In this lecture, we'll cover the following:

• Implementing patch loading by defining loads as dictionaries containing boundary points and magnitudes
• Identifying nodes within a polygonal patch using a Boolean mask
• Determining which finite elements receive loading based on included nodes
• Applying equivalent nodal forces for patch loads and assembling them into the global force vector
• Visualising intended versus actual loaded regions and diagnosing implementation errors

In this lecture, we walk through how to implement patch loading within a finite element slab model. We define patch loads as polygonal regions with associated magnitudes, then identify all mesh nodes that fall within each region using a masking approach. From there, we determine which elements should receive loading by checking whether they contain any of these nodes, and we apply equivalent nodal forces to those elements. This approach deliberately simplifies the problem by assigning the load to entire elements, even if they only partially intersect the patch.

We also explore how to visualise both the intended patch regions and the elements that actually receive the load, which highlights the effect of mesh resolution on accuracy. We conclude by reflecting on alternative, more precise strategies, such as refining the mesh to better align with patch boundaries.

Next up

In the final lecture, we will recap what has been achieved throughout the course and look ahead to the natural next step: extending from plate elements to shell elements.