كتاب Non-linear Finite Element Analysis of Solids and Structures
منتدى هندسة الإنتاج والتصميم الميكانيكى
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 كتاب Non-linear Finite Element Analysis of Solids and Structures

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تاريخ التسجيل : 01/07/2009
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مُساهمةموضوع: كتاب Non-linear Finite Element Analysis of Solids and Structures   الأربعاء 18 أبريل 2012, 3:22 pm

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Non-linear Finite Element Analysis of Solids and Structures
Vol 2- MA Crisfield

ويتناول الموضوعات الأتية :

More continuum mechanics
Relationships between some strain measures and the structures
Large strains and the Jaumann rate
Hyperelasticity
The Truesdell rate
Conjugate stress and strain measures with emphasis on isotropic
conditions
Further work on conjugate stress and strain measures
Relationship between i: and U
Relationship between the Bio! stress, B and the Kirchhoff stress, T
Relationship between U, the i’s and the spin of the Lagrangian
triad, W,
Relationship between €, the A’s and the spin, W,
Relationship between ,the ’s and the spin, W,
Relationship between €and E
Specific strain measures
Conjugate stress measures
Using log,V with isotropy
Other stress rates and objectivity
Special notation
References
Non-orthogonal coordinates and CO- and contravariant tensor
components
Non-orthogonal coordinates
Transforming the components of a vector (first-order tensor) to a new set of
base vectors
Second-order tensors in non-orthogonal coordinates
Transforming the components of a second-order tensor to a new set of
base vectors
The metric tensor
Work terms and the trace operation
vi CONTENTS
Covariant components, natural coordinates and the Jacobian
Green’s strain and the deformation gradient
Recovering the standard cartesian expressions
The second Piola-Kirchhoff stresses and the variation of the Green’s
strain
Transforming the components of the constitutive tensor
A simple two-dimensional example involving skew coordinates
Special notation
References
More finite element analysis of continua
A summary of the key equations for the total Lagrangian formulation
The internal force vector
The tangent stiffness matrix
The internal force vector for the ‘Eulerian formulation’
The tangent stiffness matrix in relation to the Truesdell rate of Kirchhoff
stress
Continuum derivation of the tangent stiffness matrix
Discretised derivation of the tangent stiffness matrix
The tangent stiffness matrix using the Jaumann rate of Kirchhoff stress
Alternative derivation of the tangent stiffness matrix
The tangent stiffness matrix using the Jaumann rate of Cauchy stress
Alternative derivation of the tangent stiffness matrix
Convected coordinates and the total Lagrangian formulation
Element formulation
The tangent stiffness matrix
Extensions to three dimensions
Special notation
References
Large strains, hyperelasticity and rubber
Introduction to hyperelasticity
Using the principal stretch ratios
Splitting the volumetric and deviatoric terms
Development using second Piola-Kirchhoff stresses and Green’s
strains
Plane strain
Plane stress with incompressibility
Total Lagrangian finite element formulation
A mixed formulation
A hybrid formulation
Developments using the Kirchhoff stress
A ‘Eulerian’ finite element formulation
Working directly with the principal stretch ratios
The compressible ‘neo-Hookean model’
Using the Green strain relationships in the principal directions
Transforming the tangent constitutive relationships for a ‘Eulerian formulation’
Examples
A simple example
The compressible neo-Hookean model
Further work with principal stretch ratios
An enerav function usina the DrinciPal loa strains fthe Henckv model)
CONTENTS vii
Ogden’s energy function
An example using Hencky’s model
Special notation
References
More plasticity and other material non-linearity-I
Introduction
Other isotropic yield criteria
The flow rules
The matrix ?a/(%
Yield functions with corners
A backward-Euler return with two active yield surfaces
A consistent tangent modular matrix with two active yield surfaces
Yield functions for shells that use stress resultants
The one-dimensional case
The two-dimensional case
A backward-Euler return with the lllyushin yield function
A backward-Euler return and consistent tangent matrix for
the llyushin yield criterion when two yield surfaces are active
Implementing a form of backward-Euler procedure for the
Mohr-Coulomb yield criterion
Implementing a two-vectored return
A return from a corner or to the apex
A consistent tangent modular matrix following
a single-vector return
A consistent tangent matrix following a two-vectored return
A consistent tangent modular matrix following a return from a corner or
an apex
Yield criteria for anisotropic plasticity
