Mechanics of Elastic Solids 弹性固体力学（英文版）
定价：￥139.00
作者： 张俊乾，宋亦诚，吕浡
出版社：高等教育出版社
- 高等教育出版社
- 9787040673173
- 1版
- 16开
- 490
内容简介
本书为国家级一流本科课程配套教材，聚焦弹性固体力学领域，采用英文编写。全书共10章，系统涵盖绪论、应力分析、变形分析、本构方程、实际问题的弹性力学建模、平面应力和平面应变小变形问题的应力函数解法、三维弹性小变形问题解法、多物理场问题、弹性力学的变分方法、薄板和圆柱壳等核心内容。本书作为改革尝试，新增和重构了弹性力学教材内容，具有显著变化的特色内容包括：变形分析一章论述有限变形的应变度量、并以一维到三维的自然推广方法讲述；本构关系一章包括了各向异性线弹性本构关系、小应变大转动弹性本构关系、超弹性本构关系；独立一章讲述实际问题力学建模的过程、方法和实例；多物理场问题通过引入具有普适性的特征应变方法进行论述。精简了平面问题解法和柱体扭转等内容。
为了克服新增内容的难度挑战性，本书每一章节的写作都具有自身的特点，力学新概念和方法都是通过简单情形和直观物理图像进行阐述，然后推广到一般情况。针对弹性力学问题，有机结合其物理图像和物理逻辑，开展相关数学工具的应用和理论推导。
本书英文讲义自2008年起在上海大学历经长期教学实践检验，教学体系成熟。
本书可作为高等学校力学类专业本科生和力学、土木工程、机械工程等专业研究生的教材，也可作为相关领域科学研究和工程技术人员的自学和参考用书。
目录
目录
前辅文
Nomenclature
1 Introduction
1.1 Basic Hypotheses of Elastic Solids
1.2 Brief History of Elastic Solid Mechanics
References
2 Analysis of Stress
2.1 Traction, Stress Tensor and Cauchy Formula
2.1.1 Traction (or Stress Vector)
2.1.2 Stress Tensor
2.1.3 Cauchy Formula
2.2 Index Notation and Transformation of Coordinates
2.2.1 Index Notation for Vectors, Tensors and Equations
2.2.2 Coordinate Transformation of Components of Traction and Stress Tensor
2.3 Principal Stresses and Stress Invariants
2.3.1 Principal Stresses and Principal Stress Directions
2.3.2 Stress Invariants
2.4 Maximum Shear Stress
2.5 Hydrostatic Stress, Deviatoric Stress and von Mises Stress
2.6 Equations of Motion (or Equilibrium)
Problems
References
3 Analysis of Deformation
3.1 One-Dimensional Deformation
3.1.1 Strain-Displacement Relations for Uniform Deformation
3.1.2 Strain-Displacement Relations for Non-Uniform Deformation
3.2 Displacement Field and Deformation Gradient
3.3 Stretch Tensors and Strain Measures
3.3.1 Elongation of a Differential Line
3.3.2 Change in Angle Between Any Two Line Elements
3.3.3 Typical Three-Dimensional Strain Measures
3.4 Principal Deformation Directions, Principal Stretches and Deformation Invariants
3.4.1 Principal Deformation Directions and Principal Stretches
3.4.2 Deformation Invariants
3.5 Strain-Displacement Relation
3.5.1 Explicit Strain-Displacement Relations
3.5.2 Calculation of Engineering Strain, Logarithmic Strain and Cauchy Strain from a Displacement Field
3.6 Deformation Rate and Material Derivative
3.7 Infinitesimal Strain and Infinitesimal Deformation
3.7.1 Infinitesimal Strain
3.7.2 Infinitesimal Deformation
3.8 Strain Compatibility for Infinitesimal Deformation
Problems
References
4 Constitutive Equations
4.1 Hooke’s Law for Isotropic Materials Undergoing Infinitesimal Deformation
4.1.1 Determination by Conducting Material Mechanics Experiments
4.1.2 Strain Energy Density
4.1.3 Stress Derived from Strain Energy Density Function
4.2 Hooke’s Law for Anisotropic Materials Undergoing Infinitesimal Deformation
4.2.1 Orthotropic Materials
4.2.2 Transversely Isotropic Materials
4.3 Stress-Strain Relation for Infinitesimal Strain but Large Rotation
4.4 Hyperelasticity
4.4.1 Stress Derived from Strain Energy Density Function
4.4.2 Incompressible Materials
4.4.3 Strain Energy Density Functions for Isotropic Incompressible Materials
4.4.4 Determination of Material Constants of Incompressible Materials
4.4.5 Strain Energy Density Functions for Isotropic Compressible Materials
