features to simulate oven test, which are significant in larger cells for electric vehicle application. The model predictions are compared to oven test results for VLP 50/62/100S-Fe (3.2 V/55 Ah) LiFePO 4/graphite cells and shown to be in great agreement.
Institute of Scientific and Technical Information of China (English)
ZENG Guangming; SU Xiaokang; HUANG Guohe; XIE Gengxin
2003-01-01
The finite element method is one of the typical methods that are used for numerical water quality modeling of the topographically complicated river. In this paper, based on the principle of probability theory the probability density of pollutants is introduced. A new model for the grid size optimization based on the finite element method is developed with the incorporation of the maximum information entropy theory when the length of the grid is given. Combined with the experiential evaluation approach of the flow discharge per unit river width, this model can be used to determine the grid size of the finite element method applied to water quality modeling of the topographically complicated river when the velocity field of the river is not given. The calculating results of the application of the model to an ideal river testified the correctness of the model. In a practical case-the application of the model to the Xingjian River (the Hengyang section of the Xiangjiang River), the optimized width of the grid of the finite element method was gained and the influence of parameters was studied, which demonstrated that the model reflected the real situation of the pollutants in the river, and that the model had many excellent characteristics such as stabilization, credibility and high applicability in practical applications.
Pantale, O.; Caperaa, S.; Rakotomalala, R.
2004-07-01
During the last 50 years, the development of better numerical methods and more powerful computers has been a major enterprise for the scientific community. In the same time, the finite element method has become a widely used tool for researchers and engineers. Recent advances in computational software have made possible to solve more physical and complex problems such as coupled problems, nonlinearities, high strain and high-strain rate problems. In this field, an accurate analysis of large deformation inelastic problems occurring in metal-forming or impact simulations is extremely important as a consequence of high amount of plastic flow. In this presentation, the object-oriented implementation, using the C++ language, of an explicit finite element code called DynELA is presented. The object-oriented programming (OOP) leads to better-structured codes for the finite element method and facilitates the development, the maintainability and the expandability of such codes. The most significant advantage of OOP is in the modeling of complex physical systems such as deformation processing where the overall complex problem is partitioned in individual sub-problems based on physical, mathematical or geometric reasoning. We first focus on the advantages of OOP for the development of scientific programs. Specific aspects of OOP, such as the inheritance mechanism, the operators overload procedure or the use of template classes are detailed. Then we present the approach used for the development of our finite element code through the presentation of the kinematics, conservative and constitutive laws and their respective implementation in C++. Finally, the efficiency and accuracy of our finite element program are investigated using a number of benchmark tests relative to metal forming and impact simulations.
User`s manual for the FEHM application -- A finite-element heat- and mass-transfer code
Energy Technology Data Exchange (ETDEWEB)
Zyvoloski, G.A.; Robinson, B.A.; Dash, Z.V.; Trease, L.L.
1997-07-01
The use of this code is applicable to natural-state studies of geothermal systems and groundwater flow. A primary use of the FEHM application will be to assist in the understanding of flow fields and mass transport in the saturated and unsaturated zones below the proposed Yucca Mountain nuclear waste repository in Nevada. The equations of heat and mass transfer for multiphase flow in porous and permeable media are solved in the FEHM application by using the finite-element method. The permeability and porosity of the medium are allowed to depend on pressure and temperature. The code also has provisions for movable air and water phases and noncoupled tracers; that is, tracer solutions that do not affect the heat- and mass-transfer solutions. The tracers can be passive or reactive. The code can simulate two-dimensional, two-dimensional radial, or three-dimensional geometries. In fact, FEHM is capable of describing flow that is dominated in many areas by fracture and fault flow, including the inherently three-dimensional flow that results from permeation to and from faults and fractures. The code can handle coupled heat and mass-transfer effects, such as boiling, dryout, and condensation that can occur in the near-field region surrounding the potential repository and the natural convection that occurs through Yucca Mountain due to seasonal temperature changes. This report outlines the uses and capabilities of the FEHM application, initialization of code variables, restart procedures, and error processing. The report describes all the data files, the input data, including individual input records or parameters, and the various output files. The system interface is described, including the software environment and installation instructions.
Energy Technology Data Exchange (ETDEWEB)
Carella, Alfredo Raul
2012-09-15
Quantifying species transport rates is a main concern in chemical and petrochemical industries. In particular, the design and operation of many large-scale industrial chemical processes is as much dependent on diffusion as it is on reaction rates. However, the existing diffusion models sometimes fail to predict experimentally observed behaviors and their accuracy is usually insufficient for process optimization purposes. Fractional diffusion models offer multiple possibilities for generalizing Flick's law in a consistent manner in order to account for history dependence and nonlocal effects. These models have not been extensively applied to the study of real systems, mainly due to their computational cost and mathematical complexity. A least squares spectral formulation was developed for solving fractional differential equations. The proposed method was proven particularly well-suited for dealing with the numerical difficulties inherent to fractional differential operators. The practical implementation was explained in detail in order to enhance reproducibility, and directions were specified for extending it to multiple dimensions and arbitrarily shaped domains. A numerical framework based on the least-squares spectral element method was developed for studying and comparing anomalous diffusion models in pellets. This simulation tool is capable of solving arbitrary integro-differential equations and can be effortlessly adapted to various problems in any number of dimensions. Simulations of the flow around a cylindrical particle were achieved by extending the functionality of the developed framework. A test case was analyzed by coupling the boundary condition yielded by the fluid model with two families of anomalous diffusion models: hyperbolic diffusion and fractional diffusion. Qualitative guidelines for determining the suitability of diffusion models can be formulated by complementing experimental data with the results obtained from this approach.(Author)
Superconvergence for rectangular serendipity finite elements
Institute of Scientific and Technical Information of China (English)
CHEN; Chuanmiao(陈传淼)
2003-01-01
Based on an orthogonal expansion and orthogonality correction in an element, superconvergenceat symmetric points for any degree rectangular serendipity finite element approximation to second order ellipticproblem is proved, and its behaviour up to the boundary is also discussed.
Finite elements and finite differences for transonic flow calculations
Hafez, M. M.; Murman, E. M.; Wellford, L. C.
1978-01-01
The paper reviews the chief finite difference and finite element techniques used for numerical solution of nonlinear mixed elliptic-hyperbolic equations governing transonic flow. The forms of the governing equations for unsteady two-dimensional transonic flow considered are the Euler equation, the full potential equation in both conservative and nonconservative form, the transonic small-disturbance equation in both conservative and nonconservative form, and the hodograph equations for the small-disturbance case and the full-potential case. Finite difference methods considered include time-dependent methods, relaxation methods, semidirect methods, and hybrid methods. Finite element methods include finite element Lax-Wendroff schemes, implicit Galerkin method, mixed variational principles, dual iterative procedures, optimal control methods and least squares.
Continuous finite element methods for Hamiltonian systems
Institute of Scientific and Technical Information of China (English)
无
2007-01-01
By applying the continuous finite element methods of ordinary differential equations, the linear element methods are proved having second-order pseudo-symplectic scheme and the quadratic element methods are proved having third-order pseudosymplectic scheme respectively for general Hamiltonian systems, and they both keep energy conservative. The finite element methods are proved to be symplectic as well as energy conservative for linear Hamiltonian systems. The numerical results are in agreement with theory.
Directory of Open Access Journals (Sweden)
Fernando Cortés
2015-01-01
Full Text Available This paper presents an analysis of the dynamic behaviour of constrained layer damping (CLD beams with thick viscoelastic layer. A homogenised model for the flexural stiffness is formulated using Reddy-Bickford’s quadratic shear in each layer, and it is compared with Ross-Kerwin-Ungar (RKU classical model, which considers a uniform shear deformation for the viscoelastic core. In order to analyse the efficiency of both models, a numerical application is accomplished and the provided results are compared with those of a 2D model using finite elements, which considers extensional and shear stress and longitudinal, transverse, and rotational inertias. The intermediate viscoelastic material is characterised by a fractional derivative model, with a frequency dependent complex modulus. Eigenvalues and eigenvectors are obtained from an iterative method avoiding the computational problems derived from the frequency dependence of the stiffness matrices. Also, frequency response functions are calculated. The results show that the new model provides better accuracy than the RKU one as the thickness of the core layer increases. In conclusion, a new model has been developed, being able to reproduce the mechanical behaviour of thick CLD beams, reducing storage needs and computational time compared with a 2D model, and improving the results from the RKU model.
Experimental and finite element analyses of multifunctional skins for morphing wing applications
Geier, Sebastian; Kintscher, Markus; Mahrholz, Thorsten; Wierach, Peter; Monner, Hans-Peter; Wiedemann, Martin
2016-04-01
As a consequence of operational eﬃciency because of rising energy costs, future transport systems need to be mission-adaptive. Especially in aircraft design the limits of lightweight construction, reduced aerodynamic drag and optimized propulsion are pushed further and further. The first two aspects can be addressed by using a morphing leading edge. Great economic advantages can be expected as a result of gapless surfaces which feature longer areas of laminar flow. Instead of focusing on the kinematics, which are already published in a great number of varieties, this paper emphasizes as major challenge, the qualification of a multi-material layup which meets the compromise of needed stiffness, flexibility and essential functions to match the flight worthiness requirements, such as erosion shielding, impact safety, lighting protection and de-icing. It is the aim to develop an gapless leading edge device and to prepare the path for higher technology readiness levels resulting in an airborne application. During several national and European projects the DLR developed a gapless smart droop nose concept, which functionality was successfully demonstrated using a two-dimensional 5 m in span prototype in low speed (up to 50 m/s) wind tunnel tests. The basic structure is made of commercially available and certified glass-fiber reinforced plastics (GFRP, Hexcel Hexply 913). This paper presents 4-point bending tests to characterize the composite with its integrated functions. The integrity and aging/fatigue issues of different material combinations are analyzed by experiments. It can be demonstrated that only by adding functional layers the mentioned requirements such as erosion-shielding or de-icing can be satisfied. The total thickness of the composite skin increases by more than 100 % when required functions are integrated as additional layers. This fact has a tremendous impact on the maximum strain of the outer surface if it features a complete monolithic build
Why do probabilistic finite element analysis ?
Thacker, B H
2008-01-01
The intention of this book is to provide an introduction to performing probabilistic finite element analysis. As a short guideline, the objective is to inform the reader of the use, benefits and issues associated with performing probabilistic finite element analysis without excessive theory or mathematical detail.
Non-linear finite element modeling
DEFF Research Database (Denmark)
Mikkelsen, Lars Pilgaard
The note is written for courses in "Non-linear finite element method". The note has been used by the author teaching non-linear finite element modeling at Civil Engineering at Aalborg University, Computational Mechanics at Aalborg University Esbjerg, Structural Engineering at the University...... on the governing equations and methods of implementing....
Finite element method for thermal analysis of concentrating solar receivers
Shtrakov, Stanko; Stoilov, Anton
2006-01-01
Application of finite element method and heat conductivity transfer model for calculation of temperature distribution in receiver for dish-Stirling concentrating solar system is described. The method yields discretized equations that are entirely local to the elements and provides complete geometric flexibility. A computer program solving the finite element method problem is created and great number of numerical experiments is carried out. Illustrative numerical results are given for an array...
Institute of Scientific and Technical Information of China (English)
Xingzhe Wang; Xiaojing Zheng
2009-01-01
Based on the generalized variational principle of magneto-thermo-elasticity of a ferromagnetic thin shell established (see, Analyses on nonlinear coupling of magneto-thermo-elasticity of ferromagnetic thin shell-Ⅰ), the present paper developed a finite element modeling for the mechanical-magneto-thermal multi-field coupling of a ferromagnetic thin shell. The numerical modeling composes of finite element equations for three sub-systems of magnetic, thermal and deformation fields, as well as iterative methods for nonlinearities of the geometrical large-deflection and the multi-field coupling of the ferromagnetic shell. As examples, the numerical simulations on magneto-elastic behaviors of a ferromagnetic cylindrical shell in an applied magnetic field, and magneto-thermo-elastic behaviors of the shell in applied magnetic and thermal fields are carried out. The results are in good agreement with the experimental ones.
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
Finite element analysis of optical waveguides
Mabaya, N.; Lagasse, P. E.; Vandenbulcke, P.
1981-06-01
Several finite element programs for the computation of the guided modes of optical waveguides are presented. The advantages and limitations of a very general program for the analysis of anisotropic guides are presented. A possible solution to the problem of the spurious numerical modes, encountered when calculating higher order modes, is proposed. For isotropic waveguides, it is shown that both EH- and HE-type modes can be very accurately approximated by two different scalar finite element programs. Finally, a boundary perturbation method is outlined that makes it possible to calculate the attenuation coefficient of leaky modes in single material guides, starting from a finite element calculation.
Will Finite Elements Replace Structural Mechanics?
Ojalvo, I. U.
1984-01-01
This paper presents a personal view regarding the need for a continued interest and activity in structural methods in general, while viewing finite elements and the computer as simply two specific tools for assisting in this endeavor. An attempt is made to provide some insight as to why finite element methods seem to have "won the war," and to give examples of their more (and less) intelligent use. Items addressed include a highlight of unnecessary limitations of many existing standard finite element codes and where it is felt that further development work is needed.
Superconvergence of tricubic block finite elements
Institute of Scientific and Technical Information of China (English)
2009-01-01
In this paper, we first introduce interpolation operator of projection type in three dimen- sions, from which we derive weak estimates for tricubic block finite elements. Then using the estimate for the W 2, 1-seminorm of the discrete derivative Green’s function and the weak estimates, we show that the tricubic block finite element solution uh and the tricubic interpolant of projection type Πh3u have superclose gradient in the pointwise sense of the L∞-norm. Finally, this supercloseness is applied to superconvergence analysis, and the global superconvergence of the finite element approximation is derived.
Application of Finite Element Based on ADINA%基于ADINA的有限元应用探讨
Institute of Scientific and Technical Information of China (English)
祝雨
2011-01-01
Today, the popularity of CAD technology, from ordinary mechanical engineering to the space shuttle, almost aU design and manufacture can not be separated with f＇mite element analysis techniques. ADINA, as the famous finite element analysis software, after thirty years＇ continuous improvement and development, has been recognized by the user, and have played an important role in many engineering fields. The leading computational theory and powerful analytical functions make ADINA have a place in many of the finite element analysis software. This paner takes ADINA software as an examnle, discusses the annlication of finite element.%在普及CAD技术的今天，从普通的工程机械到航天飞机，几乎所有的设计制造都离不开有限元分析技术，而ADINA作为现在著名的有限元分析软件，历经三十多年的不断改进与发展，得到了用户的认可，并在许多工程领域建设中发挥了重要作用。ADINA领先的计算理论、强大的分析功能，使其在众多的有限元工程分析软件中占有一席之地。这里以ADINA软件应用举例，对有限元应用进行探讨。
颈椎有限元模型的应用进展%Application progress of finite element model in cervical spine
Institute of Scientific and Technical Information of China (English)
周毅强; 张建新; 林蔚莘
2014-01-01
有限元分析法(FEA)是一种在生物力学领域广泛应用的研究方法.近年来,颈椎有限元模型已被广泛应用于研究颈椎损伤、颈椎退变及模拟各种颈椎手术,已日趋完善.回顾了颈椎有限元模型的发展,介绍了颈椎有限元建模与分析在颈椎损伤、人工椎间盘置换、椎间植骨融合、颈椎退变及颈椎失稳等方面的应用进展,展望了未来的发展趋势.%Finite element analysis (FEA) is broadly used in biomechanics.Being widely used in clinical studies on cervical spine injury,cervical degeneration and stimulating a variety of cervical spine surgeries,cervical finite element model is becoming more and more accurate in recent years.This paper aims to review the development of cervical finite element model,to introduce the application progress of the modeling and analysis in cervical spine injury,cervical disc arthroplasty,cervical interbody fusion,cervical degeneration and cervical instability,and to prospect the foreground of cervical finite element model in future.
PHG: A Toolbox for Developing Parallel Adaptive Finite Element Programs
Institute of Scientific and Technical Information of China (English)
ZHANG Linbo
2011-01-01
@@ Significance of the finite element method The finite element method (Feng, 1965) is mainly used for numerical solution of partial differential equations.It consists of partitioning the computational domain into a mesh composed of disjoint smaller sub-domains called elements which cover the whole domain, and approximating the solution in each element using simple functions (usually polynomials) so that the original problem can be turned into a suitable one to be solved on modern computers.The finite element method has a very wide range of applications as one of the most important methods in scientific and engineering computing.In the finite element method, two key factors which can affect the computational efficiency and precision of the computed solution are quality and distribution of the mesh elements.The adaptive finite element method, first proposed by I.Babuska and W.Rheinboldt in 1978 (Babuska et al., 1978), automatically adjusts and optimizes the distribution of mesh elements according to estimation on the distribution of the error of the computed solution, in order to improve the precision of the computed solution.Recent researches show that for many problems with locally singular solutions, by using mathematically rigorous a posteriori error estimates and suitable adaptive strategy, the adaptive finite element method can produce quasi-optimal meshes and dramatically improve the overall computational efficiency.
Finite element analysis of rotating beams physics based interpolation
Ganguli, Ranjan
2017-01-01
This book addresses the solution of rotating beam free-vibration problems using the finite element method. It provides an introduction to the governing equation of a rotating beam, before outlining the solution procedures using Rayleigh-Ritz, Galerkin and finite element methods. The possibility of improving the convergence of finite element methods through a judicious selection of interpolation functions, which are closer to the problem physics, is also addressed. The book offers a valuable guide for students and researchers working on rotating beam problems – important engineering structures used in helicopter rotors, wind turbines, gas turbines, steam turbines and propellers – and their applications. It can also be used as a textbook for specialized graduate and professional courses on advanced applications of finite element analysis.
Moving Finite Elements in 2-D.
1984-08-06
34 . - ; .-’- . - . -- .- -. . - -.. -- ; -. - - - - - ." . ,- . -••. - - ; . IOSR : TR. SAI-84/1299 (0 N MOVING FINITE ELEMENTS IN 2-I Final Report AFOSR Contract: F4962U-81-C-UO73 Program Manager
Finite element modeling of corneal strip extensometry
CSIR Research Space (South Africa)
Botha, N
2012-12-01
Full Text Available numerically modelled in several studies, this study focusses on accurately modelling the strip extensiometry test. Two methods were considered to simulate the experimental conditions namely, a single phase and a two phase method. A finite element model...
A survey of mixed finite element methods
Brezzi, F.
1987-01-01
This paper is an introduction to and an overview of mixed finite element methods. It discusses the mixed formulation of certain basic problems in elasticity and hydrodynamics. It also discusses special techniques for solving the discrete problem.
Effective Stiffness: Generalizing Effective Resistance Sampling to Finite Element Matrices
Avron, Haim
2011-01-01
We define the notion of effective stiffness and show that it can used to build sparsifiers, algorithms that sparsify linear systems arising from finite-element discretizations of PDEs. In particular, we show that sampling $O(n\\log n)$ elements according to probabilities derived from effective stiffnesses yields an high quality preconditioner that can be used to solve the linear system in a small number of iterations. Effective stiffness generalizes the notion of effective resistance, a key ingredient of recent progress in developing nearly linear symmetric diagonally dominant (SDD) linear solvers. Solving finite elements problems is of considerably more interest than the solution of SDD linear systems, since the finite element method is frequently used to numerically solve PDEs arising in scientific and engineering applications. Unlike SDD systems, which are relatively easy to precondition, there has been limited success in designing fast solvers for finite element systems, and previous algorithms usually tar...
Doyeux, Vincent; Chabannes, Vincent; Prud'Homme, Christophe; Ismail, Mourad
2012-01-01
A new framework for two-fluids flow using a Finite Element/Level Set method is presented and verified through the simulation of the rising of a bubble in a viscous fluid. This model is then enriched to deal with vesicles (which mimic red blood cells mechanical behavior) by introducing a Lagrange multiplier to constrain the inextensibility of the membrane. Moreover, high order polynomial approximation is used to increase the accuracy of the simulations. A validation of this model is finally presented on known behaviors of vesicles under flow such as "tank treading" and tumbling motions.
Finite element modeling of the human pelvis
Energy Technology Data Exchange (ETDEWEB)
Carlson, B.
1995-11-01
A finite element model of the human pelvis was created using a commercial wire frame image as a template. To test the final mesh, the model`s mechanical behavior was analyzed through finite element analysis and the results were displayed graphically as stress concentrations. In the future, this grid of the pelvis will be integrated with a full leg model and used in side-impact car collision simulations.
Surgery simulation using fast finite elements
DEFF Research Database (Denmark)
Bro-Nielsen, Morten
1996-01-01
This paper describes our recent work on real-time surgery simulation using fast finite element models of linear elasticity. In addition, we discuss various improvements in terms of speed and realism......This paper describes our recent work on real-time surgery simulation using fast finite element models of linear elasticity. In addition, we discuss various improvements in terms of speed and realism...
A NOTE ON FINITE ELEMENT WAVELETS
Institute of Scientific and Technical Information of China (English)
谌秋辉; 陈翰麟
2001-01-01
The refinability and approximation order of finite element multi-scale vector are discussed in [1]. But the coefficients in the conditions of approximation order of finite element multi-scale vector are incorrect there. The main purpose of this note is to make a correction of the error in the main result of [1]. These coefficients are very important for the properties of wavelets, such as vanishing moments and regularity.
Gleadall, Andrew; Pan, Jingzhe; Ding, Lifeng; Kruft, Marc-Anton; Curcó, David
2015-11-01
Molecular dynamics (MD) simulations are widely used to analyse materials at the atomic scale. However, MD has high computational demands, which may inhibit its use for simulations of structures involving large numbers of atoms such as amorphous polymer structures. An atomic-scale finite element method (AFEM) is presented in this study with significantly lower computational demands than MD. Due to the reduced computational demands, AFEM is suitable for the analysis of Young's modulus of amorphous polymer structures. This is of particular interest when studying the degradation of bioresorbable polymers, which is the topic of an accompanying paper. AFEM is derived from the inter-atomic potential energy functions of an MD force field. The nonlinear MD functions were adapted to enable static linear analysis. Finite element formulations were derived to represent interatomic potential energy functions between two, three and four atoms. Validation of the AFEM was conducted through its application to atomic structures for crystalline and amorphous poly(lactide).
Engineering and Design: Geotechnical Analysis by the Finite Element Method
2007-11-02
used it to determine stresses and movements in embank- ments, and Reyes and Deer described its application to analysis of underground openings in rock...3-D steady-state seepage analysis of permeability of the cutoff walls was varied from 10 to Cerrillos Dam near Ponce , Puerto Rico, for the U.S.-6 10...36 Hughes, T. J. R. (1987). The Finite Element Reyes , S. F., and Deene, D. K. (1966). “Elastic Method, Linear Static and Dynamic Finite Element
Finite element analysis of flexible, rotating blades
Mcgee, Oliver G.
1987-01-01
A reference guide that can be used when using the finite element method to approximate the static and dynamic behavior of flexible, rotating blades is given. Important parameters such as twist, sweep, camber, co-planar shell elements, centrifugal loads, and inertia properties are studied. Comparisons are made between NASTRAN elements through published benchmark tests. The main purpose is to summarize blade modeling strategies and to document capabilities and limitations (for flexible, rotating blades) of various NASTRAN elements.
Directory of Open Access Journals (Sweden)
Toralf eNeuling
2012-09-01
Full Text Available Transcranial direct current stimulation (tDCS has been applied in numerous scientiﬁc studies over the past decade. However, the possibility to apply tDCS in therapy of neuropsychiatric disorders is still debated. While transcranial magnetic stimulation (TMS has been approved for treatment of major depression in the United States by the Food and Drug Administration (FDA, tDCS is not as widely accepted. One of the criticisms against tDCS is the lack of spatial speciﬁcity. Focality is limited by the electrode size (35 cm2 are commonly used and the bipolar arrangement. However, a current ﬂow through the head directly from anode to cathode is an outdated view. Finite element (FE models have recently been used to predict the exact current ﬂow during tDCS. These simulations have demonstrated that the current ﬂow depends on tissue shape and conductivity. Toface the challenge to predict the location, magnitude and direction of the current ﬂow induced by tDCS and transcranial alternating current stimulation (tACS, we used a reﬁned realistic FE modeling approach. With respect to the literature on clinical tDCS and tACS, we analyzed two common setups for the location of the stimulation electrodes which target the frontal lobe and the occipital lobe, respectively. We compared lateral and medial electrode conﬁguration with regard to theirusability. We were able to demonstrate that the lateral conﬁgurations yielded more focused stimulation areas as well as higher current intensities in the target areas. The high resolution of our simulation allows one to combine the modeled current ﬂow with the knowledge of neuronal orientation to predict the consequences of tDCS and tACS. Our results not only oﬀer a basis for a deeper understanding of the stimulation sites currently in use for clinical applications but also oﬀer a better interpretation of observed eﬀects.
Ridl, Romy; Bell, David; Villeneuve, Marlene
2017-04-01
Toe buckling deformation is a temporal product of induced stresses concentrated at the base of a slope. Prolonged induced stresses may lead to yielding of an anisotropic rock mass, either through rheological creep deformation (flexural toe buckling) or brittle failure (hinge buckling). Progressive deformation can lead to the breakout at the buckled toe and ultimately result in deep seated displacements on a mountain range scale, referred to as deep seated gravitational slope deformation (DSGSD). DSGSD can have a considerable impact on civil infrastructure and should be well understood for hazard identification, to inform civil engineering design and for resource management purposes. Toe buckling deformation was identified beneath the basal sliding zone of three large (≥50 Mm3) landslides in the Cromwell Gorge, New Zealand. This area was subjected to extensive geotechnical investigations for the Clyde Hydropower Scheme. During these investigations seventeen major landslides were identified in the Cromwell Gorge and subsequently stabilised. The data from the landslide stabilisation project, including 26.7 km of boreholes and 9 km of tunnels, for the three landslides exhibiting toe buckling was made available for this study. This comprehensive database has enabled comparison and validation of numerical simulations carried out for the Cromwell Gorge. The application of numerical modelling has demonstrated that toe buckling within the Cromwell Gorge is a result of the combination of induced stresses acting on an anisotropic schistose rock mass. The induced stresses comprise: i) topographically-induced gravitational stresses parallel to the slope, associated with the evolution of the Cromwell Gorge from a relatively low relief surface to present day topography (1400 m deep valley), and ii) active far-field tectonic stresses associated with the obliquely convergent stress regime of the Australian-Pacific continent plate boundary. Finite Element Method (FEM) numerical
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 ...
Moreno, Rafael; Ramaswamy, Balasubramaniam
2003-01-01
Using object-oriented programming (OOP) techniques and philosophies, a collection of C++ tools for the rapid development of finite element applications has been created. The object-oriented finite element analysis (OOFEA) toolkit provides both the geometrical and mathematical management tools necessary for this task in the form of useful class hierarchies. In particular, the OOFEA toolkit features methods for evaluating arbitrary weak forms provided by the user in order to solve particular problems of interest. A description of the underlying concepts, philosophies and techniques used to develop the toolkit are included. A strong effort has been made to concentrate on its possibly beneficial usage in the computational fluid dynamics area. In order to demonstrate the toolkit capabilities of managing complex projects, a simulator for laminar and turbulent natural convective flows in enclosures has been developed and a numerical study of some of these flows has been conducted.
Quadrature representation of finite element variational forms
DEFF Research Database (Denmark)
Ølgaard, Kristian Breum; Wells, Garth N.
2012-01-01
This chapter addresses the conventional run-time quadrature approach for the numerical integration of local element tensors associated with finite element variational forms, and in particular automated optimizations that can be performed to reduce the number of floating point operations...
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.
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...
COHESIVE ZONE FINITE ELEMENT-BASED MODELING OF HYDRAULIC FRACTURES
Institute of Scientific and Technical Information of China (English)
Zuorong Chen; A.P. Bunger; Xi Zhang; Robert G. Jeffrey
2009-01-01
Hydraulic fracturing is a powerful technology used to stimulate fluid production from reservoirs. The fully 3-D numerical simulation of the hydraulic fracturing process is of great importance to the efficient application of this technology, but is also a great challenge because of the strong nonlinear coupling between the viscous flow of fluid and fracture propagation. By taking advantage of a cohesive zone method to simulate the fracture process, a finite element model based on the existing pore pressure cohesive finite elements has been established to investigate the propagation of a penny-shaped hydraulic fracture in an infinite elastic medium. The effect of cohesive material parameters and fluid viscosity on the hydraulic fracture behaviour has been investigated. Excellent agreement between the finite element results and analytical solutions for the limiting case where the fracture process is dominated by rock fracture toughness demonstrates the ability of the cohesive zone finite element model in simulating the hydraulic fracture growth for this case.
