A Moving Kriging-Based Meshfree Approach for Vibration Analysis of Functionally Graded TPMS Nanoplate

Triply Periodic Minimal Surfaces (TPMS) constitute a novel class of architected materials characterized by three-dimensionally periodic geometries derived from minimal surface mathematics. These materials exhibit a unique combination of low density and high mechanical efficiency, making them highly suitable for applications that demand optimized strength-to-weight performance. Due to their continuous, smoothly curved surfaces and topological complexity, TPMS structures have emerged as promising candidates for use in fields such as biomedical engineering, lightweight structural design, and energy absorption systems. TPMS architectures can be realized through two primary strategies: either by thickening the minimal surface to form sheet-based structures or by solidifying the enclosed volume to generate skeletal or solid-based configurations. This study explores the size effect on the free vibration responses of functionally graded (FG) nanoplates with triply periodic minimal surface (TPMS) design. By employing the higher-order shear deformation theory (HSDT) with five unkown variables, in combination with the moving Kriging meshfree method and incorporating nonlocal Eringen’s elasticity theory, we examine two kinds of porous nanostructures: Primitive and Gyroid patterns. For each pattern, four distinct volume dispersal scenarios are considered. The mechanical properties, including elastic modulus, shear modulus, and Poisson's ratio-are obtained through a curve-fitting approach using a two-phase piecewise model. The numerical findings are rigorously compared with reference data from existing literature, ensuring the accuracy of the results.