In this lecture, we'll cover the following:

• Building a utility function to extract finite element results at arbitrary points.
• Using SciPy’s griddata to interpolate bending moments and shear forces.
• Unpacking and preparing grid data for interpolation.
• Computing Wood and Armer design moments from bending and twisting components.
• Verifying and using the function within a completed slab finite element solver.

In this lecture, we focus on creating a practical utility function that allows us to query finite element results at any point within a slab. We take previously computed grid-based results and reorganise them into a format suitable for interpolation, using SciPy’s griddata function. This enables us to obtain bending moments $(Mx, My, Mxy)$, transverse shear forces $(Qx, Qy)$, and derived Wood and Armer design moments at arbitrary coordinates, not just at predefined grid points.

We also reinforce how design moments are calculated, particularly the role of torsional moments in increasing demand, and implement this directly in code. The lecture emphasises structuring data (through unravelling grid arrays and stacking coordinates) to make interpolation possible, and demonstrates how a compact utility function can streamline post-processing. We conclude by noting that, while a full finite element solver for a rectangular slab has now been implemented, the next critical step is validation against external tools such as OpenSeesPy.

Next up

With the first iteration of our custom solver now complete, the next section focuses on benchmarking our results against established libraries — OpenSeesPy and PyNite.