Non-linear Finite Element Analysis of 2D Catenary & Cable Structures using Python
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Introduction and Course Overview

1. Introduction and course overview
2. Course prerequisites
Support and Lecture Q&A (Please read!)
‘Heavy’ Cables - the Linear Solution

3. Section overview
4. Deriving a linear heavy cable equation
5. Accounting for cable self-weight
6. Problem-specific boundary conditions
7. Solving for max cable tension
7.1 Jupyter Notebook (lecture 7)
Getting Comfortable with Non-linearity

8. Section overview
9. What is non-linear structural behaviour?
10. Large deflections and geometric non-linearity
11. An iterative solution strategy
The Non-linear Stiffness Matrix

12. Section overview
13. Building the transformation matrix
14. The linear stiffness matrix
15. Additional force due to large deflections
16. The local non-linear stiffness matrix
17. The global non-linear stiffness matrix
Building our 2D Solver Toolbox

18. Section overview
19. Initial setup and data import
20. Plotting the initial configuration
21. Blocking out the main convergence loop
22. Building the transformation matrices
23. Adding pre-tension to each member
24. Building the stiffness matrix
25. Solving for displacements
26. Updating the internal force system
27. Building a convergence test function
28. Calculating axial forces
29. Allowing for smaller external force increments
30. Generating a text summary output
31. Adding self-weight calculation
31.1 Jupyter Notebook (lectures 19-31)
Mid-course check-in
Visualising the Results

32. Section overview
33. Plot setup and data selection
34. Plotting the undeformed structure
35. Building a colour scale
36. Plotting the deformed structure
37. Adding axial force labels
38. Plotting the applied forces
39. Plotting the reactions
39.1 Jupyter Notebook (lectures 33-39)
‘Heavy’ Cables - the Non-linear Solution

40. Section overview
41. Exploring the convergence behaviour
41.1 Jupyter Notebook (lecture 41)
42. Modelling the cable with large axial stiffness
43. Introducing non-linearity by reducing the axial stiffness
43.1 Jupyter Notebook (lectures 42-43)
44. Linear vs. Non-linear comparison for a simple truss
44.1 Jupyter Notebook (lecture 44)
Modelling Initial Geometry in Blender

45. Section overview
46. Simulating initial catenary geometry
47. Basic geometry data export
48. Exporting cable definitions
49. Exporting restraint data
50. Exporting force location data
50.1 Blender File (lectures 46-50)
Mixing Cables and Bars in the Same Model

51. Section overview
52. Modifying our code for different element types
52.1 Jupyter Notebook (lecture 52)
53. Analysing a combined cable and bar structure
54. Removing slack cable elements
54.1 Jupyter Notebook (lecture 54)
55. Antenna tower - modelling and analysis
55.1 Jupyter Notebook (lecture 55)
55.2 Blender File (lecture 55)
56. Course wrap up & completion certificate
Appendix: Introduction to Blender

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

Getting Comfortable with Non-linearity

In this section, we'll consider sources of non-linearity in structural behaviour before focusing on geometric non-linearity in particular. The aim of this section is to take any mystery out of the term 'geometric non-linearity'. We'll also explore, at concept level, how we might set about solving for the behaviour of a non-linear structure.

4 Lessons