A Unified Approach to the Finite Element Method and Error Analysis Procedures

A Unified Approach to the Finite Element Method and Error Analysis Procedures

Author: Julian A. T. Dow

Publisher: Elsevier

Published: 1998-11-09

Total Pages: 559

ISBN-13: 0080543421

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A Unified Approach to the Finite Element Method and Error Analysis Procedures provides an in-depth background to better understanding of finite element results and techniques for improving accuracy of finite element methods. Thus, the reader is able to identify and eliminate errors contained in finite element models. Three different error analysis techniques are systematically developed from a common theoretical foundation: 1) modeling erros in individual elements; 2) discretization errors in the overall model; 3) point-wise errors in the final stress or strain results. Thoroughly class tested with undergraduate and graduate students. A Unified Approach to the Finite Element Method and Error Analysis Procedures is sure to become an essential resource for students as well as practicing engineers and researchers. New, simpler element formulation techniques, model-independent results, and error measures New polynomial-based methods for identifying critical points New procedures for evaluating sheer/strain accuracy Accessible to undergraduates, insightful to researchers, and useful to practitioners Taylor series (polynomial) based Intuitive elemental and point-wise error measures Essential background information provided in 12 appendices


Book Synopsis A Unified Approach to the Finite Element Method and Error Analysis Procedures by : Julian A. T. Dow

Download or read book A Unified Approach to the Finite Element Method and Error Analysis Procedures written by Julian A. T. Dow and published by Elsevier. This book was released on 1998-11-09 with total page 559 pages. Available in PDF, EPUB and Kindle. Book excerpt: A Unified Approach to the Finite Element Method and Error Analysis Procedures provides an in-depth background to better understanding of finite element results and techniques for improving accuracy of finite element methods. Thus, the reader is able to identify and eliminate errors contained in finite element models. Three different error analysis techniques are systematically developed from a common theoretical foundation: 1) modeling erros in individual elements; 2) discretization errors in the overall model; 3) point-wise errors in the final stress or strain results. Thoroughly class tested with undergraduate and graduate students. A Unified Approach to the Finite Element Method and Error Analysis Procedures is sure to become an essential resource for students as well as practicing engineers and researchers. New, simpler element formulation techniques, model-independent results, and error measures New polynomial-based methods for identifying critical points New procedures for evaluating sheer/strain accuracy Accessible to undergraduates, insightful to researchers, and useful to practitioners Taylor series (polynomial) based Intuitive elemental and point-wise error measures Essential background information provided in 12 appendices

A Concise Overview of the Finite Element Method

A Concise Overview of the Finite Element Method

Author: John Otto Dow

Publisher: Momentum Press

Published: 2015-08-27

Total Pages: 150

ISBN-13: 1606505092

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This book presents a straightforward introduction to the finite element method, error analysis, and adaptive refinement. It provides an easy-to-read overview that allows the contents of other finite element books and finite element courses to be seen in perspective as the various procedures are encountered. Furthermore, it provides developments that improve the procedures contained in the standard finite element textbook. As a result, when this book is used alone or in conjunction with other presentations, the reader is capable of critically assessing the capabilities of the finite element method.


Book Synopsis A Concise Overview of the Finite Element Method by : John Otto Dow

Download or read book A Concise Overview of the Finite Element Method written by John Otto Dow and published by Momentum Press. This book was released on 2015-08-27 with total page 150 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents a straightforward introduction to the finite element method, error analysis, and adaptive refinement. It provides an easy-to-read overview that allows the contents of other finite element books and finite element courses to be seen in perspective as the various procedures are encountered. Furthermore, it provides developments that improve the procedures contained in the standard finite element textbook. As a result, when this book is used alone or in conjunction with other presentations, the reader is capable of critically assessing the capabilities of the finite element method.

A Posteriori Error Estimation in Finite Element Analysis

A Posteriori Error Estimation in Finite Element Analysis

Author: Mark Ainsworth

Publisher: John Wiley & Sons

Published: 2011-09-28

Total Pages: 266

ISBN-13: 1118031075

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An up-to-date, one-stop reference-complete with applications This volume presents the most up-to-date information available on aposteriori error estimation for finite element approximation inmechanics and mathematics. It emphasizes methods for ellipticboundary value problems and includes applications to incompressibleflow and nonlinear problems. Recent years have seen an explosion in the study of a posteriorierror estimators due to their remarkable influence on improvingboth accuracy and reliability in scientific computing. In an effortto provide an accessible source, the authors have sought to presentkey ideas and common principles on a sound mathematicalfooting. Topics covered in this timely reference include: * Implicit and explicit a posteriori error estimators * Recovery-based error estimators * Estimators, indicators, and hierarchic bases * The equilibrated residual method * Methodology for the comparison of estimators * Estimation of errors in quantities of interest A Posteriori Error Estimation in Finite Element Analysis is a lucidand convenient resource for researchers in almost any field offinite element methods, and for applied mathematicians andengineers who have an interest in error estimation and/or finiteelements.


