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- Herausgeber: John Wiley & Sons
- Kategorie: Fachliteratur
- Serie: Wiley Series in Computational Mechanics
- Sprache: Englisch
- Veröffentlichungsjahr: 2012
Built upon the two original books by Mike Crisfield and their own lecture notes, renowned scientist René de Borst and his team offer a thoroughly updated yet condensed edition that retains and builds upon the excellent reputation and appeal amongst students and engineers alike for which Crisfield's first edition is acclaimed. Together with numerous additions and updates, the new authors have retained the core content of the original publication, while bringing an improved focus on new developments and ideas. This edition offers the latest insights in non-linear finite element technology, including non-linear solution strategies, computational plasticity, damage mechanics, time-dependent effects, hyperelasticity and large-strain elasto-plasticity. The authors' integrated and consistent style and unrivalled engineering approach assures this book's unique position within the computational mechanics literature. Key features: * Combines the two previous volumes into one heavily revised text with obsolete material removed, an improved layout and updated references and notations * Extensive new material on more recent developments in computational mechanics * Easily readable, engineering oriented, with no more details in the main text than necessary to understand the concepts. * Pseudo-code throughout makes the link between theory and algorithms, and the actual implementation. * Accompanied by a website (www.wiley.com/go/deborst) with a Python code, based on the pseudo-code within the book and suitable for solving small-size problems. Non-linear Finite Element Analysis of Solids and Structures, 2nd Edition is an essential reference for practising engineers and researchers that can also be used as a text for undergraduate and graduate students within computational mechanics.
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Contents
Cover
Title Page
Copyright
Preface
A Personal Note
Series Preface
Notation
Linear Algebra and Mathematical Operators
Basic Continuum Mechanics
Elasticity
Finite Element Data Structures
Geometrically Non-linear Analysis
Incremental Iterative Analysis and Solution Techniques
Dynamics and Time-dependent Material Models
Damage and Fracture
Plasticity
Structural Members
Isogeometric Analysis
About the Code
Part I: Basic Concepts and Solution Techniques
Chapter 1: Preliminaries
1.1 A Simple Example of Non-linear Behaviour
1.2 A Review of Concepts from Linear Algebra
1.3 Vectors and Tensors
1.4 Stress and Strain Tensors
1.5 Elasticity
1.6 The PyFEM Finite Element Library
References
Chapter 2: Non-linear Finite Element Analysis
2.1 Equilibrium and Virtual Work
2.2 Spatial Discretisation by Finite Elements
2.3 PyFEM: Shape Function Utilities
2.4 Incremental-iterative Analysis
2.5 Load versus Displacement Control
2.6 PyFEM: A Linear Finite Element Code with Displacement Control
Reference
Chapter 3: Geometrically Non-linear Analysis
3.1 Truss Elements
3.2 PyFEM: The Shallow Truss Problem
3.3 Stress and Deformation Measures in Continua
3.4 Geometrically Non-linear Formulation of Continuum Elements
3.5 Linear Buckling Analysis
3.6 PyFEM: A Geometrically Non-linear Continuum Element
References
Chapter 4: Solution Techniques in Quasi-static Analysis
4.1 Line Searches
4.2 Path-following or Arc-length Methods
4.3 PyFEM: Implementation of Riks' Arc-length Solver
4.4 Stability and Uniqueness in Discretised Systems
4.5 Load Stepping and Convergence Criteria
4.6 Quasi-Newton Methods
References
Chapter 5: Solution Techniques for Non-linear Dynamics
5.1 The Semi-discrete Equations
5.2 Explicit Time Integration
