Optimal geometries of shape controlled structures

The geometry design of controlled trusses that must maintain a set of nodes, the controlled degrees of freedom, as undeformed as possible is dealt with. The structure is subjected to a family of disturbances whose total magnitude is bounded in an overall sense, but which is only loosely defined at any given point in time. Control is assumed by means of N-c ideal actuators, which can develop any desired displacements in the structure within a predefined subspace of deformations. Such virtual actuators usually perform in a similar manner as optimally located real actuators. The use of this mathematical concept circumvents the need for an exhaustive search for a best actuator configuration at a given geometry design of the structure. A measure of the distortions is the (N-c + 1)th singular value of the disturbance influence matrix. The purpose is, therefore, to modify the geometry of the structure in order to minimize that singular value. One of the difficulties en countered during the optimization is the problem of repeated singular values. Their derivative is different from that of a distinct singular value and requires more attention. Numerical results indicate that the design tends to generate structures composed of stiff segments with actuators located at flexible interfaces. These rather peculiar designs may harbor interesting guidelines for future implementations of smart structures.