Self-shape optimisation application: Optimisation of cold-formed steel columns

Abstract

a b s t r a c tThis paper presents the optimisation of cold-formed steel open columns using the recently developed self-shape optimisation method that aims to discover new profile shapes. The strength of the coldformed steel sections is calculated using the Direct Strength Method, and the rules developed in the present work to automatically determine the local and distortional elastic buckling stresses from the Finite Strip and constrained Finite Strip Methods are discussed. The rules are verified against conventional and optimum sections yielded in this research, and found to accurately predict the elastic buckling stresses. The optimisation method is applied to singly-symmetric (mono-symmetric) cold-formed steel columns, and the operators behind the method for the special case of singlysymmetric open profiles are introduced in this paper. ''Optimum'' cross-sections for simply supported columns, 1.2 mm thick, free to warp and subjected to a compressive axial load of 75 kN are presented for column lengths ranging from 1000 to 2500 mm. Results show that the optimum cross-sections are found in a relatively low number of generations, and typically shape to non-conventional ''bean'', ''oval'' or rounded ''S'' sections. The algorithm optimises for distortional and global buckling, therefore likely subjecting the cross-sections to buckling interaction. A manual attempt to redraw the ''optimum'' cross-sections to include limitations of current manufacturing processes is made. Future developments of the method for practical applications are also discussed.

Shape optimisation of manufacturable and usable cold-formed steel singly-symmetric and open columns

“…This paper employs the previously developed GA-based shape optimisation algorithm [4,5], referred to as the "self-shape optimisation algorithm". The algorithm uses the coordinates (x, y) of the floating points constituting the cross-sections to define the individuals in a given design space.…”

“…An augmented Lagrangian constraint-handling method [15] is used to automatically control the penalty function coefficients to remain finite in order to avoid ill-conditioned solutions. Cross-over and mutation operators are performed on the floating points constituting a cross-section (see [4,5], Sections 2.4 and 2.5 for more details). As the problem is singly-symmetric, only half of the cross-section is considered by the GA operators.…”

“…The steps to create the manufacturable half crosssections in the initial population are revised from [4,5], and are given below when fastening elements are not considered:…”

“…The one-point cross-over operator used in this study is revised from Gilbert et al [5] to keep the sections manufacturable and the fastening elements horizontal and vertical. Two parents, having the same number of elements and the same location of fastening elements, are selected for crossover.…”

“…The present study focuses on incorporating manufacturing and assembly features into the published GA-based "self-shape" optimisation algorithm for CFS columns [4,5]. The algorithm is applied to simply-supported singly-symmetric, free-to-warp open section columns.…”