5.3 PyFEM: Implementation of an Explicit Solver
5.4 Implicit Time Integration
5.5 Stability and Accuracy in the Presence of Non-linearities
5.6 Energy-conserving Algorithms
5.7 Time Step Size Control and Element Technology
References
Part II: Material Non-linearities
Chapter 6: Damage Mechanics
6.1 The Concept of Damage
6.2 Isotropic Elasticity-based Damage
6.3 PyFEM: A Plane-strain Damage Model
6.4 Stability, Ellipticity and Mesh Sensitivity
6.5 Cohesive-zone Models
6.6 Element Technology: Embedded Discontinuities
6.7 Complex Damage Models
6.8 Crack Models for Concrete and Other Quasi-brittle Materials
6.9 Regularised Damage Models
References
Chapter 7: Plasticity
7.1 A Simple Slip Model
7.2 Flow Theory of Plasticity
7.3 Integration of the Stress–strain Relation
7.4 Tangent Stiffness Operators
7.5 Multi-surface Plasticity
7.6 Soil Plasticity: Cam-clay Model
7.7 Coupled Damage–Plasticity Models
7.8 Element Technology: Volumetric Locking
References
Chapter 8: Time-dependent Material Models
8.1 Linear Visco-elasticity
8.2 Creep Models
8.3 Visco-plasticity
References
Part III: Structural Elements
Chapter 9: Beams and Arches
9.1 A Shallow Arch
9.2 PyFEM: A Kirchhoff Beam Element
9.3 Corotational Elements
9.4 A Two-dimensional Isoparametric Degenerate Continuum Beam Element
9.5 A Three-dimensional Isoparametric Degenerate Continuum Beam Element
References
Chapter 10: Plates and Shells
10.1 Shallow-shell Formulations
10.2 An Isoparametric Degenerate Continuum Shell Element
10.3 Solid-like Shell Elements
10.4 Shell Plasticity: Ilyushin's Criterion
References
Part IV: Large Strains
Chapter 11: Hyperelasticity
11.1 More Continuum Mechanics
11.2 Strain Energy Functions
11.3 Element Technology
References
Chapter 12: Large-strain Elasto-plasticity
12.1 Eulerian Formulations
12.2 Multiplicative Elasto-plasticity
12.3 Multiplicative Elasto-plasticity versus Rate Formulations
12.4 Integration of the Rate Equations
12.5 Exponential Return-mapping Algorithms
References
Part V: Advanced Discretisation Concepts
Chapter 13: Interfaces and Discontinuities
13.1 Interface Elements
13.2 Discontinuous Galerkin Methods
References
Chapter 14: Meshless and Partition-of-unity Methods
14.1 Meshless Methods
14.2 Partition-of-unity Approaches
References
Chapter 15: Isogeometric Finite Element Analysis
15.1 Basis Functions in Computer Aided Geometric Design
15.2 Isogeometric Finite Elements
15.3 PyFEM: Shape Functions for Isogeometric Analysis
15.4 Isogeometric Analysis in Non-linear Solid Mechanics
References
Index
Wiley Series in Computational Mechanics
Series Advisors:
René de Borst
Perumal Nithiarasu
Tayfun E. Tezduyar
Genki Yagawa
Tarek Zohdi
Introduction to Finite Strain Theory for Continuum Elasto-PlasticityHashiguchi and YamakawaSeptember 2012Non-linear Finite Element Analysis of Solids and Structures: Second editionDe Borst, Crisfield, Remmers and VerhooselAugust 2012An Introduction to Mathematical Modeling: A Course in MechanicsOdenNovember 2011Computational Mechanics of DiscontinuaMunjiza, Knight and RougierNovember 2011Introduction to Finite Element Analysis: Formulation, Verification and ValidationSzabó and BabuškaMarch 2011This edition first published 2012
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Library of Congress Cataloging-in-Publication Data
Non-linear finite element analysis of solids and structures. –2nd ed. / R. de Borst . . . [et al.].
p. cm.
Rev. ed. of: Non-linear finite element analysis of solids and structures / M.A. Crisfield. c1991-c1997. (2 v.)
Includes bibliographical references and index.
ISBN 978-0-470-66644-9 (hardback)
1. Structural analysis (Engineering)–Data processing. 2. Finite element
method–Data processing. I. Borst, Ren? de. II. Crisfield, M. A. Non-linear
finite element analysis of solids and structures.
