Constrained Shape Optimization of Cold-formed Steel Columns

摘要

The objective of this paper is to introduce appropriate constraints in the shape optimization of a cold-formed steel column such that the resulting optimized shapes retain the strength benefits of unconstrained optimal solutions combined with practical manufacturing and constructional needs. Unconstrained shape optimization of cold-formed steel columns, where the cross-section that maximizes axial capacity is found, has previously been performed. Here, practical manufacturing and construction constraints are introduced into the optimization algorithm. Members with three lengths: 2 ft, 4 ft, and 16 ft, are considered. Optimized sections from multiple runs show uniformity and bear a close resemblance to unconstrained results. A point-symmetric 'S'-shaped section has maximum capacity for long columns and a singly-symmetric '∑'-shaped section with complex lips performs best for shorter columns. The observed strength loss from the unconstrained optimal design, to the constrained optimal design, is within ten percent. A simultaneous perturbation stochastic approximation algorithm, with the idea of injecting randomness in the gradient approximation to save computational cost, is adopted as the local optimizer. A systematic survey on a family of lipped channel cross-sections using the same amount of material was carried out. Comparison reveals that the optimized shapes have much larger capacities and exhibit the potential to seed a new generation of commercial products.