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End User License Agreement
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
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