In this lecture, we'll cover the following:

• Constructing an evaluation grid to compute shear forces and bending moments
• Defining a data structure to store element association and coordinate information
• Using natural (local) coordinates to generate points within each finite element
• Mapping local coordinates to global coordinates via shape functions
• Visualising the evaluation grid to verify correct point distribution

In this lecture, we focus on building an evaluation grid that will later be used to calculate shear forces and bending moments across a finite element mesh. We design a structured data container where each row represents a point in the grid, storing its parent element, global x and y coordinates, and corresponding natural coordinates (r and s). By looping through each element and systematically varying the natural coordinates, we generate a consistent set of evaluation points within every element.

We use shape functions to map these local (natural) coordinates to global coordinates, allowing us to position each evaluation point correctly in the overall geometry. By selecting values of r and s such as −1, 0, and 1, we create a grid of nine points per element, covering corners, edge midpoints, and the centre. Finally, we plot these points to verify the grid visually and build intuition about how the sampling works. This prepares us for the next step, where we will compute shear forces and bending moments at each of these evaluation points.

Next up

With the evaluation grid in place, the next lecture shows how to compute the actual bending moments and shear forces at each grid point.