The Finite Element Method for Solid and Structural Mechanics

The Finite Element Method for Solid and Structural Mechanics, 7th Edition

The Finite Element Method for Solid and Structural Mechanics, 7th Edition,Olek Zienkiewicz,Robert Taylor,ISBN9781856176347






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The classic solid mechanics FEM reference that no serious engineer concerned with finite elements should be without

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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.


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.


Mechanical, Civil, Structural, Aerospace and Manufacturing Engineers, applied mathematicians and computer aided engineering software developers

Olek 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.

Affiliations and Expertise

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

Robert Taylor

R. L. Taylor is Emeritus Professor of Engineering and Professor in the Graduate School, Department of Civil and Environmental Engineering at the University of California, Berkeley.

Affiliations and Expertise

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

The Finite Element Method for Solid and Structural Mechanics, 7th Edition

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

Quotes and reviews

"...most up to date and comprehensive reference yet on the finite element method for engineers and mathematicians...part of a collection of 3 other books on the Finite Element Method... Renowned for their scope, range and authority..."--MCADCafe, March 12, 2014

"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."--MCADCafe.com, March 12, 2014

"...this is a book that you simply cannot afford to be without."--International Journal of Numerical Methods in Engineering

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