A Shell-in-Shell Homogenization Framework for the Analysis and Optimization of Periodic Plate Structures
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The mechanical performance of lightweight plate structures is strongly influenced by their geometric design. This work investigates a parameterized plate geometry inspired by a wallpaper group. A geometric design parameter, denoted by h, is introduced to modify the structural configuration and investigate its influence on the overall structural stiffness. To efficiently evaluate the mechanical response of the resulting periodic structures, a shell-in-shell homogenization framework is employed. Instead of explicitly resolving the complex mesostructure with large finite element models, the proposed approach determines the effective stiffness properties from representative volume elements (RVEs). Reissner-Mindlin shell elements are adopted for the RVE formulation. Periodic boundary conditions together with an additional constraint are applied to eliminate size-dependent shear effects and to obtain effective stiffness properties. A parametric study is conducted by systematically varying the design parameter h. The resulting effective stiffness is analyzed to quantify the influence of the geometric parameter $h$ on the overall structural response and to identify an optimal configuration. The proposed framework provides an efficient tool for the analysis and optimization of mathematically derived periodic plate geometries.
