The Finite Element Method for Solid and Structural Mechanics

The Finite Element Method for Solid and Structural Mechanics

7th Edition - October 24, 2013

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  • Authors: O. C. Zienkiewicz, R. L. Taylor
  • eBook ISBN: 9780080951362
  • Hardcover ISBN: 9781856176347

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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 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.

Key Features

  • 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

Table of Contents

  • Author Biography


    List of Figures

    List of Tables


    Chapter 1. General Problems in Solid Mechanics and Nonlinearity


    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


    Chapter 2. Galerkin Method of Approximation: Irreducible and Mixed Forms


    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


    Chapter 3. Solution of Nonlinear Algebraic Equations


    3.1 Introduction

    3.2 Iterative techniques

    3.3 General remarks: Incremental and rate methods


    Chapter 4. Inelastic and Nonlinear Materials


    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


    Chapter 5. Geometrically Nonlinear Problems: Finite Deformation


    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


    Chapter 6. Material Constitution for Finite Deformation


    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


    Chapter 7. Material Constitution Using Representative Volume Elements


    7.1 Introduction

    7.2 Coupling between scales

    7.3 Quasi-harmonic problems

    7.4 Numerical examples

    7.5 Concluding remarks


    Chapter 8. Treatment of Constraints: Contact and Tied Interfaces


    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


    Chapter 9. Pseudo-Rigid and Rigid-Flexible Bodies


    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


    Chapter 10. Background Mathematics and Linear Shell Theory


    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


    Chapter 11. Differential Geometry and Calculus on Manifolds


    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


    Chapter 12. Geometrically Nonlinear Problems in Continuum Mechanics


    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


    Chapter 13. A Nonlinear Geometrically Exact Rod Model


    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


    Chapter 14. A Nonlinear Geometrically Exact Shell Model


    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


    Chapter 15. Computer Procedures for Finite Element Analysis


    15.1 Introduction

    15.2 Solution of nonlinear problems

    15.3 Eigensolutions

    15.4 Restart option

    15.5 Concluding remarks


    Appendix A. Isoparametric Finite Element Approximations


    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


    B.1 Principal invariants

    B.2 Moment invariants

    B.3 Derivatives of invariants


    Author Index

    Subject Index

Product details

  • No. of pages: 672
  • Language: English
  • Copyright: © Butterworth-Heinemann 2013
  • Published: October 24, 2013
  • Imprint: Butterworth-Heinemann
  • eBook ISBN: 9780080951362
  • Hardcover ISBN: 9781856176347

About the Authors

O. C. Zienkiewicz

O. C. Zienkiewicz was one of the early pioneers of the finite element method and is internationally recognized as a leading figure in its development and wide-ranging application. He was awarded numerous honorary degrees, medals and awards over his career, including the Royal Medal of the Royal Society and Commander of the British Empire (CBE). He was a founding author of The Finite Element Method books and developed them through six editions over 40 years up to his death in 2009. Previous positions held by O.C. Zienkiewicz include UNESCO Professor of Numerical Methods in Engineering at the International Centre for Numerical Methods in Engineering, Barcelona, Director of the Institute for Numerical Methods in Engineering at the University of Wales, Swansea, U.K.

Affiliations and Expertise

Finite element method pioneer and former UNESCO Professor of Numerical Methods in Engineering, Barcelona, Spain

R. L. Taylor

R.L Taylor is Professor of the Graduate School at the Department of Civil and Environmental Engineering, University of California at Berkeley, USA. Awarded the Daniel C. Drucker Medal by the American Society of Mechanical Engineering in 2005, the Gauss-Newton Award and Congress Medal by the International Association for Computational Mechanics in 2002, and the Von Neumann Medal by the US Association for Computational Mechanics in 1999.

Affiliations and Expertise

Emeritus Professor of Engineering, University of California, Berkeley, USA.

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