In this lecture, we'll cover:

• Refactoring our existing structural analysis code to improve efficiency and readability
• Creating a function to calculate the global element stiffness matrix
• Automating the extraction of the structure stiffness matrix using restrained degrees of freedom
• Using list comprehensions and NumPy’s delete function to reduce the primary stiffness matrix
• Writing a reusable function to calculate member axial forces from nodal displacements

In this lecture, we focus on refactoring the code we developed previously so that it becomes cleaner, more efficient and easier to reuse. We begin by defining key problem parameters at the outset, such as the total number of degrees of freedom and the restrained degrees of freedom. We then encapsulate the repeated calculation of the global element stiffness matrix into a dedicated function. By passing in properties such as Young’s modulus, cross-sectional area, member length and orientation, we ensure that we can compute stiffness matrices for any member simply by calling the function rather than rewriting the same code multiple times.

We then improve the way we extract the structure stiffness matrix from the primary stiffness matrix. Instead of manually removing rows and columns, we use a list comprehension to determine the restrained indices and NumPy’s delete function to systematically remove the appropriate rows and columns. This makes the reduction process automatic and directly driven by the restrained degrees of freedom defined at the start of the script. Finally, we refactor the calculation of member axial forces into a separate function that takes nodal displacements and member properties as inputs. This allows us to compute forces for multiple members in a consistent and compact way, reinforcing the benefits of modular, well-structured code.

Next up:

In the next lecture, we begin Section 6, where we apply the direct stiffness method to a larger 8-bar truss, reinforcing the same procedure at a bigger scale.