Multi-objective optimisation of variable-stiffness composite cylinders with geometric imperfections: minimising mass while maximising buckling capacity and knockdown factor

This study presents an imperfection-tolerant, surrogate-assisted framework for the multi-objective optimisation of variable-stiffness (VS) composite cylinders that explicitly incorporates experimentally measured geometric imperfections. Principal component analysis (PCA) is applied to extract dominant imperfection modes from experimental data, and Latin hypercube sampling (LHS) is used to generate statistically consistent synthetic fields, which are subsequently mapped onto nonlinear finite element (FE) models. Linear buckling and geometrically nonlinear collapse analyses are performed under axial compression to determine the ideal and actual load-carrying capacities, from which the knockdown factor (KDF), quantifying imperfection sensitivity, is derived. Gaussian Process Regression (GPR) surrogates are trained to predict the mass and collapse loads of perfect and imperfect geometries with high cross-validated accuracy, while KDF is computed as their ratio. The framework enables simultaneous optimisation of three objectives: mass minimisation, collapse-load maximisation, and KDF maximisation by using Bayesian Optimisation (BO) and the Non-dominated Sorting Genetic Algorithm II (NSGA-II) independently. Results demonstrate that integrating experimentally informed imperfections with surrogate-based optimisation captures the key physical trends governing buckling and imperfection sensitivity, while achieving substantial computational savings relative to direct nonlinear analyses, and that both optimisers yield consistent Pareto fronts featuring smooth, manufacturable fibre trajectories that balance lightweight efficiency, strength, and robustness.