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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
42. Building an equivalent Pynite model
Benchmarking against OpenSeesPy and Pynite
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Summary

In this lecture, we'll cover the following:

  • Introduction to the PyNite library and how it compares with OpenSeesPy.
  • Navigating PyNite documentation and GitHub resources for implementation details.
  • Setting up a finite element model in PyNite (materials, mesh, supports, loads).
  • Use of built-in features such as mesh generation, load cases, and combinations.
  • Running an analysis and interpreting qualitative results using the built-in renderer.
  • Overview of the DKMQ element formulation and its relation to other plate theories.

In this lecture, we explore PyNite as a second tool for validating our solver, noting that while it is less feature-rich than OpenSeesPy, it is generally easier to use and more accessible. We walk through its documentation and GitHub resources, highlighting how clearly the library is presented and how its derivations align with concepts we have already studied. We then build a slab model step by step, defining materials, generating a mesh using built-in functionality, applying boundary conditions, and assigning loads with load cases and combinations.

After running the analysis, we use PyNite’s built-in renderer to visually inspect displacement and force distributions, focusing on qualitative validation rather than precise numerical comparison. Overall, we see how efficiently a complete finite element model can be constructed and analysed in PyNite, setting the stage for extracting and visualising results more flexibly in subsequent lectures.

Next up

With the PyNite model analysed, the next lecture focuses on extracting displacements and reactions from the results.

Tags

PyNiteDKMQ elementfinite element modellingload combinationsslab analysis

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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
43. Extracting displacements and reactions from Pynite