1. Introduction
2. Kinematics
3. Forces and stresses
4. Constitutive equations
5. Plasticity formulations
6. Finite element formulation: large deformation, large rotation problem
7. Finite element formulation: small deformation, large rotation problem.
PREFACE ix
1 INTRODUCTION 1
1.1 Matrices / 2
1.2 Vectors / 6
1.3 Summation Convention / 11
1.4 Cartesian Tensors / 12
1.5 Polar Decomposition Theorem / 21
1.6 D'Alembert's Principle / 23
1.7 Virtual Work Principle / 29
1.8 Approximation Methods / 32
1.9 Discrete Equations / 34
1.10 Momentum, Work, and Energy / 37
1.11 Parameter Change and Coordinate Transformation / 39
Problems / 43
2 KINEMATICS 47
2.1 Motion Description / 48
2.2 Strain Components / 55
2.3 Other Deformation Measures / 60
2.4 Decomposition of Displacement / 62
2.5 Velocity and Acceleration / 64
2.6 Coordinate Transformation / 68
2.7 Objectivity / 74
2.8 Change of Volume and Area / 77
2.9 Continuity Equation / 81
2.10 Reynolds' Transport Theorem / 82
2.11 Examples of Deformation / 84
2.12 Important Geometry Concepts / 92
Problems / 94
3 FORCES AND STRESSES 97
3.1 Equilibrium of Forces / 97
3.2 Transformation of Stresses / 100
3.3 Equations of Equilibrium / 100
3.4 Symmetry of the cauchy Stress Tensor / 102
3.5 Virtual Work of the Forces / 103
3.6 Deviatoric Stresses / 113
3.7 Stress Objectivity / 115
3.8 Energy Balance / 119
Problems / 120
4 CONSTITUTIVE EQUATIONS 123
4.1 Generalized Hooke's Law / 124
4.2 Anisotropic Linearly Elastic Materials / 126
4.3 Material Symmetry / 127
4.4 Homogeneous Isotropic Material / 129
4.5 Principal Strain Invariants / 136
4.6 Special Material Models for Large Deformations / 137
4.7 Linear Viscoelasticity / 141
4.8 Nonlinear Viscoelasticity / 155
4.9 A Simple Viscoelastic Model for Isotropic Materials / 161
4.10 Fluid Constitutive Equations / 162
4.11 Navier-Stokes Equations / 164
Problems / 164
5 FINITE ELEMENT FORMULATION: LARGE-DEFORMATION, LARGE-ROTATION PROBLEM 167
5.1 Displacement Field / 169
5.2 Element Connectivity / 176
5.3 Inertia and Elastic Forces / 178
5.4 Equations of Motion / 180
5.5 Numerical Evaluation of The Elastic Forces / 188
5.6 Finite Elements and Geometry / 193
5.7 Two-Dimensional Euler-Bernoulli Beam Element / 199
5.8 Two-Dimensional Shear Deformable Beam Element / 203
5.9 Three-Dimensional Cable Element / 205
5.10 Three-Dimensional Beam Element / 206
5.11 Thin-Plate Element / 208
5.12 Higher-Order Plate Element / 210
5.13 Brick Element / 211
5.14 Element Performance / 212
5.15 Other Finite Element Formulations / 216
5.16 Updated Lagrangian and Eulerian Formulations / 218
5.17 Concluding Remarks / 221
Problems / 223
6 FINITE ELEMENT FORMULATION: SMALL-DEFORMATION, LARGE-ROTATION PROBLEM 225
6.1 Background / 226
6.2 Rotation and Angular Velocity / 229
6.3 Floating Frame of Reference (FFR) / 234
6.4 Intermediate Element Coordinate System / 236
6.5 Connectivity and Reference Conditions / 238
6.6 Kinematic Equations / 243
6.7 Formulation of The Inertia Forces / 245
6.8 Elastic Forces / 248
6.9 Equations of Motion / 250
6.10 Coordinate Reduction / 251
6.11 Integration of Finite Element and Multibody System Algorithms / 253
Problems / 258
7 COMPUTATIONAL