Error computation for adaptive finite element analysis
Khan, A A; Memon, I R; Ming, X Y
2002-01-01
The paper gives a simple numerical procedure for computations of errors generated by the discretisation process of finite element method. The procedure given is based on the ZZ error estimator which is believed to be reasonable accurate and thus can be readily implemented in any existing finite element codes. The devised procedure not only estimates the global energy norm error but also evaluates the local errors in individual elements. In the example, the given procedure is combined with an adaptive refinement procedure, which provides guidance for optimal mesh designing and allows the user to obtain a desired accuracy with a limited number of interaction. (author)
Experimental Finite Element Approach for Stress Analysis
Directory of Open Access Journals (Sweden)
Ahmet Erklig
2014-01-01
Full Text Available This study aims to determining the strain gauge location points in the problems of stress concentration, and it includes both experimental and numerical results. Strain gauges were proposed to be positioned to corresponding locations on beam and blocks to related node of elements of finite element models. Linear and nonlinear cases were studied. Cantilever beam problem was selected as the linear case to approve the approach and conforming contact problem was selected as the nonlinear case. An identical mesh structure was prepared for the finite element and the experimental models. The finite element analysis was carried out with ANSYS. It was shown that the results of the experimental and the numerical studies were in good agreement.
Energy Technology Data Exchange (ETDEWEB)
Aristovich, K Y; Khan, S H, E-mail: kirill.aristovich.1@city.ac.u [School of Engineering and Mathematical Sciences, City University London, Northampton Square, London EC1V 0HB (United Kingdom)
2010-07-01
Complex multi-scale Finite Element (FE) analyses always involve high number of elements and therefore require very long time of computations. This is caused by the fact, that considered effects on smaller scales have greater influences on the whole model and larger scales. Thus, mesh density should be as high as required by the smallest scale factor. New submodelling routine has been developed to sufficiently decrease the time of computation without loss of accuracy for the whole solution. The presented approach allows manipulation of different mesh sizes on different scales and, therefore total optimization of mesh density on each scale and transfer results automatically between the meshes corresponding to respective scales of the whole model. Unlike classical submodelling routine, the new technique operates with not only transfer of boundary conditions but also with volume results and transfer of forces (current density load in case of electromagnetism), which allows the solution of full Maxwell's equations in FE space. The approach was successfully implemented for electromagnetic solution in the forward problem of Magnetic Field Tomography (MFT) based on Magnetoencephalography (MEG), where the scale of one neuron was considered as the smallest and the scale of whole-brain model as the largest. The time of computation was reduced about 100 times, with the initial requirements of direct computations without submodelling routine of 10 million elements.
Exact finite elements for conduction and convection
Thornton, E. A.; Dechaumphai, P.; Tamma, K. K.
1981-01-01
An appproach for developing exact one dimensional conduction-convection finite elements is presented. Exact interpolation functions are derived based on solutions to the governing differential equations by employing a nodeless parameter. Exact interpolation functions are presented for combined heat transfer in several solids of different shapes, and for combined heat transfer in a flow passage. Numerical results demonstrate that exact one dimensional elements offer advantages over elements based on approximate interpolation functions. Previously announced in STAR as N81-31507
Pugh, Barry Kevin
While open-circuit magnetic measurements are noted to involve distortions related to the image effect and, most significantly, the sample's demagnetizing factor, closed-circuit measurements are generally considered to be free of these distortions. However, it has been reported and observed within this research that for certain sample geometries and materials operating near the magnetic saturation of the electromagnet poles, there are observed distortions of up to 40.7% of the maximum magnetization at a field level of 25 kiloOersteds for a cylindrical sample with an L/D ratio of 0.2. This observed distortion in the magnetic measurement in a closed-circuit has been referred to in the literature as an "apparent image effect" error. The intent of this research is to apply finite element modeling (FEM) to replicate original experimental and published data for cylindrical samples of both hard and soft magnetic material and to observe the phenomenology of the error within the results of the model. The hard magnetic material of interest is NdFeB and the soft magnetic material used is 1018 steel. Additionally, the sample data base is extended to rectangular prisms with data generated both experimentally and with FEM. Using a validated model it is possible to develop a corrective methodology and equations to address the magnetization measurement errors noted at high field levels within both the first and third quadrants of the hysteresis curve. The methodology developed through this research produced corrective surfaces with two dimensional polynomial fits with average adjusted R-values of 0.97. As a fault study secondary to the development of the corrective methodology, this project investigated the significance of the sample's surface mating to the poles of the hysteresigraph. It was determined that a 5° partial misalignment air gap has only approximately 0.5% variation in magnetization, 4thMmax, from the baseline of an ungapped sample. It is indicated that the sample gap
Energy Technology Data Exchange (ETDEWEB)
Jeong, Sang Sub; Jang Seok Myeong [Chungnam National University(Korea)
2000-06-01
The 4-pole linear homopolar synchronous motor (LHSM), so called linear inductor motor, is composed of the figure-of-eight shaped 3-phase armature windings, DC field windings, and the segmented secondary with the transverse bar track. To reduce the calculation time, the simplified 3D finite element model with equivalent reluctance and/or permanent magnet is presented. To obtain a clear understanding, propriety and usefulness of the developed mode., we compare with the results of simplified 3D FEA and test. Consequently, the results of simplified and 3D FEM analysis are nearly identical, but much larger than that of static test at d-axis armature excitation. Therefore the improved FEA model, such as full model with half slot, is needed for the precise analysis. (author). refs., figs., tabs.
Dvorkin, Eduardo N
2013-01-01
This book presents a detailed discussion of the models that were developed to simulate the collapse and post-collapse behavior of steel pipes. The finite element method offers to engineers the possibility of developing models to simulate the collapse behavior of casings inside oil wells and the collapse behavior of deepwater pipelines. However, if technological decisions are going to be reached from these model results, with implications for the economic success of industrial operations, for the occupational safety and health and for the environment, the engineering models need to be highly reliable. Using these models engineers can quantify the effect of manufacturing tolerances, wear, corrosion, etc. This book describes in great details the experimental programs that are developed to validate the numerical results.
Klasztorny, M.; Urbanski, A.
2005-01-01
In the paper, the WL quasi-exact reinforcement theory of fibrous polymeric composites is improved. An optimum compatibility condition related to the transverse shear problem for a unit cell, which brings solutions closest to reality, is derived. This condition is formulated in the form of a linear combination of maximum radial and circumferential displacements. Optimum coefficients of this combination are determined by comparing analytical and numerical solutions for a test specimen in the form of a rectangular thin plate, which is in a plane strain state and is subject to selected loading schemes. The analytic solutions are obtained for a homogenized material by using the WL reinforcement theory. The numerical solutions are found for an actual heterogeneous composite material by using the finite-element method, and they verify the WL reinforcement theory, in particular, the admissibility of Hill's assumption. An analysis performed for two composite materials shows that the improved WL reinforcement theory gives adequate displacement fields.
Wang, Bo; Bauer, Sebastian
2016-04-01
Geological models are the prerequisite of exploring possible use of the subsurface and evaluating induced impacts. Subsurface geological models often show strong complexity in geometry and hydraulic connectivity because of their heterogeneous nature. In order to model that complexity, the corner point grid approach has been applied by geologists for decades. The corner point grid utilizes a set of hexahedral blocks to represent geological formations. Due to the appearance of eroded geological layers, some edges of those blocks may be collapsed and the blocks thus degenerate. This leads to the inconsistency and the impossibility of using the corner point grid directly with a finite element based simulator. Therefore, in this study, we introduce a workflow for transferring heterogeneous geological models to consistent finite element models. In the corner point grid, the hexahedral blocks without collapsed edges are converted to hexahedral elements directly. But if they degenerate, each block is divided into prism, pyramid and tetrahedral elements based on individual degenerated situation. This approach consistently converts any degenerated corner point grid to a consistent hybrid finite element mesh. Along with the above converting scheme, the corresponding heterogeneous geological data, e.g. permeability and porosity, can be transferred as well. Moreover, well trajectories designed in the corner point grid can be resampled to the nodes in the finite element mesh, which represents the location for source terms along the well path. As a proof of concept, we implement the workflow in the framework of transferring models from Petrel to the finite element OpenGeoSys simulator. As application scenario we choose a deep geothermal reservoir operation in the North German Basin. A well doublet is defined in a saline aquifer in the Rhaetian formation, which has a depth of roughly 4000 m. The geometric model shows all kinds of degenerated blocks due to eroded layers and the
Preconditioned CG-solvers and finite element grids
Energy Technology Data Exchange (ETDEWEB)
Bauer, R.; Selberherr, S. [Technical Univ. of Vienna (Austria)
1994-12-31
To extract parasitic capacitances in wiring structures of integrated circuits the authors developed the two- and three-dimensional finite element program SCAP (Smart Capacitance Analysis Program). The program computes the task of the electrostatic field from a solution of Poisson`s equation via finite elements and calculates the energies from which the capacitance matrix is extracted. The unknown potential vector, which has for three-dimensional applications 5000-50000 unknowns, is computed by a ICCG solver. Currently three- and six-node triangular, four- and ten-node tetrahedronal elements are supported.
Adaptive grid finite element model of the tokamak scrapeoff layer
Energy Technology Data Exchange (ETDEWEB)
Kuprat, A.P.; Glasser, A.H. [Los Alamos National Lab., NM (United States)
1995-07-01
The authors discuss unstructured grids for application to transport in the tokamak edge SOL. They have developed a new metric with which to judge element elongation and resolution requirements. Using this method, the authors apply a standard moving finite element technique to advance the SOL equations while inserting/deleting dynamically nodes that violate an elongation criterion. In a tokamak plasma, this method achieves a more uniform accuracy, and results in highly stretched triangular finite elements, except near separatrix X-point where transport is more isotropic.
Model Reduction in Dynamic Finite Element Analysis of Lightweight Structures
DEFF Research Database (Denmark)
Flodén, Ola; Persson, Kent; Sjöström, Anders
2012-01-01
The application of wood as a construction material when building multi-storey buildings has many advantages, e.g., light weight, sustainability and low energy consumption during the construction and lifecycle of the building. However, compared to heavy structures, it is a greater challenge to build...... lightweight structures without noise and disturbing vibrations between storeys and rooms. The dynamic response of floor and wall structures may be investigated using finite element models with three-dimensional solid elements [1]. In order to analyse the global response of complete buildings, finite element...
Compatible finite element spaces for geophysical fluid dynamics
Natale, Andrea
2016-01-01
Compatible finite elements provide a framework for preserving important structures in equations of geophysical fluid dynamics, and are becoming important in their use for building atmosphere and ocean models. We survey the application of compatible finite element spaces to geophysical fluid dynamics, including the application to the nonlinear rotating shallow water equations, and the three-dimensional compressible Euler equations. We summarise analytic results about dispersion relations and conservation properties, and present new results on approximation properties in three dimensions on the sphere, and on hydrostatic balance properties.
Stochastic Finite Elements in Reliability-Based Structural Optimization
DEFF Research Database (Denmark)
Sørensen, John Dalsgaard; Engelund, S.
1995-01-01
Application of stochastic finite elements in structural optimization is considered. It is shown how stochastic fields modelling e.g. the modulus of elasticity can be discretized in stochastic variables and how a sensitivity analysis of the reliability of a structural system with respect to optimi......Application of stochastic finite elements in structural optimization is considered. It is shown how stochastic fields modelling e.g. the modulus of elasticity can be discretized in stochastic variables and how a sensitivity analysis of the reliability of a structural system with respect...
Stochastic Finite Elements in Reliability-Based Structural Optimization
DEFF Research Database (Denmark)
Sørensen, John Dalsgaard; Engelund, S.
Application of stochastic finite elements in structural optimization is considered. It is shown how stochastic fields modelling e.g. the modulus of elasticity can be discretized in stochastic variables and how a sensitivity analysis of the reliability of a structural system with respect to optimi......Application of stochastic finite elements in structural optimization is considered. It is shown how stochastic fields modelling e.g. the modulus of elasticity can be discretized in stochastic variables and how a sensitivity analysis of the reliability of a structural system with respect...
National Research Council Canada - National Science Library
Ahmed Elmarakbi; Niki Fielding; Homayoun Hadavinia
2011-01-01
... the explicit finite element code LS-DYNA. Results compare the absorbed energy and the deflection of each variable, and recommend best design for the tube structure which improved vehicle crashworthiness. KEYWORDS: Energy absorption; thin-walled structures; vehicle impact; finite element analysis; design optimization 1. Introduction Currently within the UK there ar...
Orthodontic treatment: Introducing finite element analysis
Driel, W.D. van; Leeuwen, E.J. van
1998-01-01
The aim of orthodontic treatment is the displacement of teeth by means ofspecial appliances, like braces and brackets. Through these appliances the orthodontist can apply a set of forces to the teeth which wilt result in its displacement through the jawbone. Finite Element analysis of this process e
Interval Finite Element Analysis of Wing Flutter
Institute of Scientific and Technical Information of China (English)
Wang Xiaojun; Qiu Zhiping
2008-01-01
The influences of uncertainties in structural parameters on the flutter speed of wing are studied. On the basis of the deterministic flutter analysis model of wing, the uncertainties in structural parameters are considered and described by interval numbers. By virtue of first-order Taylor series expansion, the lower and upper bound curves of the transient decay rate coefficient versus wind velocity are given. So the interval estimation of the flutter critical wind speed of wing can be obtained, which is more reasonable than the point esti- mation obtained by the deterministic flutter analysis and provides the basis for the further non-probabilistic interval reliability analysis of wing flutter. The flow chart for interval finite element model of flutter analysis of wing is given. The proposed interval finite element model and the stochastic finite element model for wing flutter analysis are compared by the examples of a three degrees of freedorn airfoil and fuselage and a 15° swepthack wing, and the results have shown the effectiveness and feasibility of the presented model. The prominent advantage of the proposed interval finite element model is that only the bounds of uncertain parameters axe required, and the probabilistic distribution densities or other statistical characteristics are not needed.
Fast finite elements for surgery simulation
DEFF Research Database (Denmark)
Bro-Nielsen, Morten
1997-01-01
This paper discusses volumetric deformable models for modeling human body parts and organs in surgery simulation systems. These models are built using finite element models for linear elastic materials. To achieve real-time response condensation has been applied to the system stiffness matrix, an...
Jarray, M.; Souchet, D.; Henry, Y.; Fatu, A.
2017-02-01
Helical groove seal, is one of the very few non-contact seals that have the capability to effectively seal a liquid. It finds use mainly in turbines and compressors. Although its reliability, this type of seals has not been investigated thoroughly because of its complex characteristics. This work presents a numerical analysis of a helical groove seal operating in laminar regime by means of solving the Reynolds equations for incompressible fluid film in steady state. Equations governing the fluid flow were solved by the finite element method. Although the simplifying assumptions of Reynolds model help to keep the computational time at an acceptable level, the inertia effects are neglected which may lead to unreliable results especially where the film thickness is discontinuous. The present approach, inspired by Arghir et al. [1] is able to take into account concentrated inertia effects, as described by a generalized Bernoulli equation. Comparisons made with the classical Reynolds model show that the film discontinuities should be taken into account when dealing with helically grooved seals. In addition, the leakage of fluid towards the air side was investigated for different parameters such as the groove angle and depth.
Bhardwaj, Rajneesh; Mittal, Rajat
2011-11-01
The modeling of complex biological phenomena such as cardiac mechanics is challenging. It involves complex three dimensional geometries, moving structure boundaries inside the fluid domain and large flow-induced deformations of the structure. We present a fluid-structure interaction solver (FSI) which couples a sharp-interface immersed boundary method for flow simulation with a powerful finite-element based structure dynamics solver. An implicit partitioned (or segregated) approach is implemented to ensure the stability of the solver. We validate the FSI solver with published benchmark for a configuration which involves a thin elastic plate attached to a rigid cylinder. The frequency and amplitude of the oscillations of the plate are in good agreement with published results and non-linear dynamics of the plate and its coupling with the flow field are discussed. The FSI solver is used to understand left-ventricular hemodynamics and flow-induced dynamics of mitral leaflets during early diastolic filling and results from this study are presented.
Directory of Open Access Journals (Sweden)
R. Agarwal
2016-09-01
Full Text Available Micro-electro-mechanical systems (MEMS-based cantilever platform have capability for the detection of chemical and biological agents. This paper reports about the finite element method (FEM based design and simulations of MEMS-based piezoresistor cantilever platform to be used for detection of chemical and biological toxic agents. Bulk micromachining technique is adopted for the realisation of the device structure. MEMS piezoresistive biosensing platforms are having potential for a field-based label-free detection of various types of bio-molecules. Using the MEMMECH module of CoventorWare® simulations are performed on the designed model of the device and it is observed that principal stress is maximum along the length (among other dimensions of the micro-cantilever and remains almost constant for 90 per cent of the length of the micro-cantilever. The dimensions of piezoresistor are optimised and the output voltage vs. stress analysis for various lengths of the piezoresistor is performed using the MEMPZR module of the CoventorWare®.
Wang, Linyuan; Song, Shulei; Deng, Hongbo; Zhong, Kai
2017-07-01
In nowadays, repair method using fiber reinforced composites as the mainstream pipe repair technology, it can provide security for X100 high-grade steel energy long-distance pipelines in engineering. In this paper, analysis of cracked X100 high-grade steel pipe was conducted, simulation analysis was made on structure of pipes and crack arresters (CAs) to obtain the J-integral value in virtue of ANSYS Workbench finite element software and evaluation on crack arrest effects was done through measured elastic-plastic fracture mechanics parameter J-integral and the crack arrest coefficient K, in a bid to summarize effect laws of composite CAs and size of pipes and cracks for repairing CAs. The results indicate that the K value is correlated with laying angle λ, laying length L2/D1, laying thickness T1/T2of CAs, crack depth c/T1 and crack length a/c, and calculate recommended parameters for repairing fiber reinforced composite CAs in terms of two different crack forms.
Nordendale, Nikolas A.; Heard, William F.; Sherburn, Jesse A.; Basu, Prodyot K.
2016-03-01
The response of structural components of high-strength cementitious (HSC) materials to projectile impact is characterized by high-rate fragmentation resulting from strong compressive shock waves coupled with reflected tensile waves. Accurate modeling of armor panels of such brittle materials under high-velocity projectile impact is a complex problem requiring meticulous experimental characterization of material properties. In a recent paper by the authors, an approach to handle such problems based on a modified Advanced Fundamental Concrete (AFC) constitutive model was developed. In the HSC panels considered in this study, an analogous approach is applied, and the predictions are verified with ballistic impact test data. Traditional Lagrangian finite element analysis (FEA) of these problems tends to introduce errors and suffers from convergence issues resulting from large deformations at free surfaces. Also, FEA cannot properly account for the issues of secondary impact of spalled fragments when multiple armor panels are used. Smoothed particle hydrodynamics (SPH) is considered to be an attractive alternative to resolve these and other issues. However, SPH-based quantitative results have been found to be less accurate than the FEA-based ones when the deformations are not sufficiently large. This paper primarily focuses on a comparison of FEA and SPH models to predict high-velocity projectile impact on single and stacked HSC panels. Results are compared to recent ballistic experiments performed as a part of this research, and conclusions are drawn based on the findings.
On Hybrid and mixed finite element methods
Pian, T. H. H.
1981-01-01
Three versions of the assumed stress hybrid model in finite element methods and the corresponding variational principles for the formulation are presented. Examples of rank deficiency for stiffness matrices by the hybrid stress model are given and their corresponding kinematic deformation modes are identified. A discussion of the derivation of general semi-Loof elements for plates and shells by the hybrid stress method is given. It is shown that the equilibrium model by Fraeijs de Veubeke can be derived by the approach of the hybrid stress model as a special case of semi-Loof elements.
Finite Dynamic Elements and Modal Analysis
Directory of Open Access Journals (Sweden)
N.J. Fergusson
1993-01-01
Full Text Available A general modal analysis scheme is derived for forced response that makes use of high accuracy modes computed by the dynamic element method. The new procedure differs from the usual modal analysis in that the modes are obtained from a power series expansion for the dynamic stiffness matrix that includes an extra dynamic correction term in addition to the static stiffness matrix and the consistent mass matrix based on static displacement. A cantilevered beam example is used to demonstrate the relative accuracies of the dynamic element and the traditional finite element methods.
Finite element analysis of tibial fractures
DEFF Research Database (Denmark)
Wong, Christian Nai En; Mikkelsen, Mikkel Peter W; Hansen, Leif Berner
2010-01-01
INTRODUCTION: Fractures of the tibial shaft are relatively common injuries. There are indications that tibial shaft fractures share characteristics in terms of site, type and local fracture mechanisms. In this study, we aimed to set up a mathematical, computer-based model using finite element...... analysis of the bones of the lower leg to examine if such a model is adequate for prediction of fracture locations and patterns. In future studies, we aim to use these biomechanical results to examine fracture prevention, among others, and to simulate different types of osteosynthesis and the process...... Project. The data consisted of 21,219 3D elements with a cortical shell and a trabecular core. Three types of load of torsion, a direct lateral load and axial compression were applied. RESULTS: The finite element linear static analysis resulted in relevant fracture localizations and indicated relevant...
Finite Element Simulation for Springback Prediction Compensation
Directory of Open Access Journals (Sweden)
Agus Dwi Anggono
2011-01-01
Full Text Available An accurate modelling of the sheet metal deformations including the springback prediction is one of the key factors in the efficient utilisation of Finite Element Method (FEM process simulation in industrial application. Assuming that springback can be predicted accurately, there still remains the problem of how to use such results to appear at a suitable die design to produce a target part shape. It is this second step of springback compensation that is addressed in the current work. This paper presents an evaluation of a standard benchmark model defined as Benchmark II of Numisheet 2008, S-channel model with various drawbeads and blank holder force (BHF. The tool geometry modified based on springback calculation for a part to compensate springback. The result shows that the combination of the smooth bead with BHF of 650 kN resulted in the minimum springback and the tool compensation was successfully to accommodate the springback errors.
Jiang, Binhui; Mao, Haojie; Cao, Libo; Yang, King H
2014-09-01
Improved Cardiopulmonary Resuscitation (CPR) approaches will largely benefit the children in need. The constant peak displacement and constant peak force loading methods were analyzed on hard bed for pediatric CPR by an anatomically-detailed 10 year-old (YO) child thorax finite element (FE) model. The chest compression and rib injury risk were studied for children with various levels of thorax stiffness. We created three thorax models with different chest stiffness. Simulated CPR׳s in the above two conditions were performed. Three different compression rates were considered under the constant peak displacement condition. The model-calculated deflections and forces were analyzed. The rib maximum principle strains (MPS׳s) were used to predict the potential risk of rib injury. Under the constant peak force condition, the chest deflection ranged from 34.2 to 42.2mm. The highest rib MPS was 0.75%, predicted by the compliant thorax model. Under the normal constant peak displacement condition, the highest rib MPS was 0.52%, predicted by the compliant thorax model. The compression rate did not affect the highest rib MPS. Results revealed that the thoracic stiffness had great effects on the quality of CPR. To maintain CPR quality for various children, the constant peak displacement technique is recommended when the CPR is performed on the hard bed. Furthermore, the outcome of CPR in terms of rib strains and total work are not sensitive to the compression rate. The FE model-predicted high strains were in the ribs, which have been found to be vulnerable to CPR in the literature. Copyright © 2014 Elsevier Ltd. All rights reserved.
Ge, Changfeng; Cheng, Yujie; Shen, Yan
2013-01-01
This study demonstrated an attempt to predict temperatures of a perishable product such as vaccine inside an insulated packaging container during transport through finite element analysis (FEA) modeling. In order to use the standard FEA software for simulation, an equivalent heat conduction coefficient is proposed and calculated to describe the heat transfer of the air trapped inside the insulated packaging container. The three-dimensional, insulated packaging container is regarded as a combination of six panels, and the heat flow at each side panel is a one-dimension diffusion process. The transit-thermal analysis was applied to simulate the heat transition process from ambient environment to inside the container. Field measurements were carried out to collect the temperature during transport, and the collected data were compared to the FEA simulation results. Insulated packaging containers are used to transport temperature-sensitive products such as vaccine and other pharmaceutical products. The container is usually made of an extruded polystyrene foam filled with gel packs. World Health Organization guidelines recommend that all vaccines except oral polio vaccine be distributed in an environment where the temperature ranges between +2 to +8 °C. The primary areas of concern in designing the packaging for vaccine are how much of the foam thickness and gel packs should be used in order to keep the temperature in a desired range, and how to prevent the vaccine from exposure to freezing temperatures. This study uses numerical simulation to predict temperature change within an insulated packaging container in vaccine cold chain. It is our hope that this simulation will provide the vaccine industries with an alternative engineering tool to validate vaccine packaging and project thermal equilibrium within the insulated packaging container.
Energy Technology Data Exchange (ETDEWEB)
Klein, B. [Kassel Univ. (Germany). Leichbau, CAD und Entwicklungsmethodik
2007-07-01
Virtual product development at the workstation has become reality, creating a link between 3D-CAD, MKS, FEM, STRUOPT and Rapid Prototyping. Engineers must have good knowledge of computer-assisted techniques. The key element of CAE is the finite element method (FEM) which is a universal analytical tool providing deep insight into the elastic, dynamic, cinematic/kinetic, thermal, and fluid-mechanical characteristics of components and systems. On the basis of these simulations, reliable predictions are possible that will shorten innovation and trial periods and result in very short amortisation periods of FEM investments. This is shown by the textbook in a very clear and illustrative manner. Case studies are presented to enable the reader to deepen her knowledge by herself. (orig.)
The Development of Piezoelectric Accelerometers Using Finite Element Analysis
DEFF Research Database (Denmark)
Liu, Bin
1999-01-01
This paper describes the application of Finite Element (FE) approach for the development of piezoelectric accelerometers. An accelerometer is simulated using the FE approach as an example. Good agreement is achieved between simulated results and calibrated results. It is proved that the FE modeling...
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.
Matlab and C programming for Trefftz finite element methods
Qin, Qing-Hua
2008-01-01
Although the Trefftz finite element method (FEM) has become a powerful computational tool in the analysis of plane elasticity, thin and thick plate bending, Poisson's equation, heat conduction, and piezoelectric materials, there are few books that offer a comprehensive computer programming treatment of the subject. Collecting results scattered in the literature, MATLAB® and C Programming for Trefftz Finite Element Methods provides the detailed MATLAB® and C programming processes in applications of the Trefftz FEM to potential and elastic problems. The book begins with an introduction to th
Experimentally validated finite element model of electrocaloric multilayer ceramic structures
Energy Technology Data Exchange (ETDEWEB)
Smith, N. A. S., E-mail: nadia.smith@npl.co.uk, E-mail: maciej.rokosz@npl.co.uk, E-mail: tatiana.correia@npl.co.uk; Correia, T. M., E-mail: nadia.smith@npl.co.uk, E-mail: maciej.rokosz@npl.co.uk, E-mail: tatiana.correia@npl.co.uk [National Physical Laboratory, Hampton Road, TW11 0LW Middlesex (United Kingdom); Rokosz, M. K., E-mail: nadia.smith@npl.co.uk, E-mail: maciej.rokosz@npl.co.uk, E-mail: tatiana.correia@npl.co.uk [National Physical Laboratory, Hampton Road, TW11 0LW Middlesex (United Kingdom); Department of Materials, Imperial College London, London SW7 2AZ (United Kingdom)
2014-07-28
A novel finite element model to simulate the electrocaloric response of a multilayer ceramic capacitor (MLCC) under real environment and operational conditions has been developed. The two-dimensional transient conductive heat transfer model presented includes the electrocaloric effect as a source term, as well as accounting for radiative and convective effects. The model has been validated with experimental data obtained from the direct imaging of MLCC transient temperature variation under application of an electric field. The good agreement between simulated and experimental data, suggests that the novel experimental direct measurement methodology and the finite element model could be used to support the design of optimised electrocaloric units and operating conditions.
Robust Hybrid Finite Element Methods for Antennas and Microwave Circuits
Gong, J.; Volakis, John L.
1996-01-01
One of the primary goals in this dissertation is concerned with the development of robust hybrid finite element-boundary integral (FE-BI) techniques for modeling and design of conformal antennas of arbitrary shape. Both the finite element and integral equation methods will be first overviewed in this chapter with an emphasis on recently developed hybrid FE-BI methodologies for antennas, microwave and millimeter wave applications. The structure of the dissertation is then outlined. We conclude the chapter with discussions of certain fundamental concepts and methods in electromagnetics, which are important to this study.
