The Limited option that is available for prescribing displacements in the
Prescribed Displacement/Rotation node is implemented as a weak inequality constraint. For each displacement component
ui, a gap distance is computed as
where u0i,max and
u0i,min are the maximum and minimum limits. Given
Equation 8-5, the weak inequality constraint is formulated as
where fi is the constraint force (or contact reaction force).
where kp is the penalty factor. With the above definition of
fi,
Equation 8-6 is added as a weak contribution to the model to implement the constraint.
where flm,i is a Lagrange multiplier that is added as an extra degree of freedom to the model. The penalized contact reaction force
fi is for the augmented Lagrangian method defined as
