Elements of Elasticity

Author's Preface


1. Strain

1.1. Coordinate Systems

1.2. Displacements

1.3. Strain Components

1.4. Transformation of Strains

1.5. Compatibility of Strains

1.6. Displacement Functions

1.7. Increase in Area


2. Stress

2.1. Definitions

2.2. Stress Equilibrium Equations

2.3. Transformation of Stresses

2.4. Graphical Representation

2.5. Stress at Boundaries


3. Elasticity Equations

3.1. Linear Medium

3.2. Dilatation and Distortion

3.3. Elastic Constants

3.4. Strain Energy


4. Plane Stress and Strain

4.1. Definitions

4.2. Stress and Displacement Functions

4.3. Body Forces and Thermal Strain

4.4. Analysis of Strain Gauge Readings

4.5. Problems in Rectangular Coordinates


5. Curvilinear Coordinates

5.1. Alternative Coordinates

5.2. Conformal Transformations

5.3. Derivatives in Curvilinear Coordinates

5.4. Stress and Strain


6. Polar Coordinates

6.1. General Equations

6.2. Axial Symmetry

6.3. Harmonic Solutions

6.4. Circular Hole in a Sheet

6.5. Stresses Giving a Resultant Force

6.6. Force at Apex of Wedge


7. Rotating Discs and Thick Cylinders

7.1. Basic Equations

7.2. Solid Disc and Disc with Central Hole

7.3. Rotating Cylinder

7.4. Cylinders under Internal and External Pressure

7.5. Shrinkage Stresses

7.6. Graphical Construction


8. Strain Energy in Plates

8.1. Energy Balance for Plane Stress

8.2. Internal Stress

8.3. Strain Energy in Flexure

8.4. Strain in a Thin Plate

8.5. Compatibility Equation

8.6. Internal Stress in a Thin Plate


9. Torsion

9.1. Torsion of a Uniform Prism

9.2. Various Solid Sections

9.3. Hollow Sections

9.4. Membrane Analogy


10. Stress Propagation

10.1. One-Dimensional Stress Waves

10.2. Reflection from A Boundary

10.3. Harmonic Excitation

Appendix Condensed Suffix Notation

Index