Problems
References
5 Construction of Elastic Solid Mechanics Models for Actual Problems
5.1 Constructing an Elastic Solid Mechanics Model
5.1.1 Deciding What Mechanical Quantities to Compute
5.1.2 Defining the Geometry of the Model
5.1.3 Defining Material Behavior
5.1.4 Field Equations
5.1.5 Simplifying Loads and Replicating Boundary Conditions
5.1.6 Interface Models
5.1.7 Examples for Constructing Elastic Solid Mechanics Models
5.2 Boundary Value Problems of Mechanical Models
Problems
References
6 Solutions for Infinitesimal Plane Stress and Strain Problems
6.1 Plane Stress and Plane Strain Models
6.1.1 Plane Strain Model
6.1.2 Plane Stress Model
6.1.3 Basic Equations for Boundary Value Problems in Cartesian Coordinates
6.2 Airy Stress Function in Cartesian Coordinates
6.3 Solutions for Rectangular Beams by Polynomial Stress Functions
6.4 Solutions for Rectangular Beams by Separation of Variables
6.5 Airy Stress Function Solutions in Polar Coordinates
6.5.1 General Equations
6.5.2 Solutions for Typical Problems
Problems
Reference
7 Solutions for Infinitesimal Three-Dimensional Problems
7.1 Two Mathematical Tools
7.1.1 Integration by Parts for Higher Dimensions
7.1.2 Solution of Poisson’s Equation by Green’s Function
7.2 Helmholtz Decomposition of Displacement and Body Force
7.3 A Particular Solution of Navier’s Equation with Body Force
7.4 Papkovich–Neuber Solution
7.5 Indentation of an Elastic Half-Space by a Flat Rigid Punch
7.6 Frictionless Contact Between Two Elastic Spheres Problems
8 Multiphysics Field Problems
8.1 Eigen-Strain and Its Physical Origins
8.2 Generalized Hooke’s Law Involving Eigen-Strain
8.3 One-Way Coupling Initial-Boundary Value Problems for Isotropic Solids
8.4 One-Dimensional Problems of Eigen-Strain
8.4.1 Inhomogeneous Eigen-Strain in a Plate
8.4.2 Inhomogeneous Eigen-Strain in Spheres
8.4.3 Inhomogeneous Eigen-Strain in Disks and Cylinders
8.5 Eshelby Inclusion Problems
8.6 Displacement Potential Method for Eigen-Strain Problems
8.7 Brief Introduction to Two-Way Coupling Problems
Problems
References
9 Variational Methods for Infinitesimal Deformation Problems
9.1 Variation of Functionals
9.2 Principles of Virtual Work and Complementary Virtual Work
9.3 Principle of Minimum Potential Energy
9.4 Applications of Principle of Minimum Potential Energy for Reducing Dimensionality of Models
9.4.1 Elementary Theory of Beams
9.4.2 Saint–Venant Torsion of Shafts
9.5 Rayleigh–Ritz Method
9.6 Principle of Minimum Complementary Energy
9.7 Applications of Principle of Minimum Complementary Energy
9.7.1 Derivation of the Governing Equations of Saint–Venant Torsion
9.7.2 Numerical Solution for Problems of Saint–Venant Torsion
Problems
References
10 Thin Plates and Circular Cylindrical Shells
10.1 Basic Equations of Thin Plates
10.2 Solutions for Bending of Thin Plates
10.2.1 Pure Bending of Rectangular Plates
10.2.2 Simply Supported Rectangular Plates
10.2.3 Rectangular Plates Simply Supported at Two Opposite Edges
10.2.4 Axisymmetric Bending of Circular Plates
10.3 Vibration of Thin Plates
10.3.1 Free Vibration of Simply Supported Rectangular Plates
10.3.2 Free Vibration of Rectangular Plates Simply Supported at Two Opposite Edges
