Mathematical modeling of the mechanical behavior of three-layer plates with a tetrachiral honeycomb core
This work examines the mechanical behavior of three-layer plates with a tetrachiral honeycomb core and solid face layers under static bending conditions. The influence of discretization, relative density, and thickness of the honeycomb core on the stress state of the composite plates is investigated under two boundary conditions: rigid clamping and elastic rotational support. The first numerical experiment setup involves a constant thickness of each composite layer while varying the core relative density. The second experiment setup maintains a constant volume of the honeycomb core solid body, which causes its thickness to change as the relative density varies. Mathematical modeling is performed using the finite element method within the framework of linear elasticity, employing both three-dimensional modeling in Comsol Multiphysics and custom algorithms for solving a plane problem to analyze the stress state of the tetrachiral honeycomb-based multilayer plates. The technical process of manufacturing the composites is described, followed by laboratory tests under three-point bending conditions. Next, the diagrams showing the dependence of maximum stresses in the composite plate layers on the relative density and thickness of the honeycomb core are discussed in the first and second setups of the numerical experiments, respectively. The results demonstrate good agreement between the numerical data from the three-dimensional and plane finite element models. Furthermore, the laboratory data from the three-point bending tests qualitatively align with the numerical analysis.