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
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.
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 http://www.morganclaypool.com.
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.
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.
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.
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 (www.wiley.com/go/szabo)
Author: Nam H. Kim,Bhavani V. Sankar,Ashok V. Kumar
Publisher: John Wiley & Sons
Category: Technology & Engineering
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.
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.
An Introduction to the FEM and Adaptive Error Analysis for Engineering Students
Author: J. E. Akin
Category: Technology & Engineering
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
An Introduction to the Method and Error Estimation
Author: Ivo Babuska,John Whiteman,Theofanis Strouboulis
Publisher: Oxford University Press
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.
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.
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
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.
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.
This updated, revised and extended edition gives a comprehensive introduction to the understanding and use of the finite element method as applied to structures. The text methodically covers all the important bridges in understanding up to and including the introduction of isoparametric elements.
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