10. Accounting for plane-stress/strain
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Finite Element Analysis of Continuum Structures in Python
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1. Welcome and Preliminaries
1. Introduction and course overview
1
2. What you should cover before this course
1
Support and Lecture Q&A (Please read!)
2. The Isoparametric Finite Element Method
3. Section overview
1
4. Bar stiffness using generalised coordinates
1
5. Bar stiffness using shape functions
3
6. Quad elements and shape functions
3
7. The strain-displacement matrix, B
1
8. The Jacobian Matrix, J
1
9. Calculating the strain-displacement matrix
1
9.1 Jupyter Notebook - (lecture 9)
2
10. Accounting for plane-stress/strain
3
11. The equivalent surface force vector
3
12. The equivalent body force vector
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12.1 Jupyter Notebook - (lectures 11-12)
3. Gauss-Legendre Numerical Integration
13. Section overview
1
14. Gauss numerical integration scheme
6
15. Numerical integration in 2D
1
15.1 Jupyter Notebook - (lecture 15)
16. Calculating the element stiffness matrix
1
17. Stiffness matrix convergence
1
17.1 Jupyter Notebook - (lectures 16-17)
4. Generating Structure and Mesh Data
18. Section overview
1
19. Generating a simple quad mesh in Blender
2
20. Exporting mesh data from Blender
1
21. Exporting support and point load data
5
21.1 Blender File (lectures 19-21)
22. Importing support, loading and mesh data
2
22.1 Jupyter Notebook - (lecture 22)
5. Implementing the Isoparametric Finite Element Method
23. Section overview
1
24. Analysis parameters and plotting the structure
1
25. Building the global force vector
1
26. Defining the element stiffness matrix
3
27. Assigning element stiffness coefficients
1
28. Building the structure stiffness matrix
3
29. Solving the structure
1
30. Visualising the deformed structure
1
31. Generating detailed text output
1
32. Euler-Bernoulli deflection validation
3
32.1 Jupyter Notebook - (lectures 24-32)
2
Mid-course check-in
2
6. Visualising the Strain and Stress Fields
33. Section overview
1
34. Generating the stress calculation grid
1
35. Visualising the stress calculation grid
1
36. Calculating the strain and stress fields
1
37. Visualising the normal stress distribution
3
38. Building normal strain/stress contour plots
1
39. Building shear stress/strain contour plots
3
40. Building a stress/strain interpolation query function
1
41. Visualising stress distributions at a vertical section
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42. Euler-Bernoulli stress comparison
1
42.2 Jupyter Notebook - (lectures 34-42)
7. Implementing Area and Volume Forces
43. Section overview
1
44. Implementing self-weight in our analysis
2
45. Correcting reactions for self-weight
1
46. Distributed loading - Interpolation limits
1
47. Distributed loading - Data export from Blender
1
48. Importing distributed loading data
1
49. Surface force vector - Setup
1
50. Surface force vector - Integration
1
51. Updating the global force vector and validating
1
52. Orthogonal surface forces
1
52.1 Jupyter Notebook - (lectures 44-52)
8. Principal Stresses and von Mises stress
53. Section overview
1
54. A recap of principal stresses
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55. Calculating principal angles and stresses
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56. Sorting principal stresses
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57. Identifying max ten/comp principal stresses
1
58. Visualising the principal stress magnitude field
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59. Visualising the principal stress vector field
1
60. Combining the magnitude and vector fields
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60.1 Jupyter Notebook - (lectures 55-60)
61. The von Mises failure theory
5
62. Visualising the von Mises stress field
1
62.1 Jupyter Notebook - (lecture 62)
63. Perimeter stresses and updating plot edges - Planning
1
64. Perimeter stresses and updating plot edges - Coding
1
64.1 Jupyter Notebook - (lecture 64)
9. Generating and Analysing Complex Meshes
65. Section overview
1
66. Generating 2D geometry in Blender
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67. Meshing complex geometries
1
68. Exporting an irregular mesh
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68.1 Blender File (lectures 66-68)
69. Generalising our solver
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70. Stress distribution masks
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70.1 Jupyter Notebook - (lecture 69-70)
71. Course wrap up and Certificate of Completion
1
72. [BONUS] Cantilever model and analysis walkthrough
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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