In this lecture, we'll cover the following:

• Fixing indexing inconsistencies when storing and retrieving element numbers in the evaluation grid
• Refining the mesh density to improve visual resolution of results
• Attempting to visualise transverse shear forces (Qx and Qy) using heat maps
• Identifying issues with averaging shear values at shared nodes, leading to misleading plots
• Demonstrating the “banding” artefact caused by opposing shear contributions from adjacent elements
• Developing a method to remove non-unique data points using NumPy’s unique, inverse mapping, and counts
• Constructing a Boolean mask to retain only uniquely defined coordinate points
• Handling floating-point precision by converting coordinates into integer “keys”
• Applying the filtering process to generate a reduced shear evaluation grid for accurate visualisation

In this lecture, we focus on visualising transverse shear forces across a slab and uncover why a straightforward plotting approach fails. We begin by correcting a small indexing issue in the evaluation grid and refining the mesh to improve resolution. When we attempt to plot shear forces directly from averaged data, we observe unrealistic artefacts that present as a banding effect, caused by averaging opposing shear values from adjacent finite elements. This highlights a key distinction between bending moments, which can be safely averaged, and shear forces, which cannot.

To address this, we develop a more robust approach by filtering out non-unique data points at locations where multiple elements contribute conflicting shear values. We walk through a simplified example to build intuition, then implement a masking technique using NumPy to retain only coordinates that appear once. To ensure numerical reliability, we convert floating-point coordinates into integer-based keys before comparison. By applying this filtering process, we obtain a refined set of evaluation points that allow us to clearly represent the shear distribution and are suitable for meaningful visualisation in the next step.

Next up

With the shear data cleaned, the next lecture focuses on visualising the shear force distributions using properly ordered and reshaped grid data.