Book Synopsis A Posteriori Error Estimation in Finite Element Analysis by : Mark Ainsworth

Download or read book A Posteriori Error Estimation in Finite Element Analysis written by Mark Ainsworth and published by John Wiley & Sons. This book was released on 2011-09-28 with total page 266 pages. Available in PDF, EPUB and Kindle. Book excerpt: An up-to-date, one-stop reference-complete with applications This volume presents the most up-to-date information available on aposteriori error estimation for finite element approximation inmechanics and mathematics. It emphasizes methods for ellipticboundary value problems and includes applications to incompressibleflow and nonlinear problems. Recent years have seen an explosion in the study of a posteriorierror estimators due to their remarkable influence on improvingboth accuracy and reliability in scientific computing. In an effortto provide an accessible source, the authors have sought to presentkey ideas and common principles on a sound mathematicalfooting. Topics covered in this timely reference include: * Implicit and explicit a posteriori error estimators * Recovery-based error estimators * Estimators, indicators, and hierarchic bases * The equilibrated residual method * Methodology for the comparison of estimators * Estimation of errors in quantities of interest A Posteriori Error Estimation in Finite Element Analysis is a lucidand convenient resource for researchers in almost any field offinite element methods, and for applied mathematicians andengineers who have an interest in error estimation and/or finiteelements.

The Essentials of Finite Element Modeling and Adaptive Refinement

The Essentials of Finite Element Modeling and Adaptive Refinement

Author: John O. Dow

Publisher: Momentum Press

Published: 2012-07-01

Total Pages: 299

ISBN-13: 1606503340

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Finite Element Analysis is a very popular, computer-based tool that uses a complex system of points called nodes to make a grid called a "mesh. " The mesh contains the material and structural properties that define how the structure will react to certain loading conditions, allowing virtual testing and analysis of stresses or changes applied to the material or component design. This groundbreaking text extends the usefulness of finite element analysis by helping both beginners and advanced users alike. It simplifies, improves, and extends both the finite element method while at the same time advancing adaptive refinement procedures. These improvements are made possible due to a change in notation that embeds knowledge of solid continuum mechanics into the equations used to formulate the stiffness matrices; this allows the modeling characteristics of individual elements to be identified by visual inspection. The ability to visually relate the equations involved in element formulation to the physical process they represent is like having an x-ray of the inner workings of the finite element method; it is similar is to the effect that Graphical User Interfaces or GUI's had on computing. As a result, students at any level of finite element study are provided with an understanding of the capabilities and limitations of this powerful analytic tool. The book presents * A more simplified approach to finite element analysis based on computational continuum mechanics * Physically interpretable notation that identifies a common basis for the finite element and the finite difference methods. * New point-wise error estimators that identify errors in terms of quantities of direct interest in solid mechanics


Book Synopsis The Essentials of Finite Element Modeling and Adaptive Refinement by : John O. Dow

Download or read book The Essentials of Finite Element Modeling and Adaptive Refinement written by John O. Dow and published by Momentum Press. This book was released on 2012-07-01 with total page 299 pages. Available in PDF, EPUB and Kindle. Book excerpt: Finite Element Analysis is a very popular, computer-based tool that uses a complex system of points called nodes to make a grid called a "mesh. " The mesh contains the material and structural properties that define how the structure will react to certain loading conditions, allowing virtual testing and analysis of stresses or changes applied to the material or component design. This groundbreaking text extends the usefulness of finite element analysis by helping both beginners and advanced users alike. It simplifies, improves, and extends both the finite element method while at the same time advancing adaptive refinement procedures. These improvements are made possible due to a change in notation that embeds knowledge of solid continuum mechanics into the equations used to formulate the stiffness matrices; this allows the modeling characteristics of individual elements to be identified by visual inspection. The ability to visually relate the equations involved in element formulation to the physical process they represent is like having an x-ray of the inner workings of the finite element method; it is similar is to the effect that Graphical User Interfaces or GUI's had on computing. As a result, students at any level of finite element study are provided with an understanding of the capabilities and limitations of this powerful analytic tool. The book presents * A more simplified approach to finite element analysis based on computational continuum mechanics * Physically interpretable notation that identifies a common basis for the finite element and the finite difference methods. * New point-wise error estimators that identify errors in terms of quantities of direct interest in solid mechanics

