Structural optimization and system dynamics

TL;DR: In this paper, an alternative solution methodology for the optimization of continuous structures described in terms of one spatial coordinate is presented, using a control systems state variable formulation for the structural model, which reduces the optimization problem to simultaneously satisfying the state, costate and optimality condition together with any constraints on the problem.

Abstract: The paper presents an alternative solution methodology for the optimization of continuous structures described in terms of one spatial coordinate. Using a control systems state variable formulation for the structural model, Pontryagin's principle reduces the optimization problem to simultaneously satisfying the state, costate and optimality condition together with any constraints on the problem. System dynamics methodology is then used to obtain the numerical solution. This is achieved by constructing graphically a flow diagram representing the necessary optimality conditions; contraints are included through the use of logical relationships. The associated (DYNAMO) equations are then solved numerically as part of the standard system dynamics package.