In this lecture, we'll cover:

• How to combine the separate membrane, bending, and shear stiffness contributions into one element stiffness function,
• How to organise the stiffness calculation into a reusable utilities file,
• How to import and test the function inside a notebook,

In this lecture, we will focus on refactoring the element stiffness matrix calculation into a single function that can be reused for each element in the structure. We build the function so that it accepts the number of sampling points for membrane, bending, and shear calculations, along with the element coordinates and constitutive matrices.

We then streamline the selection of Gauss points and weights with a small dictionary, and assemble the full stiffness matrix by adding the membrane, bending, and shear contributions together. After defining and checking the function in the notebook, we move it into a separate utils.py file so the notebook stays cleaner and the function can be imported later when needed.

Next up

In the next section, we will build the transformation matrix to move from local element coordinates to global 3D coordinates.