Adaptive Finite Element Methods for Differential Equations

Adaptive Finite Element Methods for Differential Equations

Author: Wolfgang Bangerth

Publisher: Birkhäuser

Published: 2013-11-11

Total Pages: 216

ISBN-13: 303487605X

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These Lecture Notes have been compiled from the material presented by the second author in a lecture series ('Nachdiplomvorlesung') at the Department of Mathematics of the ETH Zurich during the summer term 2002. Concepts of 'self adaptivity' in the numerical solution of differential equations are discussed with emphasis on Galerkin finite element methods. The key issues are a posteriori er ror estimation and automatic mesh adaptation. Besides the traditional approach of energy-norm error control, a new duality-based technique, the Dual Weighted Residual method (or shortly D WR method) for goal-oriented error estimation is discussed in detail. This method aims at economical computation of arbitrary quantities of physical interest by properly adapting the computational mesh. This is typically required in the design cycles of technical applications. For example, the drag coefficient of a body immersed in a viscous flow is computed, then it is minimized by varying certain control parameters, and finally the stability of the resulting flow is investigated by solving an eigenvalue problem. 'Goal-oriented' adaptivity is designed to achieve these tasks with minimal cost. The basics of the DWR method and various of its applications are described in the following survey articles: R. Rannacher [114], Error control in finite element computations. In: Proc. of Summer School Error Control and Adaptivity in Scientific Computing (H. Bulgak and C. Zenger, eds), pp. 247-278. Kluwer Academic Publishers, 1998. M. Braack and R. Rannacher [42], Adaptive finite element methods for low Mach-number flows with chemical reactions.


Book Synopsis Adaptive Finite Element Methods for Differential Equations by : Wolfgang Bangerth

Download or read book Adaptive Finite Element Methods for Differential Equations written by Wolfgang Bangerth and published by Birkhäuser. This book was released on 2013-11-11 with total page 216 pages. Available in PDF, EPUB and Kindle. Book excerpt: These Lecture Notes have been compiled from the material presented by the second author in a lecture series ('Nachdiplomvorlesung') at the Department of Mathematics of the ETH Zurich during the summer term 2002. Concepts of 'self adaptivity' in the numerical solution of differential equations are discussed with emphasis on Galerkin finite element methods. The key issues are a posteriori er ror estimation and automatic mesh adaptation. Besides the traditional approach of energy-norm error control, a new duality-based technique, the Dual Weighted Residual method (or shortly D WR method) for goal-oriented error estimation is discussed in detail. This method aims at economical computation of arbitrary quantities of physical interest by properly adapting the computational mesh. This is typically required in the design cycles of technical applications. For example, the drag coefficient of a body immersed in a viscous flow is computed, then it is minimized by varying certain control parameters, and finally the stability of the resulting flow is investigated by solving an eigenvalue problem. 'Goal-oriented' adaptivity is designed to achieve these tasks with minimal cost. The basics of the DWR method and various of its applications are described in the following survey articles: R. Rannacher [114], Error control in finite element computations. In: Proc. of Summer School Error Control and Adaptivity in Scientific Computing (H. Bulgak and C. Zenger, eds), pp. 247-278. Kluwer Academic Publishers, 1998. M. Braack and R. Rannacher [42], Adaptive finite element methods for low Mach-number flows with chemical reactions.

Structural Analysis with Finite Elements

Structural Analysis with Finite Elements

Author: Friedel Hartmann

Publisher: Springer Science & Business Media

Published: 2013-04-17

Total Pages: 492

ISBN-13: 366205423X

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This book provides a solid introduction to the foundation and the application of the finite element method in structural analysis. It offers new theoretical insight and practical advice. This second edition contains additional sections on sensitivity analysis, on retrofitting structures, on the Generalized FEM (X-FEM) and on model adaptivity. An additional chapter treats the boundary element method, and related software is available at www.winfem.de.


