Mental model — Boundary conditions are part of the model
An ideal fixed support is not simply “where the part touches a wall.” It is the mathematical assumption that specific degrees of freedom have prescribed values. A nodal force is not merely a decorative arrow either: it has a magnitude, sign, direction, point of application, and reference system.
A solution can converge with wrong conditions
The solver can easily solve a completely blocked beam or a load six times greater than intended. Algebraic convergence does not correct the physical model.