It is thirty-eight years since the The Finite Element Method in Structural and Continuum Mechanics was first published. This book, which was the first dealing with the finite element method, provided the basis from which many further developments occurred. The expanding research and field of application of finite elements led to the second edition in 1971, the third in 1977, the fourth as two volumes in 1989 and 1991 and the fifth as three volumes in 2000. The size of each of these editions expanded geometrically （from 272 pages in 1967 to the fifth edition of 1482 pages）. This was necessary to do justice to a rapidly expanding field of professional application and research. Even so, much filtering of the contents was necessary to keep these editions within reasonable bounds.In the present edition we retain the three volume format of the fifth edition but have decided not to pursue having three contiguous volumes- rather we treat the whole work as an assembly of three separate works. Each one is capable of being used without the others and each one appeals perhaps to a different audience. Though naturally we recommend the use of the whole ensemble to people wishing to devote much of their time and study to the finite element method.
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。
Preface1. 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 References2. 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 References3. Solution of non-linear algebraic equations 3.1 Introduction 3.2 Iterative techniques 3.3 General remarks - incremental and rate methods References4. 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 References5. 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 References6. 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 References7. 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 References8. 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 References9. Discrete element methods10. Structural mechanics problems in one dimension - rods11. Plate bending approximation: thin (Kirchhoff) plates and C1 continuity requirements12. “Thick” Reissner-Mindlin plates - irreducible and mixed formulations13. Shells as an assembly of fiat elements14. Curved rods and axisymmetric shells15. Shells as a special case of three-dimensional analysis - Reissner-Mindlin assumptions16. Semi-analytical finite element processes - use of orthogonal functions17. Non-linear structural problems - large displacement and instability18. Multiscale modelling19. Computer procedures for finite element analysisAppendix A Isoparametric finite element approximationsAppendix B Invariants of second-order tensorsAuthor indexSubject index
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