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 ...
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 ...
7. Torsion & completing the stiffness...
7.1 Torsion & completing the stiffnes...
Rotations in 3D Space
8. Section overview
9. An introduction to 3D reference fr...
9.1 An introduction to 3D reference f...
10. Direction cosines & the 3D bar tr...
11. Building the 3D beam transformati...
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 ma...
19.1 Jupyter Notebook - (lectures 17-19)
Building the Transformation Matrix
20. Section overview
21. Defining a default member orienta...
22. How to define a local member refe...
23. Building the local member referen...
24. Calculating member reference fram...
24.1 Jupyter Notebook - (lectures 21-24)
Building and Solving the Stiffness Matrix
25. Section overview
26. Building the global element stiff...
27. Building the primary stiffness ma...
28. Extracting the structure stiffnes...
29. Solving for displacements and rea...
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 di...
34.1 Jupyter Notebook - (lectures 32-34)
35. Plotting the 3D bending moment di...
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 stiffn...
46. The structure stiffness matrix wi...
47. - Solving for axial forces in bar...
47.1 Jupyter Notebook - (lectures 40-47)
Implementing Pinned Members
48. Section overview
49. Constructing a fixed-pinned stiff...
49.1 Fixed-pinned stiffness matrix [P...
50. Exporting pinned elements from Bl...
50.1 Blender File
51. Identifying pinned members in our...
52. Element stiffness matrix with pin...
53. Element stiffness matrix with pin...
54. Adding pinned elements to the pri...
55. Solving for pinned member actions
55.1 Jupyter Notebook - (lectures 51-55)
Implementing Distributed Loading
56. Section overview
57. Identifying distributed loads in ...
57.1 Blender File
58. Importing distributed loading inf...
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 C...
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 - Identif...
72.1 Blender File
73. Member rotations part 2 - Impleme...
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 ba...
A5. Object versus Edit mode
A6. Basic modelling - rectilinear str...
A7. Basic modelling - organic/curved ...
Products
Course
Section
Lesson
44. Bar element stiffness matrix
44. Bar element stiffness matrix
Finite Element Analysis of 3D Structures using Python
Buy now
Learn more
Welcome and Preliminaries
1. Introduction and course overview
2. What you should cover before this ...
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 ...
7. Torsion & completing the stiffness...
7.1 Torsion & completing the stiffnes...
Rotations in 3D Space
8. Section overview
9. An introduction to 3D reference fr...
9.1 An introduction to 3D reference f...
10. Direction cosines & the 3D bar tr...
11. Building the 3D beam transformati...
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 ma...
19.1 Jupyter Notebook - (lectures 17-19)
Building the Transformation Matrix
20. Section overview
21. Defining a default member orienta...
22. How to define a local member refe...
23. Building the local member referen...
24. Calculating member reference fram...
24.1 Jupyter Notebook - (lectures 21-24)
Building and Solving the Stiffness Matrix
25. Section overview
26. Building the global element stiff...
27. Building the primary stiffness ma...
28. Extracting the structure stiffnes...
29. Solving for displacements and rea...
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 di...
34.1 Jupyter Notebook - (lectures 32-34)
35. Plotting the 3D bending moment di...
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 stiffn...
46. The structure stiffness matrix wi...
47. - Solving for axial forces in bar...
47.1 Jupyter Notebook - (lectures 40-47)
Implementing Pinned Members
48. Section overview
49. Constructing a fixed-pinned stiff...
49.1 Fixed-pinned stiffness matrix [P...
50. Exporting pinned elements from Bl...
50.1 Blender File
51. Identifying pinned members in our...
52. Element stiffness matrix with pin...
53. Element stiffness matrix with pin...
54. Adding pinned elements to the pri...
55. Solving for pinned member actions
55.1 Jupyter Notebook - (lectures 51-55)
Implementing Distributed Loading
56. Section overview
57. Identifying distributed loads in ...
57.1 Blender File
58. Importing distributed loading inf...
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 C...
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 - Identif...
72.1 Blender File
73. Member rotations part 2 - Impleme...
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 ba...
A5. Object versus Edit mode
A6. Basic modelling - rectilinear str...
A7. Basic modelling - organic/curved ...
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