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 |  موضوع: كتاب Finite Element Aanalysis, Thermo-mechanics of Solids السبت 22 يونيو 2013, 12:14 pm | |
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Finite Element Aanalysis
Thermo-mechanics of Solids
David W. Nicholson
ويتناول الموضوعات الأتية :
Mathematical Foundations: Vectors and Matrices
Introduction
Range and Summation Convention
Substitution Operator
Vectors
Notation
Gradient, Divergence, and Curl
Matrices
Eigenvalues and Eigenvectors
Coordinate Transformations
Transformations of Vectors
Orthogonal Curvilinear Coordinates
Gradient Operator
Divergence and Curl of Vectors
Appendix I: Divergence and Curl of Vectors in Orthogonal
Curvilinear Coordinates
Derivatives of Base Vectors
Divergence
Curl
Exercises
Mathematical Foundations: Tensors
Tensors
Divergence, Curl, and Laplacian of a Tensor
Divergence
Curl and Laplacian
Invariants
Positive Definiteness
Polar Decomposition Theorem
Kronecker Products on Tensors
VEC
Operator and the Kronecker Product
Fundamental Relations for Kronecker Products
Eigenstructures of Kronecker Products
Kronecker Form of Quadratic Products
Kronecker Product Operators for Fourth-Order Tensors
Transformation Properties of
VEC and TEN
Kronecker Product Functions for Tensor Outer Products
by CRC CRC Press LLC
Kronecker Expressions for Symmetry Classes
in Fourth-Order Tensors
Differentials of Tensor Invariants
Exercises
Introduction to Variational and Numerical Methods
Introduction to Variational Methods
Newton Iteration and Arc-Length Methods
Newton Iteration
Critical Points and the Arc-Length Method
Exercises
Kinematics of Deformation
Kinematics
Displacement
Displacement Vector
Deformation Gradient Tensor
Strain
F, E, E
and u in Orthogonal Coordinates
Velocity-Gradient Tensor, Deformation-Rate Tensor,
and Spin Tensor
Differential Volume Element
Differential Surface Element
Rotation Tensor
Compatibility Conditions For and D
Sample Problems
Exercises
Mechanical Equilibrium and the Principle of Virtual Work
Traction and Stress
Cauchy Stress
st Piola-Kirchhoff Stress
nd Piola-Kirchhoff Stress
Stress Flux
Balance of Mass, Linear Momentum, and Angular Momentum
Balance of Mass
Rayleigh Transport Theorem
Balance of Linear Momentum
Balance of Angular Momentum
Principle of Virtual Work
Sample Problems
Exercises
by CRC CRC Press LLC
Stress-Strain Relation and the Tangent-Modulus Tensor
Stress-Strain Behavior: Classical Linear Elasticity
Isothermal Tangent-Modulus Tensor
Classical Elasticity
Compressible Hyperelastic Materials
Incompressible and Near-Incompressible Hyperelastic Materials
Incompressibility
Near-Incompressibility
Nonlinear Materials at Large Deformation
Exercises
Thermal and Thermomechanical Response
Balance of Energy and Production of Entropy
Balance of Energy
Entropy Production Inequality
Thermodynamic Potentials
Classical Coupled Linear Thermoelasticity
Thermal and Thermomechanical Analogs of the Principle
of Virtual Work
Conductive Heat Transfer
Coupled Linear Isotropic Thermoelasticity
Exercises
Introduction to the Finite-Element Method
Introduction
Overview of the Finite-Element Method
Mesh Development
Element Fields in Linear Problems
Interpolation Models
One-Dimensional Members
Interpolation Models: Two Dimensions
Interpolation Models: Three Dimensions
Strain-Displacement Relations and Thermal Analogs
Strain-Displacement Relations: One Dimension
Strain-Displacement Relations: Two Dimensions
Axisymmetric Element on Axis of Revolution
Thermal Analog in Two Dimensions
Three-Dimensional Elements
Thermal Analog in Three Dimensions
