Elastic local buckling behaviour of beetle elytron plate

Beetle elytron plate (BEP) is a biomimetic sandwich structure inspired by the internal architecture of beetle elytra and characterised by trabeculae in the core. This type of structure has been shown to possess superior mechanical properties to conventional sandwich plates; however, there are no studies that evaluate its structural bending resistance. This paper develops an analytical method to calculate the key component of bending resistance of BEPs: the elastic local buckling load of the compression skin. It assumes that the compression skin of BEPs is simply supported by the trabecular core. After eliminating local buckling in the edges of the compression skin outside the trabeculae, two buckling zones, depending on the ratio (eta) of trabecular radius to the distance between two adjacent trabeculae, are identified. At low eta values (eta <= 0.25), elastic buckling occurs in the space of the compression skin surrounded by four adjacent trabeculae. Beyond the critical value of eta (eta >0.25), buckling occurs in the compression skin enclosed by individual trabecula. Guided by finite element simulation results, this paper identifies a new suite of deformation shape functions and derives local elastic buckling load for the compression skin according to the principle of minimal total potential energy. Afterwards, a convenient quadratic polynomial regression equation is proposed to modify the elastic buckling coefficient of the compression skin of equivalent conventional grid honeycomb sandwich plates, with the maximum difference between analytical calculation results and finite element simulation results being about 7%.