Optimization of Corrugated Paperboard under Local and Global Buckling Constraints

Abstract

An important design criterion for containers (boxes) made from corrugated paperboard is their resistance against buckling under compressive loads such as those arising from gravity as boxes are piled up. Since such boxes are typically means of packaging goods for transport, their weight should be as low as possible. These demands are taken into account in the presented optimization procedure for reducing the area-specific weight of corrugated paperboard under global, i.e., box wall buckling constraints and local buckling constraints pertaining to the buckling of flute and liner. The critical load with respect to global buckling is correlated to the effective bending stiffness of the paperboard (obtained by homogenization). Local buckling is predicted by a unit cell approach in combination with the finite element method. The stiffness homogenization procedure as well as the unit cell approach for computing the buckling loads are embedded into an optimization process. The geometrical parameters describing the meso-scale geometry of the corrugated paperboard act as optimization parameters. The presented approach is applied to a specific configuration of corrugated paper board, as it is used in packaging. Substantial weight saving could be achieved by the proposed optimization scheme. A further consideration concerns the post-buckling behavior. Once the side walls of corrugated paperboard containers have buckled, they typically show the formation of folds. As demonstrated in non-linear finite element analyses, these folds are the result of the localization of the initially periodic local buckling pattern.