Stress-Strain-Temperature Relations in Linear Thermoelasticity
Overview
One-Dimensional Members
Two-Dimensional Elements
by CRC CRC Press LLC
Element for Plate with Membrane and Bending Response
Axisymmetric Element
Three-Dimensional Element
Elements for Conductive Heat Transfer
Exercises
Element and Global Stiffness and Mass Matrices
Application of the Principle of Virtual Work
Thermal Counterpart of the Principle of Virtual Work
Assemblage and Imposition of Constraints
Rods
Beams
Two-Dimensional Elements
Exercises
Solution Methods for Linear Problems
Numerical Methods in FEA
Solving the Finite-Element Equations: Static Problems
Matrix Triangularization and Solution of Linear Systems
Triangularization of Asymmetric Matrices
Time Integration: Stability and Accuracy
Newmark’s Method
Integral Evaluation by Gaussian Quadrature
Modal Analysis by FEA
Modal Decomposition
Computation of Eigenvectors and Eigenvalues
Exercises
Rotating and Unrestrained Elastic Bodies
Finite Elements in Rotation
Finite-Element Analysis for Unconstrained Elastic Bodies
Exercises
Thermal, Thermoelastic, and Incompressible Media
Transient Conductive-Heat Transfer
Finite-Element Equation
Direct Integration by the Trapezoidal Rule
Modal Analysis
Coupled Linear Thermoelasticity
Finite-Element Equation
Thermoelasticity in a Rod
Compressible Elastic Media
Incompressible Elastic Media
Exercises
by CRC CRC Press LLC
Torsion and Buckling
Torsion of Prismatic Bars
Buckling of Beams and Plates
Euler Buckling of Beam Columns
Euler Buckling of Plates
Exercises
Introduction to Contact Problems
Introduction: the Gap
Point-to-Point Contact
Point-to-Surface Contact
Exercises
Introduction to Nonlinear FEA
Overview
Types of Nonlinearity
Combined Incremental and Iterative Methods: a Simple Example
Finite Stretching of a Rubber Rod under Gravity: a Simple Example
Nonlinear Strain-Displacement Relations
Stress and Tangent Modulus Relations
Incremental Equilibrium Relation
Numerical Solution by Newton Iteration
Illustration of Newton Iteration
Example
Exercises
Incremental Principle of Virtual Work
Incremental Kinematics
Incremental Stresses
Incremental Equilibrium Equation
Incremental Principle of Virtual Work
Incremental Finite-Element Equation
Incremental Contributions from Nonlinear Boundary Conditions
Effect of Variable Contact
Interpretation as Newton Iteration
Buckling
Exercises
Tangent-Modulus Tensors for Thermomechanical
Response of Elastomers
Introduction
Compressible Elastomers
Incompressible and Near-Incompressible Elastomers
Specific Expressions for the Helmholtz Potential
by CRC CRC Press LLC
Stretch Ratio-Based Models: Isothermal Conditions
Extension to Thermohyperelastic Materials
Thermomechanics of Damped Elastomers
Balance of Energy
Entropy Production Inequality
Dissipation Potential
Thermal-Field Equation for Damped Elastomers
Constitutive Model: Potential Functions
Helmholtz Free-Energy Density
Specific Dissipation Potential
Variational Principles
Mechanical Equilibrium
Thermal Equilibrium
Exercises
Inelastic and Thermoinelastic Materials
Plasticity
Kinematics
Plasticity
Thermoplasticity
Balance of Energy
Entropy-Production Inequality
Dissipation Potential
Thermoinelastic Tangent-Modulus Tensor
Example
Tangent-Modulus Tensor in Viscoplasticity
Continuum Damage Mechanics
Exercises
Advanced Numerical Methods
Iterative Triangularization of Perturbed Matrices
Introduction
Notation and Background
Iteration Scheme
Heuristic Convergence Argument
Sample Problem
Ozawa’s Method for Incompressible Materials
Exercises
Monographs and Texts
Articles and Other Sources
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