In this lecture, we'll cover:

• How to use an existing function to calculate a member’s global stiffness matrix
• How to determine the total number of degrees of freedom programmatically
• How to initialise and build the primary stiffness matrix
• How to assemble the global structure by looping through all members
• How to reduce the primary stiffness matrix to the structure stiffness matrix by removing restrained degrees of freedom

In this lecture, we focus on assembling the global stiffness matrices for a structure in a fully programmatic way. We begin by importing a previously developed function that calculates the global stiffness matrix for an individual member and returns its four quadrants. We then determine the total number of degrees of freedom by extracting the maximum node number from the members array and multiplying by two, allowing the code to work for arbitrary structures rather than relying on hard-coded values. With this information, we initialise the primary stiffness matrix as a zero matrix of appropriate size.

We then construct a for loop to iterate through every member in the structure. For each member, we compute its global stiffness matrix, determine the associated node numbers and corresponding global indices, and add the four stiffness matrix quadrants into their correct positions within the primary stiffness matrix. Finally, we reduce the primary stiffness matrix to the structure stiffness matrix by removing rows and columns corresponding to restrained degrees of freedom using previously developed code. This completes the automated assembly process.

Next up:

In the next lecture, we solve for displacements, reactions, and member forces in a fully automated loop, completing the core of the generalised solver.