Bending analysis of functionally graded triply periodic minimal surface sandwich plates

Abstract

This study investigates the bending behaviour of sandwich plates with functionally graded triply periodic minimal surface (FG-TPMS) cores under uniform loading and various boundary conditions. By employing a two-phase fitting technique, the effective properties of FG-TPMS cores are derived for three-unit cell models (primitive, gyroid, and IWP). The equilibrium equations are formulated using the virtual displacement principle and solved via the state-space method for plates with two simply supported edges. Results show that the proposed model achieves 12–15% lower deflection compared to conventional homogeneous cores, with gyroid structures exhibiting the highest stiffness (e.g. an elastic modulus 10% higher than that of the primitive structure). Comparative analysis with high-order shear deformation theory (HSDT) and refined plate theory (RPT) benchmarks shows <5% deviation, validating the accuracy of our approach. Additionally, an analysis of symmetric and asymmetric density distributions (Patterns A/B) reveals that Pattern B reduces deflection by 8–20% for slenderness ratios (a/h) of 5–20. This work advances theoretical studies on TPMS-based sandwich structures and provides a robust framework for optimizing their mechanical performance.