10.4 Buckling of Thin Plates Under Compression
10.4.1 Buckling of Simply Supported Rectangular Plates Under Compression
10.4.2 Buckling of Circular Plates
10.5 Buckling of Cylindrical Shells Subjected to Axially Compressive Loads
Problems
References
Appendix A Basic Equations in Polar, Cylindrical and Spherical Coordinate Systems, and Coordinate Transformation for Stresses and Displacements
A.1 Equations in Polar Coordinates
A.2 Equations in Cylindrical Coordinates
A.3 Equations in Spherical Coordinates
Index
前辅文
Nomenclature
1 Introduction
1.1 Basic Hypotheses of Elastic Solids
1.2 Brief History of Elastic Solid Mechanics
References
2 Analysis of Stress
2.1 Traction, Stress Tensor and Cauchy Formula
2.1.1 Traction (or Stress Vector)
2.1.2 Stress Tensor
2.1.3 Cauchy Formula
2.2 Index Notation and Transformation of Coordinates
2.2.1 Index Notation for Vectors, Tensors and Equations
2.2.2 Coordinate Transformation of Components of Traction and Stress Tensor
2.3 Principal Stresses and Stress Invariants
2.3.1 Principal Stresses and Principal Stress Directions
2.3.2 Stress Invariants
2.4 Maximum Shear Stress
2.5 Hydrostatic Stress, Deviatoric Stress and von Mises Stress
2.6 Equations of Motion (or Equilibrium)
Problems
References
3 Analysis of Deformation
3.1 One-Dimensional Deformation
3.1.1 Strain-Displacement Relations for Uniform Deformation
3.1.2 Strain-Displacement Relations for Non-Uniform Deformation
3.2 Displacement Field and Deformation Gradient
3.3 Stretch Tensors and Strain Measures
3.3.1 Elongation of a Differential Line
3.3.2 Change in Angle Between Any Two Line Elements
3.3.3 Typical Three-Dimensional Strain Measures
3.4 Principal Deformation Directions, Principal Stretches and Deformation Invariants
3.4.1 Principal Deformation Directions and Principal Stretches
3.4.2 Deformation Invariants
3.5 Strain-Displacement Relation
3.5.1 Explicit Strain-Displacement Relations
3.5.2 Calculation of Engineering Strain, Logarithmic Strain and Cauchy Strain from a Displacement Field
3.6 Deformation Rate and Material Derivative
3.7 Infinitesimal Strain and Infinitesimal Deformation
3.7.1 Infinitesimal Strain
3.7.2 Infinitesimal Deformation
3.8 Strain Compatibility for Infinitesimal Deformation
Problems
References
4 Constitutive Equations
4.1 Hooke’s Law for Isotropic Materials Undergoing Infinitesimal Deformation
4.1.1 Determination by Conducting Material Mechanics Experiments
4.1.2 Strain Energy Density
4.1.3 Stress Derived from Strain Energy Density Function
4.2 Hooke’s Law for Anisotropic Materials Undergoing Infinitesimal Deformation
4.2.1 Orthotropic Materials
4.2.2 Transversely Isotropic Materials
4.3 Stress-Strain Relation for Infinitesimal Strain but Large Rotation
4.4 Hyperelasticity
4.4.1 Stress Derived from Strain Energy Density Function
4.4.2 Incompressible Materials
4.4.3 Strain Energy Density Functions for Isotropic Incompressible Materials
4.4.4 Determination of Material Constants of Incompressible Materials
4.4.5 Strain Energy Density Functions for Isotropic Compressible Materials
Problems
References
5 Construction of Elastic Solid Mechanics Models for Actual Problems
5.1 Constructing an Elastic Solid Mechanics Model
5.1.1 Deciding What Mechanical Quantities to Compute
