Solid Mechanics Part II: Engineering Solid Mechanics small strain

This is primarily aimed at the Part II-IV Engineering undergraduate student.

Return to Mechanics Lecture Notes

 

Please send any errors, typos, comments, etc. to pa.kelly@auckland.ac.nz (I am always interested to hear who is reading these notes, and where you are from, and where you are working/studying)

 

Table of Contents

 

 

 

 

 

Last updated

1.

Differential Equations for Solid Mechanics

 

 

27-Mar-2008

 

1.1

The Equations of Motion

3

 

27-Mar-2008

 

1.2

The Strain-Displacement Relations

9

 

27-Mar-2008

 

1.3

Compatibility of Strain

17

 

27-Mar-2008

 

 

 

 

 

 

2.

One-dimensional Elasticity

19

 

27-Mar-2008

 

2.1

One-dimensional Elastostatics

21

 

27-Mar-2008

 

2.2

One-dimensional Elastodynamics

23

 

8-Oct-2013

 

 

 

 

 

 

3.

2D Elastostatic Problems in Cartesian Coordinates

41

 

1-Apr-2008

 

3.1

Plane Problems

43

 

19-Mar-2012

 

3.2

The Stress Function Method

46

 

26-Feb-2015

 

 

 

 

 

 

4.

2D Elastostatic Problems in Polar Coordinates

53

 

3-Apr-2008

 

4.1

Cylindrical and Polar Coordinates

55

 

3-Apr-2008

 

4.2

Differential Equations in Polar Coordinates

60

 

3-Apr-2008

 

4.3

Plane Axisymmetric Problems

66

 

18-Apr-2008

 

4.4

Rotating Discs

77

 

18-Apr-2008

 

4.5

Quasi-Axisymmetric Problems

 

 

 

 

4.6

The Michell Solution

 

 

 

 

4.7

The Kirsch Solution

 

 

 

 

4.8

The Curved Beam

 

 

 

 

 

 

 

 

 

5.

Further Topics in Plane Elasticity

 

 

 

 

5.1

The Concentrated Force

 

 

 

 

5.2

Contact Mechanics

 

 

 

 

5.3

The Wedge

 

 

 

 

.5.4

Fracture Mechanics

 

 

 

 

 

 

 

 

 

6.

Plate Theory

 

 

 

 

6.1

Plate Theory

120

 

20-Sep-2013

 

6.2

The Moment-Curvature Equations

125

 

10-Apr-2017

 

6.3

Plates subjected to Pure Bending and Twisting

139

 

20-Sep-2013

 

.64

Equilibrium and Lateral Loading

144

 

20-Sep-2013

 

6.5

Plate Problems in Rectangular Coordinates

149

 

20-Sep-2013

 

6.6

Plate Problems in Polar Coordinates

164

 

20-Sep-2013

 

6.7

In-Plane Forces and Plate Buckling

169

 

20-Sep-2013

 

6.8

Plate Vibrations

173

 

20-Sep-2013

 

6.9

Strain Energy in Plates

179

 

20-Sep-2013

 

6.10

Limitations of Classical Plate Theory

183

 

20-Sep-2013

 

 

 

 

 

 

7.

Three Dimensional Elasticity

187

 

16-Aug-2012

 

7.1

Vectors, Tensors and the Index Notation

189

 

16-Aug-2012

 

7.2

Analysis of Three Dimensional Stress and Strain

201

 

16-Aug-2012

 

7.3

Governing Equations of Three Dimensional Elasticity

220

 

16-Aug-2012

 

7.4

Elastodynamics

222

 

16-Aug-2012

 

7.5

General Principles

229

 

 

 

 

 

 

 

 

8.

Plasticity

 

 

 

 

8.1

Introduction to Plasticity

241

 

23-Apr-2015

 

8.2

Stress Analysis for Plasticity

252

 

16-Aug-2012

 

8.3

Yield Criteria in Three Dimensional Plasticity

259

 

28-Apr-2015

 

8.4

Elastic Perfectly Plastic Materials

280

 

16-Aug-2012

 

8.5

The Internally Pressurised Cylinder

290

 

16-Aug-2012

 

8.6

Strain Hardening

299

 

16-Aug-2012

 

8.7

Associated and Non-Associated Flow Rules

314

 

16-Aug-2012

 

 

 

 

 

 

 

Answers to Selected Problems: Chapter 1

 

 

 

 

Answers to Selected Problems: Chapter 2

 

 

 

 

Answers to Selected Problems: Chapter 3

 

 

 

 

Answers to Selected Problems: Chapter 4

 

 

 

 

Answers to Selected Problems: Chapter 7

Answers to Selected Problems: Chapter 8