Free nodal displacement along a general direction or plane
If a node is constrained to a line or plane parallel to the axes of the global coordinate system, the corresponding degrees of freedom are prescribed as zero.
If the direction of the line, or the direction of the normal to the plane, is general, the approximate penalty function method must be used. The PMD system allows an elastic attachment of a node to be specified in an arbitrary direction. This can be used by prescribing a very stiff spring in the direction of the constraint. The stiffness of the spring must be several orders of magnitude higher than the local stiffness of the body, so that the constraint condition is enforced with sufficient accuracy. However, as the spring stiffness (penalty) increases, the conditioning of the system of equations being solved deteriorates at the same time. The optimal penalty value is usually approximately $10^6~\text{N/m}$ (or more) higher than the local stiffness of the body, which must be estimated.
Example
Let us consider a beam with axial stiffness $EA/l$. Its bending and torsional stiffness are substantially smaller. If we attach the free end to the reference system by means of a spring with stiffness $k_n=EA/l+10^7~\text{N/m}$, this point will move freely in the plane perpendicular to the direction of the spring. In this case, the planar constraint will be satisfied to an accuracy of at least six decimal places.