Week Five – Chapter One

Today is the last class on chapter one. I will still answer questions online on this chapter. Test is tomorrow, 11-1pm. Next week, we begin Chapter Two, Tensor Algebra. The goal of all you have learned in chapter one is to put you on a sound footing to learn tensor analysis. If you do chapter one well, the next chapter will be about the same or even easier. If you find the next chapter harder, it is likely coming from insufficient mastery of the material under vector analysis. Tensor theory is an extension of vectors.

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We have added some of the materials that should have been covered in the Programming practice of yesterday.

Programming Clinic II

The programming examples here and subsequently are given to explain certain concepts on Vectors, tensors, continuum mechanics or show you how to use specific Mathematica functions. The following steps should be followed:
1. Type in the codes and ensure they run error-free.
2. Try to understand the working program so that you can use similar constructs in your own coding. Make use of the help system in Mathematica to understand other ways you may be able to invoke the same functions with other argument sets and options. Sometimes the codes involve technical issues or a deeper understanding of vectors, geometry and transformations. Do not rush over those issues. A good programmer learns to address such issues and increases in knowledge.
3. Write your own programs by modifying and adding to the code you have been given to do similar or other things.
These steps will help you become more confident on your ability to create your own codes.
Note that turning your understanding of a concept to computer program that works is one of the best ways to master concepts. There is no way to forget such things that you have turned into codes by yourself!

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Note that all the codes included in this practical class are either given in the Continuum Mechanics main text that you should have downloaded by now, or in the appropriate lecture slides.
We remind you again that the questions on the test on Friday are essentially paraphrases, in objective form, of the same examples that have been solved for you in the book. You are to further remember that you may be able to get further assistance from us by posting questions and comments on the same web page.
Please post questions ONLY after availing yourself of all the other facilities already available. In particular, do not ask questions that have been adequately answered in the book unless you specifically want further elucidation after a honest attempt at the one given in the book.

Parametric Design, Tensors: Introduction

For today’s lecture, I present two designs of simple hinges to illustrate the engineering aspects of the manufacture of such a simple device. The Timeline of one of these can be found here.
The slides for today’s lecture are in three parts. The first two are slow motion versions of the above timeline and they are shown next:

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and

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A Summary of the first 12 pages of the Recommended Text with solutions.

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Solved Problems:

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