Lecture 16: The local non-linear stiffness matrix | Non-linear Finite Element Analysis of 2D Catenary & Cable Structures using Python | EngineeringSkills.com

ACCESS THE COMPLETE LIBRARY OF COURSES & TUTORIALS ➡️

Section 1

Introduction and Course Breakdown

1. Introduction and course overview

08:10 (Preview)

2. Course prerequisites

02:32 (Preview)

Section 2

‘Heavy’ Cables - the Linear Solution

3. Section 2 overview

02:09 (Preview)

4. Deriving a linear heavy cable equation

5. Accounting for cable self-weight

6. Problem-specific boundary conditions

7. Solving for max cable tension 📂

23:34 (Preview)

Section 3

Getting Comfortable with Non-linearity

8. Section 3 overview

01:05 (Preview)

9. What is non-linear structural behaviour?

10. Large deflections and geometric non-linearity

11. An iterative solution strategy

Section 4

The Non-linear Stiffness Matrix

12. Section 4 overview

01:30 (Preview)

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

Section 5

Building our 2D Solver Toolbox

18. Section 5 overview

01:33 (Preview)

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 📂

Section 6

Visualising the Results

32. Section 6 overview

00:57 (Preview)

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 📂

Section 7

‘Heavy’ Cables - the Non-linear Solution

40. Section 7 overview

01:15 (Preview)

41. Exploring the convergence behaviour 📂

42. Modelling the cable with large axial stiffness

43. Introducing non-linearity by reducing the axial stiffness 📂

44. Linear vs. Non-linear comparison for a simple truss 📂

Section 8

Modelling Initial Geometry in Blender

45. Section 8 overview

01:15 (Preview)

46. Simulating initial catenary geometry

47. Basic geometry data export

48. Exporting cable definitions

49. Exporting restraint data

50. Exporting force location data 📂

Section 9

Mixing Cables and Bars in the Same Model

51. Section 9 overview

01:00 (Preview)

52. Modifying our code for different element types 📂

53. Analysing a combined cable and bar structure

54. Removing slack cable elements 📂

55. Antenna tower - modelling and analysis 📂

15:46 (Preview)

56. Course wrap up & Certificate of Completion

Section 10

Appendix - Introduction to Blender

57. How can Blender help us?

58. Downloading and installing Blender

59. Blender overview and interface

60. Object versus edit mode

61. Rectilinear modelling

62. Organic modelling 📂

18:26 (Preview)

16. The local non-linear stiffness matrix

The Non-linear Stiffness Matrix

📂 Please log in or enroll to access resources

Please log in or enroll to continue

If you've already enrolled, please log in to continue.

Non-linear Finite Element Analysis of 2D Catenary & Cable Structures using Python

Build an iterative solution toolbox to analyse structures that exhibit geometric non-linearity due to large deflections.

After completing this course...

You will understand the concept of geometric non-linearity and when it should be considered.
You will understand how to modify the axially loaded element stiffness matrix to account for large deflections and changes in geometry.
You will have implemented a Newton-Raphson iterative solution algorithm that seeks to converge on the deformed state of the structure.
You will have a workflow that leverages open-source modelling tools in Blender to quickly generate the initial structural geometry.

Next Lesson

17. The global non-linear stiffness matrix