Hill’s yield criterion
Hardening with Hill’s yield criterion
Hill’s yield criterion for plane stress
Possible return algorithms and consistent tangent modular matrices
The consistent tangent modular matrix
Hoffman’s yield criterion
The consistent tangent modular matrix
The Drucker-Prager yield criterion
Using an eigenvector expansion for the stresses
An example involving plane-stress plasticity and the von Mises
yield criterion
Cracking, fracturing and softening materials
Mesh dependency and alternative equilibrium states
‘Fixed’ and ‘rotating’ crack models in concrete
Relationship between the ‘rotating crack model’ and
a ‘deformation theory’ plasticity approach using the ‘square yield criterion’
A flow theory approach for the ‘square yield criterion’
Damage mechanics
Special notation
References
More plasticity and other material non-linearity-ll
Introduction
Mixed hardening
Kinematic hardening for plane stress
viii CONTENTS
Radial return with mixed linear hardening
Radial return with non-linear hardening
A general backward-Euler return with mixed linear hardening
A backward-Euler procedure for plane stress with mixed linear hardening
A consistent tangent modular tensor following the radial return of
Section
General form of the consistent tangent modular tensor
Overlay and other hardening models
Sophisticated overlay model
Relationship with conventional kinematic hardening
Other models
Computer exercises
Viscoplasticity
The consistent tangent matrix
Implementation
Special notation
References
Large rotations
Non-vectorial large rotations
A rotation matrix for small (infinitesimal) rotations
A rotation matrix for large rotations (Rodrigues formula)
The exponential form for the rotation matrix
Alternative forms for the rotation matrix
Approximations for the rotation matrix
Compound rotations
Obtaining the pseudo-vector from the rotation matrix, R
Quaternions and Euler parameters
Obtaining the normalised quarternion from the rotation matrix
Additive and non-additive rotation increments
The derivative of the rotation matrix
Rotating a triad so that one unit vector moves to a specified unit vector
via the ‘smallest rotation’
Curvature
Expressions for curvature that directly use nodal triads
Curvature without nodal triads
Special notation
Refe rences
Three-dimensional formulations for beams and rods
A co-rotational framework for three-dimensional beam elements
Computing the local ‘displacements’
Computation of the matrix connecting the infinitesimal local
and global variables
The tangent stiffness matrix
Numerical implementation of the rotational updates
Overall solution strategy with a non-linear ‘local element’ formulation
Possible simplifications
An interpretation of an element due to Simo and Vu-Quoc
The finite element variables
Axial and shear strains
Curvature
CONTENTS ix
Virtual work and the internal force vector
The tangent stiffness matrix
An isoparametric formulation
An isoparametric Timoshenko beam approach using the total
Lagrangian formulation
The tangent stiffness matrix
An outline of the relationship with the formulation of
Dvorkin et al
Symmetry and the use of different ‘rotation variables’
A simple model showing symmetry and non-symmetry
Using additive rotation components
Considering symmetry at equilibrium for the element of Section
Using additive (in the limit) rotation components with the element
of Section
Various forms of applied loading including ‘follower levels’
Point loads applied at a node
Concentrated moments applied at a node
Gravity loading with co-rotational elements
Introducing joints
Special notation
References
More on continuum and shell elements
Introduction
A co-rotational approach for two-dimensional continua
A co-rotational approach for three-dimensional continua
A co-rotational approach for a curved membrane using facet triangles
A co-rotational approach for a curved membrane using quadrilaterals
A co-rotational shell formulation with three rotational degrees
of freedom per node
A co-rotational facet shell formulation based on Morley’s triangle
A co-rotational shell formulation with two rotational degrees
of freedom per node
A co-rotational framework for the semi-loof shells
An alternative co-rotational framework for three-dimensional beams
Two-dimensional beams
Incompatible modes, enhanced strains and substitute strains for
continuum elements
Incompatible modes
Enhanced strains
Substitute functions
Numerical comparisons
Introducing extra internal variables into the co-rotational formulation
Introducing extra internal variables into the Eulerian formulation
Introducing large elastic strains into the co-rotational formulation
A simple stability test and alternative enhanced F formulations
Special notation
References
Large strains and plasticity
Introduction
The multiplicative F,F, approach
