Beam-like models for the post-buckling behaviour of wingbox structures

Abstract

Design and optimisation of wing structures are often constrained by buckling, even though thin-walled components, particularly stiffened panels, retain significant load-carrying capacity beyond their initial buckling point. Enabling the design for a safe use of this post-buckling regime requires a computationally efficient methodology that can be integrated into design and optimisation processes. This work provides a representation of one or more post-buckled wingbox regions through the stiffness matrix of a one-dimensional beam model. The approach is motivated by the observation that high-aspect-ratio wings exhibit global deformation patterns that closely resemble beam modes. The three-dimensional wingbox is mapped onto a one-dimensional representation using a cross-section modeller, while the reduction in stiffness induced by panel buckling is estimated using a semi-analytical post-buckling method and incorporated into the cross-sectional stiffness. This leads to a computationally efficient formulation suitable for repeated evaluations within design and optimisation loops. Results for several wingbox configurations show that the predicted buckling loads and post-buckling trends are in good agreement with Abaqus simulations in the early post-buckling regime. The Abaqus response becomes more compliant once local sagging and area reduction occur, which are not yet captured by the current model. Nevertheless, the proposed methodology accurately predicts the overall post-buckling behaviour within the range relevant for design, where wings are not expected to operate deeply into the post-buckling regime.