Analytical Modelling of Plate and Shell Structures: Part 1 - Plates
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Course Introduction

1. Welcome, course overview and getting support
Support and Lecture Q&A (Please read!)
An Introduction to Plate and Shell Structures

2. Section overview
3. Geometric considerations and assumptions
4. Shell structures in the built environment
5. Fundamental load resistance mechanisms
6. Deformation curvature for 2D plates
7. Curvature and axis rotation
8. Undeformed shell curvature
Analysis of Circular Plates

9. Section overview
10. The setup - Coordinates, limitations, assumptions and the plan
11. Establishing the radial and hoop strain
12. Jumping to stresses via Hooke’s Law
13. Determining the stress resultants
14. Equilibrium of the infinitesimal element
15. From equilibrium to the governing differential equation
15.1 Jupyter Notebooks (lecture 15)
16. Evaluating the shear force term
17. The influence of plate boundary conditions
18. Case study #1- Simply supported with edge moment
19. Case study #2- Simply supported with UDL
19.1 Jupyter Notebooks (lecture 19)
20. Case study #2- Further investigation & visualisation
20.1 Jupyter Notebooks (lecture 20)
21. Case study #3- Built-in with central point load
22. Case study #4 Built-in annular plate with UDL
22.1 Jupyter Notebooks (lecture 22)
23. Case study #5- Simply supported with linearly varying load
24. Case study #5- Code solution and plotting
24.1 Jupyter Notebooks (lecture 24)
25. Building a 3D visualisation of plate deflection
25.1 Jupyter Notebooks (lecture 25)
Analysis of Rectangular Plates

26. Section overview
27. Setting up our derivation
28. Stress and strain analysis
29. Equilibrium and the governing differential equation
30. Stress distributions
31. Fixed and simply supported boundary conditions
32. Free edges
33. The corner effect
34. Navier’s solution for rectangular plate deflection
35. Determining plate moments
36. Case study #6- Navier’s solution for UDL
37. Case study #7- Navier’s solution for linearly varying loading
37.1 Jupyter Notebooks (lecture 37)
38. Case study #8- Navier’s solution for patch loading
38.1 Jupyter Notebooks (lecture 38)
39. Case study #9 Navier’s solution for point loading
40. Building a ‘Plate Calculator’ Python script
40.1 Jupyter Notebook (lecture 40)
41. Course wrap up and certificate of completion

29. Equilibrium and the governing differential equation

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