Finite Element Analysis of 3D Structures using Python
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Welcome and Preliminaries

1. Introduction and course overview
2. What you should cover before this course
Support and Lecture Q&A (Please read!)
The 3D Beam Stiffness Matrix

3. Section overview
4. Review of the 2D stiffness matrix
5. 3D beam elements
5.1 3D beam elements [PDF Slides]
6. Minor axis bending and transverse shear
7. Torsion & completing the stiffness matrix
7.1 Torsion & completing the stiffness matrix [PDF Slides]
Rotations in 3D Space

8. Section overview
9. An introduction to 3D reference frames
9.1 An introduction to 3D reference frames [PDF Slides]
10. Direction cosines & the 3D bar transformation matrix
11. Building the 3D beam transformation matrix
Generating 3D Frame Data in Blender

12. Section overview
13. Building and exporting a basic frame
14. Exporting frame data from Blender
15. Exporting structural supports
16. Exporting point load data
16.1 Blender File - (lectures 13-16)
17. Importing our frame data
18. Building the force vector
19. Visualising our structure with matplotlib
19.1 Jupyter Notebook - (lectures 17-19)
Building the Transformation Matrix

20. Section overview
21. Defining a default member orientation
22. How to define a local member reference frame
23. Building the local member reference frame
24. Calculating member reference frames and lengths
24.1 Jupyter Notebook - (lectures 21-24)
Building and Solving the Stiffness Matrix

25. Section overview
26. Building the global element stiffness matrix
27. Building the primary stiffness matrix
28. Extracting the structure stiffness matrix
29. Solving for displacements and reactions
30. Solving for member actions
30.1 Jupyter Notebook - (lectures 26-30)
Visualising Results in 3D

31. Section overview
32. Plotting the deflected shape
33. Plotting the axial force heat map
34. Build the local bending moment diagram
34.1 Jupyter Notebook - (lectures 32-34)
35. Plotting the 3D bending moment diagram
35.1 Blender File
36. Build the local shear force diagram
37. Plotting the 3D shear force diagram
38. Generating detailed text output
39. Exporting deflections to Blender
39.1 Blender File
39.2 Jupyter Notebook - (lectures 35-39)
Mid-course check-in
Implementing Bar Bracing Elements

40. Section overview
41. Exporting bar elements from Blender
41.1 Blender File
42. Identifying rotational releases
43. Assigning areas to bar elements
44. Bar element stiffness matrix
45. Adding bars to the primary stiffness matrix
46. The structure stiffness matrix with bars
47. - Solving for axial forces in bar elements
47.1 Jupyter Notebook - (lectures 40-47)
Implementing Pinned Members

48. Section overview
49. Constructing a fixed-pinned stiffness matrix
49.1 Fixed-pinned stiffness matrix [PDF Slides]
50. Exporting pinned elements from Blender
50.1 Blender File
51. Identifying pinned members in our code
52. Element stiffness matrix with pin at node i
53. Element stiffness matrix with pin at node j
54. Adding pinned elements to the primary stiffness matrix
55. Solving for pinned member actions
55.1 Jupyter Notebook - (lectures 51-55)
Implementing Distributed Loading

56. Section overview
57. Identifying distributed loads in Blender
57.1 Blender File
58. Importing distributed loading information
59. Equivalent nodal actions - Part 1
60. Equivalent nodal actions - Part 2
61. Updating the global force vector
62. Removing ENA from reactions
63. Removing ENA from member actions
63.1 Jupyter Notebook - (lectures 58-63)
Bridge Analysis Case Study

64. Section overview
65. Reviewing the bridge structure
66. Building the structural bridge model
66.1 Blender File
67. Model data export/import
68. Reviewing our results
68.1 Jupyter Notebook - (lectures 67-68)
69. Course wrap-up & Certificate of Completion
Course Updates

70. Self-weight part 1 - bar elements
71. Self-weight part 2 - beam elements
71.1 Jupyter Notebook - (lectures 70-71)
72. Member rotations part 1 - Identifying members to rotate
72.1 Blender File
73. Member rotations part 2 - Implementing rotation overrides
73.1 Jupyter Notebook - (lectures 72-73)
Appendix: Building 3D structures in Blender

A1. Section overview
A2. How can Blender help us?
A3. Downloading and installing Blender
A4. Blender overview and interface basics
A5. Object versus Edit mode
A6. Basic modelling - rectilinear structures
A7. Basic modelling - organic/curved structures

40. Section overview