An Introduction to the Finite Element Method for Differential Equations

An Introduction to the Finite Element Method for Differential Equations
Author: Mohammad Asadzadeh
Publsiher: John Wiley & Sons
Total Pages: 352
Release: 2020-08-18
ISBN: 1119671671
Category: Mathematics
Language: EN, FR, DE, ES & NL

An Introduction to the Finite Element Method for Differential Equations Book Excerpt:

Master the finite element method with this masterful and practical volume An Introduction to the Finite Element Method (FEM) for Differential Equations provides readers with a practical and approachable examination of the use of the finite element method in mathematics. Author Mohammad Asadzadeh covers basic FEM theory, both in one-dimensional and higher dimensional cases. The book is filled with concrete strategies and useful methods to simplify its complex mathematical contents. Practically written and carefully detailed, An Introduction to the Finite Element Method covers topics including: An introduction to basic ordinary and partial differential equations The concept of fundamental solutions using Green's function approaches Polynomial approximations and interpolations, quadrature rules, and iterative numerical methods to solve linear systems of equations Higher-dimensional interpolation procedures Stability and convergence analysis of FEM for differential equations This book is ideal for upper-level undergraduate and graduate students in natural science and engineering. It belongs on the shelf of anyone seeking to improve their understanding of differential equations.

The Finite Element Method in Engineering

The Finite Element Method in Engineering
Author: S. S. Rao
Publsiher: Butterworth-Heinemann
Total Pages: 663
Release: 2005
ISBN: 0750678283
Category: Science
Language: EN, FR, DE, ES & NL

The Finite Element Method in Engineering Book Excerpt:

With the revolution in readily available computing power, the finite element method has become one of the most important tools for the modern engineer. This book offers a comprehensive introduction to the principles involved.

The Finite Element Method Theory Implementation and Applications

The Finite Element Method  Theory  Implementation  and Applications
Author: Mats G. Larson,Fredrik Bengzon
Publsiher: Springer Science & Business Media
Total Pages: 395
Release: 2013-01-13
ISBN: 3642332870
Category: Computers
Language: EN, FR, DE, ES & NL

The Finite Element Method Theory Implementation and Applications Book Excerpt:

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.​

An Introduction to Linear and Nonlinear Finite Element Analysis

An Introduction to Linear and Nonlinear Finite Element Analysis
Author: Prem Kythe,Dongming Wei
Publsiher: Springer Science & Business Media
Total Pages: 445
Release: 2011-06-27
ISBN: 0817681604
Category: Mathematics
Language: EN, FR, DE, ES & NL

An Introduction to Linear and Nonlinear Finite Element Analysis Book Excerpt:

Modern finite element analysis has grown into a basic mathematical tool for almost every field of engineering and the applied sciences. This introductory textbook fills a gap in the literature, offering a concise, integrated presentation of methods, applications, software tools, and hands-on projects. Included are numerous exercises, problems, and Mathematica/Matlab-based programming projects. The emphasis is on interdisciplinary applications to serve a broad audience of advanced undergraduate/graduate students with different backgrounds in applied mathematics, engineering, physics/geophysics. The work may also serve as a self-study reference for researchers and practitioners seeking a quick introduction to the subject for their research.

Practical Guide to Finite Elements

Practical Guide to Finite Elements
Author: Steven Lepi
Publsiher: CRC Press
Total Pages: 544
Release: 1998-03-03
ISBN: 9780824700751
Category: Science
Language: EN, FR, DE, ES & NL

Practical Guide to Finite Elements Book Excerpt:

Assuming only basic knowledge of mathematics and engineering mechanics, this lucid reference introduces the fundamentals of finite element theory using easy-to-understand terms and simple problems-systematically grounding the practitioner in the basic principles then suggesting applications to more general cases. Furnishes a wealth of practical insights drawn from the extensive experience of a specialist in the field! Generously illustrated with over 200 detailed drawings to clarify discussions and containing key literature citations for more in-depth study of particular topics, this clearly written resource is an exceptional guide for mechanical, civil, aeronautic, automotive, electrical and electronics, and design engineers; engineering managers; and upper-level undergraduate, graduate, and continuing-education students in these disciplines.

