where u0i,max and
u0i,min are the maximum and minimum limits. Given
Equation 3-176, the weak inequality constraint is formulated as
where fi is the constraint force (or contact reaction force). The integral is taken over the geometric entities of the selection, which may be domains, boundaries, edges, or points. For a point selection, the integral should be interpreted as a summation. The constraint force will have corresponding units.
where kp is the penalty factor. With the above definition of
fi,
Equation 3-177 is added as a weak contribution to the model to implement the constraint. The unit of the penalty factor depends on the type of geometrical entity that is constrained.
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