Book Synopsis Structural Analysis with Finite Elements by : Friedel Hartmann

Download or read book Structural Analysis with Finite Elements written by Friedel Hartmann and published by Springer Science & Business Media. This book was released on 2013-04-17 with total page 492 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides a solid introduction to the foundation and the application of the finite element method in structural analysis. It offers new theoretical insight and practical advice. This second edition contains additional sections on sensitivity analysis, on retrofitting structures, on the Generalized FEM (X-FEM) and on model adaptivity. An additional chapter treats the boundary element method, and related software is available at www.winfem.de.

Model Validation and Uncertainty Quantification, Volume 3

Model Validation and Uncertainty Quantification, Volume 3

Author: H. Sezer Atamturktur

Publisher: Springer Science & Business Media

Published: 2014-04-11

Total Pages: 419

ISBN-13: 3319045520

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This third volume of eight from the IMAC - XXXII Conference, brings together contributions to this important area of research and engineering. The collection presents early findings and case studies on fundamental and applied aspects of Structural Dynamics, including papers on: Linear Systems Substructure Modelling Adaptive Structures Experimental Techniques Analytical Methods Damage Detection Damping of Materials & Members Modal Parameter Identification Modal Testing Methods System Identification Active Control Modal Parameter Estimation Processing Modal Data


Book Synopsis Model Validation and Uncertainty Quantification, Volume 3 by : H. Sezer Atamturktur

Download or read book Model Validation and Uncertainty Quantification, Volume 3 written by H. Sezer Atamturktur and published by Springer Science & Business Media. This book was released on 2014-04-11 with total page 419 pages. Available in PDF, EPUB and Kindle. Book excerpt: This third volume of eight from the IMAC - XXXII Conference, brings together contributions to this important area of research and engineering. The collection presents early findings and case studies on fundamental and applied aspects of Structural Dynamics, including papers on: Linear Systems Substructure Modelling Adaptive Structures Experimental Techniques Analytical Methods Damage Detection Damping of Materials & Members Modal Parameter Identification Modal Testing Methods System Identification Active Control Modal Parameter Estimation Processing Modal Data

Minimization of Welding Distortion and Buckling

Minimization of Welding Distortion and Buckling

Author: Pan Michaleris

Publisher: Elsevier

Published: 2011-05-25

Total Pages: 319

ISBN-13: 0857092901

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Welding is a cost-effective and flexible method of fabricating large structures, but drawbacks such as residual stress, distortion and buckling must be overcome in order to optimize structural performance. Minimization of welding distortion and buckling provides a systematic overview of the methods of minimizing distortion and buckling in welded structures. Following an introductory chapter, part one focuses on understanding welding stress and distortion, with chapters on such topics as computational welding mechanics, modelling the effect of phase transformations on welding stress and distortion and using computationally efficient reduced-solution methods to understand welding distortion. Part two covers different methods of minimizing welding distortion. Chapters discuss methods such as differential heating for minimizing distortion in welded stiffeners, dynamic thermal tensioning, reverse-side heating and ways of minimizing buckling such as weld cooling and hybrid laser arc welding. With its distinguished editor and international team of contributors, Minimization of welding distortion and buckling is an essential reference for all welders and engineers involved in fabrication of metal end-products, as well as those in industry and academia with a research interest in the area. Provides a systematic overview of the methods of minimizing distortion and buckling in welded structures Focuses on understanding welding stress and distortion featuring computational welding mechanics and modelling the effect of phase transformations Explores different methods of minimizing welding distortion discussing differential heating and dynamic thermal tensioning


Book Synopsis Minimization of Welding Distortion and Buckling by : Pan Michaleris

Download or read book Minimization of Welding Distortion and Buckling written by Pan Michaleris and published by Elsevier. This book was released on 2011-05-25 with total page 319 pages. Available in PDF, EPUB and Kindle. Book excerpt: Welding is a cost-effective and flexible method of fabricating large structures, but drawbacks such as residual stress, distortion and buckling must be overcome in order to optimize structural performance. Minimization of welding distortion and buckling provides a systematic overview of the methods of minimizing distortion and buckling in welded structures. Following an introductory chapter, part one focuses on understanding welding stress and distortion, with chapters on such topics as computational welding mechanics, modelling the effect of phase transformations on welding stress and distortion and using computationally efficient reduced-solution methods to understand welding distortion. Part two covers different methods of minimizing welding distortion. Chapters discuss methods such as differential heating for minimizing distortion in welded stiffeners, dynamic thermal tensioning, reverse-side heating and ways of minimizing buckling such as weld cooling and hybrid laser arc welding. With its distinguished editor and international team of contributors, Minimization of welding distortion and buckling is an essential reference for all welders and engineers involved in fabrication of metal end-products, as well as those in industry and academia with a research interest in the area. Provides a systematic overview of the methods of minimizing distortion and buckling in welded structures Focuses on understanding welding stress and distortion featuring computational welding mechanics and modelling the effect of phase transformations Explores different methods of minimizing welding distortion discussing differential heating and dynamic thermal tensioning

