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Section 1
Course Introduction
1. Course overview
07:10 (Preview)
Section 3
Analysis of Circular Plates
9. Section 3 overview
03:14 (Preview)
10. Coordinates, limitations, assumptions and the plan
18:57
11. Establishing the radial and hoop strain
18:54
12. Jumping to stresses via Hooke’s Law
09:43
13. Determining the stress resultants
13:33
14. Equilibrium of the infinitesimal element
16:57
15. From equilibrium to the governing differential equation 📂
24:04
16. Evaluating the shear force term
07:24
17. The influence of plate boundary conditions
14:12
18. Case study #1: Simply supported with edge moment
20:10
19. Case study #2: Simply supported with UDL 📂
33:04
20. Case study #2: Further investigation & visualisation 📂
29:41
21. Case study #3: Built-in with central point load
18:10
22. Case study #4: Built-in annular plate with UDL 📂
30:09
23. Case study #5: Simply supported with linearly varying load
20:25
24. Case study #5: Code solution and plotting 📂
13:13
25. Building a 3D visualisation of plate deflection 📂
31:33
Section 4
Analysis of Rectangular Plates
26. Section 4 overview
04:35 (Preview)
27. Setting up our derivation
12:00
28. Stress and strain analysis
20:34
29. Equilibrium and the governing differential equation
24:11
30. Stress distributions
06:14
31. Fixed and simply supported boundary conditions
07:50
32. Free edges
13:22
33. The corner effect
09:04
34. Navier’s solution for rectangular plate deflection
30:45
35. Determining plate moments
09:10
36. Case study #6: Navier’s solution for UDL
19:58
37. Case study #7: Navier’s solution for linearly varying loading 📂
31:43
38. Case study #8: Navier’s solution for patch loading 📂
20:08
39. Case study #9: Navier’s solution for point loading
07:30
40. Building a ‘Plate Calculator’ script 📂
36:18
41. Course wrap up and certificate of completion
03:40
Full Preview
9. Section 3 overview
Analysis of Circular Plates
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Analytical Modelling of Plate and Shell Structures: Part 1 - Plates

A practical guide to the analysis of circular and rectangular plates under load, from first principles.

After completing this course...

  • You will have developed a deep ‘first principles’ understanding of plate behaviour – critical for the safe application of finite element solutions.
  • You will be comfortable using Python’s SymPy library to work with symbolic math and turn symbolic expressions into graphical representations of plate deflection.
  • You will have developed tools and techniques for solving the governing differential equations and unlocking the flexural behaviour of the rectangular and circular plates.
  • You will understand how to apply Navier’s solution to approximate the solution to the governing differential equation for rectangular plate bending.
Next Lesson
10. Coordinates, limitations, assumptions and the plan