7.1 Torsion & completing the stiffness matrix [PDF Slides]
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Finite Element Analysis of 3D Structures using Python
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Welcome and Preliminaries
1. Introduction and course overview
3
2. What you should cover before this course
1
Support and Lecture Q&A (Please read!)
The 3D Beam Stiffness Matrix
3. Section overview
1
4. Review of the 2D stiffness matrix
1
5. 3D beam elements
3
5.1 3D beam elements [PDF Slides]
6. Minor axis bending and transverse shear
1
7. Torsion & completing the stiffness matrix
1
7.1 Torsion & completing the stiffness matrix [PDF Slides]
Rotations in 3D Space
8. Section overview
1
9. An introduction to 3D reference frames
1
9.1 An introduction to 3D reference frames [PDF Slides]
10. Direction cosines & the 3D bar transformation matrix
1
11. Building the 3D beam transformation matrix
1
Generating 3D Frame Data in Blender
12. Section overview
1
13. Building and exporting a basic frame
6
14. Exporting frame data from Blender
8
15. Exporting structural supports
7
16. Exporting point load data
8
16.1 Blender File - (lectures 13-16)
17. Importing our frame data
6
18. Building the force vector
4
19. Visualising our structure with matplotlib
20
19.1 Jupyter Notebook - (lectures 17-19)
Building the Transformation Matrix
20. Section overview
1
21. Defining a default member orientation
12
22. How to define a local member reference frame
1
23. Building the local member reference frame
8
24. Calculating member reference frames and lengths
7
24.1 Jupyter Notebook - (lectures 21-24)
Building and Solving the Stiffness Matrix
25. Section overview
1
26. Building the global element stiffness matrix
19
27. Building the primary stiffness matrix
12
28. Extracting the structure stiffness matrix
3
29. Solving for displacements and reactions
8
30. Solving for member actions
8
30.1 Jupyter Notebook - (lectures 26-30)
Visualising Results in 3D
31. Section overview
1
32. Plotting the deflected shape
3
33. Plotting the axial force heat map
9
34. Build the local bending moment diagram
4
34.1 Jupyter Notebook - (lectures 32-34)
35. Plotting the 3D bending moment diagram
9
35.1 Blender File
36. Build the local shear force diagram
1
37. Plotting the 3D shear force diagram
7
38. Generating detailed text output
1
39. Exporting deflections to Blender
1
39.1 Blender File
39.2 Jupyter Notebook - (lectures 35-39)
Mid-course check-in
Implementing Bar Bracing Elements
40. Section overview
1
41. Exporting bar elements from Blender
3
41.1 Blender File
42. Identifying rotational releases
1
43. Assigning areas to bar elements
1
44. Bar element stiffness matrix
1
45. Adding bars to the primary stiffness matrix
1
46. The structure stiffness matrix with bars
3
47. - Solving for axial forces in bar elements
1
47.1 Jupyter Notebook - (lectures 40-47)
Implementing Pinned Members
48. Section overview
1
49. Constructing a fixed-pinned stiffness matrix
1
49.1 Fixed-pinned stiffness matrix [PDF Slides]
50. Exporting pinned elements from Blender
1
50.1 Blender File
51. Identifying pinned members in our code
1
52. Element stiffness matrix with pin at node i
1
53. Element stiffness matrix with pin at node j
1
54. Adding pinned elements to the primary stiffness matrix
1
55. Solving for pinned member actions
1
55.1 Jupyter Notebook - (lectures 51-55)
Implementing Distributed Loading
56. Section overview
1
57. Identifying distributed loads in Blender
1
57.1 Blender File
58. Importing distributed loading information
1
59. Equivalent nodal actions - Part 1
3
60. Equivalent nodal actions - Part 2
1
61. Updating the global force vector
1
62. Removing ENA from reactions
1
63. Removing ENA from member actions
9
63.1 Jupyter Notebook - (lectures 58-63)
Bridge Analysis Case Study
64. Section overview
1
65. Reviewing the bridge structure
1
66. Building the structural bridge model
1
66.1 Blender File
67. Model data export/import
1
68. Reviewing our results
1
68.1 Jupyter Notebook - (lectures 67-68)
69. Course wrap-up & Certificate of Completion
5
Course Updates
70. Self-weight part 1 - bar elements
1
71. Self-weight part 2 - beam elements
9
71.1 Jupyter Notebook - (lectures 70-71)
72. Member rotations part 1 - Identifying members to rotate
1
72.1 Blender File
73. Member rotations part 2 - Implementing rotation overrides
1
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