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
72. Wrapping up and what next?
Eliminating zero-energy displacements
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Summary

In this lecture, we'll cover the following:

  • Recap of the tools and skills developed throughout the course.
  • Restate the importance of understanding finite element analysis (FEA) fundamentals.
  • Introduction to the next step: extending from plate elements to shell elements.

In this lecture, we reflect on the journey through the course and consolidate what we have achieved. We highlight the practical skills we have developed, including working with tools such as OpenSeesPy, PyNite, Gmsh, and our own custom scripts. More importantly, we reinforced our understanding of how finite element analysis operates behind the scenes, with particular focus on how the Reissner–Mindlin formulation enables accurate modelling of both thick and thin plate behaviour.

We also look ahead to the natural progression of these ideas, noting that shell elements build directly on the plate formulations we have already developed. We recognise that much of the complexity has already been addressed, making the transition to shell analysis relatively straightforward. This lecture also includes a link to request your course completion certificate.

Tags

Reissner–Mindlin platesshell elements transition

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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.
Course Complete