Cross-level buckling mode evolution in aperiodic morphospace for stiffened structures

This work develops a hierarchical plate-strip theory for aperiodic stiffened plates and interprets buckling as an eigenvalue-evolution process. The plate-strip model is introduced by representing the stiffener topology through Voronoi-type cells and the plate-stiffener interaction through line-concentrated force potentials. The resulting theory resolves global plate buckling, local plate buckling, local stiffener or local-web buckling, and their mixed states within one framework. Starting from the total potential energy, the governing equations are obtained from the first variation for the prebuckling state and from the second variation for the incremental buckling problem about a general non-flat base state. A plate-rod reduction and a further Voronoi-Dirac reduction are then obtained in a controlled manner, which makes the applicability range of each reduction explicit. Numerical simulations and compression experiments confirm four characteristic buckling modes driven by geometric discontinuity, namely global, local-plate, local-stiffener, and coupled buckling. The results further show that non-uniform boundary conditions drive the evolution of optimal aperiodic layouts, while the strong stiffener-plate discontinuity enhances the mode-coupling effect. Under the combined action of these two factors, the evolved aperiodic geometries achieve more than 20% improvement in load capacity relative to periodic reference layouts under non-uniform loading. Modal nudging is finally used to steer the coupled-buckling state toward nearby global, local-plate, and local-stiffener-dominated responses.