In this section, we'll cover the following:

• Transitioning from preparatory work to building a complete finite element solver.
• Assembling individual element stiffness matrices into a global structure stiffness matrix.
• Constructing the global force vector and solving for nodal displacements.
• Performing post-processing to obtain additional results.
• Using a simple procedurally generated mesh to focus on the solution process rather than meshing.

In this section, we move from theoretical groundwork to implementing a full finite element solver. We focus on the core procedural steps common to all finite element analyses: assembling element stiffness contributions into a global system, forming the force vector, and solving for nodal displacements. We then extend this process with post-processing to extract meaningful results from the solution.

We emphasise that these steps are largely universal, regardless of element type, reinforcing a consistent algorithmic workflow. To keep the focus on the solution procedure, we work with a simple, procedurally generated rectangular mesh rather than addressing meshing complexities (yet). This allows us to clearly understand and validate each stage of the solver, laying a solid foundation before exploring more advanced implementations or external libraries.

Next up

In the next lecture, we will begin building the solver by procedurally generating a rectangular mesh to work with.