Introduction to the Finite Element Method 4E

Author: J. N. Reddy
Publisher: McGraw-Hill Education
ISBN: 9781259861901
Category: Technology & Engineering
Page: 816
View: 8414

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An up-to-date, self-contained introduction to the theory and applications of the finite element method This thoroughly revised classic engineering textbook offers a broad-based overview of the finite element method. Written by a world-renowned mechanical engineering researcher and author, the book shows, step-by-step, how to calculate numerical solutions to steady-state as well as time-dependent problems. You also get detailed problems with worked-out solutions and downloadable programs that can be used and modified for real-world situations. Special attention is paid to applications that are important in bioengineering, fluid and thermal sciences, structural mechanics, and a host of applied sciences. Introduction to the Finite Element Method, Fourth Edition, covers:•Mathematical preliminaries and classical variational methods•1-D finite element models of second-order differential equations•Applications to 1-D heat transfer and fluid and solid mechanics problems•Finite element analysis of beams and circular plates•Plane trusses and frames•Eigenvalue and time-dependent problems in 1-D•Numerical integration and computer implementation in 1-D•Single-variable problems in two dimensions•2-D interpolation functions, numerical integration, and computer implementation in 2-D•Flows of viscous incompressible fluids•Plane elasticity•3-D finite element analysis

An Introduction to the Finite Element Method

Author: Junuthula Narasimha Reddy
Publisher: N.A
ISBN: 9780071244732
Category: Finite element method
Page: 766
View: 2299

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The book retains its strong conceptual approach, clearly examining the mathematical underpinnings of FEM, and providing a general approach of engineering application areas.Known for its detailed, carefully selected example problems and extensive selection of homework problems, the author has comprehensively covered a wide range of engineering areas making the book approriate for all engineering majors, and underscores the wide range of use FEM has in the professional world

An Introduction to the Finite Element Method

Author: J. N. Reddy
Publisher: McGraw-Hill Medical Publishing
ISBN: 9780071267618
Category: Finite element method
Page: 766
View: 1865

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J.N. Reddy's, An Introduction to the Finite Element Method, third edition is an update of one of the most popular FEM textbooks available. The book retains its strong conceptual approach, clearly examining the mathematical underpinnings of FEM, and providing a general approach of engineering application areas. Known for its detailed, carefully selected example problems and extensive selection of homework problems, the author has comprehensively covered a wide range of engineering areas making the book approriate for all engineering majors, and underscores the wide range of use FEM has in the professional world. A supplementary text Web site located at contains password-protected solutions to end-of-chapter problems, general textbook information, supplementary chapters on the FEM1D and FEM2D computer programs, and more!

Introduction to the Finite Element Method in Electromagnetics

Author: Anastasis C. Polycarpou
Publisher: Morgan & Claypool Publishers
ISBN: 1598290460
Category: Technology & Engineering
Page: 115
View: 7430

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This lecture is written primarily for the non-expert engineer or the undergraduate or graduate student who wants to learn, for the first time, the finite element method with applications to electromagnetics. It is also designed for research engineers who have knowledge of other numerical techniques and want to familiarize themselves with the finite element method.Finite element method is a numerical method used to solve boundary-value problems characterized by a partial differential equation and a set of boundary conditions. Author Anastasis Polycarpou provides the reader with all information necessary to successfully apply the finite element method to one- and two-dimensional boundary-value problems in electromagnetics.The book is accompanied by a number of codes written by the author in Matlab. These are the finite element codes that were used to generate most of the graphs presented in this book. Specifically, there are three Matlab codes for the one-dimensional case (Chapter 1) and two Matlab codes for the two-dimensional case (Chapter 2). The reader may execute these codes, modify certain parameters such as mesh size or object dimensions, and visualize the results. The codes are available on the Morgan & Claypool Web site at

Introduction to the finite element method

Author: Niels Saabye Ottosen,Hans Petersson
Publisher: N.A
Category: Mathematics
Page: 410
View: 3347

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Providing a systematic approach and simple introduction ot the finite element method, this self-contained book will enable the reader to obtain a clear understanding of the concepts involved in this traditionally complicated methodology.

A Pragmatic Introduction to the Finite Element Method for Thermal and Stress Analysis

With the Matlab Toolkit SOFEA
Author: Petr Krysl
Publisher: World Scientific Publishing Company
ISBN: 9813101814
Category: Science
Page: 292
View: 5122

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This textbook provides an accessible and self-contained description of the Galerkin finite element method for the two important models of continuum mechanics, transient heat conduction and elastodynamics, from formulation of the governing equations to implementation in Matlab. The coverage follows an intuitive approach: the salient features of each initial boundary value problem are reviewed, including a thorough description of the boundary conditions; the method of weighted residuals is applied to derive the discrete equations; and clear examples are introduced to illustrate the method.

