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INDEX
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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INDEX
Absolute coordinates
Absolute
nodal coordinate formulation
coupled deformation modes
Acceleration
Air pressure
Almansi strains
ANCF geometry
ANCF surfaces
ANCF-coupled deformation modes
Angular acceleration
Angular momentum
Angular velocity
Anisotropic linearly elastic material
Approximation methods
classical, finite–element method, Rayleigh–Ritz method
Finite element method
see
Finite element method
Rayleigh–Ritz method
see
Rayleigh–Ritz method
Arc length
Area change
Associative flow rule
see
Associative plasticity
Associative plasticity
Assumed displacement field
Assumed strain element
Assumed stress element
Axis of rotation
Back stress
Backward implicit Euler method
Basis functions
Bauschinger effect
Beam elements
three-dimensional
Beam elements (
Continued
)
two-dimensional
Beam
theory
Bernstein polynomials
Bezier geometry
Bezier method
Binomial vector
Biot stress
Blending functions
see
Basis functions
Body(s)
coordinate system
force
reference
rigid
Boolean matrix
Breakpoints
B-spline
surfaces
Bulk modulus
Bulk viscosity coefficient
Cable element
CAD
Cartesian tensor
Cauchy
elastic material
first law of motion
second law of motion
strain
stress
97
Cauchy stress formula
Cauchy–Green deformation tensor
left
right
Cayley-Hamilton theorem
Center of mass
Change of parameters
Characteristic equation
Characteristic values
see
Eigenvalues
Chebyshev polynomials
Cholesky coordinates
Chord frame
Classical theories
Component mode techniques
Computational geometry
Computer Aided Design
see
CAD
Connectivity conditions
Conservation of mass
Consistency condition
see
Persistency condition
Consistency parameter
Consistent mass
Constitutive equations
Constitutive integration algorithm
Continuity equation
Continuum forces
Control points
Control polygon
Control volume
Convective stress rate
Convective term
Convolution integral
see
Duhamel integral
Coordinate reduction
Coordinate transformation
Co-rotational frame
Coupled deformation modes
see
ANCF-coupled deformation modes
Creep function
Curvature
Gaussian
mean
normal
principal
radius of
surface
vector
Curved
beams
Curved configuration
Curved geometry
Curved structure
Curves
theory
D'Alembert's principle
deCasteljau algorithm
Decomposition of displacement
Deformation examples
Deformation measures
Deviatoric stresses
Dilatation
Direction cosines
Discontinuities
non-structural
structural
Discrete equations
Displacement
axial
bending
decomposition
field
fluid
general
gradients
homogeneous
isochoric
modes
nodal
planar
reference
rigid-body
transverse
228
virtual
Dissipation
Divergence operator
Divergence theorem
Double product
Duhamel integral
Dummy index
Dyadic product
see
Outer product
Dynamic coupling
see
Inertia coupling
Eigenvalue analysis
Eigenvalue problem
Eigenvalues
Eigenvectors
Elastic coefficients
Elastic coordinates
Elastic energy
Elastic force
power
Elastic limit
Elastic line approach
Elastic loading
Elastic mid-surface approach
Elastic predictor
Elasto-plastic tangent modulus
Embedding technique
Energy
balance
elastic
kinetic
strain
Engineering strain
Equations of equilibrium
Equations of
motion
for deformable bodies
for fluids
for particles
for rigid bodies
Equilibrium
equations of
force
Equivalent plastic strain
Euler angles
singularity
transformation matrix in terms of
Euler equation
Euler parameters
Euler–Bernoulli beam
Eulerian coordinates
Eulerian description
Eulerian formulation
Eulerian strain
Evolution equations
Extension
Finite difference method
Finite dimensional model
Finite element
assumed displacement
assumed strain
assumed stress
beam
Boolean matrix
brick
cable
connectivity conditions
formulation
generalized forces
gradient deficient
inertia shape integrals
intermediate coordinate system
isoparametric
large deformation
mass matrix
method
nodal coordinates
performance
plate
rectangular
reference conditions
shape function
shear deformable
solid
stiffness matrix
subparametric
superparametric
tetrahedral
triangular
Finite rotation
First fundamental form of surfaces
coefficients of
First Piola-Kirchhoff stress tensor
Floating frame
of reference
Flow rule
Flow stress
Fluid
constitutive equations
ideal
incompressible
inviscid
isotropic
Newtonian
Force
body
continuum
elastic
gravitational
inertia
magnetic
pressure
surface
Frame indifference
Free index
