Bending analysis of functionally graded triply periodic minimal surface sandwich plates
Pınar Aydan Demirhan
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.