Finite Element Analysis with Error Estimators

An Introduction to the FEM and Adaptive Error Analysis for Engineering Students
Author: J. E. Akin
Publisher: Elsevier
ISBN: 9780080472751
Category: Technology & Engineering
Page: 512
View: 2290

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This key text is written for senior undergraduate and graduate engineering students. It delivers a complete introduction to finite element methods and to automatic adaptation (error estimation) that will enable students to understand and use FEA as a true engineering tool. It has been specifically developed to be accessible to non-mathematics students and provides the only complete text for FEA with error estimators for non-mathematicians. Error estimation is taught on nearly half of all FEM courses for engineers at senior undergraduate and postgraduate level; no other existing textbook for this market covers this topic. The only introductory FEA text with error estimation for students of engineering, scientific computing and applied mathematics Includes source code for creating and proving FEA error estimators

Introduction to the Explicit Finite Element Method for Nonlinear Transient Dynamics

Author: Shen R. Wu,Lei Gu
Publisher: John Wiley & Sons
ISBN: 1118382072
Category: Mathematics
Page: 352
View: 6762

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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 Finite Element 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 mastering the explicit finite element method and programming code without requiring extensive background knowledge of the general finite element. The authors present topics relating to the variational principle, numerical procedure, mechanical formulation, and fundamental achievements of the convergence theory. In addition, key topics and techniques are provided in four clearly organized sections: • Fundamentals explores a framework of the explicit finite element method for nonlinear transient dynamics and highlights achievements related to the convergence theory • Element Technology discusses four-node, three-node, eight-node, and two-node element theories • Material Models outlines models of plasticity and other nonlinear materials as well as the mechanics model of ductile damage • Contact and Constraint Conditions covers subjects related to three-dimensional surface contact, with examples solved analytically, as well as discussions on kinematic constraint conditions Throughout the book, vivid figures illustrate the ideas and key features of the explicit finite element method. Examples clearly present results, featuring both theoretical assessments and industrial applications. Introduction to the Explicit Finite Element Method for Nonlinear Transient Dynamics is an ideal book for both engineers who require more theoretical discussions and for theoreticians searching for interesting and challenging research topics. The book also serves as an excellent resource for courses on applied mathematics, applied mechanics, and numerical methods at the graduate level.

An introduction to the finite element method

theory, programming, applications
Author: Erik G. Thompson
Publisher: Wiley
ISBN: 9780471267539
Category: Computers
Page: 343
View: 7328

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Written for students with any engineering or applied science background, Erik Thompson\'s new text presents the theory, applications, and programming skills needed to understand the finite element method and use it to solve problems in engineering analysis and design. Offering concise, highly practical coverage, this introductory text provides complete finite element codes that can be run on the student version of MATLAB or easily converted to other languages. This text gives students the opportunity to:Master the basic theory: The text promotes an understanding and appreciation of the theoretical basis of finite element approximations by building on concepts that are intuitive to the students. Throughout, the text uses matrix notation to help students visualize the finite element matrices. Study problems reinforce basic theory.Experiment with the code: Numerical experiments show how to test programs for possible errors, experiment with boundary conditions, and study accuracy and stability. Code development exercises suggest ways to modify the codes to create additional capabilities. All codes are available on the book\'s web page along with sample data files for testing them. Each code can be run immediately using only the student version of MATLAB. Because each code is written using explicit programming, they also serve as pseudo-codes that can be used to develop programs in any computer language.Gain hands-on experience: Projects, representing a wide variety of engineering disciplines, enable students to conduct analyses of fairly complex problems. Many of these projects encourage investigations of new techniques for using the finite element method.

Finite Elements

An Introduction to the Method and Error Estimation
Author: Ivo Babuska,John Whiteman,Theofanis Strouboulis
Publisher: Oxford University Press
ISBN: 0198506694
Category: Mathematics
Page: 323
View: 432

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Computational modelling is the process of representing some activity, for example a physical happening, first by a mathematical model and then of solving the model using a numerical technique such as the finite element method. Both parts of this process involve approximations. As a result error estimation has to be employed to assess the reliability of the computational modelling process. This book addresses the verification of the numerical methods, in thiscase finite elements methods, involved in the process, by analysing the finite element errors. The unique feature of the book is that it brings together both theoretical error analysis and the computed solutions, highlighting their interplay.

