I got the finite element method report back today and I got full score! You can read about the first half of the project on my blog here, where I also explain the geometry a bit more. It’s a simulation of a plastic mold injection tool where there is hot plastic under pressure inside the tool and a force pushing down on the tool from the top. The abstract for the report is:
Abstract
In this report we use Matlab and CALFEM to study the temperature distribution over time on a plastic mold injection tool. We also calculate the plane stress caused by external forces as well as thermal stress for the tool.
The second half of the project was about simulating the stress exerted on the metal that the tool is made up of. The stress caused by the mechanical stresses (the pressure from the plastic and from the force above) look like this:
Mechanical stress
When metal heats up it expands, and since the tool is constrained at certain boundaries and because the heat change is different inside the metal, this will cause further stress in the material, causing thermal stress. And the stress caused by the increased heat will look something like this.
Thermal stress
If you can read Swedish and is further interested in an account of how to solve this problem using the finite element method, you should read the entire report. You can view it online here. I have removed the code from the report out of respect for the lecturer. I will however share one piece of code, that I know he wouldn’t mind, that I am particularly proud of.
[gist id="417285"]
This is the code that generates the mesh you can see a hint of in the pictures (and is shown more clearly on the first page of the report). It automatically generates this mesh given a size of the element side. Almost every other group did this by hand, by entering like 300 values into a big matrix… by hand…
here is what the school had to say about the report.
Individual comments
The problem is well described and clear to the reader. The report is well structured, nice and easy to follow. It would be easy to reproduce your code without reading the attached Matlab code. Sizes of your matrices and vectors are presented which makes it easy to follow the solution process. The geometry is presented and looks correct. The derivations from the strong formulation to the FE-formulation presented correctly. The contribution to the stiffness are correctly defined and presented with illustrations that makes it easy for the reader to follow and you describe how to calculate the boundary vectors. The inital temperature is included. The transiet scheme is implemented correctly and a discussion on the size of the time step is present. It is clear that you have understood the relationship between stresses and elastic/thermal strains, but you have used the wrong formula for calculating the effective stress. The results are discussed and seem correct. The Matlab code is well commented but a bit complicated. In general very good report! Well done!
I have fixed those small errors (and regenerated the images) in the report that is linked in this post. I’m not sure exactly how my code is complicated. I would argue that it is powerful, contrary to some other people who as I said put the shit in by hand; that’s complicated!
I could without any further changes to the code replace my mesh with a non-uniform one and I could easily change just a few parameters to solve any general problem.
Half related comment about school
I just wanted to say that I put a lot of work into this project, quite surely more than I had to. I am however very happy that I have done it. School is mostly sort of.. drudgery..
It is very, very easy to just go through the motions and do the minimum required to pass the course. I strongly believe anyone could get a masters in Engineering Physics. But I think one should put in this kind of extra effort now and again to produce something that’s actually of high quality.
Whenever I come across a course or subject I really like, I put in some extra effort to produce something above the expected. It’s a good way to learn that subject extra well, but It’s also a good confidence booster. I’ve just shown myself that if I really put in just a tiny ounce more work I will get the maximum score and I will get pretty awesome feedback from the people responsible for the course. It feels good.
It does by far not feel good enough to do it in all courses, but I think everyone should just.. take some time now and then to mark their existence by putting in a bit more effort than required. There’s a full long blog post in here somewhere on these thoughts, but I’ll leave that for another time when I can think it through more thoroughly.
