The Finite Element Method for Solid and Structural Mechanics

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