5.1.2 Defining the Geometry of the Model
5.1.3 Defining Material Behavior
5.1.4 Field Equations
5.1.5 Simplifying Loads and Replicating Boundary Conditions
5.1.6 Interface Models
5.1.7 Examples for Constructing Elastic Solid Mechanics Models
5.2 Boundary Value Problems of Mechanical Models
Problems
References
6 Solutions for Infinitesimal Plane Stress and Strain Problems
6.1 Plane Stress and Plane Strain Models
6.1.1 Plane Strain Model
6.1.2 Plane Stress Model
6.1.3 Basic Equations for Boundary Value Problems in Cartesian Coordinates
6.2 Airy Stress Function in Cartesian Coordinates
6.3 Solutions for Rectangular Beams by Polynomial Stress Functions
6.4 Solutions for Rectangular Beams by Separation of Variables
6.5 Airy Stress Function Solutions in Polar Coordinates
6.5.1 General Equations
6.5.2 Solutions for Typical Problems
Problems
Reference
7 Solutions for Infinitesimal Three-Dimensional Problems
7.1 Two Mathematical Tools
7.1.1 Integration by Parts for Higher Dimensions
7.1.2 Solution of Poisson’s Equation by Green’s Function
7.2 Helmholtz Decomposition of Displacement and Body Force
7.3 A Particular Solution of Navier’s Equation with Body Force
7.4 Papkovich–Neuber Solution
7.5 Indentation of an Elastic Half-Space by a Flat Rigid Punch
7.6 Frictionless Contact Between Two Elastic Spheres Problems
8 Multiphysics Field Problems
8.1 Eigen-Strain and Its Physical Origins
8.2 Generalized Hooke’s Law Involving Eigen-Strain
8.3 One-Way Coupling Initial-Boundary Value Problems for Isotropic Solids
8.4 One-Dimensional Problems of Eigen-Strain
8.4.1 Inhomogeneous Eigen-Strain in a Plate
8.4.2 Inhomogeneous Eigen-Strain in Spheres
8.4.3 Inhomogeneous Eigen-Strain in Disks and Cylinders
8.5 Eshelby Inclusion Problems
8.6 Displacement Potential Method for Eigen-Strain Problems
8.7 Brief Introduction to Two-Way Coupling Problems
Problems
References
9 Variational Methods for Infinitesimal Deformation Problems
9.1 Variation of Functionals
9.2 Principles of Virtual Work and Complementary Virtual Work
9.3 Principle of Minimum Potential Energy
9.4 Applications of Principle of Minimum Potential Energy for Reducing Dimensionality of Models
9.4.1 Elementary Theory of Beams
9.4.2 Saint–Venant Torsion of Shafts
9.5 Rayleigh–Ritz Method
9.6 Principle of Minimum Complementary Energy
9.7 Applications of Principle of Minimum Complementary Energy
9.7.1 Derivation of the Governing Equations of Saint–Venant Torsion
9.7.2 Numerical Solution for Problems of Saint–Venant Torsion
Problems
References
10 Thin Plates and Circular Cylindrical Shells
10.1 Basic Equations of Thin Plates
10.2 Solutions for Bending of Thin Plates
10.2.1 Pure Bending of Rectangular Plates
10.2.2 Simply Supported Rectangular Plates
10.2.3 Rectangular Plates Simply Supported at Two Opposite Edges
10.2.4 Axisymmetric Bending of Circular Plates
10.3 Vibration of Thin Plates
10.3.1 Free Vibration of Simply Supported Rectangular Plates
10.3.2 Free Vibration of Rectangular Plates Simply Supported at Two Opposite Edges
10.4 Buckling of Thin Plates Under Compression
10.4.1 Buckling of Simply Supported Rectangular Plates Under Compression
10.4.2 Buckling of Circular Plates
