Shape Optimisation of Manufacturable Cold-Formed Steel Columns for all Buckling Modes - Part I: Hough Transform

Abstract

Previous studies on unconstrained shape optimisation of cold-formed steel (CFS) crosssections, where the sole purpose was to optimise the weight-to-capacity ratio of the profiles, yielded rounded cross-sections that cannot be manufactured. This paper introduces manufacturing constraints into an evolutionary algorithm for shape optimisation of CFS profiles. The algorithm is referred to as “self-shape optimisation” and uses Genetic Algorithm (GA) together with Augmented Lagrangian (AL) method to avoid ill-conditioned problems. Specifically, this paper builds on the previous work from the authors in which the cross-sectional shapes of manufacturable singly-symmetric open profiles were only optimised for global buckling. In this study, the three buckling modes, i.e. global, local and distortional are considered. The strength of the columns is evaluated by the Direct Strength Method (DSM). Simple manufacturing rules derived from the limitations of cold-forming process, i.e. a limited ability to form continuously curved surfaces without discrete bends, are described in the paper and introduced into the algorithm. The algorithm is applied to simply-supported and singlysymmetric open-section CFS columns subjected to an axial compressive load of 75 kN. The crosssections have a uniform wall thickness of 1.2 mm. The Hough transform is used to detect straight lines and transform arbitrary drawn cross-sections into manufacturable ones. Column lengths ranging from 500 mm (short) to 3,000 mm (long) are investigated. Various numbers of roll-forming bends are investigated per column length. The optimised cross-sections are presented and discussed in the paper.