A meshfree method for functionally graded triply periodic minimal surface plates

Abstract

The goal of this study is to utilize a higher order shear deformation theory (HSDT) and the moving Kriging meshfree method for analyzing bending, free vibration, and buckling behaviors of functionally graded (FG) triply periodic minimal surface (TPMS) plates. The FG-TPMS plates are modeled using porous structures of Primitive (P), Gyroid (G) and wrapped package-graph (IWP) patterns with six different volume distribution cases for each pattern. The mechanical properties such as elastic modulus, shear modulus, and Poisson's ratio, are estimated using a fitting technique based on a two-phase piece-wise function. The governing equations of the FG-TPMS plates are established using the virtual work principle and then solved using the moving Kriging meshfree method. The study examines various geometries including square, circular, annular, and square with a cutout heart, to investigate the displacement, natural frequency, and critical buckling load parameters of the FG-TPMS plates. Additionally, those parameters are also analyzed with respect to different length-to-thickness ratios, TPMS types, volume distribution cases, and boundary conditions. The numerical results are compared to the original reference ones obtained by isogeometric analysis in the literature.