In this lecture, we'll cover the following:

• What shear locking is and how it manifests in finite element results.
• The relationship between bending and shear stiffness and their dependence on plate thickness.
• How shear stiffness dominates as thickness approaches zero, causing locking.
• The concept of selective integration as a remedy and how it is implemented.
• Practical rules for applying selective integration in plate elements.
• Potential issues such as spurious zero-energy modes (hourglassing).

In this lecture, we examine shear locking, a phenomenon where finite elements become artificially too stiff, leading to underestimated deflections. We clarify that this is not a numerical instability, as solutions still converge, but rather a modelling issue that produces incorrect results. By analysing the stiffness formulation, we see that bending stiffness scales with thickness cubed, while shear stiffness scales linearly with thickness. As the plate becomes very thin, shear stiffness dominates, effectively suppressing transverse shear deformation and causing the locking effect.

We then explore selective integration as a practical and effective solution. By reducing the integration order for the shear component (while retaining full integration for bending), we intentionally weaken the shear contribution, preventing it from overwhelming the response as thickness decreases. This approach works well across both thin and thick plates, forming a reliable default strategy. However, we also note a potential drawback: the introduction of non-physical, zero-energy deformation modes (hourglassing), which must be recognised and managed in more advanced analyses.

Next up

In the next lecture, we will implement the selective integration fix for shear locking and re-run the comparison to confirm that the issue has been resolved.