Writing a Finite Element Solver

As part of the Finite Elements grad class at RIT I wrote finite element solver and used it to analyze the pressure distribution on a plate with a thing fluid film under it. This project was especially interesting because the solver worked directly off differential equations for the thin film, so a cfd simulation in ansys would not be anywhere close to as accurate without a huge number of elements and complexity.

 Pressure distribution over the rigid, oddly shaped plate pushing on a thin film


The report for this project is here: https://docs.google.com/document/d/1weJ6BIvdVOSqEhE3k7nNX-rH0ABxvAfRUZdo0ZrNjuc/edit?usp=drivesdk

Another interesting project we did was using a thermal model in Ansys Mechanical APDL to solve a beam in torsion. This project exploits dynamic similarly: the fact that thermal conduction has the same differential equation as the stress output of a beam in torsion means we can solve a 2d torsion cross section by creating a thermal model in Ansys. This can be done without needing to create a complex and computationally expensive 3d model. 

The temperatures in the thermal model are extreme, but this is just a result of the units being somewhat meaningless because this is actually a stress problem, not a thermal problem

The report for this project is here: https://docs.google.com/document/d/1EZbkeC8dEXRf2S3burG6KFQyYg9F1Babb2lb-jCqGVU/edit?usp=drivesdk

While Finite Elements was by far the hardest I've taken at RIT, I found it to be very rewarding. I got better at time management after having 5 weeks to work on several 30 page homework assignments. There are a lot of concepts like quadrilateral elements and gaussian quadrature that I felt I would never need to apply directly, but still give me a good understanding of how a FEM solver is optimized in the background.