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Classical and Computational Solid Mechanics

ISBN-10: 9810241240
ISBN-13: 9789810241247
Edition: 2001
Authors: Y. C. Fung, Pin Tong
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Book details

List price: $62.00
Copyright year: 2001
Publisher: World Scientific Publishing Company, Incorporated
Binding: Paperback
Pages: 952
Size: 6.00" wide x 9.50" long x 2.00" tall
Weight: 3.146
Language: English

Hooke's Law
Linear Solids with Memory
Sinusoidal Oscillations in Viscoelastic Material: Models of Viscoelasticity
Prototype of Wave Dynamics
Historical Remarks
Tensor Analysis
Notation and Summation Convention
Coordinate Transformation
Euclidean Metric Tensor
Scalars, Contravariant Vectors, Covariant Vectors
Tensor Fields of Higher Rank
Some Important Special Tensors
The Significance of Tensor Characteristics
Rectangular Cartesian Tensors
Quotient Rule
Partial Derivatives in Cartesian Coordinates
Covariant Differentiation of Vector Fields
Tensor Equations
Geometric Interpretation of Tensor Components
Geometric Interpretation of Covariant Derivatives
Physical Components of a Vector
Stress Tensor
Laws of Motion
Cauchy's Formula
Equations of Equilibrium
Transformation of Coordinates
Plane State of Stress
Principal Stresses
Shearing Stresses
Mohr's Circles
Stress Deviations
Octahedral Shearing Stress
Stress Tensor in General Coordinates
Physical Components of a Stress Tensor in General Coordinates
Equations of Equilibrium in Curvilinear Coordinates
Analysis of Strain
Strain Tensors in Rectangular Cartesian Coordinates
Geometric Interpretation of Infinitesimal Strain Components
Finite Strain Components
Compatibility of Strain Components
Multiply Connected Regions
Multivalued Displacements
Properties of the Strain Tensor
Physical Components
Example--Spherical Coordinates
Example--Cylindrical Polar Coordinates
Conservation Laws
Gauss' Theorem
Material and Spatial Descriptions of Changing Configurations
Material Derivative of Volume Integral
The Equation of Continuity
Equations of Motion
Moment of Momentum
Other Field Equations
Elastic and Plastic Behavior of Materials
Generalized Hooke's Law
Stress-Strain Relationship for Isotropic Elastic Materials
Ideal Plastic Solids
Some Experimental Information
A Basic Assumption of the Mathematical Theory of Plasticity
Loading and Unloading Criteria
Isotropic Stress Theories of Yield Function
Further Examples of Yield Functions
Work Hardening--Drucker's Hypothesis and Definition
Ideal Plasticity
Flow Rule for Work-Hardening Materials
Subsequent Loading Surfaces--Isotropic and Kinematic Hardening Rules
Mroz's, Dafalias and Popov's, and Valanis' Plasticity Theories
Strain Space Formulations
Finite Deformation
Plastic Deformation of Crystals
Linearized Theory of Elasticity
Basic Equations of Elasticity for Homogeneous Isotropic Bodies
Equilibrium of an Elastic Body Under Zero Body Force
Boundary Value Problems
Equilibrium and Uniqueness of Solutions
Saint Venant's Theory of Torsion
Soap Film Analogy
Bending of Beams
Plane Elastic Waves
Rayleigh Surface Wave
Love Wave
Solutions of Problems in Linearized Theory of Elasticity by Potentials
Scalar and Vector Potentials for Displacement Vector Fields
Equations of Motion in Terms of Displacement Potentials
Strain Potential
Galerkin Vector
Equivalent Galerkin Vectors
Example--Vertical Load on the Horizontal Surface of a Semi-Infinite Solid
Love's Strain Function
Kelvin's Problem--A Single Force Acting in the Interior of an Infinite Solid
Perturbation of Elasticity Solutions by a Change of Poisson's Ratio
Boussinesq's Problem
On Biharmonic Functions
Neuber-Papkovich Representation
Other Methods of Solution of Elastostatic Problems
Reflection and Refraction of Plane P and S Waves
Lamb's Problem--Line Load Suddenly Applied on Elastic Half-Space
Two-Dimensional Problems in Linearized Theory of Elasticity
Plane State of Stress or Strain
Airy Stress Functions for Two-Dimensional Problems
Airy Stress Function in Polar Coordinates
General Case
Representation of Two-Dimensional Biharmonic Functions by Analytic Functions of a Complex Variable
Kolosoff-Muskhelishvili Method
Variational Calculus, Energy Theorems, Saint-Venant's Principle
Minimization of Functionals
Functional Involving Higher Derivatives of the Dependent Variable
Several Unknown Functions
Several Independent Variables
Subsidiary Conditions--Lagrangian Multipliers
Natural Boundary Conditions
Theorem of Minimum Potential Energy Under Small Variations of Displacements
Example of Application: Static Loading on a Beam--Natural and Rigid End Conditions
The Complementary Energy Theorem Under Small Variations of Stresses
