Assembly Process

Assembly combines all element matrices and vectors into the global system of equations. Each element contributes stiffness and force terms to the global degrees of freedom associated with its nodes.

The assembly process follows element connectivity. For every element:

1. Compute the element stiffness matrix.
2. Compute equivalent element load vectors.
3. Map local element degrees of freedom to global degrees of freedom.
4. Add element contributions into the global sparse matrix and global force vector.

Because most finite element matrices contain many zeros, the global stiffness matrix is stored using sparse matrix formats. Correct assembly is essential for preserving equilibrium and compatibility across element boundaries.