Equivalent flexural and torsional rigidity of hexagonal honeycomb

Abstract

The flexural rigidity and torsional rigidity of an open honeycomb were evaluated by analyzing the bending and torsional deformation of cell plates with consideration of the constraint condition on the plate edges. The analysis of torsional rigidity showed that if the deformation of a honeycomb satisfies periodicity conditions, the ratio of M xy ∣ unit and M yx ∣ unit acting on each unit constituting the honeycomb becomes a specific value to satisfy the continuity condition of displacement. This specific value is obtained using an equation proposed in this study; the value depends only on the geometry of the honeycomb. As a consequence of the necessity that the ratio of M xy ∣ unit and M yx ∣ unit should become a specific value, if the ratio of torsional load moments M xy ∞ and M yx ∞ acting on the boundaries is not actually equal to the above-mentioned value, scattering appears near the boundary in the ratio of M xy ∣ unit and M yx ∣ unit , and the ratio approaches the above-mentioned specific value as the distance from the boundary increases. Therefore, even if the value ( M xy ∞ - M yx ∞ ) is kept the same, the scattering of deflection depends on the combination of torsional moments, and becomes smaller as the honeycomb model becomes larger compared with the size of a unit.