The Finite Element Method: Theory, Implementation, and Applications

Author: Mats G. Larson,Fredrik Bengzon

Publisher: Springer Science & Business Media

ISBN: 3642332870

Category: Computers

Page: 395

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This book gives an introduction to the finite element method as a general computational method for solving partial differential equations approximately. Our approach is mathematical in nature with a strong focus on the underlying mathematical principles, such as approximation properties of piecewise polynomial spaces, and variational formulations of partial differential equations, but with a minimum level of advanced mathematical machinery from functional analysis and partial differential equations. In principle, the material should be accessible to students with only knowledge of calculus of several variables, basic partial differential equations, and linear algebra, as the necessary concepts from more advanced analysis are introduced when needed. Throughout the text we emphasize implementation of the involved algorithms, and have therefore mixed mathematical theory with concrete computer code using the numerical software MATLAB is and its PDE-Toolbox. We have also had the ambition to cover some of the most important applications of finite elements and the basic finite element methods developed for those applications, including diffusion and transport phenomena, solid and fluid mechanics, and also electromagnetics.​

Development and Application of the Finite Element Method based on MatLab

Author: Herbert Baaser

Publisher: Springer Science & Business Media

ISBN: 9783642131530

Category: Technology & Engineering

Page: 64

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The intention of this booklet is a brief but general introduction into the treatment of the Finite Element Method (FEM). The FEM has become the leading method in computer–oriented mechanics, so that many scienti?c brancheshavegrownup besides overthelastdecades. Nevertheless,theFEM today is a question of economy. On the one hand its industrial application is forced to reduce product development costs and time, on the other hand a large number of commercial FEM codes and a still growing number of software for e?ective pre– and postprocessors are available in the meantime. Due to that, today it is a quite challenging task to operate with all these di?erent tools at the same time and to understand all handling and so- tion techniques developed over the last years. So, we want to help in getting a deeper insight into the main “interfaces” between the “customers of the FEM” and the codes itself by providing a totally open structured FE–code based on Matlab, which is a very powerful tool in operating with matrix based formulations. That idea and conditions forced us some years ago to initiateDAEdalon as a tool for general FE developments in research appli- tions. In spite of still existing high sophisticated – mostly commercial – FE codes, the success and the acceptance of such a structured tool justify that decision afterwards more and more.

Introduction to Finite and Spectral Element Methods using MATLAB

Author: Constantine Pozrikidis

Publisher: CRC Press

ISBN: 142005709X

Category: Science

Page: 680

View: 496

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Why another book on the finite element method? There are currently more than 200 books in print with "Finite Element Method" in their titles. Many are devoted to special topics or emphasize error analysis and numerical accuracy. Others stick to the fundamentals and do little to describe the development and implementation of algorithms for solving real-world problems. Introduction to Finite and Spectral Element Methods Using MATLAB provides a means of quickly understanding both the theoretical foundation and practical implementation of the finite element method and its companion spectral element method. Written in the form of a self-contained course, it introduces the fundamentals on a need-to-know basis and emphasizes algorithm development and computer implementation of the essential procedures. Firmly asserting the importance of simultaneous practical experience when learning any numerical method, the author provides FSELIB: a software library of user-defined MATLAB functions and complete finite and spectral element codes. FSELIB is freely available for download from, which is also a host for the book, providing further information, links to resources, and FSELIB updates. The presentation is suitable for both self-study and formal course work, and its state-of-the-art review of the field make it equally valuable as a professional reference. With this book as a guide, you immediately will be able to run the codes as given and graphically display solutions to a wide variety of problems in heat transfer and solid, fluid, and structural mechanics.

Implementation of Finite Element Methods for Navier-Stokes Equations

Author: F. Thomasset

Publisher: Springer Science & Business Media

ISBN: 3642870473

Category: Science

Page: 164

View: 1299

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In structure mechanics analysis, finite element methods are now well estab lished and well documented techniques; their advantage lies in a higher flexibility, in particular for: (i) The representation of arbitrary complicated boundaries; (ii) Systematic rules for the developments of stable numerical schemes ap proximating mathematically wellposed problems, with various types of boundary conditions. On the other hand, compared to finite difference methods, this flexibility is paid by: an increased programming complexity; additional storage require ment. The application of finite element methods to fluid mechanics has been lagging behind and is relatively recent for several types of reasons: (i) Historical reasons: the early methods were invented by engineers for the analysis of torsion, flexion deformation of bearns, plates, shells, etc ... (see the historics in Strang and Fix (1972) or Zienckiewicz (1977». (ii) Technical reasons: fluid flow problems present specific difficulties: strong gradients,l of the velocity or temperature for instance, may occur which a finite mesh is unable to properly represent; a remedy lies in the various upwind finite element schemes which recently turned up, and which are reviewed in chapter 2 (yet their effect is just as controversial as in finite differences). Next, waves can propagate (e.g. in ocean dynamics with shallowwaters equations) which will be falsely distorted by a finite non regular mesh, as Kreiss (1979) pointed out. We are concerned in this course with the approximation of incompressible, viscous, Newtonian fluids, i.e. governed by N avier Stokes equations.


