On the basis of star-shaped core sandwich panel, a novel sandwich panel with petal-triangle core (SP-PSC) was proposed to improve the negative Poisson’s ratio (NPR) effect while retaining the characteristics of light weight and high strength. To study the complex structure more conveniently and quickly, a variational asymptotic method-based equivalent two-dimensional model (2D-EPM) was developed. The accuracy and efficiency of 2D-EPM were verified by the three-point bending experiment data and the 3D FE model results under different boundary and load conditions. The effects of the geometric parameters on the equivalent stiffness, buckling, natural frequency and NPR effect were also investigated. To increase the NPR of SP-PSC, the material of facesheet was changed from isotropic material to unidirectional CFPR material, and the influence of the material anisotropy on the NPR effect of SP-PSC was investigated. It is found that the NPR of SP-PSC increased first and then decreased with the increase in the fiber angle, reaching the maximum value at 40–50∘. At the same time, this law is applicable to SP-PSC with different material or geometric parameters. Finally, two improved cores, petal star-triangular core with X-shaped ligaments (PSC-X) and double-arc star-shaped core (DSC), were proposed and compared with SP-PSC in equivalent stiffness and recovered local fields to demonstrate their advantages. Compared with the original plate, the stress concentration and equivalent stiffness of the two improved PSCs significantly improved.

Due to their complex microstructures, the research on the static and dynamic behaviors of triangular honeycomb sandwich panels (triangular HSPs) is limited. In this study, the effective plate properties of triangular HSP was obtained by the homogenizing of the unit cell, and then the input to a VAM-based two-dimensional equivalent plate model (2D-EPM) to perform static and dynamic analyses. The accuracy of the proposed model for predicting the equivalent stiffness of the triangular HSP was verified by three-point bending experiments of 3D-printed specimens. Then, the static displacement, global buckling, and free vibrations predicted by 2D-EPM were verified with the results from three-dimensional finite element model simulations under various boundary conditions. The influences of structural parameters (including angle, core wall thickness, and cell side length of the unit cell) on the static and dynamic characteristics of triangular HSPs were also investigated, which can provide a useful tool for the modeling and evaluation of triangular HSPs under different conditions.