1. Welcome and course overview
Course Introduction
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Welcome to the course. This is the second course in our 2-part series looking at analytical modelling of plate and shell structures - in this course, our focus shifts to shell structures.

When you finish the course, you’ll understand how to analyse shell structures that conform to common geometries, such as spheres, cones, cylinders and hyperboloids.

This course continues in the same vein as part 1 - initially, we’ll focus on developing a toolbox of equations that we can use to model the shell’s behaviour. Then, we’ll apply these new tools in a range of case-study analyses.

What makes shells such efficient structures is their ability to resist external loading by developing membrane stresses.

When a shell is well designed, bending stresses are minimised in favour of direct membrane stresses.

For this reason, we focus exclusively on membrane behaviour in this course. While localised bending is almost always unavoidable and can’t be ignored in a production-level design, it will generally be of secondary importance.

Unlocking math through Python

In addition to helping you develop a good first-principles understanding of shell behaviour, my other main aim with this course, just like in part 1, is to help you develop the tools and techniques to work with symbolic math in Python.

I can’t overstate how much of an unlock it is for your study of engineering to be able to work with and navigate mathematics through programming. We’ll see this as we move through the course and unlock the dense mathematics that shell behaviour is typically shrouded in.

🧭 The roadmap

Next, I want to give you a quick overview of the game plan for the rest of the course.

In the following two lectures in the section, we’ll recap a couple of concepts we’ve already covered in the previous course on plate analysis. If you’ve already completed part 1, you can skip ahead to section 2.

Section 2 - The Membrane Theory of Shells

In section 2, we’ll develop the fundamental equations we’ll use for the rest of the course. Section 2 is very much the foundation of everything else that follows. We’ll build up a collection of equations that will allow us to model the membrane stress distribution and the membrane displacements. This section has a lot of theory in it, but time spent here will pay off down the line.

Section 3 - Applying the Theory to Spherical Shells

In section 3, we’ll put our equations to work on spherical shells. The spherical shell is a great geometry to start with because of its constant curvature. This allows us to simplify our equations from section 2 and focus on the analysis workflow without getting too deep into the weeds.

Section 4 - Liquid Retaining Shells

In section 4, we continue to focus on spherical shells but this time we go on a bit of a tangent investigating how to model the influence of a retained liquid. Since shells are often used as liquid and gas tanks, this is a worthwhile detour.

Section 5 - Zero & Negative Gaussian Curvature Shells

By the time we reach section 5, we’ll have plenty of spherical shell analysis under our belt and it will be time to expand into other geometries. We’ll look first at shells with zero Gaussian curvature - this means we focus on conical and cylindrical shells. From here, we move on to the hyperboloid, commonly seen in the form of a cooling tower.

Section 6 - Multi-Shell Structures

In the final section of the course, section 6, we’ll take everything we’ve learned up to this point and bring it all together in the analysis of muti-shell or compound-shell structures.

By combining different shell geometries within a single structure, we dramatically increase the range of structures we can apply our models to. By the time you finish this section in particular, you’ll really see the broad applicability of what you’ve been learning in the course.

Getting Q&A support

All lectures have a dedicated discussion thread where you can post support requests. If you have questions as you work through the course, feel free to post them in the discussion thread for the relevant lecture.

Then, either myself or possibly another learner will respond. If your question relates to a specific part of the lecture, please provide a time-stamp to help me respond as efficiently as possible.

Getting up and running with Python

Just a quick note on Python here before we wrap up; we’ll use Python throughout the course, as a means of visualising the response of our shell structures and also as a tool for handling symbolic math.

As with all EngineeringSkills courses, you don’t need to come to the course knowing Python - I’m a firm believer in learning by doing. So, you’ll pick up all the Python you need as we move through the course.

If you’ve already completed part 1 on plate analysis - you’ll have your Python environment already up and running. But if you’re coming straight into this course without any Python experience, I have some advice for you in the blue box below 👇.

Ok, that’s the introduction and housekeeping covered - now let’s get stuck into the course!

🐍 New to Python, read this...

If you haven't worked with Python before, no problem! The first thing we need to do is get your coding environment set up. In this course, we'll be working with Jupyter Notebooks inside of an environment called Jupyter Lab.

You can think of a Jupyter Notebook as an interactive document that allows you to write and run Python code in a web browser. It's a great way to mix code, text, and visualisations all in one place - for engineering analysis they're amazing!

To get set up, I want you to follow two lectures - the first introduces Jupter Notebooks and the second introduces you to using Jupyter Notebooks inside of Jupyter Lab:

  1. Getting started with Jupyter Notebooks
  2. Moving to JupyterLab

Once you've finished these lectures, come back over to this course and continue here.

FYI - we won't actually be using Python until lecture 16, so you can take your time getting set up and start working through this course now if you prefer.

If you hit any issues - just head down to the lecture comments section below and reach out. I'm here to help!

When we start working with Python - you may feel a little overwhelmed at first - this just means you're learning!!

Stick with it - by the time you get to the end of the course, you'll be so much more comfortable working with Python.

Next Lesson
2. Shell structures in the built environment (Recap)