Introduction to Finite Element Analysis Using MATLAB and Abaqus

Introduction to Finite Element Analysis Using MATLAB   and Abaqus
Author: Amar Khennane
Publsiher: CRC Press
Total Pages: 487
Release: 2013-06-10
ISBN: 1466580208
Category: Technology & Engineering
Language: EN, FR, DE, ES & NL

Introduction to Finite Element Analysis Using MATLAB and Abaqus Book Excerpt:

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.

Theory of Semiconductor Quantum Devices

Theory of Semiconductor Quantum Devices
Author: Fausto Rossi
Publsiher: Springer Science & Business Media
Total Pages: 382
Release: 2011-01-13
ISBN: 3642105564
Category: Technology & Engineering
Language: EN, FR, DE, ES & NL

Theory of Semiconductor Quantum Devices Book Excerpt:

Primary goal of this book is to provide a cohesive description of the vast field of semiconductor quantum devices, with special emphasis on basic quantum-mechanical phenomena governing the electro-optical response of new-generation nanomaterials. The book will cover within a common language different types of optoelectronic nanodevices, including quantum-cascade laser sources and detectors, few-electron/exciton quantum devices, and semiconductor-based quantum logic gates. The distinguishing feature of the present volume is a unified microscopic treatment of quantum-transport and coherent-optics phenomena on ultrasmall space- and time-scales, as well as of their semiclassical counterparts.

Introduction to Finite Element Analysis

Introduction to Finite Element Analysis
Author: Barna Szabó,Ivo Babuška
Publsiher: John Wiley & Sons
Total Pages: 372
Release: 2011-03-21
ISBN: 1119993482
Category: Technology & Engineering
Language: EN, FR, DE, ES & NL

Introduction to Finite Element Analysis Book Excerpt:

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)

Finite Element Analysis

Finite Element Analysis
Author: M Moatamedi,Hassan A. Khawaja
Publsiher: CRC Press
Total Pages: 154
Release: 2018-07-20
ISBN: 0429841604
Category: Mathematics
Language: EN, FR, DE, ES & NL

Finite Element Analysis Book Excerpt:

Finite element analysis has become the most popular technique for studying engineering structures in detail. It is particularly useful whenever the complexity of the geometry or of the loading is such that alternative methods are inappropriate. The finite element method is based on the premise that a complex structure can be broken down into finitely many smaller pieces (elements), the behaviour of each of which is known or can be postulated. These elements might then be assembled in some sense to model the behaviour of the structure. Intuitively this premise seems reasonable, but there are many important questions that need to be answered. In order to answer them it is necessary to apply a degree of mathematical rigour to the development of finite element techniques. The approach that will be taken in this book is to develop the fundamental ideas and methodologies based on an intuitive engineering approach, and then to support them with appropriate mathematical proofs where necessary. It will rapidly become clear that the finite element method is an extremely powerful tool for the analysis of structures (and for other field problems), but that the volume of calculations required to solve all but the most trivial of them is such that the assistance of a computer is necessary. As stated above, many questions arise concerning finite element analysis. Some of these questions are associated with the fundamental mathematical formulations, some with numerical solution techniques, and others with the practical application of the method. In order to answer these questions, the engineer/analyst needs to understand both the nature and limitations of the finite element approximation and the fundamental behaviour of the structure. Misapplication of finite element analysis programs is most likely to arise when the analyst is ignorant of engineering phenomena.

Introduction to the Finite Element Method using BASIC Programs

Introduction to the Finite Element Method using BASIC Programs
Author: D.K. Brown
Publsiher: CRC Press
Total Pages: 288
Release: 1990-09-01
ISBN: 9780903384629
Category: Architecture
Language: EN, FR, DE, ES & NL

Introduction to the Finite Element Method using BASIC Programs Book Excerpt:

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.

Inside Finite Elements

Inside Finite Elements
Author: Martin Weiser
Publsiher: Walter de Gruyter GmbH & Co KG
Total Pages: 157
Release: 2016-05-10
ISBN: 3110373203
Category: Mathematics
Language: EN, FR, DE, ES & NL

Inside Finite Elements Book Excerpt:

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 only as far as it gives insight into the construction of algorithms. In the exercises, a complete FE-solver for stationary 2D problems is implemented in Matlab/Octave. Contents: Finite Element Fundamentals Grids and Finite Elements Assembly Solvers Error Estimation Mesh Refinement Multigrid Elastomechanics Fluid Mechanics Grid Data Structure Function Reference

An Introduction to Nonlinear Finite Element Analysis

An Introduction to Nonlinear Finite Element Analysis
Author: J. N. Reddy
Publsiher: OUP Oxford
Total Pages: 482
Release: 2004-03-25
ISBN: 9780198525295
Category: Science
Language: EN, FR, DE, ES & NL

An Introduction to Nonlinear Finite Element Analysis Book Excerpt:

This book presents the theory and computer implementation of the finite element method as applied to nonlinear problems of heat transfer and similar field problems, fluid mechanics (flows of incompressible fluids), and solid mechanics (elasticity, beams and plates). Both geometric as well as material nonlinearities are considered, and static and transient (i.e. time-dependent) responses are studied. Although there exist a number of books on nonlinear finite elements that serve asgood references for engineers who are familiar with the subject and wish to learn advanced topics or the latest developments, there is currently no book which is suitable as a textbook for a first course on nonlinear finite element analysis. This book fills the void in the market, providing a clearunderstanding of the concepts of nonlinear finite element analyses through detailed theoretical formulations and computer implementation steps, examples and exercises. In addition, the book serves as a prelude to more advanced books on the subject.

Finite Element Analysis

Finite Element Analysis
Author: Barna Szabó,Ivo Babuška
Publsiher: John Wiley & Sons
Total Pages: 384
Release: 2021-05-20
ISBN: 1119426464
Category: Technology & Engineering
Language: EN, FR, DE, ES & NL

Finite Element Analysis Book Excerpt:

Finite Element Analysis An updated and comprehensive review of the theoretical foundation of the finite element method The revised and updated second edition of Finite Element Analysis: Method, Verification, and Validation offers a comprehensive review of the theoretical foundations of the finite element method and highlights the fundamentals of solution verification, validation, and uncertainty quantification. Written by noted experts on the topic, the book covers the theoretical fundamentals as well as the algorithmic structure of the finite element method. The text contains numerous examples and helpful exercises that clearly illustrate the techniques and procedures needed for accurate estimation of the quantities of interest. In addition, the authors describe the technical requirements for the formulation and application of design rules. Designed as an accessible resource, the book has a companion website that contains a solutions manual, PowerPoint slides for instructors, and a link to finite element software. This important text: Offers a comprehensive review of the theoretical foundations of the finite element method Puts the focus on the fundamentals of solution verification, validation, and uncertainty quantification Presents the techniques and procedures of quality assurance in numerical solutions of mathematical problems Contains numerous examples and exercises Written for students in mechanical and civil engineering, analysts seeking professional certification, and applied mathematicians, Finite Element Analysis: Method, Verification, and Validation, Second Edition includes the tools, concepts, techniques, and procedures that help with an understanding of finite element analysis.

Nonlinear Finite Elements for Continua and Structures

Nonlinear Finite Elements for Continua and Structures
Author: Ted Belytschko,Wing Kam Liu,Brian Moran,Khalil Elkhodary
Publsiher: John Wiley & Sons
Total Pages: 830
Release: 2014-01-07
ISBN: 1118632702
Category: Science
Language: EN, FR, DE, ES & NL

Nonlinear Finite Elements for Continua and Structures Book Excerpt:

