Computational aspects of structural shape control

The goal of shape control is nullification of the structural deformations caused by certain external disturbances, mainly body forces and surface traction. Dynamic structural shape control is concerned with vibration suppression. Determination of a proper distributed actuation is understood through the interaction of structural mechanics (of smart materials) and control engineering. Imposed strains (eigenstrains) are of quasistatic thermal nature in graded materials, or mainly make use of the piezoelectric effect in smart composites containing conventional ferroelectric polycrystals, natural crystals or special polymers. For large scale structures tendons or built-in hydraulic actuators are available. For discretized or discrete structures (e.g., trusses) the general solution is given in terms of the flexibility matrix and the two, orthogonal subspaces, of the impotent and nilpotent eigenstrains in Hilbert space are mentioned. Since impotent eigenstrains do not produce stress, they are ideally suited for shape control. Further, vibration suppression is discussed in the context of separation in space and time of the forcing function. In those cases, knowledge of the quasistatic load deformation suffices to define the distributed actuators producing impotent eigenstrain.