Solid Mechanics Part II: Engineering Solid Mechanics small strain

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

 

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)

 

To reference theses notes, see here.

 

Return to Mechanics Lecture Notes

 

Table of Contents

 

 

 

 

 

Last updated

1.

Differential Equations for Solid Mechanics

 

 

27-Mar-2008

 

1.1

The Equations of Motion

3

 

26-Jun-2017

 

1.2

The Strain-Displacement Relations

9

 

8-Oct-2013

 

1.3

Compatibility of Strain

17

 

30-Sep-2013

 

complete pdf

 

 

 

 

 

 

 

 

 

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

 

complete pdf

 

 

 

 

 

 

 

 

 

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

 

27-Feb-2015

 

complete pdf

 

 

 

 

 

 

 

 

 

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

 

12-Jun-2008

 

4.3

Plane Axisymmetric Problems

66

 

14-Feb-2018

 

4.4

Rotating Discs

78

 

18-Apr-2008

 

4.5

Quasi-Axisymmetric Problems

 

 

 

 

4.6

The Michell Solution

 

 

 

 

4.7

The Kirsch Solution

 

 

 

 

4.8

The Curved Beam

 

 

 

 

complete pdf

 

 

 

 

 

 

 

 

 

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

 

6.4

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

 

complete pdf

 

 

 

 

 

 

 

 

 

7.

Three Dimensional Elasticity

187

 

30-Sep-2013

 

7.1

Vectors, Tensors and the Index Notation

189

 

30-Sep-2013

 

7.2

Analysis of Three Dimensional Stress and Strain

201

 

30-Sep-2013

 

7.3

Governing Equations of Three Dimensional Elasticity

220

 

1-Oct-2013

 

7.4

Elastodynamics

222

 

1-Oct-2013

 

7.5

General Principles

229

 

 

 

complete pdf

 

 

 

 

 

 

 

 

 

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

 

15-Feb-2018

 

8.6

Strain Hardening

300

 

15-Feb-2018

 

8.7

Associated and Non-Associated Flow Rules

315

 

15-Feb-2018

 

8.8

General Theory

325

 

 

 

complete pdf

 

 

 

 

 

 

 

 

 

 

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