Finite Element Analysis of 3D Structures using Python

Build your own complete 3D structural analysis software in Python using the Direct Stiffness Method

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Welcome and Preliminaries

1. Introduction and course overview

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2. What you should cover before this course

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Support and Lecture Q&A (Please read!)

The 3D Beam Stiffness Matrix

3. Section overview

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4. Review of the 2D stiffness matrix

5. 3D beam elements

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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

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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

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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

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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

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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

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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

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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

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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

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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

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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

This section is reserved for 'post-release' updates to the course...for those good ideas and suggestions that come in from students taking the course.

So far, we have expanded to consider,

automatic self-weight calculation
Member rotations

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