Variational Approaches to Optimal Control Design for Elastic Body Motions

Abstract

Variational and projection statements of an initial-boundary value problem for the direct and inverse dynamics of elastic bodies are proposed. An optimal control problem of 3D linear elastic motions for rectilinear beams with the rectangular cross section is studied. Based on the generalized formulations, a numerical algorithm is developed to design the optimal displacement of such elastic beams. The results of numerical simulation and quality analysis are presented and discussed.

Keywords

• optimal control
• dynamics
• linear theory of elasticity
• variational principles
• semi-discretization