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
38. Extracting OpenSeesPy displacements and reactions
Benchmarking against OpenSeesPy and Pynite
Please log in or enroll to access resources

Summary

In this lecture, we'll cover the following:

  • Extracting nodal displacements from the numerical model using OpenSeesPy.
  • Identifying the maximum displacement and its location within the slab.
  • Visualising displacement fields using a heat map.
  • Computing and interpreting support reactions, including corner behaviour.
  • Verifying results through equilibrium checks and qualitative validation.

In this lecture, we focus on extracting and interpreting results from our slab model. We begin by retrieving nodal displacements, specifically the vertical component, and organising these into a usable format. From this, we identify the maximum displacement and its location, noting how this aligns with expected structural behaviour for a uniformly loaded slab. We then reshape and visualise the displacement field using a heat map, allowing us to confirm that the deformation pattern is physically reasonable.

We then move on to reaction forces, computing them at constrained nodes and examining their distribution. We pay particular attention to expected features, such as downward reactions at the corners and varying magnitudes along the edges. By visualising these reactions and summing them, we confirm vertical force equilibrium with the applied load. Throughout, we emphasise the importance of sanity checks, both visual and numerical, to ensure the model is behaving correctly before proceeding to more advanced result extraction.

Next up

Next, we will extract the bending moments and shear forces from the OpenSeesPy model, working with stress resultants at Gauss sampling points.

Tags

nodal displacementsheat map visualisationreaction forcesequilibrium verificationOpenSeesPy results

Please log in or enroll to continue

If you've already enrolled, please log in to continue.

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
39. Extracting OpenSeesPy moments and shears