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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
45. Visualising Pynite moments and shears
Benchmarking against OpenSeesPy and Pynite
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Summary

In this lecture, we'll cover the following:

  • Plotting previously computed displacement fields using a heat map visualisation.
  • Implementing interactive plotting of bending moments (Mx,My,Mxy)(M_x, M_y, M_{xy}) with widgets.
  • Visualising transverse shear forces (Qx,Qy)(Q_x, Q_y) with optional middle-strip masking.
  • Using masking and widgets to focus on specific regions and interpret peak values

In this lecture, we complete the post-processing stage of our finite element model by visualising key results. We begin by addressing a previously omitted step: plotting the displacement field using a heat map. We then move on to plotting bending moments, implementing an interactive function that allows us to switch between different moment components while dynamically displaying peak values.

We also extend the visualisation approach to transverse shear forces, introducing a masking technique that isolates a central strip of the slab. This allows us to better interpret shear distributions by focusing on relevant regions, with widget controls enabling real-time adjustments. Throughout, we confirm that the plotted results align with expectations and previously validated models, setting the stage for a more detailed comparison of different modelling approaches in the next lecture.

Next up

With results now available from all three models, the next lecture presents a qualitative comparison to assess how well they agree.

Tags

finite element postprocessingbending moment visualisationshear force plottinginteractive widgetsdata masking

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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
46. Qualitative comparison across models