10.5 Buckling of Cylindrical Shells Subjected to Axially Compressive Loads
Problems
References
Appendix A Basic Equations in Polar, Cylindrical and Spherical Coordinate Systems, and Coordinate Transformation for Stresses and Displacements
A.1 Equations in Polar Coordinates
A.2 Equations in Cylindrical Coordinates
A.3 Equations in Spherical Coordinates
Index
前辅文
Nomenclature
1 Introduction
1.1 Basic Hypotheses of Elastic Solids
1.2 Brief History of Elastic Solid Mechanics
References
2 Analysis of Stress
2.1 Traction, Stress Tensor and Cauchy Formula
2.1.1 Traction (or Stress Vector)
2.1.2 Stress Tensor
2.1.3 Cauchy Formula
2.2 Index Notation and Transformation of Coordinates
2.2.1 Index Notation for Vectors, Tensors and Equations
2.2.2 Coordinate Transformation of Components of Traction and Stress Tensor
2.3 Principal Stresses and Stress Invariants
2.3.1 Principal Stresses and Principal Stress Directions
2.3.2 Stress Invariants
2.4 Maximum Shear Stress
2.5 Hydrostatic Stress, Deviatoric Stress and von Mises Stress
2.6 Equations of Motion (or Equilibrium)
Problems
References
3 Analysis of Deformation
3.1 One-Dimensional Deformation
3.1.1 Strain-Displacement Relations for Uniform Deformation
3.1.2 Strain-Displacement Relations for Non-Uniform Deformation
3.2 Displacement Field and Deformation Gradient
3.3 Stretch Tensors and Strain Measures
3.3.1 Elongation of a Differential Line
3.3.2 Change in Angle Between Any Two Line Elements
3.3.3 Typical Three-Dimensional Strain Measures
3.4 Principal Deformation Directions, Principal Stretches and Deformation Invariants
3.4.1 Principal Deformation Directions and Principal Stretches
3.4.2 Deformation Invariants
3.5 Strain-Displacement Relation
3.5.1 Explicit Strain-Displacement Relations
3.5.2 Calculation of Engineering Strain, Logarithmic Strain and Cauchy Strain from a Displacement Field
3.6 Deformation Rate and Material Derivative
3.7 Infinitesimal Strain and Infinitesimal Deformation
3.7.1 Infinitesimal Strain
3.7.2 Infinitesimal Deformation
3.8 Strain Compatibility for Infinitesimal Deformation
Problems
References
4 Constitutive Equations
4.1 Hooke’s Law for Isotropic Materials Undergoing Infinitesimal Deformation
4.1.1 Determination by Conducting Material Mechanics Experiments
4.1.2 Strain Energy Density
4.1.3 Stress Derived from Strain Energy Density Function
4.2 Hooke’s Law for Anisotropic Materials Undergoing Infinitesimal Deformation
4.2.1 Orthotropic Materials
4.2.2 Transversely Isotropic Materials
4.3 Stress-Strain Relation for Infinitesimal Strain but Large Rotation
4.4 Hyperelasticity
4.4.1 Stress Derived from Strain Energy Density Function
4.4.2 Incompressible Materials
4.4.3 Strain Energy Density Functions for Isotropic Incompressible Materials
4.4.4 Determination of Material Constants of Incompressible Materials
4.4.5 Strain Energy Density Functions for Isotropic Compressible Materials
Problems
References
5 Construction of Elastic Solid Mechanics Models for Actual Problems
5.1 Constructing an Elastic Solid Mechanics Model
5.1.1 Deciding What Mechanical Quantities to Compute
5.1.2 Defining the Geometry of the Model
5.1.3 Defining Material Behavior
5.1.4 Field Equations
5.1.5 Simplifying Loads and Replicating Boundary Conditions
