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 equa...
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 beha...
10. Large deflections and geometric n...
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 def...
16. The local non-linear stiffness ma...
17. The global non-linear stiffness m...
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...
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 for...
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 ax...
43. Introducing non-linearity by redu...
43.1 Jupyter Notebook (lectures 42-43)
44. Linear vs. Non-linear comparison ...
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 ...
52.1 Jupyter Notebook (lecture 52)
53. Analysing a combined cable and ba...
54. Removing slack cable elements
54.1 Jupyter Notebook (lecture 54)
55. Antenna tower - modelling and ana...
55.1 Jupyter Notebook (lecture 55)
55.2 Blender File (lecture 55)
56. Course wrap up & completion certi...
Appendix: Introduction to Blender
A1. How can Blender help us?
A2. Downloading and installing Blender
A3. Blender overview and interface ba...
A4. Object versus edit mode
A5. Basic modelling - rectilinear str...
A6. Basic modelling - organic/curved ...
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Course
Section
Lesson
24. Building the stiffness matrix
24. Building the stiffness matrix
Non-linear Finite Element Analysis of 2D Catenary & Cable Structures using Python
Buy now
Learn more
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 equa...
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 beha...
10. Large deflections and geometric n...
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 def...
16. The local non-linear stiffness ma...
17. The global non-linear stiffness m...
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...
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 for...
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 ax...
43. Introducing non-linearity by redu...
43.1 Jupyter Notebook (lectures 42-43)
44. Linear vs. Non-linear comparison ...
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 ...
52.1 Jupyter Notebook (lecture 52)
53. Analysing a combined cable and ba...
54. Removing slack cable elements
54.1 Jupyter Notebook (lecture 54)
55. Antenna tower - modelling and ana...
55.1 Jupyter Notebook (lecture 55)
55.2 Blender File (lecture 55)
56. Course wrap up & completion certi...
Appendix: Introduction to Blender
A1. How can Blender help us?
A2. Downloading and installing Blender
A3. Blender overview and interface ba...
A4. Object versus edit mode
A5. Basic modelling - rectilinear str...
A6. Basic modelling - organic/curved ...
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