Naturally stabilized nodal integration of Chebyshev moving Kriging meshless approach for functionally graded triply periodic minimal surface plates

Abstract

This study introduces a novel model employing Chebyshev polynomials for both shear deformation theory and moving Kriging meshless method for computationally efficient analysis of functionally graded triply periodic minimal surface (FG-TPMS) plates. The introduction of a naturally stabilized nodal integration (NSNI) scheme significantly enhances the computational efficiency of the proposed numerical approach and guarantees a numerically stable solution, outperforming traditional methods that employ the Gaussian quadrature (GI) rule. In addition, the FG-TPMS plates are designed based on porous structures of Primitive (P), Gyroid (G) and Wrapped Package-Graph (IWP) types, each analyzed under six volume distribution cases. Mechanical properties are determined through a two-phase piecewise fitting technique. The proposed numerical approach is employed to solve the governing equations, which are derived based on the virtual work principle. Validated through parameter studies, this combined approach demonstrates efficiency and accuracy in predicting the transverse deflection and natural frequency for various geometries, volume distributions, aspect ratio, and boundary conditions. The proposed NSNI method consistently outperforms GI in terms of computational time, with numerical results showing that GI often takes more than four times longer to compute. For that reason, the proposed methodology provides a robust solution for analyzing FG-TPMS plates and advances computational methods for complex structures.