In this lecture, we will cover the following:

• We build the drilling stiffness coefficient from Young's modulus, thickness, and element area,
• We use the element normal vector to create the global rotational correction block,
• We will verify that the stabilised stiffness matrix is full rank and produces sensible results.

We start by adding a tuning parameter, alpha_drill, which scales the arbitrary drilling stiffness introduced in the previous lecture. We then calculate each quadrilateral element's area by splitting it into two triangles and using cross products to determine the triangular sub-areas. These areas are needed because the drilling stiffness coefficient is based on the element area, thickness, and Young's modulus.

We then modify the element stiffness calculation itself. For each element, we extract the normal vector from the rotation matrix, use it to form the drilling correction block, and add that block into the rotational diagonal locations of the global element stiffness matrix. Once the correction is active, the rank and condition checks show that the structure stiffness matrix is no longer rank deficient, and the displacement results return to a physically sensible form.