Solid Mechanics Part I: An Introduction to Solid Mechanics

This book is primarily aimed at the Part II-III Engineering undergraduate student (although some sections are more appropriate to the graduate student or researcher).

 

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)

 

Return to Mechanics Lecture Notes

 

 

Table of Contents

 

*

  = an advanced topic which may be skipped (certainly in a first course)

 

 

Last updated

1.

Introduction

1

 

04-May-15

 

1.1

What is Solid Mechanics?

3

 

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1.2

What is in this Book?   

7

 

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2.

Statics of Rigid Bodies

9

 

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2.1

The Fundamental Concepts and Principles of Mechanics

11

 

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2.2

The Statics of Particles

14

 

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2.3

The Statics of Rigid Bodies

19

 

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3.

Stress

29

 

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3.1

Surface and Contact Stress

31

 

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3.2

Body Forces

39

 

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3.3

Internal Stress

42

 

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3.4

Equilibrium of Stress

52

 

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3.4b

Stress Transformation: Further Aspects

59

 

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3.5

Plane Stress

62

 

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3.5b

Stress Boundary Conditions: Continued

80

 

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4.

Strain

85

 

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4.1

Strain

87

 

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4.2

Plane Strain

101

 

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4.3

Volumetric Strain

110

 

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5.

Material Behaviour and Mathematical Modelling

113

 

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5.1

Mechanics Modelling

115

 

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5.2

The Response of Real Materials

119

 

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5.3

Material Models

134

 

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5.4

The Continuum

137

 

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6.

Linear Elasticity

143

 

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6.1

The Linear Elastic Model

145

 

17-May-15

 

6.2

Homogeneous Problems in Linear Elasticity

154

 

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*

6.3 Anisotropic Elasticity

156

 

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7.

Applications of Elasticity

167

 

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7.1

One Dimensional Axial Deformations

169

 

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7.2

Torsion

179

 

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7.3

Pressure Vessels

185

 

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7.4

Beams

194

 

17-May-15

 

7.5

Buckling

222

 

17-May-15

 

 

 

8.

Energy and Virtual Work

229

 

3-Jun-15

 

8.1

Energy in Deforming Materials

231

 

3-Jun-15

 

8.2

Elastic Strain Energy

242

 

3-Jun-15

 

*

8.3 Complementary Energy

256

 

3-Jun-15

 

*

8.4 Strain Energy Potentials

258

 

3-Jun-15

 

*

8.5 Virtual Work

262

 

3-Jun-15

 

*

8.6 The Principle of Minimum Potential Energy

270

 

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9.

Failure

275

 

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9.1

Material Failure

277

 

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10.

Viscoelasticity

283

 

3-Jun-15

 

10.1

The Response of Viscoelastic Materials

285

 

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10.2

Examples and Applications of Viscoelastic Materials

289

 

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10.3

Rheological Models

292

 

3-Jun-15

 

*

10.3b Rheological Models: Spectra

302

 

3-Jun-15

 

*

10.4 The Hereditary Integral

306

 

3-Jun-15

 

*

10.5 Linear Viscoelasticity and the Laplace Transform

318

 

3-Jun-15

 

*

10.6 Oscillatory Stress, Dynamic Loading and Vibrations

325

 

3-Jun-15

 

*

10.7 Temperature-dependant Viscoelastic Materials

337

 

3-Jun-15

 

 

 

11

Plasticity

 

 

 

 

11.1

Plasticity

 

 

 

 

 

 

 

 

 

12

Viscoplasticity

 

 

 

 

12.1

Viscoplasticity

 

 

 

 

 

 

 

 

 

Index

 

 

 

Answers to Selected Problems: Chapter 2                                                             

Answers to Selected Problems: Chapter 3                                                             

Answers to Selected Problems: Chapter 4                                                             

Answers to Selected Problems: Chapter 5                                                             

Answers to Selected Problems: Chapter 6                                                             

Answers to Selected Problems: Chapter 7

Answers to Selected Problems: Chapter 8

Answers to Selected Problems: Chapter 9

Answers to Selected Problems: Chapter 10

Answers to Selected Problems: Chapter 11

Answers to Selected Problems: Chapter 12                                                           

 

 

 

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