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The Finite Element Method for Solid and Structural Mechanics
- 7th Edition - October 24, 2013
- Authors: O. C. Zienkiewicz, R. L. Taylor
- Language: English
- Hardback ISBN:9 7 8 - 1 - 8 5 6 1 7 - 6 3 4 - 7
- eBook ISBN:9 7 8 - 0 - 0 8 - 0 9 5 1 3 6 - 2
The Finite Element Method for Solid and Structural Mechanics is the key text and reference for engineers, researchers and senior students dealing with the analysis and modeling… Read more
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Request a sales quoteThe Finite Element Method for Solid and Structural Mechanics is the key text and reference for engineers, researchers and senior students dealing with the analysis and modeling of structures, from large civil engineering projects such as dams to aircraft structures and small engineered components.
This edition brings a thorough update and rearrangement of the book’s content, including new chapters on:
- Material constitution using representative volume elements
- Differential geometry and calculus on manifolds
- Background mathematics and linear shell theory
Focusing on the core knowledge, mathematical and analytical tools needed for successful structural analysis and modeling, The Finite Element Method for Solid and Structural Mechanics is the authoritative resource of choice for graduate level students, researchers and professional engineers.
- A proven keystone reference in the library of any engineer needing to apply the finite element method to solid mechanics and structural design
- 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 new chapters on topics including material constitution using representative volume elements, as well as consolidated and expanded sections on rod and shell models
Mechanical, Civil, Structural, Aerospace and Manufacturing Engineers, applied mathematicians and computer aided engineering software developers
Author Biography
Dedication
List of Figures
List of Tables
Preface
Chapter 1. General Problems in Solid Mechanics and Nonlinearity
Abstract
1.1 Introduction
1.2 Small deformation solid mechanics problems
1.3 Variational forms for nonlinear elasticity
1.4 Weak forms of governing equations
1.5 Concluding remarks
References
Chapter 2. Galerkin Method of Approximation: Irreducible and Mixed Forms
Abstract
2.1 Introduction
2.2 Finite element approximation: Galerkin method
2.3 Numerical integration: Quadrature
2.4 Nonlinear transient and steady-state problems
2.5 Boundary conditions: Nonlinear problems
2.6 Mixed or irreducible forms
2.7 Nonlinear quasi-harmonic field problems
2.8 Typical examples of transient nonlinear calculations
2.9 Concluding remarks
References
Chapter 3. Solution of Nonlinear Algebraic Equations
Abstract
3.1 Introduction
3.2 Iterative techniques
3.3 General remarks: Incremental and rate methods
References
Chapter 4. Inelastic and Nonlinear Materials
Abstract
4.1 Introduction
4.2 Tensor to matrix representation
4.3 Viscoelasticity: History dependence of deformation
4.4 Classical time-independent plasticity theory
4.5 Computation of stress increments
4.6 Isotropic plasticity models
4.7 Generalized plasticity
4.8 Some examples of plastic computation
4.9 Basic formulation of creep problems
4.10 Viscoplasticity: A generalization
4.11 Some special problems of brittle materials
4.12 Nonuniqueness and localization in elasto-plastic deformations
4.13 Nonlinear quasi-harmonic field problems
4.14 Concluding remarks
References
Chapter 5. Geometrically Nonlinear Problems: Finite Deformation
Abstract
5.1 Introduction
5.2 Governing equations
5.3 Variational description for finite deformation
5.4 Two-dimensional forms
5.5 A three-field, mixed finite deformation formulation
5.6 Forces dependent on deformation: Pressure loads
5.7 Concluding remarks
References
Chapter 6. Material Constitution for Finite Deformation
Abstract
6.1 Introduction
6.2 Isotropic elasticity
6.3 Isotropic viscoelasticity
6.4 Plasticity models
6.5 Incremental formulations
6.6 Rate constitutive models
6.7 Numerical examples
6.8 Concluding remarks
References
Chapter 7. Material Constitution Using Representative Volume Elements
Abstract
7.1 Introduction
7.2 Coupling between scales
7.3 Quasi-harmonic problems
7.4 Numerical examples
7.5 Concluding remarks
References
Chapter 8. Treatment of Constraints: Contact and Tied Interfaces
Abstract
8.1 Introduction
8.2 Node-node contact: Hertzian contact
8.3 Tied interfaces
8.4 Node-surface contact
8.5 Surface-surface contact
8.6 Numerical examples
8.7 Concluding remarks
References
Chapter 9. Pseudo-Rigid and Rigid-Flexible Bodies
Abstract
9.1 Introduction
9.2 Pseudo-rigid motions
9.3 Rigid motions
9.4 Connecting a rigid body to a flexible body
9.5 Multibody coupling by joints
9.6 Numerical examples
9.7 Concluding remarks
References
Chapter 10. Background Mathematics and Linear Shell Theory
Abstract
10.1 Introduction
10.2 Basic notation and differential calculus
10.3 Parameterized surfaces in
10.4 Vector form of three-dimensional linear elasticity
10.5 Linear shell theory
10.6 Finite element formulation
