Author Biography
Dedication
List of Figures
List of Tables
Preface
Chapter 1. General Problems in Solid Mechanics and Nonlinearity
Abstract
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
References
Chapter 2. Galerkin Method of Approximation: Irreducible and Mixed Forms
Abstract
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
References
Chapter 3. Solution of Nonlinear Algebraic Equations
Abstract
3.1 Introduction
3.2 Iterative techniques
3.3 General remarks: Incremental and rate methods
References
Chapter 4. Inelastic and Nonlinear Materials
Abstract
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
References
Chapter 5. Geometrically Nonlinear Problems: Finite Deformation
Abstract
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
References
Chapter 6. Material Constitution for Finite Deformation
Abstract
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. Material Constitution Using Representative Volume Elements
Abstract
7.1 Introduction
7.2 Coupling between scales
7.3 Quasi-harmonic problems
7.4 Numerical examples
7.5 Concluding remarks
References
Chapter 8. Treatment of Constraints: Contact and Tied Interfaces
Abstract
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
References
Chapter 9. Pseudo-Rigid and Rigid-Flexible Bodies
Abstract
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
References
Chapter 10. Background Mathematics and Linear Shell Theory
Abstract
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
References
Chapter 11. Differential Geometry and Calculus on Manifolds
Abstract
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
References
Chapter 12. Geometrically Nonlinear Problems in Continuum Mechanics
Abstract
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
References
Chapter 13. A Nonlinear Geometrically Exact Rod Model
Abstract
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
References
Chapter 14. A Nonlinear Geometrically Exact Shell Model
Abstract
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
References
Chapter 15. Computer Procedures for Finite Element Analysis
Abstract
15.1 Introduction
15.2 Solution of nonlinear problems
15.3 Eigensolutions
15.4 Restart option
15.5 Concluding remarks
References
Appendix A. Isoparametric Finite Element Approximations
Abstract
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
Abstract
B.1 Principal invariants
B.2 Moment invariants
B.3 Derivatives of invariants
References
Author Index
Subject Index
· · · · · · (
收起)
还没人写过短评呢