The Finite Element Method An Introduction with Partial Differential Equations
Davies, A J
2011-01-01
The finite element method is a technique for solving problems in applied science and engineering. The essence of this book is the application of the finite element method to the solution of boundary and initial-value problems posed in terms of partial differential equations. The method is developed for the solution of Poisson's equation, in a weighted-residual context, and then proceeds to time-dependent and nonlinear problems. The relationship with the variational approach is alsoexplained. This book is written at an introductory level, developing all the necessary concepts where required. Co
SURFACE FINITE ELEMENTS FOR PARABOLIC EQUATIONS
Institute of Scientific and Technical Information of China (English)
G. Dziuk; C.M. Elliott
2007-01-01
In this article we define a surface finite element method (SFEM) for the numerical solution of parabolic partial differential equations on hypersurfaces Γ in (R)n+1. The key idea is based on the approximation of Γ by a polyhedral surface Γh consisting of a union of simplices (triangles for n = 2, intervals for n = 1) with vertices on Γ. A finite element space of functions is then defined by taking the continuous functions on Γh which are linear affine on each simplex of the polygonal surface. We use surface gradients to define weak forms of elliptic operators and naturally generate weak formulations of elliptic and parabolic equations on Γ. Our finite element method is applied to weak forms of the equations. The computation of the mass and element stiffness matrices are simple and straightforward.We give an example of error bounds in the case of semi-discretization in space for a fourth order linear problem. Numerical experiments are described for several linear and nonlinear partial differential equations. In particular the power of the method is demonstrated by employing it to solve highly nonlinear second and fourth order problems such as surface Allen-Cahn and Cahn-Hilliard equations and surface level set equations for geodesic mean curvature flow.
Probabilistic finite elements for transient analysis in nonlinear continua
Liu, W. K.; Belytschko, T.; Mani, A.
1985-01-01
The probabilistic finite element method (PFEM), which is a combination of finite element methods and second-moment analysis, is formulated for linear and nonlinear continua with inhomogeneous random fields. Analogous to the discretization of the displacement field in finite element methods, the random field is also discretized. The formulation is simplified by transforming the correlated variables to a set of uncorrelated variables through an eigenvalue orthogonalization. Furthermore, it is shown that a reduced set of the uncorrelated variables is sufficient for the second-moment analysis. Based on the linear formulation of the PFEM, the method is then extended to transient analysis in nonlinear continua. The accuracy and efficiency of the method is demonstrated by application to a one-dimensional, elastic/plastic wave propagation problem. The moments calculated compare favorably with those obtained by Monte Carlo simulation. Also, the procedure is amenable to implementation in deterministic FEM based computer programs.
Ferguson, Stephen J; Visser, Judith M A; Polikeit, Anne
2006-02-01
Polyetheretherketone (PEEK) is a novel polymer with potential advantages for its use in demanding orthopaedic applications (e.g. intervertebral cages). However, the influence of a physiological environment on the mechanical stability of PEEK has not been reported. Furthermore, the suitability of the polymer for use in highly stressed spinal implants such as intervertebral cages has not been investigated. Therefore, a combined experimental and analytical study was performed to address these open questions. A quasi-static mechanical compression test was performed to compare the initial mechanical properties of PEEK-OPTIMA polymer in a dry, room-temperature and in an aqueous, 37 degrees C environment (n=10 per group). The creep behaviour of cylindrical PEEK polymer specimens (n=6) was measured in a simulated physiological environment at an applied stress level of 10 MPa for a loading duration of 2000 hours (12 weeks). To compare the biomechanical performance of different intervertebral cage types made from PEEK and titanium under complex loading conditions, a three-dimensional finite element model of a functional spinal unit was created. The elastic modulus of PEEK polymer specimens in a physiological environment was 1.8% lower than that of specimens tested at dry, room temperature conditions (Pcreep test showed an average creep strain of less than 0.1% after 2000 hours of loading. The finite element analysis demonstrated high strain and stress concentrations at the bone/implant interface, emphasizing the importance of cage geometry for load distribution. The stress and strain maxima in the implants were well below the material strength limits of PEEK. In summary, the experimental results verified the mechanical stability of the PEEK-OPTIMA polymer in a simulated physiological environment, and over extended loading periods. Finite element analysis supported the use of PEEK-OPTIMA for load-bearing intervertebral implants.
Finite element modeling of permanent magnet devices
Brauer, J. R.; Larkin, L. A.; Overbye, V. D.
1984-03-01
New techniques are presented for finite element modeling of permanent magnets in magnetic devices such as motors and generators. These techniques extend a previous sheet-current permanent magnet model that applies only for straight line B-H loops and rectangular-shaped magnets. Here Maxwell's equations are used to derive the model of a permanent magnet having a general curved B-H loop and any geometric shape. The model enables a nonlinear magnetic finite element program to use Newton-Raphson iteration to solve for saturable magnetic fields in a wide variety of devices containing permanent magnets and steels. The techniques are applied to a brushless dc motor with irregular-shaped permanent magnets. The calculated motor torque agrees well with measured torque.
Finite element modelling of solidification phenomena
Indian Academy of Sciences (India)
K N Seetharamu; R Paragasam; Ghulam A Quadir; Z A Zainal; B Sathya Prasad; T Sundararajan
2001-02-01
The process of solidification process is complex in nature and the simulation of such process is required in industry before it is actually undertaken. Finite element method is used to simulate the heat transfer process accompanying the solidification process. The metal and the mould along with the air gap formation is accounted in the heat transfer simulation. Distortion of the casting is caused due to non-uniform shrinkage associated with the process. Residual stresses are induced in the final castings. Simulation of the shrinkage and the thermal stresses are also carried out using finite element methods. The material behaviour is considered as visco-plastic. The simulations are compared with available experimental data and the comparison is found to be good. Special considerations regarding the simulation of solidification process are also brought out.
Finite element simulations with ANSYS workbench 16
Lee , Huei-Huang
2015-01-01
Finite Element Simulations with ANSYS Workbench 16 is a comprehensive and easy to understand workbook. It utilizes step-by-step instructions to help guide readers to learn finite element simulations. Twenty seven real world case studies are used throughout the book. Many of these cases are industrial or research projects the reader builds from scratch. All the files readers may need if they have trouble are available for download on the publishers website. Companion videos that demonstrate exactly how to preform each tutorial are available to readers by redeeming the access code that comes in the book. Relevant background knowledge is reviewed whenever necessary. To be efficient, the review is conceptual rather than mathematical. Key concepts are inserted whenever appropriate and summarized at the end of each chapter. Additional exercises or extension research problems are provided as homework at the end of each chapter. A learning approach emphasizing hands-on experiences spreads through this entire book. A...
Finite element modelling of SAW correlator
Tikka, Ajay C.; Al-Sarawi, Said F.; Abbott, Derek
2007-12-01
Numerical simulations of SAW correlators so far are limited to delta function and equivalent circuit models. These models are not accurate as they do not replicate the actual behaviour of the device. Manufacturing a correlator to specifically realise a different configuration is both expensive and time consuming. With the continuous improvement in computing capacity, switching to finite element modelling would be more appropriate. In this paper a novel way of modelling a SAW correlator using finite element analysis is presented. This modelling approach allows the consideration of different code implementation and device structures. This is demonstrated through simulation results for a 5×2-bit Barker sequence encoded SAW correlator. These results show the effect of both bulk and leaky modes on the device performance at various operating frequencies. Moreover, the ways in which the gain of the correlator can be optimised though variation of design parameters will also be outlined.
FINITE ELEMENT ANALYSIS FOR PERIFLEX COUPLINGS
Directory of Open Access Journals (Sweden)
URDEA Mihaela
2015-06-01
Full Text Available The Periflex shaft couplings with rubber sleeve have a hig elasticity and link two shafts in diesel-engine and electric drives. They are simple from the point of view of construction, easily mounted and dismounted. The main goal of this paper is to present a finite element analysis for the Periflex coupling using the Generative Structural Analysis from CATIA software package. This paper presents important information about how to prepare an assembly for creating a static analysis case and also the important steps for developing a finite element analysis. It is very important that the analysis model should have the same behavior as the real, also the loading model. The results are images corresponding to Von Mises Stresses and Translational Displacement magnitude.
Finite Element Simulation of Metal Quenching
Institute of Scientific and Technical Information of China (English)
方刚; 曾攀
2004-01-01
The evolution of the phase transformation and the resulting internal stresses and strains in metallic parts during quenching were modeled numerically. The numerical simulation of the metal quenching process was based on the metallo-thermo-mechanical theory using the finite element method to couple the temperature, phase transformation, and stress-strain fields. The numerical models are presented for the heat treatment and kinetics of the phase transformation. The finite element models and the phase transition kinetics accurately predict the distribution of the microstructure volume fractions, the temperature, the distortion, and the stress-strain relation during quenching. The two examples used to validate the models are the quenching of a small gear and of a large turbine rotor. The simulation results for the martensite phase volume fraction, the stresses, and the distortion in the gear agree well with the experimental data. The models can be used to optimize the quenching conditions to ensure product quality.
FINITE ELEMENT METHODS FOR SOBOLEV EQUATIONS
Institute of Scientific and Technical Information of China (English)
Tang Liu; Yan-ping Lin; Ming Rao; J. R. Cannon
2002-01-01
A new high-order time-stepping finite element method based upon the high-order numerical integration formula is formulated for Sobolev equations, whose computations consist of an iteration procedure coupled with a system of two elliptic equations. The optimal and superconvergence error estimates for this new method axe derived both in space and in time. Also, a class of new error estimates of convergence and superconvergence for the time-continuous finite element method is demonstrated in which there are no time derivatives of the exact solution involved, such that these estimates can be bounded by the norms of the known data. Moreover, some useful a-posteriori error estimators are given on the basis of the superconvergence estimates.
Finite element analysis of tibial fractures
DEFF Research Database (Denmark)
Wong, Christian Nai En; Mikkelsen, Mikkel Peter W; Hansen, Leif Berner
2010-01-01
INTRODUCTION: Fractures of the tibial shaft are relatively common injuries. There are indications that tibial shaft fractures share characteristics in terms of site, type and local fracture mechanisms. In this study, we aimed to set up a mathematical, computer-based model using finite element...... analysis of the bones of the lower leg to examine if such a model is adequate for prediction of fracture locations and patterns. In future studies, we aim to use these biomechanical results to examine fracture prevention, among others, and to simulate different types of osteosynthesis and the process...... of bony healing. The biomechanical results are the basis for fracture healing, biomechanical fall analysis and stability analysis of osteosynthesis. MATERIAL AND METHODS: A finite element model of the bony part of the lower leg was generated on the basis of computed tomography data from the Visible Human...
Multiphase Transformer Modelling using Finite Element Method
Directory of Open Access Journals (Sweden)
Nor Azizah Mohd Yusoff
2015-03-01
Full Text Available In the year of 1970 saw the starting invention of the five-phase motor as the milestone in advanced electric motor. Through the years, there are many researchers, which passionately worked towards developing for multiphase drive system. They developed a static transformation system to obtain a multiphase supply from the available three-phase supply. This idea gives an influence for further development in electric machines as an example; an efficient solution for bulk power transfer. This paper highlighted the detail descriptions that lead to five-phase supply with fixed voltage and frequency by using Finite-Element Method (FEM. Identifying of specification on a real transformer had been done before applied into software modeling. Therefore, Finite-Element Method provides clearly understandable in terms of visualize the geometry modeling, connection scheme and output waveform.
Introduction to nonlinear finite element analysis
Kim, Nam-Ho
2015-01-01
This book introduces the key concepts of nonlinear finite element analysis procedures. The book explains the fundamental theories of the field and provides instructions on how to apply the concepts to solving practical engineering problems. Instead of covering many nonlinear problems, the book focuses on three representative problems: nonlinear elasticity, elastoplasticity, and contact problems. The book is written independent of any particular software, but tutorials and examples using four commercial programs are included as appendices: ANSYS, NASTRAN, ABAQUS, and MATLAB. In particular, the MATLAB program includes all source codes so that students can develop their own material models, or different algorithms. This book also: · Presents clear explanations of nonlinear finite element analysis for elasticity, elastoplasticity, and contact problems · Includes many informative examples of nonlinear analyses so that students can clearly understand the nonlinear theory · ...
The finite element modeling of spiral ropes
Institute of Scientific and Technical Information of China (English)
Juan Wu
2014-01-01
Accurate understanding the behavior of spiral rope is complicated due to their complex geometry and complex contact conditions between the wires. This study proposed the finite element models of spiral ropes subjected to tensile loads. The parametric equations developed in this paper were implemented for geometric modeling of ropes. The 3D geometric models with different twisting manner, equal diameters of wires were generated in details by using Pro/ENGINEER software. The results of the present finite element analysis were on an acceptable level of accuracy as compared with those of theoretical and experimental data. Further development is ongoing to analysis the equivalent stresses induced by twisting manner of cables. The twisting manner of wires was important to spiral ropes in the three wire layers and the outer twisting manner of wires should be contrary to that of the second layer, no matter what is the first twisting manner of wires.
Finite element contact analysis of fractal surfaces
Energy Technology Data Exchange (ETDEWEB)
Sahoo, Prasanta; Ghosh, Niloy [Department of Mechanical Engineering, Jadavpur University, Kolkata 700032 (India)
2007-07-21
The present study considers finite element analysis of non-adhesive, frictionless elastic/elastic-plastic contact between a rigid flat plane and a self-affine fractal rough surface using the commercial finite element package ANSYS. Three-dimensional rough surfaces are generated using a modified two-variable Weierstrass-Mandelbrot function with given fractal parameters. Parametric studies are done to consider the general relations between contact properties and key material and surface parameters. The present analysis is validated with available experimental results in the literature. Non-dimensional contact area and displacement are obtained as functions of non-dimensional load for varying fractal surface parameters in the case of elastic contact and for varying rates of strain hardening in the case of elastic-plastic contact of fractal surfaces.
Finite element approach for transient analysis of multibody systems
Wu, Shih-Chin; Chang, Che-Wei; Housner, Jerrold M.
1992-01-01
A three-dimensional, finite element based formulation for the transient dynamics of constrained multibody systems with trusslike configurations is presented. A convected coordinate system is used to define the rigid-body motion of individual elements in the system. Deformation of each element is defined relative to its convected coordinate system. The formulation is oriented toward joint-dominated structures. Through a series of sequential transformations, the joint degree of freedom is built into the equations of motion of the element to reduce geometric constraints. Based on the derivation, a general-purpose code has been developed. Two examples are presented to illustrate the application of the code.
Adaptive Mixed Finite Element Methods for Parabolic Optimal Control Problems
Zuliang Lu
2011-01-01
We will investigate the adaptive mixed finite element methods for parabolic optimal control problems. The state and the costate are approximated by the lowest-order Raviart-Thomas mixed finite element spaces, and the control is approximated by piecewise constant elements. We derive a posteriori error estimates of the mixed finite element solutions for optimal control problems. Such a posteriori error estimates can be used to construct more efficient and reliable adaptive mixed finite element ...
Finite element simulation of heat transfer
Bergheau, Jean-Michel
2010-01-01
This book introduces the finite element method applied to the resolution of industrial heat transfer problems. Starting from steady conduction, the method is gradually extended to transient regimes, to traditional non-linearities, and to convective phenomena. Coupled problems involving heat transfer are then presented. Three types of couplings are discussed: coupling through boundary conditions (such as radiative heat transfer in cavities), addition of state variables (such as metallurgical phase change), and coupling through partial differential equations (such as electrical phenomena).? A re
Finite Element Simulation for Interfacial Evolutions
Institute of Scientific and Technical Information of China (English)
JianmingHUANG; WeiYANG
1998-01-01
A three-dimensional finite element scheme based upon a weak statement of the classical theory is explored to simulate migration of interfaces in materials under linear evaporation and condensation kinetics,The present scheme is exemplified by two cases:facet formation of single crystals;and the evolution of a tri-crystal film on a substrate where the effect of multiple kinetics is demonstrated.
FINITE-ELEMENT MODELING OF SALT TECTONICS
Directory of Open Access Journals (Sweden)
Natalia Bakhova
2012-09-01
Full Text Available The two-dimensional thermal model of graben structure in the presence of salt tectonics on the basis of a finite elements method is constructed. The analysis of the thermal field is based on the solution of stationary equation of heat conductivity with variable boundary conditions. The high precision of temperatures distribution and heat flows is received. The decision accuracy is no more than 0,6 %.
Finite element model of needle electrode sensitivity
Høyum, P.; Kalvøy, H.; Martinsen, Ø. G.; Grimnes, S.
2010-04-01
We used the Finite Element (FE) Method to estimate the sensitivity of a needle electrode for bioimpedance measurement. This current conducting needle with insulated shaft was inserted in a saline solution and current was measured at the neutral electrode. FE model resistance and reactance were calculated and successfully compared with measurements on a laboratory model. The sensitivity field was described graphically based on these FE simulations.
Finite element methods for incompressible flow problems
John, Volker
2016-01-01
This book explores finite element methods for incompressible flow problems: Stokes equations, stationary Navier-Stokes equations, and time-dependent Navier-Stokes equations. It focuses on numerical analysis, but also discusses the practical use of these methods and includes numerical illustrations. It also provides a comprehensive overview of analytical results for turbulence models. The proofs are presented step by step, allowing readers to more easily understand the analytical techniques.
Nonlinear Finite Element Analysis of Ocean Cables
Institute of Scientific and Technical Information of China (English)
Nam-Il KIM; Sang-Soo JEON; Moon-Young KIM
2004-01-01
This study has focused on developing numerical procedures for the dynamic nonlinear analysis of cable structures subjected to wave forces and ground motions in the ocean. A geometrically nonlinear finite element procedure using the isoparametric curved cable element based on the Lagrangian formulation is briefly summarized. A simple and accurate method to determine the initial equilibrium state of cable systems associated with self-weights, buoyancy and the motion of end points is presented using the load incremental method combined with penalty method. Also the Newmark method is used for dynamic nonlinear analysis of ocean cables. Numerical examples are presented to validate the present numerical method.
Finite Element Method in Machining Processes
Markopoulos, Angelos P
2013-01-01
Finite Element Method in Machining Processes provides a concise study on the way the Finite Element Method (FEM) is used in the case of manufacturing processes, primarily in machining. The basics of this kind of modeling are detailed to create a reference that will provide guidelines for those who start to study this method now, but also for scientists already involved in FEM and want to expand their research. A discussion on FEM, formulations and techniques currently in use is followed up by machining case studies. Orthogonal cutting, oblique cutting, 3D simulations for turning and milling, grinding, and state-of-the-art topics such as high speed machining and micromachining are explained with relevant examples. This is all supported by a literature review and a reference list for further study. As FEM is a key method for researchers in the manufacturing and especially in the machining sector, Finite Element Method in Machining Processes is a key reference for students studying manufacturing processes but al...
Putnam, J. B.; Unataroiu, C. D.; Somers, J. T.
2014-01-01
The THOR anthropomorphic test device (ATD) has been developed and continuously improved by the National Highway Traffic Safety Administration to provide automotive manufacturers an advanced tool that can be used to assess the injury risk of vehicle occupants in crash tests. Recently, a series of modifications were completed to improve the biofidelity of THOR ATD [1]. The updated THOR Modification Kit (THOR-K) ATD was employed at Wright-Patterson Air Base in 22 impact tests in three configurations: vertical, lateral, and spinal [2]. Although a computational finite element (FE) model of the THOR had been previously developed [3], updates to the model were needed to incorporate the recent changes in the modification kit. The main goal of this study was to develop and validate a FE model of the THOR-K ATD. The CAD drawings of the THOR-K ATD were reviewed and FE models were developed for the updated parts. For example, the head-skin geometry was found to change significantly, so its model was re-meshed (Fig. 1a). A protocol was developed to calibrate each component identified as key to the kinematic and kinetic response of the THOR-K head/neck ATD FE model (Fig. 1b). The available ATD tests were divided in two groups: a) calibration tests where the unknown material parameters of deformable parts (e.g., head skin, pelvis foam) were optimized to match the data and b) validation tests where the model response was only compared with test data by calculating their score using CORrelation and Analysis (CORA) rating system. Finally, the whole ATD model was validated under horizontal-, vertical-, and lateral-loading conditions against data recorded in the Wright Patterson tests [2]. Overall, the final THOR-K ATD model developed in this study is shown to respond similarly to the ATD in all validation tests. This good performance indicates that the optimization performed during calibration by using the CORA score as objective function is not test specific. Therefore confidence is
Ruiz-Baier, Ricardo; Lunati, Ivan
2016-10-01
We present a novel discretization scheme tailored to a class of multiphase models that regard the physical system as consisting of multiple interacting continua. In the framework of mixture theory, we consider a general mathematical model that entails solving a system of mass and momentum equations for both the mixture and one of the phases. The model results in a strongly coupled and nonlinear system of partial differential equations that are written in terms of phase and mixture (barycentric) velocities, phase pressure, and saturation. We construct an accurate, robust and reliable hybrid method that combines a mixed finite element discretization of the momentum equations with a primal discontinuous finite volume-element discretization of the mass (or transport) equations. The scheme is devised for unstructured meshes and relies on mixed Brezzi-Douglas-Marini approximations of phase and total velocities, on piecewise constant elements for the approximation of phase or total pressures, as well as on a primal formulation that employs discontinuous finite volume elements defined on a dual diamond mesh to approximate scalar fields of interest (such as volume fraction, total density, saturation, etc.). As the discretization scheme is derived for a general formulation of multicontinuum physical systems, it can be readily applied to a large class of simplified multiphase models; on the other, the approach can be seen as a generalization of these models that are commonly encountered in the literature and employed when the latter are not sufficiently accurate. An extensive set of numerical test cases involving two- and three-dimensional porous media are presented to demonstrate the accuracy of the method (displaying an optimal convergence rate), the physics-preserving properties of the mixed-primal scheme, as well as the robustness of the method (which is successfully used to simulate diverse physical phenomena such as density fingering, Terzaghi's consolidation
An 8-node tetrahedral finite element suitable for explicit transient dynamic simulations
Energy Technology Data Exchange (ETDEWEB)
Key, S.W.; Heinstein, M.W.; Stone, C.M. [Sandia National Labs., Albuquerque, NM (United States)
1997-12-31
Considerable effort has been expended in perfecting the algorithmic properties of 8-node hexahedral finite elements. Today the element is well understood and performs exceptionally well when used in modeling three-dimensional explicit transient dynamic events. However, the automatic generation of all-hexahedral meshes remains an elusive achievement. The alternative of automatic generation for all-tetrahedral finite element is a notoriously poor performer, and the 10-node quadratic tetrahedral finite element while a better performer numerically is computationally expensive. To use the all-tetrahedral mesh generation extant today, the authors have explored the creation of a quality 8-node tetrahedral finite element (a four-node tetrahedral finite element enriched with four midface nodal points). The derivation of the element`s gradient operator, studies in obtaining a suitable mass lumping and the element`s performance in applications are presented. In particular, they examine the 80node tetrahedral finite element`s behavior in longitudinal plane wave propagation, in transverse cylindrical wave propagation, and in simulating Taylor bar impacts. The element only samples constant strain states and, therefore, has 12 hourglass modes. In this regard, it bears similarities to the 8-node, mean-quadrature hexahedral finite element. Given automatic all-tetrahedral meshing, the 8-node, constant-strain tetrahedral finite element is a suitable replacement for the 8-node hexahedral finite element and handbuilt meshes.
A finite element parametric modeling technique of aircraft wing structures
Institute of Scientific and Technical Information of China (English)
Tang Jiapeng; Xi Ping; Zhang Baoyuan; Hu Bifu
2013-01-01
A finite element parametric modeling method of aircraft wing structures is proposed in this paper because of time-consuming characteristics of finite element analysis pre-processing. The main research is positioned during the preliminary design phase of aircraft structures. A knowledge-driven system of fast finite element modeling is built. Based on this method, employing a template parametric technique, knowledge including design methods, rules, and expert experience in the process of modeling is encapsulated and a finite element model is established automatically, which greatly improves the speed, accuracy, and standardization degree of modeling. Skeleton model, geometric mesh model, and finite element model including finite element mesh and property data are established on parametric description and automatic update. The outcomes of research show that the method settles a series of problems of parameter association and model update in the pro-cess of finite element modeling which establishes a key technical basis for finite element parametric analysis and optimization design.
Finite Element Based Design and Optimization for Piezoelectric Accelerometers
DEFF Research Database (Denmark)
Liu, Bin; Kriegbaum, B.; Yao, Q.
1998-01-01
A systematic Finite Element design and optimisation procedure is implemented for the development of piezoelectric accelerometers. Most of the specifications of accelerometers can be obtained using the Finite Element simulations. The deviations between the simulated and calibrated sensitivities...
Finite element modeling for materials engineers using Matlab
Oluwole, Oluleke
2014-01-01
Finite Element Modeling for Materials Engineers Using MATLAB® combines the finite element method with MATLAB to offer materials engineers a fast and code-free way of modeling for many materials processes.
Finite element simulation of thick sheet thermoforming
Mercier, Daniel
This PhD was organized as collaboration between Lehigh University and the Ecole des Mines d'Albi on the subject: "Numerical simulation of thick sheet thermoforming". The research applications cover a wide range of products from thermoforming, e.g., packaging, automobile parts, appliance parts, large-scale panels and covers. Due to the special nature of this PhD, and the requirements of each hosting institutes, the research was split accordingly into two parts: At Lehigh University, under the supervision of Prof. Herman F. Nied, a full three-dimensional finite element program was developed in order to simulate the mechanical deformation during the process of thermoforming. The material behavior is considered hyperelastic with the property of incompressibility. The deformed structure may exhibit symmetries and may use a large choice of boundary conditions. A contact procedure for molds and/or displacements caused by a plug was implemented to complete the similarity with the thermoforming process. The research focused on simulating the observed nonlinear behaviors and their instabilities. The author emphasized the impact of large deformation on the numerical results and demonstrated the need for a remeshing capability. At the Ecole des Mines d'Albi, under the supervision of Prof. Fabrice Schmidt, an equi-biaxial rheometer was developed and built in order to determine the material properties during the process of thermoforming. Thermoplastic materials consist of long macromolecular chains that when stretched, during the process of sheet extrusion, exhibit a transversal isotropic behavior. The rheometer technique is the inflation of a circular membrane made of extruded thermoplastics. The resulting strain is identified by video analysis during the membrane inflation. This dissertation focused on technical issues related to heating with the goal of overcoming the difficulty of producing a homogeneous temperature distribution.
Stochastic finite elements: Where is the physics?
Directory of Open Access Journals (Sweden)
Ostoja-Starzewski Martin
2011-01-01
Full Text Available The micromechanics based on the Hill-Mandel condition indicates that the majority of stochastic finite element methods hinge on random field (RF models of material properties (such as Hooke’s law having no physical content, or even at odds with physics. At the same time, that condition allows one to set up the RFs of stiffness and compliance tensors in function of the mesoscale and actual random microstructure of the given material. The mesoscale is defined through a Statistical Volume Element (SVE, i.e. a material domain below the Representative Volume Element (RVE level. The paper outlines a procedure for stochastic scale-dependent homogenization leading to a determination of mesoscale one-point and two-point statistics and, thus, a construction of analytical RF models.
Directory of Open Access Journals (Sweden)
Ying-juan Lu
Full Text Available Stress on the bone surrounding dental micro-implants affects implant success.To compare the stress on the bone surrounding a micro-implant after application of a single force (SF of 200 g or a composite force (CF of 200 g and 6 N.mm torque.Finite element models were developed for micro-implant diameters of 1.2, 1.6, and 2.0 mm, and lengths of 6, 8, 10, and 12 mm and either a SF or CF was applied. The maximum equivalent stress (Max EQS of the bone surrounding the micro-implant was determined, and the relationships among type of force, diameter, and length were evaluated.The Max EQS of the CF exceeded that of the SF (P 1.2 mm.
Finite rotation shells basic equations and finite elements for Reissner kinematics
Wisniewski, K
2010-01-01
This book covers theoretical and computational aspects of non-linear shells. Several advanced topics of shell equations and finite elements - not included in standard textbooks on finite elements - are addressed, and the book includes an extensive bibliography.
Finite element simulation of asphalt fatigue testing
DEFF Research Database (Denmark)
Ullidtz, Per; Kieler, Thomas Lau; Kargo, Anders
1997-01-01
damage mechanics.The paper describes how continuum damage mechanics may be used with a finite element program to explain the progressive deterioration of asphalt mixes under laboratory fatigue testing. Both constant stress and constant strain testing are simulated, and compared to the actual results from...... three point and four point fatigue test on different mixes. It is shown that the same damage law, based on energy density, may be used to explain the gradual deterioration under constant stress as well as under constant strain testing.Some of the advantages of using this method for interpreting fatigue...
