In this lecture, we'll cover the following:

• Systematic comparison of three plate models across a range of slab thicknesses.
• Use of maximum mid-span displacement as the primary comparison metric.
• Implementation of a parameter sweep over thickness.
• Validation against OpenSeesPy and PyNite solutions as benchmarks.
• Introduction of Navier’s analytical thin plate solution for additional comparison.
• Identification of shear locking as the cause of inaccuracy in the custom model.

In this lecture, we explore how our three plate models behave across a wide range of slab thicknesses, moving beyond a single “spot” comparison to a full parameter sweep. We focus on maximum displacement at the plate centre as a consistent and fundamental measure of accuracy, since all other results stem from displacement. By restructuring our code into reusable utility functions, we efficiently run repeated simulations for varying thicknesses and compare outputs from our custom Reissner–Mindlin formulation against OpenSeesPy and PyNite.

We observe that the benchmark models agree closely across all thicknesses, giving us confidence in their validity. Our custom model performs well for thick plates but becomes overly stiff as the plate becomes thin, underpredicting displacement. By also plotting Navier’s analytical solution, we confirm that it aligns well in the thin plate regime but diverges for thicker plates due to neglecting transverse shear effects. This comparison highlights the gradual transition between thin and thick plate behaviour and reveals shear locking as the key issue affecting our custom formulation.

Next up

The parameter sweep has revealed shear locking as the source of the discrepancy. In the next lecture, we will examine what shear locking is and why it occurs.