Formability of Linearly Elastic Structures with Volume‐Type Actuation

Abstract

. Formation theory concerns the modification of the geometric configuration of an elastic structure by means of attached and/or embedded actuators. In this paper we consider “volume” type actuation, which involves application of an isotropic expansive/contractive stress to the elastic medium. The question of “formability”, i.e., whether or not a given modified geometric configuration 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 optimal formation, in the “L”² norm sense, and the standard theory of conformal mapping of simply‐connected regions in the complex plane. Further results are presented for multiply‐connected domains, including a complete discussion of the case of an annulus.