In this lecture, we'll cover the following:

• Visualising heat maps on irregular grids using triangulation.
• Using matplotlib.tri and tricontourf to generate filled contour plots.
• Handling different bending moment components $(M_x, M_y, M_{xy})$.
• Adding interactive widgets to control plotted data and display options.
• Overlaying triangulation, Gauss points, and element grids for interpretation.

In this lecture, we focus on how to visualise data defined on an irregular grid, which commonly arises when working with finite element meshes. We introduce the use of triangulation via matplotlib.tri, allowing us to convert irregularly spaced data into a form suitable for contour plotting. By using tricontourf, we can generate smooth, filled contour plots that effectively represent quantities such as bending moments across the structure.

We implement an interactive plotting function that allows us to switch between different moment components $(M_x, M_y, M_{xy})$, while also controlling visual features such as triangulation, Gauss points, and the element grid. We explore how the data is prepared differently depending on the moment type, particularly noting the treatment of absolute values for bending moments versus torsional moments. Through this, we gain insight into how results from analysis (e.g. Gauss point data) map onto the physical structure.

Finally, we enhance the visualisation by overlaying triangulation lines and sampling points to better understand how the irregular grid is constructed and how results are distributed. This provides a clear and flexible framework for interpreting finite element results, setting us up to extend the same approach to shear forces in the next lecture.

Next up

Next, we will extend the same visualisation approach to transverse shear forces, incorporating masking techniques to focus on relevant regions.