An Introduction to the Mathematical Theory of Finite Elements

Author: J. T. Oden,J. N. Reddy
Publisher: Courier Corporation
ISBN: 0486142213
Category: Technology & Engineering
Page: 448
View: 334

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This introduction to the theory of Sobolev spaces and Hilbert space methods in partial differential equations is geared toward readers of modest mathematical backgrounds. It offers coherent, accessible demonstrations of the use of these techniques in developing the foundations of the theory of finite element approximations. J. T. Oden is Director of the Institute for Computational Engineering & Sciences (ICES) at the University of Texas at Austin, and J. N. Reddy is a Professor of Engineering at Texas A&M University. They developed this essentially self-contained text from their seminars and courses for students with diverse educational backgrounds. Their effective presentation begins with introductory accounts of the theory of distributions, Sobolev spaces, intermediate spaces and duality, the theory of elliptic equations, and variational boundary value problems. The second half of the text explores the theory of finite element interpolation, finite element methods for elliptic equations, and finite element methods for initial boundary value problems. Detailed proofs of the major theorems appear throughout the text, in addition to numerous examples.

Numerical Methods in Subsurface Hydrology

With an Introduction to the Finite Element Method
Author: Irwin Remson,George Milton Hornberger,Fred John Molz
Publisher: John Wiley & Sons
Category: Science
Page: 389
View: 5377

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One-Dimensional Finite Elements

An Introduction to the FE Method
Author: Andreas Öchsner,Markus Merkel
Publisher: Springer
ISBN: 331975145X
Category: Science
Page: 418
View: 7980

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This textbook presents finite element methods using exclusively one-dimensional elements. It presents the complex methodology in an easily understandable but mathematically correct fashion. The approach of one-dimensional elements enables the reader to focus on the understanding of the principles of basic and advanced mechanical problems. The reader will easily understand the assumptions and limitations of mechanical modeling as well as the underlying physics without struggling with complex mathematics. Although the description is easy, it remains scientifically correct. The approach using only one-dimensional elements covers not only standard problems but allows also for advanced topics such as plasticity or the mechanics of composite materials. Many examples illustrate the concepts and problems at the end of every chapter help to familiarize with the topics. Each chapter also includes a few exercise problems, with short answers provided at the end of the book. The second edition appears with a complete revision of all figures. It also presents a complete new chapter special elements and added the thermal conduction into the analysis of rod elements. The principle of virtual work has also been introduced for the derivation of the finite-element principal equation.

Introduction to Finite Element Analysis

Formulation, Verification and Validation
Author: Barna Szab?,Ivo Babu?ka
Publisher: John Wiley & Sons
ISBN: 1119993482
Category: Technology & Engineering
Page: 372
View: 1188

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When using numerical simulation to make a decision, how can its reliability be determined? What are the common pitfalls and mistakes when assessing the trustworthiness of computed information, and how can they be avoided? Whenever numerical simulation is employed in connection with engineering decision-making, there is an implied expectation of reliability: one cannot base decisions on computed information without believing that information is reliable enough to support those decisions. Using mathematical models to show the reliability of computer-generated information is an essential part of any modelling effort. Giving users of finite element analysis (FEA) software an introduction to verification and validation procedures, this book thoroughly covers the fundamentals of assuring reliability in numerical simulation. The renowned authors systematically guide readers through the basic theory and algorithmic structure of the finite element method, using helpful examples and exercises throughout. Delivers the tools needed to have a working knowledge of the finite element method Illustrates the concepts and procedures of verification and validation Explains the process of conceptualization supported by virtual experimentation Describes the convergence characteristics of the h-, p- and hp-methods Covers the hierarchic view of mathematical models and finite element spaces Uses examples and exercises which illustrate the techniques and procedures of quality assurance Ideal for mechanical and structural engineering students, practicing engineers and applied mathematicians Includes parameter-controlled examples of solved problems in a companion website (

Introduction to Finite Element Analysis Using MATLAB® and Abaqus

Author: Amar Khennane
Publisher: CRC Press
ISBN: 1466580216
Category: Technology & Engineering
Page: 487
View: 8141

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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.

A Simple Introduction to the Mixed Finite Element Method

Theory and Applications
Author: Gabriel N. Gatica
Publisher: Springer Science & Business Media
ISBN: 3319036955
Category: Mathematics
Page: 132
View: 2423

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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.