This updated and expanded edition of the bestselling textbook provides a comprehensive introduction to the methods and theory of nonlinear finite element analysis. New material provides a concise introduction to some of the cutting-edge methods that have evolved in recent years in the field of nonlinear finite element modeling, and includes the eXtended finite element method (XFEM), multiresolution continuum theory for multiscale microstructures, and dislocation-density-based crystalline plasticity. Nonlinear Finite Elements for Continua and Structures, Second Edition focuses on the formulation and solution of discrete equations for various classes of problems that are of principal interest in applications to solid and structural mechanics. Topics covered include the discretization by finite elements of continua in one dimension and in multi-dimensions; the formulation of constitutive equations for nonlinear materials and large deformations; procedures for the solution of the discrete equations, including considerations of both numerical and multiscale physical instabilities; and the treatment of structural and contact-impact problems. Key features: Presents a detailed and rigorous treatment of nonlinear solid mechanics and how it can be implemented in finite element analysis Covers many of the material laws used in today's software and research Introduces advanced topics in nonlinear finite element modelling of continua Introduction of multiresolution continuum theory and XFEM Accompanied by a website hosting a solution manual and MATLAB® and FORTRAN code Nonlinear Finite Elements for Continua and Structures, Second Edition is a must have textbook for graduate students in mechanical engineering, civil engineering, applied mathematics, engineering mechanics, and materials science, and is also an excellent source of information for researchers and practitioners in industry.

Mechanical Analysis of PEM Fuel Cell Stack Design

Mechanical Analysis of PEM Fuel Cell Stack Design
Author: Ahmet Evren Firat
Publsiher: Cuvillier Verlag
Total Pages: 130
Release: 2016-06-02
ISBN: 3736992572
Category: Electronic Book
Language: EN, FR, DE, ES & NL

Mechanical Analysis of PEM Fuel Cell Stack Design Book Excerpt:

Polymer electrolyte membrane (PEM) fuel cell stack was analyzed from a mechanical point of view with the help of measurements and simulations in this study. The deflection of the fuel cell stack was measured with the help of the experimental set-up under operating conditions. The effects of cell operating parameters and cyclic conditions on the mechanical properties of the fuel cell stack were investigated. In order to extend the mechanical analysis of the fuel cells, two computational models were established containing the geometrical features in detail. A large-scale fuel cell stack model was built for the thermomechanical analysis. The second model was built on a cross-section geometry for the electrochemical analysis including fluid dynamics. The internal stress distribution and buckling of fuel cell stack were examined. The influence of the mechanical compression on the cell performance and squeezing of the gas diffusion layers are investigated. A design procedure is developed for fuel cell stack regarding the durability and performance from a mechanical point of view.

The Finite Element Method

The Finite Element Method
Author: Darrell W. Pepper,Juan C. Heinrich
Publsiher: CRC Press
Total Pages: 610
Release: 2017-04-11
ISBN: 1315395088
Category: Business & Economics
Language: EN, FR, DE, ES & NL

The Finite Element Method Book Excerpt:

This self-explanatory guide introduces the basic fundamentals of the Finite Element Method in a clear manner using comprehensive examples. Beginning with the concept of one-dimensional heat transfer, the first chapters include one-dimensional problems that can be solved by inspection. The book progresses through more detailed two-dimensional elements to three-dimensional elements, including discussions on various applications, and ending with introductory chapters on the boundary element and meshless methods, where more input data must be provided to solve problems. Emphasis is placed on the development of the discrete set of algebraic equations. The example problems and exercises in each chapter explain the procedure for defining and organizing the required initial and boundary condition data for a specific problem, and computer code listings in MATLAB and MAPLE are included for setting up the examples within the text, including COMSOL files. Widely used as an introductory Finite Element Method text since 1992 and used in past ASME short courses and AIAA home study courses, this text is intended for undergraduate and graduate students taking Finite Element Methodology courses, engineers working in the industry that need to become familiar with the FEM, and engineers working in the field of heat transfer. It can also be used for distance education courses that can be conducted on the web. Highlights of the new edition include: - Inclusion of MATLAB, MAPLE code listings, along with several COMSOL files, for the example problems within the text. Power point presentations per chapter and a solution manual are also available from the web. - Additional introductory chapters on the boundary element method and the meshless method. - Revised and updated content. -Simple and easy to follow guidelines for understanding and applying the Finite Element Method.

