Formability of linearly elastic structures with volume-type actuation

Formation theory concerns the modification of the geometric configuration o f an elastic structure by means of attached and/or embedded actuators. In t his paper we consider "volume" type actuation, which involves application-o f:an: isotropic expansive/contractive stress to the elastic medium. The que stion of "formability", i.e., whether or not a given modified geometric con figuration for the elastic body can be achieved with actuation of this type , is considered at length; in both the two-and three-dimensional contexts, along with related questions of optimal formability, expressed in terms of the L-2 norm of the volume controller employed; In two dimensions, with the aid of the Airy "stress'' function, we establish-connections between optim al formation, in the L-2 norm sense, and the standard theory of conformal m apping of simply-connected regions in the complex plane. Further results ar e presented for multiply-connected domains, including a complete discussion of the case of an annulus.