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by Ahmed A. Shabana
Computational Continuum Mechanics, 3rd Edition
COVER
TITLE PAGE
COPYRIGHT
PREFACE
CHAPTER 1: INTRODUCTION
1.1 MATRICES
1.2 VECTORS
1.3 SUMMATION CONVENTION
1.4 CARTESIAN TENSORS
1.5 POLAR DECOMPOSITION THEOREM
1.6 D'ALEMBERT'S PRINCIPLE
1.7 VIRTUAL WORK PRINCIPLE
1.8 APPROXIMATION METHODS
1.9 DISCRETE EQUATIONS
1.10 MOMENTUM, WORK, AND ENERGY
1.11 PARAMETER CHANGE AND COORDINATE TRANSFORMATION
PROBLEMS
CHAPTER 2: KINEMATICS
2.1 MOTION DESCRIPTION
2.2 STRAIN COMPONENTS
2.3 OTHER DEFORMATION MEASURES
2.4 DECOMPOSITION OF DISPLACEMENT
2.5 VELOCITY AND ACCELERATION
2.6 COORDINATE TRANSFORMATION
2.7 OBJECTIVITY
2.8 CHANGE OF VOLUME AND AREA
2.9 CONTINUITY EQUATION
2.10 REYNOLDS' TRANSPORT THEOREM
2.11 EXAMPLES OF DEFORMATION
2.12 GEOMETRY CONCEPTS
PROBLEMS
CHAPTER 3: FORCES AND STRESSES
3.1 EQUILIBRIUM OF FORCES
3.2 TRANSFORMATION OF STRESSES
3.3 EQUATIONS OF EQUILIBRIUM
3.4 SYMMETRY OF THE CAUCHY STRESS TENSOR
3.5 VIRTUAL WORK OF THE FORCES
3.6 DEVIATORIC STRESSES
3.7 STRESS OBJECTIVITY
3.8 ENERGY BALANCE
PROBLEMS
CHAPTER 4: CONSTITUTIVE EQUATIONS
4.1 GENERALIZED HOOKE'S LAW
4.2 ANISOTROPIC LINEARLY ELASTIC MATERIALS
4.3 MATERIAL SYMMETRY
4.4 HOMOGENEOUS ISOTROPIC MATERIAL
4.5 PRINCIPAL STRAIN INVARIANTS
4.6 SPECIAL MATERIAL MODELS FOR LARGE DEFORMATIONS
4.7 LINEAR VISCOELASTICITY
4.8 NONLINEAR VISCOELASTICITY
4.9 A SIMPLE VISCOELASTIC MODEL FOR ISOTROPIC MATERIALS
4.10 FLUID CONSTITUTIVE EQUATIONS
4.11 NAVIER–STOKES EQUATIONS
PROBLEMS
CHAPTER 5: FINITE ELEMENT FORMULATION: LARGE-DEFORMATION, LARGE-ROTATION PROBLEM
5.1 DISPLACEMENT FIELD
5.2 ELEMENT CONNECTIVITY
5.3 INERTIA AND ELASTIC FORCES
5.4 EQUATIONS OF MOTION
5.5 NUMERICAL EVALUATION OF THE ELASTIC FORCES
5.6 FINITE ELEMENTS AND GEOMETRY
5.7 TWO-DIMENSIONAL EULER–BERNOULLI BEAM ELEMENT
5.8 TWO-DIMENSIONAL SHEAR DEFORMABLE BEAM ELEMENT
5.9 THREE-DIMENSIONAL CABLE ELEMENT
5.10 THREE-DIMENSIONAL BEAM ELEMENT
5.11 THIN-PLATE ELEMENT
5.12 HIGHER-ORDER PLATE ELEMENT
5.13 BRICK ELEMENT
5.14 ELEMENT PERFORMANCE
5.15 OTHER FINITE ELEMENT FORMULATIONS
5.16 UPDATED LAGRANGIAN AND EULERIAN FORMULATIONS
5.17 CONCLUDING REMARKS
PROBLEMS
CHAPTER 6: FINITE ELEMENT FORMULATION: SMALL-DEFORMATION, LARGE-ROTATION PROBLEM
6.1 BACKGROUND
6.2 ROTATION AND ANGULAR VELOCITY
6.3 FLOATING FRAME OF REFERENCE (FFR)
6.4 INTERMEDIATE ELEMENT COORDINATE SYSTEM
6.5 CONNECTIVITY AND REFERENCE CONDITIONS
6.6 KINEMATIC EQUATIONS
6.7 FORMULATION OF THE INERTIA FORCES
6.8 ELASTIC FORCES
6.9 EQUATIONS OF MOTION
6.10 COORDINATE REDUCTION
6.11 INTEGRATION OF FINITE ELEMENT AND MULTIBODY SYSTEM ALGORITHMS
PROBLEMS
CHAPTER 7: COMPUTATIONAL GEOMETRY AND FINITE ELEMENT ANALYSIS
7.1 GEOMETRY AND FINITE ELEMENT METHOD
7.2 ANCF GEOMETRY
7.3 BEZIER GEOMETRY
7.4 B-SPLINE CURVE REPRESENTATION
7.5 CONVERSION OF B-SPLINE GEOMETRY TO ANCF GEOMETRY
7.6 ANCF AND B-SPLINE SURFACES
7.7 STRUCTURAL AND NONSTRUCTURAL DISCONTINUITIES
PROBLEMS
CHAPTER 8: PLASTICITY FORMULATIONS
8.1 ONE-DIMENSIONAL PROBLEM
8.2 LOADING AND UNLOADING CONDITIONS
