The Optimal Design of an Arch Girder of Variable Curvature and Stiffness by Means of Control Theory

The problem of optimal design of the statically indeterminate arch girder which constitutes the primary structural system of the arch bridge is presented. The task is to determine the optimal shape of the axis of the arch girder, as well as the optimal distribution of the cross section height, ensuring the minimum arch volume as well as fulfillment of the standard requirements. This optimisation task, with numerous control functions and constraints, is formulated as a control theory problem with maintaining the formal structure of the minimum principle and then transformed to the multipoint boundary value problem and solved by means of numerical methods. The numerical results are obtained with optimal control methods, using the Dircol software. Since the changes in the shape and cross-section of the arch affect the distribution of the dead and moving loads transferred on the girder from the bridge deck, the optimisation procedure is combined with the finite element method analysis, which together with the complexity of the multidecision arch optimisation problem accounts for the novelty of the proposed approach. The numerical analysis reveals that the optimal girder shape is the frame-arched structure, with considerable lengths of straight sections and only short arch elements, in the areas of the application of concentrated forces and moments. The presented method can be successfully extended to optimisation of structures with different static schemes and load categories taken into account.