Static and Free-Boundary Vibration Analysis of Egg-Crate Honeycomb Core Sandwich Panels Using the VAM-Based Equivalent Model

This study proposes a novel egg-crate honeycomb core sandwich panel (SP-EHC) that combines the structural advantages of conventional lattice and grid configurations while mitigating their limitations in stability and mechanical performance. The design employs chamfered intersecting grid walls to create a semi-enclosed honeycomb architecture, enhancing out-of-plane stiffness, buckling resistance, and enabling ventilation and drainage. To facilitate efficient and accurate structural analysis, a two-dimensional equivalent plate model (2D-EPM) is developed using the Variational Asymptotic Method (VAM). This model significantly reduces the complexity of three-dimensional elasticity problems while preserving essential microstructural characteristics. A Reissner–Mindlin-type formulation is derived, enabling local field reconstruction for detailed stress and displacement evaluation. Model validation is conducted through experimental testing and three-dimensional finite element simulations. The 2D-EPM demonstrates high accuracy, with static analysis errors in load–displacement response within 10%, and a maximum modal frequency error of 10.23% in dynamic analysis. The buckling and bending analyses, with or without initial deformation, show strong agreement with the 3D-FEM results, with deviations in the critical buckling load not exceeding 5.23%. Local field reconstruction achieves stress and displacement prediction errors below 2.7%, confirming the model’s fidelity at both global and local scales. Overall, the VAM-based 2D-EPM provides a robust and computationally efficient framework for the structural analysis and optimization of advanced sandwich panels.