18. Section overview

1. Welcome and Preliminaries

• 1. Introduction and course overview1

• 2. What you should cover before this course1

• Support and Lecture Q&A (Please read!)

2. The Isoparametric Finite Element Method

• 3. Section overview1

• 4. Bar stiffness using generalised coordinates1

• 5. Bar stiffness using shape functions3

• 6. Quad elements and shape functions3

• 7. The strain-displacement matrix, B1

• 8. The Jacobian Matrix, J1

• 9. Calculating the strain-displacement matrix1

• 9.1 Jupyter Notebook - (lecture 9)2

• 10. Accounting for plane-stress/strain3

• 11. The equivalent surface force vector3

• 12. The equivalent body force vector1

• 12.1 Jupyter Notebook - (lectures 11-12)

3. Gauss-Legendre Numerical Integration

• 13. Section overview1

• 14. Gauss numerical integration scheme6

• 15. Numerical integration in 2D1

• 15.1 Jupyter Notebook - (lecture 15)

• 16. Calculating the element stiffness matrix1

• 17. Stiffness matrix convergence1

• 17.1 Jupyter Notebook - (lectures 16-17)

4. Generating Structure and Mesh Data

• 18. Section overview1

• 19. Generating a simple quad mesh in Blender2

• 20. Exporting mesh data from Blender1

• 21. Exporting support and point load data5

• 21.1 Blender File (lectures 19-21)

• 22. Importing support, loading and mesh data2

• 22.1 Jupyter Notebook - (lecture 22)

5. Implementing the Isoparametric Finite Element Method

• 23. Section overview1

• 24. Analysis parameters and plotting the structure1

• 25. Building the global force vector1

• 26. Defining the element stiffness matrix3

• 27. Assigning element stiffness coefficients1

• 28. Building the structure stiffness matrix3

• 29. Solving the structure1

• 30. Visualising the deformed structure1

• 31. Generating detailed text output1

• 32. Euler-Bernoulli deflection validation3

• 32.1 Jupyter Notebook - (lectures 24-32)2

• Mid-course check-in2

6. Visualising the Strain and Stress Fields

• 33. Section overview1

• 34. Generating the stress calculation grid1

• 35. Visualising the stress calculation grid1

• 36. Calculating the strain and stress fields1

• 37. Visualising the normal stress distribution3

• 38. Building normal strain/stress contour plots1

• 39. Building shear stress/strain contour plots3

• 40. Building a stress/strain interpolation query function1

• 41. Visualising stress distributions at a vertical section1

• 42. Euler-Bernoulli stress comparison1

• 42.2 Jupyter Notebook - (lectures 34-42)

7. Implementing Area and Volume Forces

• 43. Section overview1

• 44. Implementing self-weight in our analysis2

• 45. Correcting reactions for self-weight1

• 46. Distributed loading - Interpolation limits1

• 47. Distributed loading - Data export from Blender1

• 48. Importing distributed loading data1

• 49. Surface force vector - Setup1

• 50. Surface force vector - Integration1

• 51. Updating the global force vector and validating1

• 52. Orthogonal surface forces1

• 52.1 Jupyter Notebook - (lectures 44-52)

8. Principal Stresses and von Mises stress

• 53. Section overview1

• 54. A recap of principal stresses1

• 55. Calculating principal angles and stresses1

• 56. Sorting principal stresses1

• 57. Identifying max ten/comp principal stresses1

• 58. Visualising the principal stress magnitude field1

• 59. Visualising the principal stress vector field1

• 60. Combining the magnitude and vector fields1

• 60.1 Jupyter Notebook - (lectures 55-60)

• 61. The von Mises failure theory5

• 62. Visualising the von Mises stress field1

• 62.1 Jupyter Notebook - (lecture 62)

• 63. Perimeter stresses and updating plot edges - Planning1

• 64. Perimeter stresses and updating plot edges - Coding1

• 64.1 Jupyter Notebook - (lecture 64)

9. Generating and Analysing Complex Meshes

• 65. Section overview1

• 66. Generating 2D geometry in Blender1

• 67. Meshing complex geometries1

• 68. Exporting an irregular mesh1

• 68.1 Blender File (lectures 66-68)

• 69. Generalising our solver1

• 70. Stress distribution masks1

• 70.1 Jupyter Notebook - (lecture 69-70)

• 71. Course wrap up and Certificate of Completion1

• 72. [BONUS] Cantilever model and analysis walkthrough1

• 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