A three-dimensional representative volume element model with appropriate periodic boundary conditions is proposed and employed to numerically calculate the out-of-plane elastic properties of hexagonal honeycombs with variable-thickness and curved cell edges. The FEA numerical results indicate that the out-of-plane shear modulus, compressive buckling strength and shear buckling strengths of regular hexagonal honeycombs are significantly affected by the solid distribution in cell edges. Meanwhile, the compressive and shear buckling strengths of hexagonal honeycombs can be enhanced dramatically as the curvature of cell edges becomes much larger. The theoretical expressions of the shear modulus, compressive buckling strength and shear buckling strengths of hexagonal honeycombs with variable-thickness and curved cell edges can also be expressed as the product of those with same relative density and constant-thickness and straight cell edges, and two cell-geometry coefficients to account for the effects of the solid distribution in cell edges.
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