TABLE OF CONTENTS
CHAPTER 1 INTRODUCTION
CHAPTER 2 STRESS AND EQUILIBRIUM EQUATIONS
Summary of the Chapter
2-1 Concept of Stress
2-2 Stress Components and Equilibrium Equations
....2-2-1 Stress components in Cartesian coordinates. Matrix representation
....2-2-2 Symmetry of shear stresses
....2-2-3 Stresses acting on an inclined plane
....2-2-4 Normal and tangential stresses.
....2-2-5 Stress boundary conditions
....2-2-6 Stress components in polar coordinates
....2-2-7 Equilibrium equations in Cartesian coordinates
....2-2-8 Equilibrium equations in polar coordinates
....2-2-9 Applicability of equilibrium equations
2-3 Principal Stresses and Invariants
....2-3-1 Characteristic equation
....2-3-2 Principal stresses and principal directions
.... 2-3-3 Plane stress: principal stresses and principal directions
.... 2-3-4 Plane stress: Mohr's circle
.... 2-3-5 Octahedral stresses
.... 2-3-6 Mean and deviatoric stresses
2-4 Three-dimensional Mohr's Circles
2-5 Stress Analysis and Symbolic Manipulation
PROBLEMS
REFERENCES
CHAPTER 3 DISPLACEMENT AND STRAIN
Summary of the Chapter
3-1 Introduction
3-2 Strain-displacement Equations
3-3 Compatibility
3-4 Specification of the State of Strain at a Point
.... 3-4-1 Strain gages
3-5 Rotation
3-6 Principal Strains
.... 3-6-1 Example
3-7 Strain Invariants
3-8 Volume Changes and Dilatation
3-9 The Strain Deviator
3-10 Strain-displacement Equations in Polar Coordinates
PROBLEMS
REFERENCES
CHAPTER 4 RELATIONSHIPS BETWEEN STRESS AND STRAIN
Summary of the Chapter
4-1 Introduction
4-2 Isotropic Materials: A Physical Approach
.... 4-2-1 Coincidence of Principal Stress and Principal Strain Axes
.... 4-2-2 Relationship Between G and E
.... 4-2-3 Bulk Modulus
4-3 Two Dimensional Stress-strain Laws: Plane Stress
and Plane Strain
.... 4-3-1 Plane stress
.... 4-3-2 Plane strain
4-4 Restrictions on Elastic Constants for Isotropic
Materials
4-5 Anisotropic Materials
4-6 Material Symmetries
4-7 Materials with a Single Plane of Elastic Symmetry
4-8 Orthotropic Materials
.... 4-8-1 Engineering Material Constants for Orthotropic Materials
.... 4-8-2 Orthotropic Materials Under Conditions of Plane Stress
.... 4-8-3 Stress-Strain Relations in Coordinates Other than the Principal Material Coordinates
4-9 Transversely Isotropic Material
4-10 Isotropic Materials: A Mathematical Approach
4-11 Stress-Strain Relations for Viscoelastic ......Materials
4-12 Material Behavior Beyond the Elastic Limit
4-12-1 Additional Experimental Observations
4-13 Criteria for Yielding
4-13-1 Maximum Shear Theory
4-13-2 Distortion Energy Theory
4-13-3 Comparison of the Two Theories
4-14 Stress-Strain Relations for Elastic-Perfectly
Plastic Materials
4-15 Stress-Strain Relations When the Temperature Field
is Non-uniform
4-16 Stress-Strain Relations for Piezoelectric
Materials
PROBLEMS
REFERENCES
CHAPTER 5 ENERGY CONCEPTS
Summary of the Chapter
5-1 Fundamental Concepts and Definitions
5-2 Work
.... 5-2-1 Work done by stresses acting on an
infinitesimal element
5-3 The First Law of Thermodynamics
5-4 The Second Law of Thermodynamics
5-5 Some Simple Applications Involving the First Law
5-5-1 Maxwell's reciprocity theorem
5-6 Strain Energy
.... 5-6-1 Complementary strain energy
.... 5-6-2 Strain energy in beams
5-7 Castigliano's Theorem
5-8 Principle of Virtual Work
.... 5-8-1 Principle of virtual work for particles and rigid bodies
.... 5-8-2 Principle of virtual work for deformable
bodies
5-9 Theorem of Minimum Total Potential Energy
5-10 Applications of the Theorem of Minimum Total
Potential Energy
5-11 Rayleigh-Ritz Method
5-12 Principle of Minimum Complementary Energy
5-13 Betti-Rayleigh Reciprocity Theorem
5-14 General Stress-Strain Relationships for Elastic
Materials
PROBLEMS
REFERENCES
CHAPTER 6 NUMERICAL METHODS I
Summary of the Chapter
6-1 The Method of Finite Differences
.... 6-1-1 Application to ordinary differential
equations
.... 6-1-2 Application to partial differential
equations
6-2. The Method of Iteration
6-3. The Method of Collocation
PROBLEMS
REFERENCES
CHAPTER 7 INTRODUCTION TO FINITE ELEMENT ANALYSIS
Summary of the Chapter
7-1 Introduction
7-2 Two-dimensional Frames
7-3 Overall Approach
7-4 Member Force-Displacement Relationships
7-6 Solving the Problem
7-7 Example
7-8 Notes Concerning the Structure Stiffness Matrix
7-9 Finite Element Analysis
7-10 Constant Strain Triangle
7-11 Element Assembly
7-12 Example
7-13 Notes on Using Finite Element Programs
.... 7-13-1 Inter-element compatibility
.... 7-13-2 Inherent over-stiffness in a finite element.
