In this section, we'll cover:

• Building the overall code structure for stiffness matrix calculation using Gauss numerical integration,
• Focusing first on the membrane contribution to the stiffness matrix,
• Reusing the same numerical integration approach for the bending and shear contributions,
• Refactoring the calculations into a single function and moving the code into a utility script for reuse in future notebooks.

In this first coding section, we begin turning the theory into working code by focusing on one clear objective: calculating the local element stiffness matrix. We set up the overall structure for the calculation using a Gauss numerical integration scheme. Initially, we limit ourselves to the membrane contribution. The same strategy will then be repeated for the bending and shear parts of the stiffness matrix.

We also prepare for a cleaner workflow later on by combining the separate stiffness matrix calculations into one reusable function. By the end of this section, you will have a utility file containing the stiffness matrix calculation function that can be imported into future notebooks, keeping your analysis code tidy and easier to manage.

Next up

In the next lecture, we will implement the membrane stiffness matrix calculation, working through the Gauss integration loop and Jacobian handling in detail.