In this section, we will cover the following:

• We will introduce drilling degrees of freedom as the source of the hidden issue,
• We will connect drilling degrees of freedom to zero-energy modes,
• We will explain why the stiffness matrix can become singular,
• We explore drilling stabilisation as the fix that will make the solver more robust.

We begin by framing the problem exposed during the OpenSeesPy comparison. The custom solver can produce results that look excellent in one configuration but become nonsensical after a small change in the input parameters. The goal of this section is to understand why that happens rather than simply applying a fix without knowing what it is correcting.

We start this section by learning what drilling degrees of freedom are, then we will connect them to zero-energy modes and stiffness matrix singularity. Once that foundation is in place, we will implement drilling stabilisation, a relatively small code change that has a major effect on the robustness of the solver.

Next up

In the next lecture, we will start that diagnosis by defining drilling degrees of freedom and seeing how they arise in a shell element model.