Analytical Modelling of Plate and Shell Structures - New Course


The next topic we’re diving into is the Analytical Modelling of Plate and Shell Structures.

Similarly to how we took a deep dive into cable analysis last year, our exploration of plates and shells will span over several upcoming courses.

We’re going to start by focusing on understanding how to model the behaviour of these structures under load, from an analytical point of view. So, we’ll be developing closed-form solutions for a range of different geometries. The course will be divided up as follows:

  1. A General Introduction to Plate and Shell Structures
  2. Analysis of Circular Plates
  3. Analysis of Rectangular Plates
  4. The Membrane Theory of Shells
  5. Applying the Theory to Elemental Shells
  6. Compound Shell Structures

This course focuses on building a collection of models and tools to help you analyse idealised plate and shell structures. You may be thinking…

‘why focus on analytical methods when there are so many finite element (FE) solvers at our fingertips?’

The answer is simple - if you want to deploy FE with confidence, you should have a solid understanding of the fundamental behaviour first.

Taking this approach also gives us the ability to sensibly interrogate the results we get back from FE solvers. It will also be helpful when we build our own FE plate solver in an upcoming course :wink:

:unlock: Early access for members

I’ve just pushed the first 6 hours of course content covering sections 1 and 2.

All Access Subscribers and Lifetime Members can access this content now in the DegreeTutors:Labs membership area. If you’re not a member or lifetime subscriber - the course will be released for sale once it’s fully complete.

Keep an eye out here for updates on new section releases over the coming weeks.


Plates and Shells - 4 more lectures + Jupyter Notebooks added

Just a quick update to let you know that I’ve added the final 4 lectures to the circular plate analysis section.

In these final 4 lectures…

  • We take a look at annular plates
  • We dive into SymPy again to help develop our solutions
  • And we wrap up with an optional lecture on generating 3D visualisations.

Although the last lecture on 3D plotting is not directly related to plate behaviour, it will be useful as we progress onto other geometries later in the course.

I’ve also added all of the associated Jupyter Notebooks to the downloads section for each lecture - so you can get your hands directly on the code I write for each lesson.

That’s all for now. We’re moving on to rectangular plates next - keep an eye out for those course updates coming soon.


Analysis of Rectangular Plates - 9 more lectures added

I’ve added 9 more lectures (27-35) to the new Plates and Shells course - I’ll be adding another 5 analysis case study lectures later this week (36-40) . These lectures introduce the analysis of rectangular plates…here’s an overview of what we cover in this section.

We begin our exploration of rectangular plates just as we did in the previous section by developing the governing differential equation for plate bending.

We’ll build up from first principles using the same roadmap we saw previously - analyse the deformed geometry, jump from strains to stresses to stress resultants and then evaluate the equilibrium equations for the element.

From here, we’ll briefly discuss various aspects of rectangular plate behaviour, from boundary conditions to the corner uplift induced by torsional moments at plate corners.

After this, we introduce an elegant solution for simply supported rectangular plates - Navier’s solution, first proposed by Claud-Louis Navier in 1820.

The case studies that I’ll publish next week will give you a good understanding of how to apply Navier’s solution to various loading conditions.

Along the way, we’ll sprinkle in some Python, where it’s helpful and generate some visualisations of predicted plate behaviour.

Splitting into part 1 (plates) & part 2 (shells)

Our deep dive into plate analysis is currently running at approximately 11 or 12 hours over 40 lectures! By the time we cover what I plan to cover on shell structures, we’d likely be looking at a 25+ hour course! So, I think it makes sense to split the course into two standalone parts. Part 1 will focus on the analysis of plates, and part 2 will deal with shells.

Since I’ve pretty much wrapped up what I want to cover on plates, part 1 will open for general enrollment next week. Then, I’ll move on to producing part 2.

As usual, part two will be released bit-by-bit through DegreeTutors:Labs to All Access Subscribers and Lifetime Members.

That’s all for now, I’ll update again as soon as I have the analysis case studies (and associated Jupyter Notebooks :wink:) live next week.


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The course is now complete and open for general enrolment!

Full course details can be found on the course info page here.


See you inside :+1: