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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
43. Extracting displacements and reactions from Pynite
Benchmarking against OpenSeesPy and Pynite
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Summary

In this lecture, we'll cover the following:

  • Extracting nodal coordinates, displacements, and reactions from the model.
  • Organising and reshaping results to map onto a 2D grid for visualisation.
  • Identifying and locating the maximum displacement in the slab.
  • Verifying vertical force equilibrium by comparing loads and reactions.
  • Visualising reaction forces and interpreting differences between modelling approaches.

In this lecture, we focus on extracting and processing analysis results from our finite element model. We loop through each node to collect its coordinates, displacement, and reaction, and then reorganise this data so it can be mapped onto a structured 2D grid. By sorting and reshaping the displacement data, we prepare it for visualisation across the slab, and we also identify the maximum displacement and its location, confirming that it aligns with expectations and prior results.

We then verify the physical correctness of the model by checking vertical force equilibrium, ensuring that the sum of reactions matches the applied loads. Finally, we visualise the reaction forces using custom plotting tools and examine their distribution, including notable corner effects. We compare these results with those from our previous modelling approaches, noting that consistency in overall behaviour builds confidence in the model.

Next up

Next, we will extract bending moments and shear forces from the PyNite model, completing the dataset needed for a full comparison.

Tags

nodal displacementreaction forcesmeshgrid visualisationequilibrium check

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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
44. Extracting moments and shears from Pynite