Topology, shape and sizing optimization of under-deck stayed bridges

Abstract

Under-deck stayed bridges are effective structural systems formed by a rigid beam supported from beneath by an arrangement of struts and stays. The optimal scheme of these bridges can be sought tuning a large set of parameters of different character: the number of typical struts-stays sections in the longitudinal direction, topology schemes and widths of the each section, the heights of struts, and the dimensions of the cross-sections of all structural elements. Mathematically, the optimization of the bridge structure is a mixed topology/shape/sizing optimization problem with a different number of design variables, some integer variables, subject to strength, stability and displacement constraints for different loading cases. The optimization problem is converted to unconstrained optimization using a penalization technique. The objective function is evaluated by a special program connected to an optimization algorithm as a “black box”. A three-stage optimization technique has been proposed for solving similar problems of structural optimization. First, an evolutionary algorithm with variable-length genotype ascertains the promising range of leading design parameters. Since some design variables are interdependent, special operators have been suggested for the mutation, crossover, and genome repair. Second, the obtained results have been verified by optimization with a standard evolutionary algorithm having a constant genotype length. Third, the findings can be improved using consecutive pattern search. A typical plane 24 m bridge has been optimized employing the proposed technique.