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Bob McGinty

bmcginty@gmail.com

Homework #2 Solutions

Homework #3 Solutions

Homework #4 Solutions

Author | Bob McGinty, PhD, PE | |

Email | bmcginty@gmail.com |

- INTRODUCTION
- BASIC MATHEMATICS
- Vectors
- Matrices & Tensors
- Vector Calculus
- Tensor Notation (Basic)
- Tensor Notation (Advanced)
- Coordinate Transformations
- Transformation Matrices
- Divergence Theorem
- Cylindrical Coordinates
- INTRODUCTORY MECHANICS
- DEFORMATIONS AND STRAIN
- Deformation Gradients
- Polar Decompositions
- Rotation Matrices
- Finite Element Mapping
- Small Scale Strains
- Green & Almansi Strains
- Principal Strains & Invariants
- Hydrostatic & Deviatoric Strains
- Velocity Gradients
- True Strain
- Material Derivative
- Special Strain Topics
- STRESS
- Stress Introduction
- Traction Vectors
- Energetic Conjugates
- Stress Transformations
- Principal Stresses & Invariants
- Hydrostatic & Deviatoric Stresses
- Von Mises Stress
- Corotational Derivatives
- Equilibrium
- MATERIAL BEHAVIOR
- Continuity Equation
- Navier Stokes Equation
- Thermodynamics
- Hooke's Law
- Metal Plasticity
- Mooney-Rivlin Models
- Dynamic Material Properties
- Materials and Tire Behavior
- COLUMN BUCKLING
- SIGNAL PROCESSING
- MISCELLANEOUS TOPICS
- Fasteners (in development)
- Strain Gauges

- http://en.wikiversity.org/wiki/Category:Continuum_mechanics

- http://www.thefullwiki.org/Continuum_mechanics
- http://en.wikipedia.org/wiki/Continuum_mechanics
- http://en.wikipedia.org/wiki/Finite_strain_theory
- Do Not Disturb Pages (fun stuff!)

The second new technology used here is MathJax, a Javascript based display engine for mathematical equations programmed in the LaTeX language. MathJax eliminates the need to display equations as GIF or PNG graphics files (or even SVG for that matter). MathJax requires only the following line of code in the <HEAD> segment of a webpage.

```
<script type="text/javascript" src="http://cdn.mathjax.org/mathjax/latest/MathJax.js?config=default"></script>
```

It is then possible to program any math expression in the HTML source using the LaTeX language. For example, typing

`\(\sigma_{ij}\)`

produces \( \sigma_{ij} \).
I'm often asked what software I used to develop the webpages. The answer is... the Vim editor (www.vim.org). Vim is the Windows-based version of the venerable Vi editor on Unix, and now Linux systems. I typed everything by hand.

Bob McGinty

February 2012