We consider the finite element approximations of an optimal control problem consisting in the suppression of slosh arising in fluid–structure interaction problems with free surface. The vibration of a plate in contact with an incompressible fluid is considered as state equations in the optimization problem, and distributed controls on the plate are calculated to suppress the slosh.
Locking-free finite elements are used to discretize the plate, which is modeled by Reissner–Mindlin equations. The effect of the fluid is taken into account by means of an added mass formulation, discretized by standard piecewise linear tetrahedral finite elements, and the gravity waves on the free surface of the liquid are considered in the model. The control variable is the amplitude of a secondary force actuating on the structure.
Implementation issues are discussed, and numerical experiments are presented. Copyright © 2012 John Wiley & Sons, Ltd.