The serendipity family of finite elements
Arnold, Douglas N
2011-01-01
We give a new, simple, dimension-independent definition of the serendipity finite element family. The shape functions are the span of all monomials which are linear in at least s-r of the variables where s is the degree of the monomial or, equivalently, whose superlinear degree (total degree with respect to variables entering at least quadratically) is at most r. The degrees of freedom are given by moments of degree at most r-2d on each face of dimension d. We establish unisolvence and a geometric decomposition of the space.
Generalized multiscale finite element methods: Oversampling strategies
Efendiev, Yalchin R.
2014-01-01
In this paper, we propose oversampling strategies in the generalized multiscale finite element method (GMsFEM) framework. The GMsFEM, which has been recently introduced in Efendiev et al. (2013b) [Generalized Multiscale Finite Element Methods, J. Comput. Phys., vol. 251, pp. 116-135, 2013], allows solving multiscale parameter-dependent problems at a reduced computational cost by constructing a reduced-order representation of the solution on a coarse grid. The main idea of the method consists of (1) the construction of snapshot space, (2) the construction of the offline space, and (3) construction of the online space (the latter for parameter-dependent problems). In Efendiev et al. (2013b) [Generalized Multiscale Finite Element Methods, J. Comput. Phys., vol. 251, pp. 116-135, 2013], it was shown that the GMsFEM provides a flexible tool to solve multiscale problems with a complex input space by generating appropriate snapshot, offline, and online spaces. In this paper, we develop oversampling techniques to be used in this context (see Hou and Wu (1997) where oversampling is introduced for multiscale finite element methods). It is known (see Hou and Wu (1997)) that the oversampling can improve the accuracy of multiscale methods. In particular, the oversampling technique uses larger regions (larger than the target coarse block) in constructing local basis functions. Our motivation stems from the analysis presented in this paper, which shows that when using oversampling techniques in the construction of the snapshot space and offline space, GMsFEM will converge independent of small scales and high contrast under certain assumptions. We consider the use of a multiple eigenvalue problems to improve the convergence and discuss their relation to single spectral problems that use oversampled regions. The oversampling procedures proposed in this paper differ from those in Hou and Wu (1997). In particular, the oversampling domains are partially used in constructing local
Finite element modelingof spherical induction actuator
Galary, Grzegorz
2005-01-01
The thesis deals with finite element method simulations of the two-degree of freedom spherical induction actuator performed using the 2D and 3D models. In some cases non-linear magnetization curves, rotor movement and existence of higher harmonics are taken into account. The evolution of the model leading to its simplification is presented. Several rotor structures are tested, namely the one-layer, two-layers and two-layers-with-teeth rotor. The study of some rotor parameters, i.e. t...
A finite element model of ultrasonic extrusion
Energy Technology Data Exchange (ETDEWEB)
Lucas, M [Department of Mechanical Engineering, University of Glasgow, G12 8QQ (United Kingdom); Daud, Y, E-mail: m.lucas@mech.gla.ac.u [College of Science and Technology, UTM City Campus, Kuala Lumpur (Malaysia)
2009-08-01
Since the 1950's researchers have carried out investigations into the effects of applying ultrasonic excitation to metals undergoing elastic and plastic deformation. Experiments have been conducted where ultrasonic excitation is superimposed in complex metalworking operations such as wire drawing and extrusion, to identify the benefits of ultrasonic vibrations. This study presents a finite element analysis of ultrasonic excitation applied to the extrusion of a cylindrical aluminium bar. The effects of friction on the extrusion load are reported for the two excitation configurations of radially and axially applied ultrasonic vibrations and the results are compared with experimental data reported in the literature.
A finite element model of ultrasonic extrusion
Lucas, M.; Daud, Y.
2009-08-01
Since the 1950's researchers have carried out investigations into the effects of applying ultrasonic excitation to metals undergoing elastic and plastic deformation. Experiments have been conducted where ultrasonic excitation is superimposed in complex metalworking operations such as wire drawing and extrusion, to identify the benefits of ultrasonic vibrations. This study presents a finite element analysis of ultrasonic excitation applied to the extrusion of a cylindrical aluminium bar. The effects of friction on the extrusion load are reported for the two excitation configurations of radially and axially applied ultrasonic vibrations and the results are compared with experimental data reported in the literature.
Mixed finite elements for global tide models
Cotter, Colin J
2014-01-01
We study mixed finite element methods for the linearized rotating shallow water equations with linear drag and forcing terms. By means of a strong energy estimate for an equivalent second-order formulation for the linearized momentum, we prove long-time stability of the system without energy accumulation -- the geotryptic state. A priori error estimates for the linearized momentum and free surface elevation are given in $L^2$ as well as for the time derivative and divergence of the linearized momentum. Numerical results confirm the theoretical results regarding both energy damping and convergence rates.
A direct implementation for influence lines in finite element software
DEFF Research Database (Denmark)
Jepsen, Michael S.; Damkilde, Lars
2014-01-01
The use of influence lines is a recognized method for determining the critical design load conditions and this paper shows a direct method for applying influence lines in any structural finite element software. The main idea is to equate displacement or angular discontinuities with nodal forces...... to consistent nodal forces, which makes it very suitable for implementation in finite element schemes and applicable for all element types, such as shell, plates, beams etc. This paper derives the consistent nodal forces for angular, lateral and axial displacement discontinuities for a Bernoulli-Euler beam......, and subsequently obtain the influence function only applying a single load case without changing the geometry or boundary conditions of the model. The new approach for determining Influence lines is based on the Müller-Breslau principle, but the discontinuous displacement fields are in the new approach equated...
Finite Element Analysis of the Crack Propagation for Solid Materials
Directory of Open Access Journals (Sweden)
Miloud Souiyah
2009-01-01
Full Text Available Problem statement: The use of fracture mechanics techniques in the assessment of performance and reliability of structure is on increase and the prediction of crack propagation in structure play important part. The finite element method is widely used for the evaluation of SIF for various types of crack configurations. Source code program of two-dimensional finite element model had been developed, to demonstrate the capability and its limitations, in predicting the crack propagation trajectory and the SIF values under linear elastic fracture analysis. Approach: Two different geometries were used on this finite element model in order, to analyze the reliability of this program on the crack propagation in linear and nonlinear elastic fracture mechanics. These geometries were namely; a rectangular plate with crack emanating from square-hole and Double Edge Notched Plate (DENT. Where, both geometries are in tensile loading and under mode I conditions. In addition, the source code program of this model was written by FORTRAN language. Therefore, a Displacement Extrapolation Technique (DET was employed particularly, to predict the crack propagations directions and to, calculate the Stress Intensity Factors (SIFs. Furthermore, the mesh for the finite elements was the unstructured type; generated using the advancing front method. And, the global h-type adaptive mesh was adopted based on the norm stress error estimator. While, the quarter-point singular elements were uniformly generated around the crack tip in the form of a rosette. Moreover, make a comparison between this current study with other relevant and published research study. Results: The application of the source code program of 2-D finite element model showed a significant result on linear elastic fracture mechanics. Based on the findings of the two different geometries from the current study, the result showed a good agreement. And, it seems like very close compare to the other published
Finite element analysis of multilayer coextrusion.
Energy Technology Data Exchange (ETDEWEB)
Hopkins, Matthew Morgan; Schunk, Peter Randall; Baer, Thomas A. (Proctor & Gamble Company, West Chester, OH); Mrozek, Randy A. (Army Research Laboratory, Adelphi, MD); Lenhart, Joseph Ludlow (Army Research Laboratory, Adelphi, MD); Rao, Rekha Ranjana; Collins, Robert (Oak Ridge National Laboratory); Mondy, Lisa Ann
2011-09-01
Multilayer coextrusion has become a popular commercial process for producing complex polymeric products from soda bottles to reflective coatings. A numerical model of a multilayer coextrusion process is developed based on a finite element discretization and two different free-surface methods, an arbitrary-Lagrangian-Eulerian (ALE) moving mesh implementation and an Eulerian level set method, to understand the moving boundary problem associated with the polymer-polymer interface. The goal of this work is to have a numerical capability suitable for optimizing and troubleshooting the coextrusion process, circumventing flow instabilities such as ribbing and barring, and reducing variability in layer thickness. Though these instabilities can be both viscous and elastic in nature, for this work a generalized Newtonian description of the fluid is used. Models of varying degrees of complexity are investigated including stability analysis and direct three-dimensional finite element free surface approaches. The results of this work show how critical modeling can be to reduce build test cycles, improve material choices, and guide mold design.
Finite element analysis of bolted flange connections
Hwang, D. Y.; Stallings, J. M.
1994-06-01
A 2-D axisymmetric finite element model and a 3-D solid finite element model of a high pressure bolted flange joint were generated to investigate the stress behaviors. This investigation includes comparisons for axisymmetric loading of both the 2-D and 3-D models, the effects of non-axisymmetric bolt pretensions in the 3-D models, and the differences between 2-D and 3-D models subjected to non-axisymmetric loading. Comparisons indicated differences in von Mises stress up to 12% at various points due to the non-axisymmetric bolt pretensions. Applied bending moments were converted to equivalent axial forces for use in the 2-D model. It was found that the largest von Mises stresses in 3-D model did not occur on the side of the connection where the bending stresses and applied axial stresses were additive. Hence, in the 2-D model where the equivalent axial force (for bending moment) and applied axial forces were added, the 2-D model under estimated the maximum von Mises stress obtained from the 3-D model by 30%.
Impeller deflection and modal finite element analysis.
Energy Technology Data Exchange (ETDEWEB)
Spencer, Nathan A.
2013-10-01
Deflections of an impeller due to centripetal forces are calculated using finite element analysis. The lateral, or out of plane, deflections are an important design consideration for this particular impeller because it incorporates an air bearing with critical gap tolerances. The target gap distance is approximately 10 microns at a rotational velocity of 2500 rpm. The centripetal forces acting on the impeller cause it deflect in a concave fashion, decreasing the initial gap distance as a function of radial position. This deflection is characterized for a previous and updated impeller design for comparative purposes. The impact of design options such as material selection, geometry dimensions, and operating rotational velocity are also explored, followed by a sensitivity study with these parameters bounded by specific design values. A modal analysis is also performed to calculate the impeller's natural frequencies which are desired to be avoided during operation. The finite element modeling techniques continue to be exercised by the impeller design team to address specific questions and evaluate conceptual designs, some of which are included in the Appendix.
A multigrid solution method for mixed hybrid finite elements
Energy Technology Data Exchange (ETDEWEB)
Schmid, W. [Universitaet Augsburg (Germany)
1996-12-31
We consider the multigrid solution of linear equations arising within the discretization of elliptic second order boundary value problems of the form by mixed hybrid finite elements. Using the equivalence of mixed hybrid finite elements and non-conforming nodal finite elements, we construct a multigrid scheme for the corresponding non-conforming finite elements, and, by this equivalence, for the mixed hybrid finite elements, following guidelines from Arbogast/Chen. For a rectangular triangulation of the computational domain, this non-conforming schemes are the so-called nodal finite elements. We explicitly construct prolongation and restriction operators for this type of non-conforming finite elements. We discuss the use of plain multigrid and the multilevel-preconditioned cg-method and compare their efficiency in numerical tests.
Finite elements modeling of delaminations in composite laminates
DEFF Research Database (Denmark)
Gaiotti, m.; Rizzo, C.M.; Branner, Kim;
2011-01-01
The application of composite materials in many structures poses to engineers the problem to create reliable and relatively simple methods, able to estimate the strength of multilayer composite structures. Multilayer composites, like other laminated materials, suffer from layer separation, i.e., d...... by finite elements using different techniques. Results obtained with different finite element models are compared and discussed.......The application of composite materials in many structures poses to engineers the problem to create reliable and relatively simple methods, able to estimate the strength of multilayer composite structures. Multilayer composites, like other laminated materials, suffer from layer separation, i...... of the buckling strength of composite laminates containing delaminations. Namely, non-linear buckling and post-buckling analyses are carried out to predict the critical buckling load of elementary composite laminates affected by rectangular delaminations of different sizes and locations, which are modelled...
Accurate finite element modeling of acoustic waves
Idesman, A.; Pham, D.
2014-07-01
In the paper we suggest an accurate finite element approach for the modeling of acoustic waves under a suddenly applied load. We consider the standard linear elements and the linear elements with reduced dispersion for the space discretization as well as the explicit central-difference method for time integration. The analytical study of the numerical dispersion shows that the most accurate results can be obtained with the time increments close to the stability limit. However, even in this case and the use of the linear elements with reduced dispersion, mesh refinement leads to divergent numerical results for acoustic waves under a suddenly applied load. This is explained by large spurious high-frequency oscillations. For the quantification and the suppression of spurious oscillations, we have modified and applied a two-stage time-integration technique that includes the stage of basic computations and the filtering stage. This technique allows accurate convergent results at mesh refinement as well as significantly reduces the numerical anisotropy of solutions. We should mention that the approach suggested is very general and can be equally applied to any loading as well as for any space-discretization technique and any explicit or implicit time-integration method.
Finite element analysis of a deployable space structure
Hutton, D. V.
1982-01-01
To assess the dynamic characteristics of a deployable space truss, a finite element model of the Scientific Applications Space Platform (SASP) truss has been formulated. The model incorporates all additional degrees of freedom associated with the pin-jointed members. Comparison of results with SPAR models of the truss show that the joints of the deployable truss significantly affect the vibrational modes of the structure only if the truss is relatively short.
Better Finite-Element Analysis of Composite Shell Structures
Clarke, Gregory
2007-01-01
A computer program implements a finite-element-based method of predicting the deformations of thin aerospace structures made of isotropic materials or anisotropic fiber-reinforced composite materials. The technique and corresponding software are applicable to thin shell structures in general and are particularly useful for analysis of thin beamlike members having open cross-sections (e.g. I-beams and C-channels) in which significant warping can occur.
Application of LOD Technology in Groundwater Finite Element Post-processing%LOD技术在地下水有限元后处理中的应用
Institute of Scientific and Technical Information of China (English)
毕振波; 郑爱勤; 崔振东
2011-01-01
地下水有限元后处理阶段的数据量较大,这对模开重现、网络快速传输和计算结果的实时可视化造成困难.为此,分析地下水有限元后处理中面临的主要问题和LOD技术,指出顶点元素删除法是一种适应地下水有限元后处理的有效数据模型简化方法,设计顶点删除和恢复过程中的主要数据结构,并应用DT方法对“空洞”进行局部三角剖分.实例证明该方法在地下水有限元后处理中应用的有效性.%It is difficult for the reproducing, the rapid transmission based on network and the real time visualization of calculated results of finite element models that there is a large amount of data in finite element post-processing stage in groundwater. Therefore, based on analyzing the main problems existing in the post-processing of finite element in groundwater and Level of Detail(LOD) technology, this paper argues that vertex element deletion method is a effective data model simplification techniques adapted for finite element post-processing in groundwater, the main data structures of vertex element deletion and restoring are designed, DT method is used for the local triangulation meshing in the "hole" area. The real implemented example proves the effectiveness of vertex element deletion algorithm applied to finite element post-processing in groundwater.
A comparison of the finite difference and finite element methods for heat transfer calculations
Emery, A. F.; Mortazavi, H. R.
1982-01-01
The finite difference method and finite element method for heat transfer calculations are compared by describing their bases and their application to some common heat transfer problems. In general it is noted that neither method is clearly superior, and in many instances, the choice is quite arbitrary and depends more upon the codes available and upon the personal preference of the analyst than upon any well defined advantages of one method. Classes of problems for which one method or the other is better suited are defined.
A suitable low-order, eight-node tetrahedral finite element for solids
Energy Technology Data Exchange (ETDEWEB)
Key, S.W.; Heinstein, M.S.; Stone, C.M.; Mello, F.J.; Blanford, M.L.; Budge, K.G.
1998-03-01
To use the all-tetrahedral mesh generation existing today, the authors have explored the creation of a computationally efficient eight-node tetrahedral finite element (a four-node tetrahedral finite element enriched with four mid-face nodal points). The derivation of the element`s gradient operator, studies in obtaining a suitable mass lumping, and the element`s performance in applications are presented. In particular they examine the eight-node tetrahedral finite element`s behavior in longitudinal plane wave propagation, in transverse cylindrical wave propagation, and in simulating Taylor bar impacts. The element samples only constant strain states and, therefore, has 12 hour-glass modes. In this regard it bears similarities to the eight-node, mean-quadrature hexahedral finite element. Comparisons with the results obtained from the mean-quadrature eight-node hexahedral finite element and the four-node tetrahedral finite element are included. Given automatic all-tetrahedral meshing, the eight-node, constant-strain tetrahedral finite element is a suitable replacement for the eight-node hexahedral finite element in those cases where mesh generation requires an inordinate amount of user intervention and direction to obtain acceptable mesh properties.
Directory of Open Access Journals (Sweden)
J. A. Strasheim
1984-03-01
Full Text Available The central role played by finite element analysis in the structural design of the main magnets, vacuum chamber and resonator of a 200 MeV open sector cyclotron facility for the National Accelerator Centre at Faure, South Africa, is described. The design evolved through a series of conceptual layouts of the structures involved. A finite element model of a main magnet, a main magnet vacuum chamber, one of a resonator, three of a resonator vacuum chamber and three of a valley vacuum chamber have been drawn up so far.
Han, Daoru; Wang, Pu; He, Xiaoming; Lin, Tao; Wang, Joseph
2016-09-01
Motivated by the need to handle complex boundary conditions efficiently and accurately in particle-in-cell (PIC) simulations, this paper presents a three-dimensional (3D) linear immersed finite element (IFE) method with non-homogeneous flux jump conditions for solving electrostatic field involving complex boundary conditions using structured meshes independent of the interface. This method treats an object boundary as part of the simulation domain and solves the electric field at the boundary as an interface problem. In order to resolve charging on a dielectric surface, a new 3D linear IFE basis function is designed for each interface element to capture the electric field jump on the interface. Numerical experiments are provided to demonstrate the optimal convergence rates in L2 and H1 norms of the IFE solution. This new IFE method is integrated into a PIC method for simulations involving charging of a complex dielectric surface in a plasma. A numerical study of plasma-surface interactions at the lunar terminator is presented to demonstrate the applicability of the new method.
Tsai, C.; Szabo, B. A.
1973-01-01
An approch to the finite element method which utilizes families of conforming finite elements based on complete polynomials is presented. Finite element approximations based on this method converge with respect to progressively reduced element sizes as well as with respect to progressively increasing orders of approximation. Numerical results of static and dynamic applications of plates are presented to demonstrate the efficiency of the method. Comparisons are made with plate elements in NASTRAN and the high-precision plate element developed by Cowper and his co-workers. Some considerations are given to implementation of the constraint method into general purpose computer programs such as NASTRAN.
Frontal Crash Analysis of a Fully Detailed Car Model Based on Finite Element Method
Institute of Scientific and Technical Information of China (English)
Han Shan-Ling; Zhu Ping; Lin Zhong-Qin; Shi Yu-Liang
2004-01-01
This paper sets up a highly detailed finite element model of a car for frontal crashworthiness applications, and then explains the characteristics of it. The geometry model is preprocessed by Hypermesh software. The finite element method solver program selected for the simulation is LS-DYNA. After the crash simulation is carefully analyzed, the frontal crash experiment is aimed to validate the finite element model. The simulation results are basically in agreement with the experimental results. The validation of the finite element model is crucial for the further research in optimization of the automotive structure or lightweighting of the vehicle.
On conforming mixed finite element methods for incompressible viscous flow problems
Gunzburger, M. D; Nicolaides, R. A.; Peterson, J. S.
1982-01-01
The application of conforming mixed finite element methods to obtain approximate solutions of linearized Navier-Stokes equations is examined. Attention is given to the convergence rates of various finite element approximations of the pressure and the velocity field. The optimality of the convergence rates are addressed in terms of comparisons of the approximation convergence to a smooth solution in relation to the best approximation available for the finite element space used. Consideration is also devoted to techniques for efficient use of a Gaussian elimination algorithm to obtain a solution to a system of linear algebraic equations derived by finite element discretizations of linear partial differential equations.
ADAPTIVE FINITE ELEMENT METHOD FOR HIGH-SPEED FLOW-STRUCTURE INTERACTION
Institute of Scientific and Technical Information of China (English)
Wiroj LIMTRAKARN; Pramote DECHAUMPHAI
2004-01-01
An adaptive finite element method for high-speed flow-structure interaction is presented. The cell-centered finite element method is combined with an adaptive meshing technique to solve the Navier-Stokes equations for high-speed compressible flow behavior. The energy equation and the quasi-static structural equations for aerodynamically heated structures are solved by applying the Galerkin finite element method. The finite element formulation and computational procedure are described. Interactions between the high-speed flow, structural heat transfer, and deformation are studied by two applications of Mach 10 flow over an inclined plate, and Mach 4 flow in a channel.
Test Simulation using Finite Element Method
Energy Technology Data Exchange (ETDEWEB)
Ali, M B; Abdullah, S; Nuawi, M Z; Ariffin, A K, E-mail: abgbas@yahoo.com [Department of Mechanical and Materials Engineering, Faculty of Engineering and Built Environment Universiti Kebangsaan Malaysia 43600 Bangi, Selangor (Malaysia)
2011-02-15
The dynamic responses of the standard Charpy impact machine are experimentally studied using the relevant data acquisition system, for the purpose of obtaining the impact response. For this reason, the numerical analysis by means of the finite element method has been used for experiment findings. Modelling of the charpy test was performed in order to obtain strain in the striker during the test. Two types of standard charpy specimens fabricated from different materials, i.e. aluminium 6061 and low carbon steel 1050, were used for the impact simulation testing. The related parameters on between different materials, energy absorbed, strain signal, power spectrum density (PSD) and the relationship between those parameters was finally correlated and discussed.
Finite-Element Modelling of Biotransistors
Directory of Open Access Journals (Sweden)
Selvaganapathy PR
2010-01-01
Full Text Available Abstract Current research efforts in biosensor design attempt to integrate biochemical assays with semiconductor substrates and microfluidic assemblies to realize fully integrated lab-on-chip devices. The DNA biotransistor (BioFET is an example of such a device. The process of chemical modification of the FET and attachment of linker and probe molecules is a statistical process that can result in variations in the sensed signal between different BioFET cells in an array. In order to quantify these and other variations and assess their importance in the design, complete physical simulation of the device is necessary. Here, we perform a mean-field finite-element modelling of a short channel, two-dimensional BioFET device. We compare the results of this model with one-dimensional calculation results to show important differences, illustrating the importance of the molecular structure, placement and conformation of DNA in determining the output signal.
Friction welding; Magnesium; Finite element; Shear test.
Directory of Open Access Journals (Sweden)
Leonardo Contri Campanelli
2013-06-01
Full Text Available Friction spot welding (FSpW is one of the most recently developed solid state joining technologies. In this work, based on former publications, a computer aided draft and engineering resource is used to model a FSpW joint on AZ31 magnesium alloy sheets and subsequently submit the assembly to a typical shear test loading, using a linear elastic model, in order to conceive mechanical tests results. Finite element analysis shows that the plastic flow is concentrated on the welded zone periphery where yield strength is reached. It is supposed that “through the weld” and “circumferential pull-out” variants should be the main failure behaviors, although mechanical testing may provide other types of fracture due to metallurgical features.
Finite element methods in resistivity logging
Lovell, J. R.
1993-09-01
Resistivity measurements are used in geophysical logging to help determine hydrocarbon reserves. The derivation of formation parameters from resistivity measurements is a complicated nonlinear procedure often requiring additional geological information. This requires an excellent understanding of tool physics, both to design new tools and interpret the measurements of existing tools. The Laterolog measurements in particular are difficult to interpret because the response is very nonlinear as a function of electrical conductivity, unlike Induction measurements. Forward modeling of the Laterolog is almost invariably done with finite element codes which require the inversion of large sparse matrices. Modern techniques can be used to accelerate this inversion. Moreover, an understanding of the tool physics can help refine these numerical techniques.
Optimizing the Evaluation of Finite Element Matrices
Kirby, Robert C; Logg, Anders; Scott, L Ridgway; 10.1137/040607824
2012-01-01
Assembling stiffness matrices represents a significant cost in many finite element computations. We address the question of optimizing the evaluation of these matrices. By finding redundant computations, we are able to significantly reduce the cost of building local stiffness matrices for the Laplace operator and for the trilinear form for Navier-Stokes. For the Laplace operator in two space dimensions, we have developed a heuristic graph algorithm that searches for such redundancies and generates code for computing the local stiffness matrices. Up to cubics, we are able to build the stiffness matrix on any triangle in less than one multiply-add pair per entry. Up to sixth degree, we can do it in less than about two. Preliminary low-degree results for Poisson and Navier-Stokes operators in three dimensions are also promising.
Nonlinear Finite Element Analysis of Sloshing
Directory of Open Access Journals (Sweden)
Siva Srinivas Kolukula
2013-01-01
Full Text Available The disturbance on the free surface of the liquid when the liquid-filled tanks are excited is called sloshing. This paper examines the nonlinear sloshing response of the liquid free surface in partially filled two-dimensional rectangular tanks using finite element method. The liquid is assumed to be inviscid, irrotational, and incompressible; fully nonlinear potential wave theory is considered and mixed Eulerian-Lagrangian scheme is adopted. The velocities are obtained from potential using least square method for accurate evaluation. The fourth-order Runge-Kutta method is employed to advance the solution in time. A regridding technique based on cubic spline is employed to avoid numerical instabilities. Regular harmonic excitations and random excitations are used as the external disturbance to the container. The results obtained are compared with published results to validate the numerical method developed.
Adaptive finite element method for shape optimization
Morin, Pedro
2012-01-16
We examine shape optimization problems in the context of inexact sequential quadratic programming. Inexactness is a consequence of using adaptive finite element methods (AFEM) to approximate the state and adjoint equations (via the dual weighted residual method), update the boundary, and compute the geometric functional. We present a novel algorithm that equidistributes the errors due to shape optimization and discretization, thereby leading to coarse resolution in the early stages and fine resolution upon convergence, and thus optimizing the computational effort. We discuss the ability of the algorithm to detect whether or not geometric singularities such as corners are genuine to the problem or simply due to lack of resolution - a new paradigm in adaptivity. © EDP Sciences, SMAI, 2012.
Finite mathematics models and applications
Morris, Carla C
2015-01-01
Features step-by-step examples based on actual data and connects fundamental mathematical modeling skills and decision making concepts to everyday applicability Featuring key linear programming, matrix, and probability concepts, Finite Mathematics: Models and Applications emphasizes cross-disciplinary applications that relate mathematics to everyday life. The book provides a unique combination of practical mathematical applications to illustrate the wide use of mathematics in fields ranging from business, economics, finance, management, operations research, and the life and social sciences.
Finite element modeling of consolidation of composite laminates
Institute of Scientific and Technical Information of China (English)
Xiangqiao Yan
2006-01-01
Advanced fiber reinforced polymer composites have been increasingly applied to various structural corn-ponents.One of the important processes to fabricate high performance laminated composites is an autoclave assisted prepreg lay-up.Since the quality of laminated composites is largely affected by the cure cycle,selection of an appropriate cure cycle for each application is important and must be opti-mized.Thus.some fundamental model of the consolidation and cure processes is necessary for selecting suitable param-eters for a specific application.This article is concerned with the "flow-compaction" model during the autoclave process-ing of composite materials.By using a weighted residual method,two-dimensional finite element formulation for the consolidation process of thick thermosetting composites is presented and the corresponding finite element code is developed.Numerical examples.including comparison of the present numerical results with one-dimensional and two-dimensional analytical solutions,are given to illustrate the accuracy and effectiveness of the proposed finite element formulation.In addition,a consolidation simulation of As4/3501-6 graphite/epoxy laminate is carried out and compared with the experimental results available in the literature.
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.
