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

In this lecture, we'll cover the following:

  • Introduction to OpenSeesPy as a Python-based finite element analysis library
  • Installing and setting up OpenSeesPy and the OpsVis visualisation tool
  • Defining material properties and shell sections for a plate model
  • Generating nodes and element connectivity for a meshed slab
  • Building the OpenSeesPy model: nodes, elements, and shell MITC4 formulation
  • Applying boundary conditions and ensuring model stability
  • Applying self-weight loading through nodal forces
  • Running a static analysis and understanding solver configuration options

In this lecture, we begin building a finite element model using OpenSeesPy, introducing it as a powerful but somewhat under-documented library widely used in research. We walk through installing dependencies and highlight the role of OpsVis in verifying that the model has been constructed correctly. We then recreate a slab model by defining material properties, generating a mesh, and explicitly creating nodes and shell elements within OpenSeesPy, paying close attention to tagging and element formulation, particularly the MITC4 shell element suitable for both thick and thin plates.

Loads are applied as equivalent nodal forces derived from self-weight. Finally, we configure and execute a static analysis, introducing key OpenSeesPy commands for solvers, constraints, numbering, and load application. By the end, we have a complete and functioning OpenSeesPy model ready for result extraction and comparison with our custom implementation.

Next up

With the OpenSeesPy model built and analysed, the next lecture focuses on extracting displacements and reaction forces.

Tags

OpenSeesPyMITC4 shell elementfinite element modellingboundary conditionsstatic 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
38. Extracting OpenSeesPy displacements and reactions