Category Archives: Tutorials

Tutorials for undergraduate and graduate students and for the general public.

Tutorial: Define Your Strain!

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This single-page document emphasizes the need for experimentalists and theorists alike to ALWAYS define their strain measure. For every percent increase in strain, the most popular measures of strain will disagree by as much as 1.5%. This might not sound like much, but try running a simple shear Von Mises strain cycle using log strain and engineering strain. You will find that the engineering strain calculation produces anomalous PRESSURES because volumetric strain does NOT equal the trace of strain EXCEPT for logarithmic strain.

You may download the rest of the document here.

Tutorial: Mohr's Circle

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A self-study refresher with interesting tidbits such as Pole Point and how to do Mohr’s circle for nonsymmetric matrices — very useful for quickly doing a polar decomposition! (Last posted 2003, but considerable work has been performed recently to incorporate Mohr’s circle as part of the opensource VTK for visualization in finite element simulations).

You may download the rest of the document here.

Tutorial: Rotation

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A REALLY BIG (long download time) tutorial on how to describe rotation. Topics include coordinate transformations, tensor transformations, converting an axis and angle of rotation into a rotation tensor, Euler angles, quaternions, and generating a uniformly random rotation tensor. This document also discusses the common numerical problem of “mixing” rotations in such a way that the mixed rotation is physically reasonable. The pages in the document that deal with random rotations contain some complicated figures, so don’t worry if your pdf reader pauses for a while on those pages. As a matter of fact, watching the pdf viewer render the figures is like an informative movie because it draws the random dots in the same order as I computed them. By watching the rendering, you can see the nonuniform clustering quite clearly.] (Last posted here 020509, but a formal publication is anticipated)

You may download the rest of the document here.

Tutorial: Slideshow introduction to mappings in continuum mechanics

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Each time you generate output from input, you are using a mapping. The mappings in continuum mechanics have similarities with simple functions y=f(x) that you already know. This slideshow (which apparently renders properly only when viewed from PowerPoint on a PC rather than Mac) provides a step-by-step introduction to mappings of the type used in Continuum Mechanics.

You may download the rest of the document here.

Tutorial: Functional and Structured Tensor Analysis for Engineers

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A step-by-step introduction to tensor analysis that assumes you know nothing but basic calculus. Considerable emphasis is placed on a notation style that works well for applications in materials modeling, but other notation styles are also reviewed to help you better decipher the literature. Topics include: matrix and vector analysis, properties of tensors (such as “orthogonal”, “diagonalizable”, etc.), dyads and outer products, axial vectors, axial tensors, scalar invariants and spectral analysis (eigenvalues/eigenvectors), geometry (e.g., the equations for planes, ellipsoids, etc.), material symmetry such as transverse isotropy, polar decomposition, and vector/tensor calculus theorems such as the divergence theorem and Stokes theorem. (A draft of this document was last released publically on Aug. 3, 2003. The non-public version is significantly expanded in anticipation of formal publication.)

You may download the rest of the document here.

Tutorial: Use of the shell 'xargs' command

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I have found the ‘xargs’ command line utility to be very useful sometimes.  Often you can avoid writing a special shell script to perform a task by using xargs to perform a task on a list of files.  Its use can best be described through an example.  I have recenlty be migrating files from one svn repository to another.  I began by copying all of the files over using rsync.  This copied all of the .svn files from the old repository, which I didn’t want.  This left me with at least 30 directories, each with a .svn directory that needed to be removed.  What to do?  Use xargs.  Here is the command:

command-prompt> find -name .svn | xargs rm -rf

This uses the find command to generate a list of all files and directories names ‘.svn’ (case sensistive).  This list is then piped to the xargs command, which runs ‘rm -rf’ on each file in the list.  That’s it!  Note that as this command is written it will seach the current directory and all subdirectories for files with name ‘.svn’.  If you want to have ‘find’ search a directory other than the current directory you can add the path of that directory after the file name to search for.  See the man page for find for more info.

Tutorial: Use rsync instead of mv or scp when it really matters

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I’ve been running a lot of simulations on the ‘updraft’ parallel computing cluster at the University of Utah.  My input files often have to wait in the queue for quite a while (a few days sometimes) before they can be ran.  The simulations generate large data sets which I then need to use for post-processing.  The directory where these files are created on the cluster is regularly wiped by the administrators to keep space free for other users.  This means that you don’t want to leave important data sitting around on this file system.  I’d been moving it back to my home directory on the cluster using ‘mv’, and eventually transfering it to my workstation using ‘scp’.   This was kind of a pain and took FOREVER!  I also discovered something that caused me to completely abandon ‘mv’ for any data that is even somewhat important.  I was using ‘mv’ to transfer the data to my home directory when I lost my internet connection.  Big deal right.  I logged back in only to find out that the data files had been corrupted by the inturrupted ‘mv’ command.  Now I had to run the simulation all over again to generate a new data file.  Bummer.  I did a little research about ‘mv’ and found that if it is interupted for any reason, it often looses data.  Not good.  Enter rsync.  rsync is a tool which makes a copy of files and directories.  If it gets interrupted, you can simply restart it and it will essentially continue where it left off.  Why not just use cp or scp?  Two reasons.  First if cp or scp is interupted, then issued again it simply restarts.  This is really a problem when the transfer takes an hour an you need the data NOW.  Which brings me to the second reason:  speed.  If you call rsync with the -z flag, it compresses the data before copying it.  On remote file transfers this results in a HUGE speed up.  Of course with rsync, once the files are transferred you need to manually delete the unwanted copy.  You can use ‘rdiff’ to verify that the two copies are in fact identical before deleting the unwanted files.  Did I mention that rsync is also great for backups too?

Tutorial: Emacs and GDB

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I remember learning how to use a debugger and Utah State University as an undergraduate.  We learned to program in Fortran 90, and used a Microsoft debugger.  It seemed cool, but honestly with the types of programs I was writing at the time, using print statement seemed to be effective enough and less of a hassle.  Recently I have been working with the Uintah MPM code, which is MUCH larger and more complex than any code I’ve ever written.  After several months of wading through the code I finally came across a problem that “cout” just could not help me solve.  The code was suddenly crashing with an allocation error and giving no useful backtrace information.  A colleague suggested that I use gdb to find out where the problem was occurring.  It turned out to be very, very helpful and surprisingly easy to use.  I’ve recently become a convert to Emacs, and found that the gdb interface in Emacs is especially nice.  So here is goes:

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