Frenet frame
Fundamental forms
first
second
Gauss quadrature
Gauss theorem
Gaussian curvature
Gauss-Legendre coefficients
General displacement
Generalized forces
Generalized Newton–Euler equations
Geometric interpretation of strains
Geometry
see
Computational geometry
Gradient coordinates
Gradient deficient finite element
Gradient of the displacement vector
Gravitational force
Green elastic material
Green-Lagrange strain tensor
Green–Naghdi stress rate
Hardening
isotropic
kinematic
linear
nonlinear
strain
Hellinger-Reissner principle
Hermite polynomials
Homogeneous displacement
Homogeneous material
Homogeneous motion
Hookean material
Hooke's law
Hourglass modes
Householder transformation
Huber-von Mises yield function
Hu-Washizu principle
Hybrid principles
see
Multifield variational principles
Hydrostatic pressure
Hyperelastic material
Hyperelastic potential
Hyperelastic-plastic material
Hypoelastic material
I-CAD-A
Ideal fluid
Impulse response function
Incompressibility
Inelastic material
Inertia
coupling
force
mass moment of
shape integrals
tensor
Infinitesimal
rotation
Infinitesimal strains
Intermediate element coordinate system
Intermediate plastic configuration
Internal variables
Interpolating polynomial
Invariants
strain
stress
tensor
Inviscid flow
Irrotational flow
Isochoric displacement
Isoparametric property
Isotropic fluid
Isotropic hardening
Isotropic material
Isotropic plastic modulus
J2 flow theory
isotropic/kinematic hardening
Jacobian matrix
Jaumann stress rate
Kelvin viscoelastic model
Kinematic analysis
Kinematic equations
Kinematic hardening
modulus
Kinematic viscosity
Kinematics
of deformable bodies
of rigid bodies
Kirchhoff stress
Knot insertion
Knot multiplicity
Knot vector
Kronecker delta
Kuhn-Tucker complementarity condition
Lagrange multipliers
Lagrange-D'Alembert equation
Lagrangian coordinates
Lagrangian description
Lagrangian formulation
total
updated
Lagrangian strain tensor
see
Green-Lagrange strain tensor
Lame's constants
Laquerre polynomials
Large deformation problem
Large rotation
Leaf spring, (AU: Not found)
Left Cauchy-Green strain tensor
Left stretch tensor
Legendre
coefficients
polynomials
Linear momentum
Linear structural systems
Linear theory of elastodynamics
Liquid sloshing
Loading and unloading conditions
Locking
membrane
shear
volumetric
Logarithmic strain
Lumped mass
Magnetic
force
Mass
center of
conservation of
consistent
lumped
matrix
moment of inertia
Material
anisotropic
Cauchy elastic
coordinates
Green elastic
homogeneous
Hookean
hyperelastic
hypoelastic
incompressible
inelastic
isotropic
Mooney-Rivlin
Neo-Hookean
symmetry
viscoelastic
Matrix
addition
adjoint
associative law
cofactor
determinant
diagonal
displacement vector gradients
elastic coefficients
identity
inverse
mass
minor
multiplication
null
orthogonal
position vector gradients
product
projection
rectangular
singular
skew symmetric
square
stiffness
symmetric
trace
transpose
unit
zero
Maxwell viscoelastic model
Mean curvature
Mean surface traction
Mechanics
particles
rigid bodies
Membrane locking
Mixed principles
see
Multi-field variational principles
Modal coordinates
Modal transformation
Mode shapes
Modulus of elasticity
see
Young's modulus
Modulus of rigidity
Mohr's circle
Moment of inertia
Momentum
Mooney-Rivlin material
Motion description
Multibody computer programs
flexible
Multibody system
Multi-field variational principles
Multiplicative
decomposition
Nanson's formula
Natural strain
Navier-Stokes equations
Neo-Hookean material
Neutral loading
Newton equation
Newton-Cotes formulas
Newton–Euler equations
Newton-Euler formulation
Newtonian fluid
Newtonian viscous fluid
Newton's second law
Nodal
coordinates
points
Nonconservative system
Nonhomogeneous motion
Non-incremental solution
Nonstructural discontinuities
Normal curvature
Normal strain
Normal stress
Numerical Solution
plasticity equations
NURBS
Objectivity
Oldroyd stress rate
Orthogonal matrix
Orthogonal transformation
improper
proper
Osculating plane
Outer product
Overstress function
Parallel axis theorem
Partial differential equations of equilibrium
Partial stress
Particle mechanics
Patch test
Penalty method
Perfect plasticity
Persistency condition
Physical stress
see
True stress
Piola transformation
Piola-Kirchhoff stress
Pitch angle
Planar analysis
Planar motion
Plane strain
Plane stress
Plastic corrector
Plastic flow rule
Plastic loading
Plastic strain
Plasticity
associative
equations
explicit solution
