Optimal Design of Elastic Rod Motions Based on a Projection Approach ★

摘要

Dynamics modelling and control design for elastic rods with distributed parameters are under study. The constitutive laws are specified by an integral equality according with the method of integro-differential relations. A numerical algorithm is developed to solve direct and inverse dynamic problems in linear elasticity based on the Ritz method and finite element technique. The control problem is to obtain the rod motion from some initial state to terminal one at a fixed time with the minimal mean energy. The exact solution is found with a specific triangular space-time mesh and a piecewise polynomial displacement input.