Optimal Shape of Arches under Bending and Axial Compression

Abstract

The paper concerns the optimal shape of plastically designed arches under bending and axial compression. In view of the absolute term found in the specific weight, the optimization problem is that of a nonsmooth one. An optimization technique has been developed to cater to this nonsmooth objective function. The technique involves approximation as well as discretization. The process is carried out in three stages: the unspecified arch centroidal axis is first approximated; the integration is discretized; and the nonsmooth function is approximated by a smooth function. Interestingly, the optimal shape of arches under a uniformly distributed load takes the funicular form irrespective of the various boundary conditions considered.