The Finite Element Method for Three-dimensional

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• The Finite Element Method for Three-dimensional
• Contents
• Preface
• 1.1 The Reference State
• 1.2 The Spatial State
• 1.3 Strain Measures
• 1.4 Principal Strains
• 1.5 Velocity
• 1.6 Objective Tensors
• 1.7 Balance Laws
• 1.8 Localization of the Balance Laws
• 1.9 The Stress Tensor
• 1.10 The Balance Laws in Material Coordinates
• 1.11 The Weak Form of the Balance of Momentum
• 1.12 The Weak Form of the Energy Balance
• 1.13 Constitutive Equations
• 1.14 Elastic Materials
• 1.15 Fluids
• 2 Linear Mechanical Applications
• 2.1 General Equations
• 2.2 The Shape Functions
• 2.3 Numerical Integration
• 2.4 Extrapolation of Integration Point Values to the Nodes
• 2.5 Problematic Element Behavior
• 2.6 Linear Constraints
• 2.7 Transformations
• 2.8 Loading
• 2.9 Modal Analysis
• 2.10 Cyclic Symmetry
• 2.11 Dynamics: The α-Method
• 3 Geometric Nonlinear Effects
• 3.1 General Equations
• 3.2 Application to a Snapping-through Plate
• 3.3 Solution-dependent Loading
• 3.4 Nonlinear Multiple Point Constraints
• 3.5 Rigid Body Motion
• 3.6 Mean Rotation
• 3.7 Kinematic Constraints
• 3.8 Incompressibility Constraint
• 4.1 Polyconvexity of the Stored-energy Function
• 4.2 Isotropic Hyperelastic Materials
• 4.3 Nonhomogeneous Shear Experiment
• 4.4 Derivatives of Invariants and Principal Stretches
• 4.5 Tangent Stiffness Matrix at Zero Deformation
• 4.6 Inflation of a Balloon
• 4.7 Anisotropic Hyperelasticity
• 5 Infinitesimal Strain Plasticity
• 5.1 Introduction
• 5.2 The General Framework of Plasticity
• 5.3 Three-dimensional Single Surface Viscoplasticity
• 5.4 Three-dimensional Multisurface Viscoplasticity: the Cailletaud Single Crystal Model
• 5.5 Anisotropic Elasticity with a von Mises–type Yield Surface
• 6 Finite Strain Elastoplasticity
• 6.1 Multiplicative Decomposition of the Deformation Gradient
• 6.2 Deriving the Flow Rule
• 6.3 Isotropic Hyperelasticity with a von Mises–type Yield Surface
• 6.4 Extensions
• 6.5 Summary of the Equations
• 6.6 Stress Update Algorithm
• 6.7 Derivation of Consistent Elastoplastic Moduli
• 6.8 Isochoric Plastic Deformation
• 6.9 Burst Calculation of a Compressor
• 7 Heat Transfer
• 7.1 Introduction
• 7.2 The Governing Equations
• 7.3 Weak Form of the Energy Equation
• 7.4 Finite Element Procedure
• 7.5 Time Discretization and Linearization of the Governing Equation
• 7.6 Forced Fluid Convection
• 7.7 Cavity Radiation
• References
• Index

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