10.7 Numerical examples
10.8 Concluding remarks
References
Chapter 11. Differential Geometry and Calculus on Manifolds
Abstract
11.1 Introduction
11.2 Differential calculus on manifolds
11.3 Curves in: Some basic results
11.4 Analysis on manifolds and Riemannian geometry
11.5 Classical matrix groups: Introduction to Lie groups
References
Chapter 12. Geometrically Nonlinear Problems in Continuum Mechanics
Abstract
12.1 Introduction
12.2 Bodies, configurations, and placements
12.3 Configuration space parameterization
12.4 Motions: Velocity and acceleration fields
12.5 Stress tensors: Momentum equations
12.6 Concluding remarks
References
Chapter 13. A Nonlinear Geometrically Exact Rod Model
Abstract
13.1 Introduction
13.2 Restricted rod model: Basic kinematics
13.3 The exact momentum equation in stress resultants
13.4 The variational formulation and consistent linearization
13.5 Finite element formulation
13.6 Numerical examples
13.7 Concluding remarks
References
Chapter 14. A Nonlinear Geometrically Exact Shell Model
Abstract
14.1 Introduction
14.2 Shell balance equations
14.3 Conserved quantities and hyperelasticity
14.4 Weak form of the momentum balance equations
14.5 Finite element formulation
14.6 Numerical examples
References
Chapter 15. Computer Procedures for Finite Element Analysis
Abstract
15.1 Introduction
15.2 Solution of nonlinear problems
15.3 Eigensolutions
15.4 Restart option
15.5 Concluding remarks
References
Appendix A. Isoparametric Finite Element Approximations
Abstract
A.1 Introduction
A.2 Quadrilateral elements
A.3 Brick elements
A.4 Triangular elements
A.5 Tetrahedral elements
Appendix B. Invariants of Second-Order Tensors
Abstract
B.1 Principal invariants
B.2 Moment invariants
B.3 Derivatives of invariants
References
Author Index
Subject Index
- No. of pages: 672
- Language: English
- Edition: 7
- Published: October 24, 2013
- Imprint: Butterworth-Heinemann
- Hardback ISBN: 9781856176347
- eBook ISBN: 9780080951362
OZ
O. C. Zienkiewicz
Professor O.C. Zienkiewicz, CBE, FRS, FREng died on 2 January 2009. Prior to his death he was Professor Emeritus at the Civil and Computational Engineering Centre, University of Wales Swansea and previously was Director of the Institute for Numerical Methods in Engineering at the University of Wales Swansea, UK. He also held the UNESCO Chair of Numerical Methods in Engineering at the Technical University of Catalunya, Barcelona, Spain. He was the head of the Civil Engineering Department at the University of Wales Swansea between 1961 and 1989. During this period he established that department as one of the primary centres of finite element research. In 1968 he became the Founder Editor of the International Journal for Numerical Methods in Engineering which still remains today the major journal in this field. The recipient of 27 honorary degrees and many medals, Professor Zienkiewicz was a member of five academies – an honour he received for his many contributions to the fundamental developments of the finite element method. In 1978, he became a Fellow of the Royal Society and the Royal Academy of Engineering. This was followed by his election as a foreign member to the US National Academy of Engineering (1981), the Polish Academy of Science (1985), the Chinese Academy of Sciences (1998), and the National Academy of Science, Italy (Academia dei Lincei) (1999). He published the first edition of this book in 1967 and it remained the only book on the subject until 1971.
Affiliations and expertise
Swansea University, Swansea, WalesRT
R. L. Taylor
Professor R.L. Taylor has more than 60 years of experience in the modelling and simulation of structures and solid continua including eighteen years in industry. He is Professor of the Graduate School and the Emeritus T.Y. and Margaret Lin Professor of Engineering at the University of California, Berkeley and also Corporate Fellow at Dassault Systèmes Americas Corp. in Johnston, Rhode Island. In 1991 he was elected to membership in the US National Academy of Engineering in recognition of his educational and research contributions to the field of computational mechanics. Professor Taylor is a Fellow of the US Association for Computational Mechanics – USACM (1996) and a Fellow of the International Association of Computational Mechanics – IACM (1998). He has received numerous awards including the Berkeley Citation, the highest honour awarded by the University of California, Berkeley, the USACM John von Neumann Medal, the IACM Gauss–Newton Congress Medal and a Dr.-Ingenieur ehrenhalber awarded by the Technical University of Hannover, Germany. Professor Taylor has written several computer programs for finite element analysis of structural and non-structural systems, one of which, FEAP, is used world-wide in education and research environments. A personal version, FEAPpv, available on GitHub, is incorporated into this book.
Affiliations and expertise
Emeritus Professor of Engineering, University of California, Berkeley, USARead The Finite Element Method for Solid and Structural Mechanics on ScienceDirect