In this lecture, we'll cover:

• How to convert the shell element displacement field into a strain field using derivatives,
• The five strains of interest in the local reference frame: normal, shear, and transverse shear strains,
• Why the normal strain in the local $z'$ direction is taken as zero under a plane stress assumption,
• How the strain field is split into membrane, bending, and transverse shear components,
• The idea of generalised strains, with the $z'$-dependence stripped out of the bending strains,
• How a simple transformation matrix links the full strain vector to the generalised strain vector.

We start by taking the displacement field from the previous lecture and differentiating it to obtain the strain field for the shell element. We consider the local strain components $\varepsilon_{x'}$, $\varepsilon_{y'}$, $\gamma_{x'y'}$, $\gamma_{x'z'}$, and $\gamma_{y'z'}$, and show how each one follows directly from the relevant displacement derivatives. We also restate the plane stress argument used for plates.

Next up

In the next lecture, we will move on from strain to stress by developing the constitutive matrices that connect these strain components to the stress field.