The Finite Element Method in Engineering

Author: Singiresu S. Rao
Publisher: Butterworth-Heinemann
ISBN: 0128143649
Category: Technology & Engineering
Page: 782
View: 2726

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The Finite Element Method in Engineering, Sixth Edition, provides a thorough grounding in the mathematical principles behind the Finite Element Analysis technique—an analytical engineering tool originated in the 1960's by the aerospace and nuclear power industries to find usable, approximate solutions to problems with many complex variables. Rao shows how to set up finite element solutions in civil, mechanical and aerospace engineering applications. The new edition features updated real-world examples from MATLAB, Ansys and Abaqus, and a new chapter on additional FEM topics including extended FEM (X-FEM). Professional engineers will benefit from the introduction to the many useful applications of finite element analysis. Includes revised and updated chapters on MATLAB, Ansys and Abaqus Offers a new chapter, Additional Topics in Finite Element Method Includes discussion of practical considerations, errors and pitfalls in FEM singularity elements Features a brief presentation of recent developments in FEM including extended FEM (X-FEM), augmented FEM (A-FEM) and partition of unity FEM (POUFEM) Features improved pedagogy, including the addition of more design-oriented and practical examples and problems Covers real-life applications, sample review questions at the end of most chapters, and updated references

Introduction to Finite Element Analysis and Design

Author: Nam H. Kim,Bhavani V. Sankar,Ashok V. Kumar
Publisher: John Wiley & Sons
ISBN: 1119078733
Category: Technology & Engineering
Page: 552
View: 3082

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Introduces the basic concepts of FEM in an easy-to-use format so that students and professionals can use the method efficiently and interpret results properly Finite element method (FEM) is a powerful tool for solving engineering problems both in solid structural mechanics and fluid mechanics. This book presents all of the theoretical aspects of FEM that students of engineering will need. It eliminates overlong math equations in favour of basic concepts, and reviews of the mathematics and mechanics of materials in order to illustrate the concepts of FEM. It introduces these concepts by including examples using six different commercial programs online. The all-new, second edition of Introduction to Finite Element Analysis and Design provides many more exercise problems than the first edition. It includes a significant amount of material in modelling issues by using several practical examples from engineering applications. The book features new coverage of buckling of beams and frames and extends heat transfer analyses from 1D (in the previous edition) to 2D. It also covers 3D solid element and its application, as well as 2D. Additionally, readers will find an increase in coverage of finite element analysis of dynamic problems. There is also a companion website with examples that are concurrent with the most recent version of the commercial programs. Offers elaborate explanations of basic finite element procedures Delivers clear explanations of the capabilities and limitations of finite element analysis Includes application examples and tutorials for commercial finite element software, such as MATLAB, ANSYS, ABAQUS and NASTRAN Provides numerous examples and exercise problems Comes with a complete solution manual and results of several engineering design projects Introduction to Finite Element Analysis and Design, 2nd Edition is an excellent text for junior and senior level undergraduate students and beginning graduate students in mechanical, civil, aerospace, biomedical engineering, industrial engineering and engineering mechanics.

Introduction to Nonlinear Finite Element Analysis

Author: Nam-Ho Kim
Publisher: Springer Science & Business Media
ISBN: 1441917462
Category: Technology & Engineering
Page: 430
View: 3362

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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. Please visit the author's website for supplemental material, including PowerPoint presentations and MATLAB codes, at

Basic Finite Element Method as Applied to Injury Biomechanics

Author: King-Hay Yang
Publisher: Academic Press
ISBN: 0128098325
Category: Technology & Engineering
Page: 748
View: 2522

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Basic Finite Element Method as Applied to Injury Biomechanics provides a unique introduction to finite element methods. Unlike other books on the topic, this comprehensive reference teaches readers to develop a finite element model from the beginning, including all the appropriate theories that are needed throughout the model development process. In addition, the book focuses on how to apply material properties and loading conditions to the model, how to arrange the information in the order of head, neck, upper torso and upper extremity, lower torso and pelvis and lower extremity. The book covers scaling from one body size to the other, parametric modeling and joint positioning, and is an ideal text for teaching, further reading and for its unique application to injury biomechanics. With over 25 years of experience of developing finite element models, the author's experience with tissue level injury threshold instead of external loading conditions provides a guide to the "do’s and dont's" of using finite element method to study injury biomechanics. Covers the fundamentals and applications of the finite element method in injury biomechanics Teaches readers model development through a hands-on approach that is ideal for students and researchers Includes different modeling schemes used to model different parts of the body, including related constitutive laws and associated material properties