In the solution of constrained optimization problems, penalty methods consist in replacing
the constrained optimization problem with a sequence of unconstrained optimization problems.
The virtual power continues to be minimized so as to find the stationary condition, but a
penalty term is added to
Virtual Power Term Names,
Equation 5 so as to impose the
impenetrability condition:
(1)
Where,
if
if
is an arbitrary parameter known as the penalty parameter. The penalty
function
is an arbitrary function of the interpenetration and its rate. It is
emphasized that the weak form, including the virtual power and the penalty term Penalty Method, Equation 1 is not an inequality
form. The penalty function will be defined in the description of interfaces.