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Figure 4: Systematic variation of the unit cell length luc and its effect on the critical compressive membrane force |N∗ | in the 1-direction.
From:
Daxner, T., Flatscher, T. and Rammerstorfer, F.G. (Institute of Lightweight Design and Structural Biomechanics, Vienna University of Technology), “Optimum design of corrugated board under buckling constraints”, 7th World Congress on Structural and Multidisciplinary Optimization, Seoul, Korea, 21-25 May, 2007
ABSTRACT: Corrugated paper is produced in large volumes for packaging purposes, an application which places high demands on the structural stability of the employed corrugated board containers. This is taken into account in the optimization procedure for reducing the area-specific weight of corrugated board which is presented in this paper. For predicting effective properties of corrugated board designs, the geometry of the board is discretized by finite shell elements, and a periodic unit cell model, which contains a minimum of one full wave of the flute, is generated. By application of appropriate periodicity boundary conditions, the effective mechanical behavior of a theoretically infinite board can be predicted within the limits of linear shell theory. Furthermore, local loss of stability can also be calculated. It is possible to embed this model into an optimization procedure which attempts to reduce the area-specific weight of the board by modifying the governing geometrical parameters while enforcing the stiffness and buckling strength constraints. It has to be noted that the calculation of critical loads with respect to local buckling involves a minimization scheme within this optimization loop in order to find the critical buckling wavelength and adjust the unit cell size accordingly. We apply the proposed optimization scheme to a specific kind of corrugated board in order to determine if there is potential for weight-reduction. The optimization scheme gives a set of parameters which describes a new design of corrugated paper with the same buckling strength, but an area-specific weight that is reduced by more than 18% with respect to the original design. The improved corrugated board shows simultaneous buckling of fluting and liners under a compressive membrane load along the generatrix of the flute.
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