The Direct Stiffness Method for Truss Analysis with Python

Build your own finite element truss analysis software using Python and tackle large scale structures

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Introduction

1. Introduction and course overview

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2. Our approach to Python in this course

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3. Getting started with Jupyter Notebooks and Python

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Support and Lecture Q&A (Please read!)

Modelling Elastic Behaviour

4. Section overview

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5. Stress and strain in 2D

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6. Strain and displacement in 2D

7. 3-dimensions and matrix notation

8. Plane Stress condition

9. Plane Strain condition

10. Material matrix summary

Finite Element Equations & Stiffness Matrices

11. Section overview

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12. Finite Element equations and the Direct Stiffness Method

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13. The Principle of Minimum Potential Energy

14. The Finite Element equations

15. Stiffness matrix for bar element

16. Finite Element equation review

17. Transformation from local to global coordinates

Direct Stiffness Method: Step-by-Step

18. Section overview

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Section 4 - Direct Stiffness Method Step by Step - Slides

19. Analysis procedure overview

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20. Calculating element stiffness matrices

21. Building the primary stiffness matrix

22. Reducing to the structure stiffness matrix

23. Solving for unknown displacements

24. Solving for unknown reactions

25. Finding element forces

Direct Stiffness Method in Python

26. Section overview

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Jupyter notebooks.zip

27. Element stiffness matrices

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28. Whole structure stiffness matrix

29. Reactions, element forces and nodal displacements

30. Visualising our output

31. Refactor - Tidying up with functions

Mid-course check-in

Direct Stiffness Method on Larger Structures

32. Section overview

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Question Jupyter notebook

Section 6 - Direct Stiffness Method on Larger Structures - Slides

33. Calculating element stiffness matrices

34. Building the primary stiffness matrix

35. Reducing to structure stiffness matrix

36. Solving for unknown displacements

37. Solving for unknown reactions

38. Finding element forces

Optimising for Larger Structures in Python

39. Section overview

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Jupyter notebook

40. Building the primary stiffness matrix

41. Extracting the structure stiffness matrix

42. Displacements and reactions

43. Calculating member forces

44. Visualising our output

Building a Generalised Truss Solver in Python

45. Section overview

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Jupyter notebook

46. Establishing input data

47. Calculating member orientation and length

48. Primary and Structure Stiffness matrices

49. Displacements, reactions and member forces

50. Automating the output visualisation

51. Automating the text summary

Taking your Solver for a Test Drive

52. Section overview

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Jupyter notebooks

53. Test Question #1

54. Test Question #2

55. Test Question #3

56. Course wrap up and Certificate of Completion