This book is dedicated to our wives Helen and Mary Lou and our families for their support and patience during the preparation of this book，and also to all of our students and colleagues who over the years have contributed to our knowledge of the finite element method。 In particular we would like to mention Professor Eugenio Onate and his group at CIMNE for their help, encouragement and support during the preparation process。

Preface
1. General problems in solid mechanics and non-linearity
1.1 Introduction
1.2 Small deformation solid mechanics problems
1.3 Variational forms for non-linear elasticity
1.4 Weak forms of governing equations
1.5 Concluding remarks References
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 Non-linear transient and steady-state problems
2.5 Boundary conditions: non-linear problems
2.6 Mixed or irreducible forms
2.7 Non-linear quasi-harmonic field problems
2.8 Typical examples of transient non-linear calculations
2.9 Concluding remarks References
3. Solution of non-linear algebraic equations
3.1 Introduction
3.2 Iterative techniques
3.3 General remarks - incremental and rate methods References
4. Inelastic and non-linear materials
4.1 Introduction
4.2 Viscoelasticity - history dependence of deformation
4.3 Classical time-independent plasticity theory
4.4 Computation of stress increments
4.5 Isotropic plasticity models
4.6 Generalized plasticity
4.7 Some examples of plastic computation
4.8 Basic formulation of creep problems
4.9 Viscoplasticity - a generalization
4.10 Some special problems of brittle materials
4.11 Non-uniqueness and localization in elasto-plastic deformations
4.12 Non-linear quasi-harmonic field problems
4.13 Concluding remarks References
5. Geometrically non-linear 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 A mixed-enhanced finite deformation formulation
5.7 Forces dependent on deformation - pressure loads
5.8 Concluding remarks References
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 References
7. Treatment of constraints - contact and tied interfaces
7.1 Introduction
7.2 Node-node contact: Hertzian contact
7.3 Tied interfaces
7.4 Node-surface contact
7.5 Surface-surface contact
7.6 Numerical examples
7.7 Concluding remarks References
8. Pseudo-rigid and rigid-flexible bodies
8.1 Introduction
8.2 Pseudo-rigid motions
8.3 Rigid motions
8.4 Connecting a rigid body to a flexible body
8.5 Multibody coupling by joints
8.6 Numerical examples References
9. Discrete element methods
10. Structural mechanics problems in one dimension - rods
11. Plate bending approximation: thin (Kirchhoff) plates and C1 continuity
requirements
12. “Thick” Reissner-Mindlin plates - irreducible and mixed formulations
13. Shells as an assembly of fiat elements
14. Curved rods and axisymmetric shells
15. Shells as a special case of three-dimensional analysis - Reissner-Mindlin assumptions
16. Semi-analytical finite element processes - use of orthogonal functions
17. Non-linear structural problems - large displacement and instability
18. Multiscale modelling
19. Computer procedures for finite element analysis
Appendix A Isoparametric finite element approximations
Appendix B Invariants of second-order tensors
Author index
Subject index