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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
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1. Welcome to the course - roadmap overview
Welcome and Setting the Scene
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Summary

In this lecture, we'll cover:

  • The aims of the course and review the roadmap ahead.
  • The three levels of depth you can choose to engage with the course at, from a complete understanding of the core theory to focusing on implementation and validation using open-source tools.
  • A very brief overview of each section.

We begin by stating the course's goal - to equip you with both the theoretical knowledge and practical skills required for creating a custom finite element solver capable of analysing plate structures. The course is broken down into multiple sections such as the mechanics of Reisner-Mindlin theory, developing the element stiffness matrix, and deploying Gauss quadrature for numerical integration. Alongside coding exercises, we will validate our custom solver with open-source libraries like OpenSeasPy and Pynite. This validation is crucial for ensuring the reliability of our solver.

You can engage with the course at different levels of depth, from building a comprehensive understanding of the theory and coding implementation to focusing purely on analysis workflows using open-source libraries. Eventually, we will tackle advanced topics such as mesh generation, shear locking, and zero energy displacement. By the end, we will have developed a robust finite element analysis solver, and you will have gained confidence in applying these techniques to real-world scenarios using both our custom code and established open-source tools.

Next up

Next, we'll cover some important housekeeping items including prerequisites and tips to help you get the most out of this course.

Tags

Finite element analysisReisner-Mindlin theory

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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
2. Housekeeping - Python, prerequisites and tips for success