8.3 SOLUTION OF THE PLASTICITY EQUATIONS
8.4 GENERALIZATION OF THE PLASTICITY THEORY: SMALL STRAINS
8.5 J2 FLOW THEORY WITH ISOTROPIC/KINEMATIC HARDENING
8.6 NONLINEAR FORMULATION FOR HYPERELASTIC–PLASTIC MATERIALS
8.7 HYPERELASTIC–PLASTIC J2 FLOW THEORY
PROBLEMS
REFERENCES
INDEX
End User License Agreement
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COVER
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TITLE PAGE
TABLE OF CONTENTS
COVER
TITLE PAGE
COPYRIGHT
PREFACE
CHAPTER 1: INTRODUCTION
1.1 MATRICES
1.2 VECTORS
1.3 SUMMATION CONVENTION
1.4 CARTESIAN TENSORS
1.5 POLAR DECOMPOSITION THEOREM
1.6 D'ALEMBERT'S PRINCIPLE
1.7 VIRTUAL WORK PRINCIPLE
1.8 APPROXIMATION METHODS
1.9 DISCRETE EQUATIONS
1.10 MOMENTUM, WORK, AND ENERGY
1.11 PARAMETER CHANGE AND COORDINATE TRANSFORMATION
PROBLEMS
CHAPTER 2: KINEMATICS
2.1 MOTION DESCRIPTION
2.2 STRAIN COMPONENTS
2.3 OTHER DEFORMATION MEASURES
2.4 DECOMPOSITION OF DISPLACEMENT
2.5 VELOCITY AND ACCELERATION
2.6 COORDINATE TRANSFORMATION
2.7 OBJECTIVITY
2.8 CHANGE OF VOLUME AND AREA
2.9 CONTINUITY EQUATION
2.10 REYNOLDS' TRANSPORT THEOREM
2.11 EXAMPLES OF DEFORMATION
2.12 GEOMETRY CONCEPTS
PROBLEMS
CHAPTER 3: FORCES AND STRESSES
3.1 EQUILIBRIUM OF FORCES
3.2 TRANSFORMATION OF STRESSES
3.3 EQUATIONS OF EQUILIBRIUM
3.4 SYMMETRY OF THE CAUCHY STRESS TENSOR
3.5 VIRTUAL WORK OF THE FORCES
3.6 DEVIATORIC STRESSES
3.7 STRESS OBJECTIVITY
3.8 ENERGY BALANCE
PROBLEMS
CHAPTER 4: CONSTITUTIVE EQUATIONS
4.1 GENERALIZED HOOKE'S LAW
4.2 ANISOTROPIC LINEARLY ELASTIC MATERIALS
4.3 MATERIAL SYMMETRY
4.4 HOMOGENEOUS ISOTROPIC MATERIAL
4.5 PRINCIPAL STRAIN INVARIANTS
4.6 SPECIAL MATERIAL MODELS FOR LARGE DEFORMATIONS
4.7 LINEAR VISCOELASTICITY
4.8 NONLINEAR VISCOELASTICITY
4.9 A SIMPLE VISCOELASTIC MODEL FOR ISOTROPIC MATERIALS
4.10 FLUID CONSTITUTIVE EQUATIONS
4.11 NAVIER–STOKES EQUATIONS
PROBLEMS
CHAPTER 5: FINITE ELEMENT FORMULATION: LARGE-DEFORMATION, LARGE-ROTATION PROBLEM
5.1 DISPLACEMENT FIELD
5.2 ELEMENT CONNECTIVITY
5.3 INERTIA AND ELASTIC FORCES
5.4 EQUATIONS OF MOTION
5.5 NUMERICAL EVALUATION OF THE ELASTIC FORCES
5.6 FINITE ELEMENTS AND GEOMETRY
5.7 TWO-DIMENSIONAL EULER–BERNOULLI BEAM ELEMENT
5.8 TWO-DIMENSIONAL SHEAR DEFORMABLE BEAM ELEMENT
5.9 THREE-DIMENSIONAL CABLE ELEMENT
5.10 THREE-DIMENSIONAL BEAM ELEMENT
5.11 THIN-PLATE ELEMENT
5.12 HIGHER-ORDER PLATE ELEMENT
5.13 BRICK ELEMENT
5.14 ELEMENT PERFORMANCE
5.15 OTHER FINITE ELEMENT FORMULATIONS
5.16 UPDATED LAGRANGIAN AND EULERIAN FORMULATIONS
5.17 CONCLUDING REMARKS
PROBLEMS
CHAPTER 6: FINITE ELEMENT FORMULATION: SMALL-DEFORMATION, LARGE-ROTATION PROBLEM
6.1 BACKGROUND
6.2 ROTATION AND ANGULAR VELOCITY
6.3 FLOATING FRAME OF REFERENCE (FFR)
6.4 INTERMEDIATE ELEMENT COORDINATE SYSTEM
6.5 CONNECTIVITY AND REFERENCE CONDITIONS
6.6 KINEMATIC EQUATIONS
6.7 FORMULATION OF THE INERTIA FORCES
6.8 ELASTIC FORCES
6.9 EQUATIONS OF MOTION
6.10 COORDINATE REDUCTION
6.11 INTEGRATION OF FINITE ELEMENT AND MULTIBODY SYSTEM ALGORITHMS
PROBLEMS
CHAPTER 7: COMPUTATIONAL GEOMETRY AND FINITE ELEMENT ANALYSIS
