The University of Missouri’s fundamental simulation software is MATLAB, short for Matrix Laboratory. We are introduced to the program through two classes sophomore year, and then continue to use it through the rest of our upperclassmen courses.

140805 EDIT: In hindsight, I have found it very comparable to python, whereas I prefer the format of python, however MATLAB boasts impressive matrix manipulation. I am considering using both programs for the continuation of my multi-material socket project when I will write and implement my own FEA program. More to come on that.

In the meantime, I would like to give an example of my work. I have selected the final project of our MATLAB tutorial class from May of 2011. This was a two-person project, and was scheduled over the time of 3-4 weeks. This class was lead by Professor D. Smith. I have made the code for the project available for download below.

PURPOSE: The goal of this project is to design a tapered curved beam for a punch press frame as shown in Figure 1. The curved frame will be modeled as a cantilever beam as shown in Figure 2. All evaluations will be performed in terms of the angle ‘theta’, and ‘R’ defines the radius of the beam’s neutral axis as shown in Figure 2. Curved beam formulas will be used to evaluate the beam’s deflection and stress as defined below.

IMG_7002 - Version 2IMG_7003IMG_7004

PROCESS: My partner and I wrote a main script (main.m) that would call 5 other functions (GETH.m, GETMASS.m, GETDELTA.m, GETSTRESS.m, and INTGRD.m). The functions labeled as GET-.m would find there respective factors, most of them utilizing INTGRD.m, which contained all the integrand functions shown above.

These files are easy to utilize, and can be run just through running the main script. The user will be prompted to enter a number of years that the beam would have corroded over in order to add this feature to the analysis. The script will report mass, beam tip deflection, and max stress for each of six different geometries, pictured below. This visualizations is per the requirements of the prompt, using ‘theta’ as the independent variable. Here ‘height’ could be better thought of as ‘varying beam thickness.’

Height vs Theta

RESULTS: For each of the six cases, a-f, we were asked to report the mass, tip deflection, and max stress for t={0,20}. Also, we are able to plot the localized stress along the length the beam of each case in a quasi-FEA. These results, as shown below in the table and plot, could be used to choose the most applicable of the six cases. Using max stress as the first filter, it would appear case B,C,E, or F is the best choice. While B has only ~85% the mass of the other three options, it also deflects ~0.005 inches more. If this increase in deflection is tolerable, than B would be the best choice. On a purely mass to deflection ratio, case E fares the best, followed by C,F, and then B. Lastly, before making a choice, the situation after ‘t’ number of years should be accounted for, to see if the case still holds up to standards.

MATLAB results

Stress vs Theta

If you would like to download the code for this project, I have made it available here: AMadinger MATLAB sample

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