formulations
implicit solution
nonassociative
perfect
rate dependent
small strain
Plate element
thin
Point coordinates
Poisson effect
Poisson's ratio
Polar decomposition theorem
Position vector gradients,
see also
Matrix of position vector gradients
Power basis
Prager-Ziegler rule
Principal axes
Principal curvatures
Principal directions
Principal strain
Principal stress
Principal values
Principle of conservation of mass
Principle of virtual work
Projection
Matrix
Prony series
Proportional limit
Pullback
Push-forward
QR decomposition
Quadrature
Radius of curvature
Rate independent material
Rate of deformation
Rate-dependent
material
plasticity
Rayleigh–Ritz method
Rectangular element
Reduced integration
selective
Redundant coordinates
Reference conditions
Reference coordinate system
Reference coordinates
Reference motion
Reflection
Relaxation function
Relaxation time
Return mapping algorithm
radial
Reynolds' transport theorem
Right Cauchy-Green strain tensor
Right stretch tensor
Rigid body
dynamics
inertia
kinematics
mass matrix
motion
planar motion
translation
Rodriguez formula
Rodriguez parameters
Roll angle
Rotation
field
finite
infinitesimal
large
matrix
Scalar triple product
Second fundamental form of surfaces
coefficients of
Second Piola-Kirchhoff stress tensor
Selective reduced integration
Separation of
variables
Shape function
matrix
Shear
deformation
locking
modulus
strain
stress
viscosity coefficient
Shells
Simpson's rule
Singular point
Slider crank mechanism
Slip rate
Sloshing
Small deformation
Small strains
see
Infinitesimal strains
Solid element
Spatial coordinates
Spectral decomposition
Spin
tensor
Spurious singular modes
Standard viscoelastic model
Stiffness matrix
Stokes' relation
Strain
Almansi
auxiliary strain energy density function
Cauchy
components
energy
engineering
Eulerian
Geometric interpretation
Green–Lagrange
hardening
infinitesimal
invariants
logarithmic
natural
normal
plane
principal
shear
small
see
Infinitesimal strains
space formulation
transformation
vector
volumetric
Strain additive decomposition
Strain-displacement relationships
see
Constitutive equations
Stress
back
Biot
Cauchy
97
components
deviatoric
invariants
Kirchhoff
measures
normal
physical interpretation
Piola-Kirchhoff
plane
principal
rate
shear
space formulation
symmetry
transformation
true
update algorithm
vector
Stress–strain relationships
see
Constitutive equations
Stretch
Left
Right
tensor
Structural applications
Structural discontinuities
Structural systems
Subparametric finite element
Summation convention
Superparametric finite element
Surface
curvature
elliptic
hyperbolic
parabolic
planar
theory
Surface force
Surface traction
Symmetry of the stress tensor
Tangent elastoplastic modulus
Tangent frame
Tank car
Tensor
Almansi strain
alternating
antisymmetric
Cartesian
Cauchy strain
contraction
double product
Eulerian strain
Fourth-order
Green-Lagrange strain
higher order
identity
infinitesimal strain
invariants
isotropic
left Cauchy-Green strain
rate of deformation
right Cauchy-Green strain
second order
skew symmetric
spherical
spin
symmetric
third order
unit
see
Identity tensor
velocity gradient
Theory of curves
Theory of surfaces
Thin plate element
Tire
Torsion
Total Lagrangian formulation
Trace of matrix
Traction
Transformation matrix
planar
spatial
in terms of Euler angles
Translation
Transport term
Transpose of matrix
Tresca yield function
Triadic product
Trial stress
Triangular element
Triple product
True stress
Truesdell stress rate
Unit dyads
Updated Lagrangian formulation
Vector
cross product
dot product
dyadic product
inner product
length of
norm of
orthogonal
outer product
scalar product
unit
Velocity
angular
field
gradient
strain
transformation
virtual
Virtual displacement
Virtual power principle
Virtual velocity
Virtual work
of applied forces
of elastic forces
of inertia forces
principle
Viscoelastic material
Kelvin model
linear
Maxwell model
nonlinear
one-dimensional model
standard model
strain additive decomposition
Voigt model
Viscosity coefficient
Voigt viscoelastic model
Volume change
Volumetric locking
Volumetric strain
von Mises effective stress
von Mises yield function
Vorticity
Weak form
Weight
coefficients
factors
Work and energy
principle
Yaw angle
Yield condition
Yield criterion
Yield function
Huber-von Mises
Tresca
von Mises
Yield stress
Young's modulus
Zero energy modes
Ziegler's rule
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