5.1.6 Interface Models
5.1.7 Examples for Constructing Elastic Solid Mechanics Models
5.2 Boundary Value Problems of Mechanical Models
Problems
References
6 Solutions for Infinitesimal Plane Stress and Strain Problems
6.1 Plane Stress and Plane Strain Models
6.1.1 Plane Strain Model
6.1.2 Plane Stress Model
6.1.3 Basic Equations for Boundary Value Problems in Cartesian Coordinates
6.2 Airy Stress Function in Cartesian Coordinates
6.3 Solutions for Rectangular Beams by Polynomial Stress Functions
6.4 Solutions for Rectangular Beams by Separation of Variables
6.5 Airy Stress Function Solutions in Polar Coordinates
6.5.1 General Equations
6.5.2 Solutions for Typical Problems
Problems
Reference
7 Solutions for Infinitesimal Three-Dimensional Problems
7.1 Two Mathematical Tools
7.1.1 Integration by Parts for Higher Dimensions
7.1.2 Solution of Poisson’s Equation by Green’s Function
7.2 Helmholtz Decomposition of Displacement and Body Force
7.3 A Particular Solution of Navier’s Equation with Body Force
7.4 Papkovich–Neuber Solution
7.5 Indentation of an Elastic Half-Space by a Flat Rigid Punch
7.6 Frictionless Contact Between Two Elastic Spheres Problems
8 Multiphysics Field Problems
8.1 Eigen-Strain and Its Physical Origins
8.2 Generalized Hooke’s Law Involving Eigen-Strain
8.3 One-Way Coupling Initial-Boundary Value Problems for Isotropic Solids
8.4 One-Dimensional Problems of Eigen-Strain
8.4.1 Inhomogeneous Eigen-Strain in a Plate
8.4.2 Inhomogeneous Eigen-Strain in Spheres
8.4.3 Inhomogeneous Eigen-Strain in Disks and Cylinders
8.5 Eshelby Inclusion Problems
8.6 Displacement Potential Method for Eigen-Strain Problems
8.7 Brief Introduction to Two-Way Coupling Problems
Problems
References
9 Variational Methods for Infinitesimal Deformation Problems
9.1 Variation of Functionals
9.2 Principles of Virtual Work and Complementary Virtual Work
9.3 Principle of Minimum Potential Energy
9.4 Applications of Principle of Minimum Potential Energy for Reducing Dimensionality of Models
9.4.1 Elementary Theory of Beams
9.4.2 Saint–Venant Torsion of Shafts
9.5 Rayleigh–Ritz Method
9.6 Principle of Minimum Complementary Energy
9.7 Applications of Principle of Minimum Complementary Energy
9.7.1 Derivation of the Governing Equations of Saint–Venant Torsion
9.7.2 Numerical Solution for Problems of Saint–Venant Torsion
Problems
References
10 Thin Plates and Circular Cylindrical Shells
10.1 Basic Equations of Thin Plates
10.2 Solutions for Bending of Thin Plates
10.2.1 Pure Bending of Rectangular Plates
10.2.2 Simply Supported Rectangular Plates
10.2.3 Rectangular Plates Simply Supported at Two Opposite Edges
10.2.4 Axisymmetric Bending of Circular Plates
10.3 Vibration of Thin Plates
10.3.1 Free Vibration of Simply Supported Rectangular Plates
10.3.2 Free Vibration of Rectangular Plates Simply Supported at Two Opposite Edges
10.4 Buckling of Thin Plates Under Compression
10.4.1 Buckling of Simply Supported Rectangular Plates Under Compression
10.4.2 Buckling of Circular Plates
10.5 Buckling of Cylindrical Shells Subjected to Axially Compressive Loads
Problems
References
Appendix A Basic Equations in Polar, Cylindrical and Spherical Coordinate Systems, and Coordinate Transformation for Stresses and Displacements
