كتاب Finite Element Method Volume 2 - Solid Mechanics
منتدى هندسة الإنتاج والتصميم الميكانيكى
بسم الله الرحمن الرحيم

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 كتاب Finite Element Method Volume 2 - Solid Mechanics

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عدد المساهمات : 14261
التقييم : 22948
تاريخ التسجيل : 01/07/2009
العمر : 28
الدولة : مصر
العمل : مدير منتدى هندسة الإنتاج والتصميم الميكانيكى
الجامعة : المنوفية

مُساهمةموضوع: كتاب Finite Element Method Volume 2 - Solid Mechanics   الجمعة 20 ديسمبر 2013, 2:44 pm

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Finite Element Method Volume 2 - Solid Mechanics


ويتناول الموضوعات الأتية :

1.  General problems in solid mechanics and non-linearity
1.1  Introduction
1.3  Non-linear quasi-harmonic field problems
1.5  Concluding remarks
Small deformation non-linear solid mechanics problems
Some typical examples of transient non-linear calculations
References
2.  Solution of non-linear algebraic equations
2.1  Introduction
2.2  Iterative techniques
References
3.  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
References
4.  Plate bending approximation: thin (Kirchhoff) plates and C, continuity
requirements
viii  Contents
Introduction
The plate problem: thick and thin formulations
Rectangular element with corner nodes (12 degrees of freedom)
Quadrilateral and parallelogram elements
Triangular element with corner nodes (9 degrees of freedom)
Triangular element of the simplest form (6 degrees of freedom)
The patch test - an analytical requirement
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?
References
5.  ‘Thick’ Reissner-Mindlin  plates - irreducible and mixed formulations
5.1  Introduction
5.10  Forms without rotation parameters
5.1 1  Inelastic material behaviour
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
thin plate theory
Concluding remarks - adaptive refinement
References
6.  Shells as an assembly of flat elements
6.1  Introduction
6.4  Local direction cosines
Stiffness of a plane element in local coordinates
Transformation to global coordinates and assembly of elements
‘Drilling’ rotational stiffness - 6 degree-of-freedom  assembly
Elements with mid-side slope connections only 
Contents  ix
6.7  Choice of element
6.8  Practical examples
References
7.  Axisymmetric shells  244
7.1  Introduction  244
7.2  Straight element  245
7.3  Curved elements  25 1
7.4  Independent slope-displacement interpolation with penalty
functions (thick or thin shell formulations)  26 1
References  264
8.  Shells as a special case of three-dimensional analysis - Reissner-Mindlin
assumptions
8.1  Introduction
8.5  Convergence
8.6  Inelastic behaviour
8.7  Some shell examples
8.8  Concluding remarks
Shell element with displacement and rotation parameters
Special case of axisymmetric, curved, thick  shells
Special case of thick plates
References
9.  Semi-analytical finite element processes - use of orthogonal functions
and ‘finite strip’ methods
9.1  Introduction
9.2  Prismatic bar
9.3  Thin membrane box structures
9.8  Concluding remarks
Plates and boxes with flexure
Axisymmetric solids with non-symmetrical load
Axisymmetric shells with non-symmetrical load
Finite strip method - incomplete decoupling
References
10. Geometrically non-linear problems - finite deformation
10.1  Introduction
10.2  Governing equations
10.8  Contact problems
10.9  Numerical examples
Variational description for finite deformation
A three-field mixed finite deformation formulation
A mixed-enhanced finite deformation formulation
Forces dependent on deformation - pressure loads
Material constitution for finite deformation
x  Contents
10.10 Concluding remarks
References
1 1. Non-linear structural problems - large displacement and instability
1 1.1  Introduction
11.7  Shells
11.8  Concluding remarks
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
References
12. Pseudo-rigid and rigid-flexible bodies
12.1  Introduction
12.2  Pseudo-rigid motions
12.3  Rigid motions 
12.5  Multibody coupling by joints
12.6  Numerical  examples
Connecting a rigid body to a flexible body
References
13. Computer procedures for finite element analysis
13.1  Introduction
13.2
13.3  Solution of non-linear problems
13.4  Restart option
13.5  Solution of example problems
13.6  Concluding remarks
Description of additional program features
References
Appendix A:  Invariants of second-order tensors
A. 1  Principal invariants
A.2  Moment invariants
A.3  Derivatives of invariants
Author index
Subject index 
Volume 1: The basis
1. Some preliminaries: the standard discrete system
2. A direct approach to problems in elasticity
3. Generalization of the finite element concepts.  Galerkin-weighted residual and
4. Plane stress and plane strain
5. Axisymmetric stress analysis
6. Three-dimensional stress analysis
7. Steady-state field problems - heat conduction, electric and magnetic potential,
8. ‘Standard’ and ‘hierarchical’ element shape functions: some general  families of
9. Mapped elements and numerical integration - ‘infinite’ and ‘singularity’ elements
variational approaches
fluid flow, etc
C, continuity
10. The patch test, reduced integration, and non-conforming elements
1 1. Mixed formulation and constraints - complete field methods
12. Incompressible problems, mixed methods and other procedures of solution
13. Mixed formulation and constraints - incomplete (hybrid) field methods, bound-
14. Errors, recovery processes and error estimates
15. Adaptive finite element refinement
16. Point-based approximations; element-free Galerkin - and other meshless methods
17. The time dimension - semi-discretization  of field and dynamic  problems and
18. The time dimension - discrete approximation in time
19. Coupled systems
20. Computer procedures for finite element analysis
Appendix A. Matrix algebra
Appendix B. Tensor-indicia1 notation in the approximation of elasticity problems
Appendix C. Basic equations of displacement  analysis
Appendix D. Some integration formulae for a triangle
Appendix E.  Some integration formulae for a tetrahedron
Appendix F. Some vector algebra
Appendix G. Integration by parts
Appendix H. Solutions exact at nodes
Appendix I.  Matrix diagonalization or lumping
ary/Trefftz methods
analytical solution procedures
Volume 3: Fluid dynamics
1. Introduction and the equations of fluid dynamics
2. Convection dominated problems - finite element approximations
3. A general algorithm for compressible and incompressible flows - the characteristic
4. Incompressible laminar flow - newtonian and non-newtonian fluids
5. Free surfaces, buoyancy and turbulent incompressible flows
6. Compressible high speed gas flow
7. Shallow-water problems
8. Waves
9. Computer implementation of the CBS algorithm
Appendix A. Non-conservative form of Navier-Stokes equations
Appendix B. Discontinuous  Galerkin  methods in the  solution of the convection-
Appendix C. Edge-based finite element formulation
Appendix D. Multi grid methods
Appendix E. Boundary layer - inviscid flow coupling


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