Buckling and post-buckling analysis of butterfly-shaped auxetic core sandwich plates based on variational asymptotic method

Abstract

To further improve the buckling load, a novel type of butterfly-shaped auxetic core sandwich plate (butterfly CSP) was proposed based on the re-entrant honeycomb. Based on the periodic arrangement of the micro-structures within the butterfly CSP, the strain energy, constitutive relationship, and equivalent plate properties of the butterfly CSP were derived in detail using the variational asymptotic method, and the two-dimensional (2D) equivalent plate model (2D-EPM) of the butterfly CSP was developed. On this basis, the connection between the macro-plate model and the micro-unit-cell was established. A comparison with the results of the three-dimensional finite element model revealed that the 2D-EPM had high accuracy in predicting buckling and post-buckling behaviors as well as the local field distributions after buckling. Furthermore, the calculation efficiency was significantly improved due to the reduced number of elements and nodes. Finally, the effects of the structural and material parameters on the buckling behavior of the butterfly CSP were systematically analyzed. The influence of the core layer-to-facesheet thickness ratio on the buckling response was more significant than that of the core form, and the buckling load of the sandwich plate with a negative Poisson’s ratio was greater than its counterpart under the same conditions.