Welcome to section 4. We’re finally finished with the preparation work, and now we can move on to actually building our first finite element solver. This section isn’t really about covering new theory or mechanics.

Instead, we simply need to go through the fundamental steps of combining individual element stiffness matrices into a structure stiffness matrix and building a force vector. Then, we can solve for nodal displacements and perform some post-processing to extract more results.

The algorithmic steps we implement in this section are more or less the same, regardless of what type of element we’re working with! Building a finite element solver always involves the same fundamental steps. So, if you’ve completed the prerequisite course, you’ll recognise a lot of similar code in this section.

One thing to note about this section is that we’re focusing on implementing the finite element solver and are not focusing on meshing at this stage. So, we procedurally generate a relatively simple rectangular mesh to work with. This will allow us to focus on the finite element solution process and make validation more straightforward.

If you don’t want to work through building your own solver and are more interested in implementing open-source library solutions with OpenSeesPy and Pynite, you can skip this section. However, I recommend completing this section to get the most complete picture of the solution process.