Variational Functionals Frequently Used in Computational Mechanics
Saint-Venant's Principle
Saint-Venant's Principle-Boussinesq-Von Mises-Sternberg Formulation
Practical Applications of Saint-Venant's Principle
Extremum Principles for Plasticity
Limit Analysis
Hamilton's Principle, Wave Propagation, Applications of Generalized Coordinates
Hamilton's Principle
Example of Application--Equation of Vibration of a Beam
Group Velocity
Hopkinson's Experiment
Generalized Coordinates
Approximate Representation of Functions
Approximate Solution of Differential Equations
Direct Methods of Variational Calculus
Elasticity and Thermodynamics
The Laws of Thermodynamics
The Energy Equation
The Strain Energy Function
The Conditions of Thermodynamic Equilibrium
The Positive Definiteness of the Strain Energy Function
Thermodynamic Restrictions on the Stress-Strain Law of an Isotropic Elastic Material
Generalized Hooke's Law, Including the Effect of Thermal Expansion
Thermodynamic Functions for Isotropic Hookean Materials
Equations Connecting Thermal and Mechanical Properties of a Solid
Irreversible Thermodynamics and Viscoelasticity
Basic Assumptions
One-Dimensional Heat Conduction
Phenomenological Relations-Onsager Principle
Basic Equations of Thermomechanics
Equations of Evolution for a Linear Hereditary Material
Relaxation Modes
Normal Coordinates
Hidden Variables and the Force-Displacement Relationship
Anisotropic Linear Viscoelastic Materials
Basic Equations
Thermal Effects Due to a Change of Strain; Kelvin's Formula
Ratio of Adiabatic to Isothermal Elastic Moduli
Uncoupled, Quasi-Static Thermoelastic Theory
Temperature Distribution
Thermal Stresses
Particular Integral: Goodier's Method
Plane Strain
An Example--Stresses in a Turbine Disk
Variational Principle for Uncoupled Thermoelasticity
Variational Principle for Heat Conduction
Coupled Thermoelasticity
Lagrangian Equations for Heat Conduction and Thermoelasticity
Viscoelastic Material
Stress-Strain Relations in Differential Equation Form
Boundary-Value Problems and Integral Transformations
Waves in an Infinite Medium
Quasi-Static Problems
Reciprocity Relations
Large Deformation
Coordinate Systems and Tensor Notation
Deformation Gradient
Right and Left Stretch Strain and Rotation Tensors
Strain Rates
Material Derivatives of Line, Area, and Volume Elements
Example: Combined Tension and Torsion Loads
Equations of Motion
Constitutive Equations of Thermoelastic Bodies
More Examples
Variational Principles for Finite Elasticity: Compressible Materials
Variational Principles for Finite Elasticity: Nearly Incompressible or Incompressible Materials
Small Deflection of Thin Plates
Large Deflection of Plates
Incremental Approach to Solving Some Nonlinear Problems
Updated Lagrangian Description
Linearized Rates of Deformation
Linearized Rates of Stress Measures
Incremental Equations of Motion
Constitutive Laws
Incremental Variational Principles in Terms of T
Incremental Variational Principles in Terms of r
Incompressible and Nearly Incompressible Materials
Updated Solution
Incremental Loads
Infinitesimal Strain Theory
Finite Element Methods
Basic Approach
One Dimensional Problems Governed by a Second Order Differential Equation
Shape Functions and Element Matrices for Higher Order Ordinary Differential Equations
Assembling and Constraining Global Matrices
Equation Solving
Two Dimensional Problems by One-Dimensional Elements
General Finite Element Formulation
Two-Dimensional Shape Functions
Element Matrices for a Second-Order Elliptical Equation
Coordinate Transformation
Triangular Elements with Curved Sides
Quadrilateral Elements
Plane Elasticity
Three-Dimensional Shape Functions
Three Dimensional Elasticity
Dynamic Problems of Elastic Solids
Numerical Integration
Patch Tests
Locking-Free Elements
Spurious Modes in Reduced Integration
Mixed and Hybrid Formulations
Mixed Formulations
Hybrid Formulations
Hybrid Singular Elements (Super-Elements)
Elements for Heterogeneous Materials
Elements for Infinite Domain
Incompressible or Nearly Incompressible Elasticity
Finite Element Methods for Plates and Shells
Linearized Bending Theory of Thin Plates
Reissner-Mindlin Plates
Mixed Functionals for Reissner Plate Theory
Hybrid Formulations for Plates
Shell as an Assembly of Plate Elements
General Shell Elements
Locking and Stabilization in Shell Applications
Finite Element Modeling of Nonlinear Elasticity, Viscoelasticity, Plasticity, Viscoplasticity and Creep
Updated Lagrangian Solution for Large Deformation
Incremental Solution
Dynamic Solution
Newton-Raphson Iteration Method
Author Index
Subject Index

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