Gradient-based initial postbuckling optimisation of imperfection-sensitive variable angle tow shells using an implicitly differentiated reduced-order model

The optimisation of the postbuckling behaviour of lightweight composite shell structures remains a critical and largely unresolved challenge, due to the combined effect of structural nonlinearity, sensitivity to uncertain data and the typically large number of design variables. Even small-amplitude geometrical imperfections can significantly alter the postbuckling response and must therefore be explicitly accounted for within optimisation frameworks. Reduced-order models based on Koiter’s asymptotic analysis provide an efficient and accurate description of the initial postbuckling regime and of imperfection sensitivity. However, their systematic use within gradient-based optimisation problems involving many design variables is still hindered by the lack of an exact and efficient gradient evaluation.In this work, this limitation is addressed by introducing an implicit algorithmic differentiation strategy tailored to multimodal Koiter asymptotic analysis combined with finite element solid-shell discretisations. The proposed approach is applied to the postbuckling optimisation of variable angle tow composite shell structures, including configurations with cut-outs. Numerical results demonstrate that the proposed analytical gradients markedly improve both robustness and computational efficiency compared to finite-difference-based schemes, particularly in the presence of imperfections.