Optimal design of elastoplastic columns against global buckling

Abstract

This paper investigates the optimal design of self-similar columns that maximise elastoplastic global buckling load-bearing capacity for a given material volume and height. Although many classical solutions have been proposed, most neglect elastoplastic behaviour or focus on specific column types, thereby limiting their practical relevance and generality. In this study, the problem is revisited using modern numerical computational techniques. The optimal axial area distribution that maximises the global elastoplastic buckling load is first explored using Bayesian Optimisation. The column’s load-bearing capacity is evaluated through high-fidelity ABAQUS simulations that incorporate geometric and material nonlinearities, as well as initial imperfections. The Bayesian Optimisation framework efficiently guides the simulations towards near–global-optimal designs. The resulting optimal solutions inspire a heuristic design principle, termed the Edge Uniform Stress Design, which states that an optimal column is characterised by the simultaneous yielding of the compressed outer fibres across all cross-sections at the ultimate state. Based on this principle, the optimal column shape can be directly constructed for any given cross-section and normalised slenderness ratio. Compared with a uniform column, the improvement achieved by the optimal design increases with the normalised slenderness ratio, approaching an upper limit of approximately 34%.