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
References
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
10. Structural mechanics problems in one dimension - rods
10.1 Introduction
10.2 Governing equations
10.3 Weak (Gaierkin) 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
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 I8 degree-of-freedom triangular element with conforming shape functions
11.12 Compatible quadrilateral elements
11.13 Quasi-conforming elemems
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"para" label-module="para">
References
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
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
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
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
……
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 index2100433B
有限元方法在节理岩体隧洞力学分析中的应用
结构力学结构力学简介