A refined size-dependent modified strain gradient analysis of graphene platelet-reinforced functionally graded triply periodic minimal surface microplates using isogeometric analysis

In this study, a small scale dependence of graphene platelets reinforced functionally graded triply periodic minimal surface (GPR-FG-TPMS) microplates using an isogeometric analysis (IGA) is investigated. The research provides an in-depth analysis of three TPMS microplates, including Primitive (P), Gyroid (G) and I Wrapped Package (IWP) graph, along with two cellular solids, namely open and closed cell configurations. This study explores these designs under three graphene platelet distribution patterns and three distinct density distribution patterns. The governing equations are derived by integrating Hamilton’s principle in conjunction with modified strain gradient theory (MSGT) based on refined plate theory within four variables. Leveraging continuous basis functions of the IGA, higher-order strains in MSGT and displacement fields are accurately captured. To validate proposed models, a comprehensive comparison between the obtained results and reference solutions is conducted. Furthermore, the influence of geometric configurations, density, length scale parameters (LSPs), GPLs distribution patterns and TPMS geometries on deflections and natural frequencies of the GPR-FG-TPMS microplates is comprehensively evaluated. The results indicate that increasing the LSPs enhances the natural frequencies and reduces the deflections of the microplates. The Primitive structure with a P-II density distribution exhibits the highest stiffness. Moreover, the GPL-A distribution provides superior mechanical performance compared to other patterns.