Shape control by collinear actuators

We consider a two-dimensional elastic medium bounded by a free surface. The medium deforms under the influence of actuators, which are modelled as sup plying a unidirectional stress. The goal of the control mechanism provided by the actuators is to deform the body into a given shape. In a linearized situation, this means achieving a given normal displacement on the boundary . We prove that, for generic domains with smooth boundary, every normal dis placement of the boundary can be achieved. We also consider "stress-free" s tates, for which the sum of the elastic stresses in the medium and the stre ss provided by the actuators vanishes. The study of these states leads to a hyperbolic boundary value problem.