Finite element simulation of wheel impact test
Directory of Open Access Journals (Sweden)
S.H. Yang
2008-06-01
Full Text Available Purpose: In order to achieve better performance and quality, the wheel design and manufacturing use a number of wheel tests (rotating bending test, radial fatigue test, and impact test to insure that the wheel meets the safety requirements. The test is very time consuming and expensive. Computer simulation of these tests can significantly reduce the time and cost required to perform a wheel design. In this study, nonlinear dynamic finite element is used to simulate the SAE wheel impact test.Design/methodology/approach: The test fixture used for the impact test consists of a striker with specified weight. The test is intended to simulate actual vehicle impact conditions. The tire-wheel assembly is mounted at 13° angle to the vertical plane with the edge of the weight in line with outer radius of the rim. The striker is dropped from a specified height above the highest point of the tire-wheel assembly and contacts the outboard flange of the wheel.Because of the irregular geometry of the wheel, the finite element model of an aluminium wheel is constructed by tetrahedral element. A mesh convergence study is carried out to ensure the convergence of the mesh model. The striker is assumed to be rigid elements. Initially, the striker contacts the highest area of the wheel, and the initial velocity of the striker is calculated from the impact height. The simulated strains at two locations on the disc are verified by experimental measurements by strain gages. The damage parameter of a wheel during the impact test is a strain energy density from the calculated result.Findings: The prediction of a wheel failure at impact is based on the condition that fracture will occur if the maximum strain energy density of the wheel during the impact test exceeds the total plastic work of the wheel material from tensile test. The simulated results in this work show that the total plastic work can be effectively employed as a fracture criterion to predict a wheel
Convergence of adaptive finite element methods for eigenvalue problems
Garau, Eduardo M.; Morin, Pedro; Zuppa, Carlos
2008-01-01
In this article we prove convergence of adaptive finite element methods for second order elliptic eigenvalue problems. We consider Lagrange finite elements of any degree and prove convergence for simple as well as multiple eigenvalues under a minimal refinement of marked elements, for all reasonable marking strategies, and starting from any initial triangulation.
Energy Technology Data Exchange (ETDEWEB)
George A. Zyvoloski; Bruce A. Robinson; Zora V. Dash; Lynn L. Trease
1997-07-01
The mathematical models and numerical methods employed by the FEHM application, a finite-element heat- and mass-transfer computer code that can simulate nonisothermal multiphase multi-component flow in porous media, are described. The use of this code is applicable to natural-state studies of geothermal systems and groundwater flow. A primary use of the FEHM application will be to assist in the understanding of flow fields and mass transport in the saturated and unsaturated zones below the proposed Yucca Mountain nuclear waste repository in Nevada. The component models of FEHM are discussed. The first major component, Flow- and Energy-Transport Equations, deals with heat conduction; heat and mass transfer with pressure- and temperature-dependent properties, relative permeabilities and capillary pressures; isothermal air-water transport; and heat and mass transfer with noncondensible gas. The second component, Dual-Porosity and Double-Porosity/Double-Permeability Formulation, is designed for problems dominated by fracture flow. Another component, The Solute-Transport Models, includes both a reactive-transport model that simulates transport of multiple solutes with chemical reaction and a particle-tracking model. Finally, the component, Constitutive Relationships, deals with pressure- and temperature-dependent fluid/air/gas properties, relative permeabilities and capillary pressures, stress dependencies, and reactive and sorbing solutes. Each of these components is discussed in detail, including purpose, assumptions and limitations, derivation, applications, numerical method type, derivation of numerical model, location in the FEHM code flow, numerical stability and accuracy, and alternative approaches to modeling the component.
Energy Technology Data Exchange (ETDEWEB)
Lee, Jungki; Kim, Ji Hyun [Ulsan National Institute of Science and Technology, Ulsan (Korea, Republic of)
2015-10-15
With same roll speed and same friction coefficient, curvature is formed on rolled product from FEA result. To reduce this curvature and plastic strain which cause reduction in fabricability, two ways are selected; (i) controlling upper/lower roll speed, and (ii) adjusting upper/lower friction coefficient and contacts. Both results shows it can reduce the curvature and equivalent plastic strain of the plate after the rolling. It can be applied in real plate rolling processing and also the next research for pilgering process for tube and pipe production. The FEA results of equivalent stress and plastic deformation distribution are showed in figure 5. The von-Mises equivalent stress distribution showed that the stress is still concentrated on upper Fe-12Cr-2Si layer, however, it also shows that equivalent plastic strain is distributed uniformly comparing with upper and lower roll speed ratio is 1.0. In high temperature liquid metal environment, there are usually two types of corrosion; one is corrosion by dissolution of alloy elements into liquid metal, and another is corrosion by chemical reaction among impurities in liquid metal and structural alloy. There have been some researches to develop new alloys that can form more dense scale on the surface even in wider impurity range and higher temperature range . M.P Short et al. devised functionally graded composite which is composed of two layers . one is a thin corrosion resistant layer and another is thick structural layer which guarantees mechanical strength, creep rupture strength and shows less irradiation swelling.
Impact of new computing systems on finite element computations
Noor, A. K.; Storassili, O. O.; Fulton, R. E.
1983-01-01
Recent advances in computer technology that are likely to impact finite element computations are reviewed. The characteristics of supersystems, highly parallel systems, and small systems (mini and microcomputers) are summarized. The interrelations of numerical algorithms and software with parallel architectures are discussed. A scenario is presented for future hardware/software environment and finite element systems. A number of research areas which have high potential for improving the effectiveness of finite element analysis in the new environment are identified.
Radial flow of slightly compressible fluids: A finite element-finite ...
African Journals Online (AJOL)
Journal of the Nigerian Association of Mathematical Physics ... Open Access DOWNLOAD FULL TEXT Subscription or Fee Access. Radial flow of slightly compressible fluids: A finite element-finite differences approach. JA Akpobi, ED Akpobi ...
Fix, G. J.; Rose, M. E.
1983-01-01
A least squares formulation of the system divu = rho, curlu = zeta is surveyed from the viewpoint of both finite element and finite difference methods. Closely related arguments are shown to establish convergence estimates.
Ablative Thermal Response Analysis Using the Finite Element Method
Dec John A.; Braun, Robert D.
2009-01-01
A review of the classic techniques used to solve ablative thermal response problems is presented. The advantages and disadvantages of both the finite element and finite difference methods are described. As a first step in developing a three dimensional finite element based ablative thermal response capability, a one dimensional computer tool has been developed. The finite element method is used to discretize the governing differential equations and Galerkin's method of weighted residuals is used to derive the element equations. A code to code comparison between the current 1-D tool and the 1-D Fully Implicit Ablation and Thermal Response Program (FIAT) has been performed.
An improved optimal elemental method for updating finite element models
Institute of Scientific and Technical Information of China (English)
Duan Zhongdong(段忠东); Spencer B.F.; Yan Guirong(闫桂荣); Ou Jinping(欧进萍)
2004-01-01
The optimal matrix method and optimal elemental method used to update finite element models may not provide accurate results. This situation occurs when the test modal model is incomplete, as is often the case in practice. An improved optimal elemental method is presented that defines a new objective function, and as a byproduct, circumvents the need for mass normalized modal shapes, which are also not readily available in practice. To solve the group of nonlinear equations created by the improved optimal method, the Lagrange multiplier method and Matlab function fmincon are employed. To deal with actual complex structures,the float-encoding genetic algorithm (FGA) is introduced to enhance the capability of the improved method. Two examples, a 7-degree of freedom (DOF) mass-spring system and a 53-DOF planar frame, respectively, are updated using the improved method.Thc example results demonstrate the advantages of the improved method over existing optimal methods, and show that the genetic algorithm is an effective way to update the models used for actual complex structures.
A multi-mesh finite element method for Lagrange elements of arbitrary degree
Witkowski, Thomas
2010-01-01
We consider within a finite element approach the usage of different adaptively refined meshes for different variables in systems of nonlinear, time-depended PDEs. To resolve different solution behaviours of these variables, the meshes can be independently adapted. The resulting linear systems are usually much smaller, when compared to the usage of a single mesh, and the overall computational runtime can be more than halved in such cases. Our multi-mesh method works for Lagrange finite elements of arbitrary degree and is independent of the spatial dimension. The approach is well defined, and can be implemented in existing adaptive finite element codes with minimal effort. We show computational examples in 2D and 3D ranging from dendritic growth to solid-solid phase-transitions. A further application comes from fluid dynamics where we demonstrate the applicability of the approach for solving the incompressible Navier-Stokes equations with Lagrange finite elements of the same order for velocity and pressure. The...
Energy Technology Data Exchange (ETDEWEB)
Kim, S. [Purdue Univ., West Lafayette, IN (United States)
1994-12-31
Parallel iterative procedures based on domain decomposition techniques are defined and analyzed for the numerical solution of wave propagation by finite element and finite difference methods. For finite element methods, in a Lagrangian framework, an efficient way for choosing the algorithm parameter as well as the algorithm convergence are indicated. Some heuristic arguments for finding the algorithm parameter for finite difference schemes are addressed. Numerical results are presented to indicate the effectiveness of the methods.
Galerkin finite element scheme for magnetostrictive structures and composites
Kannan, Kidambi Srinivasan
The ever increasing-role of magnetostrictives in actuation and sensing applications is an indication of their importance in the emerging field of smart structures technology. As newer, and more complex, applications are developed, there is a growing need for a reliable computational tool that can effectively address the magneto-mechanical interactions and other nonlinearities in these materials and in structures incorporating them. This thesis presents a continuum level quasi-static, three-dimensional finite element computational scheme for modeling the nonlinear behavior of bulk magnetostrictive materials and particulate magnetostrictive composites. Models for magnetostriction must deal with two sources of nonlinearities-nonlinear body forces/moments in equilibrium equations governing magneto-mechanical interactions in deformable and magnetized bodies; and nonlinear coupled magneto-mechanical constitutive models for the material of interest. In the present work, classical differential formulations for nonlinear magneto-mechanical interactions are recast in integral form using the weighted-residual method. A discretized finite element form is obtained by applying the Galerkin technique. The finite element formulation is based upon three dimensional eight-noded (isoparametric) brick element interpolation functions and magnetostatic infinite elements at the boundary. Two alternative possibilities are explored for establishing the nonlinear incremental constitutive model-characterization in terms of magnetic field or in terms of magnetization. The former methodology is the one most commonly used in the literature. In this work, a detailed comparative study of both methodologies is carried out. The computational scheme is validated, qualitatively and quantitatively, against experimental measurements published in the literature on structures incorporating the magnetostrictive material Terfenol-D. The influence of nonlinear body forces and body moments of magnetic origin
Tadepalli, Srinivas C; Erdemir, Ahmet; Cavanagh, Peter R
2011-08-11
Finite element analysis has been widely used in the field of foot and footwear biomechanics to determine plantar pressures as well as stresses and strains within soft tissue and footwear materials. When dealing with anatomical structures such as the foot, hexahedral mesh generation accounts for most of the model development time due to geometric complexities imposed by branching and embedded structures. Tetrahedral meshing, which can be more easily automated, has been the approach of choice to date in foot and footwear biomechanics. Here we use the nonlinear finite element program Abaqus (Simulia, Providence, RI) to examine the advantages and disadvantages of tetrahedral and hexahedral elements under compression and shear loading, material incompressibility, and frictional contact conditions, which are commonly seen in foot and footwear biomechanics. This study demonstrated that for a range of simulation conditions, hybrid hexahedral elements (Abaqus C3D8H) consistently performed well while hybrid linear tetrahedral elements (Abaqus C3D4H) performed poorly. On the other hand, enhanced quadratic tetrahedral elements with improved stress visualization (Abaqus C3D10I) performed as well as the hybrid hexahedral elements in terms of contact pressure and contact shear stress predictions. Although the enhanced quadratic tetrahedral element simulations were computationally expensive compared to hexahedral element simulations in both barefoot and footwear conditions, the enhanced quadratic tetrahedral element formulation seems to be very promising for foot and footwear applications as a result of decreased labor and expedited model development, all related to facilitated mesh generation.
Finite Element Analysis of a Natural Fiber (Maize Composite Beam
Directory of Open Access Journals (Sweden)
D. Saravana Bavan
2013-01-01
Full Text Available Natural fiber composites are termed as biocomposites or green composites. These fibers are green, biodegradable, and recyclable and have good properties such as low density and low cost when compared to synthetic fibers. The present work is investigated on the finite element analysis of the natural fiber (maize composite beam, processed by means of hand lay-up method. Composite beam material is composed of stalk-based fiber of maize and unsaturated polyester resin polymer as matrix with methyl ethyl ketone peroxide (MEKP as a catalyst and Cobalt Octoate as a promoter. The material was modeled and resembled as a structural beam using suitable assumption and analyzed by means of finite element method using ANSYS software for determining the deflection and stress properties. Morphological analysis and X-ray diffraction (XRD analysis for the fiber were examined by means of scanning electron microscope (SEM and X-ray diffractometer. From the results, it has been found that the finite element values are acceptable with proper assumptions, and the prepared natural fiber composite beam material can be used for structural engineering applications.
Nonlinear explicit transient finite element analysis on the Intel Delta
Energy Technology Data Exchange (ETDEWEB)
Plaskacz, E.J. [Argonne National Lab., IL (United States); Ramirez, M.R.; Gupta, S. [Johns Hopkins Univ., Baltimore, MD (United States). Dept. of Civil Engineering
1993-03-01
Many large scale finite element problems are intractable on current generation production supercomputers. High-performance computer architectures offer effective avenues to bridge the gap between computational needs and the power of computational hardware. The biggest challenge lies in the substitution of the key algorithms in an application program with redesigned algorithms which exploit the new architectures and use better or more appropriate numerical techniques. A methodology for implementing nonlinear finite element analysis on a homogeneous distributed processing network is discussed. The method can also be extended to heterogeneous networks comprised of different machine architectures provided that they have a mutual communication interface. This unique feature has greatly facilitated the port of the code to the 8-node Intel Touchstone Gamma and then the 512-node Intel Touchstone Delta. The domain is decomposed serially in a preprocessor. Separate input files are written for each subdomain. These files are read in by local copies of the program executable operating in parallel. Communication between processors is addressed utilizing asynchronous and synchronous message passing. The basic kernel of message passing is the internal force exchange which is analogous to the computed interactions between sections of physical bodies in static stress analysis. Benchmarks for the Intel Delta are presented. Performance exceeding 1 gigaflop was attained. Results for two large-scale finite element meshes are presented.
Nonlinear explicit transient finite element analysis on the Intel Delta
Energy Technology Data Exchange (ETDEWEB)
Plaskacz, E.J. (Argonne National Lab., IL (United States)); Ramirez, M.R.; Gupta, S. (Johns Hopkins Univ., Baltimore, MD (United States). Dept. of Civil Engineering)
1993-01-01
Many large scale finite element problems are intractable on current generation production supercomputers. High-performance computer architectures offer effective avenues to bridge the gap between computational needs and the power of computational hardware. The biggest challenge lies in the substitution of the key algorithms in an application program with redesigned algorithms which exploit the new architectures and use better or more appropriate numerical techniques. A methodology for implementing nonlinear finite element analysis on a homogeneous distributed processing network is discussed. The method can also be extended to heterogeneous networks comprised of different machine architectures provided that they have a mutual communication interface. This unique feature has greatly facilitated the port of the code to the 8-node Intel Touchstone Gamma and then the 512-node Intel Touchstone Delta. The domain is decomposed serially in a preprocessor. Separate input files are written for each subdomain. These files are read in by local copies of the program executable operating in parallel. Communication between processors is addressed utilizing asynchronous and synchronous message passing. The basic kernel of message passing is the internal force exchange which is analogous to the computed interactions between sections of physical bodies in static stress analysis. Benchmarks for the Intel Delta are presented. Performance exceeding 1 gigaflop was attained. Results for two large-scale finite element meshes are presented.
Stresses Analysis of Petroleum Pipe Finite Element under Internal Pressure
Directory of Open Access Journals (Sweden)
Dr.Ragbe.M.Abdusslam
2016-08-01
Full Text Available This paper described the results of a nonlinear static mode within ANSYS of elastic and elastic-plastic behaviour of thin petroleum pipe that is subjected to an internal pressure and therefore a linear stress analysis performed using ANSYS 9.0 finite element software Such an analysis is important because the shape of most structures under internal pressure is cylindrical[1]. In this paper is considered only. Elastic and elastic-plastic finite element analysis is used to predict the principle stresses, effective stress results are compared with those obtained from theatrical equations in order to predict the limit and failure loads for this type of loading also the relationships between redial, hoop stresses and displacement has been used to develop a through understanding. The analysis was completed using ANAYS Version 9.0. (a finite element program for Microsoft Windows NT. The program allows pre-processing, analysis and post-processing stages to be completed within a single application. The program can be used to model a large number of situations including buckling, plastic deformation, forming and stress analysis problems. r mm (In this study ,a thin pipe of internal radiu ri 596 .9 mmand of externalo 609 .6objected to aninternal pressure 2 i 4 .83 / mm which is gradually increased to near the ultimate load that may be sustained by the pipe. The pipe is modelled as an elasto-plastic material using the Von Mises yield criterion which is normally used for metallic materials[2]. The specification of the load in several increments enables the spread of the plasticity to occur gradually and its effect on the stress distribution to be assessed. Key words: finite element analysis, elastic-plastic behavior, thin walled pipe equivalent stress, TWT.
Finite Element Program Generator and Its Application in Engineering%有限元程序生成系统及其在工程中的应用
Institute of Scientific and Technical Information of China (English)
万水; 胡红; 陈建平
2004-01-01
本文介绍了一个全新的有限元软件--有限元程序生成系统(FEPG)的设计方法和程序结构.有限元程序生成系统可以根据通用的数学原理和有限元素法规则,采用部件化和人工智能的方法,像推导数学公式那样利用计算机自动生成有限元程序.有限元程序生成系统突破了现有的有限元软件仅仅适用于某一特定领域研究的限制,适应于所有需用有限元方法求解的微分方程.目前,有限元程序生成系统已经应用于超导、电磁场、石油勘探、结构工程、交通、水利、船舶力学、液固耦合及流体力学等方面的研究.%A completely new finite element software, Finite Element Program Generator (FEPG), is introduced and its designing thought and organizing structure is presented.FEPG uses the method of components and the technique of artificial intelligence to generate finite element program automatically by a computer according to the general principles of mathematic and internal rules of finite element method,as is similar to the deduction of mathematics. FEPG breaks through the limitation of present finite element software,which only applies to special discipline,while FEPG is suitable for all kinds of differential equations solved by finite element method. Now FEPG has been applied to superconductor research,electromagnetic field study,petroleum exploration,transportation,structure engineering,water conservancy,ship mechanics,solid-liquid coupling problems and liquid dynamics,etc.in China.
Finite element form of FDV for widely varying flowfields
Richardson, G. A.; Cassibry, J. T.; Chung, T. J.; Wu, S. T.
2010-01-01
We present the Flowfield Dependent Variation (FDV) method for physical applications that have widely varying spatial and temporal scales. Our motivation is to develop a versatile numerical method that is accurate and stable in simulations with complex geometries and with wide variations in space and time scales. The use of a finite element formulation adds capabilities such as flexible grid geometries and exact enforcement of Neumann boundary conditions. While finite element schemes are used extensively by researchers solving computational fluid dynamics in many engineering fields, their use in space physics, astrophysical fluids and laboratory magnetohydrodynamic simulations with shocks has been predominantly overlooked. The FDV method is 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 these regimes. The first part of this paper concentrates on the presentation of our numerical method formulation for Newtonian and relativistic hydrodynamics. In the second part we present several standard simulation examples that test the method's limitations and verify the FDV method. We show that our finite element formulation is stable and accurate for a range of both Mach numbers and Lorentz factors in one-dimensional test problems. We also present the converging/diverging nozzle which contains both incompressible and compressible flow in the flowfield over a range of subsonic and supersonic regions. We demonstrate the stability of our method and the accuracy by comparison with the results of other methods including the finite difference Total Variation Diminishing method. We explore the use of FDV for both non-relativistic and relativistic fluids (hydrodynamics) with strong shocks in order to establish the effectiveness in future applications of this method in astrophysical and laboratory plasma environments.
SEACAS Theory Manuals: Part III. Finite Element Analysis in Nonlinear Solid Mechanics
Energy Technology Data Exchange (ETDEWEB)
Laursen, T.A.; Attaway, S.W.; Zadoks, R.I.
1999-03-01
This report outlines the application of finite element methodology to large deformation solid mechanics problems, detailing also some of the key technological issues that effective finite element formulations must address. The presentation is organized into three major portions: first, a discussion of finite element discretization from the global point of view, emphasizing the relationship between a virtual work principle and the associated fully discrete system, second, a discussion of finite element technology, emphasizing the important theoretical and practical features associated with an individual finite element; and third, detailed description of specific elements that enjoy widespread use, providing some examples of the theoretical ideas already described. Descriptions of problem formulation in nonlinear solid mechanics, nonlinear continuum mechanics, and constitutive modeling are given in three companion reports.
MORTAR FINITE VOLUME METHOD WITH ADINI ELEMENT FOR BIHARMONIC PROBLEM
Institute of Scientific and Technical Information of China (English)
Chun-jia Bi; Li-kang Li
2004-01-01
In this paper, we construct and analyse a mortar finite volume method for the dis-cretization for the biharmonic problem in R2. This method is based on the mortar-type Adini nonconforming finite element spaces. The optimal order H2-seminorm error estimate between the exact solution and the mortar Adini finite volume solution of the biharmonic equation is established.
Finite Element Analysis (FEA) in Design and Production.
Waggoner, Todd C.; And Others
1995-01-01
Finite element analysis (FEA) enables industrial designers to analyze complex components by dividing them into smaller elements, then assessing stress and strain characteristics. Traditionally mainframe based, FEA is being increasingly used in microcomputers. (SK)
A Finite Element Analysis of Optimal Variable Thickness Sheets
DEFF Research Database (Denmark)
Petersson, Joakim S
1996-01-01
A quasimixed Finite Element (FE) method for maximum stiffness of variablethickness sheets is analysed. The displacement is approximated with ninenode Lagrange quadrilateral elements and the thickness is approximated aselementwise constant. One is guaranteed that the FE displacement solutionswill...
Finite element simulation of asphalt fatigue testing
DEFF Research Database (Denmark)
Ullidtz, Per; Kieler, Thomas Lau; Kargo, Anders
1997-01-01
The traditional interpretation of fatigue tests on asphalt mixes has been in terms of a logarithmic linear relationship between the constant stress or strain amplitude and the number of load repetitions to cause failure, often defined as a decrease in modulus to half the initial value. To accomod......The traditional interpretation of fatigue tests on asphalt mixes has been in terms of a logarithmic linear relationship between the constant stress or strain amplitude and the number of load repetitions to cause failure, often defined as a decrease in modulus to half the initial value....... To accomodate non-constant stress or strain, a mode factor may be introduced or the dissipated energy may be used instead of stress or strain.Cracking of asphalt (or other materials) may be described as a process consisting of three phases. In phase one diffuse microcracking is formed in the material...... damage mechanics.The paper describes how continuum damage mechanics may be used with a finite element program to explain the progressive deterioration of asphalt mixes under laboratory fatigue testing. Both constant stress and constant strain testing are simulated, and compared to the actual results from...
An iterative algorithm for finite element analysis
Laouafa, F.; Royis, P.
2004-03-01
In this paper, we state in a new form the algebraic problem arising from the one-field displacement finite element method (FEM). The displacement approach, in this discrete form, can be considered as the dual approach (force or equilibrium) with subsidiary constraints. This approach dissociates the nonlinear operator to the linear ones and their sizes are linear functions of integration rule which is of interest in the case of reduced integration. This new form of the problem leads to an inexpensive improvement of FEM computations, which acts at local, elementary and global levels. We demonstrate the numerical performances of this approach which is independent of the mesh structure. Using the GMRES algorithm we build, for nonsymmetric problems, a new algorithm based upon the discretized field of strain. The new algorithms proposed are more closer to the mechanical problem than the classical ones because all fields appear during the resolution process. The sizes of the different operators arising in these new forms are linear functions of integration rule, which is of great interest in the case of reduced integration.
Studying a dental pathology by finite elements
Directory of Open Access Journals (Sweden)
Fernando Mejía Umaña
2010-04-01
Full Text Available Abfractives lesions or abfractions are non-cavity lesions of dental structures in which a biomechanical factor has been identified as being the most probable cause for it occurring. Even throught such lesion can be presented in any tooth, it occurs more frequently in people aged over 35. This article presents some results obtained by the Universidad Nacional de Colombia's multidisciplinary research group for studying "dental material's structure and propierties". The introduction describes such lesion's characteristics and possible causes. The results of various modelling exercises using finite elements (in two and three dimensions are presented regarding a first premolar tooth subjected to normal mastication load and also to abnormal loads produced by occlusion problems. The most important findings (accompanied by clinical observations were that: areas of high concentration of forces were identified where lesions were frequently presented, associated with loads whose line of action did not pass through the central part of the section of tooth at cervical level; a direct relationship between facets of wear being orientated with the direction of forces produced by a high concentration of force; and the presence of high compression forces in the cervical region.
Finite element modeling of retinal prosthesis mechanics
Basinger, B. C.; Rowley, A. P.; Chen, K.; Humayun, M. S.; Weiland, J. D.
2009-10-01
Epiretinal prostheses used to treat degenerative retina diseases apply stimulus via an electrode array fixed to the ganglion cell side of the retina. Mechanical pressure applied by these arrays to the retina, both during initial insertion and throughout chronic use, could cause sufficient retinal damage to reduce the device's effectiveness. In order to understand and minimize potential mechanical damage, we have used finite element analysis to model mechanical interactions between an electrode array and the retina in both acute and chronic loading configurations. Modeling indicates that an acute tacking force distributes stress primarily underneath the tack site and heel edge of the array, while more moderate chronic stresses are distributed more evenly underneath the array. Retinal damage in a canine model chronically implanted with a similar array occurred in correlating locations, and model predictions correlate well with benchtop eyewall compression tests. This model provides retinal prosthesis researchers with a tool to optimize the mechanical electrode array design, but the techniques used here represent a unique effort to combine a modifiable device and soft biological tissues in the same model and those techniques could be extended to other devices that come into mechanical contact with soft neural tissues.
Intra Plate Stresses Using Finite Element Modelling
Directory of Open Access Journals (Sweden)
Jayalakshmi S.
2016-10-01
Full Text Available One of the most challenging problems in the estimation of seismic hazard is the ability to quantify seismic activity. Empirical models based on the available earthquake catalogue are often used to obtain activity of source regions. The major limitation with this approach is the lack of sufficient data near a specified source. The non-availability of data poses difficulties in obtaining distribution of earthquakes with large return periods. Such events recur over geological time scales during which tectonic processes, including mantle convection, formation of faults and new plate boundaries, are likely to take place. The availability of geometries of plate boundaries, plate driving forces, lithospheric stress field and GPS measurements has provided numerous insights on the mechanics of tectonic plates. In this article, a 2D finite element model of Indo-Australian plate is developed with the focus of representing seismic activity in India. The effect of large scale geological features including sedimentary basins, fold belts and cratons on the stress field in India is explored in this study. In order to address long term behaviour, the orientation of stress field and tectonic faults of the present Indo-Australian plate are compared with a reconstructed stress field from the early Miocene (20 Ma.
Pavlenko, I. V.; Simonovskiy, V. I.; Demianenko, M. M.
2017-08-01
This research paper is aimed to investigating rotor dynamics of multistage centrifugal machines with ball bearings by using the computer programs “Critical frequencies of the rotor” and “Forced oscillations of the rotor,” which are implemented the mathematical model based on the use of beam finite elements. Free and forces oscillations of the rotor for the multistage centrifugal oil pump NPS 200-700 are observed by taking into account the analytical dependence of bearing stiffness on rotor speed, which is previously defined on the basis of results’ approximation for the numerical simulation in ANSYS by applying 3D finite elements. The calculations found that characteristic and constrained oscillations of rotor and corresponded to them forms of vibrations, as well as the form of constrained oscillation on the actual frequency for acceptable residual unbalance are determined.
Directory of Open Access Journals (Sweden)
M.G. Pantelyat
2016-09-01
Full Text Available Purpose. To develop an effective approach for the numerical solution of transient thermo-contact problems and present a typical example of its utilization regarding devices working on the principle of thermoelasticity produced by induction heating and specific technological processes intended for assembly and disassembly of systems containing shrink fits. Methodology. A finite element technique for solution of 2D multiphysics (electromagnetic, thermal and structural problems is developed, taking into account temperature dependences of material properties and continuous variations of the contact surfaces. Modeling of the contact interaction between two parts is based on the concept of a special contact finite element having no thickness. The functional for the temperature problem is supplemented with components corresponding to the thermal conductivity of this contact layer. The heat generated due to mutual sliding of both parts can also be taken into account, but the heat capacity (specific heat of the contact layer is neglected. Using a special 1D 4-node finite elements a system of equations for the description of the thermo-contact problem is obtained. Originality. Relatively simple analytical formulae for calculation of the contact thermal resistances occurring in specific parts of electrical machines are known. The paper offers an alternative approach for the numerical solution of transient thermo-contact problems based on the concept of a special 1D contact finite element having no thickness. Results. The presented technique is applied for the computer simulation of assembly and disassembly of a shrink fit using induction heating. Conclusions regarding the choice of technological modes are made. Comparative computations for drills made from hard alloy and alloyed tool steel are carried out.