A.1 Equations in Polar Coordinates
A.2 Equations in Cylindrical Coordinates
A.3 Equations in Spherical Coordinates
Index
前辅文
Nomenclature
1 Introduction
1.1 Basic Hypotheses of Elastic Solids
1.2 Brief History of Elastic Solid Mechanics
References
2 Analysis of Stress
2.1 Traction, Stress Tensor and Cauchy Formula
2.1.1 Traction (or Stress Vector)
2.1.2 Stress Tensor
2.1.3 Cauchy Formula
2.2 Index Notation and Transformation of Coordinates
2.2.1 Index Notation for Vectors, Tensors and Equations
2.2.2 Coordinate Transformation of Components of Traction and Stress Tensor
2.3 Principal Stresses and Stress Invariants
2.3.1 Principal Stresses and Principal Stress Directions
2.3.2 Stress Invariants
2.4 Maximum Shear Stress
2.5 Hydrostatic Stress, Deviatoric Stress and von Mises Stress
2.6 Equations of Motion (or Equilibrium)
Problems
References
3 Analysis of Deformation
3.1 One-Dimensional Deformation
3.1.1 Strain-Displacement Relations for Uniform Deformation
3.1.2 Strain-Displacement Relations for Non-Uniform Deformation
3.2 Displacement Field and Deformation Gradient
3.3 Stretch Tensors and Strain Measures
3.3.1 Elongation of a Differential Line
3.3.2 Change in Angle Between Any Two Line Elements
3.3.3 Typical Three-Dimensional Strain Measures
3.4 Principal Deformation Directions, Principal Stretches and Deformation Invariants
3.4.1 Principal Deformation Directions and Principal Stretches
3.4.2 Deformation Invariants
3.5 Strain-Displacement Relation
3.5.1 Explicit Strain-Displacement Relations
3.5.2 Calculation of Engineering Strain, Logarithmic Strain and Cauchy Strain from a Displacement Field
3.6 Deformation Rate and Material Derivative
3.7 Infinitesimal Strain and Infinitesimal Deformation
3.7.1 Infinitesimal Strain
3.7.2 Infinitesimal Deformation
3.8 Strain Compatibility for Infinitesimal Deformation
Problems
References
4 Constitutive Equations
4.1 Hooke’s Law for Isotropic Materials Undergoing Infinitesimal Deformation
4.1.1 Determination by Conducting Material Mechanics Experiments
4.1.2 Strain Energy Density
4.1.3 Stress Derived from Strain Energy Density Function
4.2 Hooke’s Law for Anisotropic Materials Undergoing Infinitesimal Deformation
4.2.1 Orthotropic Materials
4.2.2 Transversely Isotropic Materials
4.3 Stress-Strain Relation for Infinitesimal Strain but Large Rotation
4.4 Hyperelasticity
4.4.1 Stress Derived from Strain Energy Density Function
4.4.2 Incompressible Materials
4.4.3 Strain Energy Density Functions for Isotropic Incompressible Materials
4.4.4 Determination of Material Constants of Incompressible Materials
4.4.5 Strain Energy Density Functions for Isotropic Compressible Materials
Problems
References
5 Construction of Elastic Solid Mechanics Models for Actual Problems
5.1 Constructing an Elastic Solid Mechanics Model
5.1.1 Deciding What Mechanical Quantities to Compute
5.1.2 Defining the Geometry of the Model
5.1.3 Defining Material Behavior
5.1.4 Field Equations
5.1.5 Simplifying Loads and Replicating Boundary Conditions
5.1.6 Interface Models
5.1.7 Examples for Constructing Elastic Solid Mechanics Models
5.2 Boundary Value Problems of Mechanical Models
Problems
References