Author: Klaus-Jürgen Bathe

Publisher: Springer Verlag

ISBN: 9783540668060

Category: Technology & Engineering

Page: 1253

View: 8155

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Dieses Lehr- und Handbuch behandelt sowohl die elementaren Konzepte als auch die fortgeschrittenen und zukunftsweisenden linearen und nichtlinearen FE-Methoden in Statik, Dynamik, Festkörper- und Fluidmechanik. Es wird sowohl der physikalische als auch der mathematische Hintergrund der Prozeduren ausführlich und verständlich beschrieben. Das Werk enthält eine Vielzahl von ausgearbeiteten Beispielen, Rechnerübungen und Programmlisten. Als Übersetzung eines erfolgreichen amerikanischen Lehrbuchs hat es sich in zwei Auflagen auch bei den deutschsprachigen Ingenieuren etabliert. Die umfangreichen Änderungen gegenüber der Vorauflage innerhalb aller Kapitel - vor allem aber der fortgeschrittenen - spiegeln die rasche Entwicklung innerhalb des letzten Jahrzehnts auf diesem Gebiet wieder.

Advanced Finite Element Methods and Applications

Author: Thomas Apel,Olaf Steinbach

Publisher: Springer Science & Business Media

ISBN: 3642303161

Category: Technology & Engineering

Page: 376

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This volume on some recent aspects of finite element methods and their applications is dedicated to Ulrich Langer and Arnd Meyer on the occasion of their 60th birthdays in 2012. Their work combines the numerical analysis of finite element algorithms, their efficient implementation on state of the art hardware architectures, and the collaboration with engineers and practitioners. In this spirit, this volume contains contributions of former students and collaborators indicating the broad range of their interests in the theory and application of finite element methods. Topics cover the analysis of domain decomposition and multilevel methods, including hp finite elements, hybrid discontinuous Galerkin methods, and the coupling of finite and boundary element methods; the efficient solution of eigenvalue problems related to partial differential equations with applications in electrical engineering and optics; and the solution of direct and inverse field problems in solid mechanics.

Finite Element Method Electromagnetics

Antennas, Microwave Circuits, and Scattering Applications

Author: John L. Volakis,Arindam Chatterjee,Leo C. Kempel

Publisher: John Wiley & Sons

ISBN: 9780780334250

Category: Science

Page: 344

View: 3239

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Employed in a large number of commercial electromagnetic simulation packages, the finite element method is one of the most popular and well-established numerical techniques in engineering. This book covers the theory, development, implementation, and application of the finite element method and its hybrid versions to electromagnetics. FINITE ELEMENT METHOD FOR ELECTROMAGNETICS begins with a step-by-step textbook presentation of the finite method and its variations then goes on to provide up-to-date coverage of three dimensional formulations and modern applications to open and closed domain problems. Worked out examples are included to aid the reader with the fine features of the method and the implementation of its hybridization with other techniques for a robust simulation of large scale radiation and scattering. The crucial treatment of local boundary conditions is carefully worked out in several stages in the book. Sponsored by: IEEE Antennas and Propagation Society.

The mathematics of finite elements and Applications V

Mafelap 1984

Author: J Whiteman

Publisher: Elsevier

ISBN: 0323143717

Category: Mathematics

Page: 668

View: 4674

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The Mathematics of Finite Elements and Applications V is the summary of invited papers and the abstracts of the poster papers in the fifth conference on The Mathematics of Finite Elements and Applications, MAFELAP 1984, held at Brunei University in May 1984. Said symposium discussedfield of finite elements, including its techniques, theory, application, and implementation . The coverage of the book includes a wide range of mathematical topics under finite elements, including its method, calculations, analysis, and applications. The book also encompasses topics of computer-generated geometric design interface; modeling in an integrated computer design; and determination of dimensional field lines. Acidized channels in chalk formations, elastodynamics, stress analysis, and infinite elements are also discussed. The book also looks at isoparametric and hierarchical element procedures and Petrov-Galerkin methods. The text is recommended for mathematicians, engineers, and those in the field of information technology who would like to know more about finite elements and its applications in their respective fields.