Hydrothermal analysis in engineering using control volume finite element method
Sheikholeslami, Mohsen
2015-01-01
Control volume finite element methods (CVFEM) bridge the gap between finite difference and finite element methods, using the advantages of both methods for simulation of multi-physics problems in complex geometries. In Hydrothermal Analysis in Engineering Using Control Volume Finite Element Method, CVFEM is covered in detail and applied to key areas of thermal engineering. Examples, exercises, and extensive references are used to show the use of the technique to model key engineering problems such as heat transfer in nanofluids (to enhance performance and compactness of energy systems),
Vibration Analysis of Beams by Spline Finite Element
Institute of Scientific and Technical Information of China (English)
YANG Hao; SUN Li
2011-01-01
In this paper,the spline finite element method is developed to investigate free vibration problems of beams.The cubic B-spline functions are used to construct the displacement field.The assembly of elements and the introduction of boundary conditions follow the standard finite element procedure.The results under various boundary conditions are compared with those obtained by the exact method and the finite difference method.It shows that the results are in excellent agreement with the analytical results and much more accurate than the results obtained by the finite difference method,especially for higher order modes.
Finite Element Model of Cardiac Electrical Conduction.
Yin, John Zhihao
1994-01-01
In this thesis, we develop mathematical models to study electrical conduction of the heart. One important pattern of wave propagation of electrical excitation in the heart is reentry which is believed to be the underlying mechanism of some dangerous cardiac arhythmias such as ventricular tachycardia and ventricular fibrillation. We present in this thesis a new ionic channel model of the ventricular cardiac cell membrane to study the microscopic electrical properties of myocardium. We base our model on recent single channel experiment data and a simple physical diffusion model of the calcium channel. Our ionic channel model of myocardium has simpler differential equations and fewer parameters than previous models. Further more, our ionic channel model achieves better results in simulating the strength-interval curve when we connect the membrane patch model to form a one dimensional cardiac muscle strand. We go on to study a finite element model which uses multiple states and non-nearest neighbor interactions to include curvature and dispersion effects. We create a generalized lattice randomization to overcome the artifacts generated by the interaction between the local dynamics and the regularities of the square lattice. We show that the homogeneous model does not display spontaneous wavefront breakup in a reentrant wave propagation once the lattice artifacts have been smoothed out by lattice randomization with a randomization scale larger than the characteristic length of the interaction. We further develop a finite 3-D 3-state heart model which employs a probability interaction rule. This model is applied to the simulation of Body Surface Laplacian Mapping (BSLM) using a cylindrical volume conductor as the torso model. We show that BSLM has a higher spatial resolution than conventional mapping methods in revealing the underlying electrical activities of the heart. The results of these studies demonstrate that mathematical modeling and computer simulation are very
Finite element analysis for general elastic multi-structures
Institute of Scientific and Technical Information of China (English)
无
2006-01-01
A finite element method is introduced to solve the general elastic multi-structure problem, in which the displacements on bodies, the longitudinal displacements on plates and the longitudinal displacements on beams are discretized using conforming linear elements, the rotational angles on beams are discretized using conforming elements of second order, the transverse displacements on plates and beams are discretized by the Morley elements and the Hermite elements of third order, respectively. The generalized Korn's inequality is established on related nonconforming element spaces, which implies the unique solvability of the finite element method. Finally, the optimal error estimate in the energy norm is derived for the method.
THE PRACTICAL ANALYSIS OF FINITE ELEMENTS METHOD ERRORS
Directory of Open Access Journals (Sweden)
Natalia Bakhova
2011-03-01
Full Text Available Abstract. The most important in the practical plan questions of reliable estimations of finite elementsmethod errors are considered. Definition rules of necessary calculations accuracy are developed. Methodsand ways of the calculations allowing receiving at economical expenditures of computing work the best finalresults are offered.Keywords: error, given the accuracy, finite element method, lagrangian and hermitian elements.
Finite Element Modelling of Seismic Liquefaction in Soils
Galavi, V.; Petalas, A.; Brinkgreve, R.B.J.
2013-01-01
Numerical aspects of seismic liquefaction in soils as implemented in the finite element code, PLAXIS, is described in this paper. After description of finite element equations of dynamic problems, three practical dynamic boundary conditions, namely viscous boundary tractions, tied degrees of freedom
Parallel direct solver for finite element modeling of manufacturing processes
DEFF Research Database (Denmark)
Nielsen, Chris Valentin; Martins, P.A.F.
2017-01-01
The central processing unit (CPU) time is of paramount importance in finite element modeling of manufacturing processes. Because the most significant part of the CPU time is consumed in solving the main system of equations resulting from finite element assemblies, different approaches have been...
Finite element models applied in active structural acoustic control
Oude Nijhuis, Marco H.H.; Boer, de André; Rao, Vittal S.
2002-01-01
This paper discusses the modeling of systems for active structural acoustic control. The finite element method is applied to model structures including the dynamics of piezoelectric sensors and actuators. A model reduction technique is presented to make the finite element model suitable for controll
Viscoelastic finite-element analysis of human skull - dura mater ...
African Journals Online (AJOL)
SERVER
2008-03-18
Mar 18, 2008 ... In the work, the dynamic characteristics of the human skull-dura mater ... Ansys' finite element processor, a simplified three-dimensional finite element ... brain, cerebrospinal fluid (CSF), and the brain's blood ... ICP is often not preventable. .... The creep of linear viscoelastic solid can be simulated by the.
A geometric toolbox for tetrahedral finite element partitions
Brandts, J.; Korotov, S.; Křížek, M.; Axelsson, O.; Karátson, J.
2011-01-01
In this work we present a survey of some geometric results on tetrahedral partitions and their refinements in a unified manner. They can be used for mesh generation and adaptivity in practical calculations by the finite element method (FEM), and also in theoretical finite element (FE) analysis. Spec
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.
ALTERNATING DIRECTION FINITE ELEMENT METHOD FOR SOME REACTION DIFFUSION MODELS
Institute of Scientific and Technical Information of China (English)
江成顺; 刘蕴贤; 沈永明
2004-01-01
This paper is concerned with some nonlinear reaction - diffusion models. To solve this kind of models, the modified Laplace finite element scheme and the alternating direction finite element scheme are established for the system of patrical differential equations. Besides, the finite difference method is utilized for the ordinary differential equation in the models. Moreover, by the theory and technique of prior estimates for the differential equations, the convergence analyses and the optimal L2- norm error estimates are demonstrated.
OBJECT-ORIENTED FINITE ELEMENT ANALYSIS AND PROGRAMMING IN VC + +
Institute of Scientific and Technical Information of China (English)
马永其; 冯伟
2002-01-01
The design of finite element analysis program using object-oriented programming(OOP) techniques is presented. The objects, classes and the subclasses used in theprogramming are explained. The system of classes library of finite element analysis programand Windows-type Graphical User Interfaces by VC + + and its MFC are developed. Thereliability, reusability and extensibility of program are enhanced. It is a reference todevelop the large-scale, versatile and powerful systems of object-oriented finite elementsoftware.
Finite Element Method for Analysis of Material Properties
DEFF Research Database (Denmark)
Rauhe, Jens Christian
description of the material microstructure the finite element models must contain a large number of elements and this problem is solved by using the preconditioned conjugated gradient solver with an Element-By-Element preconditioner. Finite element analysis provides the volume averaged stresses and strains...... and the finite element method. The material microstructure of the heterogeneous material is non-destructively determined using X-ray microtomography. A software program has been generated which uses the X-ray tomographic data as an input for the mesh generation of the material microstructure. To obtain a proper...... which are used for the determination of the effective properties of the heterogeneous material. Generally, the properties determined using the finite element method coupled with X-ray microtomography are in good agreement with both experimentally determined properties and properties determined using...
2-D Finite Element Analysis of Massive RC Structures
DEFF Research Database (Denmark)
Saabye Ottosen, Niels
1982-01-01
Nonlinear analysis of concrete structures using finite elements is discussed. The applications include a thick-walled top-closure for a pressure vessel as well as the delicate problems of beams failing in shear. The top-closure analysis evaluates the effect of two different failure criteria...... and modeling of a realistic post-failure behavior is demonstrated to be mandatory for accurate structural predictions. For shear beams it is shown that the primary cause of failure is strain softening adjacent to the load point....
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
Galerkin finite-element simulation of a geothermal reservoir
Mercer, J.W.; Pinder, G.F.
1973-01-01
The equations describing fluid flow and energy transport in a porous medium can be used to formulate a mathematical model capable of simulating the transient response of a hot-water geothermal reservoir. The resulting equations can be solved accurately and efficiently using a numerical scheme which combines the finite element approach with the Galerkin method of approximation. Application of this numerical model to the Wairakei geothermal field demonstrates that hot-water geothermal fields can be simulated using numerical techniques currently available and under development. ?? 1973.
Modelling the viscoelasticity of ceramic tiles by finite element
Pavlovic, Ana; Fragassa, Cristiano
2016-05-01
This research details a numerical method aiming at investigating the viscoelastic behaviour of a specific family of ceramic material, the Grès Porcelain, during an uncommon transformation, known as pyroplasticity, which occurs when a ceramic tile bends under a combination of thermal stress and own weight. In general, the theory of viscoelasticity can be considered extremely large and precise, but its application on real cases is particularly delicate. A time-depending problem, as viscoelasticity naturally is, has to be merged with a temperature-depending situation. This paper investigates how the viscoelastic response of bending ceramic materials can be modelled by commercial Finite Elements codes.
Institute of Scientific and Technical Information of China (English)
SHI Dong-yang; WANG Cai-xia
2008-01-01
This paper deals with a new nonconforming anisotropic rectangular finite element approximation for the planar elasticity problem with pure displacement boundary condition. By use of the special properties of this element,and by introducing the complementary space and a series of novel techniques,the optimal error estimates of the energy norm and the L2-norm are obtained. The restrictions of regularity assumption and quasi-uniform assumption or the inverse assumption on the meshes required in the conventional finite element methods analysis are to be got rid of and the applicable scope of the nonconforming finite elements is extended.
Finite element analysis of posterior cervical fixation.
Duan, Y; Wang, H H; Jin, A M; Zhang, L; Min, S X; Liu, C L; Qiu, S J; Shu, X Q
2015-02-01
Despite largely, used in the past, biomechanical test, to investigate the fixation techniques of subaxial cervical spine, information is lacking about the internal structural response to external loading. It is not yet clear which technique represents the best choice and whether stabilization devices can be efficient and beneficial for three-column injuries (TCI). The different posterior cervical fixation techniques (pedicle screw PS, lateral mass screw LS, and transarticular screw TS) have respective indications. A detailed, geometrically accurate, nonlinear C3-C7 finite element model (FEM) had been successfully developed and validated. Then three FEMs were reconstructed from different fixation techniques after C4-C6 TCI. A compressive preload of 74N combined with a pure moment of 1.8 Nm in flexion, extension, left-right lateral bending, and left-right axial rotation was applied to the FEMs. The ROM results showed that there were obvious significant differences when comparing the different fixation techniques. PS and TS techniques can provide better immediate stabilization, compared to LS technique. The stress results showed that the variability of von Mises stress in the TS fixation device was minimum and LS fixation device was maximum. Furthermore, the screws inserted by TS technique had high stress concentration at the middle part of the screws. Screw inserted by PS and LS techniques had higher stress concentration at the actual cap-rod-screw interface. The research considers that spinal surgeon should first consider using the TS technique to treat cervical TCI. If PS technique is used, we should eventually prolong the need for external bracing in order to reduce the higher risk of fracture on fixation devices. If LS technique is used, we should add anterior cervical operation for acquire a better immediate stabilization. Copyright © 2014 Elsevier Masson SAS. All rights reserved.
Investigation of Shear Stud Performance in Flat Plate Using Finite Element Analysis
Directory of Open Access Journals (Sweden)
T.S. Viswanathan
2014-09-01
Full Text Available Three types of shear stud arrangement, respectively featuring an orthogonal, a radial and a critical perimeter pattern, were evaluated numerically. A numerical investigation was conducted using the finite element software ABAQUS to evaluate their ability to resist punching shear in a flat plate. The finite element analysis here is an application of the nonlinear analysis of reinforced concrete structures using three-dimensional solid finite elements. The nonlinear characteristics of concrete were achieved by employing the concrete damaged plasticity model in the finite element program. Transverse shear stress was evaluated using finite element analysis in terms of shear stress distribution for flat plate with and without shear stud reinforcement. The model predicted that shear studs placed along the critical perimeter are more effective compared to orthogonal and radial patterns.
Thermal Analysis of Thin Plates Using the Finite Element Method
Er, G. K.; Iu, V. P.; Liu, X. L.
2010-05-01
The isotropic thermal plate is analyzed with finite element method. The solution procedure is presented. The elementary stiffness matrix and loading vector are derived rigorously with variation principle and the principle of minimum potential energy. Numerical results are obtained based on the derived equations and tested with available exact solutions. The problems in the finite element analysis are figured out. It is found that the finite element solutions can not converge as the number of elements increases around the corners of the plate. The derived equations presented in this paper are fundamental for our further study on more complicated thermal plate analysis.
Finite Element Analysis of Fluid-Conveying Timoshenko Pipes
Directory of Open Access Journals (Sweden)
Chih-Liang Chu
1995-01-01
Full Text Available A general finite element formulation using cubic Hermitian interpolation for dynamic analysis of pipes conveying fluid is presented. Both the effects of shearing deformations and rotary inertia are considered. The development retains the use of the classical four degrees-of-freedom for a two-node element. The effect of moving fluid is treated as external distributed forces on the support pipe and the fluid finite element matrices are derived from the virtual work done due to the fluid inertia forces. Finite element matrices for both the support pipe and moving fluid are derived and given explicitly. A numerical example is given to demonstrate the validity of the model.
The Application of Finite Element Analysis in the Design of Outlet%有限元分析在插座设计中的应用
Institute of Scientific and Technical Information of China (English)
蔡映峰; 潘玲玲
2014-01-01
夹持插销的插套是插座中最重要的载流部件，不仅需要在各种状态下和插销保持良好接触，而且还要有一定的夹紧力。有限元是理论上分析和解决这些要求的有效工具。本文从材料力学的基础知识入手，通过与传统力学计算和样品实际测试结果的比较，阐述了有限元计算结果的分析方法，再后以插套和塑料搭扣为例，简要说明了有限元在插座设计中的应用。%The contact which clamp the plug pin is the most importation live parts, it does not only require the close connection with plug pin in all kinds of conditions, but also need proper clamping force.FEA(Finite Element Analysis)is an effective tool to analyze those requirements. Starting with the mechanics of materials basic knowledge,the thesis stated the analyzing method of FEA results by comparing the traditional mechanic calculation and the actual sample testing. It also briefly explains the application of FEA in socket optimal design by taking the sample of contact and plastic hasp design.
Stupkiewicz, Stanisław
2009-10-01
Soft elastohydrodynamic lubrication (EHL) problem is studied for a reciprocating elastomeric seal with full account of finite configuration changes. The fluid part is described by the Reynolds equation which is formulated on the deformed boundary of the seal treated as a hyperelastic body. The paper is concerned with the finite element (FE) treatment of this soft EHL problem. Displacement-based FE discretization is applied for the solid part. The Reynolds equation is discretized using the FE method or, alternatively, the discontinuous Galerkin method, both employing higher-order interpolation of pressure. The performance of both methods is assessed by studying convergence and stability of the solution for a benchmark problem of an O-ring seal. It is shown that the solution may exhibit spurious oscillations which occur in severe lubrication conditions. Mesh refinement results in reduction of these oscillations, while increasing the pressure interpolation order or application of the discontinuous Galerkin method does not help significantly.
Arbatani, Siamak; Callejo, Alfonso; Kövecses, József; Kalantari, Masoud; Marchand, Nick R.; Dargahi, Javad
2016-06-01
Directional drilling is a popular technique for oil well drilling. Accurate prediction of the directional performance is critical in order to achieve the desired well profile. Simplified geometry methods are, to date, the industry standard for predicting directional performance. A comprehensive, high-fidelity method for the simulation of directional drilling is presented here. It consists of a detailed discretization of the actual geometry and a rigorous application of two modeling techniques: the finite element and the finite segment methods. By doing so, the dynamic problem is addressed from two different yet complementary perspectives: structural mechanics and rigid-body motion. Collision detection and contact dynamics algorithms are also presented. Results show that both methods agree in terms of the dynamic response, and that the build rate estimations are consistent with available experimental data. Owing to the framework efficiency and physics-based nature, the presented tools are very well-suited for design engineering and real-time simulation.
PRECONDITIONING HIGHER ORDER FINITE ELEMENT SYSTEMS BY ALGEBRAIC MULTIGRID METHOD OF LINEAR ELEMENTS
Institute of Scientific and Technical Information of China (English)
Yun-qing Huang; Shi Shu; Xi-jun Yu
2006-01-01
We present and analyze a robust preconditioned conjugate gradient method for the higher order Lagrangian finite element systems of a class of elliptic problems. An auxiliary linear element stiffness matrix is chosen to be the preconditioner for higher order finite elements. Then an algebraic multigrid method of linear finite element is applied for solving the preconditioner. The optimal condition number which is independent of the mesh size is obtained. Numerical experiments confirm the efficiency of the algorithm.
Institute of Scientific and Technical Information of China (English)
朱卫平; 黄黔
2002-01-01
In order to analyze bellows effectively and practically, the finite-element-displacement-perturbation method (FEDPM) is proposed for the geometric nonlinearbehaviors of shells of revolution subjected to pure bending moments or lateral forces in one of their meridional planes. The formulations are mainly based upon the idea of perturba-tion that the nodal displacement vector and the nodal force vector of each finite elementare expanded by taking root-mean-square value of circumferential strains of the shells as aperturbation parameter. The load steps and the iteration times are not cs arbitrary andunpredictable as in usual nonlinear analysis. Instead, there are certain relations betweenthe load steps and the displacement increments, and no need of iteration for each loadstep. Besides, in the formulations, the shell is idealized into a series of conical frusta for the convenience of practice, Sander' s nonlinear geometric equations of moderate smallrotation are used, and the shell made of more than one material ply is also considered.
Finite element analysis of an inflatable torus considering air mass structural element
Gajbhiye, S. C.; Upadhyay, S. H.; Harsha, S. P.
2014-01-01
Inflatable structures, also known as gossamer structures, are at high boom in the current space technology due to their low mass and compact size comparing to the traditional spacecraft designing. Internal pressure becomes the major source of strength and rigidity, essentially stiffen the structure. However, inflatable space based membrane structure are at high risk to the vibration disturbance due to their low structural stiffness and material damping. Hence, the vibration modes of the structure should be known to a high degree of accuracy in order to provide better control authority. In the past, most of the studies conducted on the vibration analysis of gossamer structures used inaccurate or approximate theories in modeling the internal pressure. The toroidal shaped structure is one of the important key element in space application, helps to support the reflector in space application. This paper discusses the finite-element analysis of an inflated torus. The eigen-frequencies are obtained via three-dimensional small-strain elasticity theory, based on extremum energy principle. The two finite-element model (model-1 and model-2) have cases have been generated using a commercial finite-element package. The structure model-1 with shell element and model-2 with the combination of the mass of enclosed fluid (air) added to the shell elements have been taken for the study. The model-1 is computed with present analytical approach to understand the convergence rate and the accuracy. The convergence study is made available for the symmetric modes and anti-symmetric modes about the centroidal-axis plane, meeting the eigen-frequencies of an inflatable torus with the circular cross section. The structural model-2 is introduced with air mass element and analyzed its eigen-frequency with different aspect ratio and mode shape response using in-plane and out-plane loading condition are studied.
Finite Element Simulation of Blanking Process
Directory of Open Access Journals (Sweden)
Afzal Ahmed
2012-10-01
daya penembusan sebanyak 42%. Daya tebukan yang diukur melalui eksperimen dan simulasi kekal pada kira-kira 90kN melepasi penembusan punch sebanyak 62%. Apabila ketebalan keputusan kunci ditambah, ketinggian retak dikurangkan dan ini meningkatkan kualiti pengosongan.KEYWORDS: simulation; finite element simulation; blanking; computer aided manufacturing
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.
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
Model Reduction in Dynamic Finite Element Analysis of Lightweight Structures
DEFF Research Database (Denmark)
Flodén, Ola; Persson, Kent; Sjöström, Anders
2012-01-01
. The objective of the analyses presented in this paper is to evaluate methods for model reduction of detailed finite element models of floor and wall structures and to investigate the influence of reducing the number of degrees of freedom and computational cost on the dynamic response of the models in terms....... The drawback of component mode synthesis compared to modelling with structural elements is the increased computational cost, although the number of degrees of freedom is small in comparison, as a result of the large bandwidth of the system matrices.......The application of wood as a construction material when building multi-storey buildings has many advantages, e.g., light weight, sustainability and low energy consumption during the construction and lifecycle of the building. However, compared to heavy structures, it is a greater challenge to build...
Quadratic Serendipity Finite Elements on Polygons Using Generalized Barycentric Coordinates
Rand, Alexander; Bajaj, Chandrajit
2011-01-01
We introduce a finite element construction for use on the class of convex, planar polygons and show it obtains a quadratic error convergence estimate. On a convex n-gon satisfying simple geometric criteria, our construction produces 2n basis functions, associated in a Lagrange-like fashion to each vertex and each edge midpoint, by transforming and combining a set of n(n+1)/2 basis functions known to obtain quadratic convergence. The technique broadens the scope of the so-called `serendipity' elements, previously studied only for quadrilateral and regular hexahedral meshes, by employing the theory of generalized barycentric coordinates. Numerical evidence is provided on a trapezoidal quadrilateral mesh, previously not amenable to serendipity constructions, and applications to adaptive meshing are discussed.
QUADRATIC SERENDIPITY FINITE ELEMENTS ON POLYGONS USING GENERALIZED BARYCENTRIC COORDINATES.
Rand, Alexander; Gillette, Andrew; Bajaj, Chandrajit
2014-01-01
We introduce a finite element construction for use on the class of convex, planar polygons and show it obtains a quadratic error convergence estimate. On a convex n-gon, our construction produces 2n basis functions, associated in a Lagrange-like fashion to each vertex and each edge midpoint, by transforming and combining a set of n(n + 1)/2 basis functions known to obtain quadratic convergence. The technique broadens the scope of the so-called 'serendipity' elements, previously studied only for quadrilateral and regular hexahedral meshes, by employing the theory of generalized barycentric coordinates. Uniform a priori error estimates are established over the class of convex quadrilaterals with bounded aspect ratio as well as over the class of convex planar polygons satisfying additional shape regularity conditions to exclude large interior angles and short edges. Numerical evidence is provided on a trapezoidal quadrilateral mesh, previously not amenable to serendipity constructions, and applications to adaptive meshing are discussed.
Probabilistic finite elements for fatigue and fracture analysis
Belytschko, Ted; Liu, Wing Kam
1993-01-01
An overview of the probabilistic finite element method (PFEM) developed by the authors and their colleagues in recent years is presented. The primary focus is placed on the development of PFEM for both structural mechanics problems and fracture mechanics problems. The perturbation techniques are used as major tools for the analytical derivation. The following topics are covered: (1) representation and discretization of random fields; (2) development of PFEM for the general linear transient problem and nonlinear elasticity using Hu-Washizu variational principle; (3) computational aspects; (4) discussions of the application of PFEM to the reliability analysis of both brittle fracture and fatigue; and (5) a stochastic computational tool based on stochastic boundary element (SBEM). Results are obtained for the reliability index and corresponding probability of failure for: (1) fatigue crack growth; (2) defect geometry; (3) fatigue parameters; and (4) applied loads. These results show that initial defect is a critical parameter.
Probabilistic finite elements for fatigue and fracture analysis. Final report
Energy Technology Data Exchange (ETDEWEB)
Belytschko, T.; Liu, W.K.
1993-04-01
An overview of the probabilistic finite element method (PFEM) developed by the authors and their colleagues in recent years is presented. The primary focus is placed on the development of PFEM for both structural mechanics problems and fracture mechanics problems. The perturbation techniques are used as major tools for the analytical derivation. The following topics are covered: (1) representation and discretization of random fields; (2) development of PFEM for the general linear transient problem and nonlinear elasticity using Hu-Washizu variational principle; (3) computational aspects; (4) discussions of the application of PFEM to the reliability analysis of both brittle fracture and fatigue; and (5) a stochastic computational tool based on stochastic boundary element (SBEM). Results are obtained for the reliability index and corresponding probability of failure for: (1) fatigue crack growth; (2) defect geometry; (3) fatigue parameters; and (4) applied loads. These results show that initial defect is a critical parameter.
Essentials of finite element modeling and adaptive refinement
Dow, John O
2012-01-01
Finite Element Analysis is a very popular, computer-based tool that uses a complex system of points called nodes to make a grid called a ""mesh. "" The mesh contains the material and structural properties that define how the structure will react to certain loading conditions, allowing virtual testing and analysis of stresses or changes applied to the material or component design. This groundbreaking text extends the usefulness of finite element analysis by helping both beginners and advanced users alike. It simplifies, improves, and extends both the finite element method while at the same t
A mixed finite element for the analysis of laminated plates
Putcha, N. S.; Reddy, J. N.
1983-01-01
A new mixed shear-flexible finite element based on the Hellinger-Reissner's variational principle is developed. The element is constructed using a mixed formulation of the shear deformation theory of laminated composite plates, and consists of three displacements, two shear rotations, and three moments as the independent degrees of freedom. The numerical convergence and accuracy characteristics of the element are investigated for bending of laminated anisotropic composite plates. The element is relatively simple to construct and has better accuracy and convergence features when compared to other conventional finite elements.
A Dual Super-Element Domain Decomposition Approach for Parallel Nonlinear Finite Element Analysis
Jokhio, G. A.; Izzuddin, B. A.
2015-05-01
This article presents a new domain decomposition method for nonlinear finite element analysis introducing the concept of dual partition super-elements. The method extends ideas from the displacement frame method and is ideally suited for parallel nonlinear static/dynamic analysis of structural systems. In the new method, domain decomposition is realized by replacing one or more subdomains in a "parent system," each with a placeholder super-element, where the subdomains are processed separately as "child partitions," each wrapped by a dual super-element along the partition boundary. The analysis of the overall system, including the satisfaction of equilibrium and compatibility at all partition boundaries, is realized through direct communication between all pairs of placeholder and dual super-elements. The proposed method has particular advantages for matrix solution methods based on the frontal scheme, and can be readily implemented for existing finite element analysis programs to achieve parallelization on distributed memory systems with minimal intervention, thus overcoming memory bottlenecks typically faced in the analysis of large-scale problems. Several examples are presented in this article which demonstrate the computational benefits of the proposed parallel domain decomposition approach and its applicability to the nonlinear structural analysis of realistic structural systems.
Greenberg, David A.; Shore, Jennifer A.; Page, Fred H.; Dowd, Michael
A three-dimensional, triangular-mesh, finite element model has been adapted to allow for the flooding and drying of intertidal areas. The new algorithm sets velocities in dry areas to zero and removes elements from the computation when they are completely dry. Model tests simulating an idealized sloping beach that includes a tidal pool and a narrow deep channel laterally bounded by shallow drying sides, give qualitatively reasonable results. A simulation of the Quoddy region of the Bay of Fundy also gave good results when calibrated against available observations. This region includes extensive intertidal flats, tidal pools and channels that are blocked at low water by emerging shallows. The model is a clear improvement over a three-dimensional linear model and a fully nonlinear model without the drying routines using the same model grid. The drying model reproduces the tidal elevations with higher accuracy and has more realistic tidal currents.
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
Energy Technology Data Exchange (ETDEWEB)
Kim, Ju Hee [Korea Military Academy, Seoul (Korea, Republic of); Kim, Yun Jae [Korea University, Seoul (Korea, Republic of); Kim, Joung Soo [KAERI, Daejeon (Korea, Republic of)
2013-07-15
By using finite element analysis, we proposed an applicable finite element method of laser shock peening (LSP) and discussed various parameters, such as solution time, stability limit, dynamic yield stress, peak pressure, pressure pulse duration, laser spot size, and multiple LSP. The effects of parameters related to the finite element simulation of the LSP process on the residual stresses of 35CD4 30HRC steel alloy are discussed. Parametric sensitivity analyses were performed to establish the optimum processing variables of the LSP process. In addition, we evaluated the effects of initial residual stress, such as welding-induced residual stress field.
Institute of Scientific and Technical Information of China (English)
无
2006-01-01
In this paper, we study the semi-discrete mortar upwind finite volume element method with the Crouzeix-Raviart element for the parabolic convection diffusion problems.It is proved that the semi-discrete mortar upwind finite volume element approximations derived are convergent in the H1- and L2-norms.
Angela Mihai, L.
