In this final section of the course, we’ll work through the analysis of a multi-shell or compound shell structure. This is simply a structure that consists of multiple shell geometries connected to one another.

In reality, shell structures consisting of a single geometric shape are relatively rare - it’s far more common to observe structures that mix together multiple basic geometries.

Mixing geometries to form compound shells gives the designer far more flexibility to form an overall structural geometry that achieves the required outcome.

We’ll again confine our analysis to shells of revolution - so we can now imagine forming the meridian or generating curve by combining different geometries on a 2D plane. For example, a segment of a circle will generate a spherical component, vertical lines will generate cylindrical components and inclined straight lines will generate conical components. By revolving this piecewise-meridian about the generating axis, we obtain our compound shell of revolution.

The analysis of these compound structures flows directly from what we’ve already covered in the previous five sections of the course. In fact, we don’t need to cover any new theory in this section.

To determine the distribution of membrane forces, we can simply break up the structure into its constituent parts making sure to transfer the meridional force at the boundary, from one geometry into the next. Tracking the load path in this way is really the only extra step introduced in this section.

As always, it’s important to be aware of our limiting assumptions. Our analysis of membrane forces in this section will, of course, be approximate as we’re ignoring the more complex behaviour at the boundaries of each geometry. Having said that, our analysis will still give us a reasonable approximation of the membrane forces, particularly as we move away from the boundaries.

We’ll focus on the analysis of a single structure because you should really only need to see the process demonstrated once in order to be comfortable implementing it independently.

We’ll discuss the case study structure in the next lecture. Then, over the following lectures, we’ll break up the analysis of the different sub-geometries and finish the section by producing a combined plot of the membrane forces for the entire structure.

Once you’ve completed this section, you’ll have greatly increased the range of shell structures you’ll be comfortable analysing.