Ritz-based higher-order static and dynamic analysis and design optimization of butterfly-core sandwich plates

In this study, a semi-analytical higher-order model is proposed for the analysis and design optimization of butterfly-core sandwich plates. A four-variable sinusoidal higher-order shear deformation theory is combined with a hard-constraint Ritz discretization where the essential boundary conditions are directly embedded in the admissible trial functions. The butterfly core is modeled as an equivalent orthotropic continuum obtained by unit-cell homogenization and the face sheets are modeled as isotropic aluminum layers. The formulation is validated against the available benchmark results of free vibration and static bending responses. Then, it is used to study the effects of core geometry, wall thickness, core-thickness ratio, boundary condition and load position on the natural frequency, tip displacement, mass-normalized frequency and mass-normalized stiffness. Full-factorial multi-objective optimization is carried out to obtain Pareto-optimal lightweight designs by trade-offs between areal mass, tip displacement and fundamental natural frequency. The results demonstrate that the core-thickness ratio is the primary parameter to control stiffness and vibration performance, and the local geometric parameters mainly act as secondary tuning variables through changes in compliance and mass distribution. The proposed HSDT–Ritz approach provides an efficient design-oriented tool for interpretation and optimization of butterfly-core sandwich panels under practical static and dynamic requirements.