In this lecture, we'll cover the following:

• How to define the displacement field for plate elements under transverse loading.
• How Kirchhoff and Reissner–Mindlin theories differ in their displacement assumptions.
• How to derive strain components from the displacement field.
• The distinction between bending strains and transverse shear strains.
• How to construct strain and stress vectors for plate elements.

In this lecture, we develop the displacement and strain fields for plate elements, focusing on how the middle plane deforms under transverse loading. We express displacements in terms of the transverse deflection and rotations, showing how in-plane displacements arise through the thickness due to rotation, even when the middle-plane itself does not translate in-plane. We highlight the key difference between Kirchhoff and Reissner–Mindlin theories, where the latter introduces independent rotations to account for transverse shear deformation.

We then derive the full strain field from the displacement assumptions, carefully separating bending strains from transverse shear strains. We show how transverse shear strains emerge directly from the Reissner–Mindlin assumptions and are absent in Kirchhoff theory. Finally, we assemble the strain vector and introduce a generalised strain formulation to simplify later derivations, before briefly connecting these strains to their corresponding stresses to build physical intuition about how the plate resists loading.

Next up

With the strain fields established, the next lecture introduces the constitutive matrix, which relates stress to strain and captures the material behaviour of the plate.