Finite Element Method for Eigenvalue Problems in Electromagnetics

Finite Element Method for Eigenvalue Problems in Electromagnetics
Author: C. J. Reddy
Publsiher: Unknown
Total Pages: 37
Release: 1994
ISBN: 1928374650XXX
Category: Computer programs
Language: EN, FR, DE, ES & NL

Finite Element Method for Eigenvalue Problems in Electromagnetics Book Excerpt:

Introduction to Approximate Solution Techniques Numerical Modeling and Finite Element Methods

Introduction to Approximate Solution Techniques  Numerical Modeling  and Finite Element Methods
Author: Victor N. Kaliakin
Publsiher: CRC Press
Total Pages: 664
Release: 2018-04-19
ISBN: 1482271125
Category: Technology & Engineering
Language: EN, FR, DE, ES & NL

Introduction to Approximate Solution Techniques Numerical Modeling and Finite Element Methods Book Excerpt:

Functions as a self-study guide for engineers and as a textbook for nonengineering students and engineering students, emphasizing generic forms of differential equations, applying approximate solution techniques to examples, and progressing to specific physical problems in modular, self-contained chapters that integrate into the text or can stand alone! This reference/text focuses on classical approximate solution techniques such as the finite difference method, the method of weighted residuals, and variation methods, culminating in an introduction to the finite element method (FEM). Discusses the general notion of approximate solutions and associated errors! With 1500 equations and more than 750 references, drawings, and tables, Introduction to Approximate Solution Techniques, Numerical Modeling, and Finite Element Methods: Describes the approximate solution of ordinary and partial differential equations using the finite difference method Covers the method of weighted residuals, including specific weighting and trial functions Considers variational methods Highlights all aspects associated with the formulation of finite element equations Outlines meshing of the solution domain, nodal specifications, solution of global equations, solution refinement, and assessment of results Containing appendices that present concise overviews of topics and serve as rudimentary tutorials for professionals and students without a background in computational mechanics, Introduction to Approximate Solution Techniques, Numerical Modeling, and Finite Element Methods is a blue-chip reference for civil, mechanical, structural, aerospace, and industrial engineers, and a practical text for upper-level undergraduate and graduate students studying approximate solution techniques and the FEM.

Advanced Finite Element Methods with Applications

Advanced Finite Element Methods with Applications
Author: Thomas Apel,Ulrich Langer,Arnd Meyer,Olaf Steinbach
Publsiher: Springer
Total Pages: 428
Release: 2019-06-28
ISBN: 3030142442
Category: Mathematics
Language: EN, FR, DE, ES & NL

Advanced Finite Element Methods with Applications Book Excerpt:

Finite element methods are the most popular methods for solving partial differential equations numerically, and despite having a history of more than 50 years, there is still active research on their analysis, application and extension. This book features overview papers and original research articles from participants of the 30th Chemnitz Finite Element Symposium, which itself has a 40-year history. Covering topics including numerical methods for equations with fractional partial derivatives; isogeometric analysis and other novel discretization methods, like space-time finite elements and boundary elements; analysis of a posteriori error estimates and adaptive methods; enhancement of efficient solvers of the resulting systems of equations, discretization methods for partial differential equations on surfaces; and methods adapted to applications in solid and fluid mechanics, it offers readers insights into the latest results.

Geometrically Unfitted Finite Element Methods and Applications

Geometrically Unfitted Finite Element Methods and Applications
Author: Stéphane P. A. Bordas,Erik Burman,Mats G. Larson,Maxim A. Olshanskii
Publsiher: Springer
Total Pages: 361
Release: 2018-03-13
ISBN: 3319714317
Category: Mathematics
Language: EN, FR, DE, ES & NL

Geometrically Unfitted Finite Element Methods and Applications Book Excerpt:

This book provides a snapshot of the state of the art of the rapidly evolving field of integration of geometric data in finite element computations. The contributions to this volume, based on research presented at the UCL workshop on the topic in January 2016, include three review papers on core topics such as fictitious domain methods for elasticity, trace finite element methods for partial differential equations defined on surfaces, and Nitsche’s method for contact problems. Five chapters present original research articles on related theoretical topics, including Lagrange multiplier methods, interface problems, bulk-surface coupling, and approximation of partial differential equations on moving domains. Finally, two chapters discuss advanced applications such as crack propagation or flow in fractured poroelastic media. This is the first volume that provides a comprehensive overview of the field of unfitted finite element methods, including recent techniques such as cutFEM, traceFEM, ghost penalty, and augmented Lagrangian techniques. It is aimed at researchers in applied mathematics, scientific computing or computational engineering.