# Advanced elasticity

Welcome to this learning project about **Advanced elasticity**!

## Contents

## Learning Project Summary[edit]

**Project code:****Suggested Prerequisites:****Time investment:**6 months**Assessment suggestions:****Portal:Engineering and Technology****School:Engineering****Department:Mechanical Engineering****Stream:Applied Mechanics****Level: First year graduate**

## Content summary[edit]

This is an advanced course on the elastic deformations of solids.

## Goals[edit]

This learning project aims to.

- provide the mathematical foundations of advanced elasticity.

## Contents[edit]

### Syllabus and Learning Materials[edit]

- Nonlinear Elasticity
- Deformation measures
- Stress measures
- Balance laws and entropy inequality
- Constitutive relations
- Examples

- Buckling
- Refresh your basics
- /Linear buckling
- /Nonlinear buckling
- Examples

- Three-dimensional elastcity
- /Elastic potentials
- Examples

- Plates and Shells
- Dynamics
- /Vibrations
- Examples

- Fracture
- Examples

### Assignments[edit]

- Homework 1 Problem set
- Homework 2 Problem set
- Homework 3 Problem set
- Homework 4 Problem set
- Homework 5 Problem set
- Homework 6 Problem set
- Homework 7 Problem set
- Homework 8 Problem set
- Homework 9 Problem set
- Homework 10 Problem set
- Homework 11 Problem set

### Tests and Quizzes[edit]

### Textbooks and References[edit]

**Textbooks**

- R.W. Ogden, (1984), Non-linear Elastic Deformations, Dover Publications.
- A.J.M Spencer (2004), Continuum Mechanics, Dover Publications.
*An excellent introduction to continuum mechanics. You should own a copy for your personal library.* - L.E. Malvern (1969), Introduction to the Mechanics of a Continuous Medium, Prentice-Hall.
*A good reference for continuum mechanics.*

**References**

**Continuum Mechanics**:- R. M. Brannon (2004), Large Deformation Kinematics.
*An excellent introduction to kinematics.* - R. M. Brannon (2004), Rotation.
*Almost everything you ever wanted to know about rotations.*

- R. M. Brannon (2004), Large Deformation Kinematics.

**Mathematics**:- R. M. Brannon (2004), Elementary Vector and Tensor Analysis for Engineers.
*This free online book is the best introduction I have seen for vector and tensor analysis for nonlinear mechanics.* - R. M. Brannon (2004), Curvilinear Coordinates.
*Very useful if you wish to follow the literature on the nonlinear deformation of shells.* - A.P.S. Selvadurai (2000), Partial Differential Equations in Mechanics 1,2. Springer.
*Excellent introductory text on partial differential equations with engineers in mind.*

- R. M. Brannon (2004), Elementary Vector and Tensor Analysis for Engineers.

### Reading List[edit]

- ...

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