2013-03-01
Finite element simulations of different shear deformations in non-linear elasticity are presented. We pay particular attention to the Poynting effects in hyperelastic materials, complementing recent theoretical findings by showing these effects manifested by specific models. As the finite element method computes uniform deformations exactly, for simple shear deformation and pure shear stress, the Poynting effect is represented exactly, while for the generalised shear and simple torsion, where the deformation is non-uniform, the solution is approximated efficiently and guaranteed computational bounds on the magnitude of the Poynting effect are obtained. The numerical results further indicate that, for a given elastic material, the same sign effect occurs under different shearing mechanisms, showing the genericity of the Poynting effect under a variety of shearing loads. In order to derive numerical models that exhibit either the positive or the negative Poynting effect, the so-called generalised empirical inequalities, which are less restrictive than the usual empirical inequalities involving material parameters, are assumed. © 2012 Elsevier Ltd.
Finite element modeling of electromagnetic fields and waves using NASTRAN
Moyer, E. Thomas, Jr.; Schroeder, Erwin
1989-01-01
The various formulations of Maxwell's equations are reviewed with emphasis on those formulations which most readily form analogies with Navier's equations. Analogies involving scalar and vector potentials and electric and magnetic field components are presented. Formulations allowing for media with dielectric and conducting properties are emphasized. It is demonstrated that many problems in electromagnetism can be solved using the NASTRAN finite element code. Several fundamental problems involving time harmonic solutions of Maxwell's equations with known analytic solutions are solved using NASTRAN to demonstrate convergence and mesh requirements. Mesh requirements are studied as a function of frequency, conductivity, and dielectric properties. Applications in both low frequency and high frequency are highlighted. The low frequency problems demonstrate the ability to solve problems involving media inhomogeneity and unbounded domains. The high frequency applications demonstrate the ability to handle problems with large boundary to wavelength ratios.
Partitions of nonzero elements of a finite field into pairs
Karasev, R N
2010-01-01
In this paper we prove two theorems. Informally, they claim that the nonzero elements of a finite field with odd characteristic can be partitioned into pairs with prescribed difference (maybe, with some alternatives) in each pair. We also consider some generalizations of these results to packing translates in a finite or infinite field.
Finite Element Method for Analysis of Material Properties
DEFF Research Database (Denmark)
Rauhe, Jens Christian
The use of cellular and composite materials have in recent years become more and more common in all kinds of structural components and accurate knowledge of the effective properties is therefore essential. In this wok the effective properties are determined using the real material microstructure...... and the finite element method. The material microstructure of the heterogeneous material is non-destructively determined using X-ray microtomography. A software program has been generated which uses the X-ray tomographic data as an input for the mesh generation of the material microstructure. To obtain a proper...... description of the material microstructure the finite element models must contain a large number of elements and this problem is solved by using the preconditioned conjugated gradient solver with an Element-By-Element preconditioner. Finite element analysis provides the volume averaged stresses and strains...
Institute of Scientific and Technical Information of China (English)
Bahattin Kanber; O.Yavuz Bozkurt
2006-01-01
In this work,the finite element analysis of the elasto-plastic plate bending problems is carried out using transition rectangular plate elements.The shape functions of the transition plate elements are derived based on a practical rule.The transition plate elements are all quadrilateral and can be used to obtain efficient finite element models using minimum number of elements.The mesh convergence rates of the models including the transition elements are compared with the regular element models.To verify the developed elements,simple tests are demonstrated and various elasto-plastic problems are solved.Their results are compared with ANSYS results.
Finite Element Crash Simulations and Impact-Induced Injuries
Directory of Open Access Journals (Sweden)
Jaroslav Mackerle
1999-01-01
Full Text Available This bibliography lists references to papers, conference proceedings and theses/dissertations dealing with finite element simulations of crashes, impact-induced injuries and their protection that were published in 1980–1998. 390 citations are listed.
Finite Element Models for Electron Beam Freeform Fabrication Process Project
National Aeronautics and Space Administration — This Small Business Innovation Research Phase II proposal offers to develop a comprehensive computer simulation methodology based on the finite element method for...
Finite Element Models for Electron Beam Freeform Fabrication Process Project
National Aeronautics and Space Administration — This Small Business Innovation Research proposal offers to develop the most accurate, comprehensive and efficient finite element models to date for simulation of the...
Vehicle Interior Noise Prediction Using Energy Finite Element Analysis Project
National Aeronautics and Space Administration — It is proposed to develop and implement a computational technique based on Energy Finite Element Analysis (EFEA) for interior noise prediction of advanced aerospace...
Finite Element Crash Simulations and Impact-Induced Injuries
Mackerle, Jaroslav
1999-01-01
This bibliography lists references to papers, conference proceedings and theses/dissertations dealing with finite element simulations of crashes, impact-induced injuries and their protection that were published in 1980–1998. 390 citations are listed.
Finite element model updating using bayesian framework and modal properties
CSIR Research Space (South Africa)
Marwala, T
2005-01-01
Full Text Available Finite element (FE) models are widely used to predict the dynamic characteristics of aerospace structures. These models often give results that differ from measured results and therefore need to be updated to match measured results. Some...
Accurate Parallel Algorithm for Adini Nonconforming Finite Element
Institute of Scientific and Technical Information of China (English)
罗平; 周爱辉
2003-01-01
Multi-parameter asymptotic expansions are interesting since they justify the use of multi-parameter extrapolation which can be implemented in parallel and are well studied in many papers for the conforming finite element methods. For the nonconforming finite element methods, however, the work of the multi-parameter asymptotic expansions and extrapolation have seldom been found in the literature. This paper considers the solution of the biharmonic equation using Adini nonconforming finite elements and reports new results for the multi-parameter asymptotic expansions and extrapolation. The Adini nonconforming finite element solution of the biharmonic equation is shown to have a multi-parameter asymptotic error expansion and extrapolation. This expansion and a multi-parameter extrapolation technique were used to develop an accurate approximation parallel algorithm for the biharmonic equation. Finally, numerical results have verified the extrapolation theory.
SPECTRAL FINITE ELEMENT METHOD FOR A UNSTEADY TRANSPORT EQUATION
Institute of Scientific and Technical Information of China (English)
MeiLiquan
1999-01-01
In this paper,a new numerical method,the coupling method of spherical harmonic function spectral and finite elements,for a unsteady transport equation is dlscussed,and the error analysis of this scheme is proved.
On mixed finite element techniques for elliptic problems
Directory of Open Access Journals (Sweden)
M. Aslam Noor
1983-01-01
mildly nonlinear elliptic problems by means of finite element methods of mixed type. The technique is based on an extended variational principle, in which the constraint of interelement continuity has been removed at the expense of introducing a Lagrange multiplier.
Scalable, Finite Element Analysis of Electromagnetic Scattering and Radiation
Cwik, T.; Lou, J.; Katz, D.
1997-01-01
In this paper a method for simulating electromagnetic fields scattered from complex objects is reviewed; namely, an unstructured finite element code that does not use traditional mesh partitioning algorithms.
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.
Finite Element Meshes Auto-Generation for the Welted Bifurcation
Institute of Scientific and Technical Information of China (English)
YUANMei; LIYa-ping
2004-01-01
In this paper, firstly, a mathematical model for a specific kind of welted bifurcation is established, the parametric equation for the intersecting curve is resulted in. Secondly, a method for partitioning finite element meshes of the welted bifurcation is put forward, its main idea is that developing the main pipe surface and the branch pipe surface respectively, dividing meshes on each developing plane and obtaining meshes points, then transforming their plane coordinates into space coordinates. Finally, an applied program for finite element meshes auto-generation is simply introduced, which adopt ObjectARX technique and its running result can be shown in AutoCAD. The meshes generated in AutoCAD can be exported conveniently to most of finite element analysis soft wares, and the finite element computing result can satisfy the engineering precision requirement.
Finite element modeling of electrically rectified piezoelectric energy harvesters
Wu, P. H.; Shu, Y. C.
2015-09-01
Finite element models are developed for designing electrically rectified piezoelectric energy harvesters. They account for the consideration of common interface circuits such as the standard and parallel-/series-SSHI (synchronized switch harvesting on inductor) circuits, as well as complicated structural configurations such as arrays of piezoelectric oscillators. The idea is to replace the energy harvesting circuit by the proposed equivalent load impedance together with the capacitance of negative value. As a result, the proposed framework is capable of being implemented into conventional finite element solvers for direct system-level design without resorting to circuit simulators. The validation based on COMSOL simulations carried out for various interface circuits by the comparison with the standard modal analysis model. The framework is then applied to the investigation on how harvested power is reduced due to fabrication deviations in geometric and material properties of oscillators in an array system. Remarkably, it is found that for a standard array system with strong electromechanical coupling, the drop in peak power turns out to be insignificant if the optimal load is carefully chosen. The second application is to design broadband energy harvesting by developing array systems with suitable interface circuits. The result shows that significant broadband is observed for the parallel (series) connection of oscillators endowed with the parallel-SSHI (series-SSHI) circuit technique.
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.
Domain decomposition solvers for nonlinear multiharmonic finite element equations
Copeland, D. M.
2010-01-01
In many practical applications, for instance, in computational electromagnetics, the excitation is time-harmonic. Switching from the time domain to the frequency domain allows us to replace the expensive time-integration procedure by the solution of a simple elliptic equation for the amplitude. This is true for linear problems, but not for nonlinear problems. However, due to the periodicity of the solution, we can expand the solution in a Fourier series. Truncating this Fourier series and approximating the Fourier coefficients by finite elements, we arrive at a large-scale coupled nonlinear system for determining the finite element approximation to the Fourier coefficients. The construction of fast solvers for such systems is very crucial for the efficiency of this multiharmonic approach. In this paper we look at nonlinear, time-harmonic potential problems as simple model problems. We construct and analyze almost optimal solvers for the Jacobi systems arising from the Newton linearization of the large-scale coupled nonlinear system that one has to solve instead of performing the expensive time-integration procedure. © 2010 de Gruyter.
Finite element simulation of food transport through the esophageal body
Institute of Scientific and Technical Information of China (English)
Wei Yang; Tat Ching Fung; Kerm Sim Chian; Chuh Khiun Chong
2007-01-01
The peristaltic transport of swallowed material in the esophagus is a neuro-muscular function involving the nerve control, bolus-structure interaction, and structuremechanics relationship of the tissue. In this study, a finite element model (FEM) was developed to simulate food transport through the esophagus. The FEM consists of three components, i.e., tissue, food bolus and peristaltic wave, as well as the interactions between them. The transport process was simulated as three stages, i.e., the filling of fluid, contraction of circular muscle and traveling of peristaltic wave. It was found that the maximal passive intraluminal pressure due to bolus expansion was in the range of 0.8-10 kPa and it increased with bolus volume and fluid viscosity. It was found that the highest normal and shear stresses were at the inner surface of muscle layer. In addition, the peak pressure required for the fluid flow was predicted to be 1-15 kPa at the bolus tail. The diseases of systemic sclerosis or osteogenesis imperfecta, with the remodeled microstructures and mechanical properties, might induce the malfunction of esophageal transport. In conclusion, the current simulation was demonstrated to be able to capture the main characteristics in the intraluminal pressure and bolus geometry as measured experimentally. Therefore,the finite element model established in this study could be used to further explore the mechanism of esophageal transport in various clinical applications.
On the error bounds of nonconforming finite elements
Institute of Scientific and Technical Information of China (English)
无
2010-01-01
We prove that the error estimates of a large class of nonconforming finite elements are dominated by their approximation errors, which means that the well-known Cea’s lemma is still valid for these nonconforming finite element methods. Furthermore, we derive the error estimates in both energy and L2 norms under the regularity assumption u ∈ H1+s(Ω) with any s > 0. The extensions to other related problems are possible.
Anisotropic rectangular nonconforming finite element analysis for Sobolev equations
Institute of Scientific and Technical Information of China (English)
SHI Dong-yang; WANG Hai-hong; GUO Cheng
2008-01-01
An anisotropic rectangular nonconforming finite element method for solving the Sobolev equations is discussed under semi-discrete and full discrete schemes.The corresponding optimal convergence error estimates and superclose property are derived,which are the same as the traditional conforming finite elements.Furthermore,the global superconvergence is obtained using a post-processing technique.The numerical results show the validity of the theoretical analysis.
A FINITE ELEMENT MODEL FOR SEISMICITY INDUCED BY FAULT INTERACTION
Institute of Scientific and Technical Information of China (English)
Chen Huaran; Li Yiqun; He Qiaoyun; Zhang Jieqing; Ma Hongsheng; Li Li
2003-01-01
On ths basis of interaction between faults, a finite element model for Southwest China is constructed, and the stress adjustment due to the strong earthquake occurrence in this region was studied. The preliminary results show that many strong earthquakes occurred in the area of increased stress in the model. Though the results are preliminary, the quasi-3D finite element model is meaningful for strong earthquake prediction.
A FINITE ELEMENT MODEL FOR SEISMICITY INDUCED BY FAULT INTERACTION
Institute of Scientific and Technical Information of China (English)
ChenHuaran; LiYiqun; HeQiaoyun; ZhangJieqing; MaHongsheng; LiLi
2003-01-01
On ths basis of interaction between faults, a finite element model for Southwest China is constructed, and the stress adjustment due to the strong earthquake occurrence in this region was studied. The preliminary results show that many strong earthquakes occurred in the are a of increased stress in the model. Though the results are preliminary, the quasi-3D finite element model is meaningful for strong earthquake prediction.
THE DERIVATIVE PATCH INTERPOLATING RECOVERY TECHNIQUE FOR FINITE ELEMENT APPROXIMATIONS
Institute of Scientific and Technical Information of China (English)
TieZhang; Yan-pingLin; R.J.Tait
2004-01-01
A derivative patch interpolating recovery technique is analyzed for the finite element approximation to the second order elliptic boundary value problems in two dimensional case.It is shown that the convergence rate of the recovered gradient admits superc onvergence on the recovered subdomain, and is two order higher than the optimal global convergence rate (ultracovergence) at an internal node point when even order finite element spaces and local uniform meshes are used.
Integration of geometric modeling and advanced finite element preprocessing
Shephard, Mark S.; Finnigan, Peter M.
1987-01-01
The structure to a geometry based finite element preprocessing system is presented. The key features of the system are the use of geometric operators to support all geometric calculations required for analysis model generation, and the use of a hierarchic boundary based data structure for the major data sets within the system. The approach presented can support the finite element modeling procedures used today as well as the fully automated procedures under development.
Symmetric Matrix Fields in the Finite Element Method
Directory of Open Access Journals (Sweden)
Gerard Awanou
2010-07-01
Full Text Available The theory of elasticity is used to predict the response of a material body subject to applied forces. In the linear theory, where the displacement is small, the stress tensor which measures the internal forces is the variable of primal importance. However the symmetry of the stress tensor which expresses the conservation of angular momentum had been a challenge for finite element computations. We review in this paper approaches based on mixed finite element methods.
Finite element analysis to model complex mitral valve repair.
Labrosse, Michel; Mesana, Thierry; Baxter, Ian; Chan, Vincent
2016-01-01
Although finite element analysis has been used to model simple mitral repair, it has not been used to model complex repair. A virtual mitral valve model was successful in simulating normal and abnormal valve function. Models were then developed to simulate an edge-to-edge repair and repair employing quadrangular resection. Stress contour plots demonstrated increased stresses along the mitral annulus, corresponding to the annuloplasty. The role of finite element analysis in guiding clinical practice remains undetermined.
Determination of a synchronous generator characteristics via Finite Element Analysis
Directory of Open Access Journals (Sweden)
Kolondzovski Zlatko
2005-01-01
Full Text Available In the paper a determination of characteristics of a small salient pole synchronous generator (SG is presented. Machine characteristics are determined via Finite Element Analysis (FEA and for that purpose is used the software package FEMM Version 3.3. After performing their calculation and analysis, one can conclude that most of the characteristics presented in this paper can be obtained only by using the Finite Element Method (FEM.
A finite element primer for beginners the basics
Zohdi, Tarek I
2014-01-01
The purpose of this primer is to provide the basics of the Finite Element Method, primarily illustrated through a classical model problem, linearized elasticity. The topics covered are:(1) Weighted residual methods and Galerkin approximations,(2) A model problem for one-dimensional?linear elastostatics,(3) Weak formulations in one dimension,(4) Minimum principles in one dimension,(5) Error estimation in one dimension,(5) Construction of Finite Element basis functions in one dimension,(6) Gaussian Quadrature,(7) Iterative solvers and element by element data structures,(8) A model problem for th
Energy Technology Data Exchange (ETDEWEB)
Patra, Anirban [Los Alamos National Lab. (LANL), Los Alamos, NM (United States); Wen, Wei [Los Alamos National Lab. (LANL), Los Alamos, NM (United States); Martinez Saez, Enrique [Los Alamos National Lab. (LANL), Los Alamos, NM (United States); Tome, Carlos [Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
2016-05-31
This report describes the implementation of a crystal plasticity framework (VPSC) for irradiation hardening and plastic deformation in the finite element code, MOOSE. Constitutive models for irradiation hardening and the crystal plasticity framework are described in a previous report [1]. Here we describe these models briefly and then describe an algorithm for interfacing VPSC with finite elements. Example applications of tensile deformation of a dog bone specimen and a 3D pre-irradiated bar specimen performed using MOOSE are demonstrated.
Validation of Finite Element Solutions of Nonlinear, Periodic Eddy Current Problems
Directory of Open Access Journals (Sweden)
Plasser René
2014-12-01
Full Text Available An industrial application is presented to validate a finite element analysis of 3-dimensional, nonlinear eddy-current problems with periodic excitation. The harmonic- balance method and the fixed-point technique are applied to get the steady state solution using the finite element method. The losses occurring in steel reinforcements underneath a reactor due to induced eddy-currents are computed and compared to measurements.
Finite element modelling of creep process - steady state stresses and strains
Directory of Open Access Journals (Sweden)
Sedmak Aleksandar S.
2014-01-01
Full Text Available Finite element modelling of steady state creep process has been described. Using an analogy of visco-plastic problem with a described procedure, the finite element method has been used to calculate steady state stresses and strains in 2D problems. An example of application of such a procedure have been presented, using real life problem - cylindrical pipe with longitudinal crack at high temperature, under internal pressure, and estimating its residual life, based on the C*integral evaluation.
Finite Element Model Updating Using Response Surface Method
Marwala, Tshilidzi
2007-01-01
This paper proposes the response surface method for finite element model updating. The response surface method is implemented by approximating the finite element model surface response equation by a multi-layer perceptron. The updated parameters of the finite element model were calculated using genetic algorithm by optimizing the surface response equation. The proposed method was compared to the existing methods that use simulated annealing or genetic algorithm together with a full finite element model for finite element model updating. The proposed method was tested on an unsymmetri-cal H-shaped structure. It was observed that the proposed method gave the updated natural frequen-cies and mode shapes that were of the same order of accuracy as those given by simulated annealing and genetic algorithm. Furthermore, it was observed that the response surface method achieved these results at a computational speed that was more than 2.5 times as fast as the genetic algorithm and a full finite element model and 24 ti...
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.
Enhanced patch test of finite element methods
Institute of Scientific and Technical Information of China (English)
CHEN; Wanji
2006-01-01
Theoretically, the constant stress patch test is not rigorous. Also, either the patch test of non-zero constant shear for Mindlin plate problem or non-zero strain gradient curvature of the microstructures cannot be performed. To improve the theory of the patch test, in this paper, based on the variational principle with relaxed continuity requirement of nonconforming element for homogeneous differential equations, the author proposed the individual element condition for passing the patch test and the convergence condition of the element: besides passing the patch test, the element function should include the rigid body modes and constant strain modes and satisfy the weak continuity condition, and no extra zero energy modes occur. Moreover, the author further established a variational principle with relaxed continuity requirement of nonconforming element for inhomogeneous differential equations, the enhanced patch test condition and the individual element condition. To assure the convergence of the element that should pass the enhanced patch test, the element function should include the rigid body modes and non-zero strain modes which satisfied the equilibrium equations, and no spurious zero energy modes occur and should satisfy new weak continuity condition. The theory of the enhanced patch test proposed in this paper can be applied to both homogeneous and inhomogeneous differential equations. Based on this theory, the patch test of the non-zero constant shear stress for Mindlin plate and the C0-1 patch test of the non-zero constant curvature for the couple stress/strain gradient theory were established.
CSIR Research Space (South Africa)
Loveday, PW
2007-03-01
Full Text Available conventional finite element methods available in commercial software, these models tend to be very large. An alternative method is to use specially formulated waveguide finite elements (sometimes called Semi-Analytical Finite Elements). Models using...
Advances in the study of hybrid finite elements
Institute of Scientific and Technical Information of China (English)
无
2000-01-01
Some new concepts and research progress in hybrid finite elements advanced in recent years are in troduced. On the basis of incompatible energy consistency analysis, the optimal condition of hybrid elements is derived and the formulation for fulfilling this condition is given. A post-processing penalty equilibrium optimization technique of hybrid element is presented to create high quality hybrid model. For incompressible problems, a method of deviatoric hybrid element is proposed and unification of computation between compressible and incompressible media is achieved.
THE SPACE-TIME FINITE ELEMENT METHOD FOR PARABOLIC PROBLEMS
Institute of Scientific and Technical Information of China (English)
李宏; 刘儒勋
2001-01-01
Adaptive space-time finite element method, continuous in space but discontinuous in time for semi-linear parabolic problems is discussed. The approach is based on a combination of finite element and finite difference techniques. The existence and uniqueness of the weak solution are proved without any assumptions on choice of the spacetime meshes. Basic error estimates in L∞ (L2) norm, that is maximum-norm in time, L2norm in space are obtained. The numerical results are given in the last part and the analysis between theoretic and experimental results are obtained.
Combescure, D.; Lazarus, A.
2008-12-01
This paper is aimed at presenting refined finite element modelling used for dynamic analysis of large rotating machines. The first part shows an equivalence between several levels of modelling: firstly, models made of beam elements and rigid disc with gyroscopic coupling representing the position of the rotating shaft in an inertial frame; secondly full three-dimensional (3D) or 3D shell models of the rotor and the blades represented in the rotating frame and finally two-dimensional (2D) Fourier model for both rotor and stator. Simple cases are studied to better understand the results given by analysis performed using a rotating frame and the equivalence with the standard calculations with beam elements. Complete analysis of rotating machines can be performed with models in the frames best adapted for each part of the structure. The effects of several defects are analysed and compared with this approach. In the last part of the paper, the modelling approach is applied to the analysis of the large rotating shaft part of the power conversion unit of the GT-MHR nuclear reactor.
三维有限元并行计算及其工程应用%PARALLEL 3D FINITE ELEMENT ANALYSIS AND ITS APPLICATION TO HYDRAULIC ENGINEERING
Institute of Scientific and Technical Information of China (English)
刘耀儒; 周维垣; 杨强; 陈新
2005-01-01
针对水利工程中的大型复杂三维结构对大规模数值计算的需求,基于J-PCG方法(Jacobi预处理共轭梯度法),建立了有限元EBE(element-by-element)方法在分布存储并行机上的计算算法.该算法不用考虑网格拓扑结构和单元的排序,同时不形成整体刚度矩阵,而且避免了对复杂的三维结构进行区域分解.采用上述算法编制了三维有限元并行求解的PFEM(parallel finite element method)程序,并在网络机群系统上实现,然后将其应用到二滩拱坝-地基系统和水布娅地下洞室的三维有限元数值计算中.数值计算结果表明,三维有限元并行EBE方法非常适合于水利工程中三维复杂结构的大规模数值计算.
A Comparison of Continuous Mass-lumped Finite Elements and Finite Differences for 3D
Zhebel, E.; Minisini, S.; Kononov, A.; Mulder, W.A.
2012-01-01
The finite-difference method is widely used for time-domain modelling of the wave equation because of its ease of implementation of high-order spatial discretization schemes, parallelization and computational efficiency. However, finite elements on tetrahedral meshes are more accurate in complex geo
Asymptotic Behavior of the Finite Difference and the Finite Element Methods for Parabolic Equations
Institute of Scientific and Technical Information of China (English)
LIU Yang; FENG Hui
2005-01-01
The asymptotic convergence of the solution of the parabolic equation is proved. By the eigenvalues estimation, we obtain that the approximate solutions by the finite difference method and the finite element method are asymptotically convergent. Both methods are considered in continuous time.
A Comparison of Continuous Mass-lumped Finite Elements and Finite Differences for 3D
Zhebel, E.; Minisini, S.; Kononov, A.; Mulder, W.A.
2012-01-01
The finite-difference method is widely used for time-domain modelling of the wave equation because of its ease of implementation of high-order spatial discretization schemes, parallelization and computational efficiency. However, finite elements on tetrahedral meshes are more accurate in complex
FINITE ELEMENT MODELING OF PROBLEMS OF GEOMECHANICS AND GEOPHYSICS
Directory of Open Access Journals (Sweden)
Vlasov Alexander Nikolaevich
2012-10-01
Full Text Available In the article, the authors consider some classes of problems of geomechanics that are resolved through the application of SIMULIA ABAQUS software. The tasks associated with the assessment of the zone of influence of structures produced on surrounding buildings and structures in the dense urban environment, as well as the tectonic and physical simulation of rifts with the purpose of identification of deformations of the Earth surface and other defects of lithospheric plates. These seemingly different types of tasks can be grouped together on the basis of common characteristics due to the complexity of numerical modeling problems of geomechanics and geophysics. Non-linearity of physical processes, complexity of the geological structure and variable thickness of layers, bed thinning layers, lenses, as well as singular elements, make it hard to consolidate different elements (for example, engineering and geological elements and associated structures of buildings in a single model. In this regard, software SIMULIA ABAQUS looks attractive, since it provides a highly advanced finite-element modeling technique, including a convenient hexahedral mesh generator, a wide range of models of elastic and plastic strain of materials, and the ability to work with certain geometric areas that interrelate through the mechanism of contacting surface pairs that have restrictions. It is noteworthy that the research also facilitates development of personal analytical methods designated for the assessment of physical and mechanical properties of heterogeneous materials as well as new solutions applicable in the vicinity of singular elements of the area that may be used in modeling together with ABAQUS software.
Institute of Scientific and Technical Information of China (English)
陈蔚
2003-01-01
The transient behavior of a semiconductor device consists of a Poisson equation for the electric potential and of two nonlinear parabolic equations for the electron density and hole density.The electric potential equation is discretized by a mixed finite element method.The electron and hole density equations are treated by implicit-explicit multistep finite element methods.The schemes are very efficient.The optimal order error estimates both in time and space are derived.
B Free Finite Element Approach for Saturated Porous Media: Consolidation
Directory of Open Access Journals (Sweden)
M. M. Stickle
2016-01-01
Full Text Available The B free finite element approach is applied to the governing equations describing the consolidation process in saturated poroelastic medium with intrinsically incompressible solid and fluid phases. Under this approach, where Voigt notation is avoided, the finite element equilibrium equations and the linearization of the coupled governing equations are fully derived using tensor algebra. In order to assess the B free approach for the consolidation equations, direct comparison with analytical solution of the response of a homogeneous and isotropic water-saturated poroelastic finite column under harmonic load is presented. The results illustrate the capability of this finite element approach of reproducing accurately the response of quasistatic phenomena in a saturated porous medium.
Kriging-Based Finite Element Method: Element-By-Element Kriging Interpolation
Directory of Open Access Journals (Sweden)
W. Kanok-Nukulchai
2009-01-01
Full Text Available An enhancement of the finite element method with Kriging shape functions (K-FEM was recently proposed. In this method, the field variables of a boundary value problem are approximated using ‘element-by-element’ piecewise Kriging interpolation (el-KI. For each element, the interpolation function is constructed from a set of nodes within a prescribed domain of influence comprising the element and its several layers of neighbouring elements. This paper presents a numerical study on the accuracy and convergence of the el-KI in function fitting problems. Several examples of functions in two-dimensional space are employed in this study. The results show that very accurate function fittings and excellent convergence can be attained by the el-KI.
Li, Liang; Huang, Ting-Zhu; Jing, Yan-Fei; Zhang, Yong
2010-02-01
The incomplete Cholesky (IC) factorization preconditioning technique is applied to the Krylov subspace methods for solving large systems of linear equations resulted from the use of edge-based finite element method (FEM). The construction of the preconditioner is based on the fact that the coefficient matrix is represented in an upper triangular compressed sparse row (CSR) form. An efficient implementation of the IC factorization is described in detail for complex symmetric matrices. With some ordering schemes our IC algorithm can greatly reduce the memory requirement as well as the iteration numbers. Numerical tests on harmonic analysis for plane wave scattering from a metallic plate and a metallic sphere coated by a lossy dielectric layer show the efficiency of this method.