Understanding and Implementing the Finite Element Method

Author: Mark S. Gockenbach

Publisher: SIAM

ISBN: 9780898717846

Category: Finite element method

Page: 363

View: 8922

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Understanding and Implementing the Finite Element Method Mark S. Gockenbach "Upon completion of this book a student or researcher would be well prepared to employ finite elements for an application problem or proceed to the cutting edge of research in finite element methods. The accuracy and the thoroughness of the book are excellent." --Anthony Kearsley, research mathematician, National Institute of Standards and Technology The infinite element method is the most powerful general-purpose technique for computing accurate solutions to partial differential equations. Understanding and Implementing the Finite Element Method is essential reading for those interested in understanding both the theory and the implementation of the finite element method for equilibrium problems. This book contains a thorough derivation of the finite element equations as well as sections on programming the necessary calculations, solving the finite element equations, and using a posteriori error estimates to produce validated solutions. Accessible introductions to advanced topics, such as multigrid solvers, the hierarchical basis conjugate gradient method, and adaptive mesh generation, are provided. Each chapter ends with exercises to help readers master these topics.

Fundamentals of Finite Element Analysis

Linear Finite Element Analysis

Author: Ioannis Koutromanos

Publisher: John Wiley & Sons

ISBN: 1119260086

Category: Technology & Engineering

Page: 712

View: 4841

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An introductory textbook covering the fundamentals of linear finite element analysis (FEA) This book constitutes the first volume in a two-volume set that introduces readers to the theoretical foundations and the implementation of the finite element method (FEM). The first volume focuses on the use of the method for linear problems. A general procedure is presented for the finite element analysis (FEA) of a physical problem, where the goal is to specify the values of a field function. First, the strong form of the problem (governing differential equations and boundary conditions) is formulated. Subsequently, a weak form of the governing equations is established. Finally, a finite element approximation is introduced, transforming the weak form into a system of equations where the only unknowns are nodal values of the field function. The procedure is applied to one-dimensional elasticity and heat conduction, multi-dimensional steady-state scalar field problems (heat conduction, chemical diffusion, flow in porous media), multi-dimensional elasticity and structural mechanics (beams/shells), as well as time-dependent (dynamic) scalar field problems, elastodynamics and structural dynamics. Important concepts for finite element computations, such as isoparametric elements for multi-dimensional analysis and Gaussian quadrature for numerical evaluation of integrals, are presented and explained. Practical aspects of FEA and advanced topics, such as reduced integration procedures, mixed finite elements and verification and validation of the FEM are also discussed. Provides detailed derivations of finite element equations for a variety of problems. Incorporates quantitative examples on one-dimensional and multi-dimensional FEA. Provides an overview of multi-dimensional linear elasticity (definition of stress and strain tensors, coordinate transformation rules, stress-strain relation and material symmetry) before presenting the pertinent FEA procedures. Discusses practical and advanced aspects of FEA, such as treatment of constraints, locking, reduced integration, hourglass control, and multi-field (mixed) formulations. Includes chapters on transient (step-by-step) solution schemes for time-dependent scalar field problems and elastodynamics/structural dynamics. Contains a chapter dedicated to verification and validation for the FEM and another chapter dedicated to solution of linear systems of equations and to introductory notions of parallel computing. Includes appendices with a review of matrix algebra and overview of matrix analysis of discrete systems. Accompanied by a website hosting an open-source finite element program for linear elasticity and heat conduction, together with a user tutorial. Fundamentals of Finite Element Analysis: Linear Finite Element Analysis is an ideal text for undergraduate and graduate students in civil, aerospace and mechanical engineering, finite element software vendors, as well as practicing engineers and anybody with an interest in linear finite element analysis.

The Scaled Boundary Finite Element Method

Introduction to Theory and Implementation

Author: Chongmin Song

Publisher: John Wiley & Sons

ISBN: 1119388457

Category: Science

Page: 504

View: 759

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An informative look at the theory, computer implementation, and application of the scaled boundary finite element method This reliable resource, complete with MATLAB, is an easy-to-understand introduction to the fundamental principles of the scaled boundary finite element method. It establishes the theory of the scaled boundary finite element method systematically as a general numerical procedure, providing the reader with a sound knowledge to expand the applications of this method to a broader scope. The book also presents the applications of the scaled boundary finite element to illustrate its salient features and potentials. The Scaled Boundary Finite Element Method: Introduction to Theory and Implementation covers the static and dynamic stress analysis of solids in two and three dimensions. The relevant concepts, theory and modelling issues of the scaled boundary finite element method are discussed and the unique features of the method are highlighted. The applications in computational fracture mechanics are detailed with numerical examples. A unified mesh generation procedure based on quadtree/octree algorithm is described. It also presents examples of fully automatic stress analysis of geometric models in NURBS, STL and digital images. Written in lucid and easy to understand language by the co-inventor of the scaled boundary element method Provides MATLAB as an integral part of the book with the code cross-referenced in the text and the use of the code illustrated by examples Presents new developments in the scaled boundary finite element method with illustrative examples so that readers can appreciate the significant features and potentials of this novel method—especially in emerging technologies such as 3D printing, virtual reality, and digital image-based analysis The Scaled Boundary Finite Element Method: Introduction to Theory and Implementation is an ideal book for researchers, software developers, numerical analysts, and postgraduate students in many fields of engineering and science.