6 Solutions for Infinitesimal Plane Stress and Strain Problems
6.1 Plane Stress and Plane Strain Models
6.1.1 Plane Strain Model
6.1.2 Plane Stress Model
6.1.3 Basic Equations for Boundary Value Problems in Cartesian Coordinates
6.2 Airy Stress Function in Cartesian Coordinates
6.3 Solutions for Rectangular Beams by Polynomial Stress Functions
6.4 Solutions for Rectangular Beams by Separation of Variables
6.5 Airy Stress Function Solutions in Polar Coordinates
6.5.1 General Equations
6.5.2 Solutions for Typical Problems
Problems
Reference
7 Solutions for Infinitesimal Three-Dimensional Problems
7.1 Two Mathematical Tools
7.1.1 Integration by Parts for Higher Dimensions
7.1.2 Solution of Poisson’s Equation by Green’s Function
7.2 Helmholtz Decomposition of Displacement and Body Force
7.3 A Particular Solution of Navier’s Equation with Body Force
7.4 Papkovich–Neuber Solution
7.5 Indentation of an Elastic Half-Space by a Flat Rigid Punch
7.6 Frictionless Contact Between Two Elastic Spheres Problems
8 Multiphysics Field Problems
8.1 Eigen-Strain and Its Physical Origins
8.2 Generalized Hooke’s Law Involving Eigen-Strain
8.3 One-Way Coupling Initial-Boundary Value Problems for Isotropic Solids
8.4 One-Dimensional Problems of Eigen-Strain
8.4.1 Inhomogeneous Eigen-Strain in a Plate
8.4.2 Inhomogeneous Eigen-Strain in Spheres
8.4.3 Inhomogeneous Eigen-Strain in Disks and Cylinders
8.5 Eshelby Inclusion Problems
8.6 Displacement Potential Method for Eigen-Strain Problems
8.7 Brief Introduction to Two-Way Coupling Problems
Problems
References
9 Variational Methods for Infinitesimal Deformation Problems
9.1 Variation of Functionals
9.2 Principles of Virtual Work and Complementary Virtual Work
9.3 Principle of Minimum Potential Energy
9.4 Applications of Principle of Minimum Potential Energy for Reducing Dimensionality of Models
9.4.1 Elementary Theory of Beams
9.4.2 Saint–Venant Torsion of Shafts
9.5 Rayleigh–Ritz Method
9.6 Principle of Minimum Complementary Energy
9.7 Applications of Principle of Minimum Complementary Energy
9.7.1 Derivation of the Governing Equations of Saint–Venant Torsion
9.7.2 Numerical Solution for Problems of Saint–Venant Torsion
Problems
References
10 Thin Plates and Circular Cylindrical Shells
10.1 Basic Equations of Thin Plates
10.2 Solutions for Bending of Thin Plates
10.2.1 Pure Bending of Rectangular Plates
10.2.2 Simply Supported Rectangular Plates
10.2.3 Rectangular Plates Simply Supported at Two Opposite Edges
10.2.4 Axisymmetric Bending of Circular Plates
10.3 Vibration of Thin Plates
10.3.1 Free Vibration of Simply Supported Rectangular Plates
10.3.2 Free Vibration of Rectangular Plates Simply Supported at Two Opposite Edges
10.4 Buckling of Thin Plates Under Compression
10.4.1 Buckling of Simply Supported Rectangular Plates Under Compression
10.4.2 Buckling of Circular Plates
10.5 Buckling of Cylindrical Shells Subjected to Axially Compressive Loads
Problems
References
Appendix A Basic Equations in Polar, Cylindrical and Spherical Coordinate Systems, and Coordinate Transformation for Stresses and Displacements
A.1 Equations in Polar Coordinates
A.2 Equations in Cylindrical Coordinates
A.3 Equations in Spherical Coordinates
Index
