A nonlocal meshfree approach for functionally graded triply periodic minimal surface plates at the nanoscale

We are happy to announce that Dr. Thai Hoang Chien and colleagues recently published their work entitled "A nonlocal meshfree approach for functionally graded triply periodic minimal surface plates at the nanoscale” in the Elsevier.

Abstract:

This work investigates the size-dependent effects on the static and free vibration characteristics of functionally graded (FG) triply periodic minimal surface (TPMS) nanoplates. This analysis is conducted using the higher-order shear deformation theory (HSDT) and the moving Kriging meshfree method, integrated with Eringen’s nonlocal elasticity theory. Three types of porous nanostructures of Primitive, Gyroid, and I-graph and wrapped package-graph patterns are explored, and six distinct volume distribution scenarios are considered. Mechanical properties, including Poisson's ratio, shear modulus, and elastic modulus, are determined using the fitting curve model based on a two-phase piecewise function. Based on the virtual work principle, the governing equations of the FG-TPMS nanoplates are first derived and then solved using the moving Kriging meshfree formulation. To comprehensively investigate the displacement and natural frequency of nanoplates, geometries including circular, annular, square, and square with a heart-shaped cutout are examined. Moreover, these parameters, in relation to various boundary conditions, difference of TPMS types, volume distribution cases, and length-to-thickness ratios, are also exhaustedly examined. The numerical results are validated by comparing them with the reference data available in the literature