Fundamentals of the Finite Element Method for Heat and Mass Transfer

Author: Perumal Nithiarasu,Roland W. Lewis,Kankanhalli N. Seetharamu

Publisher: John Wiley & Sons

ISBN: 111853543X

Category: Science

Page: 464

View: 3215

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Fundamentals of the Finite Element Method for Heat and Mass Transfer, Second Edition is a comprehensively updated new edition and is a unique book on the application of the finite element method to heat and mass transfer. • Addresses fundamentals, applications and computer implementation • Educational computer codes are freely available to download, modify and use • Includes a large number of worked examples and exercises • Fills the gap between learning and research

Finite Element Method

Author: Gouri Dhatt,Emmanuel Lefrançois,Gilbert Touzot

Publisher: John Wiley & Sons

ISBN: 1118569709

Category: Mathematics

Page: 624

View: 2941

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This book offers an in-depth presentation of the finite element method, aimed at engineers, students and researchers in applied sciences. The description of the method is presented in such a way as to be usable in any domain of application. The level of mathematical expertise required is limited to differential and matrix calculus. The various stages necessary for the implementation of the method are clearly identified, with a chapter given over to each one: approximation, construction of the integral forms, matrix organization, solution of the algebraic systems and architecture of programs. The final chapter lays the foundations for a general program, written in Matlab, which can be used to solve problems that are linear or otherwise, stationary or transient, presented in relation to applications stemming from the domains of structural mechanics, fluid mechanics and heat transfer.

Finite Element Analysis of Antennas and Arrays

Author: Jian-Ming Jin,Douglas J. Riley

Publisher: John Wiley & Sons

ISBN: 9780470409725

Category: Technology & Engineering

Page: 472

View: 6438

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The Most Complete, Up-to-Date Coverage of the Finite Element Analysis and Modeling of Antennas and Arrays Aimed at researchers as well as practical engineers—and packed with over 200 illustrations including twenty-two color plates—Finite Element Analysis of Antennas and Arrays presents: Time- and frequency-domain formulations and mesh truncation techniques Antenna source modeling and parameter calculation Modeling of complex materials and fine geometrical details Analysis and modeling of narrowband and broadband antennas Analysis and modeling of infinite and finite phased-array antennas Analysis and modeling of antenna and platform interactions Recognizing the strengths of other numerical methods, this book goes beyond the finite element method and covers hybrid techniques that combine the finite element method with the finite difference time-domain method, the method of moments, and the high-frequency asymptotic methods to efficiently deal with a variety of complex antenna problems. Complemented with numerous examples, this cutting-edge resource fully demonstrates the power and capabilities of the finite element analysis and its many practical applications.

Finite Element Analysis and Design of Metal Structures

Author: Ehab Ellobody,Ran Feng,Ben Young

Publisher: Elsevier

ISBN: 0124165753

Category: Technology & Engineering

Page: 218

View: 6119

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Traditionally, engineers have used laboratory testing to investigate the behavior of metal structures and systems. These numerical models must be carefully developed, calibrated and validated against the available physical test results. They are commonly complex and very expensive. From concept to assembly, Finite Element Analysis and Design of Metal Structures provides civil and structural engineers with the concepts and procedures needed to build accurate numerical models without using expensive laboratory testing methods. Professionals and researchers will find Finite Element Analysis and Design of Metal Structures a valuable guide to finite elements in terms of its applications. Presents design examples for metal tubular connections Simplified review for general steps of finite element analysis Commonly used linear and nonlinear analyses in finite element modeling Realistic examples of concepts and procedures for Finite Element Analysis and Design

Introduction to Finite Element Analysis Using MATLAB® and Abaqus

Author: Amar Khennane

Publisher: CRC Press

ISBN: 9781466580206

Category: Technology & Engineering

Page: 487

View: 2838

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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® 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. MATLAB is a high-level language specially designed for dealing with matrices, making it particularly suited for programming the finite element method, while Abaqus is a suite of commercial finite element software. Includes more than 100 tables, photographs, and figures Provides MATLAB codes to generate contour plots for sample results Introduction to Finite Element Analysis Using MATLAB and Abaqus introduces and explains theory in each chapter, and provides corresponding examples. It offers introductory notes and provides matrix structural analysis for trusses, beams, and frames. The book examines the theories of stress and strain and the relationships between them. The author then covers weighted residual methods and finite element approximation and numerical integration. He presents the finite element formulation for plane stress/strain problems, introduces axisymmetric problems, and highlights the theory of plates. The text supplies step-by-step procedures for solving problems with Abaqus interactive and keyword editions. The described procedures are implemented as MATLAB codes and Abaqus files can be found on the CRC Press website.