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

Abstract Purpose 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. Methods 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. Results and Conclusion 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.