Modified strain gradient analysis of the functionally graded triply periodic minimal surface microplate using isogeometric approach

This article aims to study the free vibration, buckling and bending behaviours of the functionally graded triply periodic minimal surface (FG-TPMS) microplates using isogeometric approach. The study encompasses a comprehensive analysis of three TPMS plate models, namely the Primitive, Gyroid, and I wrapped package-graph, with two distinct density distribution patterns across the plate thickness. The governing equations for the analysis are derived by combination of the Hamilton principle with both the high-order shear deformation theory and the modified strain gradient theory (MSGT). According to the higher-order derivatives and continuous basis functions of the isogeometric analysis, the displacement fields and the high-order strains of MSGT models are accurately approximated. To demonstrate the precision and advantages of the proposed model, a comparison is made between the obtained results and reference results in the literature. The present work further investigates the effect of the length scale parameters, TPMS geometries, density distribution patterns and geometries on the natural frequency, critical buckling load and deflection of the FG-TPMS microplates.