Lecture 62: Removing ENA from reactions | Finite Element Analysis of 3D Structures using Python | EngineeringSkills.com

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Section 1

Welcome and preliminaries

1. Introduction and course overview

03:41 (Preview)

2. What you should cover before this course

03:14 (Preview)

Section 2

The 3D Beam Stiffness Matrix

3. Section 2 overview

01:13 (Preview)

4. Review of the 2D stiffness matrix

5. 3D beam elements 📂

07:43 (Preview)

6. Minor axis bending and transverse shear

7. Torsion & completing the stiffness matrix 📂

Section 3

Location and Rotation in 3D Space

8. Section 3 overview

01:12 (Preview)

9. An introduction to 3D reference frames

10. Recap of direction cosines & the 3D bar transformation matrix

11. Building the 3D beam transformation matrix

Section 4

Generating frame data in Blender

12. Section 4 overview

02:43 (Preview)

13. Building and exporting a basic frame 📂

14. Exporting frame data from Blender

15. Exporting structural supports

16. Exporting point load data

17. Importing our frame data 📂

18. Building the force vector

19. Visualising our structure with matplotlib

Section 5

Building the Transformation Matrix

20. Section 5 overview

01:14 (Preview)

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

Section 6

Building and Solving the Stiffness Matrix

25. Section 6 overview

01:06 (Preview)

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

Section 7

Visualising Results in 3D

31. Section 7 overview

02:34 (Preview)

32. Plotting the deflected shape 📂

33. Plotting the axial force heat map

34. Build the local BMD

35. Plotting the 3D bending moment diagram 📂

36. Build the local SFD

37. Plotting the 3D shear force diagram

38. Generating detailed text output

39. Exporting deflections to Blender 📂

Section 8

Implementing Bar Bracing Elements

40. Section 8 overview 📂

01:55 (Preview)

41. Identifying and exporting bar elements from Blender 📂

42. Identifying rotational releases in our code

43. Assigning different areas to bar elements

44. Building the bar element stiffness matrix

45. Adding bar elements to the primary stiffness matrix

46. Extracting the structure stiffiness matrix

47. Solving for axial forces in bar elements

Section 9

Implementing Pinned Members

48. Section 9 overview

02:43 (Preview)

49. Constructing a fixed-pinned stiffness matrix

50. Identifying and exporting pinned elements from Blender 📂

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 member actions in pinned elements

Section 10

Implementing Distributed Loading

56. Section 10 overview

02:46 (Preview)

57. Identifying distributed loads in Blender 📂

58. Importing distributed loading information 📂

59. Calculating equivalent nodal actions - Part 1

60. Calculating equivalent nodal actions - Part 2

61. Updating the global force vector

62. Removing ENA from reactions

63. Removing ENA from member actions

Section 11

Bridge Model Case Study

64. Section 11 overview

03:43 (Preview)

65. Reviewing the bridge structure

66. Building the structural bridge model 📂

67. Data export/import 📂

68. Review of results

69. Course wrap up and debrief

Section 12

Course Updates

70. Self-weight part 1 - bar elements 📂

71. Self-weight part 1 - beam elements

72. Member rotations part 1 - Identifying members to rotate 📂

73. Member rotations part 2 - Implementing rotation overrides

62. Removing ENA from reactions

Implementing Distributed Loading

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Finite Element Analysis of 3D Structures using Python

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

After completing this course...

You’ll understand how to expand the direct stiffness method to full 12 degree of freedom beam elements in 3D space.
You’ll have developed a complete 3D finite element analysis solver to simulate structures consisting of beam and axially loaded bar elements.
You’ll have the skills to efficiently build detailed structural models in Blender and export these for analysis in your own Python solver.

Next Lesson

63. Removing ENA from member actions