Front Cover -- The Finite Element Method for Solid and Structural Mechanics -- Copyright Page -- Contents -- Preface -- Chapter 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 -- 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 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 -- Chapter 3. Solution of non-linear algebraic equations -- 3.1 Introduction -- 3.2 Iterative techniques -- 3.3 General remarks - incremental and rate methods -- References -- Chapter 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 -- Chapter 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 -- 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 -- References -- Chapter 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 -- Chapter 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 -- Chapter 9. Discrete element methods -- 9.1 Introduction -- 9.2 Early DEM formulations -- 9.3 Contact detection -- 9.4 Contact constraints and boundary conditions -- 9.5 Block deformability -- 9.6 Time integration for discrete element methods -- 9.7 Associated discontinuous modelling methodologies -- 9.8 Unifying aspects of discrete element methods -- 9.9 Concluding remarks -- References -- Chapter 10. Structural mechanics problems in one dimension- rods -- 10.1 Introduction -- 10.2 Governing equations -- 10.3 Weak (Galerkin) forms for rods -- 10.4 Finite element solution: Euler-Bernoulli rods -- 10.5 Finite element solution: Timoshenko rods -- 10.6 Forms without rotation parameters -- 10.7 Moment resisting frames -- 10.8 Concluding remarks -- References.

Chapter 11. Plate bending approximation: thin (Kirchhoff) plates and C1 continuity requirements -- 11.1 Introduction -- 11.2 The plate problem: thick and thin formulations -- 11.3 Rectangular element with corner nodes (12 degrees of freedom) -- 11.4 Quadrilateral and parallelogram elements -- 11.5 Triangular element with corner nodes (9 degrees of freedom) -- 11.6 Triangular element of the simplest form (6 degrees of freedom) -- 11.7 The patch test- an analytical requirement -- 11.8 Numerical examples -- 11.9 General remarks -- 11.10 Singular shape functions for the simple triangular element -- 11.11 An 18 degree-of-freedom triangular element with conforming shape functions -- 11.12 Compatible quadrilateral elements -- 11.13 Quasi-conforming elements -- 11.14 Hermitian rectangle shape function -- 11.15 The 21 and 18 degree-of-freedom triangle -- 11.16 Mixed formulations - general remarks -- 11.17 Hybrid plate elements -- 11.18 Discrete Kirchhoff constraints -- 11.19 Rotation-free elements -- 11.20 Inelastic material behaviour -- 11.21 Concluding remarks - which elements? -- References -- Chapter 12. 'Thick' Reissner-Mindlin plates - irreducible and mixed formulations -- 12.1 Introduction -- 12.2 The irreducible formulation- reduced integration -- 12.3 Mixed formulation for thick plates -- 12.4 The patch test for plate bending elements -- 12.5 Elements with discrete collocation constraints -- 12.6 Elements with rotational bubble or enhanced modes -- 12.7 Linked interpolation- an improvement of accuracy -- 12.8 Discrete 'exact' thin plate limit -- 12.9 Performance of various 'thick' plate elements - limitations of thin plate theory -- 12.10 Inelastic material behaviour -- 12.11 Concluding remarks - adaptive refinement -- References -- Chapter 13. Shells as an assembly of flat elements -- 13.1 Introduction.

13.2 Stiffness of a plane element in local coordinates -- 13.3 Transformation to global coordinates and assembly of elements -- 13.4 Local direction cosines -- 13.5 'Drilling' rotational stiffness - 6 degree-of-freedom assembly -- 13.6 Elements with mid-side slope connections only -- 13.7 Choice of element -- 13.8 Practical examples -- References -- Chapter 14. Curved rods and axisymmetric shells -- 14.1 Introduction -- 14.2 Straight element -- 14.3 Curved elements -- 14.4 Independent slope-displacement interpolation with penalty functions (thick or thin shell formulations) -- References -- Chapter 15. Shells as a special case of three-dimensional analysis - Reissner-Mindlin assumptions -- 15.1 Introduction -- 15.2 Shell element with displacement and rotation parameters -- 15.3 Special case of axisymmetric, curved, thick shells -- 15.4 Special case of thick plates -- 15.5 Convergence -- 15.6 Inelastic behaviour -- 15.7 Some shell examples -- 15.8 Concluding remarks -- References -- Chapter 16. Semi-analytical finite element processes - use of orthogonal functions and 'finite strip' methods -- 16.1 Introduction -- 16.2 Prismatic bar -- 16.3 Thin membrane box structures -- 16.4 Plates and boxes with flexure -- 16.5 Axisymmetric solids with non-symmetrical load -- 16.6 Axisymmetric shells with non-symmetrical load -- 16.7 Concluding remarks -- References -- Chapter 17. Non-linear structural problems - large displacement and instability -- 17.1 Introduction -- 17.2 Large displacement theory of beams -- 17.3 Elastic stability - energy interpretation -- 17.4 Large displacement theory of thick plates -- 17.5 Large displacement theory of thin plates -- 17.6 Solution of large deflection problems -- 17.7 Shells -- 17.8 Concluding remarks -- References -- Chapter 18. Multiscale modelling -- 18.1 Introduction -- 18.2 Asymptotic analysis.

18.3 Statement of the problem and assumptions -- 18.4 Formalism of the homogenization procedure -- 18.5 Global solution -- 18.6 Local approximation of the stress vector -- 18.7 Finite element analysis applied to the local problem -- 18.8 The non-linear case and bridging over several scales -- 18.9 Asymptotic homogenization at three levels: micro, meso and macro -- 18.10 Recovery of the micro description of the variables of the problem -- 18.11 Material characteristics and homogenization results -- 18.12 Multilevel procedures which use homogenization as an ingredient -- 18.13 General first-order and second-order procedures -- 18.14 Discrete-to-continuum linkage -- 18.15 Local analysis of a unit cell -- 18.16 Homogenization procedure - definition of successive yield surfaces -- 18.17 Numerically developed global self-consistent elastic-plastic constitutive law -- 18.18 Global solution and stress-recovery procedure -- 18.19 Concluding remarks -- References -- Chapter 19. Computer procedures for finite element analysis -- 19.1 Introduction -- 19.2 Solution of non-linear problems -- 19.3 Eigensolutions -- 19.4 Restart option -- 19.5 Concluding remarks -- References -- Appendix A. Isoparametric finite element approximations -- Appendix B. Invariants of second-order tensors -- Author index -- Subject index -- Colour Plates.