TA647.C75 2012
624.1′71–dc23
2012011741
A catalogue record for this book is available from the British Library.
Print ISBN: 9780470666449
Preface
When the first author was approached by John Wiley & Sons, Ltd to write a new edition of the celebrated two-volume book of Mike Crisfield, Non-linear Finite Element Analysis of Solids and Structures, he was initially very hesitant. The task would of course constitute a formidable amount of work. But it would also be impossible to maintain Mike's writing style, a feature which has so much contributed to the success of the books. On the other hand, it would be rewarding to provide the engineering community with a book that is as accessible as possible, that gives a broad introduction into non-linear finite element analysis, with an outlook on the newest developments, and that maintains the engineering spirit which Mike emphasised in his books. This is the philosophy behind this second edition. Indeed, although much has been changed in terms of content, it has been the intention not to change the engineering orientation with an emphasis on practical solutions.
One of the aims of the original two-volume set was to provide the user of advanced non-linear finite element packages with sufficient background knowledge, which is a prerequisite to judiciously handle modern finite element packages. A closely related aim is to make the user of such packages aware of their possibilities, but also of their limitations and pitfalls. Major developments have taken place in computational technology since Mike Crisfield wrote about the danger of the ‘black-box syndrome’ in the Preface to Volume 1. Therefore, his warning has gained even more strength, and provides a further justification for the publication of a second edition.
Unlike the first edition, the second edition comes as a single volume. The reduction has been achieved by omitting or reducing the discussion on developments now considered to be less central in computational mechanics, by a more compact and focused treatment, and by a removal of all Fortran code from the book. Instead, a small finite element code has been developed, written in Python, which is available through a companion website. The main purpose of the code is to illustrate the models presented in the book, and to show how abstract concepts can be translated into finite element software. To this end, the theory of the book is first transformed into algorithms, mostly listed in boxes that accompany the text. Subsequently, using ideas of literate programming, it is explained how these algorithms have been implemented in the PyFEM code, which contains the basic numerical tools needed to build a finite element code. Some of the solution techniques, element formulations, and material models treated in this book have been added. These tools are used in a series of example programs with increasing complexity.
The book comes in five parts. Part I discusses basic knowledge in mathematics and in continuum mechanics, as well as solution techniques for non-linear problems in static and dynamic analysis, and provides a first introduction into geometrical non-linearity. Some notions and concepts will be familiar, but not all, and the first chapters also serve to provide a common basis for the subsequent parts of the book. Part II contains major chapters on damage, plasticity and time-dependent non-linearities, such as creep. It contains all the material non-linearity that is treated in this book. Shell plasticity forms an exception, since it is treated in Part III, which focuses on structural elements: beams, arches and shells. Starting from a basic shallow arch formulation the discussion extends to cover modern concepts like solid-like shell theories. In Part IV first some additional continuum mechanics is provided that is needed in the remainder of this part, which focuses on large-strain elastic and elastoplastic finite element analysis. Part V, finally, gives an introduction into discretisation concepts that have become popular during the past 20 years: interface elements, discontinuous Galerkin methods, meshless methods, partition-of-unity methods, and isogeometric analysis. Particular reference is made to their potential to solve problems that arise in non-linear analysis, such as locking phenomena, damage and fracture, and non-linear shell analysis.
René de Borst
Joris Remmers
Clemens Verhoosel
Glasgow and Eindhoven
A Personal Note
Like many colleagues and friends in the community I treasure wonderful memories of my meetings and discussions with Mike. I will never forget the times that I visited him at the Transport and Road Research Laboratory, and later, at Imperial College of Science, Technology and Medicine. After a full day of intense discussions on cracking, strain softening, stability and solution techniques we normally went to his home, where Kiki, his wife, joined in and discussions broadened over a good meal.
Mike was a real scientist, and a gentleman. I hope that this Second Edition will properly preserve his legacy, and will help to keep the engineering approach alive in computational mechanics, to which he has so much contributed.
