FINITE ELEMENT ANALYSIS OF SHELLS - EARLY ACCESS 
Section 4
Expanding to a full plate element solver
21. Section overview - Expanding to a full plate element solver
01:28 (Preview)
22. Procedurally generating a rectangular mesh
24:30
23. Defining plate constraints
11:08
24. Defining the self-weight force vector
10:35
25. Building the structure stiffness matrix
10:05
26. Solving the system and extracting reaction forces
28:13
27. Plotting the plate displacements
18:10
28. Building an evaluation grid for stress resultants
10:31
29. Calculating the moments and shears
22:00
30. Visualising the plate bending moments
14:13
31. Extracting shear forces
29:04
32. Visualising the plate shear forces
12:21
33. Adding strip and edge masking to the shear plot
26:04
34. Adding magnitude clipping to the shear plot
10:40
35. Building an interpolation utility function
09:53
27. Plotting the plate displacements
Expanding to a full plate element solver
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Summary

In this lecture, we'll cover the following:

  • How to generate a contour (heat map) plot of vertical slab displacements
  • Reshaping displacement data to align with the computational grid
  • Enhancing visualisation by overlaying nodal points and mesh elements
  • Interpolating results onto a finer grid using SciPy’s griddata
  • Encapsulating plotting functionality into a reusable utility function

In this lecture, we focus on visualising the computed vertical displacements of a slab using contour plots. We begin by reshaping the displacement vector so it aligns with the spatial grid, enabling us to produce a filled contour (heat map) plot. We explore how plotting choices such as colour maps, contour levels, and aspect ratio affect interpretation, and we reinforce the importance of visual checks for qualitative validation. By overlaying nodal points and mesh elements, we make clear where values are computed versus interpolated, improving transparency in the results.

We then extend this visualisation by interpolating displacement values onto a finer grid using SciPy’s griddata function. Although optional, this step produces a smoother contour plot and demonstrates how interpolation can refine presentation without altering underlying results. Finally, we consolidate the plotting workflow into a reusable function, allowing flexible inclusion of nodes, elements, labels, and titles. We conclude by confirming correctness through testing and preview the next stage of post-processing, which will focus on bending moments and shear forces.

Next up

In the next lecture, we will build an evaluation grid that enables the computation of bending moments and shear forces across the plate.

Tags

contour plottinggrid interpolationSciPy griddatadisplacement visualisationfinite element post-processing

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Finite Element Analysis of Plate and Shell Structures: Part 1 - Plates

An analysis pipeline for thick and thin plate structures, a roadmap from theory to toolbox

After completing this course...

  • You will understand how Reissner-Mindlin theory enables us to accurately capture both thin and thick plate behaviour.
  • You will understand how to turn the fundamental mechanics of plate behaviour into a custom finite element solver written in Python.
  • You will have developed meshing workflows that utilise the powerful open-source meshing engine, GMSH.
  • In addition to using your own custom finite element code, you will be comfortable validating your results using OpenSeesPy and Pynite.
Next Lesson
28. Building an evaluation grid for stress resultants