In this lecture, we'll cover the following:

• Constructing the primary (global) stiffness matrix by assembling element stiffness contributions.
• Using previously defined functions to compute element stiffness matrices with bending and shear effects.
• Mapping element degrees of freedom into the global system using index arrays.
• Reducing the primary stiffness matrix by removing entries that correspond to restrained degrees of freedom.

In this lecture, we focus on assembling the global stiffness matrix for the entire structure by looping through each element, computing its stiffness matrix, and inserting it into the correct locations within a larger matrix. We reuse a previously defined function to calculate element stiffness. A key practical step is correctly mapping local element degrees of freedom to global indices, which we handle efficiently using NumPy’s index array functionality.

We then move on to forming the reduced, or structure stiffness matrix by eliminating rows and columns associated with restrained degrees of freedom. This step ensures that the system is solvable and sets up the matrix that will be inverted in the next lecture to obtain nodal displacements. By the end, we have completed the assembly phase of the finite element procedure and are ready to solve the system and move into post-processing.

Next up

In the next lecture, we will solve the assembled system for nodal displacements and extract reaction forces to validate the model.