Boundary conditions

To enforce Dirichlet boundary conditions in numgeo, the following steps are taken:

1. The applied forces on the right-hand side are adjusted to account for any prescribed displacements, which are then stored in the reaction-force slots.

2. Appropriate rows and columns of the stiffness matrix are cleared, and ones are placed in the corresponding diagonal positions.

This process is visualized in the figure below.

Since we are solving for the correction \(c_i\) to the solution increment \(\Delta u_i\) (as detailed in Section Newton-Raphson method), the prescribed displacements stored in the reaction-force slots must be set to zero (e.g., \(\bar{u_3} = 0\)).