Finite Element Analysis of Continuum Structures in Python
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1. Welcome and Preliminaries

1. Introduction and course overview
2. What you should cover before this course
Support and Lecture Q&A (Please read!)
2. The Isoparametric Finite Element Method

3. Section overview
4. Bar stiffness using generalised coordinates
5. Bar stiffness using shape functions
6. Quad elements and shape functions
7. The strain-displacement matrix, B
8. The Jacobian Matrix, J
9. Calculating the strain-displacement matrix
9.1 Jupyter Notebook - (lecture 9)
10. Accounting for plane-stress/strain
11. The equivalent surface force vector
12. The equivalent body force vector
12.1 Jupyter Notebook - (lectures 11-12)
3. Gauss-Legendre Numerical Integration

13. Section overview
14. Gauss numerical integration scheme
15. Numerical integration in 2D
15.1 Jupyter Notebook - (lecture 15)
16. Calculating the element stiffness matrix
17. Stiffness matrix convergence
17.1 Jupyter Notebook - (lectures 16-17)
4. Generating Structure and Mesh Data

18. Section overview
19. Generating a simple quad mesh in Blender
20. Exporting mesh data from Blender
21. Exporting support and point load data
21.1 Blender File (lectures 19-21)
22. Importing support, loading and mesh data
22.1 Jupyter Notebook - (lecture 22)
5. Implementing the Isoparametric Finite Element Method

23. Section overview
24. Analysis parameters and plotting the structure
25. Building the global force vector
26. Defining the element stiffness matrix
27. Assigning element stiffness coefficients
28. Building the structure stiffness matrix
29. Solving the structure
30. Visualising the deformed structure
31. Generating detailed text output
32. Euler-Bernoulli deflection validation
32.1 Jupyter Notebook - (lectures 24-32)
Mid-course check-in
6. Visualising the Strain and Stress Fields

33. Section overview
34. Generating the stress calculation grid
35. Visualising the stress calculation grid
36. Calculating the strain and stress fields
37. Visualising the normal stress distribution
38. Building normal strain/stress contour plots
39. Building shear stress/strain contour plots
40. Building a stress/strain interpolation query function
41. Visualising stress distributions at a vertical section
42. Euler-Bernoulli stress comparison
42.2 Jupyter Notebook - (lectures 34-42)
7. Implementing Area and Volume Forces

43. Section overview
44. Implementing self-weight in our analysis
45. Correcting reactions for self-weight
46. Distributed loading - Interpolation limits
47. Distributed loading - Data export from Blender
48. Importing distributed loading data
49. Surface force vector - Setup
50. Surface force vector - Integration
51. Updating the global force vector and validating
52. Orthogonal surface forces
52.1 Jupyter Notebook - (lectures 44-52)
8. Principal Stresses and von Mises stress

53. Section overview
54. A recap of principal stresses
55. Calculating principal angles and stresses
56. Sorting principal stresses
57. Identifying max ten/comp principal stresses
58. Visualising the principal stress magnitude field
59. Visualising the principal stress vector field
60. Combining the magnitude and vector fields
60.1 Jupyter Notebook - (lectures 55-60)
61. The von Mises failure theory
62. Visualising the von Mises stress field
62.1 Jupyter Notebook - (lecture 62)
63. Perimeter stresses and updating plot edges - Planning
64. Perimeter stresses and updating plot edges - Coding
64.1 Jupyter Notebook - (lecture 64)
9. Generating and Analysing Complex Meshes

65. Section overview
66. Generating 2D geometry in Blender
67. Meshing complex geometries
68. Exporting an irregular mesh
68.1 Blender File (lectures 66-68)
69. Generalising our solver
70. Stress distribution masks
70.1 Jupyter Notebook - (lecture 69-70)
71. Course wrap up and Certificate of Completion
72. [BONUS] Cantilever model and analysis walkthrough
72.1 Blender File (lecture 72)
72.2 Jupyter Notebook - (lecture 72)
Appendix 1: Fundamentals of 2D Stress Analysis and Mohr's Circle

A1. The 2D stress element
A2. The stress transformation equations
A3. Visualising the transformation equations
A4. Principal stresses and principal planes
A5. Maximum shear stress
A6. Stress analysis worked example
A7. Stress analysis worked example - coded solution
A8. Mohr's circle of stress
A9. Mohr's circle example solution
Jupyter Notebook - 2D stress analysis and Mohr's circle

Appendix 1: Fundamentals of 2D Stress Analysis and Mohr's Circle

This appendix is provided for anyone who feels like they would benefit from a review of the fundamentals of 2D stress analysis. This will be particularly helpful before tackling sections 6 and 8 on visualising stresses and strains and principal stresses respectively.

10 Lessons