Application of mixed finite element method in elastic contact problems%混合有限元法在弹性接触问题中的应用
Institute of Scientific and Technical Information of China (English)
袁国良; 王忠东
2000-01-01
讨论了利用Hellinger-Reissner二类变量广义变分原理解决定边界接触问题的混合有限元法，并且给出这种计算方法的数值实例。数值结果表明该方法在定边界弹性接触问题中的应用行之有效。%Constant boundary contact problems in practical engineering often occur. It ismeaningful to precisely calculate stress and displacement in the contact area using an effec-tive method. A mixed finite element method for the contact problems with constant bound-ary by Hellinger-Reissner's general variation principle in two variates is studied and somenumerical examples are presented. These numerical results show that this proposed methodis effective.
Gabel, R.; Lang, P. F.; Smith, L. A.; Reed, D. A.
1989-01-01
Boeing Helicopter, together with other United States helicopter manufacturers, participated in a finite element applications program to emplace in the United States a superior capability to utilize finite element analysis models in support of helicopter airframe design. The activities relating to planning and creating a finite element vibrations model of the Boeing Model 36-0 composite airframe are summarized, along with the subsequent analytical correlation with ground shake test data.
Computationally efficient finite element evaluation of natural patellofemoral mechanics.
Fitzpatrick, Clare K; Baldwin, Mark A; Rullkoetter, Paul J
2010-12-01
Finite element methods have been applied to evaluate in vivo joint behavior, new devices, and surgical techniques but have typically been applied to a small or single subject cohort. Anatomic variability necessitates the use of many subject-specific models or probabilistic methods in order to adequately evaluate a device or procedure for a population. However, a fully deformable finite element model can be computationally expensive, prohibiting large multisubject or probabilistic analyses. The aim of this study was to develop a group of subject-specific models of the patellofemoral joint and evaluate trade-offs in analysis time and accuracy with fully deformable and rigid body articular cartilage representations. Finite element models of eight subjects were used to tune a pressure-overclosure relationship during a simulated deep flexion cycle. Patellofemoral kinematics and contact mechanics were evaluated and compared between a fully deformable and a rigid body analysis. Additional eight subjects were used to determine the validity of the rigid body pressure-overclosure relationship as a subject-independent parameter. There was good agreement in predicted kinematics and contact mechanics between deformable and rigid analyses for both the tuned and test groups. Root mean square differences in kinematics were less than 0.5 deg and 0.2 mm for both groups throughout flexion. Differences in contact area and peak and average contact pressures averaged 5.4%, 9.6%, and 3.8%, respectively, for the tuned group and 6.9%, 13.1%, and 6.4%, respectively, for the test group, with no significant differences between the two groups. There was a 95% reduction in computational time with the rigid body analysis as compared with the deformable analysis. The tuned pressure-overclosure relationship derived from the patellofemoral analysis was also applied to tibiofemoral (TF) articular cartilage in a group of eight subjects. Differences in contact area and peak and average contact
Analysis of automotive liftgate seals using finite element analysis
Directory of Open Access Journals (Sweden)
Rafael H. T Ueda
2010-01-01
Full Text Available Seals have wide application in automotive products. They are responsible for sealing the car in several parts such as the doors, the air intake cowl seal, and air intake lights seal. Strain and stress studies are very important in order to understand the behavior of polymeric materials, which are generally submitted to great workload variation and environmental influence. This study of EPDM rubber was carried out to define the strain, stress and yield stress. Tensile and compression tests were carried out on workpieces with 100 mm of length. The data were acquired using the Qmat software. A Finite Element Analysis using the MSC Marc MentatTM was conducted and compared with experimental tests. The results showed an increase of effort proportional to bulb thickness. The proportional increase of compression effort for different displacements was significant. Moreover, physical parameters such as length, thickness, and friction coefficient changed the strain and stress rate.
A multilevel finite element method for Fredholm integral eigenvalue problems
Xie, Hehu; Zhou, Tao
2015-12-01
In this work, we proposed a multigrid finite element (MFE) method for solving the Fredholm integral eigenvalue problems. The main motivation for such studies is to compute the Karhunen-Loève expansions of random fields, which play an important role in the applications of uncertainty quantification. In our MFE framework, solving the eigenvalue problem is converted to doing a series of integral iterations and eigenvalue solving in the coarsest mesh. Then, any existing efficient integration scheme can be used for the associated integration process. The error estimates are provided, and the computational complexity is analyzed. It is noticed that the total computational work of our method is comparable with a single integration step in the finest mesh. Several numerical experiments are presented to validate the efficiency of the proposed numerical method.
Finite-element modeling and analysis in nanomedicine and dentistry.
Choi, Andy H; Conway, Richard C; Ben-Nissan, Besim
2014-08-01
This article aims to provide a brief background to the current applications of finite-element analysis (FEA) in nanomedicine and dentistry. FEA was introduced in orthopedic biomechanics in the 1970s in order to assess the stresses and deformation in human bones during functional loadings and in the design and analysis of implants. Since then, it has been applied with great frequency in orthopedics and dentistry in order to analyze issues such as implant design, bone remodeling and fracture healing, the mechanical properties of biomedical coatings on implants and the interactions at the bone-implant interface. More recently, FEA has been used in nanomedicine to study the mechanics of a single cell and to gain fundamental insights into how the particulate nature of blood influences nanoparticle delivery.
Obtaining local reciprocal lattice vectors from finite-element analysis.
Sutter, John P; Connolley, Thomas; Hill, Tim P; Huang, Houcheng; Sharp, Doug W; Drakopoulos, Michael
2008-11-01
Finite-element analysis is frequently used by engineers at synchrotron beamlines to calculate the elastic deformation of a single crystal undergoing mechanical bending or thermal load. ANSYS Workbench software is widely used for such simulations. However, although ANSYS Workbench software provides useful information on the displacements, strains and stresses within the crystal, it does not yield the local reciprocal lattice vectors that would be required for X-ray diffraction calculations. To bridge this gap, a method based on the shape functions and interpolation procedures of the software itself has been developed. An application to the double-crystal bent Laue monochromator being designed for the I12 (JEEP) wiggler beamline at the Diamond Light Source is presented.
Finite element stress analysis of some ankle joint prostheses.
Falsig, J; Hvid, I; Jensen, N C
1986-05-01
A three-dimensional finite element stress analysis was employed to calculate stresses in a distal tibia modelled with three simple total ankle joint replacement tibial components. The bone was modelled as a composite structure consisting of cortical and trabecular bone in which the trabecular bone was either homogeneous with a constant modulus of elasticity or heterogenous with experimentally determined heterogeneity. The results were sensitive to variations in trabecular bone material property distributions, with lower stresses being calculated in the heterogeneous model. An anterolateral application of load, which proved the least favourable, was used in comparing the prosthetic variants. Normal and shear stresses at the trabecular bone-cement interface and supporting trabecular bone were slightly reduced by addition of metal backing to the polyethylene articular surface, and a further reduction to very low values was obtained by addition of a long intramedullary peg bypassing stresses to the cortical bone.
Institute of Scientific and Technical Information of China (English)
R ANSARI; S ROUHI; M ARYAYI
2013-01-01
By the atomistic and continuum finite element models, the free vibration behavior of single-walled carbon nanotubes (SWCNTs) is studied. In the atomistic finite element model, the bonds and atoms are modeled by the beam and point mass elements, respectively. The molecular mechanics is linked to structural mechanics to determine the elastic properties of the mentioned beam elements. In the continuum finite element approach, by neglecting the discrete nature of the atomic structure of the nanotubes, they are modeled with shell elements. By both models, the natural frequencies of SWCNTs are computed, and the effects of the geometrical parameters, the atomic structure, and the boundary conditions are investigated. The accuracy of the utilized methods is verified in comparison with molecular dynamic simulations. The molecular structural model leads to more reliable results, especially for lower aspect ratios. The present analysis provides valuable information about application of continuum models in the investigation of the mechanical behaviors of nanotubes.
An implicit discontinuous Galerkin finite element model for water waves
van der Vegt, Jacobus J.W.; Ambati, V.R.; Bokhove, Onno
2005-01-01
We discuss a new higher order accurate discontinuous Galerkin finite element method for non-linear free surface gravity waves. The algorithm is based on an arbitrary Lagrangian Eulerian description of the flow field using deforming elements and a moving mesh, which makes it possible to represent
Finite Element Vibration Analysis of Beams, Plates and Shells
Directory of Open Access Journals (Sweden)
Jaroslav Mackerle
1999-01-01
Full Text Available This bibliography lists references to papers, conference proceedings and theses/dissertations dealing with finite element vibration analysis of beams, plates and shells that were published in 1994–1998. It contains 361 citations. Also included, as separated subsections, are vibration analysis of composite materials and vibration analysis of structural elements with cracks/contacts.
A COMBINED HYBRID FINITE ELEMENT METHOD FOR PLATE BENDING PROBLEMS
Institute of Scientific and Technical Information of China (English)
Tian-xiao Zhou; Xiao-ping Xie
2003-01-01
In this paper, a combined hybrid method is applied to finite element discretization ofplate bending problems. It is shown that the resultant schemes are stabilized, i.e., theconvergence of the schemes is independent of inf-sup conditions and any other patch test.Based on this, two new series of plate elements are proposed.
Efficient Finite Element Methods for Transient Analysis of Shells.
1985-04-01
Triangular Shell Element with Improved Membrane Interpolation," Communications in Applied Numerical Methods , in press 1985. Results of this work were...in Applied Numerical Methods , to appear. G.R. Cowper, G.M. Lindberg and M.D. Olson (1970), "A Shallow Shell Finite Element of Triangular Shape," Int. J
Finite element models for the steady state analysis of moving loads
Kok, A.W.M.
2000-01-01
The analysis of structures subjected to fast moving loads is a subject of growing interest in railway and pavement engineering. The applications of transient analyses using finite element models, however, are still very limited. The faster a load moves the more elements we need to model the structu
Kaltenbacher, Manfred
2015-01-01
Like the previous editions also the third edition of this book combines the detailed physical modeling of mechatronic systems and their precise numerical simulation using the Finite Element (FE) method. Thereby, the basic chapter concerning the Finite Element (FE) method is enhanced, provides now also a description of higher order finite elements (both for nodal and edge finite elements) and a detailed discussion of non-conforming mesh techniques. The author enhances and improves many discussions on principles and methods. In particular, more emphasis is put on the description of single fields by adding the flow field. Corresponding to these field, the book is augmented with the new chapter about coupled flow-structural mechanical systems. Thereby, the discussion of computational aeroacoustics is extended towards perturbation approaches, which allows a decomposition of flow and acoustic quantities within the flow region. Last but not least, applications are updated and restructured so that the book meets mode...
An efficient wavelet finite element method in fault prognosis of incipient crack
Institute of Scientific and Technical Information of China (English)
无
2006-01-01
The method of constructing any scale wavelet finite element (WFE) based on the one-dimensional or two-dimensional Daubechies scaling functions was presented, and the corresponding WFE adaptive lifting algorithm was given. In order to obtain the nested increasing approximate subspaces of multiscale finite element, the Daubechies scaling functions with the properties of multi-resolution analysis were employed as the finite element interpolating functions. Thus, the WFE could adaptively mesh the singularity domain caused by local cracks, which resulted in better approximate solutions than the traditional finite element methods. The calculations of natural frequencies of cracked beam were used to check the accuracy of given methods. In addition, the results of cracked cantilever beam and engineering application were satisfied. So, the current methods can provide effective tools in the numerical modeling of the fault prognosis of incipient crack.
A class of hybrid finite element methods for electromagnetics: A review
Volakis, J. L.; Chatterjee, A.; Gong, J.
1993-01-01
Integral equation methods have generally been the workhorse for antenna and scattering computations. In the case of antennas, they continue to be the prominent computational approach, but for scattering applications the requirement for large-scale computations has turned researchers' attention to near neighbor methods such as the finite element method, which has low O(N) storage requirements and is readily adaptable in modeling complex geometrical features and material inhomogeneities. In this paper, we review three hybrid finite element methods for simulating composite scatterers, conformal microstrip antennas, and finite periodic arrays. Specifically, we discuss the finite element method and its application to electromagnetic problems when combined with the boundary integral, absorbing boundary conditions, and artificial absorbers for terminating the mesh. Particular attention is given to large-scale simulations, methods, and solvers for achieving low memory requirements and code performance on parallel computing architectures.
Research of Stamp Forming Simulation Based on Finite Element Method
Institute of Scientific and Technical Information of China (English)
SU Xaio-ping; XU Lian
2008-01-01
We point out that the finite element method offers a greta functional improvement for analyzing the stamp forming process of an automobile panel. Using the finite element theory and the simulation method of sheet stamping forming, the element model of sheet forming is built based on software HyperMesh,and the simulation of the product's sheet forming process is analyzed based on software Dynaform. A series of simulation results are obtained. It is clear that the simulation results from the theoretical basis for the product's die design and are useful for selecting process parameters.
Finite element analysis of two disk rotor system
Dixit, Harsh Kumar
2016-05-01
A finite element model of simple horizontal rotor system is developed for evaluating its dynamic behaviour. The model is based on Timoshenko beam element and accounts for the effect of gyroscopic couple and other rotational forces. Present rotor system consists of single shaft which is supported by bearings at both ends and two disks are mounted at different locations. The natural frequencies, mode shapes and orbits of rotating system for a specific range of rotation speed are obtained by developing a MATLAB code for solving the finite element equations of rotary system. Consequently, Campbell diagram is plotted for finding a relationship between natural whirl frequencies and rotation of the rotor.
ELASTO-PLASTIC FINITE ELEMENT ANALYSIS OF HOOK'S JOINT
Directory of Open Access Journals (Sweden)
Adnan ATICI
1996-03-01
Full Text Available In this study, stress analysis has been done in Hooke's joint by the finite element method. In finite element meshing, isoparametric quadrilateral elements with four nodes has been chosen and Lagrange polynomial has been used as the interpolation function. The special computer program has been written for the automatic mesh generation. In addition the other program has been developed to solve the finite element problems. Elastoplastic stress analysis is done to calculate the residual stresses in hooke's joint. Elasto-plastic stress values are calculated under loading from 400 daN to 1000 daN with increment of 100 daN. In this analysis "The initial stress method" is used.
Finite element analysis of piezoelectric underwater transducers for acoustic characteristics
Energy Technology Data Exchange (ETDEWEB)
Kim, Jae Hwan [Inha University, Incheon (Korea, Republic of); Kim, Heung Soo [Catholic University, Daegu (Korea, Republic of)
2009-02-15
This paper presents a simulation technique for analyzing acoustic characteristics of piezoelectric underwater transducers. A finite element method is adopted for modeling piezoelectric coupled problems including material damping and fluid-structure interaction problems by taking system matrices in complex form. For the finite element modeling of unbounded acoustic fluid, infinite wave envelope element (IWEE) is adopted to take into account the infinite domain. An in-house finite element program is developed and technical issues for implementing the program are explained. Using the simulation program, acoustic characteristics of tonpilz transducer are analyzed in terms of modal analysis, radiated pressure distribution, pressure spectrum, transmitting-voltage response and impedance analysis along with experimental comparison. The developed simulation technique can be used for designing ultrasonic transducers in the areas of nondestructive evaluation, underwater acoustics and bioengineering
Finite element analysis for acoustic characteristics of a magnetostrictive transducer
Kim, Jaehwan; Jung, Eunmi
2005-12-01
This paper presents a finite element analysis for a magnetostrictive transducer by taking into account the nonlinear behavior of the magnetostrictive material and fluid interaction. A finite element formulation is derived for the coupling of magnetostrictive and elastic materials based upon a separated magnetic and displacement field calculation and a curve fitting technique of material properties. The fluid and structure coupled problem is taken into account based upon pressure and velocity potential fields formulation. Infinite wave envelope elements are introduced at an artificial boundary to deal with the infinite fluid domain. A finite element code for the analysis of a magnetostrictive transducer is developed. A magnetostrictive tonpilz transducer is taken as an example and verification for the developed program is made by comparing with a commercial code. The acoustic characteristics of the magnetostrictive tonpilz transducer are calculated in terms of radiation pattern and transmitted current response.
有限元分析在颈椎生物力学研究中的应用%Application of Finite Element Analysis in Cervical Vertebrae Biomechanical Study
Institute of Scientific and Technical Information of China (English)
石向明; 王辉
2012-01-01
Finite element analysis is a matrix method for structure analysis, with the development of finite element technology and further understanding of mechanical characteristics of spine, it has become one of the important research methods used in spine biomechanics. Here is to introduce the concept and principle of finite element, the history in cervical vertebrae, and make a review on the biomechanical properties of cervical vertebra under pathologic , physiologic conditions , and injuries , the long term impact of different surgeries , and design and improvement assessment of internal fixation devices. With development of computer and finite element software, its application in cervical vertebrae will become increased and widespread.%有限元分析法最初是一种用于结构分析的矩阵方法,随着有限元技术的发展及人们对脊柱生物力学特性的深入了解,现已成为脊柱生物力学研究的重要方法之一.现对有限元方法的概念、原理以及应用于颈椎研究的历史进行介绍,概述应用有限元方法对颈椎生理、病理、损伤情况下生物力学特性的分析;不同手术方式的远期效果,内固定器械设计及改良的评价.随着计算机技术的提高和有限元软件的研发,有限元法在颈椎生物力学的研究将得到长足发展.
Effective Finite Elements for Shell Analysis.
1984-02-20
conjunction with a shallow shell theory . It 2 should be noteJ that contrary to the results of earlier investigators [12,19], use of a shallow shell theory in...the inadequacy of the shallow shell theory for the relatively deep element emerging from such a coarse mesh. A considerable improvement is obtained
General beam cross-section analysis using a 3D finite element slice
DEFF Research Database (Denmark)
Couturier, Philippe; Krenk, Steen
2014-01-01
A formulation for analysis of general cross-section properties has been developed. This formulation is based on the stress-strain states in the classic six equilibrium modes of a beam by considering a finite thickness slice modelled by a single layer of 3D finite elements. The displacement...... an analytical solution is available. The paper also shows an application to wind turbine blade cross-sections and discusses the effect of the finite element discretization on the cross-section properties such as stiffness parameters and the location of the elastic and shear centers....
FINITE ELEMENT METHODS FOR THE NAVIER-STOKES EQUATIONS BY H(div) ELEMENTS
Institute of Scientific and Technical Information of China (English)
Junping Wang; Xiaoshen Wang; Xiu Ye
2008-01-01
We derived and analyzed a new numerical scheme for the Navier-Stokes equations by using H(div) conforming finite elements. A great deal of effort was given to an establishment of some Sobolev-type inequalities for piecewise smooth functions. In particular, the newly derived Sobolev inequalities were employed to provide a mathematical theory for the H(div) finite element scheme. For example, it was proved that the new finite element scheme has solutions which admit a certain boundedness in terms of the input data. A solution uniqueness was also possible when the input data satisfies a certain smallness condition. Optimal-order error estimates for the corresponding finite element solutions were established in various Sobolev norms. The finite element solutions from the new scheme feature a full satisfaction of the continuity equation which is highly demanded in scientific computing.
Institute of Scientific and Technical Information of China (English)
朱卫平; 黄黔
2002-01-01
The finite-element-displacement-perturbation method (FEDPM)for thegeometric nonlinear behaviors of shells of revolution subjected to pure bending moments orlateral forces in one of their meridional planes ( Ⅰ ) was employed to calculate the stressdistributions and the stiffness of the bellows. Firstly, by applying the first-orderperturbation solution ( the linear solution ) of the FEDPM to the bellows, the obtainedresults were compared with those of the general solution and the initial parameter integrationsolution proposed by the present authors earlier, as well as of the experiments and the FEAby others. It is shown that the FEDPM is with good precision and reliability, and as it waspointed out in ( Ⅰ ) the abrupt changes of the meridian curvature of bellows would not affectthe use of the usual straight element. Then the nonlinear behaviors of the bellows werediscussed. As expected, the nonlinear effects mainly come from the bellows ring plate, andthe wider the ring plate is, the stronger the nonlinear effects are. Contrarily, the vanishingof the ring plate, like the C-shaped bellows, the nonlinear effects almost vanish. Inaddition, when the pure bending moments act on the bellows, each convolution has thesame stress distributions calculated by the linear solution and other linear theories, but bythe present nonlinear solution they vary with respect to the convolutions of the bellows. Yetfor most bellows, the linear solutions are valid in practice.
Taylor, Z A; Cheng, M; Ourselin, S
2008-05-01
The use of biomechanical modelling, especially in conjunction with finite element analysis, has become common in many areas of medical image analysis and surgical simulation. Clinical employment of such techniques is hindered by conflicting requirements for high fidelity in the modelling approach, and fast solution speeds. We report the development of techniques for high-speed nonlinear finite element analysis for surgical simulation. We use a fully nonlinear total Lagrangian explicit finite element formulation which offers significant computational advantages for soft tissue simulation. However, the key contribution of the work is the presentation of a fast graphics processing unit (GPU) solution scheme for the finite element equations. To the best of our knowledge, this represents the first GPU implementation of a nonlinear finite element solver. We show that the present explicit finite element scheme is well suited to solution via highly parallel graphics hardware, and that even a midrange GPU allows significant solution speed gains (up to 16.8 x) compared with equivalent CPU implementations. For the models tested the scheme allows real-time solution of models with up to 16,000 tetrahedral elements. The use of GPUs for such purposes offers a cost-effective high-performance alternative to expensive multi-CPU machines, and may have important applications in medical image analysis and surgical simulation.
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.
Variational formulation of high performance finite elements: Parametrized variational principles
Felippa, Carlos A.; Militello, Carmello
1991-01-01
High performance elements are simple finite elements constructed to deliver engineering accuracy with coarse arbitrary grids. This is part of a series on the variational basis of high-performance elements, with emphasis on those constructed with the free formulation (FF) and assumed natural strain (ANS) methods. Parametrized variational principles that provide a foundation for the FF and ANS methods, as well as for a combination of both are presented.
New triangular and quadrilateral plate-bending finite elements
Narayanaswami, R.
1974-01-01
A nonconforming plate-bending finite element of triangular shape and associated quadrilateral elements are developed. The transverse displacement is approximated within the element by a quintic polynomial. The formulation takes into account the effects of transverse shear deformation. Results of the static and dynamic analysis of a square plate, with edges simply supported or clamped, are compared with exact solutions. Good accuracy is obtained in all calculations.
On Using Particle Finite Element for Hydrodynamics Problems Solving
Directory of Open Access Journals (Sweden)
E. V. Davidova
2015-01-01
Full Text Available The aim of the present research is to develop software for the Particle Finite Element Method (PFEM and its verification on the model problem of viscous incompressible flow simulation in a square cavity. The Lagrangian description of the medium motion is used: the nodes of the finite element mesh move together with the fluid that allows to consider them as particles of the medium. Mesh cells deform when in time-stepping procedure, so it is necessary to reconstruct the mesh to provide stability of the finite element numerical procedure.Meshing algorithm allows us to obtain the mesh, which satisfies the Delaunay criteria: it is called \\the possible triangles method". This algorithm is based on the well-known Fortune method of Voronoi diagram constructing for a certain set of points in the plane. The graphical representation of the possible triangles method is shown. It is suitable to use generalization of Delaunay triangulation in order to construct meshes with polygonal cells in case of multiple nodes close to be lying on the same circle.The viscous incompressible fluid flow is described by the Navier | Stokes equations and the mass conservation equation with certain initial and boundary conditions. A fractional steps method, which allows us to avoid non-physical oscillations of the pressure, provides the timestepping procedure. Using the finite element discretization and the Bubnov | Galerkin method allows us to carry out spatial discretization.For form functions calculation of finite element mesh with polygonal cells, \
Finite Element Analysis of Circular Plate using SolidWorks
Energy Technology Data Exchange (ETDEWEB)
Kang, Yeo Jin; Jhung, Myung Jo [Korea Institute of Nuclear Safety, Daejeon (Korea, Republic of)
2011-10-15
Circular plates are used extensively in mechanical engineering for nuclear reactor internal components. The examples in the reactor vessel internals are upper guide structure support plate, fuel alignment plate, lower support plate etc. To verify the structural integrity of these plates, the finite element analyses are performed, which require the development of the finite element model. Sometimes it is very costly and time consuming to make the model especially for the beginners who start their engineering job for the structural analysis, necessitating a simple method to develop the finite element model for the pursuing structural analysis. Therefore in this study, the input decks are generated for the finite element analysis of a circular plate as shown in Fig. 1, which can be used for the structural analysis such as modal analysis, response spectrum analysis, stress analysis, etc using the commercial program Solid Works. The example problems are solved and the results are included for analysts to perform easily the finite element analysis of the mechanical plate components due to various loadings. The various results presented in this study would be helpful not only for the benchmark calculations and results comparisons but also as a part of the knowledge management for the future generation of young designers, scientists and computer analysts
Finite Macro-Element Mesh Deformation in a Structured Multi-Block Navier-Stokes Code
Bartels, Robert E.
2005-01-01
A mesh deformation scheme is developed for a structured multi-block Navier-Stokes code consisting of two steps. The first step is a finite element solution of either user defined or automatically generated macro-elements. Macro-elements are hexagonal finite elements created from a subset of points from the full mesh. When assembled, the finite element system spans the complete flow domain. Macro-element moduli vary according to the distance to the nearest surface, resulting in extremely stiff elements near a moving surface and very pliable elements away from boundaries. Solution of the finite element system for the imposed boundary deflections generally produces smoothly varying nodal deflections. The manner in which distance to the nearest surface has been found to critically influence the quality of the element deformation. The second step is a transfinite interpolation which distributes the macro-element nodal deflections to the remaining fluid mesh points. The scheme is demonstrated for several two-dimensional applications.
Institute of Scientific and Technical Information of China (English)
GUZELBEY Ibrahim H.; KANBER Bahattin; AKPOLAT Abdullah
2004-01-01
In this study, the stress based finite element method is coupled with the boundary element method in two different ways. In the first one, the ordinary distribution matrix is used for coupling. In the second one, the stress traction equilibrium is used at the interface line of both regions as a new coupling process. This new coupling procedure is presented without a distribution matrix. Several case studies are solved for the validation of the developed coupling procedure. The results of case studies are compared with the distribution matrix coupling, displacement based finite element method, assumed stress finite element method, boundary element method, ANSYS and analytical results whenever possible. It is shown that the coupling of the stress traction equilibrium with assumed stress finite elements gives as accurate results as those by the distribution matrix coupling.
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.
Implementation of a strain energy-based nonlinear finite element in the object-oriented environment
Wegner, Tadeusz; Pęczak, Andrzej
2010-03-01
The objective of the paper is to describe a novel finite element computational method based on a strain energy density function and to implement it in the object-oriented environment. The original energy-based finite element was put into the known standard framework of classes and handled in a different manner. The nonlinear properties of material are defined with a modified strain energy density function. The local relaxation procedure proposed as a method used to resolve a nonlinear problem is implemented in C++ language. The hexahedral element with eight nodes as well as the adaptation of the nonlinear finite element is introduced. The chosen numerical model is made of nearly incompressible hyperelastic material. The application of the proposed element is shown on the example of a rectangular parallelepiped with a hollow port.
Baskharone, Erian A.
1993-09-01
This study concerns the rotor dynamic characteristics of fluid-encompassed rotors, with special emphasis on shrouded pump impellers. The core of the study is a versatile and categorically new finite-element-based perturbation model, which is based on a rigorous flow analysis and what we have generically termed the 'virtually' deformable finite-element approach. The model is first applied to the case of a smooth annular seal for verification purposes. The rotor excitation components, in this sample problem, give rise to a purely cylindrical, purely conical, and a simultaneous cylindrical/conical rotor whirl around the housing centerline. In all cases, the computed results are compared to existing experimental and analytical data involving the same seal geometry and operating conditions. Next, two labyrinth-seal configurations, which share the same tooth-to-tooth chamber geometry but differ in the total number of chambers, were investigated. The results, in this case, are compared to experimental measurements for both seal configurations. The focus is finally shifted to the shrouded-impeller problem, where the stability effects of the leakage flow in the shroud-to-housing secondary passage are investigated. To this end, the computational model is applied to a typical shrouded-impeller pump stage, fabricated and rotor dynamically tested by Sulzer Bros., and the results compared to those of a simplified 'bulk-flow' analysis and Sulzer Bros.' test data. In addition to assessing the computed rotor dynamic coefficients, the shrouded-impeller study also covers a controversial topic, namely that of the leakage-passage inlet swirl, which was previously cited as the origin of highly unconventional (resonance-like) trends of the fluid-exerted forces. In order to validate this claim, a 'microscopic' study of the fluid/shroud interaction mechanism is conducted, with the focus being on the structure of the perturbed flow field associated with the impeller whirl. The conclusions