كتاب Finite Element Method - Solid Mechanics

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Finite Element Method - Solid Mechanics
- Zienkiewicz and Taylor

كتاب Finite Element Method - Solid Mechanics 0c34444c61f00c

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General problems in solid mechanics and
non-linearity
Introduction
Small deformation non-linear solid mechanics
problems
Non-linear quasi-harmonic field problems
Some typical examples of transient
non-linear calculations
Concluding remarks
Solution of non-linear algebraic equations
Introduction
Iterative techniques
Inelastic and non-linear materials
Introduction
Viscoelasticity - history dependence of
deformation
Classical time-independent plasticity theory
Computation of stress increments
Isotropic plasticity models
Generalized plasticity - non-associative case
Some examples of plastic computation
Basic formulation of creep problems
Viscoplasticity - a generalization
Some special problems of brittle materials
Non-uniqueness and localization in
elasto-plastic deformations
Adaptive refinement and localization
(slip-line) capture
Non-linear quasi-harmonic field problems
Plate bending approximation: thin
(Kirchhoff) plates and C1 continuity
requirements
Introduction
The plate problem: thick and thin
formulations
Rectangular element with corner nodes (12
degrees of freedom)
Quadrilateral and parallelograpm .e..l.e..ments
Triangular element with corner nodes (9
degrees of freedom)
Triangular element of the simplest form (6
degrees of freedom)
The patch test - an analytical re..q..u..ir..ement
Numerical examples
General remarks
Singular shape functions for the simple
triangular element
An 18 degree-of-freedom triangular element
with conforming shape functions
Compatible quadrilateral elements
Quasi-conforming elements
Hermitian rectangle shape function
The 21 and 18 degree-of-freedom triangle
Mixed formulations - general remarks
Hybrid plate elements
Discrete Kirchhoff constraints
Rotation-free elements
Inelastic material behaviour
Concluding remarks - which elements?
’Thick’ Reissner - Mindlin plates - irreducible
and mixed formulations
Introduction
The irreducible formulation - reduced
integration
Mixed formulation for thick plates
The patch test for plate bending elements
Elements with discrete collocation constraints
Elements with rotational bubble or enhanced
modes
Linked interpolation - an improvement of
accuracy
Discrete ’exact’ thin plate limit
Performance of various ’thick’ plate elements
- limitations of twin plate theory
Forms without rotation parameters
Inelastic material behaviour
Concluding remarks - adaptive refinement
Shells as an assembly of flat elements
Introduction
Stiffness of a plane element in local
coordinates
Transformation to global coordinates and
assembly of elements
Local direction cosines
’Drilling’ rotational stiffness - 6
degree-of-freedom assembly
Elements with mid-side slope connections
only
Choice of element
Practical examples
Axisymmetric shells
Introduction
Straight element
Curved elements
Independent slope - displacement
interpolation with penalty functions (thick or
thin shell formulations)
Shells as a special case of
three-dimensional analysis -
Reissner-Mindlin assumptions
Introduction
Shell element with displacement and rotation
parameters
Special case of axisymmetric, curved, thick
shells
Special case of thick plates
Convergence
Inelastic behaviour
Some shell examples
Concluding remarks
Semi-analytical finite element processes -
use of orthogonal functions and ’finite strip’
methods
Introduction
Prismatic bar
Thin membrane box structures
Plates and boxes and flexure
Axisymmetric solids with non-symmetrical
load
Axisymmetric shells with non-symmetrical
load
Finite strip method - incomplete de..c..o..upling
Concluding remarks
Geometrically non-linear problems - finite
deformation
Introduction
Governing equations.
Variational description for finitite deformation
A three-field mixed finite deformation
forumation
A mixed-enhanced finite deformation
forumation
Forces dependent on deformation - pressure
loads
Material constitution for finite deformation
Contact problems
Numerical examples
Concluding remarks
Non-linear structural problems - large
displacement and instability
Introduction
Large displacement theory of beams
Elastic stability - energy interpretation
Large displacement theory of thick plates
Large displacement theory of thin plates
Solution of large deflection problems
Shells
Concluding remarks
Pseudo-rigid and rigid-flexible bodies
Introduction
Pseudo-rigid motions
Rigid motions
Connecting a rigid body to a flexible body
Multibody coupling by joints
Numerical examples
Computer procedures for finite element
analysis
Introduction
Description of additional program features
Solution of non-linear problems
Restart option
Solution of example problems
Concluding remarks
Appendix A
A1 Principal invariants
A2 Moment invariants
A3 derivatives of invariants
Author index
Subject index

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