In this lecture, we will cover the following:

• How to set up the parameters that define our shell geometry
• How to procedurally generate the nodal coordinates for the mesh
• How to build the list of element definitions from those nodes
• How to add a small piece of debugging code to sanity check the mesh

Our focus in this lecture is on producing a simple, procedurally generated shell mesh that we can use as a test-bed throughout the rest of the section. The shell we'll build is a segment of a cylinder, and we describe it using five parameters:

• a dimension along the y-axis or longitudinal axis of the cyliner, $(b)$,
• the number of elements along that dimension $(n_b)$,
• the radius of the underlying cylinder $(\text{rad})$,
• the arc angle swept by the shell, $\alpha$,
• the number of elements along that arc length $(n_\alpha)$.

After bringing in the usual dependencies and defining our concrete material constants, we use these parameters to generate a set of $\theta$ angles and $y$ values that effectively define a rectangular grid wrapped onto the curved surface.

From there, we step through each $\theta$ and $y$ combination and use simple right-angle triangle geometry to compute the $x$, $y$ and $z$ coordinate of every node. With our nodes in place, we then iterate through the mesh again to package nodes together into elements. We also drop in a small block of debug code so that we can verify the node numbers for any chosen element against a reference image, giving us confidence that the mesh has been generated correctly.

Next up

In the next lecture, we will write the plotting code needed to render this shell on screen, which will give us a much clearer visual confirmation that the mesh we have just generated is correct.