René
Series Preface
The series on Computational Mechanics is a conveniently identifiable set of books covering interrelated subjects that have been receiving much attention in recent years and need to have a place in senior undergraduate and graduate school curricula, and in engineering practice. The subjects will cover applications and methods categories. They will range from biomechanics to fluid-structure interactions to multiscale mechanics and from computational geometry to meshfree techniques to parallel and iterative computing methods. Application areas will be across the board in a wide range of industries, including civil, mechanical, aerospace, automotive, environmental and biomedical engineering. Practicing engineers, researchers and software developers at universities, industry and government laboratories, and graduate students will find this book series to be an indispensible source for new engineering approaches, interdisciplinary research, and a comprehensive learning experience in computational mechanics.
Non-linear Finite Element Analysis of Solids and Structures, Second Edition is based on the two original volumes by the late Mike Crisfield, who was a remarkable scholar in computational mechanics. This new edition is a greatly enriched version, written by an author team led by René de Borst, an outstanding scholar in computational mechanics, solids, and structures. The enrichments include the major developments in computational mechanics since the original version was written, such as new numerical discretization techniques, with emphasis on meshless methods and isogeometric analysis. This new edition still retains the “engineering spirit” that was emphasized by the original author, and the algorithmic explanations, which are only part of the enrichments, make it even easier to follow and more valuable in a practical context.
Non-linear Finite Element Analysis of Solids and Structures, Second Edition will serve as an excellent textbook for introductory and advanced courses in non-linear finite element analysis of solids and structures, and will also serve as a very valuable source and guide for research in this field.
About the Code
A number of models and algorithms that are discussed in this book, have been implemented in a small finite element code named PyFEM, which is available for a free download from the website that accompanies this book. The code has been written in Python, an object-oriented, interpreted, and interactive programming language. Its clear syntax allows for the development of small, yet powerful programs. A wide range of Python packages are available, which are dedicated towards numerical simulations. Many numerical libraries and software tools have been equipped with a Python interface and can be integrated within a Python program seamlessly.
In PyFEM we restrict ourselves to the use of the packages NumPy, SciPy and Matplotlib. The NumPy package contains array objects and a collection of linear algebra operations. The SciPy package is an extension to this package and contains additional linear algebra tools, such as solvers and sparse arrays. The Matplotlib package allows the user to make graphs and plots. Python and the three aforementioned packages are standard components of most Linux distributions. The most recent versions of Python for various Windows operating systems and Mac OS X can be downloaded from www.python.org.
The PyFEM code contains the basic numerical tools which are needed to build a finite element code. These tools are used in a series of example programs with increasing complexity. The examples that illustrate the numerical techniques presented in the first chapters of this book are basically small scripts that perform a single numerical operation and do not require an input file. These small scripts are developed further, and finally result in a general finite element program which will be presented in Chapter 4: PyFEM.py. This program can be considered as a stand-alone program that can carry out a variety of simulations with different element formulations and material models. In the remaining parts of this book the implementation of some solvers, elements and material models is discussed in more detail.
The directory structure of PyFEM is shown in Figure 1. The package contains the following files and directories:
Figure 1 Directory structure of the PyFEM code. The root directory is called pyfem-x.y, where x.y indicates the version number of the code
PyFEM is an open source code and is intended for educational and scientific use. It does not contain comprehensive libraries, e.g. of material models, but it has been designed so that it is relatively easy to implement other solvers, elements, and material models, for which the theory and the algorithmic details can be found in this book. A concise user's guide how to implement these can be found at the website.
Instead of giving full listings of classes and functions, we will use a notation that is inspired by literate programming. The main idea behind literate programming is to present a code in such a way that it can be understood by humans and by computers. An important feature of literate programming is that parts of the source code are presented as small fragments, allowing for a detailed discussion of the code. A short overview of the notation, including a system to refer to other fragments, is given in Figure 2.
Figure 2 Example of a code fragment with the nomenclature and references to other code fragments
Part I
Basic Concepts and Solution Techniques
Chapter 1
Preliminaries
