Design of optimal control for motions of elastic bodies: Variational approaches

Abstract

For the forced motion of elastic bodies, we provide the variational and projection statements of initial-boundary problems. In the framework of the spatial linearmodel, we investigate the optimal control problem for an elastic rectilinear beam with a rectangular cross-section. Using the proposed generalized formulations, we develop a design algorithm for optimal displacements of elastic beams. Results of the numerical simulation and the analysis of the dynamics are provided.