Abstract
An approach to obtain analytical closed-form expressions for the macroscopic ‘buckling strength’ of various two-dimensional cellular structures is presented. The method is based on classical beam-column end-moment behaviour expressed in a matrix form. It is applied to sample honeycombs with square, triangular and hexagonal unit cells to determine their buckling strength under a general macroscopic in-plane stress state. The results were verified using finite-element Eigenvalue analysis.
Highlights
Low-density cellular materials have found widespread application for energy absorption, structural protection and as the core of lightweight sandwich panels
An interesting feature in buckling of hexagonal and triangular honeycombs is the possibility of secondary modes of buckling which are observed only under the x–y biaxial state of macroscopic stress
These secondary modes were shown to occur at the same macroscopic stress levels required by the primary modes of buckling under x–y biaxial stress state
Summary
Low-density cellular materials have found widespread application for energy absorption, structural protection and as the core of lightweight sandwich panels. Triantafyllidis & Schraad [24] studied the onset of failure in honeycombs under general in-plane loading using finite-element (FE) discretization of Bloch wave theory. The analytical method presented here is inspired by research of Gibson et al [35] on the stability of regular hexagonal honeycombs under in-plane macroscopic biaxial stress parallel to material symmetry directions (i.e. x and y in figure 1) using the beam-column solution of Manderla & Maney [36,37], as presented by Timoshenko & Gere [38].
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