In this lecture, we'll cover the following:

• The distinction between plate elements and shell elements in finite element modelling
• The types of loading and behaviour associated with plates (out-of-plane) and shells (combined in-plane and out-of-plane)
• The role of membrane forces in shell elements and why they make shells more versatile
• The assumption of flat elements and how curved geometries are approximated in practice
• The comparison between Kirchhoff plate theory and Reissner–Mindlin plate theory
• Why Reissner–Mindlin theory is chosen, particularly in relation to shear deformation

We begin by clarifying the difference between plate and shell elements, noting that plates resist only out-of-plane loading through bending and shear, whereas shells can also resist in-plane (membrane) forces. This additional capability makes shell elements more versatile and suitable for structures where bending and membrane behaviour occur simultaneously, such as domes or structural cores. We also highlight that, in practice, both plate and shell elements are treated as flat, with curved geometries approximated using a faceted mesh.

We then compare the two principal plate theories: Kirchhoff and Reissner–Mindlin. We observe that Kirchhoff theory neglects transverse shear deformation, making it suitable only for thin plates, whereas Reissner–Mindlin theory accounts for shear deformation by allowing normals to the mid-plane to remain straight but not perpendicular after deformation. This key difference enables Reissner–Mindlin theory to model both thin and thick plates accurately. As a result, we adopt this theory for the course to ensure broader applicability and improved modelling capability.

Next up

In the next lecture, we will step back to get a high-level view of what finite element analysis is trying to achieve and how the key components fit together.