7.1 GEOMETRY AND FINITE ELEMENT METHOD
7.2 ANCF GEOMETRY
7.3 BEZIER GEOMETRY
7.4 B-SPLINE CURVE REPRESENTATION
7.5 CONVERSION OF B-SPLINE GEOMETRY TO ANCF GEOMETRY
7.6 ANCF AND B-SPLINE SURFACES
7.7 STRUCTURAL AND NONSTRUCTURAL DISCONTINUITIES
PROBLEMS
CHAPTER 8: PLASTICITY FORMULATIONS
8.1 ONE-DIMENSIONAL PROBLEM
8.2 LOADING AND UNLOADING CONDITIONS
8.3 SOLUTION OF THE PLASTICITY EQUATIONS
8.4 GENERALIZATION OF THE PLASTICITY THEORY: SMALL STRAINS
8.5
J
2
FLOW THEORY WITH ISOTROPIC/KINEMATIC HARDENING
8.6 NONLINEAR FORMULATION FOR HYPERELASTIC–PLASTIC MATERIALS
8.7
HYPERELASTIC–PLASTIC
J
2
FLOW THEORY
PROBLEMS
REFERENCES
INDEX
End User License Agreement
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Guide
Cover
Table of Contents
Preface
Begin Reading
List of Illustrations
CHAPTER 1: INTRODUCTION
Figure 1 Rigid-body coordinates
Figure 2 Two-dimensional beam
Figure 3 Space curve
Figure 4 Slider crank mechanism
Figure 5 Deformation measurement.
CHAPTER 2: KINEMATICS
Figure 1 Reference and current configurations
Figure 2 Planar beam
Figure 3 Rigid-body motion
Figure 4 Floating frame of reference
Figure 5 One current configuration and two reference coordinate systems (strain transformation)
Figure 6 Two current configurations and one reference coordinate system (objectivity)
Figure 7 Nanson's formula
Figure 8 Initial geometry
Figure 9 Geometry description
CHAPTER 3: FORCES AND STRESSES
Figure 1 Surface traction
Figure 2 Tetrahedral surface forces
Figure 3 Surface forces
CHAPTER 4: CONSTITUTIVE EQUATIONS
Figure 1 Standard model
Figure 2 Generalization
CHAPTER 5: FINITE ELEMENT FORMULATION: LARGE-DEFORMATION, LARGE-ROTATION PROBLEM
Figure 1 Finite element discretization
Figure 2 Three-dimensional beam element
Figure 3 Element connectivity
Figure 4 Initial geometry
Figure 5 ANCF description of curved geometry
Figure 6 Surface geometry. (a) Elliptic surface, (b) hyperbolic surface, (c) parabolic surface, and (d) planar surface
Figure 7 Plate element
Figure 8 ANCF brick element
Figure 9 ANCF total Lagrangian fluid simulation (Wei et al., 2015)
Figure 10 Tracked vehicles
Figure 11 Tire assembly
CHAPTER 6: FINITE ELEMENT FORMULATION: SMALL-DEFORMATION, LARGE-ROTATION PROBLEM
Figure 1 Two-dimensional beam element
Figure 2 Floating frame of reference
Figure 3 Body kinematics
Figure 4 Intermediate element coordinate system
Figure 5 Slider crank mechanism
Figure 6 Scaling of the elastic coordinates
Figure 7 Liquid sloshing results using ANCF finite elements (Wei et al., 2015)
Figure 8 Liquid sloshing results using the FFR formulation (Wei et al., 2015)
CHAPTER 7: COMPUTATIONAL GEOMETRY AND FINITE ELEMENT ANALYSIS
Figure 1 Gradients and control points
Figure 2 B-spline curve
Figure 3 Knot insertion
Figure 4 Structural and nonstructural discontinuities
CHAPTER 8: PLASTICITY FORMULATIONS
Figure 1 Intermediate plastic configuration
List of Tables
CHAPTER 5: FINITE ELEMENT FORMULATION: LARGE-DEFORMATION, LARGE-ROTATION PROBLEM
Table 1 ANCF Description of Curved Geometry
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