The Finite Element Method: Its Basis and Fundamentals

The Finite Element Method: Its Basis and Fundamentals

Author: Olek C Zienkiewicz

Publisher: Butterworth-Heinemann

Published: 2013-08-31

Total Pages: 756

ISBN-13: 008095135X

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The Finite Element Method: Its Basis and Fundamentals offers a complete introduction to the basis of the finite element method, covering fundamental theory and worked examples in the detail required for readers to apply the knowledge to their own engineering problems and understand more advanced applications. This edition sees a significant rearrangement of the book’s content to enable clearer development of the finite element method, with major new chapters and sections added to cover: Weak forms Variational forms Multi-dimensional field problems Automatic mesh generation Plate bending and shells Developments in meshless techniques Focusing on the core knowledge, mathematical and analytical tools needed for successful application, The Finite Element Method: Its Basis and Fundamentals is the authoritative resource of choice for graduate level students, researchers and professional engineers involved in finite element-based engineering analysis. A proven keystone reference in the library of any engineer needing to understand and apply the finite element method in design and development. Founded by an influential pioneer in the field and updated in this seventh edition by an author team incorporating academic authority and industrial simulation experience. Features reworked and reordered contents for clearer development of the theory, plus new chapters and sections on mesh generation, plate bending, shells, weak forms and variational forms.


Book Synopsis The Finite Element Method: Its Basis and Fundamentals by : Olek C Zienkiewicz

Download or read book The Finite Element Method: Its Basis and Fundamentals written by Olek C Zienkiewicz and published by Butterworth-Heinemann. This book was released on 2013-08-31 with total page 756 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Finite Element Method: Its Basis and Fundamentals offers a complete introduction to the basis of the finite element method, covering fundamental theory and worked examples in the detail required for readers to apply the knowledge to their own engineering problems and understand more advanced applications. This edition sees a significant rearrangement of the book’s content to enable clearer development of the finite element method, with major new chapters and sections added to cover: Weak forms Variational forms Multi-dimensional field problems Automatic mesh generation Plate bending and shells Developments in meshless techniques Focusing on the core knowledge, mathematical and analytical tools needed for successful application, The Finite Element Method: Its Basis and Fundamentals is the authoritative resource of choice for graduate level students, researchers and professional engineers involved in finite element-based engineering analysis. A proven keystone reference in the library of any engineer needing to understand and apply the finite element method in design and development. Founded by an influential pioneer in the field and updated in this seventh edition by an author team incorporating academic authority and industrial simulation experience. Features reworked and reordered contents for clearer development of the theory, plus new chapters and sections on mesh generation, plate bending, shells, weak forms and variational forms.

A Posteriori Error Estimation Techniques for Finite Element Methods

A Posteriori Error Estimation Techniques for Finite Element Methods

Author: Rudiger Verfurth

Publisher: Oxford University Press

Published: 2013-04-18

Total Pages: 414

ISBN-13: 0199679428

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A posteriori error estimation techniques are fundamental to the efficient numerical solution of PDEs arising in physical and technical applications. This book gives a unified approach to these techniques and guides graduate students, researchers, and practitioners towards understanding, applying and developing self-adaptive discretization methods.


Book Synopsis A Posteriori Error Estimation Techniques for Finite Element Methods by : Rudiger Verfurth

Download or read book A Posteriori Error Estimation Techniques for Finite Element Methods written by Rudiger Verfurth and published by Oxford University Press. This book was released on 2013-04-18 with total page 414 pages. Available in PDF, EPUB and Kindle. Book excerpt: A posteriori error estimation techniques are fundamental to the efficient numerical solution of PDEs arising in physical and technical applications. This book gives a unified approach to these techniques and guides graduate students, researchers, and practitioners towards understanding, applying and developing self-adaptive discretization methods.