X CONTENTS
Using the F,F, approach to arrive at the conventional ‘rate form’
Using the rate form with an ‘explicit dynamic code’
Integrating the rate equations
An F,F, update based on the intermediate configuration
An F,F, update based on the final (current) configuration
The flow rule
The consistent tangent
The limiting case
Introducing large elasto-plastic strains into the finite element
formulation
A simple example
Special notation
References
Stability theory
Introduction
General theory without ‘higher-order terms’
Limit point
Bifurcation point
The introduction of higher-order terms
Classification of singular points
Limit points
Bifurcation points
Symmetric bifurcations
Asymmetric bifurcations
Computation of higher-order derivatives for truss elements
Amplification of notation
Truss element using Green’s strain
Truss elements using a rotated engineering strain
Computationof the stability coefficients S,-S,
Special notation
References
Branch switching and further advanced solution procedures
Indirect computation of singular points
Simple branch switching
Corrector based on a linearised arc-length method
Corrector using displacement control at a specified variable
Corrector using a ‘cylindrical arc-length method’
Branch switching using higher-order derivatives
General predictors using higher-order derivatives
Load control
Displacement control at a specified variable
The ‘cylindrical arc-length method’
Correctors using higher-order derivatives
Direct computation of the singular points
Line-searches with arc-length and similar methods
Line-searches with the RiksMlempner arc-length method
Line-searches with the cylindrical arc-length method
Uphill or downhill?
Alternative arc-length methods using relative variables
An alternative method for choosing the root for the cylindrical
arc-length method
CONTENTS xi
Statiddynamic solution procedures
Special notation (see also Section )
References
Examples from an updated non-linear finite element computer
program using truss elements
(written in conjunction with Dr Jun Shi)
A two-bar truss with an asymmetric bifurcation
Bracketing
Branch switching
The von Mises truss
Bracketing
Branch switching
A three-dimensional dome
Bracketing
Branch switching
The higher-order predictor
The higher-order correctors
Line searches
A three-dimensional arch truss
A two-dimensional circular arch
References
Contact with friction
Introduction
A two-dimensional frictionless contact formulation using a penalty approach
Some modifications
The ‘contact patch test’
Introducing ‘sticking friction’ in two dimensions
Introducing Coulomb ‘sliding friction’ in two dimensions
Using Lagrangian multipliers instead of the penalty approach
The augmented Lagrangian methods
An augmented Lagrangian technique with Coulomb ’sliding friction’
A symmetrised version
A three-dimensional frictionless contact formulation using a penalty
approach
The consistent tangent matrix
Adding ‘sticking friction’ in three dimensions
The consistent tangent matrix
Coulomb ‘sliding friction’ in three dimensions
A penalty/barrier method for contact
Amendments to the solution procedures
Special notation
References
Non-linear dynamics
Introduction
Newmark’s method
The ‘average acceleration method’ or ‘trapezoidal rule’
The ‘implicit solution procedure’
xii CONTENTS
The ‘predictor step’
The ‘corrector’
An explicit solution procedure
A staggered, central difference, explicit solution procedure
Stability
The Hilber-Hughes-Taylor s( method
More on the dynamic equilibrium equations
An energy conserving total Lagrangian formulation
The ‘predictor step’
The ‘corrector’
A co-rotational energy-conserving procedure for two-dimensional beams
Sophistications
Numerical solution
An alternative energy-conserving procedure for two-dimensional beams
Automatic time-stepping
Dynamic equilibrium with rotations
An ‘explicit co-rotational procedure’ for beams
Updating the rotational velocities and accelerations
A simple implicit co-rotational procedure using rotations
An isoparametric formulation for three-dimensional beams
An alternative implicit co-rotational formulation
(Approximately) energy-conserving co-rotational procedures
Energy-conserving isoparametric formulations
Special notation
References

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الجامعة : المنوفية

مُساهمةموضوع: رد: كتاب Non-linear Finite Element Analysis of Solids and Structures   الجمعة 02 نوفمبر 2012, 10:17 pm

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الجامعة : المنيا

مُساهمةموضوع: رد: كتاب Non-linear Finite Element Analysis of Solids and Structures   الجمعة 02 نوفمبر 2012, 10:25 pm

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مُساهمةموضوع: رد: كتاب Non-linear Finite Element Analysis of Solids and Structures   الجمعة 02 نوفمبر 2012, 10:26 pm

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