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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
56. Converting our code to a utility function
Meshing with GMSH and Python
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Summary

In this lecture, we'll cover the following:

  • Consolidating previously developed meshing functions into a reusable mesh utils Python file.
  • Adapting the element reordering function for internal use within the mesh utils file.
  • Updating the mesh generation function to include optional arguments (node reordering and log suppression)
  • Preparing the workflow for integration with a finite element analysis pipeline

In this lecture, we focus on refactoring and organising the functionality developed so far into a dedicated utility module. We take previously written functions, such as element reordering, mesh generation, and visualisation, and migrate them into a single script, making them easier to reuse across different notebooks. As part of this process, we adapt certain functions for internal use, streamline their interfaces, and introduce optional arguments to improve flexibility, such as automatic node reordering and suppression of gmsh log output.

We then demonstrate how this modular approach simplifies the workflow by reducing the amount of code needed in a notebook to just a couple of function calls. By encapsulating complexity within the utility file, we make mesh generation and visualisation more efficient and maintainable.

Next up

With the meshing utilities in place, the next section focuses on running finite element analyses using these custom-generated meshes.

Tags

mesh utilitiesgmsh integrationnode reorderingPython modularisation

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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
57. Section overview - Custom mesh finite element analysis