Static, buckling and free vibration analyses of composite sandwich plate with bi-directional trapezoidal cores using VAM-based reduced plate model

The geometry of the composite sandwich plate with bi-directional trapezoidal cores (BTCs) is characterized by its novel cores with trapezoidal convex and concave corrugations in two in-plane directions. To solve the related difficulties in mechanical problems, a reduced plate model is established and written as a variational formulation based on the variational asymptotic method (VAM). That is, the original 3D plate problem was reduced to unit cell analysis (providing effective plate properties, such as the A, B, and D matrices) and two-dimensional (2D) reference plane analysis. To validate the accuracy and effectiveness of the reduced plate model, we analyze the static displacement, global buckling, and free vibrations of the composite sandwich plate with BTCs under different boundary and load conditions. Finally, we investigate the influence of the layup configurations of the face sheet and geometric parameters of the BTCs on the effective plate properties, buckling loads, and natural frequencies of the plate, which can provide useful reference for the structure optimization of composite sandwich plate with BTCs.