In this lecture, we'll cover:

• How to assemble the primary (global) stiffness matrix from individual element stiffness matrices
• How the four quadrants of each element stiffness matrix map into the global matrix
• How to construct and interpret the stiffness matrix template for a multi-node structure
• How element connectivity (including non-sequential node numbering) affects matrix placement
• How the complete global stiffness matrix is obtained computationally

In this lecture, we focus on assembling the primary stiffness matrix using the direct stiffness method. We begin by recalling that each element stiffness matrix can be divided into four quadrants, and it is these quadrants that are positioned into the appropriate locations within the global stiffness matrix. For a structure with six nodes, we construct a six-by-six template, noting that each entry actually represents a two-by-two submatrix. This means the full primary stiffness matrix is twelve by twelve in size.

We then work through the structure element by element, identifying how each member’s node connectivity determines where its four stiffness quadrants are placed within the global template. Whether the element connects sequential nodes (such as nodes 1 and 2) or non-sequential nodes (such as nodes 1 and 5), the same logic applies: we locate the relevant rows and columns corresponding to the connected nodes and insert the submatrices accordingly. The key conceptual step is understanding how element connectivity governs placement within the primary stiffness matrix.

Next up:

In the next lecture, we reduce the primary stiffness matrix by applying boundary conditions to obtain the structure stiffness matrix.