.... 7-13-3 Bending and the constant strain triangle
7-14 Closure
PROBLEMS
REFERENCES
CHAPTER 8 BEAMS
Summary of the Chapter
8-1 Bending of Continuous Beams
....8-1-1 Introduction
....8-1-2 The method of initial parameters
....8-1-3 Application of Castigliano theorem
8-2 Unsymmetric Bending of Straight Beams
8-3 Curved Beams
....8-3-1 Out-of-plane loaded beams Rings.
....8-3-2 A transversely loaded circular ring supported by three or more supports (Biezeno Theorem)
....8-3-3 In-plane loaded curved beams (arches), rings
....8-3-4 Bending, stretching and twisting of springs
8-4 Beams on Elastic Foundation
....8-4-1 Equilibrium equation for a straight beam
....8-4-2 Infinite beams
....8-4-3 Finite beams.
....8-4-4 Stresses in storage tanks
8-5 Influence Functions (Green's Functions) For Beams
....8-5-1 Straight beams
....8-5-2 Straight beams on elastic foundation
8-6 Thermal Effects
8-7 Composite Beams
....8-7-1 Stresses, bending moments and bending stiffness of a laminated beam
....8-7-2 Differential equation for deflection of a laminated beam
8-8 Limit Analysis
8-9 Fourier Series and Applications
8-10 Approximate Methods in the Analysis of Beams
8-10-1 Examples of application of finite differences
8-10-2 Examples of application of Rayleigh-Ritz method
8-11 Piezoelectric Beams
....8-11-1 Piezoelectric Bimorph
....8-11-2 Piezoelectric Multimorph
PROBLEMS
REFERENCES
CHAPTER 9 ELEMENTARY PROBLEMS IN TWO AND THREE DIMENSIONAL SOLID
MECHANICS
Summary of the Chapter
9-1 Problem Formulation. Boundary Conditions
9-2 Compatibility of Elastic Stress Components
9-3 Thick-walled Cylinders and Circular Disks
....9-3-1 Equilibrium equation and strains
....9-3-2 Elastic, homogeneous disks and cylinders
....9-3-3 Thermal effects
....9-3-4 Plastic cylinder
.... 9-3-5 Composite disks and cylinders
....9-3-6 Rotating disks of variable thickness
9-4 Airy's Stress Function
9-5 Torsion
....9-5-1 Circular cross-section
....9-5-2 Non-circular prisms. Saint-Venant's theory
....9-5-3 Membrane analogy
....9-5-4 Rectangular, and related, cross-sections
....9-5-5 Torsion of hollow, single-cell and multiple-cell members
....9-5-6 Pure plastic torsion
9-6 Application of Numerical Methods to Solution to 2D Elastic Problems
PROBLEMS
REFERENCES
CHAPTER 10 PLATES
Summary of the Chapter
10-1 Introduction
10-2 Axisymmetric Bending of Circular Plates
....10-2-1 General expressions
....10-2-2 Particular solutions for selected types of axisymmetric load.
....10-2-3 Solid plate: boundary conditions, examples
.... 10-2-4 Solid plate: influence functions (Green's functions)
....10-2-5 Solid plate with an additional support
....10-2-6 Annular plate: boundary conditions, examples
....10-2-7 Annular plate: influence functions (Green's functions)
10-3 Bending of Rectangular Plates
....10-3-1 Boundary conditions
....10-3-2 Bending of a simply supported rectangular plate
10-4 Plates on Elastic Foundation
10-5 Strain Energy of an Elastic Plate
10-6 Membranes
10-7 Composite Plates
.... 10-7-1 Laminated plates with isotropic layers
.... 10-7-2 Laminated plates with orthotropic layers
10-8 Approximate Methods in the Analysis of Plates and Membranes
.... 10-8-1 Application of finite differences to the analysis of plates
.... 10-8-2 Examples of application of the Rayleigh-Ritz method
PROBLEMS
REFERENCES
CHAPTER 11 BUCKLING AND VIBRATION
Summary of the chapter
11-1Buckling and Vibration of Beams and Columns
11-1-1 Equation of motion and its solution.
....11-1-2 Frequencies and critical loads for various boundary conditions.
....11-1-3 Applications of Rayleigh-Ritz method
11-2 Buckling of Rings, Arches, and thin-Walled Tubes.
....11-2-1 Equations of motion and their solution.
11-3 Buckling of Thin Rectangular Plates
PROBLEMS
REFERENCES
CHAPTER 12 INTRODUCTION TO FRACTURE MECHANICS
Summary of the Chapter
12-1 Introductory Concepts
12-2 Linear Cracks in Two-dimensional, Elastic Solids. Williams' Solution. Stress Singularity.
12-3 Stress Intensity Factor
12-4. The Crack Driving Force as an Energy Rate
12-5. Relation Between G and the Stress Intensity Factors
12-6. Some Simple Cases of Calculation of Stress Intensity Factors
12-7. The J-Integral
PROBLEMS
REFERENCES
APPENDIX A
MATRICES
APPENDIX B
COORDINATE TRANSFORMATIONS
INDEX
