Thermomechanical Vibration Analysis of Double-curved Shallow Sandwich Shells with Triply Periodic Minimal Surface Core and Metal–ceramic Foam Faces

The study investigates the thermomechanical vibration and dynamic stability of curved sandwich nanoplates featuring TPMS-based cores and Nickel–Zirconia foam face sheets under thermal loading. A numerical framework was employed, integrating strain-gradient and nonlocal elasticity theories to capture size-dependent effects. The analysis evaluates varying TPMS topologies, foam ratios, and geometric parameters such as curvature and thickness-to-length ratios. Findings indicate that while TPMS porosity enhances fundamental frequencies at low temperatures, it induces premature thermal buckling at high temperatures; a balance achieved by optimizing metal-to-ceramic ratios for thermal resilience. Strain-gradient effects significantly bolster stiffness, far outweighing minor nonlocal influences, with the thickness-to-length ratio identified as the dominant geometric factor. This study establishes a critical design roadmap for deploying lightweight, thermally stable nanostructures in aerospace and radar stealth applications.